Details

series1.8m (37.3%)

Calls

433 calls:

5.0s
(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*)))))))
4.8s
(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)) (- U U*)))))
1.4s
(* (* 2.0 n) (* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

sample1.3m (27.9%)

Algorithm
61×intervals
Results
15.7s29267×body1280valid
15.5s252878×body80valid
9.7s162042×body80nan
8.8s8861×body2560valid
7.2s20556×body640valid
5.6s3434×body5120valid
2.4s9875×body320valid
1.3s9091×body160valid
562.0ms748×body10240exit
145.0ms607×body1280nan
117.0ms637×body640nan
109.0ms8256×pre80true
50.0ms365×body320nan
18.0ms186×body160nan

prune53.6s (18.5%)

rewrite20.1s (6.9%)

Algorithm
114×rewrite-expression-head
Calls

433 calls:

3.8s
(* (cos (- (/ (* K (+ m n)) 2.0) M)) (exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))))
1.2s
(- (* (exp (/ (+ (+ (+ Ev Vef) EAccept) (- mu)) KbT)) (exp (/ (+ (+ (+ Ev Vef) EAccept) (- mu)) KbT))) (* 1.0 (exp (/ (+ (+ (+ Ev Vef) EAccept) (- mu)) KbT))))
1.1s
(* (* (* (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))
629.0ms
(* (* (* (* (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))
471.0ms
(* NaChar (/ 1 (+ 1.0 (exp (/ (+ (+ (+ Ev Vef) EAccept) (- mu)) KbT)))))
Rules
47404×add-exp-log
34577×prod-exp
24324×pow-exp
17518×div-exp
11714×pow-to-exp
3835×1-exp
3597×add-sqr-sqrt
3596×rec-exp
3557×*-un-lft-identity
2830×times-frac
2758×add-cbrt-cube
2710×add-cube-cbrt
1349×sqrt-prod
1205×cbrt-unprod
1186×pow1
941×associate-*r*
788×associate-*l*
656×unpow-prod-down
586×associate-*r/
536×cbrt-undiv
511×add-log-exp
509×prod-diff
435×expm1-log1p-u
433×log1p-expm1-u
388×pow-prod-down
372×cbrt-prod
354×associate-/l*
338×distribute-lft-out
327×associate-/r*
305×pow-unpow
295×distribute-rgt-in distribute-lft-in
254×unswap-sqr
246×div-inv
234×sqrt-div
230×associate-*l/
226×distribute-rgt-neg-in
201×frac-times
185×div-sub
180×sqr-pow
171×distribute-lft-out--
160×exp-diff distribute-lft-neg-in
158×flip3-- flip--
149×*-commutative
140×difference-of-squares
134×sqrt-pow1
128×exp-sum
120×flip-+ flip3-+
99×frac-2neg clear-num
97×associate-/r/
85×frac-sub
84×pow1/2 associate--l+
81×fma-def
76×sub-neg
75×tan-quot
72×exp-prod
70×pow-pow
66×neg-sub0
57×associate-+r- unsub-neg
55×rem-sqrt-square
46×associate-+l+
36×fma-udef
35×associate-/l/
32×sum-log
30×unpow2
27×+-commutative
25×cos-sum
23×log-prod
22×swap-sqr
19×log-pow pow1/3 neg-mul-1
18×sub-div
15×fma-neg
14×frac-add hypot-def
11×pow-sub pow-flip
10×pow-prod-up
9×cbrt-div
8×associate-+r+
7×diff-log inv-pow cube-prod
6×pow-sqr distribute-neg-frac
5×pow-neg
4×sqrt-unprod acos-asin rem-log-exp
3×cube-div un-div-inv asin-acos
2×log1p-udef sin-sum log1p-expm1 hypot-udef expm1-log1p unpow3 cube-mult distribute-frac-neg neg-log expm1-udef associate-+l- pow2
1×rem-exp-log rem-cube-cbrt cos-diff pow-plus rem-square-sqrt associate--r- mul0 distribute-rgt-out-- exp-to-pow

simplify12.1s (4.2%)

Algorithm
174×egg-herbie

regimes10.2s (3.5%)

Accuracy

Total 49.4b remaining (24.5%)

Threshold costs 4.0b (2%)

10.2b15.2%Toniolo and Linder, Equation (13)
8.1b9.2%Toniolo and Linder, Equation (10+)
7.9b28%Henrywood and Agarwal, Equation (3)
6.6b72%Toniolo and Linder, Equation (7)
4.2b28.6%Toniolo and Linder, Equation (10-)

bsearch2.4s (0.8%)

localize2.2s (0.8%)

end1.0ms (0.0%)