Details

sample320.0ms

Algorithm

intervals

Results

22.0ms	250×	body	80	valid
10.0ms	134×	body	80	overflowed
5.0ms	7×	body	1280	valid
3.0ms	7×	body	640	valid
1.0ms	2×	body	320	valid

simplify39.0ms

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

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.8b

localize34.0ms

Local error

Found 4 expressions with local error:

1.3b	(* (atan2 x.im x.re) y.re)
30.5b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.5b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.3b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite47.0ms

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

series238.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(* (atan2 x.im x.re) y.re)
32.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.0ms	(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)))

simplify74.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	194	425
1	496	388
2	1117	386
3	2398	386
4	5002	386

prune352.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 17.6b

localize29.0ms

Local error

Found 4 expressions with local error:

30.5b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.6b	(cbrt (+ (* x.re x.re) (* x.im x.im)))
31.6b	(cbrt (+ (* x.re x.re) (* x.im x.im)))
32.3b	(sin (+ (* (log (* (fabs (cbrt (+ (* x.re x.re) (* x.im x.im)))) (sqrt (cbrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 49

Calls

4 calls:

8.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
5.0ms	(cbrt (+ (* x.re x.re) (* x.im x.im)))
7.0ms	(cbrt (+ (* x.re x.re) (* x.im x.im)))
33.0ms	(sin (+ (* (log (* (fabs (cbrt (+ (* x.re x.re) (* x.im x.im)))) (sqrt (cbrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

series480.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
90.0ms	(cbrt (+ (* x.re x.re) (* x.im x.im)))
89.0ms	(cbrt (+ (* x.re x.re) (* x.im x.im)))
264.0ms	(sin (+ (* (log (* (fabs (cbrt (+ (* x.re x.re) (* x.im x.im)))) (sqrt (cbrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

simplify64.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 3 (58.0ms)

Iter	Nodes	Cost
0	226	599
1	690	543
2	2010	539
3	5002	538

prune439.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 17.5b

localize34.0ms

Local error

Found 4 expressions with local error:

30.5b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.6b	(cbrt (+ (* x.re x.re) (* x.im x.im)))
32.5b	(sin (+ (* (log (* (fabs (pow (+ (* x.re x.re) (* x.im x.im)) 1/3)) (sqrt (cbrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))
33.7b	(pow (+ (* x.re x.re) (* x.im x.im)) 1/3)

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1`
5×	`add-exp-log`
4×	`add-cbrt-cube` `add-log-exp`
3×	`cbrt-prod` `unpow-prod-down` `pow-unpow` `sqrt-prod`
2×	`cbrt-div` `flip3-+` `sqrt-div` `flip-+`
1×	`pow-to-exp` `rem-sqrt-square` `pow-pow` `sqrt-pow1` `pow1/2` `unpow1/3` `sin-sum` `pow1/3` `pow-exp` `sqr-pow`

Counts

4 → 54

Calls

4 calls:

8.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
5.0ms	(cbrt (+ (* x.re x.re) (* x.im x.im)))
36.0ms	(sin (+ (* (log (* (fabs (pow (+ (* x.re x.re) (* x.im x.im)) 1/3)) (sqrt (cbrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))
10.0ms	(pow (+ (* x.re x.re) (* x.im x.im)) 1/3)

series481.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
90.0ms	(cbrt (+ (* x.re x.re) (* x.im x.im)))
268.0ms	(sin (+ (* (log (* (fabs (pow (+ (* x.re x.re) (* x.im x.im)) 1/3)) (sqrt (cbrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))
91.0ms	(pow (+ (* x.re x.re) (* x.im x.im)) 1/3)

simplify97.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 2 (22.0ms)

Iter	Nodes	Cost
0	275	590
1	894	515
2	3010	510
3	5001	510

prune467.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 17.5b

localize30.0ms

Local error

Found 4 expressions with local error:

1.2b	(* (atan2 x.im x.re) y.im)
30.5b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.5b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.8b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt 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) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))))

series252.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(* (atan2 x.im x.re) y.im)
34.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
37.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
165.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))))

simplify80.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (15.0ms)

Iter	Nodes	Cost
0	206	485
1	544	438
2	1224	436
3	2606	436
4	5002	436

prune319.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 17.5b

regimes365.0ms

Accuracy

77.6% (3.2b remaining)

Error of 22.0b against oracle of 18.9b and baseline of 33.0b

bsearch101.0ms

Steps

Iters	Range		Point
10	-2.9915123049234395e-302	6.78784030439545e-305	-5.72493342858166e-309

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	36
1	42	36

end0.0ms

sample1.6s

Algorithm

intervals

Results

650.0ms	7955×	body	80	valid
312.0ms	3960×	body	80	overflowed
85.0ms	138×	body	1280	valid
69.0ms	162×	body	640	valid
34.0ms	109×	body	320	valid
12.0ms	65×	body	160	valid