Details

sample335.0ms

Algorithm

intervals

Results

211.0ms	45×	body	640	valid
53.0ms	68×	body	1280	valid
29.0ms	254×	body	80	valid
8.0ms	23×	body	320	valid
2.0ms	10×	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

prune16.0ms

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: 34.6b

Counts

2 → 1

localize32.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (atan2 x.im x.re) y.im)
30.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.3b	(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.im)
3.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
4.0ms	(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)))

series90.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(* (atan2 x.im x.re) y.im)
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
72.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify82.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	206	434
1	539	395
2	1201	392
3	2732	392
4	5002	392

prune138.0ms

Filtered

68 candidates to 54 candidates (20.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	61	7	68
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	62	7	69

Merged error: 21.5b

Counts

69 → 7

localize30.0ms

Local error

Found 4 expressions with local error:

30.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.3b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
34.3b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
34.3b	(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

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)))

series170.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
55.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
55.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
54.0ms	(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

51 → 51

Iterations

Useful iterations: 4 (54.0ms)

Iter	Nodes	Cost
0	152	580
1	321	508
2	672	505
3	1724	505
4	5001	504

prune113.0ms

Filtered

51 candidates to 48 candidates (5.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	51	0	51
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	51	7	58

Merged error: 21.5b

Counts

58 → 7

localize25.0ms

Local error

Found 4 expressions with local error:

4.2b	(log (exp (* (atan2 x.im x.re) y.im)))
30.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.3b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite15.0ms

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)))
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)))

series73.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(log (exp (* (atan2 x.im x.re) y.im)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
55.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify63.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 4 (58.0ms)

Iter	Nodes	Cost
0	174	444
1	380	400
2	818	399
3	2053	399
4	5002	397

prune108.0ms

Filtered

64 candidates to 53 candidates (17.2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	64	0	64
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	64	7	71

Merged error: 21.5b

Counts

71 → 7

localize25.0ms

Local error

Found 4 expressions with local error:

11.9b	(cbrt (pow (sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re))) 3))
30.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.3b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite19.0ms

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)))
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)))

series121.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(cbrt (pow (sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re))) 3))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
55.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify48.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	201	743
1	526	731
2	1327	729
3	5001	729

prune101.0ms

Filtered

71 candidates to 55 candidates (22.5%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	71	0	71
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	71	7	78

Merged error: 21.5b

Counts

78 → 7

regimes426.0ms

Accuracy

79.5% (2.9b remaining)

Error of 23.0b against oracle of 20.1b and baseline of 34.3b

bsearch91.0ms

Steps

Iters	Range		Point
8	-1.1302990408342867e-306	5.5519482282290063e-306	-5.5907332575058e-311

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	35
1	42	35

end0.0ms

sample4.4s

Algorithm

intervals

Results

1.7s	2274×	body	1280	valid
897.0ms	7967×	body	80	valid
747.0ms	1435×	body	640	valid
204.0ms	569×	body	320	valid
66.0ms	40×	body	2560	valid
58.0ms	243×	body	160	valid

Details

sample335.0ms

simplify38.0ms

prune16.0ms

localize32.0ms

rewrite21.0ms

series90.0ms

simplify82.0ms

prune138.0ms

localize30.0ms

rewrite23.0ms

series170.0ms

simplify60.0ms

prune113.0ms

localize25.0ms

rewrite15.0ms

series73.0ms

simplify63.0ms

prune108.0ms

localize25.0ms

rewrite19.0ms

series121.0ms

simplify48.0ms

prune101.0ms

regimes426.0ms

bsearch91.0ms

simplify2.0ms

end0.0ms

sample4.4s

Profiling