Details

sample450.0ms

Algorithm

intervals

Results

47.0ms	78×	body	1280	valid
39.0ms	49×	body	640	valid
23.0ms	247×	body	80	valid
5.0ms	18×	body	320	valid
2.0ms	10×	body	160	valid
2.0ms	1×	body	2560	valid

simplify44.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (5.0ms)

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: 30.2b

localize24.0ms

Local error

Found 4 expressions with local error:

2.9b	(* (atan2 x.im x.re) y.im)
27.3b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
27.3b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.4b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite52.0ms

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)))
27.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series266.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* (atan2 x.im x.re) y.im)
36.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
36.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
173.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify88.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (16.0ms)

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

prune333.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 19.0b

localize30.0ms

Local error

Found 4 expressions with local error:

4.5b	(cbrt (* (atan2 x.im x.re) y.im))
27.3b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
27.3b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.4b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 47

Calls

4 calls:

3.0ms	(cbrt (* (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)))
17.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series295.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(cbrt (* (atan2 x.im x.re) y.im))
40.0ms	(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)))

simplify76.0ms

Algorithm

egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 4 (70.0ms)

Iter	Nodes	Cost
0	195	416
1	381	381
2	797	375
3	1976	373
4	5002	371

prune343.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 19.0b

localize31.0ms

Local error

Found 4 expressions with local error:

27.3b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.4b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
34.4b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
34.4b	(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)))
19.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series495.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
154.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
150.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
154.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify192.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 4 (62.0ms)

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

prune388.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 19.0b

localize41.0ms

Local error

Found 4 expressions with local error:

34.4b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
34.4b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
34.4b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
34.4b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

4×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `sin-sum` `add-cbrt-cube` `add-log-exp`

Counts

4 → 32

Calls

4 calls:

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

series616.0ms

Counts

4 → 12

Calls

4 calls:

153.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
159.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
151.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
153.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify50.0ms

Algorithm

egg-herbie

Counts

44 → 44

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	65	604
1	86	520
2	122	520
3	273	520
4	554	520
5	5001	520

prune340.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 19.0b

regimes341.0ms

Accuracy

77.2% (3.1b remaining)

Error of 22.6b against oracle of 19.5b and baseline of 33.1b

bsearch121.0ms

Steps

Iters	Range		Point
8	-1.3287558847979414e-305	4.527111501653717e-308	-5.41457234362251e-309

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	44
1	45	44

end0.0ms

sample3.4s

Algorithm

intervals

Results

1.3s	2222×	body	1280	valid
671.0ms	7935×	body	80	valid
574.0ms	1430×	body	640	valid
155.0ms	556×	body	320	valid
77.0ms	48×	body	2560	valid
45.0ms	252×	body	160	valid