Details

prune1.8m (30.8%)

series1.8m (30.5%)

Calls

425 calls:

5.0s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))
4.9s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
4.8s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
4.7s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*))))))
1.3s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*)))))

sample1.5m (25.4%)

Algorithm
61×intervals
Results
17.9s31089×body1280valid
16.5s248383×body80valid
11.1s167103×body80nan
9.0s8860×body2560valid
8.0s20675×body640valid
5.4s3303×body5120valid
2.8s10107×body320valid
1.5s9281×body160valid
880.0ms2654×body1280nan
599.0ms2382×body640nan
446.0ms624×body10240exit
218.0ms1191×body320nan
108.0ms8256×pre80true
75.0ms674×body160nan

rewrite17.4s (5.0%)

Algorithm
117×rewrite-expression-head
Calls

425 calls:

1.6s
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (/ (cos k) (/ (/ (pow (cbrt (sin k)) 4) l) l)) (pow (cbrt (sin k)) 2)))
686.0ms
(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
678.0ms
(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
532.0ms
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ l (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
423.0ms
(* (* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
Rules
41646×add-exp-log
33123×times-frac
27757×prod-exp
16342×pow-exp
15915×add-sqr-sqrt
15180×*-un-lft-identity
14992×div-exp
14513×add-cube-cbrt
8816×unpow-prod-down
7412×pow-to-exp
4787×cbrt-prod
4389×associate-*r*
2702×add-cbrt-cube
2439×1-exp
2437×rec-exp
1791×sqrt-prod
1593×sqr-pow
1136×pow1
1080×cbrt-unprod
744×associate-*l*
691×unpow2
682×associate-/l*
618×div-inv
592×prod-diff
531×cbrt-undiv
489×add-log-exp
426×expm1-log1p-u
425×log1p-expm1-u
423×associate-/r*
394×associate-*r/
376×unswap-sqr
370×pow-prod-down
254×pow-unpow
236×distribute-rgt-neg-in
232×sqrt-div
225×distribute-rgt-in associate-*l/ distribute-lft-in
210×frac-times
206×distribute-lft-out--
202×distribute-lft-neg-in
190×flip3-- flip--
175×distribute-lft-out
163×difference-of-squares
143×exp-prod
141×*-commutative
125×associate-/r/
98×flip-+ flip3-+
97×cube-prod
91×clear-num frac-2neg
75×fma-def
72×sqrt-pow1
70×tan-quot cbrt-div
67×sub-neg pow-pow
56×log-prod
55×pow1/2 fma-neg
53×exp-sum
47×cos-sum
42×rem-sqrt-square associate--l+
41×associate-/l/
39×cube-div
37×pow1/3
36×fma-udef
32×frac-sub
29×pow-flip
27×div-sub
22×log-pow neg-mul-1 associate--r+
18×exp-diff associate-+r+ sum-log
16×+-commutative neg-sub0
15×hypot-def diff-log
13×inv-pow
11×hypot-udef
10×pow-prod-up
9×unpow3 cube-mult
8×frac-add distribute-frac-neg
7×un-div-inv exp-neg swap-sqr
6×rem-cube-cbrt pow-sqr
5×rem-exp-log pow-sub
4×sqrt-pow2 unsub-neg associate-+r- acos-asin neg-log asin-acos distribute-neg-frac
3×associate-+l+ rem-cbrt-cube
2×pow-plus pow-neg associate--l- cos-diff pow2 associate--r- log-div
1×sqrt-undiv log1p-udef sin-sum log1p-expm1 expm1-log1p expm1-udef mul0 rem-log-exp

simplify14.1s (4.1%)

Algorithm
177×egg-herbie

regimes9.8s (2.8%)

Accuracy

Total 48.6b remaining (26.4%)

Threshold costs 3.4b (1.8%)

8.9b11%Toniolo and Linder, Equation (13)
8.2b38%Henrywood and Agarwal, Equation (3)
6.5b3.8%Henrywood and Agarwal, Equation (12)
5.9b75.6%Toniolo and Linder, Equation (7)
5.1b18%Toniolo and Linder, Equation (10-)

bsearch2.4s (0.7%)

localize2.3s (0.7%)

end1.0ms (0.0%)