Details

analyze524.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
37.5%	62.5%	0%	4
43.7%	56.2%	0%	5
46.9%	53.1%	0%	6
48.4%	51.5%	0%	7
49.2%	50.8%	0%	8
49.6%	50.4%	0%	9
49.8%	50.2%	0%	10
49.9%	50.1%	0%	11
49.9%	50%	0%	12
50%	50%	0%	13
50%	49.9%	0%	14

sample149.0ms

Algorithm

intervals

Results

85.0ms	71×	body	2560	valid
32.0ms	62×	body	1280	valid
16.0ms	65×	body	640	valid
5.0ms	30×	body	320	valid
2.0ms	20×	body	160	valid
1.0ms	8×	body	80	valid

simplify14.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (12.0ms)

Iter	Nodes	Cost
0	229	7
1	229	7

prune2.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 32.7b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

0.1b	(/.f64 (-.f64 1.0 (cos.f64 x)) (sin.f64 x))
2.3b	(-.f64 1.0 (cos.f64 x))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
15×	`times-frac_binary64`
12×	`add-cube-cbrt_binary64`
5×	`difference-of-squares_binary64` `associate-/l*_binary64` `distribute-lft-out--_binary64`
4×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`associate-/r*_binary64`
2×	`associate-/l/_binary64` `pow1_binary64` `flip3--_binary64` `flip--_binary64`
1×	`sub-neg_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

2 → 51

Calls

2 calls:

6.0ms	(/.f64 (-.f64 1.0 (cos.f64 x)) (sin.f64 x))
4.0ms	(-.f64 1.0 (cos.f64 x))

series13.0ms

Counts

2 → 6

Calls

2 calls:

9.0ms	(/.f64 (-.f64 1.0 (cos.f64 x)) (sin.f64 x))
4.0ms	(-.f64 1.0 (cos.f64 x))

simplify42.0ms

Algorithm

egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5058	605

prune100.0ms

Filtered

42 candidates to 57 candidates (-35.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	45	12	57
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	46	12	58

Merged error: 0.1b

Counts

58 → 12

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 1/240 (pow.f64 x 5)) (.f64 x 1/2))
0.0b	(+.f64 (.f64 1/24 (pow.f64 x 3)) (+.f64 (.f64 1/240 (pow.f64 x 5)) (*.f64 x 1/2)))
0.1b	(*.f64 1/240 (pow.f64 x 5))
0.1b	(*.f64 1/24 (pow.f64 x 3))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64`
19×	`associate-r_binary64`
14×	`add-exp-log_binary64`
11×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `add-cube-cbrt_binary64`
8×	`add-cbrt-cube_binary64` `unpow-prod-down_binary64`
7×	`unswap-sqr_binary64`
6×	`associate-l_binary64` `prod-exp_binary64`
4×	`pow1_binary64` `sqr-pow_binary64` `cube-prod_binary64` `sum-log_binary64`
2×	`pow-to-exp_binary64` `flip3-+_binary64` `cbrt-unprod_binary64` `+-commutative_binary64` `flip-+_binary64` `pow-exp_binary64` `*-commutative_binary64`
1×	`associate-+r+_binary64` `unpow3_binary64` `cube-mult_binary64`

Counts

4 → 80

Calls

4 calls:

5.0ms	(+.f64 (.f64 1/240 (pow.f64 x 5)) (.f64 x 1/2))
9.0ms	(+.f64 (.f64 1/24 (pow.f64 x 3)) (+.f64 (.f64 1/240 (pow.f64 x 5)) (*.f64 x 1/2)))
5.0ms	(*.f64 1/240 (pow.f64 x 5))
9.0ms	(*.f64 1/24 (pow.f64 x 3))

series38.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(+.f64 (.f64 1/240 (pow.f64 x 5)) (.f64 x 1/2))
8.0ms	(+.f64 (.f64 1/24 (pow.f64 x 3)) (+.f64 (.f64 1/240 (pow.f64 x 5)) (*.f64 x 1/2)))
6.0ms	(*.f64 1/240 (pow.f64 x 5))
5.0ms	(*.f64 1/24 (pow.f64 x 3))

simplify52.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5066	875

prune107.0ms

Filtered

59 candidates to 92 candidates (-55.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	91	1	92
Fresh	0	11	11
Picked	1	0	1
Done	0	0	0
Total	92	12	104

Merged error: 0.1b

Counts

104 → 12

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (+.f64 (.f64 1/24 (pow.f64 x 3)) (.f64 1/240 (pow.f64 x 5))) (*.f64 x 1/2))
0.0b	(+.f64 (.f64 1/24 (pow.f64 x 3)) (.f64 1/240 (pow.f64 x 5)))
0.1b	(*.f64 1/240 (pow.f64 x 5))
0.1b	(*.f64 1/24 (pow.f64 x 3))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64`
19×	`associate-r_binary64`
14×	`add-exp-log_binary64`
11×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `add-cube-cbrt_binary64`
8×	`add-cbrt-cube_binary64` `unpow-prod-down_binary64`
7×	`unswap-sqr_binary64`
6×	`associate-l_binary64` `prod-exp_binary64`
4×	`pow1_binary64` `sqr-pow_binary64` `cube-prod_binary64` `sum-log_binary64`
2×	`pow-to-exp_binary64` `flip3-+_binary64` `cbrt-unprod_binary64` `+-commutative_binary64` `flip-+_binary64` `pow-exp_binary64` `*-commutative_binary64`
1×	`associate-+l+_binary64` `unpow3_binary64` `cube-mult_binary64`

