Details

analyze516.0ms

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

sample150.0ms

Algorithm

intervals

Results

74.0ms	54×	body	2560	valid
44.0ms	87×	body	1280	valid
17.0ms	67×	body	640	valid
6.0ms	33×	body	320	valid
1.0ms	10×	body	160	valid
0.0ms	5×	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: 31.8b

Counts

2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

0.2b	(/.f64 (-.f64 1.0 (cos.f64 x)) (sin.f64 x))
0.9b	(-.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

prune101.0ms

Filtered

42 candidates to 57 candidates (-35.7%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	42	15	57
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	43	15	58

Merged error: 0.2b

Counts

58 → 15

localize10.0ms

Local error

Found 2 expressions with local error:

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

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64`
19×	`associate-r_binary64`
12×	`add-exp-log_binary64`
9×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
8×	`unpow-prod-down_binary64`
7×	`unswap-sqr_binary64`
6×	`add-cbrt-cube_binary64` `associate-l_binary64` `prod-exp_binary64`
4×	`sqr-pow_binary64` `cube-prod_binary64`
2×	`pow-to-exp_binary64` `add-log-exp_binary64` `pow1_binary64` `cbrt-unprod_binary64` `pow-exp_binary64` `*-commutative_binary64`
1×	`unpow3_binary64` `cube-mult_binary64`

Counts

2 → 56

Calls

2 calls:

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

series14.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify43.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5108	391

prune79.0ms

Filtered

38 candidates to 62 candidates (-63.2%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	62	0	62
Fresh	0	14	14
Picked	0	1	1
Done	0	0	0
Total	62	15	77

Merged error: 0.2b

Counts

77 → 15

localize9.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (-.f64 1.0 (cos.f64 x)) (sin.f64 x))
0.3b	(exp.f64 (/.f64 (-.f64 1.0 (cos.f64 x)) (sin.f64 x)))
0.7b	(log.f64 (exp.f64 (/.f64 (-.f64 1.0 (cos.f64 x)) (sin.f64 x))))
0.9b	(-.f64 1.0 (cos.f64 x))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

55×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
45×	`times-frac_binary64`
38×	`exp-prod_binary64`
33×	`add-cube-cbrt_binary64`
20×	`log-pow_binary64`
11×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
7×	`add-log-exp_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`pow1_binary64` `associate-/l*_binary64`
3×	`associate-/r*_binary64` `log-prod_binary64` `div-sub_binary64` `div-inv_binary64`
2×	`associate-/l/_binary64` `flip3--_binary64` `exp-diff_binary64` `flip--_binary64`
1×	`sub-neg_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `rem-log-exp_binary64` `rem-exp-log_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-exp_binary64` `log-div_binary64`

Counts

4 → 111

Calls

4 calls:

7.0ms	(/.f64 (-.f64 1.0 (cos.f64 x)) (sin.f64 x))
6.0ms	(exp.f64 (/.f64 (-.f64 1.0 (cos.f64 x)) (sin.f64 x)))
7.0ms	(log.f64 (exp.f64 (/.f64 (-.f64 1.0 (cos.f64 x)) (sin.f64 x))))
4.0ms	(-.f64 1.0 (cos.f64 x))

series34.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(/.f64 (-.f64 1.0 (cos.f64 x)) (sin.f64 x))
12.0ms	(exp.f64 (/.f64 (-.f64 1.0 (cos.f64 x)) (sin.f64 x)))
11.0ms	(log.f64 (exp.f64 (/.f64 (-.f64 1.0 (cos.f64 x)) (sin.f64 x))))
3.0ms	(-.f64 1.0 (cos.f64 x))

simplify49.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5525	1215

prune125.0ms

Filtered

88 candidates to 123 candidates (-39.8%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	118	5	123
Fresh	3	10	13
Picked	1	0	1
Done	0	1	1
Total	122	16	138

