Details

prune2.7m (40.8%)

sample2.0m (29.3%)

Algorithm
61×intervals
Results
27.7s253526×body80valid
22.9s29908×body1280valid
18.0s160881×body80nan
10.8s8697×body2560valid
10.7s20043×body640valid
6.7s3353×body5120valid
3.8s10008×body320valid
2.1s8979×body160valid
960.0ms868×body10240exit
306.0ms625×body1280nan
244.0ms8256×pre80true
232.0ms603×body640nan
106.0ms370×body320nan
37.0ms192×body160nan

rewrite43.0s (10.7%)

Algorithm
117×rewrite-expression-head
Calls

444 calls:

25.5s
(* (/ NdChar (+ (pow 1.0 3) (pow (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT)) 3))) (+ (* 1.0 1.0) (- (* (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT)) (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))) (* 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))))))
2.0s
(- (* (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT)) (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))) (* 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))))
996.0ms
(* (* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) l) (* (/ (pow (cbrt t) 3.0) l) (sin k)))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
589.0ms
(* (* (* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
476.0ms
(/ NdChar (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))))
Rules
27887×add-exp-log
18719×prod-exp
8355×pow-exp
7306×div-exp
5803×times-frac
5279×*-un-lft-identity
5009×add-sqr-sqrt
4010×add-cube-cbrt
3126×pow-to-exp
2891×sqrt-prod
2743×add-cbrt-cube
1408×pow1
1203×cbrt-unprod
1146×associate-*l*
990×associate-*r*
819×1-exp rec-exp
815×unpow-prod-down
586×associate-*r/
575×pow-unpow
562×exp-prod
517×add-log-exp
501×cbrt-undiv
471×cbrt-prod
468×distribute-lft-out
422×associate-/l*
419×pow-prod-down
400×sqrt-div
339×associate-/r*
318×frac-times
312×log-pow
303×associate-*l/
293×unswap-sqr
278×div-inv
243×distribute-lft-out--
219×flip-+ flip3-+
214×flip3-- flip--
212×sqr-pow
175×distribute-rgt-neg-in
156×*-commutative associate-/r/
152×difference-of-squares
150×cbrt-div
136×distribute-lft-neg-in
91×clear-num frac-2neg
89×distribute-rgt-in distribute-lft-in
88×cube-div exp-diff pow-pow
83×sqrt-pow1
81×sub-neg
76×div-sub
73×frac-sub tan-quot
66×pow1/2
62×exp-neg distribute-frac-neg
57×pow1/3
55×neg-sub0
54×rem-sqrt-square
47×pow-prod-up
42×associate-/l/
38×frac-add
37×log-div
35×associate--l+ log-prod
31×pow-sqr swap-sqr
28×un-div-inv cube-prod
23×exp-sum
22×pow-plus
20×sum-log
19×+-commutative
17×sub-div pow2 pow-sub
16×neg-mul-1
15×unpow2
14×diff-log
10×pow-neg
9×rem-cube-cbrt
8×pow-flip associate-+r+ unpow3 cube-mult
7×rem-exp-log inv-pow
6×cos-sum
4×unpow-prod-up unsub-neg associate-+r- sqrt-undiv acos-asin asin-acos rem-log-exp
3×cos-diff sum-cubes
1×unpow1/3 sqrt-unprod distribute-rgt-out-- rem-square-sqrt mul0 rem-cbrt-cube

regimes33.1s (8.2%)

Accuracy

Total 48.6b remaining (22.4%)

Threshold costs 5.5b (2.5%)

8.0b14.5%Toniolo and Linder, Equation (13)
7.8b16.2%Toniolo and Linder, Equation (10+)
7.5b47.7%Henrywood and Agarwal, Equation (3)
5.6b76.7%Toniolo and Linder, Equation (7)
4.9b12.1%Henrywood and Agarwal, Equation (12)

series28.6s (7.1%)

Calls

444 calls:

2.2s
(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*)))))
2.2s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
2.2s
(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*))))))
2.2s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
374.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))

simplify11.6s (2.9%)

Algorithm
177×egg-herbie

localize2.2s (0.6%)

bsearch1.5s (0.4%)

end1.0ms (0.0%)