Details

Time bar (total: 5.2s)

sample64.0ms

Algorithm
intervals
Results
22.0ms271×body80valid
9.0ms20×body1280valid
9.0ms27×body640valid
6.0ms25×body320valid
1.0ms5×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: 26.6b

Counts
2 → 1

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (cos (* 2.0 x)) (* (pow c 2.0) (* (* x (pow s 2.0)) x)))
4.1b
(* (* x (pow s 2.0)) x)
7.5b
(* x (pow s 2.0))
18.5b
(* (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))

series215.0ms

Counts
4 → 12
Calls
4 calls:
75.0ms
(/ (cos (* 2.0 x)) (* (pow c 2.0) (* (* x (pow s 2.0)) x)))
31.0ms
(* (* x (pow s 2.0)) x)
29.0ms
(* x (pow s 2.0))
80.0ms
(* (pow c 2.0) (* (* x (pow s 2.0)) x))

simplify64.0ms

Algorithm
egg-herbie
Counts
127 → 127
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
05711041
12506875
25001871

prune226.0ms

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

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1189127
Fresh000
Picked101
Done000
Total1199128

Merged error: 14.3b

Counts
128 → 9

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* 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)))
4.1b
(* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x)
18.5b
(* (pow c 2.0) (* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x))

rewrite52.0ms

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)))
13.0ms
(/ (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))

series214.0ms

Counts
4 → 12
Calls
4 calls:
29.0ms
(* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2)))
74.0ms
(/ (cos (* 2.0 x)) (* (pow c 2.0) (* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x)))
30.0ms
(* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x)
80.0ms
(* (pow c 2.0) (* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x))

simplify98.0ms

Algorithm
egg-herbie
Counts
198 → 198
Iterations

Useful iterations: 2 (75.0ms)

IterNodesCost
07212340
132341837
250011781

prune244.0ms

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

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New1926198
Fresh358
Picked101
Done000
Total19611207

Merged error: 2.5b

Counts
207 → 11

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)))))))
4.9b
(* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))
4.9b
(* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))

rewrite24.0ms

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))))

series193.0ms

Counts
4 → 12
Calls
4 calls:
15.0ms
(* (fabs (* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))) (fabs (* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))))
43.0ms
(/ (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)))))))
65.0ms
(* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))
68.0ms
(* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))

simplify54.0ms

Algorithm
egg-herbie
Counts
118 → 118
Iterations

Useful iterations: 2 (38.0ms)

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
New10711118
Fresh6410
Picked101
Done000
Total11415129

Merged error: 0.0b

Counts
129 → 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)

series156.0ms

Counts
3 → 9
Calls
3 calls:
15.0ms
(pow (fabs (* (pow (* (pow s 1.0) (pow c 1.0)) 1.0) x)) 2)
44.0ms
(/ (cos (* 2.0 x)) (pow (fabs (* (pow (* (pow s 1.0) (pow c 1.0)) 1.0) x)) 2))
96.0ms
(* (pow (* (pow s 1.0) (pow c 1.0)) 1.0) x)

simplify48.0ms

Algorithm
egg-herbie
Counts
107 → 107
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
04301351
114331234
250011222

prune251.0ms

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

16 alts after pruning (16 fresh and 0 done)

PrunedKeptTotal
New1007107
Fresh5914
Picked101
Done000
Total10616122

Merged error: 0.0b

Counts
122 → 16

regimes678.0ms

Accuracy

31.1% (1.8b remaining)

Error of 1.9b against oracle of 0.1b and baseline of 2.7b

bsearch1.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04437
14437

end0.0ms

sample2.1s

Algorithm
intervals
Results
738.0ms9041×body80valid
375.0ms814×body1280valid
288.0ms908×body640valid
132.0ms567×body320valid
49.0ms298×body160valid

Profiling

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