Details

series1.8m (35.4%)

Calls

436 calls:

5.3s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))
5.2s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* (* n (pow (/ (* (cbrt l) (cbrt l)) 1) (/ 2.0 2))) (pow (/ (cbrt l) Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))
5.2s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
5.1s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
1.4s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* (* n (pow (/ (* (cbrt l) (cbrt l)) 1) (/ 2.0 2))) (pow (/ (cbrt l) Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))

sample1.4m (27.5%)

Algorithm
61×intervals
Results
15.5s29350×body1280valid
15.4s253224×body80valid
9.5s158091×body80nan
8.7s8786×body2560valid
7.4s20641×body640valid
5.2s3346×body5120valid
2.3s9945×body320valid
1.3s9119×body160valid
393.0ms677×body10240exit
141.0ms617×body1280nan
109.0ms615×body640nan
99.0ms8256×pre80true
44.0ms340×body320nan
17.0ms195×body160nan

prune50.0s (16.4%)

rewrite37.2s (12.2%)

Algorithm
115×rewrite-expression-head
Calls

436 calls:

2.9s
(* (* (* (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (/ (pow (cbrt t) 3.0) l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
2.8s
(* (* (* (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (/ (pow t (* 1/3 3.0)) l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
1.3s
(/ (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))) (sqrt NdChar))
963.0ms
(* (* (* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (/ (pow (cbrt t) 3.0) l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
856.0ms
(/ (sqrt NdChar) (/ (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))) (sqrt NdChar)))
Rules
38022×add-exp-log
26554×prod-exp
15080×pow-exp
11561×div-exp
6959×pow-to-exp
4158×add-sqr-sqrt
3800×*-un-lft-identity
3789×times-frac
3023×add-cube-cbrt
2482×add-cbrt-cube
1860×sqrt-prod
1341×pow1
1126×1-exp
1080×rec-exp
1060×cbrt-unprod
1035×associate-*r*
984×associate-*r/
943×unpow-prod-down
721×associate-*l*
713×cbrt-prod
603×sqrt-div
550×add-log-exp
499×frac-times
431×pow-prod-down
429×cbrt-div
421×cbrt-undiv
418×associate-*l/
390×associate-/l*
368×pow-unpow
358×flip3-- flip--
345×associate-/r*
321×unswap-sqr
287×sqr-pow
271×flip-+ flip3-+
262×distribute-lft-out
257×associate-/r/
247×difference-of-squares
236×div-inv
178×distribute-lft-out--
148×*-commutative
140×distribute-rgt-neg-in
117×unpow2
108×distribute-lft-neg-in
100×pow1/3 sqrt-pow1
95×clear-num frac-2neg
75×tan-quot
66×distribute-rgt-in distribute-lft-in
62×pow1/2
60×pow-prod-up frac-sub pow-pow
59×swap-sqr
57×sub-neg
55×rem-sqrt-square
54×sum-log
42×pow-sqr
36×cube-div
35×associate-/l/
32×frac-add
31×+-commutative
26×pow-plus
24×div-sub
22×associate--l+
21×pow2 neg-sub0
20×pow-sub
19×pow-neg
16×exp-diff log-div
14×cube-prod
12×neg-mul-1
10×associate-+r+
9×un-div-inv
8×diff-log distribute-neg-frac
7×neg-log exp-prod
5×rem-cube-cbrt unpow3 cube-mult exp-sum log-prod
4×inv-pow sub-div log-pow pow-flip associate-+l- associate--r+
3×associate-+l+ unsub-neg associate-+r-
2×distribute-frac-neg acos-asin cos-sum
1×sqrt-pow2 rem-exp-log unpow1/3 sqrt-unprod cos-diff distribute-rgt-out-- rem-square-sqrt mul0 rem-cbrt-cube

simplify12.0s (3.9%)

Algorithm
175×egg-herbie

regimes10.0s (3.3%)

Accuracy

Total 43.4b remaining (20.2%)

Threshold costs 5.1b (2.4%)

7.9b23.3%Toniolo and Linder, Equation (13)
5.9b8.7%Toniolo and Linder, Equation (10+)
5.7b0%Henrywood and Agarwal, Equation (12)
5.0b78.6%Toniolo and Linder, Equation (7)
3.6b0%Toniolo and Linder, Equation (10-)

localize2.3s (0.7%)

bsearch1.6s (0.5%)

end0.0ms (0.0%)