Details

analyze773.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
50%	50%	0.1%	4
74.9%	25%	0.1%	5
74.9%	25%	0.1%	6
74.9%	25%	0.1%	7
74.9%	25%	0.1%	8
74.9%	25%	0.1%	9
74.9%	25%	0.1%	10
74.9%	25%	0.1%	11
74.9%	25%	0.1%	12
74.9%	25%	0.1%	13
74.9%	25%	0.1%	14

sample212.0ms

Algorithm

intervals

Results

114.0ms	84×	body	1280	valid
54.0ms	60×	body	640	valid
15.0ms	79×	body	80	valid
15.0ms	23×	body	320	valid
4.0ms	10×	body	160	valid

simplify60.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4925	77
1	4925	77

prune8.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 0.4b

Counts

2 → 2

localize32.0ms

Local error

Found 4 expressions with local error:

0.4b	(*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))
0.7b	(.f64 3/2 (.f64 (cos.f64 x) (-.f64 (sqrt.f64 5) 1)))
1.0b	(-.f64 3 (sqrt.f64 5))
2.9b	(-.f64 (cos.f64 x) (cos.f64 y))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64`
14×	`*-un-lft-identity_binary64`
11×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`associate-l_binary64`
8×	`add-log-exp_binary64` `sub-neg_binary64` `add-cube-cbrt_binary64`
7×	`associate-r_binary64`
6×	`associate-*r/_binary64`
5×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64` `difference-of-squares_binary64` `sqrt-prod_binary64`
4×	`pow-prod-down_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `prod-exp_binary64` `flip--_binary64`
3×	`distribute-lft-out--_binary64`
2×	`diff-log_binary64` `unswap-sqr_binary64` `*-commutative_binary64`
1×	`times-frac_binary64` `diff-cos_binary64`

Counts

4 → 81

Calls

4 calls:

12.0ms	(*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))
10.0ms	(.f64 3/2 (.f64 (cos.f64 x) (-.f64 (sqrt.f64 5) 1)))
5.0ms	(-.f64 3 (sqrt.f64 5))
7.0ms	(-.f64 (cos.f64 x) (cos.f64 y))

series146.0ms

Counts

4 → 10

Calls

4 calls:

61.0ms	(*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))
44.0ms	(.f64 3/2 (.f64 (cos.f64 x) (-.f64 (sqrt.f64 5) 1)))
0.0ms	(-.f64 3 (sqrt.f64 5))
41.0ms	(-.f64 (cos.f64 x) (cos.f64 y))

simplify86.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	5155	1546

prune197.0ms

Filtered

62 candidates to 91 candidates (-46.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	83	8	91
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	84	9	93

Merged error: 0.1b

Counts

93 → 9

localize36.0ms

Local error

Found 4 expressions with local error:

0.3b	(+.f64 (.f64 (cos.f64 y) (.f64 3/2 (/.f64 4 (+.f64 3 (sqrt.f64 5))))) (.f64 3/2 (.f64 (cos.f64 x) (-.f64 (sqrt.f64 5) 1))))
0.4b	(*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))
0.7b	(.f64 3/2 (.f64 (cos.f64 x) (-.f64 (sqrt.f64 5) 1)))
2.9b	(-.f64 (cos.f64 x) (cos.f64 y))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt_binary64`
14×	`associate-*r/_binary64`
12×	`*-un-lft-identity_binary64`
11×	`sub-neg_binary64` `pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`distribute-lft-in_binary64` `associate-l_binary64` `distribute-rgt-in_binary64`
8×	`add-log-exp_binary64` `add-cube-cbrt_binary64`
7×	`associate-r_binary64`
4×	`pow-prod-down_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `prod-exp_binary64` `flip--_binary64` `sqrt-prod_binary64` `associate-+r+_binary64`
3×	`difference-of-squares_binary64`
2×	`frac-add_binary64` `unswap-sqr_binary64` `distribute-lft-out--_binary64` `*-commutative_binary64`
1×	`flip3-+_binary64` `diff-log_binary64` `times-frac_binary64` `+-commutative_binary64` `flip-+_binary64` `diff-cos_binary64` `sum-log_binary64`

