Details

Time bar (total: 10.8s)

sample3.0s

Algorithm
intervals
sampling

Space saved by range analysis: 0%

Space saved by search: 14.199829%

Guaranteed chance to sample good point: 71.150631%

Results
17.0ms194×body80valid
7.0ms22×body640valid
7.0ms14×body1280valid
5.0ms18×body320valid
4.0ms48×body80invalid
2.0ms7×body640invalid
2.0ms8×body320invalid
1.0ms8×body160valid
1.0ms1×body1280invalid
0.0ms1×body160invalid

simplify41.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0278
1688
22438
312668
450018

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 27.6b

Counts
2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (cos (* 2.0 x)) (* (pow c 2.0) (* (* x (pow s 2.0)) x)))
3.7b
(* (* x (pow s 2.0)) x)
8.9b
(* x (pow s 2.0))
18.0b
(* (pow c 2.0) (* (* x (pow s 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 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))

series226.0ms

Counts
4 → 12
Calls
4 calls:
80.0ms
(/ (cos (* 2.0 x)) (* (pow c 2.0) (* (* x (pow s 2.0)) x)))
32.0ms
(* (* x (pow s 2.0)) x)
31.0ms
(* x (pow s 2.0))
83.0ms
(* (pow c 2.0) (* (* x (pow s 2.0)) x))

simplify65.0ms

Algorithm
egg-herbie
Counts
127 → 127
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
05711041
12506875
25001871

prune251.0ms

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: 16.2b

Counts
128 → 12

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2)))
0.2b
(/ (cos (* 2.0 x)) (* (pow c 2.0) (* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x)))
3.7b
(* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x)
18.0b
(* (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:
9.0ms
(* (* 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)
12.0ms
(* (pow c 2.0) (* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x))

series224.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2)))
78.0ms
(/ (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))

simplify97.0ms

Algorithm
egg-herbie
Counts
198 → 198
Iterations

Useful iterations: 2 (75.0ms)

IterNodesCost
07212340
132341837
250011781

prune253.0ms

Filtered
70 candidates to 198 candidates (-182.9%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New1935198
Fresh5611
Picked101
Done000
Total19911210

Merged error: 1.9b

Counts
210 → 11

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (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)))))))
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))))))
4.0b
(* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))
4.0b
(* (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:
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)))))))
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))))))
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))))

series198.0ms

Counts
4 → 12
Calls
4 calls:
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)))))))
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))))))
67.0ms
(* (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

prune362.0ms

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

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New1099118
Fresh4610
Picked101
Done000
Total11415129

Merged error: 0.0b

Counts
129 → 15

localize20.0ms

Local error

Found 3 expressions with local error:

0.2b
(/ (cos (* 2.0 x)) (pow (fabs (* (pow (* (pow s 1.0) (pow c 1.0)) 1.0) x)) 2))
0.3b
(pow (fabs (* (pow (* (pow s 1.0) (pow c 1.0)) 1.0) x)) 2)
4.7b
(* (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:
5.0ms
(/ (cos (* 2.0 x)) (pow (fabs (* (pow (* (pow s 1.0) (pow c 1.0)) 1.0) x)) 2))
2.0ms
(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)

series158.0ms

Counts
3 → 9
Calls
3 calls:
44.0ms
(/ (cos (* 2.0 x)) (pow (fabs (* (pow (* (pow s 1.0) (pow c 1.0)) 1.0) x)) 2))
15.0ms
(pow (fabs (* (pow (* (pow s 1.0) (pow c 1.0)) 1.0) x)) 2)
99.0ms
(* (pow (* (pow s 1.0) (pow c 1.0)) 1.0) x)

simplify49.0ms

Algorithm
egg-herbie
Counts
107 → 107
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
04301351
114361234
250011222

prune252.0ms

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

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New1025107
Fresh6814
Picked101
Done000
Total10913122

Merged error: 0.0b

Counts
122 → 13

regimes582.0ms

Accuracy

0% (2.8b remaining)

Error of 2.9b against oracle of 0.2b and baseline of 2.9b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02411
12411

end0.0ms

sample4.8s

Algorithm
intervals
sampling

Space saved by range analysis: 0%

Space saved by search: 14.199829%

Guaranteed chance to sample good point: 71.150631%

Results
563.0ms6027×body80valid
321.0ms659×body1280valid
255.0ms721×body640valid
124.0ms1377×body80invalid
103.0ms391×body320valid
80.0ms245×body640invalid
66.0ms143×body1280invalid
40.0ms202×body160valid
39.0ms164×body320invalid
20.0ms116×body160invalid

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