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

7.0ms	54×	body	1280	valid
5.0ms	46×	body	640	valid
4.0ms	130×	body	80	valid
1.0ms	13×	body	320	valid
1.0ms	13×	body	160	valid

simplify7.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	70	7
1	70	7

prune2.0ms

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: 30.1b

Counts

2 → 1

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt.f64 (+.f64 x 1))
3.1b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

rewrite13.0ms

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))

series16.0ms

Counts

2 → 6

Calls

2 calls:

4.0ms	(sqrt.f64 (+.f64 x 1))
12.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

simplify54.0ms

Algorithm

egg-herbie

Counts

40 → 40

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5006	484

prune51.0ms

Filtered

30 candidates to 40 candidates (-33.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	36	4	40
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	37	4	41

Merged error: 0.2b

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)))

rewrite23.0ms

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`
7×	`add-exp-log_binary64`
6×	`associate-/r*_binary64`
5×	`add-log-exp_binary64` `pow1_binary64` `add-cbrt-cube_binary64`
3×	`flip3-+_binary64` `associate-/l*_binary64` `flip-+_binary64`
2×	`associate-/r/_binary64` `div-exp_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `1-exp_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` `+-commutative_binary64` `pow-flip_binary64` `sum-log_binary64`

Counts

3 → 75

Calls

3 calls:

3.0ms	(sqrt.f64 (+.f64 x 1))
8.0ms	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
10.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))

series23.0ms

Counts

3 → 9

Calls

3 calls:

7.0ms	(sqrt.f64 (+.f64 x 1))
7.0ms	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
9.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))

simplify57.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4999	966
1	4999	966

prune116.0ms

Filtered

56 candidates to 84 candidates (-50.0%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	76	8	84
Fresh	2	1	3
Picked	0	1	1
Done	0	0	0
Total	78	10	88

Merged error: 0.0b

Counts

88 → 10

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (sqrt.f64 (+.f64 1 x)))
0.1b	(sqrt.f64 (sqrt.f64 (+.f64 1 x)))
0.2b	(/.f64 1 (+.f64 (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
0.3b	(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x))))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

106×	`sqrt-prod_binary64`
62×	`add-sqr-sqrt_binary64`
46×	`*-un-lft-identity_binary64`
40×	`sqrt-pow1_binary64`
32×	`pow1_binary64` `sqrt-div_binary64`
28×	`add-cube-cbrt_binary64`
20×	`pow1/2_binary64`
18×	`swap-sqr_binary64`
10×	`associate-r_binary64` `add-exp-log_binary64` `associate-l_binary64`
9×	`flip3-+_binary64` `pow-prod-up_binary64` `unswap-sqr_binary64` `times-frac_binary64` `flip-+_binary64`
8×	`distribute-lft-out_binary64` `add-cbrt-cube_binary64`
5×	`pow-prod-down_binary64` `pow-sqr_binary64`
4×	`add-log-exp_binary64` `rem-sqrt-square_binary64` `frac-times_binary64`
3×	`associate-/r_binary64` `associate-/l_binary64`
2×	`associate-r/_binary64` `associate-/r/_binary64` `div-exp_binary64` `associate-l/_binary64`
1×	`cbrt-unprod_binary64` `1-exp_binary64` `cbrt-undiv_binary64` `rem-square-sqrt_binary64` `pow-plus_binary64` `sqrt-unprod_binary64` `clear-num_binary64` `inv-pow_binary64` `prod-exp_binary64` `frac-2neg_binary64` `rec-exp_binary64` `div-inv_binary64` `pow-flip_binary64` `pow2_binary64` `*-commutative_binary64`

Counts

4 → 165

Calls

4 calls:

4.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 x)))
4.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 x)))
17.0ms	(/.f64 1 (+.f64 (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
19.0ms	(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x))))

series28.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 x)))
6.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 x)))
12.0ms	(/.f64 1 (+.f64 (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
5.0ms	(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x))))

simplify84.0ms

Algorithm

egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4860	1586
1	4860	1586

prune139.0ms

Filtered

89 candidates to 177 candidates (-98.9%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	175	2	177
Fresh	1	7	8
Picked	0	1	1
Done	0	1	1
Total	176	11	187

Merged error: 0.0b

Counts

187 → 11

localize9.0ms

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))

rewrite28.0ms

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` `add-exp-log_binary64`
9×	`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` `div-exp_binary64` `sqrt-div_binary64`
1×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `1-exp_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `inv-pow_binary64` `prod-exp_binary64` `frac-2neg_binary64` `rec-exp_binary64` `div-inv_binary64` `pow-flip_binary64` `*-commutative_binary64`

Counts

4 → 90

Calls

4 calls:

11.0ms	(/.f64 1 (+.f64 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
8.0ms	(*.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))

series81.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(/.f64 1 (+.f64 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
11.0ms	(*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x))))
6.0ms	(cbrt.f64 (+.f64 1 x))
6.0ms	(cbrt.f64 (+.f64 1 x))

simplify50.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	4947	1951
1	4947	1951

prune131.0ms

Filtered

79 candidates to 102 candidates (-29.1%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	100	2	102
Fresh	2	6	8
Picked	0	1	1
Done	1	1	2
Total	103	10	113

Merged error: 0.0b

Counts

113 → 10

regimes88.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	9
1	10	9

end0.0ms

sample634.0ms

Algorithm

intervals

Results

232.0ms	1750×	body	1280	valid
126.0ms	1220×	body	640	valid
116.0ms	4106×	body	80	valid
48.0ms	608×	body	320	valid
16.0ms	316×	body	160	valid

Details

analyze2.0ms

sample22.0ms

simplify7.0ms

prune2.0ms

localize9.0ms

rewrite13.0ms

series16.0ms

simplify54.0ms

prune51.0ms

localize6.0ms

rewrite23.0ms

series23.0ms

simplify57.0ms

prune116.0ms

localize15.0ms

rewrite50.0ms

series28.0ms

simplify84.0ms

prune139.0ms

localize9.0ms

rewrite28.0ms

series81.0ms

simplify50.0ms

prune131.0ms

regimes88.0ms

bsearch0.0ms

simplify4.0ms

end0.0ms

sample634.0ms

Profiling