Details

analyze2.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	25%	25%	3
50%	12.5%	37.5%	4
50%	6.2%	43.8%	5
50%	3.1%	46.9%	6
50%	1.6%	48.5%	7
50%	0.8%	49.2%	8
50%	0.4%	49.6%	9
50%	0.2%	49.8%	10
50%	0.1%	49.9%	11
50%	0%	50%	12
50%	0%	50%	13
50%	0%	50%	14

sample22.0ms

Algorithm

intervals

Results

8.0ms	140×	body	128	valid
6.0ms	63×	body	1024	valid
2.0ms	30×	body	512	valid
1.0ms	19×	body	256	valid
0.0ms	4×	body	2048	valid

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	71	11
1	71	11

prune1.0ms

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: 28.3b

Counts

2 → 1

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt.f64 (+.f64 x 1))
2.5b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64` `sqrt-prod_binary64`
4×	`add-log-exp_binary64` `difference-of-squares_binary64`
3×	`pow1_binary64` `add-cube-cbrt_binary64` `distribute-lft-out--_binary64`
2×	`distribute-lft-out_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-div_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `pow1/2_binary64` `flip3--_binary64` `diff-log_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip--_binary64` `flip-+_binary64`

Counts

2 → 34

Calls

2 calls:

3.0ms	(sqrt.f64 (+.f64 x 1))
9.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

series94.0ms

Counts

2 → 6

Calls

2 calls:

25.0ms	(sqrt.f64 (+.f64 x 1))
69.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

simplify102.0ms

Algorithm

egg-herbie

Counts

40 → 40

Iterations

Useful iterations: 0 (88.0ms)

Iter	Nodes	Cost
0	4898	755
1	4898	755

prune36.0ms

Filtered

30 candidates to 40 candidates (-33.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	37	3	40
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	37	4	41

Merged error: 0.1b

Counts

41 → 4

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt.f64 (+.f64 x 1))
0.0b	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
0.2b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

52×	`*-un-lft-identity_binary64`
24×	`sqrt-prod_binary64`
21×	`distribute-lft-out_binary64`
18×	`times-frac_binary64`
16×	`add-sqr-sqrt_binary64`
15×	`add-cube-cbrt_binary64`
6×	`associate-/r*_binary64` `add-exp-log_binary64`
5×	`add-log-exp_binary64` `pow1_binary64` `add-cbrt-cube_binary64`
3×	`flip3-+_binary64` `associate-/l*_binary64` `flip-+_binary64`
2×	`associate-/r/_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `rec-exp_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `pow-flip_binary64` `sum-log_binary64`

Counts

3 → 74

Calls

3 calls:

3.0ms	(sqrt.f64 (+.f64 x 1))
11.0ms	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
12.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))

series130.0ms

Counts

3 → 9

Calls

3 calls:

26.0ms	(sqrt.f64 (+.f64 x 1))
43.0ms	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
60.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))

simplify90.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4900	1515
1	4900	1515

prune74.0ms

Filtered

56 candidates to 83 candidates (-48.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	78	5	83
Fresh	2	0	2
Picked	0	1	1
Done	1	0	1
Total	81	6	87

Merged error: 0.0b

Counts

87 → 6

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (+.f64 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
0.2b	(*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x))))
0.3b	(cbrt.f64 (+.f64 1 x))
0.3b	(cbrt.f64 (+.f64 1 x))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
18×	`add-cube-cbrt_binary64`
13×	`cbrt-prod_binary64`
10×	`associate-r_binary64`
9×	`add-exp-log_binary64` `times-frac_binary64` `sqrt-prod_binary64`
8×	`add-cbrt-cube_binary64`
7×	`pow1_binary64`
6×	`cbrt-div_binary64`
4×	`flip3-+_binary64` `add-log-exp_binary64` `flip-+_binary64`
3×	`associate-/r_binary64` `distribute-lft-out_binary64` `associate-l_binary64` `unswap-sqr_binary64` `associate-/l_binary64`
2×	`associate-*r/_binary64` `pow1/3_binary64` `associate-/r/_binary64` `sqrt-div_binary64`
1×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `inv-pow_binary64` `prod-exp_binary64` `frac-2neg_binary64` `rec-exp_binary64` `div-inv_binary64` `div-exp_binary64` `pow-flip_binary64` `*-commutative_binary64`

Counts

4 → 89

Calls

4 calls:

12.0ms	(/.f64 1 (+.f64 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
9.0ms	(*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x))))
3.0ms	(cbrt.f64 (+.f64 1 x))
3.0ms	(cbrt.f64 (+.f64 1 x))

series735.0ms

Counts

4 → 12

Calls

4 calls:

565.0ms	(/.f64 1 (+.f64 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
85.0ms	(*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x))))
38.0ms	(cbrt.f64 (+.f64 1 x))
46.0ms	(cbrt.f64 (+.f64 1 x))

simplify62.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5320	3208

prune136.0ms

Filtered

79 candidates to 101 candidates (-27.8%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	101	0	101
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	101	6	107

Merged error: 0.0b

Counts

107 → 6

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
0.1b	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
0.2b	(/.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))
0.2b	(/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))

rewrite159.0ms

Algorithm

rewrite-expression-head

Rules

742×	`*-un-lft-identity_binary64`
700×	`sqrt-prod_binary64`
594×	`times-frac_binary64`
280×	`distribute-lft-out_binary64`
254×	`add-sqr-sqrt_binary64`
252×	`add-cube-cbrt_binary64`
36×	`associate-/l*_binary64`
28×	`sqrt-div_binary64`
24×	`associate-/r/_binary64`
18×	`associate-/r*_binary64`
14×	`flip3-+_binary64` `add-exp-log_binary64` `flip-+_binary64`
12×	`div-inv_binary64`
11×	`add-cbrt-cube_binary64`
8×	`pow1_binary64`
5×	`div-exp_binary64`
4×	`add-log-exp_binary64` `cbrt-undiv_binary64`
3×	`pow1/2_binary64` `sqrt-pow1_binary64` `pow-flip_binary64`
2×	`rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `rec-exp_binary64`
1×	`associate-/l/_binary64` `inv-pow_binary64`

Counts

4 → 451

Calls

4 calls:

9.0ms	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
10.0ms	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
35.0ms	(/.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))
16.0ms	(/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))

series314.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
70.0ms	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
60.0ms	(/.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))
103.0ms	(/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))

simplify186.0ms

Algorithm

egg-herbie

Counts

463 → 463

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5134	17559

prune252.0ms

Filtered

132 candidates to 463 candidates (-250.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	461	2	463
Fresh	0	3	3
Picked	1	0	1
Done	0	2	2
Total	462	7	469

Merged error: 0b

Counts

469 → 7

regimes19.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	14
1	10	14

end0.0ms

sample536.0ms

Algorithm

intervals

Results

198.0ms	1986×	body	1024	valid
114.0ms	4288×	body	128	valid
75.0ms	977×	body	512	valid
26.0ms	209×	body	2048	valid
26.0ms	540×	body	256	valid
0.0ms	2×	body	128	nan

Details

analyze2.0ms

sample22.0ms

simplify11.0ms

prune1.0ms

localize5.0ms

rewrite15.0ms

series94.0ms

simplify102.0ms

prune36.0ms

localize6.0ms

rewrite32.0ms

series130.0ms

simplify90.0ms

prune74.0ms

localize10.0ms

rewrite37.0ms

series735.0ms

simplify62.0ms

prune136.0ms

localize12.0ms

rewrite159.0ms

series314.0ms

simplify186.0ms

prune252.0ms

regimes19.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample536.0ms

Profiling