Details

sample428.0ms

Algorithm

intervals

Results

48.0ms	65×	body	1280	valid
47.0ms	257×	body	80	valid
23.0ms	46×	body	640	valid
6.0ms	18×	body	320	valid
2.0ms	1×	body	2560	valid
2.0ms	8×	body	160	valid

simplify42.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	31	21
1	53	20
2	84	20
3	203	20
4	879	20
5	5001	20

prune13.0ms

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: 31.5b

Counts

2 → 1

localize25.0ms

Local error

Found 4 expressions with local error:

1.7b	(* (atan2 x.im x.re) y.re)
27.6b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
27.6b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.9b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite30.0ms

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×	`sqrt-div` `add-log-exp`
3×	`associate-r` `associate-l`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
1×	`sin-sum` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 56

Calls

4 calls:

3.0ms	(* (atan2 x.im x.re) y.re)
10.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
10.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series246.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(* (atan2 x.im x.re) y.re)
35.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
39.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
156.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify74.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	194	425
1	496	388
2	1117	386
3	2390	386
4	5002	386

prune308.0ms

Filtered

68 candidates to 54 candidates (79.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	60	8	68
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	60	9	69

Merged error: 19.1b

Counts

69 → 9

localize27.0ms

Local error

Found 4 expressions with local error:

27.6b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.9b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
32.9b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
32.9b	(sin (+ (* (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

6×	`add-sqr-sqrt`
5×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`sin-sum` `sqrt-prod`
2×	`sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 39

Calls

4 calls:

4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
7.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
7.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series466.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
142.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
142.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
144.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify162.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 4 (53.0ms)

Iter	Nodes	Cost
0	142	553
1	288	487
2	611	487
3	1512	487
4	4748	486
5	5001	486

prune334.0ms

Filtered

51 candidates to 48 candidates (94.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	47	4	51
Fresh	2	5	7
Picked	1	0	1
Done	0	1	1
Total	50	10	60

Merged error: 19.1b

Counts

60 → 10

localize25.0ms

Local error

Found 4 expressions with local error:

11.1b	(cbrt (pow (sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re))) 3))
27.6b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
27.6b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.9b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
11×	`add-sqr-sqrt`
9×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `sqrt-prod`
4×	`add-exp-log` `sqrt-div` `add-cbrt-cube` `add-log-exp`
3×	`unpow-prod-down` `cube-prod`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
1×	`cube-mult` `sin-sum` `pow1/3` `unpow3` `rem-cbrt-cube` `sqr-pow`

Counts

4 → 59

Calls

4 calls:

5.0ms	(cbrt (pow (sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re))) 3))
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series362.0ms

Counts

4 → 12

Calls

4 calls:

143.0ms	(cbrt (pow (sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re))) 3))
39.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
36.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
144.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify150.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 4 (142.0ms)

Iter	Nodes	Cost
0	191	725
1	493	717
2	1262	717
3	4720	717
4	5001	647

prune339.0ms

Filtered

71 candidates to 53 candidates (74.6%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	70	1	71
Fresh	1	7	8
Picked	0	1	1
Done	0	1	1
Total	71	10	81

Merged error: 19.1b

Counts

81 → 10

localize22.0ms

Local error

Found 4 expressions with local error:

1.7b	(* (atan2 x.im x.re) y.im)
1.7b	(* (atan2 x.im x.re) y.re)
18.2b	(sin (+ (* (log x.re) y.im) (* (atan2 x.im x.re) y.re)))
27.6b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
9×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate-r` `associate-l`
4×	`add-log-exp`
3×	`sqrt-prod`
2×	`sqrt-div` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `sin-sum` `flip-+`

Counts

4 → 59

Calls

4 calls:

3.0ms	(* (atan2 x.im x.re) y.im)
3.0ms	(* (atan2 x.im x.re) y.re)
8.0ms	(sin (+ (* (log x.re) y.im) (* (atan2 x.im x.re) y.re)))
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series160.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(* (atan2 x.im x.re) y.im)
16.0ms	(* (atan2 x.im x.re) y.re)
92.0ms	(sin (+ (* (log x.re) y.im) (* (atan2 x.im x.re) y.re)))
36.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify91.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 4 (86.0ms)

Iter	Nodes	Cost
0	240	355
1	670	319
2	1580	316
3	3230	316
4	5001	312

prune251.0ms

Filtered

71 candidates to 50 candidates (70.4%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	68	3	71
Fresh	1	6	7
Picked	1	0	1
Done	0	2	2
Total	70	11	81

Merged error: 12.9b

Counts

81 → 11

Details

sample428.0ms

simplify42.0ms

prune13.0ms

localize25.0ms

rewrite30.0ms

series246.0ms

simplify74.0ms

prune308.0ms

localize27.0ms

rewrite24.0ms

series466.0ms

simplify162.0ms

prune334.0ms

localize25.0ms

rewrite20.0ms

series362.0ms

simplify150.0ms

prune339.0ms

localize22.0ms

rewrite20.0ms

series160.0ms

simplify91.0ms

prune251.0ms

regimes470.0ms

bsearch5.0ms

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