Details

sample2.2m (39.1%)

Algorithm
61×intervals
Results
36.9s252956×body80valid
24.1s160708×body80nan
21.7s29672×body1280valid
11.3s8913×body2560valid
10.5s20020×body640valid
7.0s3403×body5120valid
3.8s9784×body320valid
2.3s8912×body160valid
644.0ms620×body10240exit
334.0ms620×body1280nan
275.0ms612×body640nan
169.0ms8256×pre80true
111.0ms328×body320nan
39.0ms167×body160nan
8.0ms75×body80overflowed

series1.6m (28.2%)

Calls

454 calls:

4.9s
(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*)))))
4.7s
(sqrt (* (* (* 2.0 n) U) (* (* (cbrt (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))) (cbrt (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))) (cbrt (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))))
4.7s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
4.6s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
1.3s
(* (* (* 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*))))

prune1.0m (18.1%)

rewrite21.4s (6.3%)

Algorithm
117×rewrite-expression-head
Calls

454 calls:

1.0s
(/ 1 (exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))))
879.0ms
(pow (pow (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))) 3) 3)
848.0ms
(cbrt (/ 1 (exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n)))))))
846.0ms
(cbrt (/ 1 (exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n)))))))
843.0ms
(cbrt (/ 1 (exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n)))))))
Rules
25600×add-exp-log
17483×prod-exp
10081×times-frac
9018×pow-exp
7659×div-exp
7075×add-sqr-sqrt
6975×*-un-lft-identity
6096×add-cube-cbrt
4642×sqrt-prod
4447×pow-to-exp
2636×add-cbrt-cube
1750×associate-*r/
1641×sqrt-div
1576×frac-times
1431×unpow-prod-down
1373×associate-*l*
1355×pow1
1344×flip3-- flip--
1097×1-exp rec-exp
1075×cbrt-unprod
989×associate-*r*
956×cbrt-div
856×pow-unpow
737×cbrt-prod
643×frac-sub
614×associate-*l/
573×add-log-exp
552×associate-/l*
525×associate-/r*
496×cbrt-undiv
460×pow-prod-down
405×div-inv
355×sqr-pow
275×unswap-sqr
265×distribute-lft-out--
255×distribute-lft-out
198×difference-of-squares
176×flip-+ flip3-+
163×distribute-rgt-neg-in
155×sqrt-pow1
145×*-commutative
136×associate-/r/
132×exp-prod
123×distribute-lft-neg-in
99×cube-prod
97×clear-num frac-2neg
81×pow1/2
72×distribute-rgt-in distribute-lft-in
70×tan-quot
67×sub-neg
65×pow-pow
57×rem-sqrt-square
54×associate-/l/
51×pow1/3
47×unpow2
37×sum-log
36×div-sub
34×pow-flip
31×associate--l+
30×log-pow
29×swap-sqr
25×diff-log pow-prod-up
24×+-commutative
22×frac-add exp-sum
21×log-prod
19×cube-div exp-diff
18×pow-sub neg-sub0
17×pow-sqr
15×unpow3 cube-mult neg-mul-1
14×pow-neg
13×inv-pow
11×rem-cube-cbrt
10×associate-+r+ log-div
9×associate-+r- rem-log-exp
8×pow-div distribute-neg-frac
7×rem-exp-log
6×un-div-inv
4×cos-sum pow-plus pow2 associate--r+ unsub-neg
3×distribute-frac-neg acos-asin asin-acos
2×sqrt-unprod cos-diff neg-log sub-div rem-square-sqrt rem-cbrt-cube associate-+l-
1×sqrt-undiv associate-+l+ associate--l- sum-cubes distribute-rgt-out-- mul0 exp-to-pow

simplify12.3s (3.6%)

Algorithm
177×egg-herbie

regimes11.0s (3.2%)

Accuracy

Total 37.9b remaining (18.6%)

Threshold costs 5.3b (2.6%)

7.9b17.7%Toniolo and Linder, Equation (13)
5.5b77.5%Toniolo and Linder, Equation (7)
4.7b0%Henrywood and Agarwal, Equation (12)
3.5b54.2%Toniolo and Linder, Equation (10+)
3.2b56.5%Toniolo and Linder, Equation (10-)

bsearch3.0s (0.9%)

localize2.3s (0.7%)

end0.0ms (0.0%)