Details

sample346.0ms

Algorithm

intervals

Results

34.0ms	54×	body	1280	valid
22.0ms	259×	body	80	valid
16.0ms	32×	body	640	valid
6.0ms	23×	body	320	valid
0.0ms	2×	body	160	valid

simplify38.0ms

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

prune27.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 34.6b

localize24.0ms

Local error

Found 4 expressions with local error:

1.3b	(* (atan2 x.im x.re) y.re)
31.9b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.9b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.8b	(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

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

series248.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(* (atan2 x.im x.re) y.re)
37.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
159.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify71.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (13.0ms)

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

prune334.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 18.8b

localize26.0ms

Local error

Found 4 expressions with local error:

31.9b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.8b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
32.8b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
32.8b	(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)))

series463.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
144.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
140.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
144.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify159.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 4 (52.0ms)

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

prune354.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 18.8b

localize22.0ms

Local error

Found 4 expressions with local error:

1.3b	(* (atan2 x.im x.re) y.re)
31.9b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.9b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.8b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite21.0ms

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.re)
7.0ms	(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)))

series231.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(* (atan2 x.im x.re) y.re)
36.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
40.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
140.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify71.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (13.0ms)

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

prune327.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 18.8b

localize24.0ms

Local error

Found 4 expressions with local error:

10.2b	(cbrt (pow (sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re))) 3))
31.9b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.9b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.8b	(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×	`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))
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)))

series358.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(cbrt (pow (sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re))) 3))
39.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
146.0ms	(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

prune334.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 18.8b

regimes373.0ms

Accuracy

76.8% (3.2b remaining)

Error of 22.8b against oracle of 19.6b and baseline of 33.5b

bsearch72.0ms

Steps

Iters	Range		Point
5	-1.0680487192983464e-308	2.5344995100410685e-308	-5.614403745474914e-309

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	35
1	39	35

end0.0ms

sample3.2s

Algorithm

intervals

Results

1.4s	2171×	body	1280	valid
677.0ms	7967×	body	80	valid
558.0ms	1359×	body	640	valid
156.0ms	559×	body	320	valid
78.0ms	48×	body	2560	valid
41.0ms	230×	body	160	valid