Details

sample3.6s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0.183105%

Guaranteed chance to sample good point: 64.693653%

Results

40.0ms	50×	body	1280	invalid
27.0ms	238×	body	80	valid
27.0ms	54×	body	640	invalid
6.0ms	6×	body	1280	valid
5.0ms	14×	body	320	invalid
3.0ms	13×	body	160	invalid
2.0ms	6×	body	320	valid
2.0ms	4×	body	640	valid
1.0ms	12×	body	80	invalid
1.0ms	2×	body	160	valid

simplify400.0ms

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

prune22.0ms

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: 33.3b

Counts

2 → 2

localize35.0ms

Local error

Found 4 expressions with local error:

2.2b	(* (atan2 x.im x.re) y.im)
29.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.6b	(cos (+ (* (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

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:

4.0ms	(* (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)))

series91.0ms

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)))
72.0ms	(cos (+ (* (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: 3 (32.0ms)

Iter	Nodes	Cost
0	199	426
1	523	389
2	1301	389
3	2775	387
4	5001	387

prune149.0ms

Filtered

54 candidates to 68 candidates (-25.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	61	7	68
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	62	8	70

Merged error: 16.3b

Counts

70 → 8

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)
2.2b	(* (atan2 x.im x.re) y.im)
29.0b	(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:

6.0ms	(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)))

series74.0ms

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)))
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)))

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

prune150.0ms

Filtered

60 candidates to 81 candidates (-35.0%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	77	4	81
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	79	10	89

Merged error: 4.3b

Counts

89 → 10

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (pow x.re y.re) (exp (* (atan2 x.im x.re) y.im)))
0.0b	(exp (* (atan2 x.im x.re) y.im))
2.2b	(* (atan2 x.im x.re) y.im)

rewrite13.0ms

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:

5.0ms	(/ (pow x.re y.re) (exp (* (atan2 x.im x.re) y.im)))
2.0ms	(exp (* (atan2 x.im x.re) y.im))
4.0ms	(* (atan2 x.im x.re) y.im)

series42.0ms

Counts

3 → 9

Calls

3 calls:

27.0ms	(/ (pow x.re y.re) (exp (* (atan2 x.im x.re) y.im)))
9.0ms	(exp (* (atan2 x.im x.re) y.im))
6.0ms	(* (atan2 x.im x.re) y.im)

simplify38.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (28.0ms)

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

prune128.0ms

Filtered

58 candidates to 82 candidates (-41.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	81	1	82
Fresh	0	9	9
Picked	1	0	1
Done	0	0	0
Total	82	10	92

Merged error: 4.3b

Counts

92 → 10

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (pow x.re y.re) (log (exp (exp (* (atan2 x.im x.re) y.im)))))
0.0b	(exp (* (atan2 x.im x.re) y.im))
0.3b	(log (exp (exp (* (atan2 x.im x.re) y.im))))
2.2b	(* (atan2 x.im x.re) y.im)

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

49×	`times-frac`
42×	`add-sqr-sqrt`
40×	`add-cube-cbrt` `*-un-lft-identity`
36×	`log-pow`
28×	`exp-prod`
24×	`unpow-prod-down`
15×	`pow1`
11×	`add-exp-log`
8×	`add-cbrt-cube` `sqr-pow`
7×	`associate-/r` `associate-/l`
6×	`add-log-exp`
3×	`log-prod` `div-exp` `associate-r` `associate-l`
1×	`cbrt-undiv` `pow-to-exp` `exp-to-pow` `frac-2neg` `rem-log-exp` `pow-prod-down` `pow-exp` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `div-inv` `rem-exp-log` `unswap-sqr`

Counts

4 → 120

Calls

4 calls:

6.0ms	(/ (pow x.re y.re) (log (exp (exp (* (atan2 x.im x.re) y.im)))))
2.0ms	(exp (* (atan2 x.im x.re) y.im))
2.0ms	(log (exp (exp (* (atan2 x.im x.re) y.im))))
4.0ms	(* (atan2 x.im x.re) y.im)

series51.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(/ (pow x.re y.re) (log (exp (exp (* (atan2 x.im x.re) y.im)))))
8.0ms	(exp (* (atan2 x.im x.re) y.im))
9.0ms	(log (exp (exp (* (atan2 x.im x.re) y.im))))
6.0ms	(* (atan2 x.im x.re) y.im)

simplify43.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	339	1169
1	1136	1046
2	5001	1029

prune113.0ms

Filtered

87 candidates to 132 candidates (-51.7%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	131	1	132
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	131	11	142

Merged error: 4.3b

Counts

142 → 11

regimes578.0ms

Accuracy

74.3% (7.2b remaining)

Error of 11.1b against oracle of 3.9b and baseline of 31.8b

bsearch463.0ms

Steps

Iters	Range		Point
10	1.61118683445263e-49	1.856820959590781e-33	2.744432728213749e-41
8	2.150845629868087e-152	2.073583369554214e-148	6.10638643596487e-151
9	1.0952901157250081e-250	1.3838278931131376e-241	2.156677059327629e-250
6	3.0409148893564322e-263	1.5492017645221345e-262	1.5263318606953946e-262
11	-1.6168763158563456e-290	4.6037683339880027e-299	-2.2436014628515e-310

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	74	101
1	78	101
2	78	101

end0.0ms

sample7.1s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0.183105%

Guaranteed chance to sample good point: 64.693653%

Results

1.3s	1885×	body	1280	invalid
865.0ms	7543×	body	80	valid
628.0ms	1286×	body	640	invalid
190.0ms	549×	body	320	invalid
86.0ms	121×	body	1280	valid
74.0ms	154×	body	640	valid
63.0ms	281×	body	160	invalid
50.0ms	409×	body	80	invalid
39.0ms	115×	body	320	valid
15.0ms	67×	body	160	valid

Details

sample3.6s

simplify400.0ms

prune22.0ms

localize35.0ms

rewrite22.0ms

series91.0ms

simplify81.0ms

prune149.0ms

localize17.0ms

rewrite20.0ms

series74.0ms

simplify60.0ms

prune150.0ms

localize11.0ms

rewrite13.0ms

series42.0ms

simplify38.0ms

prune128.0ms

localize14.0ms

rewrite18.0ms

series51.0ms

simplify43.0ms

prune113.0ms

regimes578.0ms

bsearch463.0ms

simplify3.0ms

end0.0ms

sample7.1s

Profiling