Details

Time bar (total: 6.8s)

sample60.0ms

Algorithm
intervals
Results
23.0ms297×body80valid
12.0ms32×body1280valid
7.0ms28×body640valid
2.0ms11×body320valid
1.0ms9×body160valid

simplify39.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0278
1688
22438
312668
450018

prune3.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.2b

localize13.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
5.2b
(* (* x (pow sin 2.0)) x)
10.3b
(* x (pow sin 2.0))
17.9b
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

rewrite33.0ms

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 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 → 115
Calls
4 calls:
10.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
6.0ms
(* (* x (pow sin 2.0)) x)
5.0ms
(* x (pow sin 2.0))
9.0ms
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

series829.0ms

Counts
4 → 12
Calls
4 calls:
298.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
142.0ms
(* (* x (pow sin 2.0)) x)
134.0ms
(* x (pow sin 2.0))
255.0ms
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

simplify57.0ms

Algorithm
egg-herbie
Counts
127 → 127
Iterations

Useful iterations: 1 (11.0ms)

IterNodesCost
0435927
12042771
25002771

prune269.0ms

Filtered
127 candidates to 65 candidates (51.2%)
Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 14.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
0.4b
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
5.2b
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
17.9b
(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

rewrite54.0ms

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×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 → 186
Calls
4 calls:
7.0ms
(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
14.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
9.0ms
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
12.0ms
(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

series836.0ms

Counts
4 → 12
Calls
4 calls:
139.0ms
(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
287.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
151.0ms
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
259.0ms
(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

simplify86.0ms

Algorithm
egg-herbie
Counts
198 → 198
Iterations

Useful iterations: 2 (67.0ms)

IterNodesCost
05862140
127921433
250021421

prune285.0ms

Filtered
198 candidates to 62 candidates (31.3%)
Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 1.5b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
0.4b
(/ (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)))))))
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))))

rewrite25.0ms

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×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 → 106
Calls
4 calls:
3.0ms
(* (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
5.0ms
(/ (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
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
7.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

series542.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(* (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
99.0ms
(/ (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)))))))
208.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
204.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

simplify45.0ms

Algorithm
egg-herbie
Counts
118 → 118
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
03161464
112291194
250021122

prune364.0ms

Filtered
118 candidates to 67 candidates (56.8%)
Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.0b

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))))))
0.9b
(/ (cos (* 2.0 x)) (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))))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
84×times-frac
63×add-exp-log
58×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
42×prod-exp
21×add-cbrt-cube
16×associate-/l*
14×pow-to-exp associate-*l* pow-exp
6×unpow-prod-down associate-/r* cbrt-unprod div-inv
4×pow1 cbrt-undiv div-exp add-log-exp
2×frac-2neg associate-*r* clear-num *-commutative sqr-pow
1×associate-/l/
Counts
4 → 157
Calls
4 calls:
6.0ms
(/ (/ (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))))))
4.0ms
(/ (cos (* 2.0 x)) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
10.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
7.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

series582.0ms

Counts
4 → 12
Calls
4 calls:
100.0ms
(/ (/ (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))))))
70.0ms
(/ (cos (* 2.0 x)) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
206.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
206.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

simplify67.0ms

Algorithm
egg-herbie
Counts
169 → 169
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
05103289
118302994
250012909

prune517.0ms

Filtered
169 candidates to 109 candidates (64.5%)
Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

regimes339.0ms

Accuracy

0% (2.6b remaining)

Error of 2.7b against oracle of 0.2b and baseline of 2.7b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02319
12319

end0.0ms

sample1.7s

Algorithm
intervals
Results
621.0ms8950×body80valid
319.0ms784×body1280valid
275.0ms962×body640valid
128.0ms608×body320valid
46.0ms325×body160valid