ENERGYPLUS 10X LBNL: TIANZHEN HONG, PHD; XUAN LUO ORNL: MARK ADAMS , ENERGY.GOV
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EnergyPlus 10X LBNL: Tianzhen Hong, PhD; Xuan Luo ORNL: Mark Adams thong@lbl.gov , adamsmb@ornl.gov U.S. DEP ARTMENT OF ENERGY OFFICE OF ENERGY EFFICIENCY & RENEW ABLE ENERGY 1
Project Summary Timeline : Key Partners : St a rt d a t e : 10 /1/2 0 18 P la nne d e nd d a t e : 9 /3 0 /2 0 2 1 Key Milestones : 1. Ene rg yP lus 9 .4 , 9 /3 0 /2 0 2 0 GARD Analytics 2 . Ene rg yP lus 9 .5 , 4 /3 0 /2 0 2 1 3 . Ene rg yP lus 9 .6 , 9 /3 0 /2 0 2 1 Budget : Project Outcome : This proje ct a pplie d a n int e g ra t e d s e t of com put ing Total Project $ to Date : t e chnique s t o im prove runt im e pe rform a nce of Ene rg yP lus . Re s ult s s how runt im e re duct ions ra ng e from 3 .2 % t o 9 3 % • DOE: $ 1.3 M (m e a n 23 %) wit h t he s am e s e t t ing s be t we e n Ene rg yP lus 9 .6 • Co s t Sha re : N/A a nd 9 .0 . If running a t a hig h s pe e d m ode wit h s om e a ccura cy t ra de offs , t he re duct ions ra ng e from 2 0 % t o 9 8 % (m e a n Total Project $: 8 3 %). Such s pe e d im prove m e nt s e na ble Ene rg yP lus for la rg e s ca le s im ula t ions a nd incre as e us e r product ivit y. • DOE: $ 1.6 M Cha ng e s t o t he da t a s t ruct ure , a lg orit hm s , a nd code a ls o • Co s t Sha re : N/A im prove Ene rg yP lus cont inuous de ve lopm e nt a nd m a int e na nce . U.S. DEP ARTMENT OF ENERGY OFFICE OF ENERGY EFFICIENCY & RENEW ABLE ENERGY 2
Team - A diverse project team spans expertise in building science, EnergyPlus, and computer science Tianzhen Hong Xuan Luo Wanni Zhang Mark Adams Jason DeGraw Senior Scientist EnergyPlus Developer Programmer EnergyPlus Developer EnergyPlus Developer PI, LBNL LBNL LBNL PI, ORNL ORNL Edwin Lee Mike Witte Jason Glazer Lixing Gu Joshua New EnergyPlus Developer, EnergyPlus Developer, EnergyPlus Developer, EnergyPlus Developer Computer Scientist NREL GARD Analytics GARD Analytics FSEC ORNL U.S. DEP ARTMENT OF ENERGY OFFICE OF ENERGY EFFICIENCY & RENEW ABLE ENERGY 3
Challenge Com p a re d wit h o t he r c o m m o nly us e d b uild ing e ne rg y m ode ling pro g ra m s , Ene rg yP lus runs s lo we r b y a n o rde r of m a g nit ud e . This hind e rs Ene rg yP lus fo r us e c a s e s t ha t ne e d m a ny s im ula t ions . Ene rg yP lus c o d e b a s e is b ig a nd c o m p le x: t ra ns la t e d from FORTRAN t o C in 2 0 14 (ve rs io n 8 .2 ), a b o ut 1M line s of c ode writ t e n b y m a ny d e ve lo p e rs a c ro s s 2 5 ye a rs . P a s t e ffort s fo c us o n ne w fe a t ure d e ve lo p m e nt s t o m ode l t e c hno lo g ie s , s ys t e m s a nd c o nt ro ls , ra t he r t ha n runt im e p e rfo rm a nc e . U.S. DEP ARTMENT OF ENERGY OFFICE OF ENERGY EFFICIENCY & RENEW ABLE ENERGY 4
