Details

sample375.0ms

Algorithm

intervals

Results

42.0ms	70×	body	1280	valid
26.0ms	67×	body	640	valid
23.0ms	250×	body	80	valid
8.0ms	30×	body	320	valid
3.0ms	14×	body	160	valid

simplify49.0ms

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

prune17.0ms

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: 33.0b

Counts

2 → 2

localize24.0ms

Local error

Found 4 expressions with local error:

1.6b	(* (atan2 x.im x.re) y.im)
29.1b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.1b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.6b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite22.0ms

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.im)
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)))

series242.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(* (atan2 x.im x.re) y.im)
37.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
154.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify80.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (15.0ms)

Iter	Nodes	Cost
0	207	456
1	556	415
2	1286	411
3	2863	411
4	5002	411

prune389.0ms

Filtered

78 candidates to 66 candidates (84.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	73	5	78
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	74	6	80

Merged error: 20.0b

Counts

80 → 6

localize20.0ms

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))
0.3b	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
1.6b	(* (atan2 x.im x.re) y.im)
29.1b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite19.0ms

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)))

series264.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
90.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
17.0ms	(* (atan2 x.im x.re) y.im)
36.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify83.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 3 (76.0ms)

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

prune337.0ms

Filtered

89 candidates to 70 candidates (78.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	88	1	89
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	88	7	95

Merged error: 4.6b

Counts

95 → 7

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b	(exp (+ (fma y.re (log (hypot x.re x.im)) (- (* (atan2 x.im x.re) y.im))) 0))
0.1b	(fma y.re (log (hypot x.re x.im)) (- (* (atan2 x.im x.re) y.im)))
1.6b	(* (atan2 x.im x.re) y.im)

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 46

Calls

3 calls:

4.0ms	(exp (+ (fma y.re (log (hypot x.re x.im)) (- (* (atan2 x.im x.re) y.im))) 0))
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)

series227.0ms

Counts

3 → 9

Calls

3 calls:

82.0ms	(exp (+ (fma y.re (log (hypot x.re x.im)) (- (* (atan2 x.im x.re) y.im))) 0))
129.0ms	(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)

simplify42.0ms

Algorithm

egg-herbie

Counts

55 → 55

Iterations

Useful iterations: 3 (38.0ms)

Iter	Nodes	Cost
0	156	344
1	478	303
2	1498	297
3	5001	296

prune233.0ms

Filtered

55 candidates to 45 candidates (81.8%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	53	2	55
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	53	9	62

Merged error: 4.6b

Counts

62 → 9

localize21.0ms

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)))
0.1b	(fma y.re (log (hypot x.re x.im)) (- (* (atan2 x.im x.re) y.im)))
1.6b	(* (atan2 x.im x.re) y.im)
1.6b	(* (atan2 x.im x.re) y.im)

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 60

Calls

4 calls:

1.0ms	(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)
4.0ms	(* (atan2 x.im x.re) y.im)

series293.0ms

Counts

4 → 12

Calls

4 calls:

129.0ms	(fma y.re (log (hypot x.re x.im)) (- (* (atan2 x.im x.re) y.im)))
132.0ms	(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)
16.0ms	(* (atan2 x.im x.re) y.im)

simplify71.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 2 (10.0ms)

Iter	Nodes	Cost
0	118	372
1	347	326
2	879	320
3	2273	320
4	5001	320

prune356.0ms

Filtered

72 candidates to 56 candidates (77.8%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	72	0	72
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	72	9	81

Merged error: 4.6b

Counts

81 → 9

regimes215.0ms

Accuracy

0% (0.6b remaining)

Error of 4.1b against oracle of 3.5b and baseline of 4.1b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	8
1	29	8
2	29	8

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.2s	1998×	body	1280	valid
677.0ms	7972×	body	80	valid
562.0ms	1416×	body	640	valid
178.0ms	655×	body	320	valid
55.0ms	293×	body	160	valid