Details

analyze4.1s

Algorithm

sampling

Space saved by range analysis: 0.195169%

Space saved by search: 0.633765%

Guaranteed chance to sample good point: 55.118931%

sample120.0ms

Algorithm

intervals

Results

38.0ms	53×	body	1280	invalid
27.0ms	243×	body	80	valid
20.0ms	42×	body	640	invalid
5.0ms	13×	body	320	invalid
3.0ms	4×	body	1280	valid
3.0ms	7×	body	320	valid
2.0ms	9×	body	160	invalid
1.0ms	6×	body	80	invalid
1.0ms	1×	body	640	valid
0.0ms	1×	body	160	valid

simplify376.0ms

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

prune29.0ms

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: 32.8b

Counts

2 → 2

localize24.0ms

Local error

Found 4 expressions with local error:

1.3b	(* (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)))
33.8b	(cos (+ (* (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×	`cos-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	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series84.0ms

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)))
66.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify82.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	199	428
1	523	391
2	1179	387
3	2665	387
4	5002	387

prune125.0ms

Filtered

54 candidates to 68 candidates (-25.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	63	5	68
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	64	6	70

Merged error: 18.1b

Counts

70 → 6

localize15.0ms

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)
1.3b	(* (atan2 x.im x.re) y.im)
29.1b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite17.0ms

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`
3×	`exp-prod` `sqrt-prod` `log-pow`
2×	`sqrt-pow1` `pow1/2` `sqrt-div` `exp-sum` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `rem-exp-log` `unswap-sqr`
1×	`sub-neg` `rem-sqrt-square` `flip3-+` `exp-diff` `diff-log` `flip-+`

Counts

4 → 69

Calls

4 calls:

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

series71.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
21.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
8.0ms	(* (atan2 x.im x.re) y.im)
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify59.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 3 (52.0ms)

Iter	Nodes	Cost
0	299	556
1	864	496
2	2274	481
3	5002	479

prune140.0ms

Filtered

60 candidates to 81 candidates (-35.0%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	75	6	81
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	77	10	87

Merged error: 3.3b

Counts

87 → 10

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(log (exp (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)
1.3b	(* (atan2 x.im x.re) y.im)
29.1b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 71

Calls

4 calls:

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

series70.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(log (exp (exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))))
21.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
6.0ms	(* (atan2 x.im x.re) y.im)
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify58.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 3 (51.0ms)

Iter	Nodes	Cost
0	305	634
1	854	552
2	2133	537
3	5001	535

prune147.0ms

Filtered

60 candidates to 83 candidates (-38.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	82	1	83
Fresh	0	9	9
Picked	1	0	1
Done	0	0	0
Total	83	10	93

Merged error: 3.3b

Counts

93 → 10

localize26.0ms

Local error

Found 4 expressions with local error:

1.3b	(* (atan2 x.im x.re) y.im)
1.3b	(* (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)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 66

Calls

4 calls:

3.0ms	(* (atan2 x.im x.re) y.im)
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)))

series23.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(* (atan2 x.im x.re) y.im)
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)))

simplify66.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (12.0ms)

Iter	Nodes	Cost
0	145	348
1	428	322
2	1017	320
3	2145	320
4	5002	320

prune108.0ms

Filtered

56 candidates to 78 candidates (-39.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	76	2	78
Fresh	0	9	9
Picked	1	0	1
Done	0	0	0
Total	77	11	88

Merged error: 3.3b

Counts

88 → 11

Details

analyze4.1s

sample120.0ms

simplify376.0ms

prune29.0ms

localize24.0ms

rewrite21.0ms

series84.0ms

simplify82.0ms

prune125.0ms

localize15.0ms

rewrite17.0ms

series71.0ms

simplify59.0ms

prune140.0ms

localize19.0ms

rewrite18.0ms

series70.0ms

simplify58.0ms

prune147.0ms

localize26.0ms

rewrite16.0ms

series23.0ms

simplify66.0ms

prune108.0ms

regimes553.0ms

bsearch2.0ms

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