Details

analyze236.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
75%	25%	0%	4
75%	25%	0%	5
75%	25%	0%	6
78.1%	21.9%	0%	7
78.1%	21.9%	0%	8
78.1%	21.9%	0%	9
78.1%	21.9%	0%	10
78.1%	21.9%	0%	11
78.1%	21.9%	0%	12
78.1%	21.9%	0%	13
78.1%	21.8%	0%	14

sample71.0ms

Algorithm

intervals

Results

41.0ms	71×	body	2560	valid
9.0ms	34×	body	1280	valid
7.0ms	45×	body	640	valid
4.0ms	29×	body	320	valid
2.0ms	67×	body	80	valid
1.0ms	10×	body	160	valid

simplify25.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	500	8
1	500	8

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: 34.8b

Counts

2 → 1

localize5.0ms

Local error

Found 2 expressions with local error:

1.6b	(-.f64 1.0 (cos.f64 x))
19.9b	(/.f64 (-.f64 1.0 (cos.f64 x)) (*.f64 x x))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
7×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`associate-/l*_binary64` `times-frac_binary64`
4×	`add-log-exp_binary64` `add-cube-cbrt_binary64`
3×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
2×	`associate-/l/_binary64` `pow1_binary64` `flip3--_binary64` `cbrt-undiv_binary64` `div-exp_binary64` `flip--_binary64`
1×	`associate-/r*_binary64` `sub-neg_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `div-sub_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-inv_binary64`

Counts

2 → 41

Calls

2 calls:

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

series10.0ms

Counts

2 → 6

Calls

2 calls:

3.0ms	(-.f64 1.0 (cos.f64 x))
7.0ms	(/.f64 (-.f64 1.0 (cos.f64 x)) (*.f64 x x))

simplify54.0ms

Algorithm

egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4894	437
1	4894	437

prune73.0ms

Filtered

34 candidates to 47 candidates (-38.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	37	10	47
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	38	10	48

Merged error: 0.0b

Counts

48 → 10

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b	(*.f64 (pow.f64 x 4) 1/720)
0.2b	(.f64 (.f64 x x) 1/24)
13.0b	(+.f64 (.f64 (pow.f64 x 4) 1/720) (-.f64 1/2 (.f64 (*.f64 x x) 1/24)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-exp-log_binary64` `add-sqr-sqrt_binary64`
10×	`add-cbrt-cube_binary64`
8×	`add-log-exp_binary64` `pow1_binary64` `associate-l_binary64`
7×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
6×	`associate-r_binary64` `prod-exp_binary64`
4×	`cbrt-unprod_binary64` `unswap-sqr_binary64` `unpow-prod-down_binary64`
3×	`pow-prod-down_binary64`
2×	`sqr-pow_binary64` `sum-log_binary64` `*-commutative_binary64`
1×	`pow-to-exp_binary64` `flip3-+_binary64` `sub-neg_binary64` `associate-+r-_binary64` `diff-log_binary64` `+-commutative_binary64` `flip-+_binary64` `associate-+r+_binary64` `pow-exp_binary64`

Counts

3 → 58

Calls

3 calls:

5.0ms	(*.f64 (pow.f64 x 4) 1/720)
6.0ms	(.f64 (.f64 x x) 1/24)
7.0ms	(+.f64 (.f64 (pow.f64 x 4) 1/720) (-.f64 1/2 (.f64 (*.f64 x x) 1/24)))

series15.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(*.f64 (pow.f64 x 4) 1/720)
4.0ms	(.f64 (.f64 x x) 1/24)
6.0ms	(+.f64 (.f64 (pow.f64 x 4) 1/720) (-.f64 1/2 (.f64 (*.f64 x x) 1/24)))

simplify30.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5259	575

prune68.0ms

Filtered

42 candidates to 67 candidates (-59.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	67	0	67
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	67	10	77

Merged error: 0.0b

Counts

77 → 10

localize7.0ms

Local error

Found 3 expressions with local error:

0.1b	(*.f64 (/.f64 1 x) (/.f64 (-.f64 1.0 (cos.f64 x)) x))
0.1b	(/.f64 (-.f64 1.0 (cos.f64 x)) x)
1.6b	(-.f64 1.0 (cos.f64 x))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

