Details

prune1.8m (31.9%)

series1.6m (28.6%)

Calls

438 calls:

4.9s
(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*)))))
4.8s
(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*)))))
4.8s
(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*))))))
1.5s
(* (* (* 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*))))

sample1.4m (25.4%)

Algorithm
61×intervals
Results
17.6s31089×body1280valid
16.1s248383×body80valid
10.9s167103×body80nan
8.9s8860×body2560valid
7.8s20675×body640valid
5.2s3303×body5120valid
2.6s10107×body320valid
1.5s9281×body160valid
883.0ms2654×body1280nan
605.0ms2382×body640nan
445.0ms624×body10240exit
210.0ms1191×body320nan
113.0ms8256×pre80true
74.0ms674×body160nan

rewrite19.6s (5.7%)

Algorithm
116×rewrite-expression-head
Calls

438 calls:

1.4s
(* (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)))
844.0ms
(* (* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
561.0ms
(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
557.0ms
(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
465.0ms
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
Rules
40764×add-exp-log
34524×times-frac
27287×prod-exp
16524×add-sqr-sqrt
16133×pow-exp
15824×*-un-lft-identity
15157×add-cube-cbrt
14657×div-exp
8673×unpow-prod-down
7373×pow-to-exp
4929×cbrt-prod
4502×associate-*r*
3463×sqrt-prod
2632×add-cbrt-cube
2434×1-exp rec-exp
1594×associate-*l*
1582×sqr-pow
1213×pow1
1047×cbrt-unprod
709×unpow2
686×associate-/l*
595×div-inv
543×add-log-exp
495×cbrt-undiv
434×associate-*r/
424×unswap-sqr
388×associate-/r*
347×pow-prod-down
284×pow-unpow sqrt-div
249×associate-/r/
240×distribute-lft-out
232×flip-+ flip3-+
228×associate-*l/
209×exp-prod
200×cbrt-div
197×frac-times
166×flip3-- flip--
165×distribute-rgt-neg-in
164×distribute-lft-out--
151×*-commutative
122×distribute-lft-neg-in sqrt-pow1
91×difference-of-squares
88×clear-num frac-2neg
81×pow1/2
78×distribute-rgt-in distribute-lft-in
73×pow-pow
67×sub-neg
63×pow1/3
58×tan-quot
55×rem-sqrt-square
52×pow-prod-up
50×cube-prod
49×frac-sub
44×associate-/l/
37×cube-div
34×div-sub
32×pow-sqr sum-log
28×swap-sqr
26×+-commutative
23×neg-sub0
22×diff-log associate--l+
21×pow-plus
20×exp-diff
16×frac-add pow2
14×neg-mul-1
12×associate-+r+ pow-sub
10×pow-neg un-div-inv unpow3 cube-mult
sub-div
cos-sum unsub-neg distribute-frac-neg associate-+r-
inv-pow exp-neg pow-flip rem-cbrt-cube
rem-cube-cbrt rem-exp-log neg-log acos-asin associate--r+
cos-diff distribute-rgt-out-- sqrt-undiv asin-acos
associate--l- sqrt-unprod rem-square-sqrt associate--r- distribute-neg-frac
associate-+l+ mul0

simplify14.4s (4.2%)

Algorithm
176×egg-herbie

regimes9.8s (2.9%)

Accuracy

Total 50.0b remaining (24%)

Threshold costs 6.7b (3.2%)

8.9b11%Toniolo and Linder, Equation (13)
8.2b38%Henrywood and Agarwal, Equation (3)
6.5b3.8%Henrywood and Agarwal, Equation (12)
6.0b75.5%Toniolo and Linder, Equation (7)
5.1b17.6%Toniolo and Linder, Equation (10-)

localize2.2s (0.7%)

bsearch2.1s (0.6%)

end1.0ms (0.0%)