Details

sample27.0ms

Algorithm

intervals

Results

6.0ms	189×	body	80	valid
4.0ms	22×	body	2560	valid
3.0ms	12×	body	5120	valid
2.0ms	13×	body	1280	valid
1.0ms	11×	body	640	valid
0.0ms	5×	body	320	valid
0.0ms	4×	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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* re re) (* im im))
1.5b	(+ (sqrt (+ (* re re) (* im im))) re)
31.6b	(sqrt (+ (* re re) (* im im)))

rewrite25.0ms

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))
18.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series112.0ms

Counts

3 → 9

Calls

3 calls:

27.0ms	(+ (* re re) (* im im))
49.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
36.0ms	(sqrt (+ (* re re) (* im im)))

simplify70.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 3 (65.0ms)

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

prune170.0ms

Filtered

61 candidates to 53 candidates (86.9%)

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 6.4b

localize7.0ms

Local error

Found 1 expressions with local error:

1.3b	(+ (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)

series59.0ms

Counts

1 → 3

Calls

1 calls:

59.0ms

(+ (hypot re im) re)

simplify74.0ms

Algorithm

egg-herbie

Counts

20 → 20

Iterations

Useful iterations: 3 (13.0ms)

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

prune57.0ms

Filtered

20 candidates to 18 candidates (90.0%)

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 6.3b

localize9.0ms

Local error

Found 1 expressions with local error:

16.3b

(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)

series146.0ms

Counts

1 → 3

Calls

1 calls:

146.0ms

(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

prune41.0ms

Filtered

13 candidates to 11 candidates (84.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 6.3b

localize15.0ms

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))
16.0b	(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))
0.0ms	(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)

series484.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(cbrt (hypot re im))
119.0ms	(cbrt (hypot re im))
113.0ms	(cbrt (hypot re im))
138.0ms	(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) re)

simplify130.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 4 (125.0ms)

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

prune188.0ms

Filtered

61 candidates to 54 candidates (88.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 6.3b

regimes115.0ms

Accuracy

32.1% (4.0b remaining)

Error of 11.3b against oracle of 7.3b and baseline of 13.2b

bsearch141.0ms

Steps

Iters	Range		Point
7	-1.901214192353153e-14	-7.432278704161316e-16	-4.026179673256086e-15
7	-1052513.600169936	-9253.133766593879	-9913.059103329042
10	-1.0719231849388273e+91	-1.1809596141379282e+75	-4.407661401632079e+87

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

sample694.0ms

Algorithm

intervals

Results

207.0ms	6044×	body	80	valid
148.0ms	715×	body	2560	valid
81.0ms	494×	body	1280	valid
63.0ms	263×	body	5120	valid
36.0ms	261×	body	640	valid
16.0ms	146×	body	320	valid
5.0ms	77×	body	160	valid