Counts

4 → 84

Calls

4 calls:

14.0ms	(+.f64 (.f64 (cos.f64 y) (.f64 3/2 (/.f64 4 (+.f64 3 (sqrt.f64 5))))) (.f64 3/2 (.f64 (cos.f64 x) (-.f64 (sqrt.f64 5) 1))))
12.0ms	(*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))
10.0ms	(.f64 3/2 (.f64 (cos.f64 x) (-.f64 (sqrt.f64 5) 1)))
5.0ms	(-.f64 (cos.f64 x) (cos.f64 y))

series382.0ms

Counts

4 → 12

Calls

4 calls:

184.0ms	(+.f64 (.f64 (cos.f64 y) (.f64 3/2 (/.f64 4 (+.f64 3 (sqrt.f64 5))))) (.f64 3/2 (.f64 (cos.f64 x) (-.f64 (sqrt.f64 5) 1))))
99.0ms	(*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))
59.0ms	(.f64 3/2 (.f64 (cos.f64 x) (-.f64 (sqrt.f64 5) 1)))
39.0ms	(-.f64 (cos.f64 x) (cos.f64 y))

simplify54.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5068	2139

prune222.0ms

Filtered

68 candidates to 96 candidates (-41.2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	90	6	96
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	93	12	105

Merged error: 0.1b

Counts

105 → 12

localize33.0ms

Local error

Found 4 expressions with local error:

0.3b	(.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16)))
0.3b	(+.f64 (.f64 (cos.f64 y) (.f64 3/2 (/.f64 4 (+.f64 3 (sqrt.f64 5))))) (/.f64 (*.f64 (cos.f64 x) 6) (+.f64 (sqrt.f64 5) 1)))
0.4b	(*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))
2.9b	(-.f64 (cos.f64 x) (cos.f64 y))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64`
14×	`*-un-lft-identity_binary64`
12×	`associate-r_binary64` `associate-*r/_binary64`
11×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`add-log-exp_binary64` `flip3--_binary64` `add-cube-cbrt_binary64` `flip--_binary64`
7×	`associate-l_binary64`
5×	`sub-neg_binary64` `difference-of-squares_binary64`
4×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `prod-exp_binary64` `sqrt-prod_binary64` `frac-times_binary64`
3×	`distribute-lft-out--_binary64`
2×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `times-frac_binary64` `associate-l/_binary64` `-commutative_binary64`
1×	`flip3-+_binary64` `diff-log_binary64` `frac-add_binary64` `+-commutative_binary64` `flip-+_binary64` `diff-cos_binary64` `sum-log_binary64`

Counts

4 → 86

Calls

4 calls:

21.0ms	(.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16)))
16.0ms	(+.f64 (.f64 (cos.f64 y) (.f64 3/2 (/.f64 4 (+.f64 3 (sqrt.f64 5))))) (/.f64 (*.f64 (cos.f64 x) 6) (+.f64 (sqrt.f64 5) 1)))
12.0ms	(*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))
5.0ms	(-.f64 (cos.f64 x) (cos.f64 y))

series328.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16)))
117.0ms	(+.f64 (.f64 (cos.f64 y) (.f64 3/2 (/.f64 4 (+.f64 3 (sqrt.f64 5))))) (/.f64 (*.f64 (cos.f64 x) 6) (+.f64 (sqrt.f64 5) 1)))
62.0ms	(*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))
43.0ms	(-.f64 (cos.f64 x) (cos.f64 y))

simplify68.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	4951	2790
1	4951	2790

prune249.0ms

Filtered

72 candidates to 98 candidates (-36.1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	95	3	98
Fresh	2	9	11
Picked	1	0	1
Done	0	0	0
Total	98	12	110

