Details

analyze1.5s

Algorithm: search

sample133.0ms

Algorithm

intervals

Results

49.0ms	61×	body	1280	invalid
27.0ms	243×	body	80	valid
17.0ms	34×	body	640	invalid
6.0ms	16×	body	320	invalid
5.0ms	6×	body	1280	valid
3.0ms	10×	body	160	invalid
2.0ms	18×	body	80	invalid
2.0ms	4×	body	640	valid
0.0ms	2×	body	160	valid
0.0ms	1×	body	320	valid

simplify404.0ms

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

prune20.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Merged error: 33.2b

Counts

2 → 2

localize42.0ms

Local error

Found 4 expressions with local error:

1.9b	(* (atan2 x.im x.re) y.im)
29.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.6b	(cos (+ (* (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×	`cos-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)))
8.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series85.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(* (atan2 x.im x.re) y.im)
10.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
63.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify79.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	199	426
1	523	389
2	1179	387
3	2665	387
4	5002	387

prune122.0ms

Filtered

54 candidates to 68 candidates (-25.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	64	4	68
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	65	5	70

Merged error: 18.5b

Counts

70 → 5

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
0.3b	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
1.9b	(* (atan2 x.im x.re) y.im)
29.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
11×	`pow1`
10×	`add-cube-cbrt` `*-un-lft-identity`
9×	`associate-l`
8×	`add-exp-log` `add-cbrt-cube`
7×	`add-log-exp`
6×	`associate-r`
3×	`exp-prod` `sqrt-prod` `log-pow`
2×	`sqrt-pow1` `pow1/2` `sqrt-div` `exp-sum` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `rem-exp-log` `unswap-sqr`
1×	`sub-neg` `rem-sqrt-square` `flip3-+` `exp-diff` `diff-log` `flip-+`

Counts

4 → 69

Calls

4 calls:

4.0ms	(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
5.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
3.0ms	(* (atan2 x.im x.re) y.im)
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series76.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
23.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
7.0ms	(* (atan2 x.im x.re) y.im)
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify57.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 3 (51.0ms)

Iter	Nodes	Cost
0	299	556
1	864	496
2	2274	481
3	5002	479

prune136.0ms

Filtered

60 candidates to 81 candidates (-35.0%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	76	5	81
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	78	8	86

Merged error: 3.2b

Counts

86 → 8

localize11.0ms

Local error

Found 1 expressions with local error:

1.9b	(* (atan2 x.im x.re) y.im)

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt`
3×	`pow1` `add-exp-log` `add-cube-cbrt` `-un-lft-identity` `associate-r` `associate-l*` `add-cbrt-cube`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `add-log-exp` `unswap-sqr`

Counts

1 → 18

Calls

1 calls:

3.0ms

(* (atan2 x.im x.re) y.im)

series7.0ms

Counts

1 → 3

Calls

1 calls:

7.0ms

(* (atan2 x.im x.re) y.im)

simplify58.0ms

Algorithm

egg-herbie

Counts

21 → 21

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	61	74
1	220	64
2	517	64
3	797	64
4	1893	64
5	5001	64

prune56.0ms

Filtered

13 candidates to 21 candidates (-61.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	21	0	21
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	21	8	29

Merged error: 3.2b

Counts

29 → 8

localize29.0ms

Local error

Found 4 expressions with local error:

29.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.6b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
30.6b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
30.6b	(cos (+ (* (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×	`cos-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	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
7.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
8.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series164.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
51.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
55.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
52.0ms	(cos (+ (* (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 (53.0ms)

Iter	Nodes	Cost
0	145	556
1	305	490
2	651	490
3	1674	490
4	5002	489

prune86.0ms

Filtered

48 candidates to 51 candidates (-6.3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	49	2	51
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	50	9	59

Merged error: 3.2b

Counts

59 → 9

regimes505.0ms

Accuracy

76.2% (6.6b remaining)

Error of 10.1b against oracle of 3.5b and baseline of 31.0b

bsearch1.4s

Steps

Iters	Range		Point
9	-3.9890087616420344e-304	2.6773387154964622e-306	1.1372450740628e-310

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	14
1	33	14
2	33	14

end0.0ms

analyze1.3s

Algorithm: search

sample3.7s

Algorithm

intervals

Results

1.3s	1847×	body	1280	invalid
848.0ms	7565×	body	80	valid
624.0ms	1282×	body	640	invalid
178.0ms	523×	body	320	invalid
89.0ms	180×	body	640	valid
88.0ms	117×	body	1280	valid
49.0ms	214×	body	160	invalid
46.0ms	402×	body	80	invalid
27.0ms	79×	body	320	valid
16.0ms	59×	body	160	valid

Details

analyze1.5s

sample133.0ms

simplify404.0ms

prune20.0ms

localize42.0ms

rewrite21.0ms

series85.0ms

simplify79.0ms

prune122.0ms

localize17.0ms

rewrite18.0ms

series76.0ms

simplify57.0ms

prune136.0ms

localize11.0ms

rewrite4.0ms

series7.0ms

simplify58.0ms

prune56.0ms

localize29.0ms

rewrite26.0ms

series164.0ms

simplify60.0ms

prune86.0ms

regimes505.0ms

bsearch1.4s

simplify4.0ms

end0.0ms

analyze1.3s

sample3.7s

Profiling