Approaches This proje ct e m ploys a n int e g ra t e d a pproa ch t o s ig nifica nt ly im prove Ene rg yP lus ’ a nnua l s im ula t ion run-t im e pe rform a nce from t he ba s e line Ene rg yP lus 9 .0 . The a pproa che s include but a re not re s t rict e d t o: 1. Baseline : De ve lop a s uit e of m ode ls cove ring dive rs e us e ca s e s a nd com ple xit y, a nd e s t a blis h a n ove ra ll b a s e line run t im e of t he s uit e t ha t t he p ro je c t e d im prove m e nt will be ba s e d on. 2. Analysis : P rofile m ode ls t o ide nt ify pe rform a nce hot s pot s , a nd us e corre la t ion t e chnique s t o ide nt ify proble m a t ic com pone nt m ode ls or s t ruct ure s . 3. Refactoring : Enha nce code in m a jor rout ine s of s urfa ce a nd zone he a t ba la nce , t he pla nt com pone nt s a nd loops , t he ne s t e d HVAC s im ula t ions , t he ca lcula t ions of CTF, s ola r a nd window he a t t ra ns fe r us ing ne w da t a s t ruct ure s , im prove d a lg orit hm s , a nd opt im ize d conve rg e nce crit e ria . 4. Threading : Te s t t a s k pa ra lle lis m t o t a ke a dva nt a g e of m ult i-core proce s s ors us ing Ope nMP 5. GPU: P a ra lle l com put ing for s ola r s ha ding ca lcula t ions 6. Speed up workflow : Ca che int e rm e dia t e re s ult s (e .g ., CTF, s ola r s ha ding ) a nd re us e t he m be t we e n s im ula t ions . U.S. DEP ARTMENT OF ENERGY OFFICE OF ENERGY EFFICIENCY & RENEW ABLE ENERGY 5
63 Models for Performance Benchmark ● 16 DOE Re fe re nc e Building m ode ls 20 Hot Spots of the Benchmark Models in EnergyPlus 9.0 o Chic a g o c lim a t e , ASHRAE 9 0 .1-2 0 0 4 , a nnua l run, 10 -m inut e t im e s t e p, a s -is re port ing Functions Percentage CPU Functions Percentage CPU time over time over ● 16 la rg e m ode ls benchmark suite benchmark suite o La rg e s c a le building wit h ra dia nt unde rfloor SolarShading::CLIPP he a t ing __pow 4.582 OLY 1.852 CalcHeatBalanceInside o Na t ura l ve nt ila t ion wit h a irflow ne t work Surf 4.020 CalcZoneSums 0.437 CalcInteriorRadExchan o 12 la rg e m ode ls wit h m a ny zone s or s urfa c e s ge 3.772 PsyTsatFnHPb 0.683 o 2 re s ide nt ia l building s Psychrometrics::cache d_psat_t 2.561 PierceSurface 1.597 UpdateThermalHistorie ReportSurfaceHeatBa ● 3 1 dia g nos t ic s m ode ls s 1.919 ance 0.407 ○ From s hoe box no HVAC t o c om ple x InitSolarHeatGains 1.505 InitIntSolarDistribution 0.335 g e om e t ry a nd HVAC s ys t e m s CalcInteriorSolarDistri __GI___exp 1.283 bution 0.379 ○ From no s ha ding t o lot s of s ha ding ○ From no window t o m a ny windows InitSurfaceHeatBalance 0.692 __ieee754_log_fma 0.316 CalcHeatBalanceOuts ○ From 5 zone s t o 5 0 0 zone s __memset_avx2_erms 0.623 ideSurf 0.379 SetZoneEquipSimOrd UpdateDataandReport 0.471 er 0.279 U.S. DEP ARTMENT OF ENERGY OFFICE OF ENERGY EFFICIENCY & RENEW ABLE ENERGY 6
Algorithms - Caching & Optimization of Utility Functions ➢ Caching of utility functions ● Subroutine functionality: ○ P s yTs a t FnP b(pb) - Ca lc ula t e t he s a t ura t ion t e m pe ra t ure from ba rom e t ric pre s s ure ○ P s yTs a t FnHP b(h, pb) - Ca lc ula t e t he s a t ura t ion t e m pe ra t ure from t he e nt ha lpy a nd ba rom e t ric pre s s ure . ○ Ge t Spe c ific He a t Glyc ol (T, Glyc olInde x) - Ca lc ula t e t he Glyc ol s pe c ific he a t by int e rpola t ion ● Performance: ○ Ea c h c a c hing im ple m e nt a t ion a c hie ve d a n a ve ra g e of 1-3 % s pe e d up of t he t ot a l run t im e of a ll 6 2 3 Ene rg yP lus rout ine t e s t file s ➢ Cubic interpolation of psychrometric functions ● P s yTs a t FnP b(pb) - Up t o 10 % s pe e d up t o s e le c t e d t e s t file s ● A ne w pe rform a nc e pre c is ion t ra de off opt ion in Ene rg yP lus 9 .6 re le a s e * Psychrometric functions: compute properties of moist air from other properties U.S. DEP ARTMENT OF ENERGY OFFICE OF ENERGY EFFICIENCY & RENEW ABLE ENERGY 7
