Details

analyze3.0ms

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

sample21.0ms

Algorithm

intervals

Results

8.0ms	76×	body	1024	valid
3.0ms	42×	body	512	valid
3.0ms	117×	body	128	valid
2.0ms	14×	body	2048	valid
0.0ms	7×	body	256	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: 33.8b

Counts

2 → 1

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt.f64 (+.f64 x 1))
1.0b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

rewrite16.0ms

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:

4.0ms	(sqrt.f64 (+.f64 x 1))
10.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

series107.0ms

Counts

2 → 6

Calls

2 calls:

34.0ms	(sqrt.f64 (+.f64 x 1))
73.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

simplify100.0ms

Algorithm

egg-herbie

Counts

40 → 40

Iterations

Useful iterations: 0 (87.0ms)

Iter	Nodes	Cost
0	4898	755
1	4898	755

prune34.0ms

Filtered

30 candidates to 40 candidates (-33.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	38	2	40
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	38	3	41

Merged error: 0.2b

Counts

41 → 3

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)))

rewrite38.0ms

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:

4.0ms	(sqrt.f64 (+.f64 x 1))
9.0ms	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
20.0ms	(/.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))
41.0ms	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
62.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))

simplify99.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4900	1515
1	4900	1515

prune79.0ms

Filtered

56 candidates to 83 candidates (-48.2%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	76	7	83
Fresh	1	0	1
Picked	0	1	1
Done	0	1	1
Total	77	9	86

Merged error: 0.0b

Counts

86 → 9

localize10.0ms

Local error

Found 4 expressions with local error:

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

10.0ms	(*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x))))
12.0ms	(/.f64 1 (+.f64 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
3.0ms	(cbrt.f64 (+.f64 1 x))
3.0ms	(cbrt.f64 (+.f64 1 x))

series754.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x))))
592.0ms	(/.f64 1 (+.f64 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
39.0ms	(cbrt.f64 (+.f64 1 x))
52.0ms	(cbrt.f64 (+.f64 1 x))

simplify73.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5320	3208

prune159.0ms

Filtered

79 candidates to 101 candidates (-27.8%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	99	2	101
Fresh	0	6	6
Picked	1	0	1
Done	0	2	2
Total	100	10	110

Merged error: 0.0b

Counts

110 → 10

localize22.0ms

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 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
0.3b	(/.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))))

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)))
9.0ms	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
14.0ms	(/.f64 1 (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))))

series330.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
76.0ms	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
92.0ms	(/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
78.0ms	(/.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))))

simplify189.0ms

Algorithm

egg-herbie

Counts

463 → 463

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5134	17559

prune277.0ms

Filtered

131 candidates to 463 candidates (-253.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	457	6	463
Fresh	6	1	7
Picked	1	0	1
Done	1	1	2
Total	465	8	473

Merged error: 0b

Counts

473 → 8

regimes26.0ms

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

sample578.0ms

Algorithm

intervals

Results

217.0ms	2006×	body	1024	valid
122.0ms	4310×	body	128	valid
80.0ms	947×	body	512	valid
32.0ms	233×	body	2048	valid
30.0ms	504×	body	256	valid
0.0ms	4×	body	128	nan

Details

analyze3.0ms

sample21.0ms

simplify11.0ms

prune1.0ms

localize5.0ms

rewrite16.0ms

series107.0ms

simplify100.0ms

prune34.0ms

localize6.0ms

rewrite38.0ms

series130.0ms

simplify99.0ms

prune79.0ms

localize10.0ms

rewrite37.0ms

series754.0ms

simplify73.0ms

prune159.0ms

localize22.0ms

rewrite159.0ms

series330.0ms

simplify189.0ms

prune277.0ms

regimes26.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample578.0ms

Profiling