Details

simplify9.2m (35.5%)

prune8.7m (33.8%)

series3.5m (13.5%)

Calls

434 calls:

12.8s
(sqrt (* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (+ (* (pow (/ l Om) (/ 2.0 2)) (* (* (pow (/ l Om) (/ 2.0 2)) n) (- U U*))) (* (fma (- U*) 1 (* U* 1)) (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2)))))))) 2.0)))
12.0s
(sqrt (* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (+ (* (pow (/ l Om) (/ 2.0 2)) (* (* (pow (/ l Om) (/ 2.0 2)) n) (- U U*))) (* (fma (- U*) 1 (* U* 1)) (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2)))))))) 2.0)))
11.8s
(sqrt (* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (+ (* (pow (/ l Om) (/ 2.0 2)) (* (* (pow (/ l Om) (/ 2.0 2)) n) (- U U*))) (* (fma (- U*) 1 (* U* 1)) (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2)))))))) 2.0)))
9.2s
(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)))
8.7s
(sqrt (* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* n (pow (/ l Om) 2.0)) (- U U*))))) 2.0)))

sample2.8m (10.8%)

Algorithm
60×intervals
Results
39.7s250113×body80valid
29.0s160173×body80nan
28.7s25455×body1280valid
14.9s17755×body640valid
9.6s6513×body2560valid
6.4s8961×body320valid
4.4s8657×body160valid
4.3s2434×body5120valid
902.0ms644×body10240exit
363.0ms623×body1280nan
264.0ms670×body640nan
154.0ms8256×pre80true
93.0ms340×body320nan
34.0ms176×body160nan

rewrite1.1m (4.1%)

Algorithm
114×rewrite-expression-head
Calls

434 calls:

4.3s
(* (* (* (* (/ (/ (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))
3.0s
(* (* (* (/ (/ (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))
1.8s
(+ (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))
1.7s
(+ (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))
1.6s
(+ (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
460288×times-frac
182095×add-sqr-sqrt
181485×*-un-lft-identity
180917×add-cube-cbrt
151121×unpow-prod-down
134808×cbrt-prod
87213×sqrt-prod
15453×sqr-pow
15030×add-exp-log
13010×div-inv
8678×prod-exp
4552×div-exp
3724×associate-/r/
3076×pow-exp
2667×tan-quot add-cbrt-cube
1365×prod-diff
1324×pow-to-exp
1252×associate-/l*
1250×pow1
1069×associate-/r*
1062×cbrt-unprod
878×associate-*r/
821×associate-*r*
811×associate-*l*
766×cbrt-div
647×cbrt-undiv
533×associate-*l/
529×frac-times
499×add-log-exp
434×expm1-log1p-u log1p-expm1-u
423×pow-prod-down
325×distribute-rgt-in distribute-lft-in
315×1-exp
313×rec-exp
287×pow-unpow
259×difference-of-squares
245×unswap-sqr
221×sqrt-div
188×flip3-- flip--
166×distribute-lft-out--
148×distribute-lft-out
144×*-commutative
128×exp-sum
118×flip-+ flip3-+
108×sqrt-pow1
106×unpow-prod-up
98×frac-2neg clear-num
87×pow1/2
84×rem-sqrt-square
69×pow1/3
66×fma-def
60×fma-neg
53×swap-sqr
49×sub-neg
48×associate-/l/ frac-add
42×pow-pow
40×distribute-lft-neg-in distribute-rgt-neg-in
35×associate--l+
33×pow-sub
26×exp-prod
24×div-sub pow-prod-up
23×cos-sum
20×diff-log
18×neg-sub0 fma-udef pow-neg
14×pow-sqr
13×sum-log +-commutative
12×hypot-def
11×frac-sub
pow-flip
pow2 pow-plus rem-exp-log associate-+l-
inv-pow un-div-inv log-pow
log-prod neg-mul-1 acos-asin
hypot-udef
exp-diff sqrt-unprod asin-acos rem-square-sqrt
expm1-log1p expm1-udef sqrt-undiv distribute-rgt-neg-out sub-div associate--l- rem-log-exp cos-diff

regimes24.4s (1.6%)

Accuracy

Total 55.6b remaining (28.8%)

Threshold costs 3.6b (1.9%)

8.8b42.2%Henrywood and Agarwal, Equation (3)
8.7b43.1%Toniolo and Linder, Equation (10+)
8.5b-3.1%Henrywood and Agarwal, Equation (12)
7.3b27%Toniolo and Linder, Equation (13)
7.1b10.4%Henrywood and Agarwal, Equation (13)

localize7.6s (0.5%)

bsearch3.2s (0.2%)

end1.0ms (0.0%)