Details

Time bar (total: 6.8s)

sample68.0ms

Algorithm
intervals
Results
25.0ms297×body80valid
11.0ms22×body1280valid
10.0ms30×body640valid
6.0ms23×body320valid
2.0ms10×body160valid

simplify39.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0278
1688
22438
312668
450018

prune3.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 27.4b

Counts
2 → 1

localize17.0ms

Local error

Found 4 expressions with local error:

0.8b
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
3.6b
(* (* x (pow sin 2.0)) x)
7.3b
(* x (pow sin 2.0))
18.8b
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

rewrite35.0ms

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)))
6.0ms
(* (* 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))

series828.0ms

Counts
4 → 12
Calls
4 calls:
292.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
146.0ms
(* (* x (pow sin 2.0)) x)
133.0ms
(* x (pow sin 2.0))
257.0ms
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

simplify68.0ms

Algorithm
egg-herbie
Counts
127 → 127
Iterations

Useful iterations: 1 (11.0ms)

IterNodesCost
0435927
12042771
25002771

prune257.0ms

Filtered
127 candidates to 65 candidates (51.2%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1189127
Fresh000
Picked101
Done000
Total1199128

Merged error: 15.7b

Counts
128 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
0.8b
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
3.6b
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
18.8b
(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

rewrite61.0ms

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)))
15.0ms
(/ (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)
13.0ms
(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

series847.0ms

Counts
4 → 12
Calls
4 calls:
141.0ms
(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
296.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
150.0ms
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
259.0ms
(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

simplify88.0ms

Algorithm
egg-herbie
Counts
198 → 198
Iterations

Useful iterations: 2 (68.0ms)

IterNodesCost
05862140
127921433
250021421

prune238.0ms

Filtered
198 candidates to 63 candidates (31.8%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New1926198
Fresh538
Picked011
Done000
Total19710207

Merged error: 4.1b

Counts
207 → 10

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
0.8b
(/ (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)))))))
5.9b
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
5.9b
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

rewrite27.0ms

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 cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
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)))))))
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))))

series567.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(* (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
104.0ms
(/ (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)))))))
215.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
215.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

simplify48.0ms

Algorithm
egg-herbie
Counts
118 → 118
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
03161464
112291194
250021122

prune334.0ms

Filtered
118 candidates to 67 candidates (56.8%)
Pruning

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New10612118
Fresh538
Picked101
Done101
Total11315128

Merged error: 0.1b

Counts
128 → 15

localize18.0ms

Local error

Found 3 expressions with local error:

0.2b
(pow (fabs (* (pow (* (pow cos 1.0) (pow sin 1.0)) 1.0) x)) 2)
0.8b
(/ (cos (* 2.0 x)) (pow (fabs (* (pow (* (pow cos 1.0) (pow sin 1.0)) 1.0) x)) 2))
4.0b
(* (pow (* (pow cos 1.0) (pow sin 1.0)) 1.0) x)

rewrite18.0ms

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 cos 1.0) (pow sin 1.0)) 1.0) x)) 2)
5.0ms
(/ (cos (* 2.0 x)) (pow (fabs (* (pow (* (pow cos 1.0) (pow sin 1.0)) 1.0) x)) 2))
7.0ms
(* (pow (* (pow cos 1.0) (pow sin 1.0)) 1.0) x)

series449.0ms

Counts
3 → 9
Calls
3 calls:
29.0ms
(pow (fabs (* (pow (* (pow cos 1.0) (pow sin 1.0)) 1.0) x)) 2)
98.0ms
(/ (cos (* 2.0 x)) (pow (fabs (* (pow (* (pow cos 1.0) (pow sin 1.0)) 1.0) x)) 2))
322.0ms
(* (pow (* (pow cos 1.0) (pow sin 1.0)) 1.0) x)

simplify44.0ms

Algorithm
egg-herbie
Counts
107 → 107
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
03291314
111401198
250011189

prune292.0ms

Filtered
107 candidates to 65 candidates (60.7%)
Pruning

16 alts after pruning (16 fresh and 0 done)

PrunedKeptTotal
New1016107
Fresh41014
Picked101
Done000
Total10616122

Merged error: 0.0b

Counts
122 → 16

regimes404.0ms

Accuracy

0% (2.4b remaining)

Error of 2.4b against oracle of 0.1b and baseline of 2.4b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02118
12118

end0.0ms

sample2.1s

Algorithm
intervals
Results
810.0ms9046×body80valid
382.0ms791×body1280valid
339.0ms994×body640valid
154.0ms600×body320valid
51.0ms292×body160valid