Algorithms - Optimized Subroutines ➢ Polygon clipping for shadow calculation ● Methods: Us e Liang -Barsky a lg orit hm for c lipping re c t a ng ula r polyg ons ● Performance gain: – 1.5 X s pe e d up for t he s ubrout ine it s e lf – 6 % s pe e d up for Hos pit a lLowEne rg y.idf, a s ha ding c a lc ula t ion int e ns ive t e s t file ➢ Direct solution to get part load ratio (PLR) of coils ● Method: Us e line a r re la t ions hip be t we e n pa rt loa d ra t io a nd s ys t e m /c oil out put wit h g ive n inle t c ondit ions . ● Performance : 2 x s pe e d is a c hie ve d for c oil s ubrout ine ➢ Speedier schedule manager ● Method: m ore e ffic ie nt ly ope n a nd pa rs e e xt e rna l s c he dule file da t a , re duc ing runt im e in proport ion t o t he num be r of c olum ns of da t a in a file ● Performance : 9 2 % run t im e s a ving on Ma c for a s c he dule im port ing t e s t file For a file wit h ~10 0 colum ns of da t a t he runt im e is cut in ha lf. U.S. DEP ARTMENT OF ENERGY OFFICE OF ENERGY EFFICIENCY & RENEW ABLE ENERGY 8
Logic - Make the Common Case Faster ➢ Zone surface grouping and reordering ● Surfa c e s a re g roupe d by zone ● W it hin e a c h zone opa que s urfa c e s a re g roupe d s e pa ra t e ly from window s urfa c e s ● Ma in loops e xe c ut e d by zone a nd t he n by s urfa c e ● The s e a llow - ■ He a t ba la nc e loops t o ope ra t e on a c ont inuous s e t of s urfa c e s wit hout if c ondit ions wit hin t he loops ■ Fut ure pa ra lle liza t ion by zone Zo ne 1 Zo ne 2 He a t Ba la nc e Airwall Opaque Window Other Airwall Opaque Window Other Arra ys idx = W inS urfa c e Firs t idx = W inS urfa c e Las t idx = He a t Tra ns fe rFirs t idx = He a t Tra ns fe rLas t U.S. DEP ARTMENT OF ENERGY OFFICE OF ENERGY EFFICIENCY & RENEW ABLE ENERGY 9
Logic - Make the Common Case Faster ➢ Inside surface heat balance ● Two funct ions , one for s im ple Conduct ion Tra ns fe r Funct ion (CTF) - only s im ula t ions a nd a not he r for m ore com ple x s im ula t ions ● Elim ina t e if condit ions wit hin t he loops ➢ Move uncommon conditional calculations ✓ Allows e a s ie r bra nch out of the main loop pre dict ion a nd ve ct oriza t ion, ● Tubula r da ylig ht ing de vice a nd be t t e r ca che ● Mova ble ins ula t ion for opa que s urfa ce s pe rform a nce for com pile rs ● Mova ble s la t s for wind ow blinds ● St orm windows ● Source or s ink s urfa ce For e a c h s urfa c e : For e a c h s urfa c e : Do s t uff B If s t orm window: Do s t uff A If a ny s t orm window e xis t s : Els e : Do s t uff B For e a c h s t orm window: Do s t uff A U.S. DEP ARTMENT OF ENERGY OFFICE OF ENERGY EFFICIENCY & RENEW ABLE ENERGY 10
