Details

prune9.2m (41.0%)

simplify6.4m (28.7%)

sample4.3m (19.4%)

Algorithm
60×intervals
Results
1.1m257947×body80valid
49.4s27968×body1280valid
37.8s161464×body80nan
26.8s19091×body640valid
18.9s8488×body10240exit
15.3s8058×body2560valid
11.8s3451×body5120valid
9.0s9427×body320valid
5.3s9174×body160valid
644.0ms603×body1280nan
550.0ms631×body640nan
360.0ms8256×pre80true
270.0ms366×body320nan
126.0ms201×body160nan

series1.5m (6.6%)

Calls

442 calls:

Slowest
7.4s
(sqrt (* (* (* 2 (cbrt U)) (- t (* (fma l 2 (* (* (- U U*) (/ l Om)) n)) (/ l Om)))) n))
3.9s
(sqrt (* (* (cbrt U) (cbrt U)) (* (* 2 (cbrt U)) (* (- t (* (/ l Om) (+ (* 2 l) (* (* (/ l Om) n) (- U U*))))) n))))
2.3s
(sqrt (* U (* 2 (* n (- t (fma (/ l Om) (* 2 l) (* (/ l Om) (* (/ l Om) (* (- U U*) n)))))))))
2.2s
(sqrt (* U (* 2 (* n (- t (fma (/ l Om) (* 2 l) (* (/ l Om) (* (* (/ l Om) (- U U*)) n))))))))
1.5s
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

regimes24.2s (1.8%)

Accuracy

Total 52.5b remaining (30.8%)

Threshold costs 3.2b (1.9%)

11.0b-11%Henrywood and Agarwal, Equation (13)
9.3b39.2%Henrywood and Agarwal, Equation (3)
5.9b74.7%Toniolo and Linder, Equation (7)
5.6b39.2%Toniolo and Linder, Equation (13)
4.0b-5.7%Maksimov and Kolovsky, Equation (3)

rewrite21.3s (1.6%)

Algorithm
116×rewrite-expression-head
Calls

442 calls:

Slowest
2.6s
(* (/ c0 (* w 2)) (+ (sqrt (- (* (/ (/ (* (* c0 (/ d D)) (/ d D)) w) h) (/ (/ (* (* c0 (/ d D)) (/ d D)) w) h)) (* M M))) (/ (/ (* (* c0 (/ d D)) (/ d D)) w) h)))
1.9s
(+ (/ NaChar (+ 1 (exp (/ (+ EAccept (- (+ Ev Vef) mu)) KbT)))) (/ NdChar (+ (exp (/ (- mu (- (- Ec Vef) EDonor)) KbT)) 1)))
1.2s
(+ (sqrt (- (* (/ (/ (* (* c0 (/ d D)) (/ d D)) w) h) (/ (/ (* (* c0 (/ d D)) (/ d D)) w) h)) (* M M))) (/ (/ (* (* c0 (/ d D)) (/ d D)) w) h))
1.1s
(+ (sqrt (- (* (/ (/ (* (* c0 (/ d D)) (/ d D)) w) h) (/ (/ (* (* c0 (/ d D)) (/ d D)) w) h)) (* M M))) (/ (/ (* (* c0 (/ d D)) (/ d D)) w) h))
522.0ms
(+ (exp (/ (- mu (- (- Ec Vef) EDonor)) KbT)) 1)
Rules
27461×times-frac
27249×add-exp-log
14934×add-sqr-sqrt
14569×prod-exp
14307×*-un-lft-identity
13681×add-cube-cbrt
10532×div-exp
7641×add-cbrt-cube
6673×sqrt-prod
5516×pow-exp
3708×cbrt-undiv
2288×cbrt-unprod
2177×associate-*r*
1728×pow-to-exp
1478×div-inv
1347×pow1
1101×associate-*l*
1026×1-exp
970×associate-/l*
731×prod-diff
723×rec-exp
713×associate-/r*
552×cbrt-prod
494×add-log-exp
442×expm1-log1p-u log1p-expm1-u insert-posit16
426×pow-prod-down
361×unpow-prod-down
351×pow-unpow
317×distribute-rgt-in distribute-lft-in
297×unswap-sqr
226×difference-of-squares
200×distribute-lft-out--
173×log-pow
171×associate-*r/
170×associate-/r/
147×exp-prod
146×sqr-pow
134×*-commutative
131×associate-*l/
127×frac-2neg clear-num
100×associate-/l/
98×sqrt-div
94×frac-times sqrt-pow1
87×flip3-- flip--
82×distribute-lft-out
73×tan-quot
71×fma-def
69×pow1/2
64×swap-sqr fma-neg
57×fma-udef
53×rem-sqrt-square
44×pow-prod-up sub-neg
37×pow1/3
35×distribute-rgt-out--
32×distribute-lft-neg-in distribute-rgt-neg-in div-sub
28×flip-+ flip3-+
27×pow-sqr
25×associate--l+ cos-sum
24×pow-pow
22×log-prod pow-plus pow-sub
21×pow-flip
17×frac-add
15×exp-sum pow2
14×sum-log diff-log
13×inv-pow
12×cbrt-div +-commutative pow-neg
10×neg-sub0
9×frac-sub
8×difference-of-sqr-1 hypot-def
7×cos-diff
5×sqrt-undiv pow3 un-div-inv acos-asin rem-log-exp
4×neg-mul-1
3×cos-mult associate-+r+
2×associate--l- sub-div sqr-sin hypot-udef asin-acos sin-mult
1×associate-+l+ exp-diff sqrt-unprod rem-exp-log rem-square-sqrt rem-cbrt-cube

localize8.1s (0.6%)

bsearch3.2s (0.2%)

end1.0ms (0.0%)