Details

Time bar (total: 7.8s)

sample56.0ms

Algorithm
intervals
Results
18.0ms285×body80valid
9.0ms23×body1280valid
8.0ms32×body640valid
3.0ms17×body320valid
2.0ms16×body160valid

simplify42.0ms

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: 29.4b

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)))
3.2b
(* (* x (pow sin 2.0)) x)
7.3b
(* x (pow sin 2.0))
21.4b
(* (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:
25.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
9.0ms
(* (* x (pow sin 2.0)) x)
6.0ms
(* x (pow sin 2.0))
30.0ms
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

series855.0ms

Counts
4 → 12
Calls
4 calls:
301.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
146.0ms
(* (* x (pow sin 2.0)) x)
144.0ms
(* x (pow sin 2.0))
264.0ms
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

simplify60.0ms

Algorithm
egg-herbie
Counts
135 → 135
Iterations

Useful iterations: 1 (12.0ms)

IterNodesCost
0448971
12063815
25002815

prune302.0ms

Filtered
135 candidates to 73 candidates (54.1%)
Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 16.4b

localize17.0ms

Local error

Found 4 expressions with local error:

3.2b
(* (* x (pow sin 2.0)) x)
7.0b
(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x)))
7.2b
(* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x))
7.3b
(* x (pow sin 2.0))

rewrite121.0ms

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:
11.0ms
(* (* x (pow sin 2.0)) x)
68.0ms
(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x)))
29.0ms
(* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x))
6.0ms
(* x (pow sin 2.0))

series824.0ms

Counts
4 → 12
Calls
4 calls:
150.0ms
(* (* x (pow sin 2.0)) x)
266.0ms
(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x)))
266.0ms
(* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x))
141.0ms
(* x (pow sin 2.0))

simplify63.0ms

Algorithm
egg-herbie
Counts
166 → 166
Iterations

Useful iterations: 1 (11.0ms)

IterNodesCost
04501288
11880989
25002989

prune325.0ms

Filtered
166 candidates to 71 candidates (42.8%)
Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 11.5b

localize18.0ms

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))))
3.2b
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
7.0b
(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
7.2b
(* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

rewrite677.0ms

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:
249.0ms
(/ (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))))
31.0ms
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
258.0ms
(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
92.0ms
(* (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:
313.0ms
(/ (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))))
152.0ms
(* (* (* 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)))
278.0ms
(* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

simplify125.0ms

Algorithm
egg-herbie
Counts
414 → 414
Iterations

Useful iterations: 2 (78.0ms)

IterNodesCost
08316060
131614041
250023451

prune324.0ms

Filtered
414 candidates to 70 candidates (16.9%)
Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 2.8b

localize17.0ms

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)))))))
5.6b
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
5.6b
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

rewrite33.0ms

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)))))))
10.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
11.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

series566.0ms

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))))))
103.0ms
(/ (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)))))))
211.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
219.0ms
(* (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

prune345.0ms

Filtered
126 candidates to 75 candidates (59.5%)
Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes177.0ms

Accuracy

2.7% (2.4b remaining)

Error of 2.5b against oracle of 0.2b and baseline of 2.6b

bsearch126.0ms

Steps
ItersRangePoint
10
-1.2338451977441667e-217
-6.912057286316748e-234
-2.614521882835997e-226

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03228
13228

end0.0ms

sample1.6s

Algorithm
intervals
Results
583.0ms9065×body80valid
302.0ms814×body1280valid
255.0ms933×body640valid
117.0ms577×body320valid
44.0ms313×body160valid