Details

simplify23.0m (58.2%)

series5.9m (15.0%)

Calls

434 calls:

23.6s
(sqrt (* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) (/ 2.0 2)) (* (pow (/ (cbrt l) (cbrt Om)) (/ 2.0 2)) (- U U*))))))) 2.0)))
23.2s
(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)))
23.2s
(sqrt (* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* n (pow (/ l Om) 2.0)) (- U U*))))) 2.0)))
22.9s
(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)))
12.2s
(- (pow (* (* 1.0 1.0) 1.0) 3) (pow (* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) 3))

prune5.2m (13.1%)

sample3.1m (7.7%)

Algorithm
60×intervals
Results
39.6s246896×body80valid
36.6s28698×body1280valid
25.4s147596×body80nan
18.9s19970×body640valid
18.3s7093×body2560valid
7.7s1148×body5120valid
6.0s9792×body320valid
3.6s8862×body160valid
358.0ms621×body1280nan
280.0ms152×body10240exit
252.0ms650×body640nan
217.0ms8256×pre80true
196.0ms340×body320nan
83.0ms189×body160nan

rewrite1.1m (2.7%)

Algorithm
114×rewrite-expression-head
Calls

434 calls:

10.9s
(* (* (* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) l)) (* (* (cbrt (/ (pow (cbrt t) 3.0) l)) (cbrt (/ (pow (cbrt t) 3.0) l))) (* (cbrt (/ (pow (cbrt t) 3.0) l)) (sin k)))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
3.1s
(+ (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))
2.7s
(* (sqrt (* (- (* 1.0 (* 1.0 1.0)) (* (* (* (* v v) 3.0) (* (* v v) 3.0)) (* (* v v) 3.0))) 2.0)) t)
2.7s
(/ (/ (- 1.0 (* (* v 5.0) v)) PI) (* (sqrt (* (- (* 1.0 (* 1.0 1.0)) (* (* (* (* v v) 3.0) (* (* v v) 3.0)) (* (* v v) 3.0))) 2.0)) t))
2.2s
(* (* (* (* (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))
Rules
45914×add-exp-log
31057×prod-exp
17781×pow-exp
15860×times-frac
15452×div-exp
8898×add-sqr-sqrt
8581×*-un-lft-identity
7972×add-cube-cbrt
7085×pow-to-exp
3851×unpow-prod-down
3733×sqrt-prod
2724×1-exp rec-exp
2470×add-cbrt-cube
1432×pow1
1107×associate-*l*
1019×cbrt-prod
999×cbrt-unprod
998×div-inv
783×sqr-pow
780×associate-*r/
686×associate-*r*
610×associate-/r/
569×prod-diff
545×associate-/r*
528×cbrt-undiv associate-/l*
509×tan-quot
489×add-log-exp
472×pow-prod-down
443×pow-unpow
434×expm1-log1p-u log1p-expm1-u insert-posit16
422×associate-*l/
365×frac-times
271×unswap-sqr
223×distribute-lft-out
165×cbrt-div
148×sqrt-div
145×difference-of-squares
132×distribute-lft-out--
130×*-commutative
118×distribute-rgt-in distribute-lft-in
117×flip-- flip3--
116×sqrt-pow1
103×flip-+ flip3-+
100×frac-2neg clear-num
83×pow1/2
82×fma-neg
78×pow-prod-up
67×exp-prod
66×swap-sqr pow1/3
63×rem-sqrt-square
54×pow-pow
52×distribute-rgt-neg-in sub-neg distribute-lft-neg-in
50×log-pow
49×pow-sub
48×associate-/l/ pow-sqr
44×div-sub
35×associate--l+
33×pow-plus
26×fma-def distribute-rgt-out
24×neg-sub0 pow-neg cos-sum fma-udef
22×log-prod pow2
21×diff-log
19×frac-add
18×cube-prod unpow3 cube-mult
12×hypot-def
11×pow-flip
10×distribute-rgt1-in distribute-lft1-in
8×associate-+l- cube-div count-2
7×sum-log unpow2
6×+-commutative inv-pow
5×exp-sum
4×neg-mul-1 associate--r+ rem-log-exp
3×rem-cube-cbrt remove-posit16 exp-diff frac-sub sqrt-unprod associate--l- hypot-udef rem-exp-log acos-asin
2×distribute-rgt-neg-out pow3 sub-div un-div-inv asin-acos rem-square-sqrt cos-diff log-div
1×log1p-expm1 difference-cubes rem-cbrt-cube unsub-neg log1p-udef

regimes60.0s (2.5%)

Accuracy

Total 47.3b remaining (30.6%)

Threshold costs 4.0b (2.6%)

9.3b29.2%Toniolo and Linder, Equation (10+)
7.4b30.3%Toniolo and Linder, Equation (13)
6.0b13.8%Henrywood and Agarwal, Equation (12)
5.7b0%Toniolo and Linder, Equation (10-)
5.3b77.2%Toniolo and Linder, Equation (7)

localize15.5s (0.7%)

bsearch2.6s (0.1%)

end1.0ms (0.0%)