Details

analyze496.0ms

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

sample155.0ms

Algorithm

intervals

Results

81.0ms	58×	body	2560	valid
41.0ms	78×	body	1280	valid
19.0ms	76×	body	640	valid
5.0ms	26×	body	320	valid
1.0ms	10×	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: 32.1b

Counts

2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

0.1b	(/.f64 (-.f64 1.0 (cos.f64 x)) (sin.f64 x))
0.8b	(-.f64 1.0 (cos.f64 x))

rewrite13.0ms

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:

7.0ms	(/.f64 (-.f64 1.0 (cos.f64 x)) (sin.f64 x))
4.0ms	(-.f64 1.0 (cos.f64 x))

series14.0ms

Counts

2 → 6

Calls

2 calls:

10.0ms	(/.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

prune92.0ms

Filtered

42 candidates to 57 candidates (-35.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	46	11	57
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	47	11	58

Merged error: 0.2b

Counts

58 → 11

localize11.0ms

Local error

Found 3 expressions with local error:

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))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 69

Calls

3 calls:

10.0ms	(+.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))
7.0ms	(*.f64 1/24 (pow.f64 x 3))

series24.0ms

Counts

3 → 9

Calls

3 calls:

8.0ms	(+.f64 (.f64 1/24 (pow.f64 x 3)) (+.f64 (.f64 1/240 (pow.f64 x 5)) (*.f64 x 1/2)))
10.0ms	(*.f64 1/240 (pow.f64 x 5))
6.0ms	(*.f64 1/24 (pow.f64 x 3))

simplify49.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5093	700

prune91.0ms

Filtered

50 candidates to 78 candidates (-56.0%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	78	0	78
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	78	11	89

Merged error: 0.2b

Counts

89 → 11

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (cos.f64 x) (+.f64 1.0 (cos.f64 x)))
0.3b	(pow.f64 (cos.f64 x) 3)
0.4b	(+.f64 1.0 (cos.f64 x))
0.6b	(-.f64 (pow.f64 1.0 3) (pow.f64 (cos.f64 x) 3))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt_binary64`
23×	`*-un-lft-identity_binary64`
16×	`difference-of-squares_binary64`
15×	`unpow-prod-down_binary64` `cube-prod_binary64`
9×	`add-cube-cbrt_binary64` `sqr-pow_binary64`
8×	`add-log-exp_binary64`
7×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`distribute-lft-out--_binary64`
4×	`associate-r_binary64`
3×	`pow-unpow_binary64` `associate-l_binary64`
2×	`flip3-+_binary64` `distribute-lft-out_binary64` `associate-*r/_binary64` `flip-+_binary64`
1×	`pow-to-exp_binary64` `pow-prod-down_binary64` `difference-cubes_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `pow-pow_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `rem-cube-cbrt_binary64` `prod-exp_binary64` `+-commutative_binary64` `flip--_binary64` `pow-exp_binary64` `unpow3_binary64` `sum-log_binary64` `*-commutative_binary64` `cube-mult_binary64`

Counts

4 → 91

Calls

4 calls:

7.0ms	(*.f64 (cos.f64 x) (+.f64 1.0 (cos.f64 x)))
3.0ms	(pow.f64 (cos.f64 x) 3)
5.0ms	(+.f64 1.0 (cos.f64 x))
13.0ms	(-.f64 (pow.f64 1.0 3) (pow.f64 (cos.f64 x) 3))

series26.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(*.f64 (cos.f64 x) (+.f64 1.0 (cos.f64 x)))
7.0ms	(pow.f64 (cos.f64 x) 3)
2.0ms	(+.f64 1.0 (cos.f64 x))
10.0ms	(-.f64 (pow.f64 1.0 3) (pow.f64 (cos.f64 x) 3))

simplify58.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5011	963

prune121.0ms

Filtered

61 candidates to 103 candidates (-68.9%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	97	6	103
Fresh	2	7	9
Picked	1	0	1
Done	0	1	1
Total	100	14	114

Merged error: 0.2b

Counts

114 → 14

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow.f64 (cos.f64 x) 3)
0.4b	(+.f64 1.0 (cos.f64 x))
0.6b	(-.f64 (pow.f64 1.0 3) (log.f64 (exp.f64 (pow.f64 (cos.f64 x) 3))))
0.8b	(log.f64 (exp.f64 (pow.f64 (cos.f64 x) 3)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt_binary64`
17×	`*-un-lft-identity_binary64`
14×	`log-pow_binary64`
12×	`add-cube-cbrt_binary64` `exp-prod_binary64`
7×	`add-log-exp_binary64` `pow1_binary64` `unpow-prod-down_binary64` `cube-prod_binary64`
6×	`log-prod_binary64`
5×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`difference-of-squares_binary64`
3×	`pow-unpow_binary64` `associate--r+_binary64` `sqr-pow_binary64`
2×	`distribute-lft-out--_binary64` `unpow3_binary64` `cube-mult_binary64`
1×	`pow-to-exp_binary64` `flip3-+_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `distribute-lft-out_binary64` `rem-log-exp_binary64` `pow-pow_binary64` `rem-cube-cbrt_binary64` `+-commutative_binary64` `flip--_binary64` `flip-+_binary64` `pow-exp_binary64` `sum-log_binary64`

Counts

4 → 79

Calls

4 calls:

3.0ms	(pow.f64 (cos.f64 x) 3)
4.0ms	(+.f64 1.0 (cos.f64 x))
18.0ms	(-.f64 (pow.f64 1.0 3) (log.f64 (exp.f64 (pow.f64 (cos.f64 x) 3))))
5.0ms	(log.f64 (exp.f64 (pow.f64 (cos.f64 x) 3)))

series28.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(pow.f64 (cos.f64 x) 3)
2.0ms	(+.f64 1.0 (cos.f64 x))
10.0ms	(-.f64 (pow.f64 1.0 3) (log.f64 (exp.f64 (pow.f64 (cos.f64 x) 3))))
8.0ms	(log.f64 (exp.f64 (pow.f64 (cos.f64 x) 3)))

simplify50.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5204	653

prune90.0ms

Filtered

61 candidates to 91 candidates (-49.2%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	87	4	91
Fresh	1	11	12
Picked	1	0	1
Done	0	1	1
Total	89	16	105

Merged error: 0.1b

Counts

105 → 16

regimes159.0ms

Accuracy

98.9% (0.3b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 31.6b

bsearch34.0ms

Steps

Iters	Range		Point
10	6.515877835829287e-05	18669351.880964175	0.0237498496172468
7	-0.027740174261797323	-0.001582594379722933	-0.02393634628213539

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	81	89
1	81	89

end0.0ms

sample4.5s

Algorithm

intervals

Results

2.3s	1619×	body	2560	valid
1.4s	2822×	body	1280	valid
459.0ms	1824×	body	640	valid
153.0ms	882×	body	320	valid
57.0ms	476×	body	160	valid
41.0ms	9×	body	5120	valid
26.0ms	368×	body	80	valid

Details

analyze496.0ms

sample155.0ms

simplify14.0ms

prune2.0ms

localize7.0ms

rewrite13.0ms

series14.0ms

simplify42.0ms

prune92.0ms

localize11.0ms

rewrite26.0ms

series24.0ms

simplify49.0ms

prune91.0ms

localize17.0ms

rewrite32.0ms

series26.0ms

simplify58.0ms

prune121.0ms

localize19.0ms

rewrite33.0ms

series28.0ms

simplify50.0ms

prune90.0ms

regimes159.0ms

bsearch34.0ms

simplify2.0ms

end0.0ms

sample4.5s

Profiling