Counts

4 → 80

Calls

4 calls:

9.0ms	(+.f64 (+.f64 (.f64 1/24 (pow.f64 x 3)) (.f64 1/240 (pow.f64 x 5))) (*.f64 x 1/2))
7.0ms	(+.f64 (.f64 1/24 (pow.f64 x 3)) (.f64 1/240 (pow.f64 x 5)))
5.0ms	(*.f64 1/240 (pow.f64 x 5))
6.0ms	(*.f64 1/24 (pow.f64 x 3))

series38.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(+.f64 (+.f64 (.f64 1/24 (pow.f64 x 3)) (.f64 1/240 (pow.f64 x 5))) (*.f64 x 1/2))
18.0ms	(+.f64 (.f64 1/24 (pow.f64 x 3)) (.f64 1/240 (pow.f64 x 5)))
7.0ms	(*.f64 1/240 (pow.f64 x 5))
5.0ms	(*.f64 1/24 (pow.f64 x 3))

simplify51.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5104	909

prune105.0ms

Filtered

59 candidates to 92 candidates (-55.9%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	92	0	92
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	92	12	104

Merged error: 0.1b

Counts

104 → 12

localize8.0ms

Local error

Found 3 expressions with local error:

0.1b	(/.f64 1 (sin.f64 x))
0.2b	(*.f64 (-.f64 1.0 (cos.f64 x)) (/.f64 1 (sin.f64 x)))
2.3b	(-.f64 1.0 (cos.f64 x))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt_binary64`
24×	`*-un-lft-identity_binary64`
20×	`times-frac_binary64`
19×	`add-cube-cbrt_binary64`
16×	`add-exp-log_binary64`
13×	`associate-r_binary64`
10×	`add-cbrt-cube_binary64`
6×	`pow1_binary64`
5×	`add-log-exp_binary64` `associate-l_binary64`
4×	`prod-exp_binary64` `div-exp_binary64`
3×	`associate-/r_binary64` `flip3--_binary64` `unswap-sqr_binary64` `associate-/l_binary64` `flip--_binary64`
2×	`cbrt-unprod_binary64` `1-exp_binary64` `cbrt-undiv_binary64` `difference-of-squares_binary64` `rec-exp_binary64` `distribute-lft-out--_binary64` `div-inv_binary64` `frac-times_binary64` `associate-*l/_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `diff-log_binary64` `associate-r/_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `un-div-inv_binary64` `pow-flip_binary64` `-commutative_binary64`

Counts

3 → 86

Calls

3 calls:

4.0ms	(/.f64 1 (sin.f64 x))
10.0ms	(*.f64 (-.f64 1.0 (cos.f64 x)) (/.f64 1 (sin.f64 x)))
4.0ms	(-.f64 1.0 (cos.f64 x))

series20.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(/.f64 1 (sin.f64 x))
11.0ms	(*.f64 (-.f64 1.0 (cos.f64 x)) (/.f64 1 (sin.f64 x)))
3.0ms	(-.f64 1.0 (cos.f64 x))

simplify46.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5161	778

prune64.0ms

Filtered

58 candidates to 95 candidates (-63.8%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	92	3	95
Fresh	2	8	10
Picked	1	0	1
Done	0	1	1
Total	95	12	107

Merged error: 0.1b

Counts

107 → 12

regimes125.0ms

Accuracy

98.8% (0.4b remaining)

Error of 0.6b against oracle of 0.2b and baseline of 31.4b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	62	67
1	62	67

end0.0ms

sample4.6s

Algorithm

intervals

Results

2.4s	1692×	body	2560	valid
1.3s	2666×	body	1280	valid
482.0ms	1834×	body	640	valid
175.0ms	982×	body	320	valid
56.0ms	465×	body	160	valid
26.0ms	357×	body	80	valid
19.0ms	4×	body	5120	valid

Details

analyze524.0ms

sample149.0ms

simplify14.0ms

prune2.0ms

localize6.0ms

rewrite12.0ms

series13.0ms

simplify42.0ms

prune100.0ms

localize10.0ms

rewrite31.0ms

series38.0ms

simplify52.0ms

prune107.0ms

localize10.0ms

rewrite30.0ms

series38.0ms

simplify51.0ms

prune105.0ms

localize8.0ms

rewrite21.0ms

series20.0ms

simplify46.0ms

prune64.0ms

regimes125.0ms

bsearch1.0ms

simplify2.0ms

end0.0ms

sample4.6s

Profiling