Details

simplify6.5m (42.9%)

sample3.4m (22.1%)

Algorithm
61×intervals
Results
48.3s252422×body80valid
39.1s29240×body1280valid
26.6s160639×body80nan
19.4s20132×body640valid
18.4s8695×body2560valid
10.1s3322×body5120valid
7.0s10001×body320valid
2.8s9239×body160valid
1.3s988×body10240exit
394.0ms572×body1280nan
332.0ms8256×pre80true
239.0ms629×body640nan
218.0ms372×body320nan
40.0ms200×body160nan

series2.5m (16.3%)

Calls

446 calls:

8.0s
(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*))))))
7.4s
(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*)))))
6.7s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
6.7s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
2.2s
(* (* (* 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*))))

prune1.5m (9.6%)

rewrite54.5s (6.0%)

Algorithm
116×rewrite-expression-head
Calls

446 calls:

4.1s
(* (* (* (* (/ (pow (cbrt t) 3.0) (* (cbrt l) (cbrt l))) (/ (pow (cbrt t) 3.0) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
1.5s
(/ NdChar (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))))
1.4s
(/ NdChar (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))))
1.4s
(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ 1 (/ (* (* w h) (* D D)) (* c0 (* d d)))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))
1.3s
(* (* (* (/ (pow (cbrt t) 3.0) (* (cbrt l) (cbrt l))) (/ (pow (cbrt t) 3.0) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (* (tan k) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)))
Rules
51541×add-exp-log
37698×prod-exp
24847×pow-exp
18246×div-exp
12031×pow-to-exp
9007×times-frac
6659×*-un-lft-identity
6366×add-sqr-sqrt
5882×sqrt-prod
5537×add-cube-cbrt
3763×1-exp rec-exp
2839×add-cbrt-cube
1488×associate-*l*
1447×pow1
1282×cbrt-unprod
987×unpow-prod-down
806×associate-*r*
611×associate-/r*
531×associate-*r/
526×add-log-exp
525×cbrt-undiv
486×cbrt-prod
474×associate-/l*
457×associate-*l/
456×frac-times
435×pow-prod-down
407×distribute-lft-out
388×sqrt-div
370×div-inv
301×pow-unpow
285×unswap-sqr flip-+ flip3-+
253×associate-/r/
240×sqr-pow
209×distribute-lft-out--
191×flip3-- flip--
182×sqrt-pow1
178×log-pow
152×exp-prod
149×*-commutative
138×tan-quot
136×distribute-rgt-neg-in
123×distribute-lft-neg-in
117×difference-of-squares
111×cbrt-div
100×pow1/3
98×pow-prod-up
95×clear-num frac-2neg
70×distribute-rgt-in distribute-lft-in
64×pow1/2
58×pow-sqr
56×rem-sqrt-square
54×sub-neg
52×pow-plus
46×unpow2
44×cube-prod pow-pow
42×associate-/l/
39×log-prod
34×pow2
32×frac-sub
31×sum-log
27×frac-add
26×swap-sqr
24×+-commutative
21×div-sub
20×associate--l+
16×neg-sub0
15×pow-sub neg-mul-1
14×pow-neg
11×un-div-inv
10×diff-log
distribute-neg-frac rem-log-exp
pow-flip associate-+r+
inv-pow acos-asin cos-sum
rem-cube-cbrt unpow3 cube-mult
asin-acos
associate-+l+ cos-diff associate-+l- distribute-frac-neg neg-log exp-sum
sqrt-unprod pow3 associate--r+
cube-div sqrt-undiv difference-cubes rem-exp-log associate--l- unsub-neg associate-+r- mul0 exp-to-pow

regimes17.5s (1.9%)

Accuracy

Total 47.5b remaining (20.8%)

Threshold costs 5.7b (2.5%)

9.8b8.4%Toniolo and Linder, Equation (13)
6.5b12.2%Toniolo and Linder, Equation (10+)
6.1b52.8%Henrywood and Agarwal, Equation (3)
5.3b77.8%Toniolo and Linder, Equation (7)
4.7b0%Henrywood and Agarwal, Equation (12)

bsearch5.0s (0.6%)

localize4.9s (0.5%)

end1.0ms (0.0%)