Details

simplify4.2m (47.1%)

series1.6m (17.3%)

Calls

443 calls:

1.9s
(sqrt (* (* (- t (fma 2.0 (/ l (/ Om l)) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))) (* 2.0 n)) U))
1.9s
(sqrt (* (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (* (* 2.0 n) U)))
1.9s
(sqrt (* (* (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (* 2.0 n)) U))
1.9s
(sqrt (* (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (* (* 2.0 n) U)))
1.1s
(/ (/ (- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5)) (sqrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))) (sqrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))

sample1.4m (15.7%)

Algorithm
61×intervals
Results
15.3s29296×body1280valid
15.2s252203×body80valid
9.6s160849×body80nan
8.9s8909×body2560valid
7.1s19720×body640valid
5.8s3420×body5120valid
2.4s10169×body320valid
1.3s9177×body160valid
555.0ms862×body10240exit
146.0ms637×body1280nan
122.0ms652×body640nan
104.0ms8256×pre80true
49.0ms360×body320nan
17.0ms191×body160nan

prune1.0m (11.4%)

rewrite31.7s (5.9%)

Algorithm
119×rewrite-expression-head
Calls

443 calls:

3.8s
(* (cbrt (+ (exp (/ (- (+ (+ Ev Vef) EAccept) mu) KbT)) 1.0)) (cbrt (+ (exp (/ (- (+ (+ Ev Vef) EAccept) mu) KbT)) 1.0)))
1.8s
(/ 1 (* (cbrt (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT)))) (cbrt (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))))))
1.1s
(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
1.1s
(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
938.0ms
(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (* (* (cbrt (/ (* c0 (* d d)) (* (* w h) (* D D)))) (cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))) (cbrt (/ (* c0 (* d d)) (* (* w h) (* D D)))))) (* M M))))
Rules
40195×add-exp-log
27335×prod-exp
13239×pow-exp
12378×div-exp
7780×times-frac
5980×add-sqr-sqrt
5921×*-un-lft-identity
5833×pow-to-exp
5045×add-cube-cbrt
2867×add-cbrt-cube
2458×sqrt-prod
1748×1-exp
1746×rec-exp
1348×unpow-prod-down
1185×cbrt-unprod
1151×pow1
859×prod-diff
780×associate-*r*
702×cbrt-undiv
674×associate-*l*
618×cbrt-prod
552×associate-/l*
522×add-log-exp
470×div-inv
447×associate-*l/
444×expm1-log1p-u
443×log1p-expm1-u
435×associate-/r*
363×sqr-pow
356×pow-prod-down
351×associate-*r/
336×associate-/r/
314×frac-times
311×distribute-rgt-neg-in
295×distribute-lft-out--
290×pow-unpow
279×distribute-lft-neg-in
237×unswap-sqr
208×difference-of-squares
207×distribute-lft-out
184×distribute-rgt-in distribute-lft-in
171×sqrt-div
165×tan-quot
161×cos-sum
145×flip-- flip3--
144×*-commutative
120×exp-prod
116×fma-def
104×clear-num frac-2neg
82×fma-neg sqrt-pow1
73×flip-+ flip3-+
66×sub-neg
62×associate-/l/ pow1/3
58×pow1/2
53×pow-pow
50×cube-prod
47×unpow2
46×cbrt-div
41×rem-sqrt-square
34×div-sub
33×fma-udef
31×neg-mul-1
28×pow-flip
26×diff-log
22×associate--r+
14×sum-log
13×neg-sub0
12×pow-prod-up hypot-def
11×pow-sub +-commutative
10×pow-sqr
9×swap-sqr log-prod
8×rem-cube-cbrt inv-pow
7×cos-diff frac-add log-pow unpow3 cube-mult neg-log distribute-neg-frac
5×pow2 pow-plus
4×pow-div hypot-udef associate-+r+ distribute-frac-neg
3×exp-diff un-div-inv acos-asin exp-sum rem-cbrt-cube associate-+l- associate--l+
2×cube-div rem-exp-log pow-neg asin-acos associate--l- exp-neg sum-cubes unsub-neg associate--r- rem-log-exp associate-+r-
1×sqrt-pow2 log1p-udef sqrt-unprod unpow-1 log1p-expm1 mul0 exp-to-pow log-div

regimes9.9s (1.8%)

Accuracy

Total 41.8b remaining (20.8%)

Threshold costs 4.9b (2.4%)

12.3b4.8%Toniolo and Linder, Equation (13)
6.0b74.2%Toniolo and Linder, Equation (7)
5.1b24.1%Toniolo and Linder, Equation (10-)
4.7b13.8%Henrywood and Agarwal, Equation (12)
3.1b0%Henrywood and Agarwal, Equation (13)

localize2.5s (0.5%)

bsearch1.8s (0.3%)

end0.0ms (0.0%)