Details

sample419.0ms

Algorithm

intervals

Results

65.0ms	74×	body	1280	valid
44.0ms	256×	body	80	valid
34.0ms	57×	body	640	valid
8.0ms	18×	body	320	valid
4.0ms	2×	body	2560	valid
2.0ms	6×	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

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.8b

localize24.0ms

Local error

Found 4 expressions with local error:

1.7b	(* (atan2 x.im x.re) y.im)
31.9b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
33.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite26.0ms

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×	`sin-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)
12.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
3.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series246.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(* (atan2 x.im x.re) y.im)
149.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
36.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
44.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify74.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	196	427
1	506	390
2	1139	386
3	2509	386
4	5001	386

prune340.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 19.6b

localize34.0ms

Local error

Found 4 expressions with local error:

20.2b	(cos (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im))
33.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite13.0ms

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-+`

Counts

4 → 52

Calls

4 calls:

2.0ms	(cos (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im))
3.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
3.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
3.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series218.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(cos (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im))
34.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
37.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify61.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 4 (56.0ms)

Iter	Nodes	Cost
0	126	390
1	283	364
2	636	363
3	1696	363
4	5001	360

prune411.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 19.6b

localize27.0ms

Local error

Found 4 expressions with local error:

33.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `sqrt-prod`
8×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-div`
4×	`add-exp-log` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `add-cbrt-cube` `flip-+` `add-log-exp`

Counts

4 → 60

Calls

4 calls:

3.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
3.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
5.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
3.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series141.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
37.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify141.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 5 (136.0ms)

Iter	Nodes	Cost
0	89	400
1	215	388
2	503	388
3	1265	388
4	4227	388
5	5002	384

prune449.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 19.6b

localize25.0ms

Local error

Found 4 expressions with local error:

10.8b	(cbrt (pow (sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re))) 3))
31.9b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
33.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
11×	`add-sqr-sqrt`
9×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `sqrt-prod`
4×	`add-exp-log` `sqrt-div` `add-cbrt-cube` `add-log-exp`
3×	`unpow-prod-down` `cube-prod`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
1×	`cube-mult` `sin-sum` `pow1/3` `unpow3` `rem-cbrt-cube` `sqr-pow`

Counts

4 → 59

Calls

4 calls:

5.0ms	(cbrt (pow (sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re))) 3))
6.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
3.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
3.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series353.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(cbrt (pow (sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re))) 3))
141.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
35.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
38.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify147.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 4 (140.0ms)

Iter	Nodes	Cost
0	191	725
1	493	717
2	1262	717
3	4742	717
4	5001	647

prune311.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 19.6b

regimes365.0ms

Accuracy

79.3% (2.9b remaining)

Error of 22.1b against oracle of 19.2b and baseline of 33.3b

bsearch148.0ms

Steps

Iters	Range		Point
9	-5.459969929633657e-306	2.8649750194033813e-305	1.73062623171225e-310

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	36
1	45	36

end0.0ms

sample4.6s

Algorithm

intervals

Results

1.9s	2168×	body	1280	valid
1.1s	7914×	body	80	valid
850.0ms	1414×	body	640	valid
245.0ms	581×	body	320	valid
71.0ms	38×	body	2560	valid
66.0ms	235×	body	160	valid