Details

Time bar (total: 5.7s)

sample78.0ms

Algorithm
intervals
Results
26.0ms267×body80valid
19.0ms40×body1280valid
11.0ms34×body640valid
3.0ms13×body320valid
1.0ms5×body160valid

simplify40.0ms

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: 31.5b

Counts
2 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ (cos (* 2.0 x)) (* (pow c 2.0) (* (* x (pow s 2.0)) x)))
4.9b
(* (* x (pow s 2.0)) x)
11.4b
(* x (pow s 2.0))
18.4b
(* (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))

series220.0ms

Counts
4 → 12
Calls
4 calls:
76.0ms
(/ (cos (* 2.0 x)) (* (pow c 2.0) (* (* x (pow s 2.0)) x)))
30.0ms
(* (* x (pow s 2.0)) x)
31.0ms
(* x (pow s 2.0))
81.0ms
(* (pow c 2.0) (* (* x (pow s 2.0)) x))

simplify65.0ms

Algorithm
egg-herbie
Counts
127 → 127
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
05711041
12506875
25001871

prune266.0ms

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

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New11215127
Fresh000
Picked101
Done000
Total11315128

Merged error: 13.0b

Counts
128 → 15

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2)))
0.5b
(/ (cos (* 2.0 x)) (* (pow c 2.0) (* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x)))
4.9b
(* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x)
18.4b
(* (pow c 2.0) (* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x))

rewrite53.0ms

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)))
13.0ms
(/ (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))

series215.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2)))
73.0ms
(/ (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)
80.0ms
(* (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

prune277.0ms

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

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New1908198
Fresh8614
Picked101
Done000
Total19914213

Merged error: 1.9b

Counts
213 → 14

localize16.0ms

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))))))
0.5b
(/ (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)))))))
3.2b
(* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))
3.2b
(* (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))))))
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))))

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)))))))
65.0ms
(* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))
66.0ms
(* (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

prune364.0ms

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

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New10711118
Fresh11213
Picked101
Done000
Total11913132

Merged error: 0.0b

Counts
132 → 13

localize16.0ms

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))))))
1.0b
(/ (cos (* 2.0 x)) (fabs (* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))))
3.2b
(* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))
3.2b
(* (pow c (/ 2.0 2)) (* x (pow s (/ 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 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))))))
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))))

series203.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(/ (/ (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))))))
29.0ms
(/ (cos (* 2.0 x)) (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))))

simplify74.0ms

Algorithm
egg-herbie
Counts
169 → 169
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
05953343
120823048
250012963

prune583.0ms

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

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New1654169
Fresh4812
Picked101
Done000
Total17012182

Merged error: 0.0b

Counts
182 → 12

regimes483.0ms

Accuracy

6.8% (2.4b remaining)

Error of 2.6b against oracle of 0.2b and baseline of 2.7b

bsearch1.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03738
13738

end0.0ms

sample2.2s

Algorithm
intervals
Results
935.0ms9001×body80valid
398.0ms850×body1280valid
321.0ms941×body640valid
144.0ms565×body320valid
57.0ms332×body160valid

Profiling

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