Details

sample388.0ms

Algorithm

intervals

Results

53.0ms	79×	body	1280	valid
21.0ms	245×	body	80	valid
17.0ms	42×	body	640	valid
8.0ms	27×	body	320	valid
4.0ms	2×	body	2560	valid
2.0ms	9×	body	160	valid

simplify40.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	31	21
1	53	20
2	84	20
3	203	20
4	879	20
5	5001	20

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.7b

localize26.0ms

Local error

Found 4 expressions with local error:

2.4b	(* (atan2 x.im x.re) y.im)
27.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
27.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.0b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite20.0ms

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)))
8.0ms	(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:

20.0ms	(* (atan2 x.im x.re) y.im)
34.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
160.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify77.0ms

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

prune336.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 20.2b

localize27.0ms

Local error

Found 4 expressions with local error:

27.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
27.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
27.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.0b	(sin (+ (* (log (* (sqrt (sqrt (+ (* x.re x.re) (* x.im x.im)))) (sqrt (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite38.0ms

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-+`
1×	`sin-sum`

Counts

4 → 53

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)))
3.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
27.0ms	(sin (+ (* (log (* (sqrt (sqrt (+ (* x.re x.re) (* x.im x.im)))) (sqrt (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:

35.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
38.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
143.0ms	(sin (+ (* (log (* (sqrt (sqrt (+ (* x.re x.re) (* x.im x.im)))) (sqrt (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

simplify67.0ms

Algorithm

egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 4 (60.0ms)

Iter	Nodes	Cost
0	146	535
1	313	491
2	719	491
3	1920	491
4	5002	488

prune387.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 20.1b

localize33.0ms

Local error

Found 4 expressions with local error:

27.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.0b	(sin (+ (* (log (* (sqrt (sqrt (+ (* x.re x.re) (* x.im x.im)))) (sqrt (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))
35.0b	(sin (+ (* (log (* (sqrt (sqrt (+ (* x.re x.re) (* x.im x.im)))) (sqrt (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))
35.0b	(sin (+ (* (log (* (sqrt (sqrt (+ (* x.re x.re) (* x.im x.im)))) (sqrt (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite83.0ms

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)))
25.0ms	(sin (+ (* (log (* (sqrt (sqrt (+ (* x.re x.re) (* x.im x.im)))) (sqrt (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))
28.0ms	(sin (+ (* (log (* (sqrt (sqrt (+ (* x.re x.re) (* x.im x.im)))) (sqrt (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))
26.0ms	(sin (+ (* (log (* (sqrt (sqrt (+ (* x.re x.re) (* x.im x.im)))) (sqrt (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

series457.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
141.0ms	(sin (+ (* (log (* (sqrt (sqrt (+ (* x.re x.re) (* x.im x.im)))) (sqrt (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))
138.0ms	(sin (+ (* (log (* (sqrt (sqrt (+ (* x.re x.re) (* x.im x.im)))) (sqrt (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))
144.0ms	(sin (+ (* (log (* (sqrt (sqrt (+ (* x.re x.re) (* x.im x.im)))) (sqrt (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

simplify66.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 4 (59.0ms)

Iter	Nodes	Cost
0	146	805
1	313	697
2	719	697
3	1920	697
4	5002	696

prune419.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 20.0b

localize31.0ms

Local error

Found 4 expressions with local error:

27.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
27.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
27.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.0b	(sin (+ (* (log (* (sqrt (sqrt (+ (* x.re x.re) (* x.im x.im)))) (sqrt (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite39.0ms

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-+`
1×	`sin-sum`

Counts

4 → 53

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)))
3.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
27.0ms	(sin (+ (* (log (* (sqrt (sqrt (+ (* x.re x.re) (* x.im x.im)))) (sqrt (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

series247.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
37.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
139.0ms	(sin (+ (* (log (* (sqrt (sqrt (+ (* x.re x.re) (* x.im x.im)))) (sqrt (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

simplify66.0ms

Algorithm

egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 4 (59.0ms)

Iter	Nodes	Cost
0	146	538
1	313	494
2	719	494
3	1920	494
4	5002	488

prune391.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 20.0b

regimes382.0ms

Accuracy

75.6% (3.6b remaining)

Error of 22.9b against oracle of 19.3b and baseline of 34.0b

bsearch260.0ms

Steps

Iters	Range		Point
8	4.315441191209963e-248	4.400136552617363e-245	5.083230997006564e-248
9	-2.26016353878232e-246	-1.0506129615557526e-252	-3.4715063518587293e-252

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	59	103
1	59	103

end0.0ms

sample3.4s

Algorithm

intervals

Results

1.4s	2259×	body	1280	valid
688.0ms	7925×	body	80	valid
588.0ms	1380×	body	640	valid
164.0ms	588×	body	320	valid
82.0ms	52×	body	2560	valid
43.0ms	232×	body	160	valid