Details

sample25.0ms

Algorithm

intervals

Results

6.0ms	196×	body	80	valid
5.0ms	27×	body	2560	valid
2.0ms	16×	body	1280	valid
1.0ms	8×	body	640	valid
1.0ms	4×	body	5120	valid
0.0ms	3×	body	320	valid
0.0ms	2×	body	160	valid

simplify7.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	8
1	30	8
2	33	8
3	33	8

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.6b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.3b	(+ (sqrt (+ (* re re) (* im im))) re)
28.2b	(sqrt (+ (* re re) (* im im)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 52

Calls

3 calls:

8.0ms	(+ (* re re) (* im im))
34.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
8.0ms	(sqrt (+ (* re re) (* im im)))

series111.0ms

Counts

3 → 9

Calls

3 calls:

27.0ms	(+ (* re re) (* im im))
48.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
36.0ms	(sqrt (+ (* re re) (* im im)))

simplify65.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 3 (61.0ms)

Iter	Nodes	Cost
0	194	279
1	769	246
2	2332	233
3	5002	230

prune165.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 8.1b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(hypot re im)
0.3b	(+ (hypot re im) re)

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

5×	`*-un-lft-identity`
4×	`add-log-exp`
3×	`add-sqr-sqrt` `add-cube-cbrt` `fma-def`
2×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
1×	`+-commutative` `hypot-udef` `flip3-+` `sum-log` `flip-+` `distribute-lft-out`

Counts

2 → 27

Calls

2 calls:

0.0ms	(hypot re im)
5.0ms	(+ (hypot re im) re)

series104.0ms

Counts

2 → 6

Calls

2 calls:

45.0ms	(hypot re im)
59.0ms	(+ (hypot re im) re)

simplify73.0ms

Algorithm

egg-herbie

Counts

33 → 33

Iterations

Useful iterations: 3 (13.0ms)

Iter	Nodes	Cost
0	87	85
1	176	79
2	380	79
3	1030	78
4	3143	78
5	5001	78

prune93.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 8.1b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (hypot re im))
0.0b	(hypot re im)
0.0b	(hypot re im)
14.6b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt`
5×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-prod`
2×	`hypot-udef`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-udef`

Counts

4 → 45

Calls

4 calls:

1.0ms	(sqrt (hypot re im))
0.0ms	(hypot re im)
0.0ms	(hypot re im)
0.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

series321.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(sqrt (hypot re im))
50.0ms	(hypot re im)
45.0ms	(hypot re im)
141.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

simplify46.0ms

Algorithm

egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 3 (42.0ms)

Iter	Nodes	Cost
0	128	219
1	344	188
2	1419	179
3	5002	174

prune184.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 8.1b

localize14.0ms

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))
14.5b	(fma (sqrt (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)))) (sqrt (hypot re im)) re)

rewrite4.0ms

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))
0.0ms	(fma (sqrt (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)))) (sqrt (hypot re im)) re)

series477.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(cbrt (hypot re im))
110.0ms	(cbrt (hypot re im))
112.0ms	(cbrt (hypot re im))
143.0ms	(fma (sqrt (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)))) (sqrt (hypot re im)) re)

simplify137.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 4 (132.0ms)

Iter	Nodes	Cost
0	100	381
1	249	336
2	841	330
3	4138	294
4	5001	282

prune217.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 8.1b

regimes86.0ms

Accuracy

22.2% (4.3b remaining)

Error of 12.0b against oracle of 7.6b and baseline of 13.2b

bsearch132.0ms

Steps

Iters	Range	Point
9	-1.257508563021492e-70	-2.656711351641578e-76	-1.941232155667052e-71
7	-1.989428328455626e-07	-1.1960025753651706e-08	-1.0136200979503546e-07
9	-1.621829926510464e+42	-8.804681707553006e+35	-1.7761354360071877e+40

Iters

Range

Point

-1.257508563021492e-70

-2.656711351641578e-76

-1.941232155667052e-71

-1.989428328455626e-07

-1.1960025753651706e-08

-1.0136200979503546e-07

-1.621829926510464e+42

-8.804681707553006e+35

-1.7761354360071877e+40

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	33	24
1	36	12
2	39	12
3	39	12

end0.0ms

sample690.0ms

Algorithm

intervals

Results

191.0ms	6034×	body	80	valid
133.0ms	716×	body	2560	valid
71.0ms	463×	body	1280	valid
66.0ms	279×	body	5120	valid
30.0ms	262×	body	640	valid
14.0ms	158×	body	320	valid
5.0ms	88×	body	160	valid