Details

sample368.0ms

Algorithm

intervals

Results

42.0ms	70×	body	1280	valid
26.0ms	67×	body	640	valid
23.0ms	250×	body	80	valid
8.0ms	30×	body	320	valid
3.0ms	14×	body	160	valid

simplify48.0ms

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

prune17.0ms

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: 33.0b

Counts

2 → 2

localize24.0ms

Local error

Found 4 expressions with local error:

1.6b	(* (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)))
30.6b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

112×	`add-sqr-sqrt`
52×	`hypot-def`
32×	`*-un-lft-identity`
24×	`swap-sqr`
21×	`*-commutative` `unswap-sqr`
16×	`sqrt-prod`
11×	`associate-l`
10×	`distribute-lft-out`
8×	`pow1` `add-cube-cbrt`
6×	`add-exp-log` `add-cbrt-cube`
4×	`expm1-log1p-u` `sqrt-div` `log1p-expm1-u` `add-log-exp`
3×	`+-commutative` `associate-r`
2×	`rem-sqrt-square` `cos-sum` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
1×	`pow-prod-down` `prod-exp` `cbrt-unprod`

Counts

4 → 127

Calls

4 calls:

3.0ms	(* (atan2 x.im x.re) y.im)
19.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
25.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
20.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series239.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(* (atan2 x.im x.re) y.im)
35.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
39.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
148.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify94.0ms

Algorithm

egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	210	484
1	559	443
2	1308	443
3	3349	443
4	5001	443

prune495.0ms

Filtered

139 candidates to 84 candidates (60.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	134	5	139
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	135	6	141

Merged error: 20.0b

Counts

141 → 6

localize16.0ms

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)
1.6b	(* (atan2 x.im x.re) y.im)
29.1b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

216×	`add-sqr-sqrt`
180×	`prod-diff`
143×	`associate-l`
115×	`*-un-lft-identity`
93×	`add-cube-cbrt`
90×	`associate-r`
44×	`log-pow` `unswap-sqr`
40×	`*-commutative`
39×	`pow1`
26×	`hypot-def`
15×	`sqrt-pow1` `pow1/2` `fma-neg`
12×	`swap-sqr`
8×	`add-exp-log` `sqrt-prod` `add-cbrt-cube`
6×	`distribute-lft-out--` `add-log-exp`
5×	`distribute-lft-out`
4×	`expm1-log1p-u` `log1p-expm1-u` `difference-of-squares`
2×	`sqrt-div` `pow-prod-down` `prod-exp` `cbrt-unprod`
1×	`+-commutative` `sub-neg` `rem-sqrt-square` `flip3--` `flip3-+` `diff-log` `flip--` `flip-+`

Counts

4 → 310

Calls

4 calls:

24.0ms	(- (* (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)
3.0ms	(* (atan2 x.im x.re) y.im)
18.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series266.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(- (* (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)
20.0ms	(* (atan2 x.im x.re) y.im)
35.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify97.0ms

Algorithm

egg-herbie

Counts

322 → 322

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	742	5735
1	1966	4190
2	5001	3797

prune538.0ms

Filtered

322 candidates to 110 candidates (34.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	321	1	322
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	321	7	328

Merged error: 4.6b

Counts

328 → 7

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (- (* (log (hypot x.im x.re)) y.re) (* (atan2 x.im x.re) y.im)))
0.0b	(- (* (log (hypot x.im x.re)) y.re) (* (atan2 x.im x.re) y.im))
0.3b	(* (log (hypot x.im x.re)) y.re)
1.6b	(* (atan2 x.im x.re) y.im)

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

312×	`prod-diff`
292×	`add-sqr-sqrt`
199×	`associate-l`
182×	`*-un-lft-identity`
162×	`add-cube-cbrt`
159×	`associate-r`
158×	`exp-sum`
61×	`unswap-sqr`
53×	`*-commutative`
38×	`pow1`
30×	`log-pow`
13×	`exp-prod` `fma-neg`
12×	`distribute-lft-out--`
9×	`add-log-exp`
8×	`add-exp-log` `add-cbrt-cube` `difference-of-squares`
4×	`expm1-log1p-u` `log1p-expm1-u`
2×	`sub-neg` `diff-log` `pow-prod-down` `prod-exp` `cbrt-unprod` `rem-exp-log`
1×	`flip3--` `exp-diff` `flip--`

Counts

4 → 417

Calls

4 calls:

29.0ms	(exp (- (* (log (hypot x.im x.re)) y.re) (* (atan2 x.im x.re) y.im)))
19.0ms	(- (* (log (hypot x.im x.re)) y.re) (* (atan2 x.im x.re) y.im))
4.0ms	(* (log (hypot x.im x.re)) y.re)
4.0ms	(* (atan2 x.im x.re) y.im)

series358.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(exp (- (* (log (hypot x.im x.re)) y.re) (* (atan2 x.im x.re) y.im)))
135.0ms	(- (* (log (hypot x.im x.re)) y.re) (* (atan2 x.im x.re) y.im))
102.0ms	(* (log (hypot x.im x.re)) y.re)
16.0ms	(* (atan2 x.im x.re) y.im)

simplify109.0ms

Algorithm

egg-herbie

Counts

429 → 429

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	780	8349
1	1997	5963
2	5001	4498

prune523.0ms

Filtered

429 candidates to 107 candidates (24.9%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	427	2	429
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	427	9	436

Merged error: 4.6b

Counts

436 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (log (hypot x.im x.re)) y.re)
0.3b	(* (log (hypot x.im x.re)) y.re)
1.6b	(* (atan2 x.im x.re) y.im)
1.6b	(* (atan2 x.im x.re) y.im)

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
14×	`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`
2×	`log-pow`

Counts

4 → 82

Calls

4 calls:

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

series237.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(* (log (hypot x.im x.re)) y.re)
101.0ms	(* (log (hypot x.im x.re)) y.re)
16.0ms	(* (atan2 x.im x.re) y.im)
20.0ms	(* (atan2 x.im x.re) y.im)

simplify64.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	151	380
1	492	332
2	1137	328
3	2152	328
4	5002	328

prune369.0ms

Filtered

94 candidates to 66 candidates (70.2%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	94	0	94
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	94	9	103

Merged error: 4.6b

Counts

103 → 9

regimes222.0ms

Accuracy

0% (0.6b remaining)

Error of 4.1b against oracle of 3.5b and baseline of 4.1b

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

sample3.0s

Algorithm

intervals

Results

1.2s	1998×	body	1280	valid
670.0ms	7972×	body	80	valid
555.0ms	1416×	body	640	valid
177.0ms	655×	body	320	valid
57.0ms	293×	body	160	valid