Details

analyze1.5s

Algorithm

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
9.4%	90.4%	0.2%	6
17.2%	82.7%	0.2%	7
19.5%	80.3%	0.2%	8
30.8%	69%	0.2%	9
35.5%	64.3%	0.2%	10
42.4%	57.4%	0.2%	11
47.1%	52.7%	0.2%	12
48.9%	50.8%	0.3%	13
50%	49.7%	0.4%	14

sample148.0ms

Algorithm

intervals

Results

49.0ms	68×	body	1280	invalid
32.0ms	236×	body	80	valid
22.0ms	42×	body	640	invalid
7.0ms	19×	body	320	invalid
6.0ms	8×	body	1280	valid
3.0ms	14×	body	160	invalid
3.0ms	6×	body	640	valid
2.0ms	16×	body	80	invalid
2.0ms	5×	body	320	valid
0.0ms	1×	body	160	valid

simplify537.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4970	36
1	4970	36

prune19.0ms

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: 32.6b

Counts

2 → 2

localize26.0ms

Local error

Found 4 expressions with local error:

1.9b	(* (atan2 x.im x.re) y.im)
28.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
28.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.9b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite32.0ms

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)
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
65.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify57.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4737	680
1	4737	680

prune138.0ms

Filtered

56 candidates to 68 candidates (-21.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	62	6	68
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	63	7	70

Merged error: 19.8b

Counts

70 → 7

localize17.0ms

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)
1.9b	(* (atan2 x.im x.re) y.im)
28.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite18.0ms

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

Counts

4 → 68

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)))

series78.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
23.0ms	(* (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)))

simplify30.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5242	850

prune143.0ms

Filtered

61 candidates to 80 candidates (-31.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	77	3	80
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	77	10	87

Merged error: 4.8b

Counts

87 → 10

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
0.5b	(exp (atan2 x.im x.re))
2.6b	(log (pow (exp (atan2 x.im x.re)) y.im))
28.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `*-un-lft-identity`
9×	`pow1`
7×	`add-exp-log` `log-prod`
6×	`associate-l` `add-cbrt-cube`
5×	`add-log-exp`
4×	`log-pow`
3×	`unpow-prod-down` `exp-prod` `rem-log-exp` `associate-r` `sqrt-prod`
2×	`sqrt-pow1` `pow1/2` `sqrt-div`
1×	`pow-to-exp` `rem-sqrt-square` `flip3-+` `pow-prod-down` `pow-exp` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `rem-exp-log` `unswap-sqr` `sqr-pow`

Counts

4 → 65

Calls

4 calls:

5.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
2.0ms	(exp (atan2 x.im x.re))
2.0ms	(log (pow (exp (atan2 x.im x.re)) y.im))
5.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series46.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
4.0ms	(exp (atan2 x.im x.re))
13.0ms	(log (pow (exp (atan2 x.im x.re)) y.im))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify37.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	4967	666
1	4967	666

prune131.0ms

Filtered

56 candidates to 77 candidates (-37.5%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	77	0	77
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	77	10	87

Merged error: 4.8b

Counts

87 → 10

localize30.0ms

Local error

Found 4 expressions with local error:

1.9b	(* (atan2 x.im x.re) y.im)
28.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
28.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.9b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite19.0ms

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)))
7.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series74.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(* (atan2 x.im x.re) y.im)
8.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
53.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify57.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4737	680
1	4737	680

prune98.0ms

Filtered

56 candidates to 68 candidates (-21.4%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	68	0	68
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	68	10	78

Merged error: 4.8b

Counts

78 → 10

regimes431.0ms

Accuracy

66.1% (5.4b remaining)

Error of 9.1b against oracle of 3.7b and baseline of 19.6b

bsearch1.5s

Steps

Iters	Range		Point
9	-6.343422754389152e-304	4.857988002970338e-308	-3.43063627896148e-310

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	27
1	27	27

end0.0ms

analyze1.2s

Algorithm

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
9.4%	90.4%	0.2%	6
17.2%	82.7%	0.2%	7
19.5%	80.3%	0.2%	8
30.8%	69%	0.2%	9
35.5%	64.3%	0.2%	10
42.4%	57.4%	0.2%	11
47.1%	52.7%	0.2%	12
48.9%	50.8%	0.3%	13
50%	49.7%	0.4%	14

sample3.8s

Algorithm

intervals

Results

1.4s	1923×	body	1280	invalid
837.0ms	7538×	body	80	valid
648.0ms	1344×	body	640	invalid
191.0ms	537×	body	320	invalid
114.0ms	153×	body	1280	valid
82.0ms	164×	body	640	valid
56.0ms	239×	body	160	invalid
45.0ms	404×	body	80	invalid
36.0ms	94×	body	320	valid
12.0ms	51×	body	160	valid

Details

analyze1.5s

sample148.0ms

simplify537.0ms

prune19.0ms

localize26.0ms

rewrite32.0ms

series84.0ms

simplify57.0ms

prune138.0ms

localize17.0ms

rewrite18.0ms

series78.0ms

simplify30.0ms

prune143.0ms

localize20.0ms

rewrite16.0ms

series46.0ms

simplify37.0ms

prune131.0ms

localize30.0ms

rewrite19.0ms

series74.0ms

simplify57.0ms

prune98.0ms

regimes431.0ms

bsearch1.5s

simplify2.0ms

end0.0ms

analyze1.2s

sample3.8s

Profiling