Data Structure - Heat Balance Array Refactoring ➢ Array of objects to array of scalars ● Conve rt la rg e obje c t a rra ys (e .g . Surfa c e W indow wit h 2 0 0 + fie lds a nd Surfa c e wit h 10 0 + fie lds ) t o a rra ys of s c a la rs for c a c he loc a lit y a nd fut ure ve c t oriza t ion ➢ Efficient initialization of data structure ● Re m ove t hird-pa rt y init ia liza t ion func t ion c a lls for ve c t oriza t ion ● Loop-wis e init ia liza t ion wit h s m a ll loops t o m a ke t he m a xim um us e of ve c t or re g is t e rs ● Re duc e re -init ia liza t ions (e .g . unne c e s s a ry s ola r a rra ys re s e t whe n s un is down a t e a c h t im e s t e p) ➢ Optimized multi -dimensional arrays ● Re orde r m ult i-dim e ns iona l a rra ys t o loop e xe cut ion orde r for ca che loca lit y ● Re duce a rra y s licing a nd re cons t ruct ion (2 D a rra y -> a rra y of a rra y) ● Re duce dim e ns ion of a rra ys U.S. DEP ARTMENT OF ENERGY OFFICE OF ENERGY EFFICIENCY & RENEW ABLE ENERGY 11
GPU Accelerate Solar Shading ➢ Performance improvements: ● Up t o 10 -14 x im prove m e nt ● Sc a le s wit h num be r of s ha ding s urfa c e s ➢ Penumbra: ● Ope n-s ourc e libra ry for GP U s ola r s ha ding ● Ope nGL 2 .1 (c ros s pla t form , wide ly s upport ) ➢ Benefits: ● Ena ble s m ode ling of la rg e building s wit h m a ny s ha ding s urfa c e s ● Sc a le s wit h GP U powe r U.S. DEP ARTMENT OF ENERGY OFFICE OF ENERGY EFFICIENCY & RENEW ABLE ENERGY 12
Profiling Guided Performance Improvements ➢ CarrolMRT: ● Alt e rna t e int e rior ra dia nt he a t e xc ha ng e m ode l ● O(n) vs O(n^2 ) a lg orit hm ● Up t o 9 5 % runt im e re duc t ion (s c a le s wit h num be r of int e rior s urfa c e s in a zone ) ➢ Native C++ CSV output / conditional output: ● Alt e rna t ive t o Re a dVa rs ESO ● 2 5 -8 2 +% runt im e re duc t ion, s c a ling on num be r of out put s ● Condit iona lly t urn on/off out put file s ■ Up t o 4 2 % runt im e re duc t ion ➢ Function approximation: ● Min/m a x a nd s om e pow func t ions t o us e ne w, fa s t e r a pproxim a t ions ● Up t o 13 % runt im e re duc t ion, a ve ra g e 4 % U.S. DEP ARTMENT OF ENERGY OFFICE OF ENERGY EFFICIENCY & RENEW ABLE ENERGY 13
Runtime: EnergyPlus 9.6 (Sep21) vs. 9.0 (Sep18) Machine: Intel Xeon W-2123 CPU @ 3.60GHz, Ubuntu 18.04.2 LTS Models: 63 EnergyPlus IDFs Runtime Decrease Histogram Same default settings: 9.6 vs 9.0 Number of Models Runtime Decrease (%) Mean: 23%, median: 20%, min: 3.2%, max: 93%
Parallelization - OpenMP ➢ Applied OpenMP parallel in major heat balance code blocks ● Ma jor funct iona lit ie s : ■ Init s urfa c e he a t ba la nc e (ra dia nt e xc ha ng e , c onve c t ive c oe ffic ie nt s , e t c .) ■ Ca lc ula t e ins ide a nd out s ide s urfa c e t e m pe ra t ure s ■ Upda t e t he rm a l his t orie s a nd re port ing ● Ge ne ra t e ide nt ica l re s ult s wit h s ing le t hre a d # Threads 2 4 8 10x_incr_100Zones100Surfaces 1.4x 1.7x - (4-CPU desktop) 10x_incr_100Zones100Surfaces 1.5x 1.9x 2.1x (24-CPU cluster) 10x_large_82zones_ASHRAE_HQ 1.6x 1.8x 2.2x (24-CPU cluster) U.S. DEP ARTMENT OF ENERGY OFFICE OF ENERGY EFFICIENCY & RENEW ABLE ENERGY 15
Runtime: Parallelization with OpenMP 9.6 with OpenMP: 8 vs 1 CPU for 6 “large” (> 20 surfaces/zone) models Runtime Decrease Histogram Number of Models Runtime Decrease (%) U.S. DEP ARTMENT OF ENERGY OFFICE OF ENERGY EFFICIENCY & RENEW ABLE ENERGY 16
