Details

sample25.0ms

Algorithm

intervals

Results

7.0ms	203×	body	80	valid
3.0ms	19×	body	1280	valid
3.0ms	14×	body	2560	valid
2.0ms	9×	body	5120	valid
1.0ms	6×	body	640	valid
0.0ms	5×	body	320	valid

simplify10.0ms

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: 36.8b

Counts

2 → 1

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.5b	(- (sqrt (+ (* re re) (* im im))) re)
27.7b	(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)))

series115.0ms

Counts

3 → 9

Calls

3 calls:

27.0ms	(+ (* re re) (* im im))
51.0ms	(- (sqrt (+ (* re re) (* im im))) re)
37.0ms	(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

prune174.0ms

Filtered

82 candidates to 56 candidates (68.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	77	5	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	78	5	83

Merged error: 5.6b

Counts

83 → 5

localize7.0ms

Local error

Found 1 expressions with local error:

0.5b	(- (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)

series59.0ms

Counts

1 → 3

Calls

1 calls:

59.0ms

(- (hypot re im) re)

simplify49.0ms

Algorithm

egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 3 (45.0ms)

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

prune59.0ms

Filtered

31 candidates to 20 candidates (64.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	30	1	31
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	31	5	36

Merged error: 5.6b

Counts

36 → 5

localize10.0ms

Local error

Found 1 expressions with local error:

12.9b

(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))

simplify56.0ms

Algorithm

egg-herbie

Counts

13 → 13

Iterations

Useful iterations: 3 (15.0ms)

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

prune46.0ms

Filtered

13 candidates to 12 candidates (92.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	12	1	13
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	12	6	18

Merged error: 5.6b

Counts

18 → 6

localize15.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)))
12.9b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))
12.9b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))
12.9b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

5×	`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×	`cbrt-prod` `fma-udef`
1×	`pow1/3`

Counts

4 → 43

Calls

4 calls:

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

series662.0ms

Counts

4 → 12

Calls

4 calls:

225.0ms	(cbrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)))
144.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))
148.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))
146.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

simplify48.0ms

Algorithm

egg-herbie

Counts

55 → 55

Iterations

Useful iterations: 3 (42.0ms)

Iter	Nodes	Cost
0	178	497
1	479	435
2	1621	418
3	5001	395

prune218.0ms

Filtered

55 candidates to 52 candidates (94.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	53	2	55
Fresh	0	3	3
Picked	1	0	1
Done	1	1	2
Total	55	6	61

Merged error: 5.6b

Counts

61 → 6

regimes137.0ms

Accuracy

32.7% (4.0b remaining)

Error of 11.8b against oracle of 7.8b and baseline of 13.8b

bsearch66.0ms

Steps

Iters	Range		Point
11	1.018541337974767e-30	1.8364001780596707e-08	2.869173686874317e-11

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

sample692.0ms

Algorithm

intervals

Results

203.0ms	5962×	body	80	valid
142.0ms	725×	body	2560	valid
84.0ms	525×	body	1280	valid
64.0ms	277×	body	5120	valid
35.0ms	294×	body	640	valid
13.0ms	146×	body	320	valid
4.0ms	71×	body	160	valid