Details

sample347.0ms

Algorithm

intervals

Results

36.0ms	63×	body	1280	valid
22.0ms	251×	body	80	valid
17.0ms	46×	body	640	valid
5.0ms	18×	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

prune29.0ms

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: 32.5b

Counts

2 → 2

localize25.0ms

Local error

Found 4 expressions with local error:

2.4b	(* (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)))
33.5b	(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)))
9.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series247.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* (atan2 x.im x.re) y.im)
35.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
36.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
157.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify83.0ms

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

prune350.0ms

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: 17.4b

Counts

80 → 7

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp (- (* (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)
2.4b	(* (atan2 x.im x.re) y.im)
29.1b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 79

Calls

4 calls:

5.0ms	(exp (- (* (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)))

series239.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(exp (- (* (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)
16.0ms	(* (atan2 x.im x.re) y.im)
38.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify67.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 3 (60.0ms)

Iter	Nodes	Cost
0	308	585
1	921	522
2	2504	484
3	5002	467

prune311.0ms

Filtered

91 candidates to 74 candidates (81.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	88	3	91
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	90	8	98

Merged error: 4.3b

Counts

98 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* (log (hypot x.re x.im)) y.re) (* (atan2 x.im x.re) y.im))
0.1b	(exp (- (* (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)
2.4b	(* (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:

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

series348.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(- (* (log (hypot x.re x.im)) y.re) (* (atan2 x.im x.re) y.im))
100.0ms	(exp (- (* (log (hypot x.re x.im)) y.re) (* (atan2 x.im x.re) y.im)))
102.0ms	(* (log (hypot x.re x.im)) y.re)
17.0ms	(* (atan2 x.im x.re) y.im)

simplify83.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 3 (75.0ms)

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

prune250.0ms

Filtered

87 candidates to 65 candidates (74.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	86	1	87
Fresh	0	7	7
Picked	1	0	1
Done	0	0	0
Total	87	8	95

Merged error: 4.3b

Counts

95 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* (log (hypot x.re x.im)) y.re) (* (atan2 x.im x.re) y.im))
0.1b	(pow E (- (* (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)
2.4b	(* (atan2 x.im x.re) y.im)

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 81

Calls

4 calls:

4.0ms	(- (* (log (hypot x.re x.im)) y.re) (* (atan2 x.im x.re) y.im))
4.0ms	(pow E (- (* (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)

series357.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(- (* (log (hypot x.re x.im)) y.re) (* (atan2 x.im x.re) y.im))
110.0ms	(pow E (- (* (log (hypot x.re x.im)) y.re) (* (atan2 x.im x.re) y.im)))
98.0ms	(* (log (hypot x.re x.im)) y.re)
19.0ms	(* (atan2 x.im x.re) y.im)

simplify130.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 3 (119.0ms)

Iter	Nodes	Cost
0	323	597
1	1107	560
2	4620	549
3	5001	548

prune238.0ms

Filtered

93 candidates to 68 candidates (73.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	92	1	93
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	92	9	101

Merged error: 4.3b

Counts

101 → 9

regimes210.0ms

Accuracy

0% (0.7b remaining)

Error of 4.3b against oracle of 3.6b and baseline of 4.3b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	7
1	22	7
2	22	7

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.2s	2053×	body	1280	valid
650.0ms	7978×	body	80	valid
562.0ms	1482×	body	640	valid
170.0ms	636×	body	320	valid
57.0ms	314×	body	160	valid