Performance Precision Tradeoffs ➢ Successive modes to trade speed for precision: ● Us e e xis t ing s im ula t ion pa ra m e t e rs ● Expos e e xis t ing int e rna l c onve rg e nc e va ria ble s t o t he us e r ● Ne w opt im iza t ions ➢ The s im ula t ion t im e c a n be dra m a t ic a lly re duc e d ➢ Im pa c t s s im ula t ion re s ult s ➢ “_pe rflog .c s v” file provide s us e r t he im pa c t of c ha ng ing m ode s on a nnua l e ne rg y, runt im e , wa rning s , a nd t e m pe ra t ure os c illa t ions ➢ Ot he r s e t t ing s : Us e Co il Dire c t So lut io ns (Y/N), Zo ne Ra d ia nt Exc ha ng e Alg o rit hm (Sc rip t F, Ca rro llMRT) ➢ Addit iona l m ode s in Ene rg yP lus 9 .6 (e .g . P s yc hrom e t ric ) U.S. DEP ARTMENT OF ENERGY OFFICE OF ENERGY EFFICIENCY & RENEW ABLE ENERGY 17
Runtime: Speed Mode4 + CarrollMRT Runtime Decrease Histogram Total Site Energy Variance Histogram Number of Models Runtime Decrease (%) Total Site Energy Variance (%) Mean: 76%, min: 20%, median: 78%, max: 98%
Runtime: Speed Mode7 + CarrollMRT Runtime Decrease Histogram Total Site Energy Variance Histogram Runtime Decrease (%) Total Site Energy Variance (%) Mean: 83%, min: 21%, median: 88%, max: 98%
Performance Precision Tradeoff Characterization ➢ P e rfo rm a nce P re cis io n t ra d e o ffs int ro d uce va ria nce in re s ult s which ca n b e la rg e ➢ Five m o d e ls s ho w e s p e cia lly hig h va ria nce ➢ Fut ure wo rk: und e rs t a nd which m o d e ling fe a t ure s le a d t o hig h va ria nce a nd p ro vid e g uid a nce o n whe n P re cis io n-P e rfo rm a nce Tra d e o ffs a re s a fe t o us e
Impacts ● The 3 -ye a r p ro je c t a p p lie d a n int e g ra t e d s e t o f c o m p ut ing t e c hnique s t o re duc e runt im e o f Ene rg yP lus . P e rform a nc e im prove m e nt s we re inc lude d in Ene rg yP lus re le a s e s . ● Com pa re d t he runt im e s o f 6 3 be nc hm a rk m ode ls be t we e n Ene rg yP lus 9 .0 a nd 9 .6 , runt im e re d uc t io ns ra ng e fro m 3 % t o 9 3 % (i.e ., 1X t o 14 X, m e dia n 1.2 5 X) wit h d e fa ult s e t t ing s , a nd fro m 2 0 % t o 9 8 % (i.e ., 1.3 X t o 5 0 X, m e dia n 7 .7 X) in a hig h s p e e d m o d e wit h s o m e a c c ura c y t ra d e o ffs (e xc luding Ope nMP ). ● Re d uc ing runt im e o f c o m p le x Ene rg yP lus s im ula t io n m ode ls im prove s us e r pro duc t ivit y a nd s up p o rt s q uic k d e c is io n m a king (e .g ., d e s ig n c ha rre t t e ). U.S. DEP ARTMENT OF ENERGY OFFICE OF ENERGY EFFICIENCY & RENEW ABLE ENERGY 21
Stakeholder Engagement and Outreach • Annua l s t a ke hold e r b rie fing • Biwe e kly m e e t ing s t o provid e t im e ly fe e d b a c k • A ha c ka t hon s e s s ion wit h NERSC on Ope nMP • Eng a g e d t he b roa d e r Ene rg yP lus d e ve lopm e nt t e a m a nd c om m unit y • P re s e nt a t ion a t ASHRAE BP A Confe re nc e , Se pt e m b e r 2 5 , 2 0 19 U.S. DEP ARTMENT OF ENERGY OFFICE OF ENERGY EFFICIENCY & RENEW ABLE ENERGY 22
