Details

simplify6.0m (38.4%)

sample3.2m (20.4%)

Algorithm
59×intervals
Results
42.2s243618×body80valid
39.4s29317×body1280valid
28.6s157721×body80nan
19.7s8872×body2560valid
19.2s20690×body640valid
11.1s3487×body5120valid
6.5s9713×body320valid
3.8s9130×body160valid
973.0ms829×body10240exit
516.0ms617×body1280nan
455.0ms8256×pre80true
427.0ms646×body640nan
104.0ms346×body320nan
39.0ms197×body160nan

prune2.6m (16.5%)

series2.4m (15.3%)

Calls

423 calls:

6.6s
(sqrt (* 2.0 (* (* n U) (- t (fma (/ l Om) (* 2.0 l) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*))))))))
6.0s
(sqrt (* 2.0 (* (* n U) (- t (fma (/ l Om) (* 2.0 l) (* n (* (pow (/ l Om) (/ 2.0 2)) (* (pow (/ l Om) (/ 2.0 2)) (- U U*)))))))))
5.9s
(sqrt (* 2.0 (* (* n U) (- t (fma (/ l Om) (* 2.0 l) (* n (* (pow (/ l Om) 2.0) (- U U*))))))))
5.7s
(sqrt (* (* n U) (- t (fma (/ l Om) (* 2.0 l) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*)))))))
2.0s
(/ (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0)) F)

rewrite52.8s (5.6%)

Algorithm
112×rewrite-expression-head
Calls

423 calls:

7.7s
(* (cos (- (/ (* K (+ m n)) 2.0) M)) (exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))))
2.7s
(+ (sqrt (- (* (* (* (/ d D) (/ d D)) (/ c0 (* w h))) (* (* (/ d D) (/ d D)) (/ c0 (* w h)))) (* M M))) (* (* (/ d D) (/ d D)) (/ c0 (* w h))))
2.6s
(+ (sqrt (- (* (* (* (/ d D) (/ d D)) (/ c0 (* w h))) (* (* (/ d D) (/ d D)) (/ c0 (* w h)))) (* M M))) (* (* (/ d D) (/ d D)) (/ c0 (* w h))))
2.6s
(+ (sqrt (- (* (* (* (/ d D) (/ d D)) (/ c0 (* w h))) (* (* (/ d D) (/ d D)) (/ c0 (* w h)))) (* M M))) (* (* (/ d D) (/ d D)) (/ c0 (* w h))))
2.5s
(+ (sqrt (- (* (* (* (/ d D) (/ d D)) (/ c0 (* w h))) (* (* (/ d D) (/ d D)) (/ c0 (* w h)))) (* M M))) (* (* (/ d D) (/ d D)) (/ c0 (* w h))))
Rules
46308×add-exp-log
32409×prod-exp
16883×pow-exp
14710×times-frac
14289×div-exp
9447×add-sqr-sqrt
8768×*-un-lft-identity
7915×add-cube-cbrt
7301×sqrt-prod
5990×pow-to-exp
3176×1-exp rec-exp
2867×unpow-prod-down
2452×add-cbrt-cube
1560×sqrt-div
1336×frac-times
1327×pow1
1053×associate-*r/
1033×associate-*l*
984×cbrt-unprod
920×prod-diff
885×associate-*r*
884×sqr-pow
732×flip3-- flip--
702×associate-*l/
515×associate-/l*
512×add-log-exp
481×div-inv
474×cbrt-undiv
447×pow-prod-down
443×difference-of-squares
432×associate-/r*
423×expm1-log1p-u log1p-expm1-u
370×exp-sum
347×distribute-rgt-in distribute-lft-in
342×pow-unpow
327×distribute-lft-out--
242×distribute-rgt-neg-in
236×distribute-lft-neg-in
228×cbrt-div
220×unswap-sqr
180×exp-prod
178×associate-/r/
165×cbrt-prod
163×sqrt-pow1
139×distribute-lft-out
138×*-commutative
115×pow1/2
84×frac-2neg clear-num
77×rem-sqrt-square
72×tan-quot
67×sub-neg
65×fma-neg
64×flip-+ flip3-+
58×fma-def
56×swap-sqr frac-add
46×div-sub
44×pow-prod-up
36×associate-/l/ pow-sub
35×pow1/3 pow-pow
32×pow-sqr
31×fma-udef
27×diff-log
26×cos-sum
23×neg-mul-1
18×hypot-def
17×associate--r+ rem-exp-log
16×sum-log log-prod +-commutative
15×log-pow
11×exp-diff
10×pow-plus
9×sqrt-unprod
8×pow2
7×neg-sub0 associate-+r-
6×pow-neg neg-log
5×pow-flip inv-pow rem-square-sqrt
4×hypot-udef associate--r- rem-log-exp
3×acos-asin
2×sin-sum frac-sub associate--l+
1×mul0 cube-unmult pow3 sub-div associate--l- difference-cubes un-div-inv asin-acos cos-diff log-div

regimes24.9s (2.6%)

Accuracy

Total 45.1b remaining (24.6%)

Threshold costs 4.4b (2.4%)

10.1b-3.4%Toniolo and Linder, Equation (10+)
7.0b0%Henrywood and Agarwal, Equation (12)
5.9b19.5%Henrywood and Agarwal, Equation (13)
5.8b39.4%Toniolo and Linder, Equation (13)
5.4b77.6%Toniolo and Linder, Equation (7)

localize7.4s (0.8%)

bsearch3.0s (0.3%)

end1.0ms (0.0%)