Details

sample36.0ms

Algorithm

intervals

Results

10.0ms	189×	body	80	valid
6.0ms	21×	body	2560	valid
5.0ms	23×	body	1280	valid
4.0ms	12×	body	5120	valid
1.0ms	7×	body	640	valid
0.0ms	3×	body	160	valid
0.0ms	1×	body	320	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: 38.3b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.2b	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
0.6b	(- (sqrt (+ (* re re) (* im im))) re)
28.5b	(sqrt (+ (* re re) (* im im)))

rewrite31.0ms

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)))
11.0ms	(- (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series263.0ms

Counts

3 → 9

Calls

3 calls:

176.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
50.0ms	(- (sqrt (+ (* re re) (* im im))) re)
37.0ms	(sqrt (+ (* re re) (* im im)))

simplify46.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 2 (37.0ms)

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

prune182.0ms

Filtered

83 candidates to 59 candidates (71.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	77	6	83
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	78	6	84

Merged error: 7.5b

Counts

84 → 6

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(hypot re im)
0.2b	(sqrt (* 2.0 (- (hypot re im) re)))
0.6b	(- (hypot re im) re)

rewrite15.0ms

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:

1.0ms	(hypot re im)
8.0ms	(sqrt (* 2.0 (- (hypot re im) re)))
4.0ms	(- (hypot re im) re)

series292.0ms

Counts

3 → 9

Calls

3 calls:

45.0ms	(hypot re im)
186.0ms	(sqrt (* 2.0 (- (hypot re im) re)))
60.0ms	(- (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

prune134.0ms

Filtered

62 candidates to 48 candidates (77.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	57	5	62
Fresh	3	2	5
Picked	0	1	1
Done	0	0	0
Total	60	8	68

Merged error: 7.3b

Counts

68 → 8

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(hypot re im)
0.4b	(* (sqrt 2.0) (sqrt (- (hypot re im) re)))
0.6b	(- (hypot re im) re)

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 74

Calls

3 calls:

1.0ms	(hypot re im)
8.0ms	(* (sqrt 2.0) (sqrt (- (hypot re im) re)))
4.0ms	(- (hypot re im) re)

series305.0ms

Counts

3 → 9

Calls

3 calls:

47.0ms	(hypot re im)
200.0ms	(* (sqrt 2.0) (sqrt (- (hypot re im) re)))
58.0ms	(- (hypot re im) re)

simplify41.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	287	494
1	1097	397
2	5001	380

prune179.0ms

Filtered

83 candidates to 59 candidates (71.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	82	1	83
Fresh	0	6	6
Picked	1	0	1
Done	0	1	1
Total	83	8	91

Merged error: 7.3b

Counts

91 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot re im)
0.2b	(* (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (* (cbrt (sqrt 2.0)) (sqrt (- (hypot re im) re))))
0.2b	(* (cbrt (sqrt 2.0)) (sqrt (- (hypot re im) re)))
0.6b	(- (hypot re im) re)

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
20×	`*-un-lft-identity`
18×	`pow1` `add-exp-log`
16×	`add-cube-cbrt`
13×	`sqrt-prod`
11×	`add-cbrt-cube`
10×	`cbrt-prod` `associate-l`
9×	`associate-r` `prod-diff` `pow-prod-down` `prod-exp` `cbrt-unprod`
6×	`associate-*r/` `add-log-exp` `unswap-sqr`
4×	`expm1-log1p-u` `sqrt-div` `log1p-expm1-u`
3×	`flip3--` `fma-neg` `flip--`
2×	`*-commutative` `distribute-lft-out--` `difference-of-squares`
1×	`sub-neg` `hypot-udef` `diff-log`

Counts

4 → 102

Calls

4 calls:

1.0ms	(hypot re im)
14.0ms	(* (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (* (cbrt (sqrt 2.0)) (sqrt (- (hypot re im) re))))
9.0ms	(* (cbrt (sqrt 2.0)) (sqrt (- (hypot re im) re)))
4.0ms	(- (hypot re im) re)

series744.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(hypot re im)
202.0ms	(* (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (* (cbrt (sqrt 2.0)) (sqrt (- (hypot re im) re))))
427.0ms	(* (cbrt (sqrt 2.0)) (sqrt (- (hypot re im) re)))
60.0ms	(- (hypot re im) re)

simplify69.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	456	991
1	1898	770
2	5002	709

prune258.0ms

Filtered

114 candidates to 80 candidates (70.2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	114	0	114
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	114	8	122

Merged error: 7.3b

Counts

122 → 8

regimes101.0ms

Accuracy

26.6% (4.3b remaining)

Error of 11.8b against oracle of 7.5b and baseline of 13.4b

bsearch63.0ms

Steps

Iters	Range		Point
8	3.329794309571498e+100	2.8997891855909196e+104	8.585239363616927e+102

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

sample937.0ms

Algorithm

intervals

Results

294.0ms	6008×	body	80	valid
200.0ms	712×	body	2560	valid
116.0ms	493×	body	1280	valid
105.0ms	295×	body	5120	valid
49.0ms	269×	body	640	valid
20.0ms	147×	body	320	valid
7.0ms	76×	body	160	valid