Details

series1.8m (35.0%)

Calls

448 calls:

10.1s
(sqrt (pow (* (* (* 2.0 n) (- t (- (* 2.0 (* l (/ l Om))) (* (- (- U U*)) (* n (pow (/ l Om) (* 2 (/ 2.0 2)))))))) U) 1))
5.2s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
5.2s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))
5.0s
(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 (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))

sample1.4m (26.5%)

Algorithm
61×intervals
Results
15.4s29570×body1280valid
15.3s252860×body80valid
9.4s159219×body80nan
8.8s8847×body2560valid
6.9s19822×body640valid
5.5s3372×body5120valid
2.4s10030×body320valid
1.3s9342×body160valid
428.0ms644×body10240exit
130.0ms573×body1280nan
116.0ms639×body640nan
113.0ms8256×pre80true
49.0ms356×body320nan
17.0ms191×body160nan

prune1.0m (19.1%)

rewrite33.9s (10.7%)

Algorithm
117×rewrite-expression-head
Calls

448 calls:

3.4s
(* (sqrt (/ NdChar (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))))) (sqrt (/ NdChar (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))))))
3.4s
(* (/ 1 (sqrt (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))))) (/ NdChar (sqrt (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))))))
1.1s
(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
1.1s
(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
879.0ms
(/ 1 (sqrt (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT)))))
Rules
41753×add-exp-log
29531×prod-exp
18227×pow-exp
13782×div-exp
8579×pow-to-exp
6104×add-sqr-sqrt
5965×times-frac
5245×*-un-lft-identity
4234×add-cube-cbrt
2994×sqrt-prod
2563×add-cbrt-cube
2086×1-exp rec-exp
1327×pow1
1128×unpow-prod-down
987×cbrt-unprod
954×sqrt-div
897×associate-*l*
849×cbrt-div
820×associate-*r*
694×cbrt-prod
651×associate-*r/
594×pow-unpow
573×frac-times
560×prod-diff
547×difference-of-squares
541×add-log-exp
515×cbrt-undiv
448×log1p-expm1-u expm1-log1p-u
435×distribute-lft-out--
431×pow-prod-down associate-/r*
412×flip3-- flip--
397×associate-/l*
332×distribute-rgt-neg-in
326×div-inv
323×sqr-pow
312×distribute-lft-neg-in
298×unswap-sqr
269×associate-*l/
225×associate-/r/
218×flip-+ flip3-+
161×distribute-rgt-in distribute-lft-in
144×*-commutative
142×sqrt-pow1
137×fma-def
122×distribute-lft-out
103×frac-2neg swap-sqr clear-num
101×pow1/2
94×cube-div
88×cube-prod
75×fma-neg
64×rem-sqrt-square
55×sub-neg
53×pow-pow
44×pow1/3
40×associate-/l/ pow-prod-up
36×neg-mul-1
35×associate--l+
30×unpow2
29×pow-sqr cos-sum
28×div-sub
27×frac-add sum-log
26×fma-udef tan-quot
25×frac-sub
23×diff-log
22×associate--r+
20×+-commutative
14×hypot-def
13×neg-sub0 distribute-neg-frac
12×pow-sub
10×pow-plus
9×unpow3 sqrt-unprod pow-flip cube-mult
8×exp-neg distribute-rgt-neg-out
7×inv-pow pow2 neg-log
6×associate-+r+
5×un-div-inv rem-square-sqrt
4×sqrt-undiv exp-prod log-rec distribute-frac-neg acos-asin associate-+l- mul-1-neg rem-cbrt-cube
3×rem-cube-cbrt pow-neg asin-acos cos-diff exp-sum log-prod
2×associate-+l+ associate--l- distribute-lft-neg-out expm1-log1p hypot-udef associate--r- expm1-udef
1×rem-exp-log sqrt-pow2 associate-+r- log-pow unsub-neg mul0

simplify12.8s (4.0%)

Algorithm
177×egg-herbie

regimes11.0s (3.5%)

Accuracy

Total 44.1b remaining (21.7%)

Threshold costs 5.5b (2.7%)

9.3b25.1%Toniolo and Linder, Equation (13)
9.2b37.1%Henrywood and Agarwal, Equation (3)
6.4b0%Henrywood and Agarwal, Equation (12)
5.7b76.1%Toniolo and Linder, Equation (7)
3.1b-0.7%Toniolo and Linder, Equation (10+)

localize2.3s (0.7%)

bsearch1.2s (0.4%)

end0.0ms (0.0%)