Details

Time bar (total: 5.8s)

sample77.0ms

Algorithm
intervals
Results
24.0ms289×body80valid
14.0ms33×body640valid
12.0ms27×body1280valid
5.0ms23×body320valid
2.0ms9×body160valid

simplify41.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0278
1688
22438
312668
450018

prune4.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 28.0b

Counts
2 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (cos (* 2.0 x)) (* (pow c 2.0) (* (* x (pow s 2.0)) x)))
4.2b
(* (* x (pow s 2.0)) x)
10.5b
(* x (pow s 2.0))
16.0b
(* (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))

series222.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(/ (cos (* 2.0 x)) (* (pow c 2.0) (* (* x (pow s 2.0)) x)))
33.0ms
(* (* x (pow s 2.0)) x)
29.0ms
(* x (pow s 2.0))
83.0ms
(* (pow c 2.0) (* (* x (pow s 2.0)) x))

simplify64.0ms

Algorithm
egg-herbie
Counts
127 → 127
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
05711041
12506875
25001871

prune229.0ms

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

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New11710127
Fresh000
Picked101
Done000
Total11810128

Merged error: 14.6b

Counts
128 → 10

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2)))
0.3b
(/ (cos (* 2.0 x)) (* (pow c 2.0) (* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x)))
4.2b
(* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x)
16.0b
(* (pow c 2.0) (* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x))

rewrite55.0ms

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)))
11.0ms
(* (* (* 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))

series217.0ms

Counts
4 → 12
Calls
4 calls:
29.0ms
(* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2)))
74.0ms
(/ (cos (* 2.0 x)) (* (pow c 2.0) (* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x)))
31.0ms
(* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x)
81.0ms
(* (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

prune236.0ms

Filtered
69 candidates to 198 candidates (-187.0%)
Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New1926198
Fresh549
Picked011
Done000
Total19711208

Merged error: 2.1b

Counts
208 → 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))))))
0.3b
(/ (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)))))))
3.9b
(* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))
3.9b
(* (pow c (/ 2.0 2)) (* x (pow s (/ 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:
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))))))
4.0ms
(/ (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))))

series191.0ms

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))))))
44.0ms
(/ (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)))))))
64.0ms
(* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))
67.0ms
(* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))

simplify50.0ms

Algorithm
egg-herbie
Counts
118 → 118
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
04021518
114821245
250021172

prune355.0ms

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

15 alts after pruning (14 fresh and 1 done)

PrunedKeptTotal
New10612118
Fresh729
Picked101
Done011
Total11415129

Merged error: 0.1b

Counts
129 → 15

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))))))
0.5b
(/ (cos (* 2.0 x)) (fabs (* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))))
3.9b
(* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))
3.9b
(* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))

rewrite28.0ms

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 c (/ 2.0 2)) (* x (pow s (/ 2.0 2)))))) (fabs (* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))))
3.0ms
(/ (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))))

series201.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(/ (/ (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))))))
27.0ms
(/ (cos (* 2.0 x)) (fabs (* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))))
66.0ms
(* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))
67.0ms
(* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))

simplify72.0ms

Algorithm
egg-herbie
Counts
169 → 169
Iterations

Useful iterations: 2 (42.0ms)

IterNodesCost
05953343
120823048
250012963

prune719.0ms

Filtered
111 candidates to 169 candidates (-52.3%)
Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New1618169
Fresh10313
Picked101
Done011
Total17212184

Merged error: 0.0b

Counts
184 → 12

regimes692.0ms

Accuracy

73.7% (0.7b remaining)

Error of 0.9b against oracle of 0.2b and baseline of 2.9b

bsearch2.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04346
14346

end0.0ms

sample2.1s

Algorithm
intervals
Results
745.0ms9055×body80valid
374.0ms858×body1280valid
321.0ms962×body640valid
146.0ms623×body320valid
53.0ms327×body160valid

Profiling

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