Details

sample41.0ms

Algorithm

intervals

Results

14.0ms	197×	body	80	valid
6.0ms	19×	body	2560	valid
5.0ms	18×	body	1280	valid
3.0ms	6×	body	5120	valid
2.0ms	7×	body	640	valid
1.0ms	7×	body	320	valid
0.0ms	2×	body	160	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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.6b

localize10.0ms

Local error

Found 2 expressions with local error:

0.6b	(- (sqrt (+ (* re re) (* im im))) re)
26.6b	(sqrt (+ (* re re) (* im im)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 59

Calls

2 calls:

22.0ms	(- (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series84.0ms

Counts

2 → 6

Calls

2 calls:

45.0ms	(- (sqrt (+ (* re re) (* im im))) re)
39.0ms	(sqrt (+ (* re re) (* im im)))

simplify108.0ms

Algorithm

egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 3 (100.0ms)

Iter	Nodes	Cost
0	211	590
1	687	366
2	3279	321
3	5001	295

prune158.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 6.1b

localize8.0ms

Local error

Found 1 expressions with local error:

0.6b	(- (* 1 (hypot re im)) re)

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

1 → 19

Calls

1 calls:

3.0ms

(- (* 1 (hypot re im)) re)

series59.0ms

Counts

1 → 3

Calls

1 calls:

59.0ms

(- (* 1 (hypot re im)) re)

simplify46.0ms

Algorithm

egg-herbie

Counts

22 → 22

Iterations

Useful iterations: 3 (43.0ms)

Iter	Nodes	Cost
0	117	109
1	346	79
2	1545	76
3	5002	72

prune71.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 6.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (sqrt (+ (* re re) (* im im))))
14.4b	(fma (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))) (* -1 re))
26.6b	(sqrt (+ (* re re) (* im im)))
26.6b	(sqrt (+ (* re re) (* im im)))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

16×	`sqrt-prod`
12×	`add-sqr-sqrt`
8×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-div`
6×	`sqrt-pow1`
4×	`add-exp-log` `expm1-log1p-u` `rem-sqrt-square` `pow1/2` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`flip3-+` `flip-+`
2×	`hypot-def`
1×	`fma-udef`

Counts

4 → 69

Calls

4 calls:

5.0ms	(sqrt (sqrt (+ (* re re) (* im im))))
0.0ms	(fma (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))) (* -1 re))
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series250.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(sqrt (sqrt (+ (* re re) (* im im))))
94.0ms	(fma (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))) (* -1 re))
39.0ms	(sqrt (+ (* re re) (* im im)))
35.0ms	(sqrt (+ (* re re) (* im im)))

simplify57.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 3 (45.0ms)

Iter	Nodes	Cost
0	185	541
1	507	489
2	1477	487
3	5001	480

prune317.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 6.1b

localize18.0ms

Local error

Found 4 expressions with local error:

14.5b	(fma (sqrt (sqrt (+ (* re re) (* im im)))) (* (fabs (cbrt (sqrt (+ (* re re) (* im im))))) (sqrt (cbrt (sqrt (+ (* re re) (* im im)))))) (* -1 re))
26.6b	(sqrt (+ (* re re) (* im im)))
26.6b	(sqrt (+ (* re re) (* im im)))
26.6b	(sqrt (+ (* re re) (* im im)))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
6×	`sqrt-div`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+` `hypot-def`
1×	`fma-udef`

Counts

4 → 64

Calls

4 calls:

0.0ms	(fma (sqrt (sqrt (+ (* re re) (* im im)))) (* (fabs (cbrt (sqrt (+ (* re re) (* im im))))) (sqrt (cbrt (sqrt (+ (* re re) (* im im)))))) (* -1 re))
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series231.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(fma (sqrt (sqrt (+ (* re re) (* im im)))) (* (fabs (cbrt (sqrt (+ (* re re) (* im im))))) (sqrt (cbrt (sqrt (+ (* re re) (* im im)))))) (* -1 re))
34.0ms	(sqrt (+ (* re re) (* im im)))
39.0ms	(sqrt (+ (* re re) (* im im)))
35.0ms	(sqrt (+ (* re re) (* im im)))

simplify67.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 3 (54.0ms)

Iter	Nodes	Cost
0	179	620
1	630	563
2	1965	558
3	5002	555

prune378.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 6.1b

regimes132.0ms

Accuracy

23.1% (4.4b remaining)

Error of 12.0b against oracle of 7.6b and baseline of 13.3b

bsearch63.0ms

Steps

Iters	Range		Point
7	1.1608947055862536e+73	1.608126041204279e+75	3.5638508626778457e+74

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	13
1	32	13
2	32	13

end0.0ms

sample1.2s

Algorithm

intervals

Results

423.0ms	6008×	body	80	valid
230.0ms	658×	body	2560	valid
144.0ms	482×	body	1280	valid
135.0ms	324×	body	5120	valid
67.0ms	295×	body	640	valid
29.0ms	162×	body	320	valid
10.0ms	71×	body	160	valid