Details

analyze820.0ms

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

sample44.0ms

Algorithm

intervals

Results

10.0ms	193×	body	80	valid
9.0ms	27×	body	2560	valid
7.0ms	256×	pre	80	true
6.0ms	22×	body	1280	valid
2.0ms	9×	body	640	valid
1.0ms	4×	body	320	valid
0.0ms	1×	body	160	valid

simplify7.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	38	17
1	38	17

prune6.0ms

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 0.5 (+.f64 1.0 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4.0 p) p) (.f64 x x)))))))
0.0b	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4.0 p) p) (*.f64 x x))))
0.6b	(+.f64 1.0 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4.0 p) p) (*.f64 x x)))))
12.8b	(sqrt.f64 (+.f64 (.f64 (.f64 4.0 p) p) (*.f64 x x)))

rewrite49.0ms

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:

15.0ms	(sqrt.f64 (.f64 0.5 (+.f64 1.0 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4.0 p) p) (.f64 x x)))))))
8.0ms	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4.0 p) p) (*.f64 x x))))
16.0ms	(+.f64 1.0 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4.0 p) p) (*.f64 x x)))))
6.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 4.0 p) p) (*.f64 x x)))

series126.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(sqrt.f64 (.f64 0.5 (+.f64 1.0 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4.0 p) p) (.f64 x x)))))))
22.0ms	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4.0 p) p) (*.f64 x x))))
22.0ms	(+.f64 1.0 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4.0 p) p) (*.f64 x x)))))
12.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 4.0 p) p) (*.f64 x x)))

simplify89.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	5576	1479

prune146.0ms

Filtered

74 candidates to 93 candidates (-25.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	85	8	93
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	86	8	94

Merged error: 13.3b

Counts

94 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 4.0 p)) (*.f64 x x))))
0.2b	(.f64 x (/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 4.0 p)) (.f64 x x)))))
4.8b	(+.f64 1.0 (.f64 x (/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 4.0 p)) (.f64 x x))))))
12.8b	(sqrt.f64 (+.f64 (.f64 p (.f64 4.0 p)) (*.f64 x x)))

rewrite46.0ms

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:

10.0ms	(/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 4.0 p)) (*.f64 x x))))
18.0ms	(.f64 x (/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 4.0 p)) (.f64 x x)))))
5.0ms	(+.f64 1.0 (.f64 x (/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 4.0 p)) (.f64 x x))))))
7.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4.0 p)) (*.f64 x x)))

series93.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 4.0 p)) (*.f64 x x))))
17.0ms	(.f64 x (/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 4.0 p)) (.f64 x x)))))
21.0ms	(+.f64 1.0 (.f64 x (/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 4.0 p)) (.f64 x x))))))
15.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4.0 p)) (*.f64 x x)))

simplify90.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	5032	1905

prune180.0ms

Filtered

87 candidates to 134 candidates (-54.0%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	131	3	134
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	134	8	142

Merged error: 13.3b

Counts

142 → 8

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 p 4.0)) (.f64 x x))))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4.0 p)) (.f64 x x)))))
8.9b	(+.f64 1.0 (.f64 x (/.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 p 4.0)) (.f64 x x))))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4.0 p)) (*.f64 x x)))))))
12.8b	(sqrt.f64 (+.f64 (.f64 p (.f64 4.0 p)) (*.f64 x x)))
12.8b	(sqrt.f64 (+.f64 (.f64 p (.f64 p 4.0)) (*.f64 x x)))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

582×	`sqrt-prod_binary64`
567×	`times-frac_binary64`
300×	`add-sqr-sqrt_binary64`
298×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
48×	`sqrt-div_binary64`
33×	`associate-/l*_binary64`
22×	`associate-/r/_binary64`
14×	`flip3-+_binary64` `flip-+_binary64`
13×	`add-exp-log_binary64`
11×	`div-inv_binary64`
9×	`associate-/r*_binary64` `add-cbrt-cube_binary64`
6×	`add-log-exp_binary64` `pow1_binary64` `div-exp_binary64`
3×	`cbrt-undiv_binary64`
2×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`
1×	`associate-/l/_binary64` `1-exp_binary64` `clear-num_binary64` `frac-2neg_binary64` `rec-exp_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

4 → 399

Calls

4 calls:

