Details

series1.8m (34.0%)

Calls

452 calls:

10.0s
(sqrt (pow (* (* (* 2.0 n) (- t (- (* 2.0 (* l (/ l Om))) (* (- (* n (pow (/ l Om) (* 2 (/ 2.0 2))))) (- U U*))))) U) 1))
5.0s
(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*)))))
4.9s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
1.5s
(* (* (* 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 (26.6%)

Algorithm
61×intervals
Results
15.5s29570×body1280valid
15.1s252860×body80valid
9.2s159219×body80nan
8.9s8847×body2560valid
6.8s19822×body640valid
5.5s3372×body5120valid
2.3s10030×body320valid
1.3s9342×body160valid
443.0ms644×body10240exit
129.0ms573×body1280nan
118.0ms639×body640nan
98.0ms8256×pre80true
47.0ms356×body320nan
17.0ms191×body160nan

prune57.2s (18.3%)

rewrite38.6s (12.3%)

Algorithm
117×rewrite-expression-head
Calls

452 calls:

3.3s
(* (/ 1 (sqrt (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))))) (/ NdChar (sqrt (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))))))
3.3s
(* (sqrt (/ NdChar (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))))) (sqrt (/ NdChar (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))))))
1.6s
(/ 1 (exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))))
1.1s
(* (* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
819.0ms
(/ 1 (sqrt (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT)))))
Rules
41450×add-exp-log
29420×prod-exp
18249×pow-exp
13582×div-exp
8677×pow-to-exp
5617×times-frac
5266×add-sqr-sqrt
4728×*-un-lft-identity
3870×add-cube-cbrt
2515×add-cbrt-cube
1994×rec-exp 1-exp
1784×sqrt-prod
1553×unpow-prod-down
1370×pow1
1355×associate-*l*
1011×cbrt-unprod
987×sqrt-div
881×cbrt-div
850×associate-*r*
749×associate-*r/
670×frac-times
648×cbrt-prod
615×pow-unpow
552×add-log-exp
452×cbrt-undiv
451×associate-/r*
445×pow-prod-down
424×flip3-- flip--
404×associate-*l/
397×sqr-pow
371×associate-/l*
336×unswap-sqr
322×distribute-lft-out--
306×div-inv
294×difference-of-squares
293×flip-+ flip3-+
236×associate-/r/
165×distribute-rgt-neg-in
158×distribute-lft-out
153×distribute-lft-neg-in
148×*-commutative
144×sqrt-pow1
112×pow1/2
97×cube-div
96×frac-2neg clear-num
89×cube-prod
86×swap-sqr
77×rem-sqrt-square
71×tan-quot
70×distribute-rgt-in distribute-lft-in
63×sub-neg
61×unpow2
58×pow-pow
53×associate-/l/
52×pow1/3
38×frac-sub
36×pow-prod-up
33×sum-log
32×frac-add
27×pow-sqr div-sub
25×associate--l+
22×diff-log
21×+-commutative neg-mul-1
18×pow-sub exp-prod
16×associate-+r+
15×pow-flip
14×pow-neg log-pow neg-sub0
10×unpow3 cube-mult pow-plus
sqrt-unprod log-prod
inv-pow distribute-neg-frac associate--r+
pow2
un-div-inv
associate-+r- rem-square-sqrt sqrt-undiv rem-cbrt-cube
distribute-frac-neg acos-asin exp-sum
cos-sum rem-cube-cbrt associate-+l+ distribute-lft-neg-out asin-acos
exp-diff sqrt-pow2 cos-diff unsub-neg mul0 rem-log-exp

simplify13.0s (4.1%)

Algorithm
177×egg-herbie

regimes11.2s (3.6%)

Accuracy

Total 48.7b remaining (22.2%)

Threshold costs 4.3b (2%)

9.3b25.1%Toniolo and Linder, Equation (13)
9.2b37.1%Henrywood and Agarwal, Equation (3)
6.4b0%Henrywood and Agarwal, Equation (12)
5.7b76.2%Toniolo and Linder, Equation (7)
3.9b48%Toniolo and Linder, Equation (10+)

localize2.4s (0.8%)

bsearch1.2s (0.4%)

end1.0ms (0.0%)