Details

Time bar (total: 7.4s)

analyze988.0ms

Algorithm
search

sample62.0ms

Algorithm
intervals
Results
20.0ms200×body80valid
10.0ms21×body1280valid
8.0ms23×body640valid
5.0ms52×body80invalid
3.0ms12×body320invalid
2.0ms10×body320valid
1.0ms4×body640invalid
1.0ms4×body160invalid
0.0ms2×body160valid

simplify41.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0278
1688
22438
312668
450018

prune4.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 27.1b

Counts
2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (cos (* 2.0 x)) (* (pow c 2.0) (* (* x (pow s 2.0)) x)))
2.8b
(* (* x (pow s 2.0)) x)
9.4b
(* x (pow s 2.0))
18.1b
(* (pow c 2.0) (* (* x (pow s 2.0)) x))

rewrite34.0ms

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 c 2.0) (* (* x (pow s 2.0)) x)))
5.0ms
(* (* x (pow s 2.0)) x)
5.0ms
(* x (pow s 2.0))
9.0ms
(* (pow c 2.0) (* (* x (pow s 2.0)) x))

series225.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(/ (cos (* 2.0 x)) (* (pow c 2.0) (* (* x (pow s 2.0)) x)))
34.0ms
(* (* x (pow s 2.0)) x)
30.0ms
(* x (pow s 2.0))
84.0ms
(* (pow c 2.0) (* (* x (pow s 2.0)) x))

simplify66.0ms

Algorithm
egg-herbie
Counts
127 → 127
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
05711041
12506875
25001871

prune261.0ms

Filtered
70 candidates to 127 candidates (-81.4%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New11512127
Fresh000
Picked101
Done000
Total11612128

Merged error: 14.5b

Counts
128 → 12

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2)))
0.3b
(/ (cos (* 2.0 x)) (* (pow c 2.0) (* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x)))
2.8b
(* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x)
18.1b
(* (pow c 2.0) (* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x))

rewrite55.0ms

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 s (/ 2.0 2))) (pow s (/ 2.0 2)))
14.0ms
(/ (cos (* 2.0 x)) (* (pow c 2.0) (* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x)))
9.0ms
(* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x)
14.0ms
(* (pow c 2.0) (* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x))

series224.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2)))
77.0ms
(/ (cos (* 2.0 x)) (* (pow c 2.0) (* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x)))
32.0ms
(* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x)
84.0ms
(* (pow c 2.0) (* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x))

simplify95.0ms

Algorithm
egg-herbie
Counts
198 → 198
Iterations

Useful iterations: 2 (74.0ms)

IterNodesCost
07212340
132341837
250011781

prune273.0ms

Filtered
68 candidates to 198 candidates (-191.2%)
Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New1908198
Fresh5611
Picked101
Done000
Total19614210

Merged error: 2.6b

Counts
210 → 14

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (fabs (* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))) (fabs (* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))))
0.3b
(/ (cos (* 2.0 x)) (* (fabs (* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))) (fabs (* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2)))))))
5.0b
(* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))
5.0b
(* (pow c (/ 2.0 2)) (* x (pow s (/ 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 c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))) (fabs (* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))))
5.0ms
(/ (cos (* 2.0 x)) (* (fabs (* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))) (fabs (* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2)))))))
7.0ms
(* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))
7.0ms
(* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))

series199.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(* (fabs (* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))) (fabs (* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))))
45.0ms
(/ (cos (* 2.0 x)) (* (fabs (* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))) (fabs (* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2)))))))
69.0ms
(* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))
69.0ms
(* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))

simplify51.0ms

Algorithm
egg-herbie
Counts
118 → 118
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
04021518
114821245
250021172

prune392.0ms

Filtered
69 candidates to 118 candidates (-71.0%)
Pruning

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New10810118
Fresh8513
Picked101
Done000
Total11715132

Merged error: 0.1b

Counts
132 → 15

localize17.0ms

Local error

Found 3 expressions with local error:

0.3b
(pow (fabs (* (pow (* (pow s 1.0) (pow c 1.0)) 1.0) x)) 2)
0.3b
(/ (cos (* 2.0 x)) (pow (fabs (* (pow (* (pow s 1.0) (pow c 1.0)) 1.0) x)) 2))
3.5b
(* (pow (* (pow s 1.0) (pow c 1.0)) 1.0) x)

rewrite16.0ms

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×pow-unpow div-exp associate-*r* associate-/l* add-log-exp
2×unswap-sqr
1×cbrt-undiv pow-pow frac-2neg clear-num *-commutative cbrt-unprod div-inv
Counts
3 → 98
Calls
3 calls:
2.0ms
(pow (fabs (* (pow (* (pow s 1.0) (pow c 1.0)) 1.0) x)) 2)
5.0ms
(/ (cos (* 2.0 x)) (pow (fabs (* (pow (* (pow s 1.0) (pow c 1.0)) 1.0) x)) 2))
6.0ms
(* (pow (* (pow s 1.0) (pow c 1.0)) 1.0) x)

series162.0ms

Counts
3 → 9
Calls
3 calls:
16.0ms
(pow (fabs (* (pow (* (pow s 1.0) (pow c 1.0)) 1.0) x)) 2)
46.0ms
(/ (cos (* 2.0 x)) (pow (fabs (* (pow (* (pow s 1.0) (pow c 1.0)) 1.0) x)) 2))
100.0ms
(* (pow (* (pow s 1.0) (pow c 1.0)) 1.0) x)

simplify48.0ms

Algorithm
egg-herbie
Counts
107 → 107
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
04301351
114331234
250011222

prune278.0ms

Filtered
63 candidates to 107 candidates (-69.8%)
Pruning

18 alts after pruning (17 fresh and 1 done)

PrunedKeptTotal
New989107
Fresh6814
Picked011
Done000
Total10418122

Merged error: 0.0b

Counts
122 → 18

regimes969.0ms

Accuracy

0% (2.5b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01816
11816

end0.0ms

analyze987.0ms

Algorithm
search

sample1.9s

Algorithm
intervals
Results
549.0ms6010×body80valid
320.0ms660×body1280valid
254.0ms728×body640valid
160.0ms1906×body80invalid
103.0ms411×body320valid
75.0ms226×body640invalid
55.0ms121×body1280invalid
41.0ms176×body320invalid
33.0ms191×body160valid
19.0ms120×body160invalid

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