Merged error: 0.1b

Counts

110 → 12

localize39.0ms

Local error

Found 4 expressions with local error:

0.3b	(+.f64 (.f64 (cos.f64 y) (.f64 3/2 (/.f64 4 (+.f64 3 (sqrt.f64 5))))) (/.f64 (*.f64 (cos.f64 x) 6) (+.f64 (sqrt.f64 5) 1)))
0.4b	(*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))
2.9b	(-.f64 (cos.f64 x) (cos.f64 y))
3.9b	(log.f64 (pow.f64 (exp.f64 (*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64`
13×	`*-un-lft-identity_binary64`
10×	`log-prod_binary64`
9×	`add-cube-cbrt_binary64`
8×	`add-log-exp_binary64`
7×	`add-exp-log_binary64`
6×	`sub-neg_binary64` `pow1_binary64` `associate-r_binary64` `add-cbrt-cube_binary64` `associate-l_binary64`
5×	`unpow-prod-down_binary64`
4×	`associate-*r/_binary64` `sqrt-prod_binary64`
3×	`rem-log-exp_binary64` `difference-of-squares_binary64`
2×	`flip3--_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `exp-sum_binary64` `distribute-lft-out--_binary64` `flip--_binary64`
1×	`pow-to-exp_binary64` `pow-prod-down_binary64` `flip3-+_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `frac-add_binary64` `log-pow_binary64` `sqr-pow_binary64` `unpow-prod-up_binary64` `pow-sub_binary64` `prod-exp_binary64` `times-frac_binary64` `log-div_binary64` `+-commutative_binary64` `flip-+_binary64` `pow-exp_binary64` `diff-cos_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 77

Calls

4 calls:

18.0ms	(+.f64 (.f64 (cos.f64 y) (.f64 3/2 (/.f64 4 (+.f64 3 (sqrt.f64 5))))) (/.f64 (*.f64 (cos.f64 x) 6) (+.f64 (sqrt.f64 5) 1)))
13.0ms	(*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))
5.0ms	(-.f64 (cos.f64 x) (cos.f64 y))
5.0ms	(log.f64 (pow.f64 (exp.f64 (*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))))

series427.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(+.f64 (.f64 (cos.f64 y) (.f64 3/2 (/.f64 4 (+.f64 3 (sqrt.f64 5))))) (/.f64 (*.f64 (cos.f64 x) 6) (+.f64 (sqrt.f64 5) 1)))
62.0ms	(*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))
42.0ms	(-.f64 (cos.f64 x) (cos.f64 y))
216.0ms	(log.f64 (pow.f64 (exp.f64 (*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))))

simplify57.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	4928	2433
1	4928	2433

prune193.0ms

Filtered

68 candidates to 89 candidates (-30.9%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	86	3	89
Fresh	0	11	11
Picked	1	0	1
Done	0	0	0
Total	87	14	101

Merged error: 0.1b

Counts

101 → 14

regimes187.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	107	89
1	107	89

end0.0ms

sample6.7s

Algorithm

intervals

Results

3.7s	2749×	body	1280	valid
1.8s	1873×	body	640	valid
469.0ms	763×	body	320	valid
439.0ms	2266×	body	80	valid
142.0ms	349×	body	160	valid

Details

analyze773.0ms

sample212.0ms

simplify60.0ms

prune8.0ms

localize32.0ms

rewrite36.0ms

series146.0ms

simplify86.0ms

prune197.0ms

localize36.0ms

rewrite43.0ms

series382.0ms

simplify54.0ms

prune222.0ms

localize33.0ms

rewrite57.0ms

series328.0ms

simplify68.0ms

prune249.0ms

localize39.0ms

rewrite44.0ms

series427.0ms

simplify57.0ms

prune193.0ms

regimes187.0ms

bsearch0.0ms

simplify4.0ms

end0.0ms

sample6.7s

Profiling