Details

sample34.0ms

Algorithm

intervals

Results

8.0ms	184×	body	80	valid
7.0ms	27×	body	2560	valid
3.0ms	15×	body	1280	valid
3.0ms	8×	body	5120	valid
2.0ms	14×	body	320	valid
1.0ms	7×	body	640	valid
0.0ms	1×	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: 36.0b

Counts

2 → 1

localize10.0ms

Local error

Found 2 expressions with local error:

0.7b	(+ (sqrt (+ (* re re) (* im im))) re)
26.5b	(sqrt (+ (* re re) (* im im)))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

7×	`*-un-lft-identity`
6×	`add-sqr-sqrt` `fma-def` `sqrt-prod`
5×	`add-cube-cbrt`
4×	`add-log-exp`
3×	`pow1`
2×	`add-exp-log` `expm1-log1p-u` `flip3-+` `sqrt-div` `add-cbrt-cube` `flip-+` `log1p-expm1-u`
1×	`+-commutative` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `sum-log` `hypot-def` `distribute-lft-out`

Counts

2 → 38

Calls

2 calls:

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

series85.0ms

Counts

2 → 6

Calls

2 calls:

44.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
40.0ms	(sqrt (+ (* re re) (* im im)))

simplify88.0ms

Algorithm

egg-herbie

Counts

44 → 44

Iterations

Useful iterations: 4 (84.0ms)

Iter	Nodes	Cost
0	155	205
1	421	183
2	1067	180
3	3190	179
4	5001	178

prune123.0ms

Filtered

44 candidates to 40 candidates (90.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	40	4	44
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	41	4	45

Merged error: 8.2b

Counts

45 → 4

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(hypot re im)
0.7b	(+ (hypot re im) re)

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

5×	`*-un-lft-identity`
4×	`add-log-exp`
3×	`add-sqr-sqrt` `add-cube-cbrt` `fma-def`
2×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
1×	`+-commutative` `hypot-udef` `flip3-+` `sum-log` `flip-+` `distribute-lft-out`

Counts

2 → 27

Calls

2 calls:

1.0ms	(hypot re im)
3.0ms	(+ (hypot re im) re)

series102.0ms

Counts

2 → 6

Calls

2 calls:

44.0ms	(hypot re im)
58.0ms	(+ (hypot re im) re)

simplify80.0ms

Algorithm

egg-herbie

Counts

33 → 33

Iterations

Useful iterations: 3 (14.0ms)

Iter	Nodes	Cost
0	87	85
1	176	79
2	380	79
3	1030	78
4	3143	78
5	5001	78

prune83.0ms

Filtered

33 candidates to 31 candidates (93.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	30	3	33
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	31	6	37

Merged error: 8.1b

Counts

37 → 6

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(hypot re im)
0.0b	(hypot re im)
17.4b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

3×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`hypot-udef`
1×	`fma-udef`

Counts

3 → 30

Calls

3 calls:

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

series238.0ms

Counts

3 → 9

Calls

3 calls:

50.0ms	(hypot re im)
44.0ms	(hypot re im)
144.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

simplify50.0ms

Algorithm

egg-herbie

Counts

39 → 39

Iterations

Useful iterations: 3 (15.0ms)

Iter	Nodes	Cost
0	61	142
1	158	121
2	456	117
3	1647	114
4	5002	114

prune133.0ms

Filtered

39 candidates to 37 candidates (94.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	35	4	39
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	37	8	45

Merged error: 8.1b

Counts

45 → 8

localize11.0ms

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))
17.0b	(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) re)

rewrite5.0ms

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)

series653.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(cbrt (hypot re im))
296.0ms	(cbrt (hypot re im))
116.0ms	(cbrt (hypot re im))
133.0ms	(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) re)

simplify126.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 4 (121.0ms)

Iter	Nodes	Cost
0	79	316
1	179	276
2	648	268
3	3295	254
4	5002	251

prune166.0ms

Filtered

61 candidates to 54 candidates (88.5%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	55	6	61
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	57	12	69

Merged error: 8.1b

Counts

69 → 12

regimes105.0ms

Accuracy

20.9% (4.7b remaining)

Error of 12.3b against oracle of 7.6b and baseline of 13.5b

bsearch43.0ms

Steps

Iters	Range		Point
8	-3.3950484069829986e-106	-1.639652645814304e-110	-2.846088878062426e-106

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	12
1	24	12

end0.0ms

sample888.0ms

Algorithm

intervals

Results

281.0ms	6005×	body	80	valid
191.0ms	700×	body	2560	valid
109.0ms	497×	body	1280	valid
88.0ms	267×	body	5120	valid
48.0ms	283×	body	640	valid
19.0ms	149×	body	320	valid
11.0ms	99×	body	160	valid