Details

sample448.0ms

Algorithm

intervals

Results

72.0ms	66×	body	1280	valid
28.0ms	256×	body	80	valid
23.0ms	47×	body	640	valid
6.0ms	18×	body	320	valid
3.0ms	10×	body	160	valid

simplify41.0ms

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

prune17.0ms

Filtered

1 candidates to 1 candidates (100.0%)

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: 33.4b

Counts

2 → 2

localize37.0ms

Local error

Found 4 expressions with local error:

1.3b	(* (atan2 x.im x.re) y.im)
31.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.9b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite23.0ms

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)))
9.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series238.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(* (atan2 x.im x.re) y.im)
35.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
38.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
148.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify76.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	191	422
1	501	385
2	1134	381
3	2494	381
4	5002	381

prune299.0ms

Filtered

68 candidates to 54 candidates (79.4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	64	4	68
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	65	5	70

Merged error: 19.7b

Counts

70 → 5

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)))
0.2b	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
1.3b	(* (atan2 x.im x.re) y.im)
31.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite19.0ms

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:

5.0ms	(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)))

series241.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
91.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
20.0ms	(* (atan2 x.im x.re) y.im)
36.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify59.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (21.0ms)

Iter	Nodes	Cost
0	280	545
1	825	486
2	2165	481
3	5001	481

prune261.0ms

Filtered

81 candidates to 60 candidates (74.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	76	5	81
Fresh	2	2	4
Picked	0	1	1
Done	0	0	0
Total	78	8	86

Merged error: 3.2b

Counts

86 → 8

localize16.0ms

Local error

Found 2 expressions with local error:

0.0b	(exp (neg (* (atan2 x.im x.re) y.im)))
1.3b	(* (atan2 x.im x.re) y.im)

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-sqr-sqrt`
6×	`exp-prod`
5×	`add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`associate-r` `associate-l`
2×	`rem-exp-log`
1×	`neg-sub0` `distribute-lft-neg-in` `exp-neg` `neg-mul-1` `distribute-rgt-neg-in` `exp-diff` `pow-prod-down` `neg-log` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

2 → 35

Calls

2 calls:

2.0ms	(exp (neg (* (atan2 x.im x.re) y.im)))
4.0ms	(* (atan2 x.im x.re) y.im)

series40.0ms

Counts

2 → 6

Calls

2 calls:

23.0ms	(exp (neg (* (atan2 x.im x.re) y.im)))
17.0ms	(* (atan2 x.im x.re) y.im)

simplify55.0ms

Algorithm

egg-herbie

Counts

41 → 41

Iterations

Useful iterations: 3 (52.0ms)

Iter	Nodes	Cost
0	119	163
1	468	147
2	2129	147
3	5001	146

prune126.0ms

Filtered

41 candidates to 28 candidates (68.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	39	2	41
Fresh	0	6	6
Picked	1	0	1
Done	0	1	1
Total	40	9	49

Merged error: 3.2b

Counts

49 → 9

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (exp (neg (* (atan2 x.im x.re) y.im))))
1.3b	(* (atan2 x.im x.re) y.im)
1.3b	(* (atan2 x.im x.re) y.im)
1.3b	(* (atan2 x.im x.re) y.im)

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
11×	`add-cube-cbrt` `*-un-lft-identity`
10×	`pow1` `add-exp-log` `add-cbrt-cube`
9×	`associate-r` `associate-l`
4×	`add-log-exp`
3×	`cbrt-prod` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`cbrt-div`
1×	`neg-sub0` `exp-neg` `exp-diff` `pow1/3`

Counts

4 → 67

Calls

4 calls:

2.0ms	(cbrt (exp (neg (* (atan2 x.im x.re) y.im))))
4.0ms	(* (atan2 x.im x.re) y.im)
4.0ms	(* (atan2 x.im x.re) y.im)
4.0ms	(* (atan2 x.im x.re) y.im)

series96.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(cbrt (exp (neg (* (atan2 x.im x.re) y.im))))
16.0ms	(* (atan2 x.im x.re) y.im)
16.0ms	(* (atan2 x.im x.re) y.im)
19.0ms	(* (atan2 x.im x.re) y.im)

simplify55.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 3 (49.0ms)

Iter	Nodes	Cost
0	119	340
1	434	305
2	1851	303
3	5001	299

prune252.0ms

Filtered

79 candidates to 52 candidates (65.8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	76	3	79
Fresh	1	6	7
Picked	1	0	1
Done	0	1	1
Total	78	10	88

Merged error: 3.2b

Counts

88 → 10

regimes289.0ms

Accuracy

66.8% (5.4b remaining)

Error of 9.4b against oracle of 4.0b and baseline of 20.3b

bsearch124.0ms

Steps

Iters	Range		Point
8	-2.713494972300769e-307	5.813193115847266e-307	4.13952476059083e-310

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	15
1	35	15
2	35	15

end0.0ms

sample3.7s

Algorithm

intervals

Results

1.4s	2004×	body	1280	valid
852.0ms	7885×	body	80	valid
703.0ms	1427×	body	640	valid
240.0ms	698×	body	320	valid
83.0ms	328×	body	160	valid

Details

sample448.0ms

simplify41.0ms

prune17.0ms

localize37.0ms

rewrite23.0ms

series238.0ms

simplify76.0ms

prune299.0ms

localize17.0ms

rewrite19.0ms

series241.0ms

simplify59.0ms

prune261.0ms

localize16.0ms

rewrite7.0ms

series40.0ms

simplify55.0ms

prune126.0ms

localize17.0ms

rewrite16.0ms

series96.0ms

simplify55.0ms

prune252.0ms

regimes289.0ms

bsearch124.0ms

simplify2.0ms

end0.0ms

sample3.7s

Profiling