Details

simplify24.6m (51.1%)

series11.7m (24.4%)

Calls

365 calls:

6.7m
(/ (/ (- (* (* (* 1.0 (* 1.0 1.0)) (* (* 1.0 1.0) (* 1.0 1.0))) (* 1.0 1.0)) (* (* (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0)) (sqrt (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0)))) (* (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0)) (* (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0)) (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0)))))) (fma (* 1.0 (* 1.0 1.0)) (* 1.0 (* 1.0 1.0)) (* (* (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0)) (sqrt (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0)))) (fma 1.0 (* 1.0 1.0) (* (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0)) (sqrt (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0)))))))) (fma 1.0 1.0 (fma 1.0 (sqrt (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0))) (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0)))))
26.8s
(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))))
23.3s
(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)))
23.1s
(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)))
22.5s
(sqrt (* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* n (pow (/ l Om) 2.0)) (- U U*))))) 2.0)))

prune5.9m (12.3%)

sample2.9m (5.9%)

Algorithm
54×intervals
Results
42.2s210528×body80valid
36.3s21729×body1280valid
21.6s103318×body80nan
19.8s17458×body640valid
10.0s3247×body2560valid
7.7s1075×body5120valid
6.5s8170×body320valid
4.1s8414×body160valid
495.0ms601×body1280nan
362.0ms627×body640nan
255.0ms343×body320nan
238.0ms8256×pre80true
199.0ms140×body10240exit
43.0ms171×body160nan

rewrite1.7m (3.5%)

Algorithm
96×rewrite-expression-head
Calls

365 calls:

7.3s
(* (* (* (* (/ (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))
6.7s
(* (pow (/ 1 (pow t 1.0)) 1.0) (* (* (* (* (/ l (sin k)) (/ l (sin k))) (cos k)) (pow (/ 1 (pow k (/ 2.0 2))) 1.0)) (pow (/ 1 (pow k (/ 2.0 2))) 1.0)))
6.5s
(* (* (* (/ (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))
5.7s
(/ 2.0 (* (* (* (/ (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)))
4.7s
(+ (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))
Rules
95136×add-exp-log
69004×prod-exp
44056×pow-exp
32440×div-exp
14409×times-frac
14361×pow-to-exp
8941×1-exp
8937×rec-exp
8204×add-sqr-sqrt
7725×*-un-lft-identity
7165×add-cube-cbrt
3777×unpow-prod-down
3218×sqrt-prod
2729×add-cbrt-cube
1246×cbrt-unprod
1240×pow1
1182×associate-*l*
981×div-inv
952×frac-times
877×associate-*r/
801×associate-*r*
706×sqr-pow
698×prod-diff
631×associate-*l/
606×cbrt-undiv
567×associate-/r/
533×tan-quot
525×flip-+ flip3-+
420×associate-/r*
415×pow-prod-down add-log-exp
395×associate-/l*
365×expm1-log1p-u log1p-expm1-u insert-posit16
290×unswap-sqr
285×sqrt-div
277×cbrt-prod
254×distribute-rgt-in distribute-lft-in
224×distribute-lft-out
192×sqrt-pow1
180×pow-unpow
134×difference-of-squares
124×*-commutative
115×pow1/2
108×distribute-lft-out--
105×swap-sqr
91×rem-sqrt-square
82×frac-2neg clear-num
79×flip3-- flip--
68×pow-prod-up
66×exp-prod
58×fma-neg
52×sub-neg
44×associate-/l/
42×pow1/3
32×pow-sqr
29×fma-def
27×associate-+r+ pow-pow
26×distribute-rgt-neg-in distribute-lft-neg-in
25×associate--l+ cos-sum
18×frac-add
17×div-sub diff-log
16×pow-plus
15×associate-+l-
14×pow2
13×fma-udef
12×neg-sub0 pow-sub hypot-def pow-neg
11×pow3
pow-flip sum-log associate--r+ inv-pow
+-commutative
cbrt-div difference-cubes distribute-rgt-out--
frac-sub
exp-diff cube-unmult hypot-udef unpow2 asin-acos rem-exp-log log-pow count-2 distribute-rgt-out
associate--l- sqrt-unprod neg-mul-1 rem-square-sqrt unpow1/3
cos-mult associate-+r- sub-div un-div-inv sqr-cos acos-asin cos-diff

regimes53.1s (1.8%)

Accuracy

Total 45.6b remaining (32.8%)

Threshold costs 3.4b (2.4%)

9.5b-11.9%Toniolo and Linder, Equation (10+)
6.2b38.5%Toniolo and Linder, Equation (10-)
5.6b54.9%Henrywood and Agarwal, Equation (3)
5.4b77.1%Toniolo and Linder, Equation (7)
5.0b21.1%Henrywood and Agarwal, Equation (12)

localize22.1s (0.8%)

bsearch5.5s (0.2%)

end0.0ms (0.0%)