Details

sample360.0ms

Algorithm

intervals

Results

45.0ms	76×	body	1280	valid
23.0ms	257×	body	80	valid
16.0ms	42×	body	640	valid
4.0ms	15×	body	320	valid
2.0ms	9×	body	160	valid

simplify42.0ms

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: 33.7b

Counts

2 → 2

localize26.0ms

Local error

Found 4 expressions with local error:

1.4b	(* (atan2 x.im x.re) y.re)
30.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.0b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite24.0ms

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)))
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.re)
34.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
158.0ms	(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

prune384.0ms

Filtered

78 candidates to 66 candidates (84.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	74	4	78
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	76	4	80

Merged error: 19.2b

Counts

80 → 4

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(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)
1.1b	(* (atan2 x.im x.re) y.im)
30.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite23.0ms

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)))
6.0ms	(* (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)))

series235.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
88.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
16.0ms	(* (atan2 x.im x.re) y.im)
35.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify66.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 3 (59.0ms)

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

prune344.0ms

Filtered

91 candidates to 74 candidates (81.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	87	4	91
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	88	7	95

Merged error: 4.0b

Counts

95 → 7

localize14.0ms

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))))
0.1b	(fma y.re (log (hypot x.re x.im)) (- (* (atan2 x.im x.re) y.im)))
1.1b	(* (atan2 x.im x.re) y.im)

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 44

Calls

3 calls:

2.0ms	(exp (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)))
7.0ms	(* (atan2 x.im x.re) y.im)

series221.0ms

Counts

3 → 9

Calls

3 calls:

78.0ms	(exp (fma y.re (log (hypot x.re x.im)) (- (* (atan2 x.im x.re) y.im))))
126.0ms	(fma y.re (log (hypot x.re x.im)) (- (* (atan2 x.im x.re) y.im)))
17.0ms	(* (atan2 x.im x.re) y.im)

simplify113.0ms

Algorithm

egg-herbie

Counts

53 → 53

Iterations

Useful iterations: 3 (31.0ms)

Iter	Nodes	Cost
0	154	331
1	426	291
2	1148	287
3	3857	284
4	5001	284

prune215.0ms

Filtered

53 candidates to 42 candidates (79.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	49	4	53
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	52	8	60

Merged error: 4.0b

Counts

60 → 8

localize19.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (fma y.re (log (hypot x.re x.im)) (- (* (atan2 x.im x.re) y.im))))
1.1b	(* (atan2 x.im x.re) y.im)
1.1b	(* (atan2 x.im x.re) y.im)
1.1b	(* (atan2 x.im x.re) y.im)

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
11×	`add-cube-cbrt` `*-un-lft-identity`
10×	`pow1` `add-exp-log` `add-cbrt-cube`
9×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`pow1/3`

Counts

4 → 73

Calls

4 calls:

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

series304.0ms

Counts

4 → 12

Calls

4 calls:

252.0ms	(cbrt (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)
20.0ms	(* (atan2 x.im x.re) y.im)
16.0ms	(* (atan2 x.im x.re) y.im)

simplify66.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 3 (59.0ms)

Iter	Nodes	Cost
0	215	432
1	623	393
2	2358	390
3	5001	382

prune378.0ms

Filtered

85 candidates to 59 candidates (69.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	84	1	85
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	85	8	93

Merged error: 4.0b

Counts

93 → 8

regimes203.0ms

Accuracy

0% (0.5b remaining)

Error of 3.7b against oracle of 3.2b and baseline of 3.7b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	24
1	28	24
2	28	24

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.2s	2070×	body	1280	valid
666.0ms	8001×	body	80	valid
538.0ms	1407×	body	640	valid
171.0ms	641×	body	320	valid
47.0ms	274×	body	160	valid