Details

sample26.0ms

Algorithm

intervals

Results

6.0ms	196×	body	80	valid
3.0ms	18×	body	2560	valid
3.0ms	17×	body	1280	valid
2.0ms	15×	body	640	valid
1.0ms	5×	body	5120	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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.8b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.1b	(- (sqrt (+ (* re re) (* im im))) re)
29.7b	(sqrt (+ (* re re) (* im im)))

rewrite69.0ms

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:

8.0ms	(+ (* re re) (* im im))
51.0ms	(- (sqrt (+ (* re re) (* im im))) re)
8.0ms	(sqrt (+ (* re re) (* im im)))

series101.0ms

Counts

3 → 9

Calls

3 calls:

24.0ms	(+ (* re re) (* im im))
44.0ms	(- (sqrt (+ (* re re) (* im im))) re)
33.0ms	(sqrt (+ (* re re) (* im im)))

simplify37.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (30.0ms)

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

prune175.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 6.1b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(hypot re im)
0.1b	(- (hypot re im) re)

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`add-cube-cbrt` `prod-diff`
4×	`add-log-exp`
3×	`fma-neg`
2×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
1×	`sub-neg` `hypot-udef` `flip3--` `diff-log` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 38

Calls

2 calls:

0.0ms	(hypot re im)
7.0ms	(- (hypot re im) re)

series92.0ms

Counts

2 → 6

Calls

2 calls:

42.0ms	(hypot re im)
50.0ms	(- (hypot re im) re)

simplify51.0ms

Algorithm

egg-herbie

Counts

44 → 44

Iterations

Useful iterations: 3 (47.0ms)

Iter	Nodes	Cost
0	130	223
1	366	140
2	1695	131
3	5001	109

prune98.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 6.0b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(hypot re im)
0.0b	(hypot re im)
14.8b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (* -1 re))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

3×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`hypot-udef`
1×	`fma-udef`

Counts

3 → 30

Calls

3 calls:

0.0ms	(hypot re im)
0.0ms	(hypot re im)
0.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (* -1 re))

series207.0ms

Counts

3 → 9

Calls

3 calls:

40.0ms	(hypot re im)
43.0ms	(hypot re im)
124.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (* -1 re))

simplify64.0ms

Algorithm

egg-herbie

Counts

39 → 39

Iterations

Useful iterations: 3 (16.0ms)

Iter	Nodes	Cost
0	63	154
1	172	133
2	521	130
3	2202	126
4	5003	126

prune153.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 6.0b

localize13.0ms

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))
9.5b	(- (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im))) re)

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`add-log-exp`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`pow1/3` `prod-diff`
1×	`sub-neg` `flip3--` `fma-neg` `diff-log` `flip--`

Counts

4 → 57

Calls

4 calls:

1.0ms	(cbrt (hypot re im))
1.0ms	(cbrt (hypot re im))
1.0ms	(cbrt (hypot re im))
33.0ms	(- (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im))) re)

series362.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(cbrt (hypot re im))
102.0ms	(cbrt (hypot re im))
108.0ms	(cbrt (hypot re im))
51.0ms	(- (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im))) re)

simplify90.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 3 (85.0ms)

Iter	Nodes	Cost
0	167	446
1	570	322
2	2968	294
3	5001	292

prune194.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.0b

regimes114.0ms

Accuracy

22.7% (4.7b remaining)

Error of 12.1b against oracle of 7.3b and baseline of 13.4b

bsearch127.0ms

Steps

Iters	Range		Point
8	1.5130510757279288e+54	2.214368242189096e+57	1.0333038407224694e+55
7	105711978.38856223	21864197814.473186	242668761.66222733
8	1.3336169194388861e-70	1.8614563384609176e-67	1.8312791588701464e-67

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

sample687.0ms

Algorithm

intervals

Results

189.0ms	6022×	body	80	valid
133.0ms	714×	body	2560	valid
76.0ms	484×	body	1280	valid
63.0ms	263×	body	5120	valid
34.0ms	295×	body	640	valid
13.0ms	149×	body	320	valid
4.0ms	73×	body	160	valid