Details

sample447.0ms

Algorithm

intervals

Results

49.0ms	262×	body	80	valid
47.0ms	63×	body	1280	valid
19.0ms	34×	body	640	valid
5.0ms	15×	body	320	valid
5.0ms	2×	body	2560	valid
1.0ms	6×	body	160	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

prune18.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 32.8b

Counts

2 → 1

localize33.0ms

Local error

Found 4 expressions with local error:

2.3b	(* (atan2 x.im x.re) y.im)
29.6b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.6b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.7b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite23.0ms

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)
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)))

series295.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* (atan2 x.im x.re) y.im)
47.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
45.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
183.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify75.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (13.0ms)

Iter	Nodes	Cost
0	196	425
1	506	388
2	1139	386
3	2507	386
4	5002	386

prune449.0ms

Filtered

68 candidates to 54 candidates (20.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	60	8	68
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	61	8	69

Merged error: 19.2b

Counts

69 → 8

localize29.0ms

Local error

Found 4 expressions with local error:

29.6b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.7b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
31.7b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
31.7b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite26.0ms

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

series536.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
163.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
161.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
166.0ms	(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 (51.0ms)

Iter	Nodes	Cost
0	142	553
1	288	487
2	611	487
3	1512	487
4	4748	486
5	5001	486

prune399.0ms

Filtered

51 candidates to 48 candidates (5.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	50	1	51
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	50	9	59

Merged error: 19.2b

Counts

59 → 9

localize24.0ms

Local error

Found 4 expressions with local error:

3.5b	(log (exp (* (atan2 x.im x.re) y.im)))
29.6b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.6b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.7b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 52

Calls

4 calls:

2.0ms	(log (exp (* (atan2 x.im x.re) y.im)))
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
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)))

series273.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(log (exp (* (atan2 x.im x.re) y.im)))
43.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
46.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
164.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify60.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 4 (55.0ms)

Iter	Nodes	Cost
0	164	435
1	347	393
2	757	393
3	1835	393
4	5002	391

prune418.0ms

Filtered

64 candidates to 53 candidates (17.2%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	64	0	64
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	64	9	73

Merged error: 19.2b

Counts

73 → 9

localize28.0ms

Local error

Found 4 expressions with local error:

12.2b	(cbrt (pow (sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re))) 3))
29.6b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.6b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.7b	(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))
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
7.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series414.0ms

Counts

4 → 12

Calls

4 calls:

162.0ms	(cbrt (pow (sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re))) 3))
45.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
43.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
164.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify153.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 4 (145.0ms)

Iter	Nodes	Cost
0	191	725
1	493	717
2	1262	717
3	4720	717
4	5001	647

prune386.0ms

Filtered

71 candidates to 53 candidates (25.4%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	71	0	71
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	71	9	80

Merged error: 19.2b

Counts

80 → 9

regimes495.0ms

Accuracy

76.9% (3.3b remaining)

Error of 22.7b against oracle of 19.4b and baseline of 33.5b

bsearch388.0ms

Steps

Iters	Range	Point
10	-5.561573377002615e-304	3.0877076910478216e-302	-5.55828335649831e-309
4	-4.3940009064737685e-150	-2.250718756727284e-150	-4.1749528611157483e-150
9	-1.2147220719604092e-68	-1.0646474794999867e-75	-1.498168830979673e-74

Iters

Range

Point

-5.561573377002615e-304

3.0877076910478216e-302

-5.55828335649831e-309

-4.3940009064737685e-150

-2.250718756727284e-150

-4.1749528611157483e-150

-1.2147220719604092e-68

-1.0646474794999867e-75

-1.498168830979673e-74

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	76
1	56	76

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.6s	2216×	body	1280	valid
880.0ms	7985×	body	80	valid
705.0ms	1396×	body	640	valid
185.0ms	524×	body	320	valid
80.0ms	47×	body	2560	valid
53.0ms	230×	body	160	valid

Details

sample447.0ms

simplify39.0ms

prune18.0ms

localize33.0ms

rewrite23.0ms

series295.0ms

simplify75.0ms

prune449.0ms

localize29.0ms

rewrite26.0ms

series536.0ms

simplify159.0ms

prune399.0ms

localize24.0ms

rewrite16.0ms

series273.0ms

simplify60.0ms

prune418.0ms

localize28.0ms

rewrite20.0ms

series414.0ms

simplify153.0ms

prune386.0ms

regimes495.0ms

bsearch388.0ms

simplify2.0ms

end0.0ms

sample4.2s

Profiling