31.0ms	(/.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 p 4.0)) (.f64 x x))))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4.0 p)) (.f64 x x)))))
5.0ms	(+.f64 1.0 (.f64 x (/.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 p 4.0)) (.f64 x x))))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4.0 p)) (*.f64 x x)))))))
6.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4.0 p)) (*.f64 x x)))
6.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 p 4.0)) (*.f64 x x)))

series102.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(/.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 p 4.0)) (.f64 x x))))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4.0 p)) (.f64 x x)))))
22.0ms	(+.f64 1.0 (.f64 x (/.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 p 4.0)) (.f64 x x))))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4.0 p)) (*.f64 x x)))))))
10.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4.0 p)) (*.f64 x x)))
12.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 p 4.0)) (*.f64 x x)))

simplify137.0ms

Algorithm

egg-herbie

Counts

411 → 411

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5002	14072

prune393.0ms

Filtered

134 candidates to 411 candidates (-206.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	409	2	411
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	410	9	419

Merged error: 13.3b

Counts

419 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

0.5b	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4.0 p)) (.f64 x x)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4.0 p)) (*.f64 x x)))))
9.1b	(+.f64 1.0 (/.f64 x (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4.0 p)) (.f64 x x)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4.0 p)) (*.f64 x x)))))))
12.8b	(sqrt.f64 (+.f64 (.f64 p (.f64 4.0 p)) (*.f64 x x)))
12.8b	(sqrt.f64 (+.f64 (.f64 p (.f64 4.0 p)) (*.f64 x x)))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

72×	`sqrt-prod_binary64`
50×	`add-sqr-sqrt_binary64`
34×	`sqrt-pow1_binary64`
29×	`pow1_binary64`
28×	`sqrt-div_binary64`
20×	`*-un-lft-identity_binary64`
18×	`pow1/2_binary64` `add-cube-cbrt_binary64`
15×	`swap-sqr_binary64`
9×	`flip3-+_binary64` `associate-r_binary64` `pow-prod-up_binary64` `associate-l_binary64` `unswap-sqr_binary64` `flip-+_binary64`
6×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`pow-prod-down_binary64` `pow-sqr_binary64`
4×	`frac-times_binary64`
2×	`associate-r/_binary64` `rem-sqrt-square_binary64` `associate-l/_binary64`
1×	`cbrt-unprod_binary64` `distribute-lft-out_binary64` `rem-square-sqrt_binary64` `pow-plus_binary64` `sqrt-unprod_binary64` `prod-exp_binary64` `+-commutative_binary64` `pow2_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 125

Calls

4 calls:

26.0ms	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4.0 p)) (.f64 x x)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4.0 p)) (*.f64 x x)))))
11.0ms	(+.f64 1.0 (/.f64 x (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4.0 p)) (.f64 x x)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4.0 p)) (*.f64 x x)))))))
6.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4.0 p)) (*.f64 x x)))
6.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4.0 p)) (*.f64 x x)))

series56.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4.0 p)) (.f64 x x)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4.0 p)) (*.f64 x x)))))
21.0ms	(+.f64 1.0 (/.f64 x (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4.0 p)) (.f64 x x)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4.0 p)) (*.f64 x x)))))))
12.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4.0 p)) (*.f64 x x)))
12.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4.0 p)) (*.f64 x x)))

simplify51.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5089	1899

prune129.0ms

Filtered

85 candidates to 137 candidates (-61.2%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	135	2	137
Fresh	2	5	7
Picked	0	1	1
Done	0	1	1
Total	137	9	146

Merged error: 13.3b

Counts

146 → 9

regimes117.0ms

Accuracy

0% (1.3b remaining)

Error of 14.5b against oracle of 13.2b and baseline of 14.5b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	32
1	25	32

end0.0ms

sample1.4s

Algorithm

intervals

Results

381.0ms	6003×	body	80	valid
304.0ms	809×	body	2560	valid
198.0ms	628×	body	1280	valid
169.0ms	8000×	pre	80	true
79.0ms	320×	body	640	valid
31.0ms	171×	body	320	valid
8.0ms	69×	body	160	valid

Details

analyze820.0ms

sample44.0ms

simplify7.0ms

prune6.0ms

localize11.0ms

rewrite49.0ms

series126.0ms

simplify89.0ms

prune146.0ms

localize13.0ms

rewrite46.0ms

series93.0ms

simplify90.0ms

prune180.0ms

localize22.0ms

rewrite84.0ms

series102.0ms

simplify137.0ms

prune393.0ms

localize15.0ms

rewrite55.0ms

series56.0ms

simplify51.0ms

prune129.0ms

regimes117.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.4s

Profiling