Details

sample4.9s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0.183105%

Guaranteed chance to sample good point: 49.663691%

Results

38.0ms	53×	body	1280	invalid
27.0ms	239×	body	80	valid
18.0ms	37×	body	640	invalid
9.0ms	28×	body	320	invalid
4.0ms	8×	body	640	valid
2.0ms	11×	body	160	invalid
2.0ms	2×	body	1280	valid
1.0ms	13×	body	80	invalid
1.0ms	4×	body	320	valid
1.0ms	3×	body	160	valid

simplify368.0ms

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

prune30.0ms

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: 35.0b

Counts

2 → 2

localize23.0ms

Local error

Found 4 expressions with local error:

1.4b	(* (atan2 x.im x.re) y.im)
30.8b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.8b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.3b	(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)))

series85.0ms

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)))
67.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify79.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	199	426
1	523	389
2	1179	387
3	2665	387
4	5002	387

prune134.0ms

Filtered

54 candidates to 68 candidates (-25.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	61	7	68
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	63	7	70

Merged error: 19.1b

Counts

70 → 7

localize16.0ms

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)
1.4b	(* (atan2 x.im x.re) y.im)
30.8b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite20.0ms

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)
6.0ms	(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)))
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)))

simplify61.0ms

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

prune134.0ms

Filtered

60 candidates to 81 candidates (-35.0%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	77	4	81
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	79	9	88

Merged error: 3.7b

Counts

88 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (log (log (exp (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.re)
1.4b	(* (atan2 x.im x.re) y.im)
3.3b	(log (exp (sqrt (+ (* x.re x.re) (* x.im x.im)))))
30.8b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

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

series42.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(* (log (log (exp (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.re)
6.0ms	(* (atan2 x.im x.re) y.im)
6.0ms	(log (exp (sqrt (+ (* x.re x.re) (* x.im x.im)))))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify102.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (17.0ms)

Iter	Nodes	Cost
0	261	514
1	727	445
2	1711	432
3	3709	432
4	5001	432

prune133.0ms

Filtered

61 candidates to 82 candidates (-34.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	81	1	82
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	82	9	91

Merged error: 3.7b

Counts

91 → 9

localize26.0ms

Local error

Found 4 expressions with local error:

1.3b	(* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im)))
30.8b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.8b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.3b	(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

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

Counts

4 → 57

Calls

4 calls:

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

series86.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
51.0ms	(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

69 → 69

Iterations

Useful iterations: 3 (48.0ms)

Iter	Nodes	Cost
0	275	515
1	668	463
2	1794	448
3	5001	442

prune83.0ms

Filtered

55 candidates to 69 candidates (-25.5%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	69	0	69
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	69	9	78

Merged error: 3.7b

Counts

78 → 9

regimes547.0ms

Accuracy

82.8% (5.4b remaining)

Error of 9.0b against oracle of 3.5b and baseline of 35.2b

bsearch210.0ms

Steps

Iters	Range		Point
9	-2.39638253738344e-305	1.5904371949932397e-304	3.2929543682718e-310
5	-9.952989512993498e-65	-3.0842229109411626e-65	-9.752848790142804e-65
7	-2.530682891571387e-34	-1.5040095855804174e-35	-6.400708351997873e-35

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	36
1	57	36
2	57	36

end0.0ms

sample8.4s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0.183105%

Guaranteed chance to sample good point: 49.663691%

Results

1.3s	1825×	body	1280	invalid
835.0ms	7560×	body	80	valid
610.0ms	1293×	body	640	invalid
188.0ms	560×	body	320	invalid
108.0ms	138×	body	1280	valid
88.0ms	163×	body	640	valid
56.0ms	252×	body	160	invalid
44.0ms	389×	body	80	invalid
29.0ms	85×	body	320	valid
15.0ms	54×	body	160	valid

Details

sample4.9s

simplify368.0ms

prune30.0ms

localize23.0ms

rewrite21.0ms

series85.0ms

simplify79.0ms

prune134.0ms

localize16.0ms

rewrite20.0ms

series71.0ms

simplify61.0ms

prune134.0ms

localize16.0ms

rewrite17.0ms

series42.0ms

simplify102.0ms

prune133.0ms

localize26.0ms

rewrite21.0ms

series86.0ms

simplify57.0ms

prune83.0ms

regimes547.0ms

bsearch210.0ms

simplify2.0ms

end0.0ms

sample8.4s

Profiling