Details

sample27.0ms

Algorithm

intervals

Results

7.0ms	197×	body	80	valid
4.0ms	22×	body	2560	valid
2.0ms	10×	body	5120	valid
2.0ms	13×	body	1280	valid
1.0ms	7×	body	640	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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.4b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
1.3b	(- (sqrt (+ (* re re) (* im im))) re)
32.8b	(sqrt (+ (* re re) (* im im)))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 74

Calls

3 calls:

31.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
22.0ms	(- (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series252.0ms

Counts

3 → 9

Calls

3 calls:

170.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
48.0ms	(- (sqrt (+ (* re re) (* im im))) re)
35.0ms	(sqrt (+ (* re re) (* im im)))

simplify44.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	314	760
1	1192	522
2	5001	473

prune201.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 6.9b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (* 2.0 (+ (- (hypot re im) re) 0)))
1.3b	(- (hypot re im) re)

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`add-cube-cbrt` `prod-diff`
5×	`pow1`
4×	`add-log-exp`
3×	`fma-neg`
2×	`add-exp-log` `expm1-log1p-u` `sqrt-pow1` `sqrt-div` `associate-*r/` `add-cbrt-cube` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `flip3-+` `pow1/2` `diff-log` `pow-prod-down` `sqrt-prod` `flip--` `flip-+` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 43

Calls

2 calls:

10.0ms	(sqrt (* 2.0 (+ (- (hypot re im) re) 0)))
6.0ms	(- (hypot re im) re)

series240.0ms

Counts

2 → 6

Calls

2 calls:

186.0ms	(sqrt (* 2.0 (+ (- (hypot re im) re) 0)))
55.0ms	(- (hypot re im) re)

simplify45.0ms

Algorithm

egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	273	321
1	1082	232
2	5001	228

prune125.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 6.9b

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (* 2.0 (+ (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 0)))
14.4b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

5×	`pow1`
2×	`add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `-un-lft-identity` `sqrt-pow1` `sqrt-div` `associate-r/` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
1×	`flip3-+` `pow1/2` `pow-prod-down` `sqrt-prod` `flip-+` `fma-udef`

Counts

2 → 25

Calls

2 calls:

4.0ms	(sqrt (* 2.0 (+ (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 0)))
0.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

series375.0ms

Counts

2 → 6

Calls

2 calls:

233.0ms	(sqrt (* 2.0 (+ (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 0)))
141.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

simplify40.0ms

Algorithm

egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	192	304
1	720	267
2	5001	251

prune116.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 6.9b

localize19.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)))
14.4b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))
14.4b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))
14.4b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

rewrite2.0ms

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)))
0.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))
0.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))
0.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

series633.0ms

Counts

4 → 12

Calls

4 calls:

206.0ms	(cbrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)))
145.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))
143.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))
140.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

simplify48.0ms

Algorithm

egg-herbie

Counts

55 → 55

Iterations

Useful iterations: 3 (43.0ms)

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

prune255.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 6.8b

regimes164.0ms

Accuracy

11.6% (5.2b remaining)

Error of 12.3b against oracle of 7.2b and baseline of 13.0b

bsearch140.0ms

Steps

Iters	Range		Point
10	4.009959817432213e+225	1.4977125951265683e+237	2.1063886874167957e+226
9	43768.65998072103	667933791257.4816	84660.47455442467
0	1.526869511170923e-62	1.5527426425931768e-62	1.5398060768820498e-62

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	38	28
1	45	14
2	48	14
3	48	14

end0.0ms

sample709.0ms

Algorithm

intervals

Results

222.0ms	6101×	body	80	valid
138.0ms	676×	body	2560	valid
88.0ms	500×	body	1280	valid
62.0ms	240×	body	5120	valid
32.0ms	247×	body	640	valid
15.0ms	147×	body	320	valid
8.0ms	89×	body	160	valid