Details

simplify7.2m (38.0%)

prune3.6m (19.0%)

series3.5m (18.6%)

Calls

447 calls:

10.5s
(- (/ (* 1.0 (* 1.0 1.0)) (fma (sqrt (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x)))) 1.0 (fma 1.0 1.0 (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x)))))) (/ (* (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x))) (sqrt (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x))))) (fma (sqrt (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x)))) 1.0 (fma 1.0 1.0 (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x)))))))
10.5s
(sqrt (* (* (cbrt U) (cbrt U)) (* (cbrt U) (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))) 2.0))))
9.5s
(- (/ (* 1.0 (* 1.0 1.0)) (fma (sqrt (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x)))) 1.0 (fma 1.0 1.0 (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x)))))) (/ (exp (+ (log (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x)))) (log (sqrt (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x))))))) (fma (sqrt (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x)))) 1.0 (fma 1.0 1.0 (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x)))))))
9.3s
(sqrt (* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))) 2.0)))
9.3s
(sqrt (* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))) 2.0)))

sample3.2m (17.1%)

Algorithm
61×intervals
Results
46.8s252728×body80valid
37.7s29502×body1280valid
27.7s159842×body80nan
18.9s19777×body640valid
18.6s8847×body2560valid
11.3s3467×body5120valid
7.1s10183×body320valid
4.0s9070×body160valid
865.0ms661×body10240exit
488.0ms604×body1280nan
266.0ms637×body640nan
237.0ms8256×pre80true
117.0ms212×body160nan
82.0ms329×body320nan

rewrite44.8s (3.9%)

Algorithm
117×rewrite-expression-head
Calls

447 calls:

7.0s
(+ (sqrt (- (* (* (/ (* c0 (* (cbrt (/ d D)) (cbrt (/ d D)))) w) (/ (/ d D) (/ h (cbrt (/ d D))))) (* (/ c0 w) (/ (/ d D) (/ h (/ d D))))) (* M M))) (* (/ c0 w) (/ (/ d D) (/ h (/ d D)))))
4.1s
(* (/ c0 w) (/ (+ (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) 2.0))
3.2s
(+ (sqrt (- (* (* (/ c0 w) (/ (/ d D) (/ h (/ d D)))) (* (/ c0 w) (/ (/ d D) (/ h (/ d D))))) (* M M))) (* (/ c0 w) (/ (/ d D) (/ h (/ d D)))))
2.5s
(* (exp (/ (+ (+ (- EDonor Ec) Vef) mu) KbT)) (exp (/ (+ (+ (- EDonor Ec) Vef) mu) KbT)))
1.8s
(+ (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))
Rules
44412×add-exp-log
27623×prod-exp
25916×times-frac
18694×pow-exp
18090×div-exp
13132×*-un-lft-identity
13118×add-sqr-sqrt
11878×add-cube-cbrt
7147×pow-to-exp
4774×sqrt-prod
4566×unpow-prod-down
3387×1-exp rec-exp
2749×associate-*r*
2672×add-cbrt-cube
1573×div-inv
1413×associate-*l*
1189×pow1
1091×cbrt-prod
901×cbrt-unprod
861×sqr-pow
723×associate-/r/
720×prod-diff
717×cbrt-undiv
675×associate-*r/
674×associate-/r*
579×associate-/l*
572×distribute-lft-out
495×add-log-exp
448×log1p-expm1-u
447×expm1-log1p-u
434×tan-quot
402×pow-prod-down
392×unswap-sqr
367×exp-prod
326×pow-unpow
209×sqrt-div
177×flip3-- flip--
172×associate-*l/
167×distribute-lft-out--
150×frac-times
149×sqrt-pow1
118×*-commutative
111×frac-2neg clear-num
101×distribute-rgt-in pow-prod-up distribute-lft-in
100×pow1/2
82×pow1/3
81×pow-sqr
80×rem-sqrt-square
76×fma-def
74×difference-of-squares
73×fma-neg
69×associate-/l/
64×flip-+ flip3-+
63×swap-sqr
42×sub-neg pow-sub
39×distribute-lft-neg-in pow-pow distribute-rgt-neg-in div-sub
38×frac-add
30×neg-sub0 pow-neg
25×cos-sum
21×exp-sum
20×pow-plus
19×cbrt-div fma-udef
18×log-prod hypot-def log-pow
17×associate-+l-
13×diff-log
12×pow2
10×sum-log pow3
+-commutative unpow2
distribute-rgt-out--
expm1-log1p expm1-udef
pow-flip frac-sub cube-unmult difference-cubes inv-pow rem-log-exp
exp-diff log-div
neg-mul-1 sub-div exp-to-pow hypot-udef acos-asin
associate--l+ sqrt-unprod un-div-inv asin-acos rem-square-sqrt sin-mult
associate-+l+ quot-tan log1p-expm1 sqr-sin rem-cbrt-cube cos-diff log1p-udef

regimes28.1s (2.5%)

Accuracy

Total 48.9b remaining (26%)

Threshold costs 4.4b (2.3%)

8.0b16%Henrywood and Agarwal, Equation (13)
7.5b12.8%Henrywood and Agarwal, Equation (12)
7.3b28.8%Toniolo and Linder, Equation (13)
6.3b51.4%Henrywood and Agarwal, Equation (3)
5.9b75.3%Toniolo and Linder, Equation (7)

localize8.6s (0.8%)

bsearch2.0s (0.2%)

end1.0ms (0.0%)