Details

simplify4.3m (33.1%)

sample3.3m (25.7%)

Algorithm
61×intervals
Results
44.6s253081×body80valid
38.8s28927×body1280valid
25.8s159995×body80nan
19.5s8837×body2560valid
18.8s20624×body640valid
11.8s3428×body5120valid
7.0s9932×body320valid
3.1s8933×body160valid
1.1s710×body10240exit
624.0ms8256×pre80true
343.0ms585×body1280nan
290.0ms630×body640nan
185.0ms348×body320nan
108.0ms184×body160nan

prune2.3m (17.8%)

series2.2m (17.0%)

Calls

431 calls:

3.1s
(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)))
2.8s
(sqrt (* (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (* (* 2.0 n) U)))
2.7s
(sqrt (* (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (- U U*) (pow (/ l Om) (/ 2.0 2)))))) (* (* 2.0 n) U)))
2.6s
(sqrt (* (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (* (* 2.0 n) U)))
1.7s
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite30.4s (3.9%)

Algorithm
117×rewrite-expression-head
Calls

431 calls:

2.0s
(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
2.0s
(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
979.0ms
(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))
977.0ms
(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ d (cbrt h)) (/ 1.0 2.0))) (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
729.0ms
(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ d (cbrt h)) (/ 1.0 2.0))) (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l)))))
Rules
35657×add-exp-log
23629×prod-exp
22480×times-frac
12399×pow-exp
11627×div-exp
11193×add-sqr-sqrt
10821×*-un-lft-identity
10236×add-cube-cbrt
5623×pow-to-exp
2814×add-cbrt-cube
2489×unpow-prod-down
1668×sqrt-prod
1456×rec-exp 1-exp
1184×div-inv
1131×pow1
1071×cbrt-unprod
1017×associate-/l*
1010×sqr-pow
836×associate-/r*
760×cbrt-undiv
753×associate-*r*
635×associate-*l/
627×associate-/r/
625×prod-diff
601×associate-*r/
540×associate-*l*
517×cbrt-prod
506×pow-unpow
486×add-log-exp
436×expm1-log1p-u
431×log1p-expm1-u
348×pow-prod-down
259×sqrt-div
253×difference-of-squares
232×distribute-lft-out--
206×unswap-sqr
184×cos-sum
171×frac-times
163×distribute-rgt-neg-in
159×distribute-lft-neg-in
148×flip-- flip3--
131×exp-prod
122×*-commutative
117×fma-def
106×sqrt-pow1
102×clear-num distribute-lft-out frac-2neg
101×distribute-rgt-in distribute-lft-in
66×pow1/2
63×pow-pow
61×fma-neg cube-prod
55×tan-quot
48×rem-sqrt-square pow1/3
47×unpow2
43×sub-neg
41×fma-udef
39×div-sub
38×associate-/l/
32×cbrt-div
31×swap-sqr
29×exp-diff
23×log-div
22×associate--r+
21×flip-+ flip3-+
19×diff-log
18×cube-div
16×pow-prod-up pow-sub
15×neg-mul-1
14×pow-flip
12×pow-sqr hypot-def
11×log-pow
10×rem-cube-cbrt inv-pow unpow3 cube-mult
8×cos-diff hypot-udef +-commutative sum-log
7×log-prod
5×rem-exp-log un-div-inv log1p-udef pow2 log1p-expm1 expm1-log1p neg-sub0 expm1-udef
4×pow-plus acos-asin neg-log rem-cbrt-cube
3×sqrt-undiv asin-acos associate-+r+ pow-neg
2×associate--l- sqrt-unprod frac-add associate--r- associate--l+ rem-log-exp associate-+r-
1×sqrt-pow2 rem-square-sqrt exp-sum mul0

regimes14.6s (1.9%)

Accuracy

Total 43.6b remaining (20.8%)

Threshold costs 5.3b (2.5%)

10.1b4.9%Toniolo and Linder, Equation (13)
7.2b46.3%Henrywood and Agarwal, Equation (3)
5.4b0%Henrywood and Agarwal, Equation (12)
5.3b77.5%Toniolo and Linder, Equation (7)
3.6b51.5%Toniolo and Linder, Equation (10-)

localize4.4s (0.6%)

bsearch1.1s (0.1%)

end1.0ms (0.0%)