Details

sample26.0ms

Algorithm

intervals

Results

7.0ms	200×	body	80	valid
5.0ms	26×	body	2560	valid
2.0ms	12×	body	1280	valid
2.0ms	8×	body	5120	valid
1.0ms	7×	body	640	valid
0.0ms	2×	body	320	valid
0.0ms	1×	body	160	valid

simplify9.0ms

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

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: 38.0b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
0.3b	(- (sqrt (+ (* re re) (* im im))) re)
30.9b	(sqrt (+ (* re re) (* im im)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
20×	`*-un-lft-identity`
18×	`add-cube-cbrt` `prod-diff`
17×	`sqrt-prod`
7×	`pow1`
6×	`fma-neg`
5×	`add-log-exp`
4×	`sqrt-div`
3×	`add-exp-log` `expm1-log1p-u` `sqrt-pow1` `add-cbrt-cube` `log1p-expm1-u`
2×	`flip3--` `pow1/2` `associate-*r/` `flip--` `difference-of-squares`
1×	`sub-neg` `rem-sqrt-square` `flip3-+` `diff-log` `pow-prod-down` `flip-+` `hypot-def` `distribute-lft-out--`

Counts

3 → 74

Calls

3 calls:

13.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
8.0ms	(- (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series251.0ms

Counts

3 → 9

Calls

3 calls:

168.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
44.0ms	(- (sqrt (+ (* re re) (* im im))) re)
39.0ms	(sqrt (+ (* re re) (* im im)))

simplify44.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	314	760
1	1192	522
2	5001	473

prune170.0ms

Filtered

83 candidates to 59 candidates (71.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	80	3	83
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	81	3	84

Merged error: 5.9b

Counts

84 → 3

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (* 2.0 (- (hypot re im) re)))
0.0b	(hypot re im)
0.3b	(- (hypot re im) re)

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `*-un-lft-identity`
10×	`add-cube-cbrt`
9×	`prod-diff`
6×	`pow1`
5×	`add-log-exp`
3×	`add-exp-log` `expm1-log1p-u` `fma-neg` `add-cbrt-cube` `log1p-expm1-u`
2×	`flip3--` `sqrt-pow1` `sqrt-div` `associate-*r/` `flip--`
1×	`sub-neg` `hypot-udef` `pow1/2` `diff-log` `pow-prod-down` `sqrt-prod` `distribute-lft-out--` `difference-of-squares`

Counts

3 → 53

Calls

3 calls:

10.0ms	(sqrt (* 2.0 (- (hypot re im) re)))
1.0ms	(hypot re im)
4.0ms	(- (hypot re im) re)

series279.0ms

Counts

3 → 9

Calls

3 calls:

179.0ms	(sqrt (* 2.0 (- (hypot re im) re)))
46.0ms	(hypot re im)
54.0ms	(- (hypot re im) re)

simplify137.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 3 (131.0ms)

Iter	Nodes	Cost
0	231	336
1	764	242
2	4704	227
3	5001	217

prune126.0ms

Filtered

62 candidates to 49 candidates (79.0%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	60	2	62
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	61	4	65

Merged error: 5.9b

Counts

65 → 4

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (hypot re im))
0.0b	(hypot re im)
0.0b	(hypot re im)
13.6b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (* -1 re))

rewrite4.0ms

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))
1.0ms	(hypot re im)
1.0ms	(hypot re im)
1.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (* -1 re))

series317.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(sqrt (hypot re im))
48.0ms	(hypot re im)
44.0ms	(hypot re im)
139.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (* -1 re))

simplify49.0ms

Algorithm

egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 3 (45.0ms)

Iter	Nodes	Cost
0	130	231
1	357	200
2	1503	192
3	5001	187

prune191.0ms

Filtered

57 candidates to 52 candidates (91.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	53	4	57
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	55	6	61

Merged error: 5.9b

Counts

61 → 6

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (sqrt (hypot re im)))
0.1b	(sqrt (sqrt (hypot re im)))
0.5b	(* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im))))
13.6b	(fma (sqrt (hypot re im)) (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (* -1 re))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

86×	`sqrt-prod`
54×	`add-sqr-sqrt`
40×	`sqrt-pow1`
31×	`pow1`
20×	`add-cube-cbrt` `*-un-lft-identity` `pow1/2`
15×	`swap-sqr`
9×	`associate-r` `associate-l` `pow-prod-up` `unswap-sqr`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow-prod-down` `pow-sqr`
4×	`expm1-log1p-u` `rem-sqrt-square` `log1p-expm1-u` `add-log-exp`
1×	`pow2` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod` `fma-udef`

Counts

4 → 129

Calls

4 calls:

2.0ms	(sqrt (sqrt (hypot re im)))
2.0ms	(sqrt (sqrt (hypot re im)))
10.0ms	(* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im))))
1.0ms	(fma (sqrt (hypot re im)) (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (* -1 re))

series452.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(sqrt (sqrt (hypot re im)))
112.0ms	(sqrt (sqrt (hypot re im)))
84.0ms	(* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im))))
144.0ms	(fma (sqrt (hypot re im)) (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (* -1 re))

simplify46.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	255	756
1	985	649
2	5001	628

prune278.0ms

Filtered

141 candidates to 75 candidates (53.2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	141	0	141
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	141	6	147

Merged error: 5.9b

Counts

147 → 6

regimes87.0ms

Accuracy

31.1% (4.3b remaining)

Error of 11.7b against oracle of 7.4b and baseline of 13.6b

bsearch55.0ms

Steps

Iters	Range		Point
8	6.532858726341657e+111	3.274976537115098e+114	1.4326139727646058e+113

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	13
1	29	13
2	29	13

end0.0ms

sample691.0ms

Algorithm

intervals

Results

203.0ms	6000×	body	80	valid
134.0ms	694×	body	2560	valid
85.0ms	499×	body	1280	valid
64.0ms	262×	body	5120	valid
39.0ms	297×	body	640	valid
15.0ms	164×	body	320	valid
5.0ms	84×	body	160	valid