Details

sample456.0ms

Algorithm

intervals

Results

64.0ms	73×	body	1280	valid
24.0ms	264×	body	80	valid
18.0ms	47×	body	640	valid
6.0ms	23×	body	320	valid
3.0ms	2×	body	2560	valid
0.0ms	1×	body	160	valid

simplify40.0ms

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

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.5b

localize24.0ms

Local error

Found 4 expressions with local error:

1.8b	(* (atan2 x.im x.re) y.im)
33.5b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.5b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.2b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite50.0ms

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:

7.0ms	(* (atan2 x.im x.re) y.im)
8.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
8.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
25.0ms	(sin (+ (* (log (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:

18.0ms	(* (atan2 x.im x.re) y.im)
32.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
150.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify75.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (13.0ms)

Iter	Nodes	Cost
0	196	425
1	506	388
2	1139	386
3	2509	386
4	5001	386

prune327.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 23.4b

localize28.0ms

Local error

Found 4 expressions with local error:

1.8b	(* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im)))
33.5b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.5b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.2b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

11×	`pow1`
10×	`add-sqr-sqrt`
9×	`add-exp-log`
7×	`add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
6×	`sqrt-prod`
4×	`sqrt-div` `add-log-exp`
3×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
1×	`sin-sum` `associate-r` `*-commutative` `unswap-sqr`

Counts

4 → 57

Calls

4 calls:

21.0ms	(* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im)))
8.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
8.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
17.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series279.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im)))
34.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
137.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify138.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 4 (130.0ms)

Iter	Nodes	Cost
0	237	500
1	591	448
2	1598	444
3	4562	437
4	5002	436

prune363.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 23.4b

localize25.0ms

Local error

Found 4 expressions with local error:

1.2b	(* (* (atan2 x.im x.re) (cbrt y.im)) (cbrt y.im))
33.5b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.5b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.2b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

11×	`pow1`
10×	`add-sqr-sqrt`
9×	`add-exp-log`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`associate-r` `sqrt-prod` `add-cbrt-cube`
4×	`sqrt-div` `add-log-exp`
3×	`cbrt-prod` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
1×	`sin-sum` `associate-l` `*-commutative`

Counts

4 → 59

Calls

4 calls:

21.0ms	(* (* (atan2 x.im x.re) (cbrt y.im)) (cbrt y.im))
9.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
8.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
17.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series276.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(* (* (atan2 x.im x.re) (cbrt y.im)) (cbrt y.im))
32.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
134.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify75.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 3 (69.0ms)

Iter	Nodes	Cost
0	257	507
1	790	466
2	3035	457
3	5001	452

prune359.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 23.4b

localize26.0ms

Local error

Found 4 expressions with local error:

33.5b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.2b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
34.2b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
34.2b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 39

Calls

4 calls:

8.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
17.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
17.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
20.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series445.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
142.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
134.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
137.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify157.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 4 (52.0ms)

Iter	Nodes	Cost
0	142	554
1	288	488
2	611	488
3	1523	488
4	4766	486
5	5002	486

prune317.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 23.4b

regimes324.0ms

Accuracy

75.7% (3.3b remaining)

Error of 23.1b against oracle of 19.8b and baseline of 33.3b

bsearch151.0ms

Steps

Iters	Range		Point
11	-7.519470916193732e-280	1.7139560852676268e-307	-5.20017416521053e-309

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	41
1	50	41

end0.0ms

sample3.4s

Algorithm

intervals

Results

1.3s	2193×	body	1280	valid
688.0ms	7947×	body	80	valid
590.0ms	1452×	body	640	valid
156.0ms	555×	body	320	valid
59.0ms	38×	body	2560	valid
49.0ms	257×	body	160	valid