Details

sample415.0ms

Algorithm

intervals

Results

70.0ms	88×	body	1280	valid
41.0ms	251×	body	80	valid
25.0ms	48×	body	640	valid
6.0ms	3×	body	2560	valid
6.0ms	15×	body	320	valid
1.0ms	5×	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

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 35.6b

localize25.0ms

Local error

Found 4 expressions with local error:

2.3b	(* (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)))
34.1b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite27.0ms

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)
9.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
8.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series262.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(* (atan2 x.im x.re) y.im)
38.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
41.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
166.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify76.0ms

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

prune355.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 18.7b

localize30.0ms

Local error

Found 4 expressions with local error:

31.6b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.1b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
34.1b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
34.1b	(sin (+ (* (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

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:

4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
6.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
6.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series496.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
152.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
156.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
146.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify164.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 4 (53.0ms)

Iter	Nodes	Cost
0	142	553
1	288	487
2	611	487
3	1523	487
4	4766	486
5	5002	486

prune384.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 18.7b

localize23.0ms

Local error

Found 4 expressions with local error:

2.3b	(* (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)))
34.1b	(sin (+ (* (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×	`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)
3.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
3.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series250.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(* (atan2 x.im x.re) y.im)
43.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
37.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
153.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify76.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (14.0ms)

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

prune358.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 18.6b

localize30.0ms

Local error

Found 4 expressions with local error:

12.6b	(cbrt (pow (sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re))) 3))
31.6b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.6b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.1b	(sin (+ (* (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×	`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))
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
3.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series383.0ms

Counts

4 → 12

Calls

4 calls:

155.0ms	(cbrt (pow (sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re))) 3))
36.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
36.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
155.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify145.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 4 (137.0ms)

Iter	Nodes	Cost
0	191	729
1	493	719
2	1274	719
3	4723	719
4	5001	649

prune338.0ms

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 18.6b

regimes448.0ms

Accuracy

78.2% (3.1b remaining)

Error of 22.4b against oracle of 19.3b and baseline of 33.6b

bsearch190.0ms

Steps

Iters	Range		Point
10	-9.53539283584192e-295	2.2826757702542398e-303	-6.2360011819834e-309

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	36
1	42	36

end0.0ms

sample4.3s

Algorithm

intervals

Results

1.6s	2171×	body	1280	valid
1.2s	7955×	body	80	valid
725.0ms	1427×	body	640	valid
205.0ms	552×	body	320	valid
69.0ms	42×	body	2560	valid
60.0ms	224×	body	160	valid