Details

sample14.3m (75.2%)

Algorithm
61×intervals
Results
12.2m231155×body10240exit
23.4s33228×body1280valid
21.2s214593×body80nan
20.0s238795×body80valid
11.0s22809×body640valid
9.4s8947×body2560valid
5.6s3336×body5120valid
3.4s10593×body320valid
1.8s9235×body160valid
1.2s2645×body1280nan
774.0ms2365×body640nan
283.0ms1247×body320nan
112.0ms8256×pre80true
77.0ms563×body160nan

prune1.8m (9.4%)

series1.7m (9.0%)

Calls

454 calls:

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)) (- U U*))))))
4.6s
(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*))))))
4.6s
(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)) (- U U*)))))

rewrite24.1s (2.1%)

Algorithm
118×rewrite-expression-head
Calls

454 calls:

1.5s
(* (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)))))
982.0ms
(* (pow (* (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))) (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT)))) (- 1/3)) (/ NdChar (cbrt (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))))))
973.0ms
(/ 1 (* (cbrt (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT)))) (cbrt (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))))))
Rules
32886×times-frac
29959×add-exp-log
18891×prod-exp
16428×add-sqr-sqrt
15501×*-un-lft-identity
14477×add-cube-cbrt
12091×div-exp
11828×pow-exp
8960×unpow-prod-down
6180×pow-to-exp
4586×associate-*r*
4521×cbrt-prod
3052×sqrt-prod
2594×add-cbrt-cube
1761×1-exp
1668×sqr-pow
1465×rec-exp
1324×pow1
1237×associate-*l*
1138×sqrt-div
1050×cbrt-unprod
742×associate-/l*
728×unpow2
679×associate-*r/
564×add-log-exp
555×unswap-sqr div-inv
513×frac-times
454×pow-prod-down
440×flip-+ flip3-+
434×cbrt-undiv
392×cbrt-div
381×associate-/r/
369×distribute-lft-out
347×associate-/r*
318×associate-*l/
290×cube-prod
286×pow-unpow
207×difference-of-squares
202×flip3-- flip--
168×distribute-lft-out--
167×swap-sqr
163×*-commutative
126×sqrt-pow1
118×distribute-rgt-in distribute-lft-in
113×distribute-rgt-neg-in
99×frac-2neg clear-num
77×sub-neg
75×pow1/2
74×pow-pow
71×distribute-lft-neg-in
68×pow1/3
65×tan-quot
60×frac-sub
50×rem-sqrt-square
37×associate-/l/
34×associate--l+
30×sum-log
28×diff-log
27×exp-prod
26×pow-prod-up +-commutative
22×frac-add pow-flip div-sub
18×pow-sqr
15×cube-div
14×unpow3 inv-pow cube-mult
13×rem-cube-cbrt
11×neg-sub0 neg-mul-1
10×rem-exp-log associate-+r+
8×pow-sub log-prod
7×distribute-rgt-out--
6×cos-sum pow-plus pow2 neg-log sub-div pow-neg asin-acos exp-sum
5×rem-cbrt-cube
4×difference-cubes associate--r- distribute-neg-frac
3×cos-diff unsub-neg rem-log-exp associate-+r-
2×exp-diff sqrt-pow2 associate-+l+ sqrt-unprod unpow-prod-up rem-square-sqrt distribute-frac-neg acos-asin associate--r+
1×un-div-inv distribute-lft-neg-out associate--l- log-pow mul0 distribute-rgt-neg-out associate-+l-

bsearch21.7s (1.9%)

simplify14.0s (1.2%)

Algorithm
178×egg-herbie

regimes10.6s (0.9%)

Accuracy

Total 42.8b remaining (23.4%)

Threshold costs 5.3b (2.9%)

9.0b31.6%Toniolo and Linder, Equation (13)
8.6b20.1%Maksimov and Kolovsky, Equation (3)
6.4b73.1%Toniolo and Linder, Equation (7)
4.8b25.9%Toniolo and Linder, Equation (10-)
3.9b35.6%Toniolo and Linder, Equation (10+)

localize2.3s (0.2%)

end1.0ms (0.0%)