Details

sample32.0ms

Algorithm

intervals

Results

9.0ms	200×	body	80	valid
6.0ms	25×	body	2560	valid
3.0ms	10×	body	5120	valid
2.0ms	9×	body	1280	valid
1.0ms	8×	body	640	valid
0.0ms	2×	body	320	valid
0.0ms	2×	body	160	valid

simplify7.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	8
1	24	8
2	30	8
3	35	8
4	35	8

prune3.0ms

Filtered

1 candidates to 0 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: 40.2b

Counts

2 → 1

localize13.0ms

Local error

Found 2 expressions with local error:

0.4b	(- (sqrt (+ (* re re) (* im im))) re)
33.4b	(sqrt (+ (* re re) (* im im)))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
5×	`*-un-lft-identity`
4×	`sqrt-prod` `add-log-exp`
3×	`pow1` `add-cube-cbrt`
2×	`add-exp-log` `sqrt-div` `add-cbrt-cube` `difference-of-squares`
1×	`sub-neg` `rem-sqrt-square` `flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip--` `flip-+` `distribute-lft-out--`

Counts

2 → 30

Calls

2 calls:

7.0ms	(- (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series84.0ms

Counts

2 → 6

Calls

2 calls:

49.0ms	(- (sqrt (+ (* re re) (* im im))) re)
36.0ms	(sqrt (+ (* re re) (* im im)))

simplify82.0ms

Algorithm

egg-herbie

Counts

36 → 36

Iterations

Useful iterations: 4 (77.0ms)

Iter	Nodes	Cost
0	135	228
1	332	216
2	839	212
3	2503	211
4	5002	210

prune111.0ms

Filtered

36 candidates to 28 candidates (77.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	31	5	36
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	31	6	37

Merged error: 18.9b

Counts

37 → 6

localize14.0ms

Local error

Found 4 expressions with local error:

1.2b	(+ (sqrt (+ (* re re) (* im im))) re)
5.9b	(sqrt (* 2.0 (/ (* im im) (+ (sqrt (+ (* re re) (* im im))) re))))
26.1b	(/ (* im im) (+ (sqrt (+ (* re re) (* im im))) re))
33.4b	(sqrt (+ (* re re) (* im im)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
9×	`add-exp-log` `add-cbrt-cube`
8×	`pow1` `add-sqr-sqrt`
7×	`add-cube-cbrt`
6×	`add-log-exp`
4×	`times-frac` `associate-/r*` `sqrt-prod`
3×	`sqrt-pow1` `flip3-+` `sqrt-div` `flip-+` `distribute-lft-out`
2×	`cbrt-undiv` `pow1/2` `div-exp` `associate-/r/`
1×	`+-commutative` `rem-sqrt-square` `frac-2neg` `associate-r/` `pow-prod-down` `prod-exp` `clear-num` `sum-log` `cbrt-unprod` `div-inv` `associate-/l`

Counts

4 → 64

Calls

4 calls:

7.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
11.0ms	(sqrt (* 2.0 (/ (* im im) (+ (sqrt (+ (* re re) (* im im))) re))))
11.0ms	(/ (* im im) (+ (sqrt (+ (* re re) (* im im))) re))
4.0ms	(sqrt (+ (* re re) (* im im)))

series335.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
188.0ms	(sqrt (* 2.0 (/ (* im im) (+ (sqrt (+ (* re re) (* im im))) re))))
66.0ms	(/ (* im im) (+ (sqrt (+ (* re re) (* im im))) re))
34.0ms	(sqrt (+ (* re re) (* im im)))

simplify41.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	365	616
1	1407	542
2	5001	532

prune205.0ms

Filtered

76 candidates to 61 candidates (80.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	72	4	76
Fresh	2	2	4
Picked	1	0	1
Done	0	1	1
Total	75	7	82

Merged error: 6.4b

Counts

82 → 7

localize17.0ms

Local error

Found 4 expressions with local error:

5.9b	(sqrt (* 2.0 (* (/ im (* (cbrt (+ (sqrt (+ (* re re) (* im im))) re)) (cbrt (+ (sqrt (+ (* re re) (* im im))) re)))) (/ im (cbrt (+ (sqrt (+ (* re re) (* im im))) re))))))
33.4b	(sqrt (+ (* re re) (* im im)))
33.4b	(sqrt (+ (* re re) (* im im)))
33.4b	(sqrt (+ (* re re) (* im im)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

