Details

Time bar (total: 5.6s)

sample77.0ms

Algorithm
intervals
Results
26.0ms301×body80valid
18.0ms31×body1280valid
9.0ms25×body640valid
4.0ms14×body320valid
2.0ms10×body160valid

simplify43.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0278
1688
22438
312668
450018

prune4.0ms

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: 28.6b

Counts
2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

1.4b
(/ (cos (* 2.0 x)) (* (pow c 2.0) (* (* x (pow s 2.0)) x)))
5.1b
(* (* x (pow s 2.0)) x)
9.1b
(* x (pow s 2.0))
17.0b
(* (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))
8.0ms
(* (pow c 2.0) (* (* x (pow s 2.0)) x))

series218.0ms

Counts
4 → 12
Calls
4 calls:
76.0ms
(/ (cos (* 2.0 x)) (* (pow c 2.0) (* (* x (pow s 2.0)) x)))
30.0ms
(* (* x (pow s 2.0)) x)
31.0ms
(* x (pow s 2.0))
81.0ms
(* (pow c 2.0) (* (* x (pow s 2.0)) x))

simplify66.0ms

Algorithm
egg-herbie
Counts
127 → 127
Iterations

Useful iterations: 2 (55.0ms)

IterNodesCost
05711041
12506875
25001871

prune243.0ms

Filtered
127 candidates to 70 candidates (44.9%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New11512127
Fresh000
Picked101
Done000
Total11612128

Merged error: 15.5b

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)))
1.4b
(/ (cos (* 2.0 x)) (* (pow c 2.0) (* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x)))
5.1b
(* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x)
17.0b
(* (pow c 2.0) (* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x))

rewrite53.0ms

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)))
8.0ms
(* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x)
13.0ms
(* (pow c 2.0) (* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x))

series212.0ms

Counts
4 → 12
Calls
4 calls:
29.0ms
(* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2)))
73.0ms
(/ (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)
79.0ms
(* (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 (74.0ms)

IterNodesCost
07212340
132341837
250011781

prune245.0ms

Filtered
198 candidates to 68 candidates (65.7%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New1917198
Fresh7411
Picked101
Done000
Total19911210

Merged error: 3.0b

Counts
210 → 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))))))
1.4b
(/ (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)))))))
4.4b
(* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))
4.4b
(* (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))))

series187.0ms

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))))))
41.0ms
(/ (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))))
65.0ms
(* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))

simplify51.0ms

Algorithm
egg-herbie
Counts
118 → 118
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
04021518
114821245
250021172

prune359.0ms

Filtered
118 candidates to 69 candidates (41.5%)
Pruning

16 alts after pruning (16 fresh and 0 done)

PrunedKeptTotal
New10612118
Fresh6410
Picked101
Done000
Total11316129

Merged error: 0.2b

Counts
129 → 16

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))))))
0.6b
(/ (cos (* 2.0 x)) (fabs (* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))))
4.4b
(* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))
4.4b
(* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))

rewrite27.0ms

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:
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))))))
4.0ms
(/ (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))))

series198.0ms

Counts
4 → 12
Calls
4 calls:
41.0ms
(/ (/ (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))))))
26.0ms
(/ (cos (* 2.0 x)) (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))))
66.0ms
(* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))

simplify73.0ms

Algorithm
egg-herbie
Counts
169 → 169
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
05953343
120823048
250012963

prune560.0ms

Filtered
169 candidates to 110 candidates (34.9%)
Pruning

17 alts after pruning (17 fresh and 0 done)

PrunedKeptTotal
New1654169
Fresh21315
Picked101
Done000
Total16817185

Merged error: 0.2b

Counts
185 → 17

regimes558.0ms

Accuracy

0% (2.6b remaining)

Error of 2.7b against oracle of 0.2b and baseline of 2.7b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02319
12319

end0.0ms

sample2.3s

Algorithm
intervals
Results
945.0ms9247×body80valid
386.0ms830×body1280valid
320.0ms948×body640valid
142.0ms557×body320valid
57.0ms317×body160valid

Profiling

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