Details

simplify3.9m (44.7%)

series1.7m (19.4%)

Calls

455 calls:

5.1s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))
5.0s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
4.9s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*))))))
4.9s
(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 (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))

sample1.4m (16.2%)

Algorithm
61×intervals
Results
15.6s29296×body1280valid
15.0s252203×body80valid
9.5s160849×body80nan
9.0s8909×body2560valid
6.8s19720×body640valid
5.5s3420×body5120valid
2.3s10169×body320valid
1.3s9177×body160valid
538.0ms862×body10240exit
146.0ms637×body1280nan
117.0ms652×body640nan
102.0ms8256×pre80true
48.0ms360×body320nan
17.0ms191×body160nan

prune53.6s (10.3%)

rewrite34.0s (6.5%)

Algorithm
119×rewrite-expression-head
Calls

455 calls:

2.5s
(* (* (* (* (/ (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))
2.2s
(* (* (* (/ (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
(* (cbrt (+ 1.0 (exp (/ (- (+ (+ Ev Vef) EAccept) mu) KbT)))) (cbrt (+ 1.0 (exp (/ (- (+ (+ Ev Vef) EAccept) mu) KbT)))))
1.1s
(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (* (* (cbrt (/ (* c0 (* d d)) (* (* w h) (* D D)))) (cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))) (cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))
963.0ms
(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
Rules
34920×add-exp-log
24638×prod-exp
12183×pow-exp
10040×div-exp
7307×times-frac
5728×pow-to-exp
5454×add-sqr-sqrt
5184×*-un-lft-identity
4566×add-cube-cbrt
3481×sqrt-prod
2788×add-cbrt-cube
1363×unpow-prod-down
1356×1-exp
1353×rec-exp
1257×pow1
1252×cbrt-unprod
917×associate-*l*
856×associate-*r*
556×add-log-exp
505×cbrt-undiv
498×associate-*r/
450×associate-*l/
427×associate-/l*
421×sqrt-div
419×pow-prod-down
412×frac-times
404×associate-/r*
401×cbrt-prod
395×sqr-pow
335×div-inv
330×unswap-sqr
306×associate-/r/
263×pow-unpow
252×flip-+ flip3-+
223×distribute-lft-out
218×flip-- flip3--
162×*-commutative
140×tan-quot
137×difference-of-squares
121×distribute-lft-out--
110×sqrt-pow1
98×cbrt-div
93×clear-num frac-2neg
85×distribute-rgt-in distribute-lft-in
83×sub-neg
78×pow1/2
71×unpow2
64×cube-prod
63×rem-sqrt-square
59×pow1/3
57×exp-prod
56×pow-pow
45×associate-/l/
34×frac-sub
32×diff-log
24×div-sub
22×associate--l+
21×sum-log
18×associate--r+
17×distribute-rgt-neg-in
16×cos-sum frac-add +-commutative
15×swap-sqr
13×distribute-lft-neg-in
11×unpow3 cube-mult log-prod
10×rem-cube-cbrt associate-+r+ log-pow
9×pow-prod-up pow-sub
8×cos-diff exp-sum
7×pow-sqr
5×exp-diff rem-exp-log neg-sub0
4×neg-log rem-cbrt-cube pow-neg associate-+r-
3×pow-plus un-div-inv inv-pow pow2 pow-flip acos-asin
2×cube-div associate--l- asin-acos associate--r- rem-log-exp log-div
1×sqrt-undiv sqrt-pow2 associate-+l+ sqrt-unprod sub-div neg-mul-1 mul0 sum-cubes

regimes11.2s (2.1%)

Accuracy

Total 43.9b remaining (20.6%)

Threshold costs 4.8b (2.3%)

9.2b13.1%Toniolo and Linder, Equation (13)
6.0b74.2%Toniolo and Linder, Equation (7)
5.9b18.9%Toniolo and Linder, Equation (10+)
5.2b23.8%Toniolo and Linder, Equation (10-)
4.7b13.9%Henrywood and Agarwal, Equation (12)

localize2.3s (0.5%)

bsearch2.0s (0.4%)

end1.0ms (0.0%)