13×	`pow1`
10×	`add-sqr-sqrt` `sqrt-prod`
9×	`sqrt-div`
7×	`add-cube-cbrt` `*-un-lft-identity`
6×	`sqrt-pow1`
4×	`add-exp-log` `pow1/2` `associate-*r/` `add-cbrt-cube` `add-log-exp`
3×	`rem-sqrt-square` `flip3-+` `pow-prod-down` `flip-+`
1×	`frac-times` `associate-*l/`

Counts

4 → 60

Calls

4 calls:

30.0ms	(sqrt (* 2.0 (* (/ im (* (cbrt (+ (sqrt (+ (* re re) (* im im))) re)) (cbrt (+ (sqrt (+ (* re re) (* im im))) re)))) (/ im (cbrt (+ (sqrt (+ (* re re) (* im im))) re))))))
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series297.0ms

Counts

4 → 12

Calls

4 calls:

189.0ms	(sqrt (* 2.0 (* (/ im (* (cbrt (+ (sqrt (+ (* re re) (* im im))) re)) (cbrt (+ (sqrt (+ (* re re) (* im im))) re)))) (/ im (cbrt (+ (sqrt (+ (* re re) (* im im))) re))))))
37.0ms	(sqrt (+ (* re re) (* im im)))
33.0ms	(sqrt (+ (* re re) (* im im)))
38.0ms	(sqrt (+ (* re re) (* im im)))

simplify84.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (76.0ms)

Iter	Nodes	Cost
0	260	665
1	806	624
2	2945	618
3	5001	602

prune277.0ms

Filtered

72 candidates to 60 candidates (83.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	69	3	72
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	71	8	79

Merged error: 6.4b

Counts

79 → 8

localize27.0ms

Local error

Found 4 expressions with local error:

33.4b	(sqrt (+ (* re re) (* im im)))
33.4b	(sqrt (+ (* re re) (* im im)))
33.4b	(sqrt (+ (* re re) (* im im)))
33.4b	(sqrt (+ (* re re) (* im im)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `sqrt-prod`
8×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-div`
4×	`add-exp-log` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `add-cbrt-cube` `flip-+` `add-log-exp`

Counts

4 → 60

Calls

4 calls:

4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series145.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(sqrt (+ (* re re) (* im im)))
39.0ms	(sqrt (+ (* re re) (* im im)))
34.0ms	(sqrt (+ (* re re) (* im im)))
37.0ms	(sqrt (+ (* re re) (* im im)))

simplify142.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 5 (136.0ms)

Iter	Nodes	Cost
0	89	400
1	215	388
2	503	388
3	1265	388
4	4227	388
5	5002	384

prune398.0ms

Filtered

72 candidates to 60 candidates (83.3%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	72	0	72
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	72	8	80

Merged error: 6.4b

Counts

80 → 8

regimes402.0ms

Accuracy

44.4% (17.8b remaining)

Error of 24.5b against oracle of 6.7b and baseline of 38.8b

bsearch155.0ms

Steps

Iters	Range	Point
9	8.653923406070421e-221	4.3735973696411213e-212	1.2274681436980806e-216
8	-4.304488098541857e-166	-5.427563317172151e-169	-4.253813230095163e-166
8	-4.256776728825532e+46	-1.555584016455579e+44	-1.8033863025812665e+46

Iters

Range

Point

8.653923406070421e-221

4.3735973696411213e-212

1.2274681436980806e-216

-4.304488098541857e-166

-5.427563317172151e-169

-4.253813230095163e-166

-4.256776728825532e+46

-1.555584016455579e+44

-1.8033863025812665e+46

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	26
1	62	26
2	63	26
3	63	26

end0.0ms

sample868.0ms

Algorithm

intervals

Results

283.0ms	6051×	body	80	valid
171.0ms	656×	body	2560	valid
109.0ms	485×	body	1280	valid
90.0ms	291×	body	5120	valid
52.0ms	299×	body	640	valid
17.0ms	137×	body	320	valid
7.0ms	81×	body	160	valid

Details

sample32.0ms

simplify7.0ms

prune3.0ms

localize13.0ms

rewrite12.0ms

series84.0ms

simplify82.0ms

prune111.0ms

localize14.0ms

rewrite34.0ms

series335.0ms

simplify41.0ms

prune205.0ms

localize17.0ms

rewrite44.0ms

series297.0ms

simplify84.0ms

prune277.0ms

localize27.0ms

rewrite18.0ms

series145.0ms

simplify142.0ms

prune398.0ms

regimes402.0ms

bsearch155.0ms

simplify2.0ms

end0.0ms

sample868.0ms

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