Details

sample41.0ms

Algorithm

intervals

Results

15.0ms	197×	body	80	valid
7.0ms	21×	body	2560	valid
5.0ms	18×	body	1280	valid
2.0ms	5×	body	5120	valid
1.0ms	6×	body	640	valid
1.0ms	6×	body	320	valid
0.0ms	3×	body	160	valid

simplify7.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 37.0b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.7b	(+ (sqrt (+ (* re re) (* im im))) re)
27.5b	(sqrt (+ (* re re) (* im im)))

rewrite23.0ms

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:

3.0ms	(+ (* re re) (* im im))
16.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series112.0ms

Counts

3 → 9

Calls

3 calls:

26.0ms	(+ (* re re) (* im im))
50.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
35.0ms	(sqrt (+ (* re re) (* im im)))

simplify70.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 3 (66.0ms)

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

prune186.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 6.2b

localize8.0ms

Local error

Found 1 expressions with local error:

0.7b	(+ (hypot re im) re)

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

1 → 17

Calls

1 calls:

3.0ms

(+ (hypot re im) re)

series60.0ms

Counts

1 → 3

Calls

1 calls:

59.0ms

(+ (hypot re im) re)

simplify76.0ms

Algorithm

egg-herbie

Counts

20 → 20

Iterations

Useful iterations: 3 (14.0ms)

Iter	Nodes	Cost
0	74	61
1	162	55
2	350	55
3	952	54
4	3051	54
5	5001	54

prune65.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 6.2b

localize9.0ms

Local error

Found 1 expressions with local error:

14.2b

(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:

0.0ms

(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

series140.0ms

Counts

1 → 3

Calls

1 calls:

140.0ms

(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

simplify47.0ms

Algorithm

egg-herbie

Counts

13 → 13

Iterations

Useful iterations: 3 (13.0ms)

Iter	Nodes	Cost
0	45	88
1	118	73
2	387	69
3	1530	66
4	5001	66

prune51.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 6.2b

localize10.0ms

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))
14.2b	(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) re)

rewrite3.0ms

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:

0.0ms	(cbrt (hypot re im))
1.0ms	(cbrt (hypot re im))
1.0ms	(cbrt (hypot re im))
0.0ms	(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) re)

series458.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(cbrt (hypot re im))
108.0ms	(cbrt (hypot re im))
107.0ms	(cbrt (hypot re im))
136.0ms	(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) re)

simplify129.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 4 (124.0ms)

Iter	Nodes	Cost
0	79	316
1	179	276
2	648	268
3	3295	254
4	5002	251

prune193.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.2b

regimes108.0ms

Accuracy

30% (4.2b remaining)

Error of 11.2b against oracle of 7.0b and baseline of 13.0b

bsearch59.0ms

Steps

Iters	Range		Point
8	-0.0019174381104543623	-3.774608270569166e-06	-8.274027779590291e-06

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	12
1	24	12

end0.0ms

sample1.2s

Algorithm

intervals

Results

479.0ms	6066×	body	80	valid
223.0ms	629×	body	2560	valid
153.0ms	503×	body	1280	valid
125.0ms	297×	body	5120	valid
67.0ms	270×	body	640	valid
29.0ms	163×	body	320	valid
9.0ms	72×	body	160	valid