Details

simplify6.7m (44.9%)

sample3.3m (22.2%)

Algorithm
61×intervals
Results
43.2s253625×body80valid
39.7s29567×body1280valid
28.4s161758×body80nan
21.3s20460×body640valid
17.3s8754×body2560valid
10.1s3394×body5120valid
7.5s9846×body320valid
2.9s9186×body160valid
679.0ms661×body10240exit
345.0ms642×body1280nan
311.0ms635×body640nan
152.0ms8256×pre80true
132.0ms327×body320nan
70.0ms191×body160nan

series2.5m (16.8%)

Calls

434 calls:

2.9s
(sqrt (* (* (- t (fma 2.0 (/ l (/ Om l)) (* (* (* (cbrt (* n (pow (/ l Om) 2.0))) (cbrt (* n (pow (/ l Om) 2.0)))) (cbrt (* n (pow (/ l Om) 2.0)))) (- U U*)))) (* 2.0 n)) U))
2.8s
(sqrt (* (* (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (* 2.0 n)) U))
2.8s
(sqrt (* (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (* (* 2.0 n) U)))
2.7s
(sqrt (* (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (* (* 2.0 n) U)))
2.5s
(sqrt (fma (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (- (fma 0.04444444444444444 (pow ky 6) (pow ky 2)) (* 0.3333333333333333 (pow ky 4)))) 1.0))

prune1.4m (9.5%)

rewrite35.0s (3.9%)

Algorithm
117×rewrite-expression-head
Calls

434 calls:

3.2s
(/ (+ (pow (exp (/ (- (+ (+ Ev Vef) EAccept) mu) KbT)) 3) (pow 1.0 3)) (fma 1.0 1.0 (* (exp (/ (- (+ (+ Ev Vef) EAccept) mu) KbT)) (- (exp (/ (- (+ (+ Ev Vef) EAccept) mu) KbT)) 1.0))))
1.6s
(- (exp (/ (- (+ (+ Ev Vef) EAccept) mu) KbT)) 1.0)
974.0ms
(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))
919.0ms
(exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))
846.0ms
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0))) (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (/ (* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))))
Rules
48600×add-exp-log
33719×prod-exp
21509×pow-exp
17096×div-exp
10277×pow-to-exp
4460×add-sqr-sqrt
3987×times-frac
3832×*-un-lft-identity
3159×add-cube-cbrt
2703×add-cbrt-cube
1895×1-exp
1893×rec-exp
1401×unpow-prod-down
1198×sqrt-prod
1096×pow1
1065×cbrt-unprod
760×associate-*r*
753×associate-*l*
644×prod-diff
608×associate-*r/
582×cbrt-undiv
510×sqr-pow
506×add-log-exp
486×associate-/l*
478×difference-of-squares
435×expm1-log1p-u
434×log1p-expm1-u
368×associate-/r*
351×pow-unpow
346×sqrt-div
344×cbrt-prod
331×pow-prod-down
329×associate-*l/
324×div-inv
307×frac-times
279×associate-/r/
262×cube-prod
249×flip3-- flip--
244×cbrt-div
238×distribute-lft-out
216×unswap-sqr
192×exp-prod
158×distribute-lft-out--
127×*-commutative
120×tan-quot
115×cos-sum
114×distribute-rgt-in distribute-lft-in
102×distribute-rgt-neg-in
99×clear-num frac-2neg
87×sqrt-pow1
71×fma-neg
67×log-prod
66×fma-def
62×pow1/3
60×pow1/2 distribute-lft-neg-in
58×exp-sum
49×rem-sqrt-square sub-neg pow-pow
36×flip-+ flip3-+
35×div-sub
32×associate-/l/
30×swap-sqr
28×unpow2
25×log-pow
24×associate-+r+
23×fma-udef
21×pow-sub
20×sum-log
16×+-commutative
15×diff-log
14×neg-sub0 hypot-def
10×exp-diff pow-flip pow-neg
8×difference-cubes
7×pow-sqr pow-prod-up
6×inv-pow associate-+r- neg-mul-1
5×rem-exp-log cos-diff asin-acos
4×un-div-inv sum-cubes pow2 frac-add hypot-udef unsub-neg
3×sqrt-undiv pow-plus rem-log-exp
2×sqrt-pow2 unpow3 cube-mult acos-asin frac-sub
1×rem-cube-cbrt rem-cbrt-cube associate-+l+ log1p-udef exp-neg log1p-expm1 expm1-log1p expm1-udef distribute-frac-neg associate--r- mul0 associate--l+ log-div

regimes14.8s (1.6%)

Accuracy

Total 34.3b remaining (17.7%)

Threshold costs 6.1b (3.1%)

9.7b26.8%Toniolo and Linder, Equation (13)
5.0b78.8%Toniolo and Linder, Equation (7)
4.1b57.5%Toniolo and Linder, Equation (10-)
3.7b28.8%Henrywood and Agarwal, Equation (12)
2.6b0%Henrywood and Agarwal, Equation (13)

bsearch4.7s (0.5%)

localize4.4s (0.5%)

end0.0ms (0.0%)