Details

sample351.0ms

Algorithm

intervals

Results

213.0ms	245×	body	80	valid
62.0ms	68×	body	1280	valid
32.0ms	53×	body	640	valid
11.0ms	26×	body	320	valid
4.0ms	12×	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

prune32.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.9b

localize24.0ms

Local error

Found 4 expressions with local error:

2.4b	(* (atan2 x.im x.re) y.im)
27.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
27.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.4b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite20.0ms

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)
3.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
3.0ms	(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)))

series90.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(* (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)))

simplify74.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (13.0ms)

Iter	Nodes	Cost
0	191	420
1	501	383
2	1134	381
3	2496	381
4	5001	381

prune899.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 20.2b

localize15.0ms

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)
2.4b	(* (atan2 x.im x.re) y.im)
27.0b	(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:

8.0ms	(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)
3.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series75.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
20.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
7.0ms	(* (atan2 x.im x.re) y.im)
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify56.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (19.0ms)

Iter	Nodes	Cost
0	280	546
1	825	487
2	2118	481
3	5001	481

prune759.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.2b

localize26.0ms

Local error

Found 4 expressions with local error:

2.4b	(* (atan2 x.im x.re) y.im)
27.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
27.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.4b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite16.0ms

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)
3.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
3.0ms	(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)))

series73.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(* (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)))
51.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify72.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (13.0ms)

Iter	Nodes	Cost
0	191	420
1	501	383
2	1134	381
3	2496	381
4	5001	381

prune1.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.2b

localize27.0ms

Local error

Found 4 expressions with local error:

2.4b	(* (atan2 x.im x.re) y.im)
27.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
27.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.4b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite17.0ms

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)))
3.0ms	(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:

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

simplify73.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (13.0ms)

Iter	Nodes	Cost
0	191	420
1	501	383
2	1134	381
3	2496	381
4	5001	381

prune1.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.2b

regimes636.0ms

Accuracy

81.7% (5.5b remaining)

Error of 9.2b against oracle of 3.7b and baseline of 33.7b

bsearch88.0ms

Steps

Iters	Range		Point
7	-1.0325669680604107e-307	7.896313722166774e-308	3.5063895551657e-310

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	16
1	42	16
2	42	16

end0.0ms

sample4.5s

Algorithm

intervals

Results

1.8s	2085×	body	1280	valid
1.1s	7947×	body	80	valid
854.0ms	1412×	body	640	valid
292.0ms	684×	body	320	valid
91.0ms	308×	body	160	valid