Details

sample311.0ms

Algorithm

intervals

Results

44.0ms	60×	body	1280	valid
30.0ms	254×	body	80	valid
19.0ms	38×	body	640	valid
7.0ms	19×	body	320	valid
2.0ms	9×	body	160	valid

simplify38.0ms

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

prune26.0ms

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: 34.9b

Counts

2 → 2

localize26.0ms

Local error

Found 4 expressions with local error:

1.6b	(* (atan2 x.im x.re) y.im)
31.6b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.6b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
37.7b	(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:

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)))

series89.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(* (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)))
70.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify78.0ms

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	5001	387

prune126.0ms

Filtered

68 candidates to 54 candidates (20.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	63	5	68
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	65	5	70

Merged error: 17.1b

Counts

70 → 5

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)
1.6b	(* (atan2 x.im x.re) y.im)
31.6b	(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` `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)))

series76.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
25.0ms	(* (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)))

simplify58.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 3 (51.0ms)

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

prune122.0ms

Filtered

81 candidates to 60 candidates (25.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	78	3	81
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	79	7	86

Merged error: 4.0b

Counts

86 → 7

localize28.0ms

Local error

Found 4 expressions with local error:

1.6b	(* (atan2 x.im x.re) y.im)
31.6b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.6b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
37.7b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite18.0ms

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

series70.0ms

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)))
52.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify80.0ms

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

prune126.0ms

Filtered

68 candidates to 54 candidates (20.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	67	1	68
Fresh	0	5	5
Picked	1	0	1
Done	0	1	1
Total	68	7	75

Merged error: 4.0b

Counts

75 → 7

localize30.0ms

Local error

Found 4 expressions with local error:

1.6b	(* (atan2 x.im x.re) y.im)
31.6b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.6b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
37.7b	(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)))
6.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series72.0ms

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)))
54.0ms	(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

prune131.0ms

Filtered

68 candidates to 54 candidates (20.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	68	0	68
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	68	7	75

Merged error: 4.0b

Counts

75 → 7

regimes375.0ms

Accuracy

59.3% (6.5b remaining)

Error of 10.1b against oracle of 3.5b and baseline of 19.6b

bsearch404.0ms

Steps

Iters	Range		Point
3	7.97286736368623e-35	1.0063179645485215e-34	8.089964071187759e-35
8	1.460973685560194e-189	4.280630909328093e-187	1.0357395792640826e-188
5	3.492739746172915e-256	1.08688690581464e-255	6.921280589325799e-256
7	-1.206656504665561e-248	-1.2349811494724944e-250	-1.6718081751263931e-249
10	-3.638426086380447e-77	-2.1455022919475984e-89	-1.3202902702034764e-81
6	-1.9829548386146398e+113	-1.6077610660282576e+112	-1.6349441744323402e+112

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	61	63
1	70	63
2	73	63
3	73	63

end0.0ms

sample3.8s

Algorithm

intervals

Results

1.3s	1942×	body	1280	valid
850.0ms	7970×	body	80	valid
665.0ms	1402×	body	640	valid
209.0ms	621×	body	320	valid
70.0ms	320×	body	160	valid

Details

sample311.0ms

simplify38.0ms

prune26.0ms

localize26.0ms

rewrite22.0ms

series89.0ms

simplify78.0ms

prune126.0ms

localize16.0ms

rewrite18.0ms

series76.0ms

simplify58.0ms

prune122.0ms

localize28.0ms

rewrite18.0ms

series70.0ms

simplify80.0ms

prune126.0ms

localize30.0ms

rewrite19.0ms

series72.0ms

simplify79.0ms

prune131.0ms

regimes375.0ms

bsearch404.0ms

simplify3.0ms

end0.0ms

sample3.8s

Profiling