62×	`add-sqr-sqrt_binary64`
47×	`*-un-lft-identity_binary64`
46×	`times-frac_binary64`
29×	`add-cube-cbrt_binary64`
27×	`add-exp-log_binary64`
19×	`associate-r_binary64`
17×	`add-cbrt-cube_binary64`
13×	`associate-l_binary64`
9×	`div-exp_binary64`
8×	`prod-exp_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64`
6×	`unswap-sqr_binary64`
5×	`add-log-exp_binary64` `pow1_binary64` `cbrt-undiv_binary64` `associate-/l*_binary64`
4×	`cbrt-unprod_binary64`
3×	`associate-/r*_binary64` `div-inv_binary64`
2×	`associate-/l/_binary64` `flip3--_binary64` `1-exp_binary64` `rec-exp_binary64` `flip--_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `diff-log_binary64` `associate-r/_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `frac-times_binary64` `associate-l/_binary64` `*-commutative_binary64`

Counts

3 → 113

Calls

3 calls:

14.0ms	(*.f64 (/.f64 1 x) (/.f64 (-.f64 1.0 (cos.f64 x)) x))
8.0ms	(/.f64 (-.f64 1.0 (cos.f64 x)) x)
4.0ms	(-.f64 1.0 (cos.f64 x))

series15.0ms

Counts

3 → 9

Calls

3 calls:

6.0ms	(*.f64 (/.f64 1 x) (/.f64 (-.f64 1.0 (cos.f64 x)) x))
6.0ms	(/.f64 (-.f64 1.0 (cos.f64 x)) x)
3.0ms	(-.f64 1.0 (cos.f64 x))

simplify44.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5658	1207

prune118.0ms

Filtered

79 candidates to 122 candidates (-54.4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	119	3	122
Fresh	4	4	8
Picked	0	1	1
Done	0	1	1
Total	123	9	132

Merged error: 0.0b

Counts

132 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (sqrt.f64 (-.f64 1.0 (cos.f64 x))) x)
0.1b	(/.f64 (sqrt.f64 (-.f64 1.0 (cos.f64 x))) x)
1.6b	(-.f64 1.0 (cos.f64 x))
1.6b	(-.f64 1.0 (cos.f64 x))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

58×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
48×	`times-frac_binary64`
40×	`sqrt-prod_binary64`
38×	`add-cube-cbrt_binary64`
16×	`associate-/l*_binary64`
10×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
8×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`associate-/r*_binary64`
4×	`associate-/l/_binary64` `pow1_binary64` `flip3--_binary64` `flip--_binary64` `sqrt-div_binary64`
2×	`sub-neg_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

4 → 124

Calls

4 calls:

7.0ms	(/.f64 (sqrt.f64 (-.f64 1.0 (cos.f64 x))) x)
7.0ms	(/.f64 (sqrt.f64 (-.f64 1.0 (cos.f64 x))) x)
8.0ms	(-.f64 1.0 (cos.f64 x))
8.0ms	(-.f64 1.0 (cos.f64 x))

series28.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(/.f64 (sqrt.f64 (-.f64 1.0 (cos.f64 x))) x)
10.0ms	(/.f64 (sqrt.f64 (-.f64 1.0 (cos.f64 x))) x)
3.0ms	(-.f64 1.0 (cos.f64 x))
5.0ms	(-.f64 1.0 (cos.f64 x))

simplify47.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	4980	1524
1	4980	1524

prune106.0ms

Filtered

92 candidates to 136 candidates (-47.8%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	134	2	136
Fresh	1	5	6
Picked	0	1	1
Done	0	2	2
Total	135	10	145

Merged error: 0.0b

Counts

145 → 10

regimes59.0ms

Accuracy

99.5% (0.1b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 31.5b

bsearch30.0ms

Steps

Iters	Range		Point
9	3.2576454935691815e-07	0.029958914207946503	0.029706365761949148
10	-0.35037948264050944	-3.301560155890433e-12	-0.032035318607155715

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	73	46
1	73	46

end0.0ms

sample1.8s

Algorithm

intervals

Results

832.0ms	1624×	body	2560	valid
351.0ms	1224×	body	1280	valid
240.0ms	1443×	body	640	valid
120.0ms	955×	body	320	valid
87.0ms	2293×	body	80	valid
42.0ms	461×	body	160	valid

Details

analyze236.0ms

sample71.0ms

simplify25.0ms

prune2.0ms

localize5.0ms

rewrite12.0ms

series10.0ms

simplify54.0ms

prune73.0ms

localize10.0ms

rewrite20.0ms

series15.0ms

simplify30.0ms

prune68.0ms

localize7.0ms

rewrite30.0ms

series15.0ms

simplify44.0ms

prune118.0ms

localize13.0ms

rewrite33.0ms

series28.0ms

simplify47.0ms

prune106.0ms

regimes59.0ms

bsearch30.0ms

simplify2.0ms

end0.0ms

sample1.8s

Profiling