Details

simplify4.1m (28.1%)

prune3.8m (26.1%)

sample3.3m (23.0%)

Algorithm
61×intervals
Results
46.6s253510×body80valid
39.6s29904×body1280valid
27.9s159444×body80nan
18.9s20118×body640valid
16.5s8631×body2560valid
10.6s3441×body5120valid
5.3s9633×body320valid
3.6s8922×body160valid
1.7s635×body10240exit
635.0ms8256×pre80true
335.0ms584×body1280nan
276.0ms602×body640nan
167.0ms327×body320nan
32.0ms180×body160nan

series2.4m (16.4%)

Calls

437 calls:

2.9s
(sqrt (* (- t (fma 2.0 (* l (/ l Om)) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))) (* (* 2.0 n) U)))
2.9s
(sqrt (* (* (- t (fma 2.0 (* l (/ l Om)) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (* 2.0 n)) U))
2.6s
(sqrt (* (- t (fma 2.0 (* l (/ l Om)) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (* (* 2.0 n) U)))
2.5s
(sqrt (* (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (* (* 2.0 n) U)))
2.1s
(/ (- (* (pow 1.0 3) 1.0) (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (+ 3 1))) (fma 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0)))

rewrite32.8s (3.8%)

Algorithm
116×rewrite-expression-head
Calls

437 calls:

1.5s
(cos (+ (- (* (/ 1 (sqrt (* (cbrt 2.0) (cbrt 2.0)))) (* (/ K (sqrt (cbrt 2.0))) (/ (+ m n) (sqrt 2.0)))) M) (+ (- M) M)))
987.0ms
(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))
949.0ms
(exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))
917.0ms
(+ (/ c0 (/ (* (* w h) (* D D)) (* d d))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))
885.0ms
(/ (- (- (- (- Ec Vef) EDonor) mu)) KbT)
Rules
56565×times-frac
55111×add-exp-log
40029×prod-exp
28565×pow-exp
24611×add-sqr-sqrt
23352×*-un-lft-identity
22381×add-cube-cbrt
20550×div-exp
12789×pow-to-exp
6471×unpow-prod-down
4906×1-exp
4804×rec-exp
3688×sqrt-prod
2777×cbrt-prod
2440×add-cbrt-cube
2156×div-inv
1337×associate-/r/
1320×sqr-pow
1223×associate-*l/
1197×associate-*r/
1080×pow1
985×associate-/r*
906×associate-*r*
832×prod-diff
822×associate-*l*
788×cbrt-unprod
777×difference-of-squares
627×associate-/l*
614×cbrt-undiv
484×add-log-exp
440×expm1-log1p-u
437×log1p-expm1-u
377×fma-def
325×distribute-lft-out--
324×pow-unpow
313×unswap-sqr
299×pow-prod-down
146×flip3-- sqrt-div flip--
140×distribute-lft-out
135×sqrt-pow1
130×*-commutative
126×distribute-rgt-neg-in
122×frac-times
120×distribute-rgt-in distribute-lft-in
103×clear-num cube-prod frac-2neg
100×distribute-lft-neg-in
92×rem-sqrt-square
84×pow1/2
66×exp-prod tan-quot
60×pow1/3 cbrt-div
49×pow-pow
47×div-sub
41×fma-neg
39×sub-neg
38×unpow2
37×associate-/l/
33×unpow3 cube-mult
30×pow-sub
28×flip-+ flip3-+
27×fma-udef swap-sqr
25×cos-sum
22×pow-prod-up
20×pow-flip log-prod
17×exp-sum
15×sum-log neg-mul-1
14×pow-sqr
13×pow-plus neg-sub0
12×+-commutative hypot-def
8×diff-log pow2
7×inv-pow frac-add associate-+l- distribute-neg-frac
5×cos-diff
4×pow-neg associate-+r- acos-asin
3×distribute-frac-neg rem-exp-log exp-diff un-div-inv log1p-udef log1p-expm1 log-pow expm1-log1p hypot-udef expm1-udef neg-log asin-acos
2×cube-div sqrt-pow2 unpow-prod-up unsub-neg associate--l+ log-div
1×rem-cube-cbrt rem-cbrt-cube sqrt-unprod pow3 exp-neg frac-sub mul0 rem-log-exp

regimes15.4s (1.8%)

Accuracy

Total 46.1b remaining (21.4%)

Threshold costs 5.1b (2.4%)

11.6b9.9%Toniolo and Linder, Equation (13)
6.7b47.7%Henrywood and Agarwal, Equation (3)
6.4b14.2%Toniolo and Linder, Equation (10-)
5.3b77.8%Toniolo and Linder, Equation (7)
4.9b23.1%Henrywood and Agarwal, Equation (12)

localize4.5s (0.5%)

bsearch2.7s (0.3%)

end1.0ms (0.0%)