Details

series2.1m (35.2%)

Calls

444 calls:

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*)))))
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) (- (- 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*)))))
4.7s
(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*)))))

prune1.6m (26.7%)

sample1.4m (23.2%)

Algorithm
61×intervals
Results
16.3s29672×body1280valid
15.5s252956×body80valid
9.6s160708×body80nan
8.8s8913×body2560valid
7.1s20020×body640valid
5.5s3403×body5120valid
2.3s9784×body320valid
1.3s8912×body160valid
377.0ms695×body10240exit
149.0ms620×body1280nan
115.0ms612×body640nan
113.0ms8256×pre80true
51.0ms328×body320nan
18.0ms167×body160nan

rewrite22.2s (6.4%)

Algorithm
117×rewrite-expression-head
Calls

444 calls:

1.0s
(* (sqrt (* (* (* (/ (sqrt 2.0) 4.0) (sqrt (- 1.0 (* 3.0 (* v v))))) (+ (sqrt 1.0) v)) (- (sqrt 1.0) v))) (sqrt (* (* (* (/ (sqrt 2.0) 4.0) (sqrt (- 1.0 (* 3.0 (* v v))))) (+ (sqrt 1.0) v)) (- (sqrt 1.0) v))))
1.0s
(/ 1 (exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))))
946.0ms
(pow (pow (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))) 3) 3)
883.0ms
(cbrt (/ 1 (exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n)))))))
861.0ms
(cbrt (/ 1 (exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n)))))))
Rules
25528×add-exp-log
17419×prod-exp
12018×frac-times
9945×sqrt-div
8990×times-frac
8964×pow-exp
7677×div-exp
6857×add-sqr-sqrt
6403×*-un-lft-identity
5423×add-cube-cbrt
4764×associate-*l/
4405×pow-to-exp
4234×flip-- flip3--
3381×associate-*r/
2745×add-cbrt-cube
2415×sqrt-prod
2108×flip-+ flip3-+
1684×unpow-prod-down
1463×pow1
1272×cbrt-prod
1127×cbrt-unprod
1082×associate-*l*
1078×associate-*r*
1077×1-exp rec-exp
1015×prod-diff
827×pow-unpow
569×div-inv
560×pow-prod-down
546×cbrt-undiv
542×difference-of-squares
521×add-log-exp
486×sqr-pow
456×associate-/l*
445×log1p-expm1-u
444×associate-/r* expm1-log1p-u
328×distribute-lft-out--
314×associate-/r/
240×distribute-lft-out
224×unswap-sqr
186×distribute-rgt-in distribute-lft-in
185×sqrt-pow1
165×distribute-rgt-neg-in
157×exp-prod
142×*-commutative
126×distribute-lft-neg-in
110×fma-neg
97×clear-num frac-2neg
89×unpow2
76×tan-quot
69×pow1/2
63×sub-neg
59×log-pow
58×fma-def
56×pow-pow
47×associate--l+
46×frac-sub cos-sum
45×cube-prod
44×associate-/l/
42×rem-sqrt-square pow1/3
35×fma-udef div-sub
34×pow-prod-up
29×exp-diff
24×pow-sqr
22×associate--r+ sum-log exp-sum
21×cbrt-div
20×log-prod
18×pow-sub log-div
17×hypot-def
16×diff-log +-commutative neg-sub0 swap-sqr neg-mul-1
14×pow-neg pow-flip
11×associate-+r+
10×cube-div
9×associate-+r- rem-log-exp
8×unpow3 cube-mult
7×rem-exp-log inv-pow hypot-udef
6×un-div-inv distribute-neg-frac
4×rem-cube-cbrt sqrt-pow2 pow-plus pow2 frac-add unsub-neg asin-acos
3×sqrt-unprod distribute-frac-neg acos-asin
2×associate-+l+ cos-diff expm1-log1p rem-square-sqrt expm1-udef
1×log1p-udef associate--l- log1p-expm1 sum-cubes mul0 distribute-rgt-neg-out

simplify13.8s (3.9%)

Algorithm
177×egg-herbie

regimes11.0s (3.1%)

Accuracy

Total 37.0b remaining (20.1%)

Threshold costs 3.9b (2.1%)

7.9b19%Toniolo and Linder, Equation (13)
5.5b77.5%Toniolo and Linder, Equation (7)
4.7b0%Henrywood and Agarwal, Equation (12)
3.6b53.7%Toniolo and Linder, Equation (10+)
3.2b56.5%Toniolo and Linder, Equation (10-)

bsearch2.7s (0.8%)

localize2.2s (0.6%)

end0.0ms (0.0%)