Merged error: 0.1b

Counts

138 → 16

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (-.f64 (pow.f64 1.0 3) (pow.f64 (cos.f64 x) 3)) (+.f64 (.f64 1.0 1.0) (.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))
0.7b	(-.f64 (pow.f64 1.0 3) (pow.f64 (cos.f64 x) 3))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

157×	`add-sqr-sqrt_binary64`
89×	`*-un-lft-identity_binary64`
80×	`difference-of-squares_binary64`
75×	`times-frac_binary64`
63×	`unpow-prod-down_binary64` `cube-prod_binary64`
41×	`sqr-pow_binary64`
37×	`add-cube-cbrt_binary64`
25×	`associate-/l*_binary64` `distribute-lft-out--_binary64`
8×	`add-log-exp_binary64`
7×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`difference-cubes_binary64` `pow1_binary64`
3×	`pow-unpow_binary64` `associate-/r*_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `flip3--_binary64` `associate-/r/_binary64` `flip--_binary64` `flip-+_binary64`
1×	`pow-to-exp_binary64` `sub-neg_binary64` `diff-log_binary64` `distribute-lft-out_binary64` `cbrt-undiv_binary64` `pow-pow_binary64` `div-sub_binary64` `clear-num_binary64` `rem-cube-cbrt_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `pow-exp_binary64` `unpow3_binary64` `sum-log_binary64` `cube-mult_binary64`

Counts

4 → 188

Calls

4 calls:

19.0ms	(/.f64 (-.f64 (pow.f64 1.0 3) (pow.f64 (cos.f64 x) 3)) (+.f64 (.f64 1.0 1.0) (.f64 (cos.f64 x) (+.f64 1.0 (cos.f64 x)))))
3.0ms	(pow.f64 (cos.f64 x) 3)
4.0ms	(+.f64 1.0 (cos.f64 x))
11.0ms	(-.f64 (pow.f64 1.0 3) (pow.f64 (cos.f64 x) 3))

series51.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(/.f64 (-.f64 (pow.f64 1.0 3) (pow.f64 (cos.f64 x) 3)) (+.f64 (.f64 1.0 1.0) (.f64 (cos.f64 x) (+.f64 1.0 (cos.f64 x)))))
6.0ms	(pow.f64 (cos.f64 x) 3)
2.0ms	(+.f64 1.0 (cos.f64 x))
9.0ms	(-.f64 (pow.f64 1.0 3) (pow.f64 (cos.f64 x) 3))

simplify52.0ms

Algorithm

egg-herbie

Counts

200 → 200

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5200	4897

prune188.0ms

Filtered

105 candidates to 200 candidates (-90.5%)

Pruning

19 alts after pruning (18 fresh and 1 done)

	Pruned	Kept	Total
New	192	8	200
Fresh	4	10	14
Picked	1	0	1
Done	0	1	1
Total	197	19	216

Merged error: 0.1b

Counts

216 → 19

regimes200.0ms

Accuracy

98% (0.6b remaining)

Error of 0.8b against oracle of 0.2b and baseline of 31.6b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	63	69
1	63	69

end0.0ms

sample4.6s

Algorithm

intervals

Results

2.3s	1611×	body	2560	valid
1.4s	2796×	body	1280	valid
489.0ms	1853×	body	640	valid
172.0ms	936×	body	320	valid
58.0ms	469×	body	160	valid
30.0ms	5×	body	5120	valid
24.0ms	330×	body	80	valid

Details

analyze516.0ms

sample150.0ms

simplify14.0ms

prune2.0ms

localize7.0ms

rewrite12.0ms

series13.0ms

simplify42.0ms

prune101.0ms

localize10.0ms

rewrite13.0ms

series14.0ms

simplify43.0ms

prune79.0ms

localize9.0ms

rewrite28.0ms

series34.0ms

simplify49.0ms

prune125.0ms

localize16.0ms

rewrite46.0ms

series51.0ms

simplify52.0ms

prune188.0ms

regimes200.0ms

bsearch1.0ms

simplify2.0ms

end0.0ms

sample4.6s

Profiling