Details

analyze1.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
100%	0%	0%	1

sample35.0ms

Algorithm

intervals

Results

19.0ms	89×	body	1280	valid
5.0ms	130×	body	80	valid
3.0ms	18×	body	640	valid
1.0ms	12×	body	320	valid
1.0ms	7×	body	160	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	44	10
1	44	10

prune4.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 15.4b

Counts

2 → 1

localize6.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot.f64 1 x)
0.0b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
0.0b	(/.f64 1/2 (hypot.f64 1 x))
2.4b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
13×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
8×	`sqrt-prod_binary64`
6×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`pow1_binary64`
4×	`difference-of-squares_binary64`
3×	`associate-/r_binary64` `associate-/l_binary64` `distribute-lft-out--_binary64`
2×	`distribute-lft-out_binary64` `sqrt-div_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `pow1/2_binary64` `flip3--_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `flip--_binary64` `flip-+_binary64`

Counts

4 → 68

Calls

4 calls:

1.0ms	(hypot.f64 1 x)
6.0ms	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
3.0ms	(/.f64 1/2 (hypot.f64 1 x))
14.0ms	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

series27.0ms

Counts

4 → 12

Calls

4 calls:

1.0ms	(hypot.f64 1 x)
10.0ms	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
5.0ms	(/.f64 1/2 (hypot.f64 1 x))
11.0ms	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

simplify64.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4987	797
1	4987	797

prune56.0ms

Filtered

53 candidates to 80 candidates (-50.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	75	5	80
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	76	5	81

Merged error: 14.9b

Counts

81 → 5

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.f64 1/2 (hypot.f64 1 x))
0.0b	(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
0.0b	(+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
1.9b	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

82×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
53×	`times-frac_binary64`
32×	`distribute-lft-out_binary64`
26×	`add-cube-cbrt_binary64`
16×	`difference-of-squares_binary64` `sqrt-prod_binary64`
9×	`associate-/r_binary64` `associate-/l_binary64`
8×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `distribute-lft-out--_binary64`
4×	`pow1_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `flip3--_binary64` `cbrt-undiv_binary64` `associate-/r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `flip--_binary64` `flip-+_binary64`
1×	`sub-neg_binary64` `diff-log_binary64` `div-sub_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

4 → 120

Calls

4 calls:

3.0ms	(/.f64 1/2 (hypot.f64 1 x))
18.0ms	(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
9.0ms	(+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
9.0ms	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))

series54.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(/.f64 1/2 (hypot.f64 1 x))
31.0ms	(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
11.0ms	(+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
7.0ms	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))

simplify59.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4922	2417
1	4922	2417

prune126.0ms

Filtered

81 candidates to 132 candidates (-63.0%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	127	5	132
Fresh	4	0	4
Picked	1	0	1
Done	0	0	0
Total	132	5	137

Merged error: 14.9b

Counts

137 → 5

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (/.f64 (-.f64 1/4 (/.f64 1/4 (*.f64 (hypot.f64 1 x) (hypot.f64 1 x)))) (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
0.0b	(/.f64 (-.f64 1/4 (/.f64 1/4 (*.f64 (hypot.f64 1 x) (hypot.f64 1 x)))) (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
0.6b	(/.f64 1/4 (*.f64 (hypot.f64 1 x) (hypot.f64 1 x)))
1.9b	(-.f64 1/4 (/.f64 1/4 (*.f64 (hypot.f64 1 x) (hypot.f64 1 x))))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

447×	`*-un-lft-identity_binary64`
409×	`times-frac_binary64`
324×	`add-sqr-sqrt_binary64`
173×	`distribute-lft-out_binary64`
126×	`add-cube-cbrt_binary64`
68×	`difference-of-squares_binary64`
62×	`sqrt-prod_binary64`
39×	`associate-/l*_binary64`
34×	`distribute-lft-out--_binary64`
18×	`associate-/r/_binary64`
16×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
11×	`associate-/r*_binary64`
10×	`div-inv_binary64`
9×	`flip3-+_binary64` `flip-+_binary64`
6×	`add-log-exp_binary64` `cbrt-undiv_binary64` `div-exp_binary64`
4×	`pow1_binary64`
3×	`associate-/l/_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64`
2×	`flip3--_binary64` `flip--_binary64`
1×	`sub-neg_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`

Counts

4 → 320

Calls

4 calls:

