Details

sample24.0ms

Algorithm

intervals

Results

6.0ms	199×	body	80	valid
4.0ms	20×	body	2560	valid
2.0ms	15×	body	1280	valid
1.0ms	10×	body	640	valid
1.0ms	5×	body	5120	valid
0.0ms	4×	body	320	valid
0.0ms	3×	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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.6b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.6b	(- (sqrt (+ (* re re) (* im im))) re)
31.6b	(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)))

simplify36.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (29.0ms)

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

prune189.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 7.0b

localize8.0ms

Local error

Found 1 expressions with local error:

0.6b	(- (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)

series56.0ms

Counts

1 → 3

Calls

1 calls:

56.0ms

(- (hypot re im) re)

simplify46.0ms

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

prune76.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 6.9b

localize11.0ms

Local error

Found 1 expressions with local error:

14.0b

(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))

simplify54.0ms

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

prune56.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 6.9b

localize12.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (hypot re im))
0.6b	(cbrt (hypot re im))
0.6b	(cbrt (hypot re im))
13.7b	(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))

series460.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(cbrt (hypot re im))
107.0ms	(cbrt (hypot re im))
111.0ms	(cbrt (hypot re im))
134.0ms	(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) (- re))

simplify134.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 4 (129.0ms)

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

prune201.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 6.9b

regimes184.0ms

Accuracy

-6.7% (6.4b remaining)

Error of 13.7b against oracle of 7.3b and baseline of 13.3b

bsearch2.0ms

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 2 (1.0ms)

Iter	Nodes	Cost
0	42	38
1	49	38
2	55	18
3	58	18
4	64	18
5	75	18
6	82	18
7	83	18
8	83	18

end0.0ms

sample653.0ms

Algorithm

intervals

Results

190.0ms	6029×	body	80	valid
139.0ms	707×	body	2560	valid
77.0ms	491×	body	1280	valid
59.0ms	260×	body	5120	valid
37.0ms	275×	body	640	valid
13.0ms	143×	body	320	valid
6.0ms	95×	body	160	valid