Details

Time bar (total: 7.2s)

sample91.0ms

Algorithm
intervals
Results
33.0ms297×body80valid
15.0ms22×body1280valid
13.0ms30×body640valid
8.0ms23×body320valid
3.0ms10×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

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 27.4b

Counts
2 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

0.8b
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
3.6b
(* (* x (pow sin 2.0)) x)
7.3b
(* x (pow sin 2.0))
18.8b
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

rewrite43.0ms

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:
12.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
6.0ms
(* (* x (pow sin 2.0)) x)
6.0ms
(* x (pow sin 2.0))
14.0ms
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

series957.0ms

Counts
4 → 12
Calls
4 calls:
297.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
145.0ms
(* (* x (pow sin 2.0)) x)
134.0ms
(* x (pow sin 2.0))
381.0ms
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

simplify58.0ms

Algorithm
egg-herbie
Counts
135 → 135
Iterations

Useful iterations: 1 (12.0ms)

IterNodesCost
0448971
12063815
25002815

prune296.0ms

Filtered
135 candidates to 73 candidates (54.1%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1269135
Fresh000
Picked101
Done000
Total1279136

Merged error: 15.7b

Counts
136 → 9

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
0.8b
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
3.6b
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
18.8b
(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

rewrite69.0ms

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:
8.0ms
(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
19.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
10.0ms
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
17.0ms
(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

series869.0ms

Counts
4 → 12
Calls
4 calls:
133.0ms
(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
296.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
147.0ms
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
292.0ms
(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

simplify94.0ms

Algorithm
egg-herbie
Counts
206 → 206
Iterations

Useful iterations: 2 (68.0ms)

IterNodesCost
06032216
128211509
250021497

prune279.0ms

Filtered
206 candidates to 71 candidates (34.5%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New2006206
Fresh538
Picked011
Done000
Total20510215

Merged error: 4.1b

Counts
215 → 10

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))))))
0.8b
(/ (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)))))))
5.9b
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
5.9b
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

rewrite30.0ms

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:
4.0ms
(* (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)))))))
8.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
9.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

series565.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(* (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
106.0ms
(/ (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)))))))
214.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
212.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

simplify49.0ms

Algorithm
egg-herbie
Counts
126 → 126
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
03251562
112441292
250011217

prune393.0ms

Filtered
126 candidates to 75 candidates (59.5%)
Pruning

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New11412126
Fresh538
Picked101
Done101
Total12115136

Merged error: 0.1b

Counts
136 → 15

localize18.0ms

Local error

Found 3 expressions with local error:

0.2b
(pow (fabs (* (pow (* (pow cos 1.0) (pow sin 1.0)) 1.0) x)) 2)
0.8b
(/ (cos (* 2.0 x)) (pow (fabs (* (pow (* (pow cos 1.0) (pow sin 1.0)) 1.0) x)) 2))
4.0b
(* (pow (* (pow cos 1.0) (pow sin 1.0)) 1.0) x)

rewrite19.0ms

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:
2.0ms
(pow (fabs (* (pow (* (pow cos 1.0) (pow sin 1.0)) 1.0) x)) 2)
6.0ms
(/ (cos (* 2.0 x)) (pow (fabs (* (pow (* (pow cos 1.0) (pow sin 1.0)) 1.0) x)) 2))
7.0ms
(* (pow (* (pow cos 1.0) (pow sin 1.0)) 1.0) x)

series448.0ms

Counts
3 → 9
Calls
3 calls:
29.0ms
(pow (fabs (* (pow (* (pow cos 1.0) (pow sin 1.0)) 1.0) x)) 2)
101.0ms
(/ (cos (* 2.0 x)) (pow (fabs (* (pow (* (pow cos 1.0) (pow sin 1.0)) 1.0) x)) 2))
317.0ms
(* (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
111571248
250021239

prune348.0ms

Filtered
113 candidates to 71 candidates (62.8%)
Pruning

16 alts after pruning (16 fresh and 0 done)

PrunedKeptTotal
New1076113
Fresh41014
Picked101
Done000
Total11216128

Merged error: 0.0b

Counts
128 → 16

regimes436.0ms

Accuracy

0% (2.4b remaining)

Error of 2.4b against oracle of 0.1b and baseline of 2.4b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02118
12118

end0.0ms

sample2.0s

Algorithm
intervals
Results
806.0ms9046×body80valid
365.0ms791×body1280valid
338.0ms994×body640valid
148.0ms600×body320valid
50.0ms292×body160valid