27.0ms	(/.f64 (/.f64 (-.f64 1/4 (/.f64 1/4 (*.f64 (hypot.f64 1 x) (hypot.f64 1 x)))) (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
13.0ms	(/.f64 (-.f64 1/4 (/.f64 1/4 (*.f64 (hypot.f64 1 x) (hypot.f64 1 x)))) (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
5.0ms	(/.f64 1/4 (*.f64 (hypot.f64 1 x) (hypot.f64 1 x)))
6.0ms	(-.f64 1/4 (/.f64 1/4 (*.f64 (hypot.f64 1 x) (hypot.f64 1 x))))

series119.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(/.f64 (/.f64 (-.f64 1/4 (/.f64 1/4 (*.f64 (hypot.f64 1 x) (hypot.f64 1 x)))) (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
33.0ms	(/.f64 (-.f64 1/4 (/.f64 1/4 (*.f64 (hypot.f64 1 x) (hypot.f64 1 x)))) (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
12.0ms	(/.f64 1/4 (*.f64 (hypot.f64 1 x) (hypot.f64 1 x)))
15.0ms	(-.f64 1/4 (/.f64 1/4 (*.f64 (hypot.f64 1 x) (hypot.f64 1 x))))

simplify116.0ms

Algorithm

egg-herbie

Counts

332 → 332

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5655	11817

prune519.0ms

Filtered

163 candidates to 332 candidates (-103.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	329	3	332
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	331	6	337

Merged error: 14.6b

Counts

337 → 6

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 4)
0.6b	(/.f64 1/16 (pow.f64 (hypot.f64 1 x) 2))
0.6b	(/.f64 1/4 (*.f64 (hypot.f64 1 x) (hypot.f64 1 x)))
1.8b	(-.f64 (pow.f64 1/4 3) (pow.f64 (/.f64 1/4 (*.f64 (hypot.f64 1 x) (hypot.f64 1 x))) 3))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

69×	`add-sqr-sqrt_binary64`
44×	`times-frac_binary64`
43×	`unpow-prod-down_binary64`
41×	`*-un-lft-identity_binary64`
31×	`add-cube-cbrt_binary64`
24×	`difference-of-squares_binary64`
18×	`cube-prod_binary64`
17×	`add-exp-log_binary64`
15×	`sqr-pow_binary64`
11×	`add-cbrt-cube_binary64`
9×	`associate-/r*_binary64`
6×	`add-log-exp_binary64` `associate-/l*_binary64` `div-exp_binary64`
5×	`pow1_binary64` `distribute-lft-out--_binary64`
4×	`unpow2_binary64`
3×	`pow-unpow_binary64` `cbrt-undiv_binary64` `div-inv_binary64` `pow-exp_binary64`
2×	`pow-to-exp_binary64` `clear-num_binary64` `frac-2neg_binary64`
1×	`difference-cubes_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `pow-pow_binary64` `prod-exp_binary64` `flip--_binary64`

Counts

4 → 139

Calls

4 calls:

5.0ms	(pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 4)
5.0ms	(/.f64 1/16 (pow.f64 (hypot.f64 1 x) 2))
5.0ms	(/.f64 1/4 (*.f64 (hypot.f64 1 x) (hypot.f64 1 x)))
17.0ms	(-.f64 (pow.f64 1/4 3) (pow.f64 (/.f64 1/4 (*.f64 (hypot.f64 1 x) (hypot.f64 1 x))) 3))

series244.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 4)
12.0ms	(/.f64 1/16 (pow.f64 (hypot.f64 1 x) 2))
12.0ms	(/.f64 1/4 (*.f64 (hypot.f64 1 x) (hypot.f64 1 x)))
208.0ms	(-.f64 (pow.f64 1/4 3) (pow.f64 (/.f64 1/4 (*.f64 (hypot.f64 1 x) (hypot.f64 1 x))) 3))

simplify63.0ms

Algorithm

egg-herbie

Counts

151 → 151

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5083	1845

prune289.0ms

Filtered

91 candidates to 151 candidates (-65.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	150	1	151
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	151	6	157

Merged error: 14.6b

Counts

157 → 6

regimes57.0ms

Accuracy

0% (0.3b remaining)

Error of 15.2b against oracle of 14.9b and baseline of 15.2b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	41	50
1	41	50

end0.0ms

sample1.1s

Algorithm

intervals

Results

631.0ms	2870×	body	1280	valid
155.0ms	4032×	body	80	valid
110.0ms	629×	body	640	valid
42.0ms	313×	body	320	valid
12.0ms	156×	body	160	valid

Details

analyze1.0ms

sample35.0ms

simplify6.0ms

prune4.0ms

localize6.0ms

rewrite26.0ms

series27.0ms

simplify64.0ms

prune56.0ms

localize9.0ms

rewrite44.0ms

series54.0ms

simplify59.0ms

prune126.0ms

localize15.0ms

rewrite77.0ms

series119.0ms

simplify116.0ms

prune519.0ms

localize24.0ms

rewrite38.0ms

series244.0ms

simplify63.0ms

prune289.0ms

regimes57.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.1s

Profiling