Details

analyze235.0ms

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
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	87.4%	12.6%	6
20.3%	59.3%	20.4%	7
21.1%	51.5%	27.4%	8
35.5%	30.4%	34%	9
35.7%	26.1%	38.1%	10
42.8%	15.4%	41.8%	11
42.9%	13.2%	44%	12
46.4%	7.8%	45.8%	13
46.4%	6.6%	47%	14

sample65.0ms

Algorithm

intervals

Results

29.0ms	64×	body	1024	valid
11.0ms	143×	body	128	valid
8.0ms	32×	body	512	valid
4.0ms	6×	body	2048	valid
2.0ms	11×	body	256	valid
0.0ms	6×	body	128	overflowed
0.0ms	1×	body	1024	invalid
0.0ms	4×	body	128	invalid

simplify52.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5465	41

prune5.0ms

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: 28.5b

Counts

2 → 1

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(*.f64 (+.f64 1 eps) x)
0.0b	(.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x))))
0.0b	(.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x))))
2.4b	(-.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x)))) (.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x)))))

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

81×	`frac-sub_binary64`
80×	`exp-neg_binary64` `frac-times_binary64`
60×	`neg-sub0_binary64` `exp-diff_binary64`
42×	`associate-*l/_binary64`
40×	`associate-*r/_binary64`
31×	`flip3-+_binary64` `flip3--_binary64` `add-sqr-sqrt_binary64` `flip--_binary64` `flip-+_binary64`
24×	`*-un-lft-identity_binary64`
23×	`associate-l_binary64`
20×	`un-div-inv_binary64`
10×	`pow1_binary64` `add-cube-cbrt_binary64` `add-cbrt-cube_binary64`
9×	`associate-r_binary64`
8×	`add-exp-log_binary64`
6×	`add-log-exp_binary64` `difference-of-squares_binary64` `times-frac_binary64`
3×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `distribute-lft-out_binary64` `difference-of-sqr-1_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `*-commutative_binary64`
2×	`distribute-lft-out--_binary64` `div-inv_binary64`
1×	`sub-neg_binary64` `diff-log_binary64`

Counts

4 → 180

Calls

4 calls:

7.0ms	(*.f64 (+.f64 1 eps) x)
17.0ms	(.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x))))
15.0ms	(.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x))))
23.0ms	(-.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x)))) (.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x)))))

series422.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(*.f64 (+.f64 1 eps) x)
72.0ms	(.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x))))
58.0ms	(.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x))))
256.0ms	(-.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x)))) (.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x)))))

simplify137.0ms

Algorithm

egg-herbie

Counts

192 → 192

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	5038	9587

prune487.0ms

Filtered

149 candidates to 192 candidates (-28.9%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	189	3	192
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	190	3	193

Merged error: 0.9b

Counts

193 → 3

localize8.0ms

Local error

Found 2 expressions with local error:

0.1b	(*.f64 (pow.f64 x 3) 2/3)
5.8b	(-.f64 (+.f64 (.f64 (pow.f64 x 3) 2/3) 2) (.f64 x x))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64`
12×	`associate-l_binary64`
7×	`add-log-exp_binary64` `add-exp-log_binary64`
6×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
4×	`add-cbrt-cube_binary64` `unswap-sqr_binary64` `unpow-prod-down_binary64` `cube-prod_binary64`
3×	`associate-r_binary64` `prod-exp_binary64`
2×	`pow1_binary64` `diff-log_binary64` `sqr-pow_binary64`
1×	`pow-to-exp_binary64` `sub-neg_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `difference-of-squares_binary64` `flip--_binary64` `pow-exp_binary64` `unpow3_binary64` `associate--l+_binary64` `sum-log_binary64` `*-commutative_binary64` `cube-mult_binary64`

Counts

2 → 45

Calls

2 calls:

6.0ms	(*.f64 (pow.f64 x 3) 2/3)
9.0ms	(-.f64 (+.f64 (.f64 (pow.f64 x 3) 2/3) 2) (.f64 x x))

series85.0ms

Counts

2 → 6

Calls

2 calls:

46.0ms	(*.f64 (pow.f64 x 3) 2/3)
39.0ms	(-.f64 (+.f64 (.f64 (pow.f64 x 3) 2/3) 2) (.f64 x x))

simplify56.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4860	681
1	4860	681

prune49.0ms

Filtered

32 candidates to 51 candidates (-59.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	49	2	51
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	49	5	54

Merged error: 0.9b

Counts

54 → 5

localize11.0ms

Local error

Found 4 expressions with local error:

5.8b	(-.f64 (+.f64 (.f64 (pow.f64 x 3) 2/3) 2) (.f64 x x))
5.8b	(-.f64 (+.f64 (.f64 (pow.f64 x 3) 2/3) 2) (.f64 x x))
5.9b	(sqrt.f64 (-.f64 (+.f64 (.f64 (pow.f64 x 3) 2/3) 2) (.f64 x x)))
5.9b	(sqrt.f64 (-.f64 (+.f64 (.f64 (pow.f64 x 3) 2/3) 2) (.f64 x x)))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-log-exp_binary64`
12×	`add-sqr-sqrt_binary64`
8×	`sqrt-prod_binary64`
6×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64`
4×	`flip3--_binary64` `diff-log_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `difference-of-squares_binary64` `flip--_binary64` `sqrt-div_binary64`
2×	`sub-neg_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `associate--l+_binary64` `sum-log_binary64`

