Details

sample26.0ms

Algorithm

intervals

Results

6.0ms	189×	body	80	valid
3.0ms	19×	body	2560	valid
3.0ms	14×	body	5120	valid
2.0ms	15×	body	1280	valid
1.0ms	9×	body	640	valid
1.0ms	8×	body	320	valid
0.0ms	2×	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

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 37.2b

Counts

2 → 1

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.5b	(+ (sqrt (+ (* re re) (* im im))) re)
27.7b	(sqrt (+ (* re re) (* im im)))

rewrite16.0ms

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:

4.0ms	(+ (* re re) (* im im))
7.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series109.0ms

Counts

3 → 9

Calls

3 calls:

26.0ms	(+ (* re re) (* im im))
49.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
34.0ms	(sqrt (+ (* re re) (* im im)))

simplify66.0ms

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

prune172.0ms

Filtered

61 candidates to 53 candidates (86.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	54	7	61
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	55	7	62

Merged error: 7.5b

Counts

62 → 7

localize7.0ms

Local error

Found 1 expressions with local error:

0.5b	(+ (hypot re im) re)

rewrite4.0ms

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)

series84.0ms

Counts

1 → 3

Calls

1 calls:

84.0ms

(+ (hypot re im) re)

simplify82.0ms

Algorithm

egg-herbie

Counts

20 → 20

Iterations

Useful iterations: 3 (17.0ms)

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

prune56.0ms

Filtered

20 candidates to 18 candidates (90.0%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	18	2	20
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	20	7	27

Merged error: 7.4b

Counts

27 → 7

localize13.0ms

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:

1.0ms

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

series135.0ms

Counts

1 → 3

Calls

1 calls:

135.0ms

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

simplify44.0ms

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

prune54.0ms

Filtered

13 candidates to 11 candidates (84.6%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	11	2	13
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	11	9	20

Merged error: 7.4b

Counts

20 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re))
16.3b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)
16.3b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)
16.3b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

rewrite4.0ms

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

series628.0ms

Counts

4 → 12

Calls

4 calls:

198.0ms	(cbrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re))
145.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)
140.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)
144.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

simplify46.0ms

Algorithm

egg-herbie

Counts

55 → 55

Iterations

Useful iterations: 3 (40.0ms)

Iter	Nodes	Cost
0	173	442
1	453	382
2	1495	365
3	5001	343

prune209.0ms

Filtered

55 candidates to 52 candidates (94.5%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	54	1	55
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	54	10	64

Merged error: 7.4b

Counts

64 → 10

regimes184.0ms

Accuracy

28.8% (4.3b remaining)

Error of 11.7b against oracle of 7.4b and baseline of 13.4b

bsearch151.0ms

Steps

Iters	Range		Point
8	-2.9574509151749e-25	-2.754411649284367e-29	-2.903575120643544e-25
7	-2.936676120684958e+34	-5.483479790892862e+32	-3.390257965100829e+33
10	-2.65204728689218e+170	-7.85932808106197e+156	-1.6153049614391933e+157

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

sample668.0ms

Algorithm

intervals

Results

199.0ms	6028×	body	80	valid
129.0ms	692×	body	2560	valid
81.0ms	497×	body	1280	valid
60.0ms	264×	body	5120	valid
38.0ms	286×	body	640	valid
14.0ms	160×	body	320	valid
4.0ms	73×	body	160	valid