Details

sample37.0ms

Algorithm

intervals

Results

10.0ms	189×	body	80	valid
9.0ms	30×	body	2560	valid
4.0ms	15×	body	1280	valid
3.0ms	10×	body	5120	valid
2.0ms	10×	body	640	valid
0.0ms	1×	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: 35.2b

Counts

2 → 1

localize10.0ms

Local error

Found 2 expressions with local error:

0.6b	(- (sqrt (+ (* re re) (* im im))) re)
26.5b	(sqrt (+ (* re re) (* im im)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 59

Calls

2 calls:

8.0ms	(- (sqrt (+ (* re re) (* im im))) re)
7.0ms	(sqrt (+ (* re re) (* im im)))

series86.0ms

Counts

2 → 6

Calls

2 calls:

49.0ms	(- (sqrt (+ (* re re) (* im im))) re)
37.0ms	(sqrt (+ (* re re) (* im im)))

simplify109.0ms

Algorithm

egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 3 (102.0ms)

Iter	Nodes	Cost
0	211	590
1	687	366
2	3279	321
3	5001	295

prune134.0ms

Filtered

65 candidates to 43 candidates (66.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	61	4	65
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	62	4	66

Merged error: 9.4b

Counts

66 → 4

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(hypot re im)
0.6b	(- (hypot re im) re)

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`add-cube-cbrt` `prod-diff`
4×	`add-log-exp`
3×	`fma-neg`
2×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
1×	`sub-neg` `hypot-udef` `flip3--` `diff-log` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 38

Calls

2 calls:

1.0ms	(hypot re im)
4.0ms	(- (hypot re im) re)

series103.0ms

Counts

2 → 6

Calls

2 calls:

44.0ms	(hypot re im)
59.0ms	(- (hypot re im) re)

simplify53.0ms

Algorithm

egg-herbie

Counts

44 → 44

Iterations

Useful iterations: 3 (49.0ms)

Iter	Nodes	Cost
0	130	223
1	366	140
2	1695	131
3	5001	109

prune93.0ms

Filtered

44 candidates to 32 candidates (72.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	40	4	44
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	41	7	48

Merged error: 9.3b

Counts

48 → 7

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

54×	`add-sqr-sqrt`
47×	`*-un-lft-identity`
35×	`sqrt-prod`
27×	`add-cube-cbrt`
20×	`pow1`
18×	`prod-diff`
14×	`sqrt-div`
12×	`swap-sqr`
9×	`flip3--` `sqrt-pow1` `pow1/2` `flip--` `distribute-lft-out--`
8×	`associate-r` `associate-l` `add-log-exp`
7×	`difference-of-squares`
6×	`add-exp-log` `fma-neg` `add-cbrt-cube`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `frac-times` `log1p-expm1-u` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`sub-neg` `diff-log` `associate-r/` `associate-l/`
1×	`pow2` `rem-sqrt-square` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 142

Calls

4 calls:

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

series298.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(sqrt (- (hypot re im) re))
55.0ms	(* (sqrt (- (hypot re im) re)) (sqrt (- (hypot re im) re)))
58.0ms	(- (hypot re im) re)
59.0ms	(- (hypot re im) re)

simplify52.0ms

Algorithm

egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	286	899
1	1123	706
2	5001	691

prune289.0ms

Filtered

154 candidates to 93 candidates (60.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	153	1	154
Fresh	0	5	5
Picked	1	0	1
Done	0	1	1
Total	154	7	161

Merged error: 9.3b

Counts

161 → 7

localize20.0ms

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))
16.3b	(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) (- re))

rewrite6.0ms

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:

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

series474.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(cbrt (hypot re im))
113.0ms	(cbrt (hypot re im))
113.0ms	(cbrt (hypot re im))
137.0ms	(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) (- re))

simplify140.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 4 (135.0ms)

Iter	Nodes	Cost
0	84	329
1	188	287
2	663	279
3	3464	272
4	5001	263

prune215.0ms

Filtered

61 candidates to 55 candidates (90.2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	61	0	61
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	61	7	68

Merged error: 9.3b

Counts

68 → 7

regimes92.0ms

Accuracy

18% (4.7b remaining)

Error of 12.1b against oracle of 7.4b and baseline of 13.1b

bsearch162.0ms

Steps

Iters	Range	Point
8	1.5412126804408514e+192	5.871468893721034e+195	1.0028199647798038e+194
5	1.9303370681519622e+121	4.0160950957056723e+121	3.8425622158719786e+121
9	1.5152024321248757e-44	3.618980236523305e-39	1.3130202236219853e-40

Iters

Range

Point

1.5412126804408514e+192

5.871468893721034e+195

1.0028199647798038e+194

1.9303370681519622e+121

4.0160950957056723e+121

3.8425622158719786e+121

1.5152024321248757e-44

3.618980236523305e-39

1.3130202236219853e-40

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

sample952.0ms

Algorithm

intervals

Results

305.0ms	6062×	body	80	valid
197.0ms	669×	body	2560	valid
116.0ms	485×	body	1280	valid
104.0ms	281×	body	5120	valid
55.0ms	295×	body	640	valid
22.0ms	144×	body	320	valid
6.0ms	64×	body	160	valid