Details

Time bar (total: 7.2s)

sample54.0ms

Algorithm
intervals
Results
17.0ms315×body80valid
8.0ms24×body1280valid
5.0ms23×body640valid
4.0ms12×body160valid
3.0ms20×body320valid

simplify39.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0278
1688
22438
312668
450018

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 22.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
2.8b
(* (* x (pow sin 2.0)) x)
5.3b
(* x (pow sin 2.0))
16.5b
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

rewrite152.0ms

Algorithm
rewrite-expression-head
Rules
122×add-exp-log
82×prod-exp
34×add-cbrt-cube
18×pow-to-exp pow-exp
17×add-sqr-sqrt
16×div-exp cbrt-unprod
12×add-cube-cbrt *-un-lft-identity
11×associate-*r* associate-*l*
7×unpow-prod-down
6×pow1
4×cbrt-undiv expm1-log1p-u log1p-expm1-u add-log-exp
3×times-frac *-commutative associate-/l* unswap-sqr sqr-pow
1×frac-2neg pow-prod-down clear-num associate-/r* div-inv
Counts
4 → 123
Calls
4 calls:
57.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
21.0ms
(* (* x (pow sin 2.0)) x)
11.0ms
(* x (pow sin 2.0))
58.0ms
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

series863.0ms

Counts
4 → 12
Calls
4 calls:
294.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
141.0ms
(* (* x (pow sin 2.0)) x)
171.0ms
(* x (pow sin 2.0))
258.0ms
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

simplify56.0ms

Algorithm
egg-herbie
Counts
135 → 135
Iterations

Useful iterations: 1 (11.0ms)

IterNodesCost
0448971
12063815
25002815

prune279.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 14.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
0.2b
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
2.8b
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
16.5b
(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

rewrite487.0ms

Algorithm
rewrite-expression-head
Rules
416×add-exp-log
343×prod-exp
84×pow-to-exp pow-exp
52×add-cbrt-cube
43×div-exp
29×cbrt-unprod
11×add-sqr-sqrt add-cube-cbrt *-un-lft-identity associate-*r*
9×associate-*l*
6×pow1 unpow-prod-down
5×cbrt-undiv
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×times-frac *-commutative associate-/l*
2×sqr-pow
1×frac-2neg pow-prod-down clear-num associate-/r* div-inv
Counts
4 → 194
Calls
4 calls:
27.0ms
(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
184.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
71.0ms
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
191.0ms
(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

series870.0ms

Counts
4 → 12
Calls
4 calls:
143.0ms
(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
309.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
148.0ms
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
270.0ms
(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

simplify89.0ms

Algorithm
egg-herbie
Counts
206 → 206
Iterations

Useful iterations: 2 (71.0ms)

IterNodesCost
06032216
128211509
250021497

prune448.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 2.3b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (cos (* 2.0 x)) (* (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))))))
0.3b
(* (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
4.6b
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
4.6b
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

rewrite82.0ms

Algorithm
rewrite-expression-head
Rules
63×add-exp-log
44×prod-exp
21×add-cbrt-cube
17×associate-*l*
16×add-sqr-sqrt
14×pow-to-exp add-cube-cbrt *-un-lft-identity pow-exp
11×pow1
8×cbrt-unprod
6×unpow-prod-down
5×associate-*r*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×times-frac swap-sqr *-commutative associate-/l*
2×cbrt-undiv div-exp sqr-pow
1×pow2 frac-2neg pow-plus pow-prod-down clear-num associate-/r* pow-sqr pow-prod-up div-inv unswap-sqr
Counts
4 → 114
Calls
4 calls:
17.0ms
(/ (cos (* 2.0 x)) (* (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))))))
7.0ms
(* (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
26.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
28.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

series585.0ms

Counts
4 → 12
Calls
4 calls:
115.0ms
(/ (cos (* 2.0 x)) (* (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))))))
34.0ms
(* (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
219.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
217.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

simplify49.0ms

Algorithm
egg-herbie
Counts
126 → 126
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
03251562
112441292
250011217

prune373.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize17.0ms

Local error

Found 3 expressions with local error:

0.2b
(/ (cos (* 2.0 x)) (pow (fabs (* (pow (* (pow cos 1.0) (pow sin 1.0)) 1.0) x)) 2))
0.3b
(pow (fabs (* (pow (* (pow cos 1.0) (pow sin 1.0)) 1.0) x)) 2)
5.1b
(* (pow (* (pow cos 1.0) (pow sin 1.0)) 1.0) x)

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
35×add-exp-log
27×add-sqr-sqrt
24×add-cube-cbrt *-un-lft-identity times-frac
21×prod-exp
18×pow-exp
16×unpow-prod-down
9×pow-to-exp
8×associate-/r*
7×add-cbrt-cube sqr-pow
5×associate-*l* unpow2
4×pow1
3×expm1-log1p-u pow-unpow div-exp associate-*r* log1p-expm1-u associate-/l* add-log-exp
2×unswap-sqr
1×cbrt-undiv pow-pow frac-2neg clear-num *-commutative cbrt-unprod div-inv
Counts
3 → 104
Calls
3 calls:
15.0ms
(/ (cos (* 2.0 x)) (pow (fabs (* (pow (* (pow cos 1.0) (pow sin 1.0)) 1.0) x)) 2))
3.0ms
(pow (fabs (* (pow (* (pow cos 1.0) (pow sin 1.0)) 1.0) x)) 2)
22.0ms
(* (pow (* (pow cos 1.0) (pow sin 1.0)) 1.0) x)

series471.0ms

Counts
3 → 9
Calls
3 calls:
106.0ms
(/ (cos (* 2.0 x)) (pow (fabs (* (pow (* (pow cos 1.0) (pow sin 1.0)) 1.0) x)) 2))
37.0ms
(pow (fabs (* (pow (* (pow cos 1.0) (pow sin 1.0)) 1.0) x)) 2)
328.0ms
(* (pow (* (pow cos 1.0) (pow sin 1.0)) 1.0) x)

simplify44.0ms

Algorithm
egg-herbie
Counts
113 → 113
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
03421364
111601248
250021239

prune336.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.0b

regimes341.0ms

Accuracy

0% (2.5b remaining)

Error of 2.7b against oracle of 0.1b and baseline of 2.7b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0157
1157

end0.0ms

sample1.5s

Algorithm
intervals
Results
505.0ms9029×body80valid
274.0ms826×body1280valid
231.0ms975×body640valid
91.0ms565×body320valid
34.0ms301×body160valid