Details

analyze1.9s

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
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
0%	99.9%	0.1%	7
15.6%	84.3%	0.1%	8
15.6%	84.3%	0.1%	9
15.6%	84.3%	0.1%	10
30.4%	69.4%	0.1%	11
30.4%	69.4%	0.1%	12
30.4%	69.4%	0.1%	13
39.6%	60.3%	0.1%	14

sample103.0ms

Algorithm

intervals

Results

40.0ms	48×	body	1280	valid
24.0ms	42×	body	640	valid
15.0ms	128×	body	80	valid
9.0ms	22×	body	320	valid
4.0ms	16×	body	160	valid

simplify71.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4870	24
1	4870	24

prune10.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 19.4b

Counts

2 → 1

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))
0.2b	(pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)
8.1b	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
10.1b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-exp-log_binary64`
20×	`pow1_binary64`
18×	`add-cbrt-cube_binary64`
15×	`*-un-lft-identity_binary64`
12×	`prod-exp_binary64` `add-sqr-sqrt_binary64`
11×	`add-cube-cbrt_binary64`
10×	`associate-r_binary64`
9×	`pow-prod-down_binary64` `cbrt-unprod_binary64`
8×	`sqrt-prod_binary64`
7×	`unpow-prod-down_binary64`
4×	`add-log-exp_binary64` `pow-exp_binary64` `sqrt-div_binary64`
3×	`pow-unpow_binary64` `times-frac_binary64` `div-exp_binary64`
2×	`flip3-+_binary64` `distribute-lft-out_binary64` `associate-r/_binary64` `associate-l_binary64` `flip-+_binary64` `-commutative_binary64`
1×	`pow-to-exp_binary64` `pow1/2_binary64` `unpow2_binary64` `pow-pow_binary64` `sqr-pow_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `div-inv_binary64`

Counts

4 → 86

Calls

4 calls:

6.0ms	(.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))
8.0ms	(pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)
17.0ms	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
8.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

series116.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))
25.0ms	(pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)
44.0ms	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
39.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

simplify57.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5166	1556

prune107.0ms

Filtered

62 candidates to 98 candidates (-58.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	91	7	98
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	92	7	99

Merged error: 13.7b

Counts

99 → 7

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))
0.2b	(pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)
8.1b	(.f64 (.f64 -2 J) (.f64 (cos.f64 (/.f64 K 2)) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))))
10.1b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-exp-log_binary64`
23×	`pow1_binary64`
21×	`add-cbrt-cube_binary64`
14×	`prod-exp_binary64`
11×	`pow-prod-down_binary64` `*-un-lft-identity_binary64` `cbrt-unprod_binary64`
10×	`add-sqr-sqrt_binary64`
9×	`add-cube-cbrt_binary64`
7×	`unpow-prod-down_binary64`
4×	`add-log-exp_binary64` `associate-r_binary64` `associate-*r/_binary64` `sqrt-prod_binary64` `pow-exp_binary64` `sqrt-div_binary64`
3×	`pow-unpow_binary64` `times-frac_binary64` `div-exp_binary64`
2×	`flip3-+_binary64` `associate-l_binary64` `flip-+_binary64` `*-commutative_binary64`
1×	`pow-to-exp_binary64` `pow1/2_binary64` `distribute-lft-out_binary64` `unpow2_binary64` `pow-pow_binary64` `sqr-pow_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `div-inv_binary64`

Counts

4 → 83

Calls

4 calls:

6.0ms	(.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))
8.0ms	(pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)
16.0ms	(.f64 (.f64 -2 J) (.f64 (cos.f64 (/.f64 K 2)) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))))
9.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

series116.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))
24.0ms	(pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)
44.0ms	(.f64 (.f64 -2 J) (.f64 (cos.f64 (/.f64 K 2)) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))))
39.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

simplify44.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	4973	1500
1	4973	1500

prune87.0ms

Filtered

58 candidates to 95 candidates (-63.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	94	1	95
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	95	7	102

Merged error: 13.7b

Counts

102 → 7

localize23.0ms

Local error

Found 4 expressions with local error:

8.0b	(sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
8.0b	(sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
10.1b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
10.1b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

32×	`sqrt-prod_binary64`
18×	`*-un-lft-identity_binary64`
16×	`add-sqr-sqrt_binary64`
12×	`sqrt-div_binary64`
10×	`pow1_binary64` `add-cube-cbrt_binary64` `sqrt-pow1_binary64`
6×	`pow1/2_binary64` `rem-sqrt-square_binary64`
4×	`flip3-+_binary64` `add-log-exp_binary64` `distribute-lft-out_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `flip-+_binary64`

Counts

4 → 76

Calls

4 calls:

10.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
9.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
9.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
9.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

series215.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
68.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
41.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
37.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

simplify51.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5672	1522

prune139.0ms

Filtered

60 candidates to 88 candidates (-46.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	86	2	88
Fresh	0	5	5
Picked	1	0	1
Done	0	1	1
Total	87	8	95

Merged error: 13.7b

Counts

95 → 8

localize27.0ms

Local error

Found 4 expressions with local error:

8.0b	(sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
10.1b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
15.3b	(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
15.3b	(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

17×	`*-un-lft-identity_binary64`
16×	`sqrt-prod_binary64`
12×	`add-sqr-sqrt_binary64`
9×	`add-cube-cbrt_binary64`
8×	`cbrt-prod_binary64`
7×	`pow1_binary64`
6×	`sqrt-div_binary64`
5×	`sqrt-pow1_binary64`
4×	`cbrt-div_binary64` `flip3-+_binary64` `add-log-exp_binary64` `distribute-lft-out_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `flip-+_binary64`
3×	`pow1/2_binary64` `rem-sqrt-square_binary64`
2×	`pow1/3_binary64`

Counts

4 → 66

Calls

4 calls:

10.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
9.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
8.0ms	(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
11.0ms	(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

series247.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
37.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
68.0ms	(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
73.0ms	(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

simplify62.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5165	1459

prune161.0ms

Filtered

58 candidates to 78 candidates (-34.5%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	78	0	78
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	78	8	86

Merged error: 13.7b

Counts

86 → 8

regimes271.0ms

Accuracy

-8.9% (5.9b remaining)

Error of 18.6b against oracle of 12.6b and baseline of 18.1b

bsearch111.0ms

Steps

Iters	Range		Point
8	1.6282540184637033e-196	2.7681727462030808e-192	1.6576375658546962e-196
7	-3.176199222948149e-303	-1.8619380377689093e-304	-1.012694507951569e-303

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	46	52
1	46	52

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.3s	1514×	body	1280	valid
697.0ms	1212×	body	640	valid
500.0ms	4308×	body	80	valid
266.0ms	632×	body	320	valid
88.0ms	334×	body	160	valid
0.0ms	1×	body	320	invalid
0.0ms	2×	body	80	invalid

Details

analyze1.9s

sample103.0ms

simplify71.0ms

prune10.0ms

localize16.0ms

rewrite44.0ms

series116.0ms

simplify57.0ms

prune107.0ms

localize16.0ms

rewrite42.0ms

series116.0ms

simplify44.0ms

prune87.0ms

localize23.0ms

rewrite39.0ms

series215.0ms

simplify51.0ms

prune139.0ms

localize27.0ms

rewrite40.0ms

series247.0ms

simplify62.0ms

prune161.0ms

regimes271.0ms

bsearch111.0ms

simplify2.0ms

end0.0ms

sample3.1s

Profiling