Details

Time bar (total: 6.8s)

sample58.0ms

Algorithm
intervals
Results
23.0ms290×body80valid
10.0ms25×body1280valid
8.0ms29×body640valid
3.0ms14×body320valid
1.0ms6×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: 24.2b

Counts
2 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
3.1b
(* (* x (pow sin 2.0)) x)
5.8b
(* x (pow sin 2.0))
16.6b
(* (pow cos 2.0) (* (* x (pow sin 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 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))

series798.0ms

Counts
4 → 12
Calls
4 calls:
277.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
136.0ms
(* (* x (pow sin 2.0)) x)
140.0ms
(* x (pow sin 2.0))
245.0ms
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

simplify56.0ms

Algorithm
egg-herbie
Counts
127 → 127
Iterations

Useful iterations: 1 (11.0ms)

IterNodesCost
0435927
12042771
25002771

prune245.0ms

Filtered
127 candidates to 65 candidates (51.2%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New11710127
Fresh000
Picked101
Done000
Total11810128

Merged error: 11.4b

Counts
128 → 10

localize16.0ms

Local error

Found 4 expressions with local error:

3.1b
(* (* x (pow sin 2.0)) x)
4.9b
(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x)))
5.8b
(* x (pow sin 2.0))
5.9b
(* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
226×add-exp-log
202×prod-exp
50×pow-to-exp pow-exp
34×add-cbrt-cube
20×cbrt-unprod
18×associate-*l*
17×add-sqr-sqrt
12×add-cube-cbrt *-un-lft-identity associate-*r*
10×unpow-prod-down
6×pow1
4×*-commutative add-log-exp sqr-pow
3×unswap-sqr
1×pow-prod-down
Counts
4 → 146
Calls
4 calls:
9.0ms
(* (* x (pow sin 2.0)) x)
13.0ms
(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x)))
5.0ms
(* x (pow sin 2.0))
9.0ms
(* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x))

series797.0ms

Counts
4 → 12
Calls
4 calls:
150.0ms
(* (* x (pow sin 2.0)) x)
258.0ms
(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x)))
130.0ms
(* x (pow sin 2.0))
260.0ms
(* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x))

simplify63.0ms

Algorithm
egg-herbie
Counts
158 → 158
Iterations

Useful iterations: 1 (11.0ms)

IterNodesCost
04291240
11850941
25001941

prune244.0ms

Filtered
158 candidates to 63 candidates (39.9%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New1526158
Fresh459
Picked101
Done000
Total15711168

Merged error: 8.3b

Counts
168 → 11

localize17.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ (cos (* 2.0 x)) (* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))))
3.1b
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
4.9b
(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
5.9b
(* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

rewrite104.0ms

Algorithm
rewrite-expression-head
Rules
1410×add-exp-log
1300×prod-exp
338×pow-to-exp pow-exp
130×div-exp
74×add-cbrt-cube
46×cbrt-unprod
15×associate-*l*
11×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×pow1 cbrt-undiv unpow-prod-down
5×associate-*r*
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 → 394
Calls
4 calls:
25.0ms
(/ (cos (* 2.0 x)) (* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* (* 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)
17.0ms
(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
13.0ms
(* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

series980.0ms

Counts
4 → 12
Calls
4 calls:
294.0ms
(/ (cos (* 2.0 x)) (* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))))
151.0ms
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
269.0ms
(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
266.0ms
(* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

simplify132.0ms

Algorithm
egg-herbie
Counts
406 → 406
Iterations

Useful iterations: 2 (78.0ms)

IterNodesCost
07975960
131123941
250013351

prune256.0ms

Filtered
406 candidates to 63 candidates (15.5%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New4015406
Fresh4610
Picked101
Done000
Total40611417

Merged error: 1.4b

Counts
417 → 11

localize16.0ms

Local error

Found 4 expressions with local error:

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))))))
0.5b
(/ (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)))))))
3.8b
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
3.8b
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 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 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)))))))
8.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
7.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

series551.0ms

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))))))
101.0ms
(/ (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)))))))
212.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
207.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

simplify48.0ms

Algorithm
egg-herbie
Counts
118 → 118
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
03161464
112291194
250021122

prune287.0ms

Filtered
118 candidates to 67 candidates (56.8%)
Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New1099118
Fresh6410
Picked101
Done000
Total11613129

Merged error: 0.1b

Counts
129 → 13

regimes299.0ms

Accuracy

0% (2.5b remaining)

Error of 2.6b against oracle of 0.2b and baseline of 2.6b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02319
12319

end0.0ms

sample1.7s

Algorithm
intervals
Results
629.0ms8984×body80valid
332.0ms829×body1280valid
281.0ms951×body640valid
129.0ms569×body320valid
45.0ms324×body160valid