Details

Time bar (total: 5.4s)

sample85.0ms

Algorithm
intervals
Results
24.0ms303×body80valid
22.0ms41×body1280valid
11.0ms37×body640valid
4.0ms19×body320valid
2.0ms11×body160valid

simplify40.0ms

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: 28.1b

Counts
2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

0.7b
(/ (cos (* 2.0 x)) (* (pow c 2.0) (* (* x (pow s 2.0)) x)))
3.8b
(* (* x (pow s 2.0)) x)
10.7b
(* x (pow s 2.0))
17.8b
(* (pow c 2.0) (* (* x (pow s 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 c 2.0) (* (* x (pow s 2.0)) x)))
5.0ms
(* (* x (pow s 2.0)) x)
5.0ms
(* x (pow s 2.0))
9.0ms
(* (pow c 2.0) (* (* x (pow s 2.0)) x))

series222.0ms

Counts
4 → 12
Calls
4 calls:
76.0ms
(/ (cos (* 2.0 x)) (* (pow c 2.0) (* (* x (pow s 2.0)) x)))
33.0ms
(* (* x (pow s 2.0)) x)
30.0ms
(* x (pow s 2.0))
82.0ms
(* (pow c 2.0) (* (* x (pow s 2.0)) x))

simplify65.0ms

Algorithm
egg-herbie
Counts
127 → 127
Iterations

Useful iterations: 2 (54.0ms)

IterNodesCost
05711041
12506875
25001871

prune248.0ms

Filtered
127 candidates to 70 candidates (44.9%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New11611127
Fresh000
Picked101
Done000
Total11711128

Merged error: 13.6b

Counts
128 → 11

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2)))
0.7b
(/ (cos (* 2.0 x)) (* (pow c 2.0) (* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x)))
3.8b
(* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x)
17.8b
(* (pow c 2.0) (* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x))

rewrite57.0ms

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:
9.0ms
(* (* 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)))
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))

series221.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2)))
77.0ms
(/ (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)
83.0ms
(* (pow c 2.0) (* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x))

simplify95.0ms

Algorithm
egg-herbie
Counts
198 → 198
Iterations

Useful iterations: 2 (72.0ms)

IterNodesCost
07212340
132341837
250011781

prune252.0ms

Filtered
198 candidates to 68 candidates (65.7%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New1917198
Fresh6410
Picked101
Done000
Total19811209

Merged error: 2.6b

Counts
209 → 11

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))))))
0.7b
(/ (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)))))))
3.7b
(* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))
3.7b
(* (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))))

series193.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(* (fabs (* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))) (fabs (* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))))
45.0ms
(/ (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))))
68.0ms
(* (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

prune381.0ms

Filtered
118 candidates to 69 candidates (41.5%)
Pruning

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New10810118
Fresh5510
Picked101
Done000
Total11415129

Merged error: 0.1b

Counts
129 → 15

localize17.0ms

Local error

Found 4 expressions with local error:

0.8b
(/ 1 (fabs (* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))))
0.8b
(/ (cos (* 2.0 x)) (fabs (* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))))
3.7b
(* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))
3.7b
(* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
62×add-exp-log
42×prod-exp
24×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
18×times-frac add-cbrt-cube
14×pow-to-exp associate-*l* pow-exp
6×unpow-prod-down associate-/r* cbrt-unprod associate-/l*
5×pow1
4×add-log-exp
3×div-exp
2×cbrt-undiv frac-2neg associate-*r* clear-num *-commutative div-inv sqr-pow
1×rec-exp pow-flip 1-exp inv-pow
Counts
4 → 118
Calls
4 calls:
3.0ms
(/ 1 (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))))

series179.0ms

Counts
4 → 12
Calls
4 calls:
17.0ms
(/ 1 (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))))))
65.0ms
(* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))
68.0ms
(* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))

simplify50.0ms

Algorithm
egg-herbie
Counts
130 → 130
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
04131459
114051311
250021297

prune350.0ms

Filtered
130 candidates to 76 candidates (41.5%)
Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New1246130
Fresh7714
Picked101
Done000
Total13213145

Merged error: 0.1b

Counts
145 → 13

regimes500.0ms

Accuracy

10.3% (2.1b remaining)

Error of 2.3b against oracle of 0.1b and baseline of 2.5b

bsearch190.0ms

Steps
ItersRangePoint
10
1.0022054548372538e-276
1.3555215139444704e-263
3.5729429666998667e-270
9
-9.660865120865964e-152
-1.01488138848425e-156
-1.8687719630024611e-152

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04539
14539

end0.0ms

sample2.0s

Algorithm
intervals
Results
722.0ms8997×body80valid
354.0ms786×body1280valid
306.0ms954×body640valid
133.0ms556×body320valid
55.0ms326×body160valid

Profiling

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