Details

sample385.0ms

Algorithm

intervals

Results

53.0ms	70×	body	1280	valid
26.0ms	67×	body	640	valid
24.0ms	250×	body	80	valid
8.0ms	30×	body	320	valid
3.0ms	14×	body	160	valid

simplify40.0ms

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

prune17.0ms

Filtered

1 candidates to 1 candidates (100.0%)

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: 33.0b

Counts

2 → 2

localize26.0ms

Local error

Found 4 expressions with local error:

1.6b	(* (atan2 x.im x.re) y.im)
29.1b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.1b	(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)))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

32×	`*-un-lft-identity`
16×	`sqrt-prod`
12×	`add-sqr-sqrt`
11×	`associate-l`
10×	`distribute-lft-out`
8×	`pow1` `add-cube-cbrt`
6×	`add-exp-log` `add-cbrt-cube`
4×	`sqrt-div` `swap-sqr` `add-log-exp`
3×	`associate-r`
2×	`rem-sqrt-square` `cos-sum` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
1×	`+-commutative` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 67

Calls

4 calls:

3.0ms	(* (atan2 x.im x.re) y.im)
17.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
24.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
20.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series237.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(* (atan2 x.im x.re) y.im)
34.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
38.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
148.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify84.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	194	482
1	504	443
2	1156	443
3	2942	443
4	5003	443

prune324.0ms

Filtered

79 candidates to 54 candidates (68.4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	75	4	79
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	76	5	81

Merged error: 20.0b

Counts

81 → 5

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* (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)
1.6b	(* (atan2 x.im x.re) y.im)
29.1b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

31×	`*-un-lft-identity`
26×	`add-sqr-sqrt`
20×	`associate-l`
13×	`pow1`
9×	`add-cube-cbrt`
8×	`add-exp-log` `sqrt-prod` `add-cbrt-cube`
6×	`associate-r` `distribute-lft-out--` `add-log-exp` `unswap-sqr`
5×	`log-pow` `distribute-lft-out`
4×	`difference-of-squares`
2×	`sqrt-pow1` `pow1/2` `sqrt-div` `swap-sqr` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod`
1×	`sub-neg` `rem-sqrt-square` `flip3--` `flip3-+` `diff-log` `flip--` `flip-+`

Counts

4 → 81

Calls

4 calls:

17.0ms	(- (* (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)
4.0ms	(* (atan2 x.im x.re) y.im)
20.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series259.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
87.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
16.0ms	(* (atan2 x.im x.re) y.im)
34.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify82.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (26.0ms)

Iter	Nodes	Cost
0	311	709
1	922	669
2	2714	661
3	5001	661

prune293.0ms

Filtered

93 candidates to 60 candidates (64.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	91	2	93
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	91	7	98

Merged error: 4.7b

Counts

98 → 7

localize26.0ms

Local error

Found 4 expressions with local error:

6.0b	(cbrt (atan2 x.im x.re))
29.1b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.1b	(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)))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

31×	`*-un-lft-identity`
16×	`sqrt-prod`
10×	`distribute-lft-out`
9×	`add-sqr-sqrt`
8×	`associate-l`
7×	`add-cube-cbrt`
6×	`pow1`
4×	`add-exp-log` `sqrt-div` `swap-sqr` `add-cbrt-cube` `add-log-exp`
3×	`cbrt-prod`
2×	`rem-sqrt-square` `cos-sum` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
1×	`+-commutative` `pow1/3`

Counts

4 → 60

Calls

4 calls:

1.0ms	(cbrt (atan2 x.im x.re))
17.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
16.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
20.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series242.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(cbrt (atan2 x.im x.re))
37.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
132.0ms	(cos (+ (* (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

72 → 72

Iterations

Useful iterations: 2 (11.0ms)

Iter	Nodes	Cost
0	158	460
1	340	428
2	773	425
3	2490	425
4	5002	425

prune325.0ms

Filtered

72 candidates to 51 candidates (70.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	69	3	72
Fresh	2	3	5
Picked	1	0	1
Done	0	1	1
Total	72	7	79

Merged error: 4.7b

Counts

79 → 7

localize32.0ms

Local error

Found 4 expressions with local error:

6.0b	(cbrt (atan2 x.im x.re))
29.1b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.1b	(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)))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

31×	`*-un-lft-identity`
16×	`sqrt-prod`
10×	`distribute-lft-out`
9×	`add-sqr-sqrt`
8×	`associate-l`
7×	`add-cube-cbrt`
6×	`pow1`
4×	`add-exp-log` `sqrt-div` `swap-sqr` `add-cbrt-cube` `add-log-exp`
3×	`cbrt-prod`
2×	`rem-sqrt-square` `cos-sum` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
1×	`+-commutative` `pow1/3`

Counts

4 → 60

Calls

4 calls:

1.0ms	(cbrt (atan2 x.im x.re))
21.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
16.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
18.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series242.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(cbrt (atan2 x.im x.re))
38.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
36.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
130.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify76.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 2 (11.0ms)

Iter	Nodes	Cost
0	158	460
1	340	428
2	773	425
3	2490	425
4	5002	425

prune343.0ms

Filtered

72 candidates to 51 candidates (70.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	70	2	72
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	72	7	79

Merged error: 4.7b

Counts

79 → 7

regimes246.0ms

Accuracy

71.7% (4.7b remaining)

Error of 8.3b against oracle of 3.7b and baseline of 20.1b

bsearch326.0ms

Steps

Iters	Range		Point
8	3.159809033014604e-05	0.08433677106829839	0.05615461888199686
10	4.4072838724023594e-163	3.5040898023099104e-150	1.8308924480226544e-158
9	-8.737757419100074e-307	3.830079511393951e-305	3.60424188099793e-310

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	53	34
1	65	34
2	65	34

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.2s	1998×	body	1280	valid
680.0ms	7972×	body	80	valid
563.0ms	1416×	body	640	valid
178.0ms	655×	body	320	valid
52.0ms	293×	body	160	valid