Details

Time bar (total: 6.6s)

sample73.0ms

Algorithm
intervals
Results
26.0ms277×body80valid
12.0ms26×body1280valid
8.0ms27×body640valid
5.0ms21×body320valid
1.0ms9×body160valid

simplify39.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0278
1688
22438
312668
450018

prune5.0ms

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

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
3.5b
(* (* x (pow sin 2.0)) x)
8.1b
(* x (pow sin 2.0))
20.7b
(* (pow cos 2.0) (* (* x (pow sin 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 cos 2.0) (* (* x (pow sin 2.0)) x)))
5.0ms
(* (* x (pow sin 2.0)) x)
5.0ms
(* x (pow sin 2.0))
9.0ms
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

series222.0ms

Counts
4 → 12
Calls
4 calls:
81.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
32.0ms
(* (* x (pow sin 2.0)) x)
29.0ms
(* x (pow sin 2.0))
79.0ms
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

simplify85.0ms

Algorithm
egg-herbie
Counts
127 → 127
Iterations

Useful iterations: 2 (67.0ms)

IterNodesCost
05721025
12501875
25002871

prune583.0ms

Filtered
127 candidates to 70 candidates (44.9%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New11611127
Fresh000
Picked101
Done000
Total11711128

Merged error: 16.2b

Counts
128 → 11

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
0.2b
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
3.5b
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
20.7b
(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

rewrite58.0ms

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 sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
14.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
9.0ms
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
12.0ms
(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

series250.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
97.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
33.0ms
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
77.0ms
(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

simplify93.0ms

Algorithm
egg-herbie
Counts
198 → 198
Iterations

Useful iterations: 2 (71.0ms)

IterNodesCost
07222324
132291837
250011781

prune546.0ms

Filtered
198 candidates to 68 candidates (65.7%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New1926198
Fresh4610
Picked101
Done000
Total19712209

Merged error: 2.3b

Counts
209 → 12

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (cos (* 2.0 x)) (* (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))))))
0.3b
(* (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
3.7b
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
3.7b
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 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 cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))))))
3.0ms
(* (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
7.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
7.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

series192.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(/ (cos (* 2.0 x)) (* (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))))))
17.0ms
(* (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
65.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
67.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

simplify52.0ms

Algorithm
egg-herbie
Counts
118 → 118
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
04121518
114931245
250021172

prune509.0ms

Filtered
118 candidates to 69 candidates (41.5%)
Pruning

19 alts after pruning (19 fresh and 0 done)

PrunedKeptTotal
New10216118
Fresh8311
Picked101
Done000
Total11119130

Merged error: 0.1b

Counts
130 → 19

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (/ (cos (* 2.0 x)) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))))) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
0.5b
(/ (cos (* 2.0 x)) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
3.7b
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
3.7b
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

rewrite29.0ms

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 cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))))) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
4.0ms
(/ (cos (* 2.0 x)) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
7.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
7.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

series206.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(/ (/ (cos (* 2.0 x)) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))))) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
29.0ms
(/ (cos (* 2.0 x)) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
65.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
69.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

simplify72.0ms

Algorithm
egg-herbie
Counts
169 → 169
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
06053343
120963048
250012963

prune712.0ms

Filtered
169 candidates to 109 candidates (35.5%)
Pruning

19 alts after pruning (19 fresh and 0 done)

PrunedKeptTotal
New15811169
Fresh10818
Picked101
Done000
Total16919188

Merged error: 0.0b

Counts
188 → 19

regimes773.0ms

Accuracy

0% (2.6b 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

sample2.0s

Algorithm
intervals
Results
718.0ms9031×body80valid
356.0ms817×body1280valid
287.0ms905×body640valid
126.0ms560×body320valid
46.0ms293×body160valid

Profiling

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