Details

sample31.0ms

Algorithm

intervals

Results

9.0ms	187×	body	80	valid
5.0ms	24×	body	2560	valid
4.0ms	22×	body	1280	valid
2.0ms	7×	body	5120	valid
1.0ms	9×	body	640	valid
1.0ms	6×	body	320	valid
0.0ms	1×	body	160	valid

simplify9.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	8
1	28	8
2	36	8
3	44	8
4	46	8
5	46	8

prune3.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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: 39.3b

Counts

2 → 1

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.4b	(- (sqrt (+ (* re re) (* im im))) re)
29.3b	(sqrt (+ (* re re) (* im im)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
20×	`*-un-lft-identity`
18×	`add-cube-cbrt` `prod-diff`
16×	`sqrt-prod`
7×	`add-log-exp`
6×	`fma-neg`
4×	`pow1`
3×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
2×	`flip3-+` `sqrt-div` `flip-+` `difference-of-squares`
1×	`+-commutative` `sub-neg` `rem-sqrt-square` `flip3--` `fma-def` `sqrt-pow1` `pow1/2` `diff-log` `sum-log` `flip--` `hypot-def` `distribute-lft-out--`

Counts

3 → 73

Calls

3 calls:

4.0ms	(+ (* re re) (* im im))
8.0ms	(- (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series112.0ms

Counts

3 → 9

Calls

3 calls:

27.0ms	(+ (* re re) (* im im))
49.0ms	(- (sqrt (+ (* re re) (* im im))) re)
36.0ms	(sqrt (+ (* re re) (* im im)))

simplify39.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	250	664
1	1037	430
2	5002	381

prune182.0ms

Filtered

82 candidates to 56 candidates (68.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	76	6	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	77	6	83

Merged error: 7.9b

Counts

83 → 6

localize7.0ms

Local error

Found 1 expressions with local error:

0.4b	(- (hypot re im) re)

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`prod-diff`
8×	`add-cube-cbrt`
3×	`fma-neg` `add-log-exp`
1×	`pow1` `add-exp-log` `expm1-log1p-u` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`

Counts

1 → 28

Calls

1 calls:

4.0ms

(- (hypot re im) re)

series61.0ms

Counts

1 → 3

Calls

1 calls:

60.0ms

(- (hypot re im) re)

simplify47.0ms

Algorithm

egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 3 (43.0ms)

Iter	Nodes	Cost
0	119	199
1	333	125
2	1490	116
3	5001	85

prune62.0ms

Filtered

31 candidates to 20 candidates (64.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	29	2	31
Fresh	2	3	5
Picked	0	1	1
Done	0	0	0
Total	31	6	37

Merged error: 7.9b

Counts

37 → 6

localize10.0ms

Local error

Found 1 expressions with local error:

16.5b

(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

1×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `fma-udef` `log1p-expm1-u` `add-log-exp`

Counts

1 → 10

Calls

1 calls:

1.0ms

(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

series142.0ms

Counts

1 → 3

Calls

1 calls:

142.0ms

(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

simplify53.0ms

Algorithm

egg-herbie

Counts

13 → 13

Iterations

Useful iterations: 3 (14.0ms)

Iter	Nodes	Cost
0	48	100
1	133	85
2	439	82
3	1931	78
4	5001	78

prune52.0ms

Filtered

13 candidates to 12 candidates (92.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	11	2	13
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	12	7	19

Merged error: 7.9b

Counts

19 → 7

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (hypot re im))
0.5b	(cbrt (hypot re im))
0.5b	(cbrt (hypot re im))
16.2b	(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) (- re))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`fma-udef`

Counts

4 → 49

Calls

4 calls:

1.0ms	(cbrt (hypot re im))
1.0ms	(cbrt (hypot re im))
1.0ms	(cbrt (hypot re im))
1.0ms	(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) (- re))

series491.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(cbrt (hypot re im))
113.0ms	(cbrt (hypot re im))
115.0ms	(cbrt (hypot re im))
152.0ms	(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) (- re))

simplify139.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 4 (133.0ms)

Iter	Nodes	Cost
0	84	329
1	188	287
2	663	279
3	3464	272
4	5001	263

prune184.0ms

Filtered

61 candidates to 55 candidates (90.2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	56	5	61
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	58	10	68

Merged error: 7.8b

Counts

68 → 10

regimes182.0ms

Accuracy

24.8% (4.2b remaining)

Error of 11.6b against oracle of 7.4b and baseline of 13.0b

bsearch45.0ms

Steps

Iters	Range		Point
7	1.7947041849682734e+52	3.0177612373656884e+53	9.420547715814937e+52

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	13
1	29	13
2	29	13

end0.0ms

sample721.0ms

Algorithm

intervals

Results

220.0ms	6060×	body	80	valid
139.0ms	665×	body	2560	valid
84.0ms	500×	body	1280	valid
74.0ms	290×	body	5120	valid
35.0ms	274×	body	640	valid
13.0ms	134×	body	320	valid
5.0ms	77×	body	160	valid