Details

sample4.4s

Algorithm

intervals

sampling

Space saved by range analysis: 0.633765%

Space saved by search: 0.195169%

Guaranteed chance to sample good point: 0%

Results

44.0ms	60×	body	1280	invalid
31.0ms	230×	body	80	valid
23.0ms	45×	body	640	invalid
5.0ms	7×	body	1280	valid
5.0ms	10×	body	640	valid
4.0ms	13×	body	320	invalid
2.0ms	7×	body	160	invalid
1.0ms	4×	body	320	valid
1.0ms	11×	body	80	invalid
1.0ms	5×	body	160	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

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: 35.6b

Counts

2 → 2

localize47.0ms

Local error

Found 4 expressions with local error:

1.8b	(* (atan2 x.im x.re) y.im)
30.1b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.1b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
36.4b	(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)))

series86.0ms

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)))
11.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
63.0ms	(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 (13.0ms)

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

prune124.0ms

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: 22.3b

Counts

70 → 6

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(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)
1.8b	(* (atan2 x.im x.re) y.im)
30.1b	(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)))

series75.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
24.0ms	(* (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)))

simplify60.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 3 (53.0ms)

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

prune133.0ms

Filtered

60 candidates to 81 candidates (-35.0%)

Pruning

10 alts after pruning (9 fresh and 1 done)

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

Merged error: 6.5b

Counts

87 → 10

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(exp (* (atan2 x.im x.re) y.im))
0.3b	(/ (pow x.re y.re) (exp (* (atan2 x.im x.re) y.im)))
1.8b	(* (atan2 x.im x.re) y.im)

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
21×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
12×	`unpow-prod-down`
7×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
5×	`pow1` `add-log-exp`
4×	`sqr-pow`
3×	`div-exp` `associate-r` `associate-l` `associate-/r*`
1×	`cbrt-undiv` `pow-to-exp` `exp-prod` `exp-to-pow` `frac-2neg` `pow-prod-down` `pow-exp` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `div-inv` `rem-exp-log` `unswap-sqr`

Counts

3 → 73

Calls

3 calls:

2.0ms	(exp (* (atan2 x.im x.re) y.im))
5.0ms	(/ (pow x.re y.re) (exp (* (atan2 x.im x.re) y.im)))
3.0ms	(* (atan2 x.im x.re) y.im)

series44.0ms

Counts

3 → 9

Calls

3 calls:

9.0ms	(exp (* (atan2 x.im x.re) y.im))
27.0ms	(/ (pow x.re y.re) (exp (* (atan2 x.im x.re) y.im)))
9.0ms	(* (atan2 x.im x.re) y.im)

simplify35.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	266	599
1	1004	563
2	5001	558

prune108.0ms

Filtered

58 candidates to 82 candidates (-41.4%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	82	0	82
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	82	10	92

Merged error: 6.5b

Counts

92 → 10

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (pow (/ -1 x.re) y.re))
0.0b	(exp (* (atan2 x.im x.re) y.im))
0.2b	(/ (/ 1 (pow (/ -1 x.re) y.re)) (exp (* (atan2 x.im x.re) y.im)))
1.8b	(* (atan2 x.im x.re) y.im)

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

564×	`times-frac`
282×	`add-sqr-sqrt`
280×	`add-cube-cbrt` `*-un-lft-identity`
208×	`unpow-prod-down`
58×	`associate-/l*`
39×	`add-exp-log`
35×	`div-exp`
22×	`div-inv`
20×	`associate-/r*`
16×	`sqr-pow`
13×	`add-cbrt-cube`
12×	`pow-exp`
8×	`rec-exp` `1-exp`
6×	`pow1` `pow-to-exp` `add-log-exp`
4×	`cbrt-undiv`
3×	`associate-r` `associate-l`
2×	`frac-2neg` `clear-num`
1×	`exp-prod` `exp-to-pow` `pow-flip` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `rem-exp-log` `associate-/l/` `inv-pow` `unswap-sqr`

Counts

4 → 373

Calls

4 calls:

8.0ms	(/ 1 (pow (/ -1 x.re) y.re))
2.0ms	(exp (* (atan2 x.im x.re) y.im))
18.0ms	(/ (/ 1 (pow (/ -1 x.re) y.re)) (exp (* (atan2 x.im x.re) y.im)))
3.0ms	(* (atan2 x.im x.re) y.im)

series60.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(/ 1 (pow (/ -1 x.re) y.re))
9.0ms	(exp (* (atan2 x.im x.re) y.im))
31.0ms	(/ (/ 1 (pow (/ -1 x.re) y.re)) (exp (* (atan2 x.im x.re) y.im)))
6.0ms	(* (atan2 x.im x.re) y.im)

simplify77.0ms

Algorithm

egg-herbie

Counts

385 → 385

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1437	4944
1	5002	4672

prune588.0ms

Filtered

241 candidates to 385 candidates (-59.8%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	382	3	385
Fresh	1	6	7
Picked	1	0	1
Done	0	2	2
Total	384	11	395

Merged error: 6.5b

Counts

395 → 11

regimes482.0ms

Accuracy

50.1% (7.9b remaining)

Error of 12.2b against oracle of 4.3b and baseline of 20.2b

bsearch416.0ms

Steps

Iters	Range		Point
10	2.1268374295369894e-78	5.495029501303663e-67	4.835437917345077e-73
9	-3.684632596192235e-275	-1.380358447849174e-282	-1.5775093623743453e-281
8	-2.302059237858308e-212	-4.0936481142640626e-216	-6.720569622323342e-215
7	-2.3436073232027523e+104	-1.0077299007601604e+103	-1.2760520745232182e+103

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	54
1	65	54
2	65	54

end0.0ms

sample7.7s

Algorithm

intervals

sampling

Space saved by range analysis: 0.633765%

Space saved by search: 0.195169%

Guaranteed chance to sample good point: 0%

Results

1.4s	1919×	body	1280	invalid
839.0ms	7539×	body	80	valid
636.0ms	1278×	body	640	invalid
178.0ms	521×	body	320	invalid
104.0ms	142×	body	1280	valid
77.0ms	153×	body	640	valid
61.0ms	272×	body	160	invalid
46.0ms	392×	body	80	invalid
35.0ms	101×	body	320	valid
15.0ms	65×	body	160	valid

Details

sample4.4s

simplify381.0ms

prune19.0ms

localize47.0ms

rewrite21.0ms

series86.0ms

simplify79.0ms

prune124.0ms

localize15.0ms

rewrite17.0ms

series75.0ms

simplify60.0ms

prune133.0ms

localize10.0ms

rewrite12.0ms

series44.0ms

simplify35.0ms

prune108.0ms

localize12.0ms

rewrite57.0ms

series60.0ms

simplify77.0ms

prune588.0ms

regimes482.0ms

bsearch416.0ms

simplify3.0ms

end0.0ms

sample7.7s

Profiling