Details

Time bar (total: 5.3s)

sample71.0ms

Algorithm
intervals
sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 100%

Results
22.0ms261×body80valid
12.0ms25×body1280valid
11.0ms33×body640valid
5.0ms22×body320valid
2.0ms12×body160valid

simplify41.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0278
1688
22438
312668
450018

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 26.6b

Counts
2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (cos (* 2.0 x)) (* (pow c 2.0) (* (* x (pow s 2.0)) x)))
3.7b
(* (* x (pow s 2.0)) x)
7.2b
(* x (pow s 2.0))
17.7b
(* (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))

series229.0ms

Counts
4 → 12
Calls
4 calls:
81.0ms
(/ (cos (* 2.0 x)) (* (pow c 2.0) (* (* x (pow s 2.0)) x)))
32.0ms
(* (* x (pow s 2.0)) x)
30.0ms
(* x (pow s 2.0))
85.0ms
(* (pow c 2.0) (* (* x (pow s 2.0)) x))

simplify65.0ms

Algorithm
egg-herbie
Counts
127 → 127
Iterations

Useful iterations: 2 (54.0ms)

IterNodesCost
05711041
12506875
25001871

prune222.0ms

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

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1198127
Fresh000
Picked101
Done000
Total1208128

Merged error: 12.9b

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)))
0.4b
(/ (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)
17.7b
(* (pow c 2.0) (* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x))

rewrite54.0ms

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))

series226.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(* (* 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))

simplify94.0ms

Algorithm
egg-herbie
Counts
198 → 198
Iterations

Useful iterations: 2 (73.0ms)

IterNodesCost
07212340
132341837
250011781

prune224.0ms

Filtered
67 candidates to 198 candidates (-195.5%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1917198
Fresh527
Picked101
Done000
Total1979206

Merged error: 2.0b

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))))))
0.4b
(/ (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)))))))
4.3b
(* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))
4.3b
(* (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:
4.0ms
(* (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))))

series198.0ms

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))))))
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)))))))
68.0ms
(* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))
68.0ms
(* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))

simplify51.0ms

Algorithm
egg-herbie
Counts
118 → 118
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
04021518
114821245
250021172

prune336.0ms

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

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New1108118
Fresh448
Picked101
Done000
Total11512127

Merged error: 0.0b

Counts
127 → 12

localize17.0ms

Local error

Found 4 expressions with local error:

0.8b
(/ (cos (* 2.0 x)) (fabs (* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))))
0.8b
(/ 1 (fabs (* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))))
4.3b
(* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))
4.3b
(* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
62×add-exp-log
42×prod-exp
24×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
18×times-frac add-cbrt-cube
14×pow-to-exp associate-*l* pow-exp
6×unpow-prod-down associate-/r* cbrt-unprod associate-/l*
5×pow1
4×add-log-exp
3×div-exp
2×cbrt-undiv frac-2neg associate-*r* clear-num *-commutative div-inv sqr-pow
1×rec-exp pow-flip 1-exp inv-pow
Counts
4 → 118
Calls
4 calls:
4.0ms
(/ (cos (* 2.0 x)) (fabs (* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))))
3.0ms
(/ 1 (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))))

series182.0ms

Counts
4 → 12
Calls
4 calls:
29.0ms
(/ (cos (* 2.0 x)) (fabs (* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))))
17.0ms
(/ 1 (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))))

simplify49.0ms

Algorithm
egg-herbie
Counts
130 → 130
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
04131461
114031311
250021297

prune328.0ms

Filtered
76 candidates to 130 candidates (-71.1%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New1255130
Fresh4711
Picked101
Done000
Total13012142

Merged error: 0.0b

Counts
142 → 12

regimes681.0ms

Accuracy

0% (2.5b remaining)

Error of 2.6b against oracle of 0.1b and baseline of 2.6b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02529
12529

end0.0ms

sample2.1s

Algorithm
intervals
sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 100%

Results
771.0ms8955×body80valid
398.0ms806×body1280valid
334.0ms977×body640valid
151.0ms584×body320valid
56.0ms328×body160valid

Profiling

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