Details

Time bar (total: 7.6s)

sample54.0ms

Algorithm
intervals
Results
21.0ms294×body80valid
9.0ms25×body1280valid
6.0ms27×body640valid
2.0ms13×body320valid
1.0ms9×body160valid

simplify43.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0278
1688
22438
312668
450018

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.6b

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
4.4b
(* (* x (pow sin 2.0)) x)
7.1b
(* x (pow sin 2.0))
19.6b
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

rewrite74.0ms

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:
29.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
9.0ms
(* (* x (pow sin 2.0)) x)
5.0ms
(* x (pow sin 2.0))
26.0ms
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

series858.0ms

Counts
4 → 12
Calls
4 calls:
296.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
157.0ms
(* (* x (pow sin 2.0)) x)
135.0ms
(* x (pow sin 2.0))
270.0ms
(* (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

8 alts after pruning (8 fresh and 0 done)

Merged error: 15.5b

localize15.0ms

Local error

Found 4 expressions with local error:

4.4b
(* (* x (pow sin 2.0)) x)
4.8b
(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x)))
6.9b
(* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x))
7.1b
(* x (pow sin 2.0))

rewrite116.0ms

Algorithm
rewrite-expression-head
Rules
226×add-exp-log
202×prod-exp
50×pow-to-exp pow-exp
34×add-cbrt-cube
20×cbrt-unprod
18×associate-*l*
17×add-sqr-sqrt
12×add-cube-cbrt *-un-lft-identity associate-*r*
10×unpow-prod-down
6×pow1
4×expm1-log1p-u *-commutative log1p-expm1-u add-log-exp sqr-pow
3×unswap-sqr
1×pow-prod-down
Counts
4 → 154
Calls
4 calls:
9.0ms
(* (* x (pow sin 2.0)) x)
70.0ms
(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x)))
25.0ms
(* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x))
5.0ms
(* x (pow sin 2.0))

series836.0ms

Counts
4 → 12
Calls
4 calls:
148.0ms
(* (* x (pow sin 2.0)) x)
274.0ms
(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x)))
277.0ms
(* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x))
137.0ms
(* x (pow sin 2.0))

simplify69.0ms

Algorithm
egg-herbie
Counts
166 → 166
Iterations

Useful iterations: 1 (11.0ms)

IterNodesCost
04501288
11880989
25002989

prune325.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 10.6b

localize17.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ (cos (* 2.0 x)) (* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))))
4.4b
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
4.8b
(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
6.9b
(* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

rewrite682.0ms

Algorithm
rewrite-expression-head
Rules
1410×add-exp-log
1300×prod-exp
338×pow-to-exp pow-exp
130×div-exp
74×add-cbrt-cube
46×cbrt-unprod
15×associate-*l*
11×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×pow1 cbrt-undiv unpow-prod-down
5×associate-*r*
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 → 402
Calls
4 calls:
254.0ms
(/ (cos (* 2.0 x)) (* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))))
32.0ms
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
263.0ms
(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
96.0ms
(* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

series1.0s

Counts
4 → 12
Calls
4 calls:
302.0ms
(/ (cos (* 2.0 x)) (* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))))
156.0ms
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
273.0ms
(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
274.0ms
(* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

simplify128.0ms

Algorithm
egg-herbie
Counts
414 → 414
Iterations

Useful iterations: 2 (76.0ms)

IterNodesCost
08316060
131614041
250023451

prune317.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.6b

localize19.0ms

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))))))
0.5b
(/ (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)))))))
5.1b
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
5.1b
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

rewrite32.0ms

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:
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)))))))
11.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
11.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

series554.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(* (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
101.0ms
(/ (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)))))))
213.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
207.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

simplify49.0ms

Algorithm
egg-herbie
Counts
126 → 126
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
03251562
112441292
250011217

prune335.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes256.0ms

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
01818
11818

end0.0ms

sample1.5s

Algorithm
intervals
Results
537.0ms9087×body80valid
297.0ms824×body1280valid
237.0ms970×body640valid
106.0ms574×body320valid
38.0ms324×body160valid