Details

Time bar (total: 5.6s)

sample75.0ms

Algorithm
intervals
Results
26.0ms294×body80valid
12.0ms27×body1280valid
10.0ms32×body640valid
4.0ms16×body320valid
3.0ms18×body160valid

simplify40.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0278
1688
22438
312668
450018

prune9.0ms

Filtered
1 candidates to 0 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 30.0b

Counts
2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

0.8b
(/ (cos (* 2.0 x)) (* (pow c 2.0) (* (* x (pow s 2.0)) x)))
4.6b
(* (* x (pow s 2.0)) x)
6.5b
(* x (pow s 2.0))
21.1b
(* (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))

series235.0ms

Counts
4 → 12
Calls
4 calls:
81.0ms
(/ (cos (* 2.0 x)) (* (pow c 2.0) (* (* x (pow s 2.0)) x)))
33.0ms
(* (* x (pow s 2.0)) x)
32.0ms
(* x (pow s 2.0))
88.0ms
(* (pow c 2.0) (* (* x (pow s 2.0)) x))

simplify63.0ms

Algorithm
egg-herbie
Counts
127 → 127
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
05711041
12506875
25001871

prune227.0ms

Filtered
127 candidates to 70 candidates (44.9%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1198127
Fresh000
Picked101
Done000
Total1208128

Merged error: 17.8b

Counts
128 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2)))
0.8b
(/ (cos (* 2.0 x)) (* (pow c 2.0) (* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x)))
4.6b
(* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x)
21.1b
(* (pow c 2.0) (* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x))

rewrite56.0ms

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)
12.0ms
(* (pow c 2.0) (* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x))

series232.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2)))
79.0ms
(/ (cos (* 2.0 x)) (* (pow c 2.0) (* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x)))
35.0ms
(* (* (* 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))

simplify94.0ms

Algorithm
egg-herbie
Counts
198 → 198
Iterations

Useful iterations: 2 (73.0ms)

IterNodesCost
07212340
132341837
250011781

prune236.0ms

Filtered
198 candidates to 69 candidates (65.2%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1917198
Fresh527
Picked101
Done000
Total1979206

Merged error: 3.4b

Counts
206 → 9

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))))))
0.8b
(/ (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)))))))
5.1b
(* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))
5.1b
(* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))

rewrite26.0ms

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))))))
6.0ms
(/ (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))))

series209.0ms

Counts
4 → 12
Calls
4 calls:
18.0ms
(* (fabs (* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))) (fabs (* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))))
46.0ms
(/ (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)))))))
73.0ms
(* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))
72.0ms
(* (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

prune358.0ms

Filtered
118 candidates to 69 candidates (41.5%)
Pruning

14 alts after pruning (13 fresh and 1 done)

PrunedKeptTotal
New10711118
Fresh628
Picked011
Done000
Total11314127

Merged error: 0.0b

Counts
127 → 14

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
(/ (cos (* 2.0 x)) (fabs (* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))))
5.1b
(* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))
5.1b
(* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
84×times-frac
63×add-exp-log
58×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
42×prod-exp
21×add-cbrt-cube
16×associate-/l*
14×pow-to-exp associate-*l* pow-exp
6×unpow-prod-down associate-/r* cbrt-unprod div-inv
4×pow1 cbrt-undiv div-exp add-log-exp
2×frac-2neg associate-*r* clear-num *-commutative sqr-pow
1×associate-/l/
Counts
4 → 157
Calls
4 calls:
6.0ms
(/ (/ (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
(/ (cos (* 2.0 x)) (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))))

series218.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(/ (/ (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))))))
29.0ms
(/ (cos (* 2.0 x)) (fabs (* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))))
71.0ms
(* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))
70.0ms
(* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))

simplify71.0ms

Algorithm
egg-herbie
Counts
169 → 169
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
05953343
120823048
250012963

prune568.0ms

Filtered
169 candidates to 109 candidates (35.5%)
Pruning

16 alts after pruning (15 fresh and 1 done)

PrunedKeptTotal
New1636169
Fresh3912
Picked101
Done011
Total16716183

Merged error: 0.0b

Counts
183 → 16

regimes551.0ms

Accuracy

0% (2.7b remaining)

Error of 2.8b against oracle of 0.1b and baseline of 2.8b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02319
12319

end0.0ms

sample2.1s

Algorithm
intervals
Results
749.0ms9046×body80valid
362.0ms803×body1280valid
332.0ms993×body640valid
137.0ms553×body320valid
52.0ms315×body160valid

Profiling

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