Details

sample401.0ms

Algorithm

intervals

Results

50.0ms	73×	body	1280	valid
39.0ms	249×	body	80	valid
21.0ms	44×	body	640	valid
9.0ms	27×	body	320	valid
3.0ms	14×	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

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: 33.8b

Counts

2 → 2

localize24.0ms

Local error

Found 4 expressions with local error:

1.6b	(* (atan2 x.im x.re) y.im)
28.9b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
28.9b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.9b	(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)))

series247.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(* (atan2 x.im x.re) y.im)
38.0ms	(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)))

simplify84.0ms

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

prune349.0ms

Filtered

78 candidates to 66 candidates (84.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	74	4	78
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	75	5	80

Merged error: 19.9b

Counts

80 → 5

localize20.0ms

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)
1.6b	(* (atan2 x.im x.re) y.im)
28.9b	(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)))

series236.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(exp (- (* (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)
36.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify67.0ms

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

prune302.0ms

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	1	3	4
Picked	1	0	1
Done	0	0	0
Total	89	7	96

Merged error: 4.5b

Counts

96 → 7

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot x.re x.im)
0.0b	(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)
1.6b	(* (atan2 x.im x.re) y.im)

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 69

Calls

4 calls:

1.0ms	(hypot x.re x.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)

series261.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(hypot x.re x.im)
101.0ms	(exp (- (* (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)
18.0ms	(* (atan2 x.im x.re) y.im)

simplify54.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (18.0ms)

Iter	Nodes	Cost
0	232	382
1	692	340
2	1887	332
3	5001	332

prune232.0ms

Filtered

81 candidates to 63 candidates (77.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	79	2	81
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	82	6	88

Merged error: 4.5b

Counts

88 → 6

localize17.0ms

Local error

Found 4 expressions with local error:

0.9b	(* (cbrt (atan2 x.im x.re)) (cbrt (atan2 x.im x.re)))
4.1b	(cbrt (atan2 x.im x.re))
4.1b	(cbrt (atan2 x.im x.re))
4.1b	(cbrt (atan2 x.im x.re))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 81

Calls

4 calls:

6.0ms	(* (cbrt (atan2 x.im x.re)) (cbrt (atan2 x.im x.re)))
1.0ms	(cbrt (atan2 x.im x.re))
1.0ms	(cbrt (atan2 x.im x.re))
1.0ms	(cbrt (atan2 x.im x.re))

series174.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(* (cbrt (atan2 x.im x.re)) (cbrt (atan2 x.im x.re)))
43.0ms	(cbrt (atan2 x.im x.re))
39.0ms	(cbrt (atan2 x.im x.re))
44.0ms	(cbrt (atan2 x.im x.re))

simplify84.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 3 (77.0ms)

Iter	Nodes	Cost
0	88	456
1	355	404
2	2581	372
3	5002	365

prune279.0ms

Filtered

93 candidates to 64 candidates (68.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	91	2	93
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	93	6	99

Merged error: 4.5b

Counts

99 → 6

regimes161.0ms

Accuracy

0% (0.5b remaining)

Error of 3.9b against oracle of 3.4b and baseline of 3.9b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	17
1	28	17
2	28	17

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.4s	2003×	body	1280	valid
827.0ms	7995×	body	80	valid
659.0ms	1432×	body	640	valid
222.0ms	668×	body	320	valid
72.0ms	336×	body	160	valid