Details

analyze4.3s

Algorithm

sampling

Space saved by range analysis: 0.195169%

Space saved by search: 0.320047%

Guaranteed chance to sample good point: 55.092126%

sample153.0ms

Algorithm

intervals

Results

59.0ms	68×	body	1280	invalid
29.0ms	241×	body	80	valid
22.0ms	42×	body	640	invalid
5.0ms	6×	body	1280	valid
4.0ms	11×	body	320	invalid
4.0ms	2×	body	2560	invalid
3.0ms	7×	body	320	valid
2.0ms	7×	body	160	invalid
1.0ms	9×	body	80	invalid
1.0ms	2×	body	640	valid

simplify381.0ms

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

prune20.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 36.8b

Counts

2 → 2

localize45.0ms

Local error

Found 4 expressions with local error:

2.5b	(* (atan2 x.im x.re) y.im)
32.4b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.4b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.0b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite21.0ms

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

series87.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(* (atan2 x.im x.re) y.im)
5.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
70.0ms	(sin (+ (* (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

68 → 68

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	206	434
1	539	395
2	1201	392
3	2732	392
4	5002	392

prune165.0ms

Filtered

54 candidates to 68 candidates (-25.9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	58	10	68
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	59	11	70

Merged error: 20.8b

Counts

70 → 11

localize30.0ms

Local error

Found 4 expressions with local error:

32.4b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.4b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.4b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.0b	(sin (+ (* (log (* (* (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im))))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 53

Calls

4 calls:

4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
22.0ms	(sin (+ (* (log (* (* (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im))))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

series73.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
56.0ms	(sin (+ (* (log (* (* (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im))))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

simplify68.0ms

Algorithm

egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 4 (61.0ms)

Iter	Nodes	Cost
0	158	616
1	336	558
2	704	557
3	2021	557
4	5001	554

prune156.0ms

Filtered

55 candidates to 65 candidates (-18.2%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	64	1	65
Fresh	1	9	10
Picked	0	1	1
Done	0	0	0
Total	65	11	76

Merged error: 20.8b

Counts

76 → 11

localize27.0ms

Local error

Found 4 expressions with local error:

32.4b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.0b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
34.0b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
34.0b	(sin (+ (* (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

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

series166.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
54.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
52.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
54.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify61.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 4 (54.0ms)

Iter	Nodes	Cost
0	152	580
1	321	508
2	672	505
3	1724	505
4	5001	504

prune138.0ms

Filtered

48 candidates to 51 candidates (-6.3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	50	1	51
Fresh	0	9	9
Picked	1	0	1
Done	0	1	1
Total	51	11	62

Merged error: 20.8b

Counts

62 → 11

localize28.0ms

Local error

Found 4 expressions with local error:

32.4b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.4b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.0b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
35.0b	(cbrt (pow (* (atan2 x.im x.re) y.im) 3))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 55

Calls

4 calls:

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)))
2.0ms	(cbrt (pow (* (atan2 x.im x.re) y.im) 3))

series77.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
55.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
10.0ms	(cbrt (pow (* (atan2 x.im x.re) y.im) 3))

simplify83.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 4 (77.0ms)

Iter	Nodes	Cost
0	211	456
1	537	424
2	1142	423
3	2771	423
4	5001	421

prune117.0ms

Filtered

55 candidates to 67 candidates (-21.8%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	66	1	67
Fresh	0	9	9
Picked	1	0	1
Done	0	1	1
Total	67	11	78

Merged error: 20.8b

Counts

78 → 11

Details

analyze4.3s

sample153.0ms

simplify381.0ms

prune20.0ms

localize45.0ms

rewrite21.0ms

series87.0ms

simplify81.0ms

prune165.0ms

localize30.0ms

rewrite34.0ms

series73.0ms

simplify68.0ms

prune156.0ms

localize27.0ms

rewrite22.0ms

series166.0ms

simplify61.0ms

prune138.0ms

localize28.0ms

rewrite16.0ms

series77.0ms

simplify83.0ms

prune117.0ms

regimes548.0ms

bsearch2.0ms

Profiling