Details

sample14.3m (74.8%)

Algorithm
61×intervals
Results
12.2m231155×body10240exit
23.3s33228×body1280valid
21.7s214593×body80nan
20.0s238795×body80valid
11.1s22809×body640valid
9.7s8947×body2560valid
5.6s3336×body5120valid
3.4s10593×body320valid
1.9s9235×body160valid
1.4s2645×body1280nan
766.0ms2365×body640nan
277.0ms1247×body320nan
114.0ms8256×pre80true
72.0ms563×body160nan

prune1.9m (9.7%)

series1.8m (9.5%)

Calls

450 calls:

4.9s
(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))
4.8s
(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*))))))
4.7s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
1.4s
(/ (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0)) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))

bsearch21.6s (1.9%)

rewrite20.1s (1.8%)

Algorithm
119×rewrite-expression-head
Calls

450 calls:

1.8s
(* (cbrt (/ NdChar (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))))) (cbrt (/ NdChar (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))))))
1.4s
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (/ (cos k) (/ (/ (pow (cbrt (sin k)) 4) l) l)) (pow (cbrt (sin k)) 2)))
1.1s
(exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))
1.1s
(exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))
655.0ms
(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
Rules
36638×add-exp-log
33678×times-frac
23878×prod-exp
17013×add-sqr-sqrt
16089×*-un-lft-identity
15203×add-cube-cbrt
14427×pow-exp
14117×div-exp
9325×unpow-prod-down
7042×pow-to-exp
4684×associate-*r*
4483×cbrt-prod
2655×add-cbrt-cube
2341×1-exp
1813×sqrt-prod
1804×sqr-pow
1749×rec-exp
1130×pow1
1003×cbrt-unprod
827×prod-diff
803×associate-*l*
801×associate-/l*
723×unpow2
572×div-inv
545×cbrt-undiv
544×add-log-exp
474×unswap-sqr
451×expm1-log1p-u
450×log1p-expm1-u
336×pow-prod-down
335×associate-/r*
334×associate-*r/
291×difference-of-squares
284×sqrt-div
283×pow-unpow
281×distribute-rgt-neg-in
276×distribute-rgt-in distribute-lft-in
273×distribute-lft-out--
255×exp-sum
238×distribute-lft-neg-in
229×distribute-lft-out
211×flip3-- flip--
192×cube-prod
168×associate-/r/
155×*-commutative
135×frac-times
101×associate-*l/
97×fma-def frac-2neg clear-num
92×sqrt-pow1
89×swap-sqr
84×cbrt-div
77×flip-+ flip3-+ pow1/3
76×sub-neg
72×associate--l+
56×pow1/2
52×fma-neg
45×pow-pow
44×rem-sqrt-square
41×log-prod
40×exp-prod
38×fma-udef
36×frac-sub
35×associate-/l/
31×div-sub
29×log-pow
27×cos-sum neg-mul-1
26×sum-log
25×tan-quot
24×pow-prod-up
23×diff-log
20×+-commutative
19×pow-sqr
18×hypot-def
17×pow-sub
15×rem-log-exp
12×rem-exp-log
11×neg-sub0 associate--r+
9×unpow3 pow2 cube-mult
8×hypot-udef associate-+r+ neg-log
7×pow-plus
6×cube-div frac-add asin-acos distribute-neg-frac log-div
5×inv-pow pow-flip
4×rem-cube-cbrt pow-neg associate--r-
3×associate-+r- unsub-neg
2×exp-diff sqrt-undiv associate-+l+ sin-sum associate-+l- distribute-frac-neg acos-asin rem-cbrt-cube
1×sqrt-pow2 un-div-inv log1p-udef associate--l- sqrt-unprod log1p-expm1 cos-diff expm1-log1p rem-square-sqrt mul0 expm1-udef

simplify14.3s (1.2%)

Algorithm
179×egg-herbie

regimes10.3s (0.9%)

Accuracy

Total 36.0b remaining (22.7%)

Threshold costs 5.9b (3.7%)

9.5b30.4%Toniolo and Linder, Equation (13)
8.4b65.9%Toniolo and Linder, Equation (7)
4.8b25.8%Toniolo and Linder, Equation (10-)
2.6b55.4%Toniolo and Linder, Equation (10+)
2.4b0%Henrywood and Agarwal, Equation (13)

localize2.3s (0.2%)

end0.0ms (0.0%)