Details

simplify6.5m (43.9%)

sample3.3m (22.2%)

Algorithm
61×intervals
Results
41.5s252422×body80valid
40.8s29240×body1280valid
27.9s160639×body80nan
19.0s8695×body2560valid
17.8s20132×body640valid
10.6s3322×body5120valid
8.1s10001×body320valid
3.1s9239×body160valid
1.5s988×body10240exit
434.0ms572×body1280nan
336.0ms629×body640nan
169.0ms8256×pre80true
112.0ms372×body320nan
38.0ms200×body160nan

series2.3m (15.6%)

Calls

439 calls:

2.8s
(sqrt (* (- t (fma 2.0 (* l (/ l Om)) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*))))) (* (* 2.0 n) U)))
2.8s
(sqrt (* (- t (fma 2.0 (* l (/ l Om)) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))) (* (* 2.0 n) U)))
2.6s
(sqrt (* (- t (fma 2.0 (* l (/ l Om)) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (* (* 2.0 n) U)))
2.5s
(sqrt (* (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (* (* 2.0 n) U)))
2.5s
(/ (pow E (log (- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))

prune1.5m (10.1%)

rewrite47.9s (5.4%)

Algorithm
117×rewrite-expression-head
Calls

439 calls:

2.5s
(/ (+ (exp (/ (- (+ (+ Ev Vef) EAccept) mu) KbT)) 1.0) NaChar)
2.4s
(/ (sqrt (+ (exp (/ (- (+ (+ Ev Vef) EAccept) mu) KbT)) 1.0)) (/ NaChar (sqrt (+ (exp (/ (- (+ (+ Ev Vef) EAccept) mu) KbT)) 1.0))))
2.3s
(* (+ (exp (/ (- (+ (+ Ev Vef) EAccept) mu) KbT)) 1.0) (/ 1 NaChar))
1.8s
(/ 1 (/ (sqrt (+ (exp (/ (- (+ (+ Ev Vef) EAccept) mu) KbT)) 1.0)) (/ NaChar (sqrt (+ (exp (/ (- (+ (+ Ev Vef) EAccept) mu) KbT)) 1.0)))))
1.8s
(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
Rules
37914×add-exp-log
26535×prod-exp
15922×pow-exp
12674×div-exp
8025×pow-to-exp
7803×times-frac
6235×*-un-lft-identity
5842×add-sqr-sqrt
5076×add-cube-cbrt
3042×sqrt-prod
2618×add-cbrt-cube
1692×1-exp rec-exp
1133×pow1
1127×unpow-prod-down
992×cbrt-unprod
903×associate-*r*
659×associate-*l*
612×associate-/r*
555×cbrt-undiv
519×associate-/l*
516×prod-diff
497×add-log-exp
451×div-inv
439×log1p-expm1-u expm1-log1p-u
415×cbrt-prod
389×distribute-lft-out
332×pow-prod-down
322×pow-unpow associate-*l/
318×associate-*r/
317×associate-/r/
252×sqrt-div
241×distribute-lft-out--
230×frac-times
223×distribute-rgt-neg-in
209×distribute-lft-neg-in
207×sqr-pow
196×unswap-sqr
161×flip3-- flip--
158×sqrt-pow1
150×log-pow
149×difference-of-squares
135×*-commutative
128×distribute-rgt-in distribute-lft-in
127×exp-prod
125×flip-+ flip3-+
110×clear-num frac-2neg
100×tan-quot
81×pow1/3
69×cos-sum
67×fma-neg
66×log-prod
50×pow1/2
47×pow-pow
45×rem-sqrt-square cbrt-div
43×associate-/l/
42×sub-neg
37×fma-def
30×unpow2
23×neg-mul-1
22×pow-prod-up
20×div-sub
19×fma-udef
18×unpow-prod-up exp-sum
15×sum-log diff-log
14×pow-sub pow-plus
13×+-commutative hypot-def
12×frac-add swap-sqr
11×associate--r+
10×pow-sqr pow-flip
9×inv-pow neg-sub0
8×log-div
7×un-div-inv cube-prod distribute-neg-frac rem-log-exp
6×pow2
4×exp-diff rem-cube-cbrt pow-neg acos-asin asin-acos
3×unpow3 cos-diff cube-mult distribute-frac-neg distribute-rgt-out--
2×sqrt-undiv e-exp-1 associate-+r+ pow3 expm1-log1p hypot-udef expm1-udef frac-sub neg-log
1×rem-exp-log sqrt-pow2 associate-+l+ associate--l- associate-+r- unsub-neg sub-div associate--r- mul0 rem-cbrt-cube distribute-rgt-neg-out exp-to-pow

regimes16.2s (1.8%)

Accuracy

Total 43.2b remaining (20.8%)

Threshold costs 5.1b (2.4%)

10.0b11.5%Toniolo and Linder, Equation (13)
6.1b52.8%Henrywood and Agarwal, Equation (3)
5.3b0%Henrywood and Agarwal, Equation (12)
5.3b77.7%Toniolo and Linder, Equation (7)
4.6b50.3%Toniolo and Linder, Equation (10-)

bsearch4.3s (0.5%)

localize4.2s (0.5%)

end0.0ms (0.0%)