Details

sample385.0ms

Algorithm

intervals

Results

51.0ms	69×	body	1280	valid
36.0ms	250×	body	80	valid
20.0ms	41×	body	640	valid
10.0ms	31×	body	320	valid
2.0ms	8×	body	160	valid

simplify39.0ms

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

prune14.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 31.8b

Counts

2 → 1

localize24.0ms

Local error

Found 4 expressions with local error:

2.7b	(* (atan2 x.im x.re) y.im)
27.4b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
27.4b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.0b	(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)))

series252.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(* (atan2 x.im x.re) y.im)
39.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
36.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
161.0ms	(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

prune356.0ms

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	0	0	0
Picked	1	0	1
Done	0	0	0
Total	73	6	79

Merged error: 18.1b

Counts

79 → 6

localize19.0ms

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)
2.7b	(* (atan2 x.im x.re) y.im)
27.4b	(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)))

series246.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
93.0ms	(* (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)))

simplify65.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 3 (58.0ms)

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

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	88	3	91
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	88	9	97

Merged error: 5.2b

Counts

97 → 9

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt y.re)
0.6b	(cbrt y.re)
0.6b	(cbrt y.re)
2.7b	(* (atan2 x.im x.re) y.im)

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 59

Calls

4 calls:

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

series569.0ms

Counts

4 → 12

Calls

4 calls:

186.0ms	(cbrt y.re)
182.0ms	(cbrt y.re)
180.0ms	(cbrt y.re)
20.0ms	(* (atan2 x.im x.re) y.im)

simplify55.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 3 (19.0ms)

Iter	Nodes	Cost
0	102	209
1	300	190
2	710	184
3	1530	181
4	5001	181

prune281.0ms

Filtered

71 candidates to 57 candidates (80.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	70	1	71
Fresh	0	7	7
Picked	1	0	1
Done	0	1	1
Total	71	9	80

Merged error: 5.2b

Counts

80 → 9

localize22.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt y.re)
0.6b	(cbrt y.re)
0.6b	(cbrt (cbrt y.re))
2.7b	(* (atan2 x.im x.re) y.im)

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 62

Calls

4 calls:

1.0ms	(cbrt y.re)
1.0ms	(cbrt y.re)
2.0ms	(cbrt (cbrt y.re))
4.0ms	(* (atan2 x.im x.re) y.im)

series628.0ms

Counts

4 → 12

Calls

4 calls:

181.0ms	(cbrt y.re)
183.0ms	(cbrt y.re)
246.0ms	(cbrt (cbrt y.re))
17.0ms	(* (atan2 x.im x.re) y.im)

simplify66.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 3 (24.0ms)

Iter	Nodes	Cost
0	135	246
1	362	225
2	876	219
3	2213	214
4	5001	214

prune303.0ms

Filtered

74 candidates to 59 candidates (79.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	73	1	74
Fresh	0	7	7
Picked	1	0	1
Done	0	1	1
Total	74	9	83

Merged error: 5.2b

Counts

83 → 9

regimes221.0ms

Accuracy

0% (0.5b remaining)

Error of 4.2b against oracle of 3.7b and baseline of 4.2b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	26
1	36	26
2	36	26

end0.0ms

sample3.7s

Algorithm

intervals

Results

1.4s	2083×	body	1280	valid
842.0ms	7968×	body	80	valid
710.0ms	1482×	body	640	valid
228.0ms	666×	body	320	valid
75.0ms	329×	body	160	valid