Details

sample26.0ms

Algorithm

intervals

Results

7.0ms	214×	body	80	valid
3.0ms	9×	body	320	valid
3.0ms	13×	body	2560	valid
2.0ms	7×	body	5120	valid
1.0ms	8×	body	1280	valid
0.0ms	3×	body	640	valid
0.0ms	2×	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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.7b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* re re) (* im im))
1.0b	(- (sqrt (+ (* re re) (* im im))) re)
29.6b	(sqrt (+ (* re re) (* im im)))

rewrite30.0ms

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:

3.0ms	(+ (* re re) (* im im))
22.0ms	(- (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series114.0ms

Counts

3 → 9

Calls

3 calls:

27.0ms	(+ (* re re) (* im im))
46.0ms	(- (sqrt (+ (* re re) (* im im))) re)
41.0ms	(sqrt (+ (* re re) (* im im)))

simplify39.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (30.0ms)

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

prune177.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 5.9b

localize8.0ms

Local error

Found 1 expressions with local error:

1.0b	(- (* 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)

series61.0ms

Counts

1 → 3

Calls

1 calls:

61.0ms

(- (* 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

prune57.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 5.9b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
10.3b	(fma (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))) (* -1 re))
29.6b	(sqrt (+ (* re re) (* im im)))
29.6b	(sqrt (+ (* re re) (* im im)))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 60

Calls

4 calls:

3.0ms	(+ (* re re) (* im im))
0.0ms	(fma (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))) (* -1 re))
3.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series197.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(+ (* re re) (* im im))
95.0ms	(fma (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))) (* -1 re))
35.0ms	(sqrt (+ (* re re) (* im im)))
39.0ms	(sqrt (+ (* re re) (* im im)))

simplify67.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (61.0ms)

Iter	Nodes	Cost
0	157	440
1	648	380
2	2168	374
3	5002	371

prune266.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 5.9b

localize19.0ms

Local error

Found 4 expressions with local error:

29.6b	(sqrt (+ (* re re) (* im im)))
29.6b	(sqrt (+ (* re re) (* im im)))
29.6b	(sqrt (+ (* re re) (* im im)))
29.6b	(sqrt (+ (* re re) (* im im)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 72

Calls

4 calls:

3.0ms	(sqrt (+ (* re re) (* im im)))
3.0ms	(sqrt (+ (* re re) (* im im)))
3.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series151.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(sqrt (+ (* re re) (* im im)))
41.0ms	(sqrt (+ (* re re) (* im im)))
35.0ms	(sqrt (+ (* re re) (* im im)))
40.0ms	(sqrt (+ (* re re) (* im im)))

simplify57.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	98	412
1	254	392
2	619	392
3	1573	392
4	5001	392

prune421.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 5.9b

regimes78.0ms

Accuracy

27.2% (4.1b remaining)

Error of 11.9b against oracle of 7.8b and baseline of 13.4b

bsearch51.0ms

Steps

Iters	Range		Point
8	3.047530528666286e+89	2.1241537053097443e+92	4.3140974653675633e+89

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	14
1	37	14
2	37	14

end0.0ms

sample667.0ms

Algorithm

intervals

Results

199.0ms	6000×	body	80	valid
140.0ms	728×	body	2560	valid
76.0ms	301×	body	5120	valid
73.0ms	478×	body	1280	valid
32.0ms	268×	body	640	valid
12.0ms	138×	body	320	valid
5.0ms	87×	body	160	valid