Details

Time bar (total: 5.5s)

sample82.0ms

Algorithm
intervals
Results
23.0ms270×body80valid
14.0ms30×body1280valid
8.0ms24×body640valid
5.0ms21×body320valid
3.0ms17×body160valid

simplify43.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0278
1688
22438
312668
450018

prune4.0ms

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: 23.0b

Counts
2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (cos (* 2.0 x)) (* (pow c 2.0) (* (* x (pow s 2.0)) x)))
3.1b
(* (* x (pow s 2.0)) x)
4.7b
(* x (pow s 2.0))
16.1b
(* (pow c 2.0) (* (* x (pow s 2.0)) x))

rewrite41.0ms

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:
11.0ms
(/ (cos (* 2.0 x)) (* (pow c 2.0) (* (* x (pow s 2.0)) x)))
6.0ms
(* (* x (pow s 2.0)) x)
5.0ms
(* x (pow s 2.0))
14.0ms
(* (pow c 2.0) (* (* x (pow s 2.0)) x))

series222.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(/ (cos (* 2.0 x)) (* (pow c 2.0) (* (* x (pow s 2.0)) x)))
31.0ms
(* (* x (pow s 2.0)) x)
30.0ms
(* x (pow s 2.0))
83.0ms
(* (pow c 2.0) (* (* x (pow s 2.0)) x))

simplify66.0ms

Algorithm
egg-herbie
Counts
127 → 127
Iterations

Useful iterations: 2 (55.0ms)

IterNodesCost
05711041
12506875
25001871

prune247.0ms

Filtered
127 candidates to 70 candidates (44.9%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1189127
Fresh000
Picked101
Done000
Total1199128

Merged error: 13.0b

Counts
128 → 9

localize18.0ms

Local error

Found 4 expressions with local error:

3.1b
(* (* x (pow s 2.0)) x)
4.4b
(* (pow c (/ 2.0 2)) (* (pow c (/ 2.0 2)) (* (* x (pow s 2.0)) x)))
4.7b
(* x (pow s 2.0))
7.0b
(* (pow c (/ 2.0 2)) (* (* x (pow s 2.0)) x))

rewrite41.0ms

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:
6.0ms
(* (* x (pow s 2.0)) x)
13.0ms
(* (pow c (/ 2.0 2)) (* (pow c (/ 2.0 2)) (* (* x (pow s 2.0)) x)))
5.0ms
(* x (pow s 2.0))
9.0ms
(* (pow c (/ 2.0 2)) (* (* x (pow s 2.0)) x))

series224.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(* (* x (pow s 2.0)) x)
80.0ms
(* (pow c (/ 2.0 2)) (* (pow c (/ 2.0 2)) (* (* x (pow s 2.0)) x)))
30.0ms
(* x (pow s 2.0))
82.0ms
(* (pow c (/ 2.0 2)) (* (* x (pow s 2.0)) x))

simplify77.0ms

Algorithm
egg-herbie
Counts
158 → 158
Iterations

Useful iterations: 2 (61.0ms)

IterNodesCost
06081377
124511164
250011160

prune280.0ms

Filtered
158 candidates to 69 candidates (56.3%)
Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New1517158
Fresh178
Picked101
Done000
Total15314167

Merged error: 10.1b

Counts
167 → 14

localize17.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (cos (* 2.0 x)) (* (pow c (/ 2.0 2)) (* (pow c (/ 2.0 2)) (* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x))))
3.1b
(* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x)
4.4b
(* (pow c (/ 2.0 2)) (* (pow c (/ 2.0 2)) (* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x)))
7.0b
(* (pow c (/ 2.0 2)) (* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x))

rewrite110.0ms

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:
24.0ms
(/ (cos (* 2.0 x)) (* (pow c (/ 2.0 2)) (* (pow c (/ 2.0 2)) (* (* (* 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)
17.0ms
(* (pow c (/ 2.0 2)) (* (pow c (/ 2.0 2)) (* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x)))
14.0ms
(* (pow c (/ 2.0 2)) (* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x))

series268.0ms

Counts
4 → 12
Calls
4 calls:
74.0ms
(/ (cos (* 2.0 x)) (* (pow c (/ 2.0 2)) (* (pow c (/ 2.0 2)) (* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x))))
34.0ms
(* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x)
78.0ms
(* (pow c (/ 2.0 2)) (* (pow c (/ 2.0 2)) (* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x)))
82.0ms
(* (pow c (/ 2.0 2)) (* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x))

simplify141.0ms

Algorithm
egg-herbie
Counts
406 → 406
Iterations

Useful iterations: 2 (86.0ms)

IterNodesCost
09806240
136934690
250034512

prune309.0ms

Filtered
406 candidates to 71 candidates (82.5%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New4006406
Fresh8513
Picked101
Done000
Total40911420

Merged error: 2.6b

Counts
420 → 11

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b
(cos (* 2.0 x))
0.4b
(/ (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)))))))
5.8b
(* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))
5.8b
(* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
61×add-exp-log
43×prod-exp
19×add-cbrt-cube
14×pow-to-exp associate-*l* pow-exp
10×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
7×cbrt-unprod
6×unpow-prod-down
4×pow1 add-log-exp
3×times-frac associate-/l*
2×cbrt-undiv div-exp associate-*r* *-commutative sqr-pow
1×frac-2neg clear-num associate-/r* div-inv
Counts
4 → 88
Calls
4 calls:
2.0ms
(cos (* 2.0 x))
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)))))))
9.0ms
(* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))
7.0ms
(* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))

series180.0ms

Counts
4 → 12
Calls
4 calls:
2.0ms
(cos (* 2.0 x))
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)))))))
68.0ms
(* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))
66.0ms
(* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))

simplify47.0ms

Algorithm
egg-herbie
Counts
100 → 100
Iterations

Useful iterations: 1 (10.0ms)

IterNodesCost
03861139
11267954
25001954

prune270.0ms

Filtered
100 candidates to 62 candidates (38.0%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New928100
Fresh6410
Picked101
Done000
Total9912111

Merged error: 0.3b

Counts
111 → 12

regimes443.0ms

Accuracy

0% (2.7b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01910
11910

end0.0ms

sample2.3s

Algorithm
intervals
Results
846.0ms8106×body80valid
439.0ms897×body1280valid
374.0ms1083×body640valid
167.0ms652×body320valid
61.0ms352×body160valid

Profiling

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