Details

sample368.0ms

Algorithm

intervals

Results

42.0ms	60×	body	1280	valid
29.0ms	255×	body	80	valid
17.0ms	36×	body	640	valid
6.0ms	19×	body	320	valid
2.0ms	9×	body	160	valid

simplify41.0ms

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

prune16.0ms

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: 33.7b

Counts

2 → 2

localize25.0ms

Local error

Found 4 expressions with local error:

1.4b	(* (atan2 x.im x.re) y.im)
29.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.2b	(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:

3.0ms	(* (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)))
153.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify81.0ms

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

prune345.0ms

Filtered

78 candidates to 66 candidates (84.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	72	6	78
Fresh	1	0	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)
1.4b	(* (atan2 x.im x.re) y.im)
29.7b	(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)
4.0ms	(* (atan2 x.im x.re) y.im)
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series263.0ms

Counts

4 → 12

Calls

4 calls:

124.0ms	(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
89.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
16.0ms	(* (atan2 x.im x.re) y.im)
34.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify84.0ms

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

prune281.0ms

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	1	4	5
Picked	1	0	1
Done	0	0	0
Total	89	6	95

Merged error: 4.1b

Counts

95 → 6

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (- (* (log (hypot x.re x.im)) y.re) (* (atan2 x.im x.re) y.im)))
0.0b	(- (* (log (hypot x.re x.im)) y.re) (* (atan2 x.im x.re) y.im))
0.3b	(* (log (hypot x.re x.im)) y.re)
1.4b	(* (atan2 x.im x.re) y.im)

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
9×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
8×	`add-exp-log` `add-cbrt-cube`
7×	`associate-l`
6×	`associate-r`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`exp-prod` `exp-sum`
2×	`sub-neg` `diff-log` `prod-diff` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `rem-exp-log` `unswap-sqr`
1×	`flip3--` `exp-diff` `fma-neg` `log-pow` `flip--`

Counts

4 → 75

Calls

4 calls:

5.0ms	(exp (- (* (log (hypot x.re x.im)) y.re) (* (atan2 x.im x.re) y.im)))
4.0ms	(- (* (log (hypot x.re x.im)) y.re) (* (atan2 x.im x.re) y.im))
4.0ms	(* (log (hypot x.re x.im)) y.re)
4.0ms	(* (atan2 x.im x.re) y.im)

series346.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(exp (- (* (log (hypot x.re x.im)) y.re) (* (atan2 x.im x.re) y.im)))
128.0ms	(- (* (log (hypot x.re x.im)) y.re) (* (atan2 x.im x.re) y.im))
97.0ms	(* (log (hypot x.re x.im)) y.re)
19.0ms	(* (atan2 x.im x.re) y.im)

simplify80.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 3 (73.0ms)

Iter	Nodes	Cost
0	265	517
1	869	474
2	2937	463
3	5001	458

prune246.0ms

Filtered

87 candidates to 66 candidates (75.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	85	2	87
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	85	8	93

Merged error: 4.1b

Counts

93 → 8

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (log (hypot x.re x.im)) y.re)
1.4b	(* (atan2 x.im x.re) y.im)
1.4b	(* (atan2 x.im x.re) y.im)
1.4b	(* (atan2 x.im x.re) y.im)

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
13×	`pow1` `associate-l`
12×	`add-exp-log` `add-cube-cbrt` `-un-lft-identity` `associate-r*` `add-cbrt-cube`
4×	`expm1-log1p-u` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
1×	`log-pow`

Counts

4 → 81

Calls

4 calls:

4.0ms	(* (log (hypot x.re x.im)) y.re)
4.0ms	(* (atan2 x.im x.re) y.im)
7.0ms	(* (atan2 x.im x.re) y.im)
4.0ms	(* (atan2 x.im x.re) y.im)

series154.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(* (log (hypot x.re x.im)) y.re)
22.0ms	(* (atan2 x.im x.re) y.im)
18.0ms	(* (atan2 x.im x.re) y.im)
16.0ms	(* (atan2 x.im x.re) y.im)

simplify61.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (13.0ms)

Iter	Nodes	Cost
0	150	350
1	493	306
2	1139	304
3	2178	304
4	5001	304

prune301.0ms

Filtered

93 candidates to 63 candidates (67.7%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	93	0	93
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	93	8	101

Merged error: 4.1b

Counts

101 → 8

regimes189.0ms

Accuracy

0% (0.5b remaining)

Error of 4.0b against oracle of 3.5b and baseline of 4.0b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	7
1	20	7
2	20	7

end0.0ms

sample3.6s

Algorithm

intervals

Results

1.3s	1969×	body	1280	valid
839.0ms	7977×	body	80	valid
698.0ms	1472×	body	640	valid
223.0ms	650×	body	320	valid
64.0ms	294×	body	160	valid