Details

sample37.0ms

Algorithm

intervals

Results

9.0ms	185×	body	80	valid
9.0ms	24×	body	2560	valid
4.0ms	17×	body	1280	valid
3.0ms	10×	body	5120	valid
2.0ms	13×	body	640	valid
0.0ms	3×	body	320	valid
0.0ms	4×	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

prune2.0ms

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: 40.9b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
1.2b	(- (sqrt (+ (* re re) (* im im))) re)
29.6b	(sqrt (+ (* re re) (* im im)))

rewrite27.0ms

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)))

series247.0ms

Counts

3 → 9

Calls

3 calls:

165.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
44.0ms	(- (sqrt (+ (* re re) (* im im))) re)
38.0ms	(sqrt (+ (* re re) (* im im)))

simplify45.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 2 (37.0ms)

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

prune172.0ms

Filtered

83 candidates to 59 candidates (71.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	79	4	83
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	80	4	84

Merged error: 7.6b

Counts

84 → 4

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (* 2.0 (- (hypot re im) re)))
1.2b	(- (hypot re im) re)

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 43

Calls

2 calls:

7.0ms	(sqrt (* 2.0 (- (hypot re im) re)))
4.0ms	(- (hypot re im) re)

series231.0ms

Counts

2 → 6

Calls

2 calls:

175.0ms	(sqrt (* 2.0 (- (hypot re im) re)))
57.0ms	(- (hypot re im) re)

simplify131.0ms

Algorithm

egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 3 (126.0ms)

Iter	Nodes	Cost
0	221	312
1	728	227
2	4440	212
3	5001	202

prune97.0ms

Filtered

49 candidates to 37 candidates (75.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	47	2	49
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	48	5	53

Merged error: 7.5b

Counts

53 → 5

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (* 2.0 (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))))
17.3b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

5×	`pow1`
2×	`add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `sqrt-pow1` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
1×	`pow1/2` `pow-prod-down` `sqrt-prod` `fma-udef`

Counts

2 → 23

Calls

2 calls:

3.0ms	(sqrt (* 2.0 (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))))
1.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

series365.0ms

Counts

2 → 6

Calls

2 calls:

230.0ms	(sqrt (* 2.0 (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))))
134.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

simplify51.0ms

Algorithm

egg-herbie

Counts

29 → 29

Iterations

Useful iterations: 3 (47.0ms)

Iter	Nodes	Cost
0	135	250
1	408	217
2	1603	205
3	5001	200

prune89.0ms

Filtered

29 candidates to 25 candidates (86.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	26	3	29
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	27	7	34

Merged error: 7.5b

Counts

34 → 7

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (hypot re im))
0.5b	(cbrt (hypot re im))
0.5b	(* (cbrt (hypot re im)) (cbrt (hypot re im)))
17.1b	(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) (- re))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

22×	`cbrt-prod` `add-sqr-sqrt`
14×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
8×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef`

Counts

4 → 78

Calls

4 calls:

1.0ms	(cbrt (hypot re im))
1.0ms	(cbrt (hypot re im))
5.0ms	(* (cbrt (hypot re im)) (cbrt (hypot re im)))
1.0ms	(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) (- re))

series464.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(cbrt (hypot re im))
107.0ms	(cbrt (hypot re im))
118.0ms	(* (cbrt (hypot re im)) (cbrt (hypot re im)))
133.0ms	(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) (- re))

simplify121.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 3 (113.0ms)

Iter	Nodes	Cost
0	169	543
1	648	485
2	3287	451
3	5001	437

prune233.0ms

Filtered

90 candidates to 71 candidates (78.9%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	84	6	90
Fresh	2	3	5
Picked	1	0	1
Done	0	1	1
Total	87	10	97

Merged error: 7.5b

Counts

97 → 10

regimes121.0ms

Accuracy

18.5% (4.7b remaining)

Error of 11.8b against oracle of 7.1b and baseline of 12.8b

bsearch167.0ms

Steps

Iters	Range		Point
9	1.2068094430300476e+123	1.3096497762430056e+132	2.0604803870602927e+123
9	2.8581313333735045e+30	2.3444880623575728e+36	2.703749889328005e+33
7	2.7269607775172767e-97	1.3737072162010779e-95	1.2907693089520678e-95

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	36	26
1	41	13
2	44	13
3	44	13

end0.0ms

sample890.0ms

Algorithm

intervals

Results

294.0ms	6087×	body	80	valid
190.0ms	684×	body	2560	valid
106.0ms	472×	body	1280	valid
86.0ms	270×	body	5120	valid
48.0ms	280×	body	640	valid
17.0ms	131×	body	320	valid
7.0ms	76×	body	160	valid