Counts

4 → 60

Calls

4 calls:

9.0ms	(-.f64 (+.f64 (.f64 (pow.f64 x 3) 2/3) 2) (.f64 x x))
9.0ms	(-.f64 (+.f64 (.f64 (pow.f64 x 3) 2/3) 2) (.f64 x x))
8.0ms	(sqrt.f64 (-.f64 (+.f64 (.f64 (pow.f64 x 3) 2/3) 2) (.f64 x x)))
9.0ms	(sqrt.f64 (-.f64 (+.f64 (.f64 (pow.f64 x 3) 2/3) 2) (.f64 x x)))

series165.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(-.f64 (+.f64 (.f64 (pow.f64 x 3) 2/3) 2) (.f64 x x))
39.0ms	(-.f64 (+.f64 (.f64 (pow.f64 x 3) 2/3) 2) (.f64 x x))
48.0ms	(sqrt.f64 (-.f64 (+.f64 (.f64 (pow.f64 x 3) 2/3) 2) (.f64 x x)))
42.0ms	(sqrt.f64 (-.f64 (+.f64 (.f64 (pow.f64 x 3) 2/3) 2) (.f64 x x)))

simplify67.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5742	1750

prune110.0ms

Filtered

56 candidates to 72 candidates (-28.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	71	1	72
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	72	5	77

Merged error: 0.9b

Counts

77 → 5

localize16.0ms

Local error

Found 4 expressions with local error:

5.9b	(sqrt.f64 (-.f64 (+.f64 (.f64 (pow.f64 x 3) 2/3) 2) (.f64 x x)))
5.9b	(sqrt.f64 (-.f64 (+.f64 (.f64 (pow.f64 x 3) 2/3) 2) (.f64 x x)))
5.9b	(sqrt.f64 (-.f64 (+.f64 (.f64 (pow.f64 x 3) 2/3) 2) (.f64 x x)))
5.9b	(sqrt.f64 (-.f64 (+.f64 (.f64 (pow.f64 x 3) 2/3) 2) (.f64 x x)))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64` `sqrt-prod_binary64`
8×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `sqrt-div_binary64`
4×	`add-log-exp_binary64` `pow1/2_binary64` `flip3--_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `difference-of-squares_binary64` `flip--_binary64`

Counts

4 → 64

Calls

4 calls:

8.0ms	(sqrt.f64 (-.f64 (+.f64 (.f64 (pow.f64 x 3) 2/3) 2) (.f64 x x)))
9.0ms	(sqrt.f64 (-.f64 (+.f64 (.f64 (pow.f64 x 3) 2/3) 2) (.f64 x x)))
9.0ms	(sqrt.f64 (-.f64 (+.f64 (.f64 (pow.f64 x 3) 2/3) 2) (.f64 x x)))
9.0ms	(sqrt.f64 (-.f64 (+.f64 (.f64 (pow.f64 x 3) 2/3) 2) (.f64 x x)))

series161.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(sqrt.f64 (-.f64 (+.f64 (.f64 (pow.f64 x 3) 2/3) 2) (.f64 x x)))
37.0ms	(sqrt.f64 (-.f64 (+.f64 (.f64 (pow.f64 x 3) 2/3) 2) (.f64 x x)))
37.0ms	(sqrt.f64 (-.f64 (+.f64 (.f64 (pow.f64 x 3) 2/3) 2) (.f64 x x)))
42.0ms	(sqrt.f64 (-.f64 (+.f64 (.f64 (pow.f64 x 3) 2/3) 2) (.f64 x x)))

simplify67.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5222	2016

prune221.0ms

Filtered

64 candidates to 76 candidates (-18.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	75	1	76
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	76	5	81

Merged error: 0.9b

Counts

81 → 5

regimes70.0ms

Accuracy

96.7% (0.6b remaining)

Error of 0.9b against oracle of 0.4b and baseline of 17.2b

bsearch81.0ms

Steps

Iters	Range		Point
10	10.701924333464511	434315497206.54956	212.09421422413288

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	160	66
1	160	66

end0.0ms

sample1.9s

Algorithm

intervals

Results

857.0ms	1953×	body	1024	valid
353.0ms	4310×	body	128	valid
267.0ms	1043×	body	512	valid
153.0ms	199×	body	2048	valid
78.0ms	495×	body	256	valid
18.0ms	193×	body	128	invalid
14.0ms	191×	body	128	overflowed
12.0ms	27×	body	1024	invalid
3.0ms	11×	body	512	invalid
1.0ms	5×	body	256	invalid

Details

analyze235.0ms

sample65.0ms

simplify52.0ms

prune5.0ms

localize18.0ms

rewrite97.0ms

series422.0ms

simplify137.0ms

prune487.0ms

localize8.0ms

rewrite19.0ms

series85.0ms

simplify56.0ms

prune49.0ms

localize11.0ms

rewrite42.0ms

series165.0ms

simplify67.0ms

prune110.0ms

localize16.0ms

rewrite48.0ms

series161.0ms

simplify67.0ms

prune221.0ms

regimes70.0ms

bsearch81.0ms

simplify4.0ms

end0.0ms

sample1.9s

Profiling