Details

analyze815.0ms

Algorithm

Search

True	Other	False	Iter
0%	48.6%	51.4%	0
0%	48.6%	51.4%	1
24.3%	24.3%	51.4%	2
24.3%	24.3%	51.4%	3
30.4%	18.2%	51.4%	4
30.4%	18.2%	51.4%	5
33.4%	15.2%	51.4%	6
33.4%	15.2%	51.4%	7
34.6%	14.1%	51.4%	8
34.8%	13.9%	51.4%	9
35.4%	13.2%	51.4%	10
35.6%	13.1%	51.4%	11
35.9%	12.7%	51.4%	12
36%	12.6%	51.4%	13
36.2%	12.4%	51.4%	14

sample39.0ms

Algorithm

intervals

Results

10.0ms	193×	body	80	valid
9.0ms	27×	body	2560	valid
4.0ms	256×	pre	80	true
4.0ms	14×	body	1280	valid
2.0ms	11×	body	640	valid
1.0ms	8×	body	320	valid
0.0ms	3×	body	160	valid

simplify16.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	39	26
1	39	26

prune3.0ms

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: 13.5b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (.f64 x x)))))))
0.2b	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x))))
1.3b	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))))
14.0b	(sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity_binary64`
21×	`add-sqr-sqrt_binary64`
20×	`add-cube-cbrt_binary64`
18×	`times-frac_binary64`
16×	`sqrt-prod_binary64`
8×	`pow1_binary64`
6×	`associate-/r*_binary64` `add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-div_binary64`
4×	`flip3-+_binary64` `flip-+_binary64`
3×	`sqrt-pow1_binary64` `associate-/l*_binary64`
2×	`pow1/2_binary64` `associate-*r/_binary64` `associate-/r/_binary64`
1×	`pow-prod-down_binary64` `distribute-lft-out_binary64` `cbrt-undiv_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

4 → 81

Calls

4 calls:

14.0ms	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (.f64 x x)))))))
9.0ms	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x))))
13.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))))
6.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))

series210.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (.f64 x x)))))))
33.0ms	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x))))
47.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))))
30.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))

simplify134.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (106.0ms)

Iter	Nodes	Cost
0	5672	2228

prune137.0ms

Filtered

74 candidates to 93 candidates (-25.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	81	12	93
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	82	12	94

Merged error: 13.2b

Counts

94 → 12

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(.f64 x (/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))))
0.2b	(/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x))))
4.0b	(+.f64 1 (.f64 x (/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x))))))
14.0b	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

47×	`add-sqr-sqrt_binary64`
40×	`times-frac_binary64`
36×	`*-un-lft-identity_binary64`
34×	`add-cube-cbrt_binary64`
26×	`sqrt-prod_binary64`
24×	`associate-r_binary64`
17×	`add-exp-log_binary64`
11×	`add-cbrt-cube_binary64`
9×	`pow1_binary64`
6×	`associate-/r*_binary64` `add-log-exp_binary64` `sqrt-div_binary64`
5×	`unswap-sqr_binary64`
4×	`flip3-+_binary64` `associate-/r/_binary64` `prod-exp_binary64` `div-exp_binary64` `flip-+_binary64`
3×	`associate-l_binary64` `associate-/l*_binary64` `pow-flip_binary64`
2×	`pow1/2_binary64` `cbrt-unprod_binary64` `1-exp_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `rec-exp_binary64` `div-inv_binary64`
1×	`pow-prod-down_binary64` `associate-r/_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `un-div-inv_binary64` `+-commutative_binary64` `sum-log_binary64` `-commutative_binary64`

Counts

4 → 122

Calls

4 calls:

16.0ms	(.f64 x (/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))))
9.0ms	(/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x))))
3.0ms	(+.f64 1 (.f64 x (/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x))))))
6.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

series147.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(.f64 x (/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))))
35.0ms	(/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x))))
45.0ms	(+.f64 1 (.f64 x (/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x))))))
28.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

simplify111.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 0 (79.0ms)

Iter	Nodes	Cost
0	4940	2888
1	4940	2888

prune152.0ms

Filtered

87 candidates to 134 candidates (-54.0%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	130	4	134
Fresh	5	6	11
Picked	0	1	1
Done	0	0	0
Total	135	11	146

Merged error: 13.2b

Counts

146 → 11

localize19.0ms

Local error

Found 4 expressions with local error:

1.3b	(+.f64 1 (pow.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))) 3))
4.1b	(/.f64 (.f64 x x) (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))
14.0b	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))
14.0b	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
9×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`add-cube-cbrt_binary64`
6×	`add-log-exp_binary64` `pow1_binary64` `sqrt-prod_binary64`
4×	`flip3-+_binary64` `flip-+_binary64` `sqrt-div_binary64`
3×	`associate-/r*_binary64` `times-frac_binary64`
2×	`pow1/2_binary64` `cbrt-undiv_binary64` `associate-/r/_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `div-exp_binary64`
1×	`cbrt-unprod_binary64` `distribute-lft-out_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `associate-/l*_binary64` `div-inv_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

4 → 65

Calls

4 calls:

24.0ms	(+.f64 1 (pow.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))) 3))
10.0ms	(/.f64 (.f64 x x) (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))
6.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))
6.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

series150.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(+.f64 1 (pow.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))) 3))
35.0ms	(/.f64 (.f64 x x) (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))
30.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))
29.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

simplify74.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5357	1543

prune163.0ms

Filtered

65 candidates to 77 candidates (-18.5%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	77	0	77
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	77	11	88

Merged error: 13.2b

Counts

88 → 11

localize17.0ms

Local error

Found 4 expressions with local error:

1.3b	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))
14.0b	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))
14.0b	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))
14.0b	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64`
9×	`*-un-lft-identity_binary64` `sqrt-prod_binary64`
7×	`pow1_binary64` `add-cube-cbrt_binary64`
6×	`add-log-exp_binary64` `sqrt-div_binary64`
4×	`flip3-+_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `flip-+_binary64`
3×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`
1×	`distribute-lft-out_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

4 → 57

Calls

4 calls:

13.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))
6.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))
6.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))
6.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

series129.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))
27.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))
27.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))
28.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

simplify128.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (108.0ms)

Iter	Nodes	Cost
0	5226	1276

prune168.0ms

Filtered

62 candidates to 69 candidates (-11.3%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	69	0	69
Fresh	0	8	8
Picked	0	1	1
Done	0	2	2
Total	69	11	80

Merged error: 13.2b

Counts

80 → 11

regimes62.0ms

Accuracy

0% (0.5b remaining)

Error of 13.3b against oracle of 12.8b and baseline of 13.3b

bsearch0.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	29
1	24	29

end0.0ms

sample1.1s

Algorithm

intervals

Results

321.0ms	6058×	body	80	valid
260.0ms	805×	body	2560	valid
154.0ms	594×	body	1280	valid
138.0ms	8000×	pre	80	true
63.0ms	296×	body	640	valid
25.0ms	166×	body	320	valid
10.0ms	81×	body	160	valid

Details

analyze815.0ms

sample39.0ms

simplify16.0ms

prune3.0ms

localize11.0ms

rewrite45.0ms

series210.0ms

simplify134.0ms

prune137.0ms

localize13.0ms

rewrite38.0ms

series147.0ms

simplify111.0ms

prune152.0ms

localize19.0ms

rewrite47.0ms

series150.0ms

simplify74.0ms

prune163.0ms

localize17.0ms

rewrite32.0ms

series129.0ms

simplify128.0ms

prune168.0ms

regimes62.0ms

bsearch0.0ms

simplify3.0ms

end0.0ms

sample1.1s

Profiling