Remaining Project Work ● Cont rib ut e t o t he Ene rg yP lus 9 .6 re le a s e ● Re -run fina l pe rform a nc e b e nc hm a rk wit h t he offic ia l Ene rg yP lus 9 .6 ● P roje c t wra p up m e e t ing wit h s t a ke hold e rs ● Aft e r t he proje c t , c ont inue t he pe rform a nc e work a s pa rt of t he Ene rg yP lus c ore proje c t in a re a s , e .g .: ○ Re fa c t o r d a t a s t ruc t ure a nd c o d e ○ Ve c t o riza t io n a nd p a ra lle liza t io n ○ Re d uc e unne c e s s a ry c a lls ○ Op t im ize lo o p ing a nd it e ra t io ns ○ Ca lc ula t e o ut p ut va ria b le s o nly whe n re q uire d U.S. DEP ARTMENT OF ENERGY OFFICE OF ENERGY EFFICIENCY & RENEW ABLE ENERGY 23
Tha nk Yo u LBNL a nd ORNL Tia nzhe n Hong a nd Ma rk Ada m s thong@lbl.gov , adamsmb@ornl.gov U.S. DEP ARTMENT OF ENERGY OFFICE OF ENERGY EFFICIENCY & RENEW ABLE ENERGY 24
REFERENCE SLIDES U.S. DEP ARTMENT OF ENERGY OFFICE OF ENERGY EFFICIENCY & RENEW ABLE ENERGY 25
Project Budget Project Budget : $ 1.6 M Variances : N/A Cost to Date : $ 1.3 M Additional Funding : N/A Budget History FY 2019 FY 2020 FY 2021 (past) (past) (current) DOE Cost-share DOE Cost-share DOE Cost-share $50 0 k N/A $50 0 k N/A $6 0 0 k N/A U.S. DEP ARTMENT OF ENERGY OFFICE OF ENERGY EFFICIENCY & RENEW ABLE ENERGY 26
Project Plan and Schedule U.S. DEP ARTMENT OF ENERGY OFFICE OF ENERGY EFFICIENCY & RENEW ABLE ENERGY 27
Logic - Remove Redundant Subroutines ➢ Skip unnecessary interzone window calculation • Methods: – Skip c a lc ula t ing t he diffus e s ola r e xc ha ng e fa c t ors be t we e n zone s if no int e rzone window e xis t s • Performance gain: – Re duc e d 6 +% t ot a l E+ run t im e in la rg e m ode ls (5 0 0 zone s a nd up) in c a lc ula t ing t he int e rzone s ola r e xc ha ng e fa c t or m a t rix ➢ Reduce run time solar and thermal absorptance calculation • Methods: – Re duc e unne c e s s a ry loop it e ra t ions t o c a lc ula t e s ola r a nd t he rm a l a bs orpt a nc e fa c t ors a t e a c h t im e s t e p by pre -c he c king if a ny s ha ding or g la zing s t a t us c ha ng e • Performance gain: – Re duc e d 9 0 +% func t ion c a lls a nd run t im e of s ubrout ine it s e lf U.S. DEP ARTMENT OF ENERGY OFFICE OF ENERGY EFFICIENCY & RENEW ABLE ENERGY 28
Runtime benchmarking 9.6 vs. 9.0 All default settings (Machine: Intel Xeon W-2123 CPU @ 3.60GHz, Ubuntu 18.04.2 LTS) Models with largest runtime decrease: count 63 mean 23.113265 min 3.245094 median 20.465755 max 93.003413
Runtime benchmarking 9.6 vs. 9.0 Version 9.6 with fast mode 04 and radiant exchange algorithm CarrollMRT Models with largest runtime decrease: count 63 mean 75.602455 min 20.079103 median 77.948718 max 97.884805
Runtime benchmarking 9.6 vs. 9.0 Version 9.6 with fast mode 07 and radiant exchange algorithm CarrollMRT Models with largest runtime decrease: count 63 mean 82.878219 min 20.378319 median 86.796048 max 98.241773
Runtime benchmarking 9.6 vs. 9.0 Version 9.6 with fast mode 07 and radiant exchange algorithm CarrollMRT + OpenMP 4 threads Models with largest runtime decrease: count 63 mean 83.286181 min 20.650021 median 88.107236 max 98.355650
9.6: OpenMP 8 threads vs. w/o OpenMP count 21 count 6 mean 8.1% mean 42.8% min -8.4% min 5.7% meidan -0.4% median 47.9% max 66.0% max 66.0%
9.6 fast mode 07: w/ OpenMP vs. w/o OpenMP Models with runtime increase: count 63 mean 4.186573 min - 24.137931 median 3.316062 max Models with largest runtime 30.15974 decrease: 4
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