Details

sample350.0ms

Algorithm

intervals

Results

38.0ms	64×	body	1280	valid
24.0ms	257×	body	80	valid
18.0ms	47×	body	640	valid
5.0ms	20×	body	320	valid
3.0ms	14×	body	160	valid

simplify39.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	35	21
1	63	17
2	98	17
3	217	17
4	895	17
5	5001	17

prune30.0ms

Filtered

1 candidates to 1 candidates (100.0%)

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: 32.0b

Counts

2 → 2

localize24.0ms

Local error

Found 4 expressions with local error:

0.7b	(* (atan2 x.im x.re) y.re)
29.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.3b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
6×	`add-exp-log` `sqrt-prod` `add-cbrt-cube`
4×	`expm1-log1p-u` `sqrt-div` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `associate-l`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+` `hypot-def`
1×	`cos-sum` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 66

Calls

4 calls:

4.0ms	(* (atan2 x.im x.re) y.re)
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
8.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series248.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* (atan2 x.im x.re) y.re)
36.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
38.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
156.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify79.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (15.0ms)

Iter	Nodes	Cost
0	205	456
1	546	415
2	1264	411
3	2748	411
4	5001	411

prune354.0ms

Filtered

78 candidates to 66 candidates (84.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	72	6	78
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	73	7	80

Merged error: 18.2b

Counts

80 → 7

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
0.2b	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
0.7b	(* (atan2 x.im x.re) y.im)
29.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
11×	`pow1`
9×	`add-cube-cbrt` `-un-lft-identity` `associate-l*`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate-r` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`sqrt-prod` `log-pow`
2×	`sqrt-pow1` `pow1/2` `sqrt-div` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`sub-neg` `rem-sqrt-square` `flip3--` `flip3-+` `fma-neg` `diff-log` `prod-diff` `flip--` `flip-+` `hypot-def`

Counts

4 → 77

Calls

4 calls:

4.0ms	(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
5.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
3.0ms	(* (atan2 x.im x.re) y.im)
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series269.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
91.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
16.0ms	(* (atan2 x.im x.re) y.im)
39.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify88.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 3 (78.0ms)

Iter	Nodes	Cost
0	320	595
1	1020	544
2	3156	516
3	5001	484

prune288.0ms

Filtered

89 candidates to 70 candidates (78.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	87	2	89
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	90	6	96

Merged error: 3.3b

Counts

96 → 6

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma y.re (log (hypot x.re x.im)) (- (* (atan2 x.im x.re) y.im)))
0.3b	(pow (fma y.re (log (hypot x.re x.im)) (- (* (atan2 x.im x.re) y.im))) 3)
0.7b	(* (atan2 x.im x.re) y.im)
35.1b	(cbrt (pow (fma y.re (log (hypot x.re x.im)) (- (* (atan2 x.im x.re) y.im))) 3))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
12×	`cbrt-prod` `add-cube-cbrt` `*-un-lft-identity`
7×	`pow1` `add-exp-log` `add-cbrt-cube`
6×	`unpow-prod-down` `cube-prod`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `associate-r` `associate-l`
2×	`cube-mult` `unpow3` `sqr-pow`
1×	`pow-to-exp` `pow-pow` `pow1/3` `pow-prod-down` `pow-exp` `prod-exp` `*-commutative` `rem-cbrt-cube` `cbrt-unprod` `fma-udef` `rem-cube-cbrt` `unswap-sqr`

Counts

4 → 78

Calls

4 calls:

1.0ms	(fma y.re (log (hypot x.re x.im)) (- (* (atan2 x.im x.re) y.im)))
2.0ms	(pow (fma y.re (log (hypot x.re x.im)) (- (* (atan2 x.im x.re) y.im))) 3)
4.0ms	(* (atan2 x.im x.re) y.im)
2.0ms	(cbrt (pow (fma y.re (log (hypot x.re x.im)) (- (* (atan2 x.im x.re) y.im))) 3))

series559.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(fma y.re (log (hypot x.re x.im)) (- (* (atan2 x.im x.re) y.im)))
283.0ms	(pow (fma y.re (log (hypot x.re x.im)) (- (* (atan2 x.im x.re) y.im))) 3)
17.0ms	(* (atan2 x.im x.re) y.im)
131.0ms	(cbrt (pow (fma y.re (log (hypot x.re x.im)) (- (* (atan2 x.im x.re) y.im))) 3))

simplify49.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	299	737
1	1300	693
2	5002	683

prune301.0ms

Filtered

90 candidates to 61 candidates (67.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	87	3	90
Fresh	0	5	5
Picked	1	0	1
Done	0	0	0
Total	88	8	96

Merged error: 3.3b

Counts

96 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(expm1 (fma y.re (log (hypot x.re x.im)) (- (* (atan2 x.im x.re) y.im))))
0.0b	(log1p (expm1 (fma y.re (log (hypot x.re x.im)) (- (* (atan2 x.im x.re) y.im)))))
0.1b	(fma y.re (log (hypot x.re x.im)) (- (* (atan2 x.im x.re) y.im)))
0.7b	(* (atan2 x.im x.re) y.im)

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
5×	`log1p-expm1-u`
4×	`expm1-log1p-u` `add-log-exp`
3×	`associate-r` `associate-l`
1×	`log1p-udef` `expm1-log1p` `log1p-expm1` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef` `expm1-udef` `unswap-sqr`

Counts

4 → 52

Calls

4 calls:

1.0ms	(expm1 (fma y.re (log (hypot x.re x.im)) (- (* (atan2 x.im x.re) y.im))))
1.0ms	(log1p (expm1 (fma y.re (log (hypot x.re x.im)) (- (* (atan2 x.im x.re) y.im)))))
1.0ms	(fma y.re (log (hypot x.re x.im)) (- (* (atan2 x.im x.re) y.im)))
4.0ms	(* (atan2 x.im x.re) y.im)

series364.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(expm1 (fma y.re (log (hypot x.re x.im)) (- (* (atan2 x.im x.re) y.im))))
109.0ms	(log1p (expm1 (fma y.re (log (hypot x.re x.im)) (- (* (atan2 x.im x.re) y.im)))))
135.0ms	(fma y.re (log (hypot x.re x.im)) (- (* (atan2 x.im x.re) y.im)))
16.0ms	(* (atan2 x.im x.re) y.im)

simplify51.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 2 (15.0ms)

Iter	Nodes	Cost
0	185	419
1	525	364
2	1790	357
3	5001	357

prune218.0ms

Filtered

64 candidates to 52 candidates (81.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	62	2	64
Fresh	0	7	7
Picked	1	0	1
Done	0	0	0
Total	63	9	72

Merged error: 3.3b

Counts

72 → 9

regimes217.0ms

Accuracy

0% (0.6b remaining)

Error of 4.0b against oracle of 3.4b and baseline of 4.0b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	28
1	31	28
2	31	28

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.1s	1896×	body	1280	valid
687.0ms	8026×	body	80	valid
563.0ms	1436×	body	640	valid
169.0ms	619×	body	320	valid
57.0ms	322×	body	160	valid