Details

sample373.0ms

Algorithm

intervals

Results

33.0ms	49×	body	1280	valid
29.0ms	263×	body	80	valid
22.0ms	47×	body	640	valid
4.0ms	11×	body	320	valid
1.0ms	6×	body	160	valid

simplify36.0ms

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

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 32.6b

Counts

2 → 1

localize25.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (atan2 x.im x.re) y.re)
29.3b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.3b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.6b	(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:

3.0ms	(* (atan2 x.im x.re) y.re)
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)))

series237.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(* (atan2 x.im x.re) y.re)
37.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
150.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify71.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (12.0ms)

Iter	Nodes	Cost
0	189	422
1	491	385
2	1112	381
3	2385	381
4	5001	381

prune421.0ms

Filtered

68 candidates to 54 candidates (79.4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	63	5	68
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	64	5	69

Merged error: 17.1b

Counts

69 → 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)))
0.2b	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
1.0b	(* (atan2 x.im x.re) y.im)
29.3b	(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:

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)))

series223.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
84.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
16.0ms	(* (atan2 x.im x.re) y.im)
36.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify56.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (20.0ms)

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

prune403.0ms

Filtered

81 candidates to 60 candidates (74.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	77	4	81
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	79	7	86

Merged error: 3.9b

Counts

86 → 7

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (log (log (exp (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.re)
1.0b	(* (atan2 x.im x.re) y.im)
4.2b	(log (exp (sqrt (+ (* x.re x.re) (* x.im x.im)))))
29.3b	(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)))

series170.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(* (log (log (exp (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.re)
15.0ms	(* (atan2 x.im x.re) y.im)
34.0ms	(log (exp (sqrt (+ (* x.re x.re) (* x.im x.im)))))
36.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify102.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (16.0ms)

Iter	Nodes	Cost
0	256	510
1	732	441
2	1709	432
3	3751	432
4	5002	432

prune407.0ms

Filtered

82 candidates to 59 candidates (72.0%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	81	1	82
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	82	7	89

Merged error: 3.9b

Counts

89 → 7

localize29.0ms

Local error

Found 4 expressions with local error:

29.3b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.3b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.3b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.6b	(cos (+ (* (log (* (* (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im))))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
6×	`sqrt-div`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
1×	`cos-sum`

Counts

4 → 53

Calls

4 calls:

4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
24.0ms	(cos (+ (* (log (* (* (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im))))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

series232.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
36.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
128.0ms	(cos (+ (* (log (* (* (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im))))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

simplify62.0ms

Algorithm

egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 4 (55.0ms)

Iter	Nodes	Cost
0	143	602
1	298	546
2	638	546
3	1805	546
4	5002	543

prune444.0ms

Filtered

65 candidates to 56 candidates (86.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	63	2	65
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	65	7	72

Merged error: 3.9b

Counts

72 → 7

regimes502.0ms

Accuracy

79.8% (6.3b remaining)

Error of 10.1b against oracle of 3.8b and baseline of 34.9b

bsearch399.0ms

Steps

Iters	Range		Point
9	2.190530622938087e-76	2.4239314156889567e-70	6.384061532363716e-74
9	8.26523105319876e-204	8.747928736751176e-198	8.617207416529642e-198
11	-4.12462284493205e-301	9.914604343488792e-294	8.4964026544742e-311

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	66	58
1	70	58
2	70	58

end0.0ms

sample3.7s

Algorithm

intervals

Results

1.3s	1958×	body	1280	valid
816.0ms	7966×	body	80	valid
662.0ms	1443×	body	640	valid
212.0ms	660×	body	320	valid
71.0ms	312×	body	160	valid

Details

sample373.0ms

simplify36.0ms

prune17.0ms

localize25.0ms

rewrite22.0ms

series237.0ms

simplify71.0ms

prune421.0ms

localize16.0ms

rewrite18.0ms

series223.0ms

simplify56.0ms

prune403.0ms

localize17.0ms

rewrite17.0ms

series170.0ms

simplify102.0ms

prune407.0ms

localize29.0ms

rewrite37.0ms

series232.0ms

simplify62.0ms

prune444.0ms

regimes502.0ms

bsearch399.0ms

simplify3.0ms

end0.0ms

sample3.7s

Profiling