Details

sample76.0ms

Algorithm

intervals

Results

10.0ms	188×	body	80	valid
7.0ms	25×	body	2560	valid
3.0ms	10×	body	5120	valid
3.0ms	13×	body	1280	valid
2.0ms	13×	body	640	valid
1.0ms	5×	body	320	valid
0.0ms	2×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	8
1	24	8
2	24	8

prune3.0ms

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: 39.8b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
0.0b	(+ (* re re) (* im im))
0.5b	(+ (sqrt (+ (* re re) (* im im))) re)
29.3b	(sqrt (+ (* re re) (* im im)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

8×	`pow1` `add-log-exp`
7×	`*-un-lft-identity`
6×	`add-sqr-sqrt`
5×	`add-cube-cbrt`
4×	`add-exp-log` `flip3-+` `sqrt-div` `sqrt-prod` `add-cbrt-cube` `flip-+`
3×	`sqrt-pow1`
2×	`+-commutative` `pow1/2` `associate-*r/` `sum-log`
1×	`rem-sqrt-square` `pow-prod-down` `distribute-lft-out`

Counts

4 → 51

Calls

4 calls:

7.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
4.0ms	(+ (* re re) (* im im))
6.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
3.0ms	(sqrt (+ (* re re) (* im im)))

series41.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
7.0ms	(+ (* re re) (* im im))
7.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify92.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 3 (86.0ms)

Iter	Nodes	Cost
0	277	428
1	1024	399
2	3458	393
3	5002	391

prune115.0ms

Filtered

52 candidates to 63 candidates (-21.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	57	6	63
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	58	6	64

Merged error: 20.6b

Counts

64 → 6

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
8.3b	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
29.3b	(sqrt (+ (* re re) (* im im)))
29.3b	(sqrt (+ (* re re) (* im im)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

72×	`sqrt-prod`
50×	`add-sqr-sqrt`
34×	`sqrt-pow1`
29×	`pow1`
28×	`sqrt-div`
18×	`add-cube-cbrt` `*-un-lft-identity` `pow1/2`
15×	`swap-sqr`
9×	`flip3-+` `associate-r` `associate-l` `pow-prod-up` `flip-+` `unswap-sqr`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
5×	`pow-prod-down` `pow-sqr`
4×	`frac-times`
2×	`rem-sqrt-square` `associate-r/` `associate-l/`
1×	`+-commutative` `pow2` `pow-plus` `sqrt-unprod` `prod-exp` `sum-log` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 124

Calls

4 calls:

14.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
13.0ms	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
3.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series24.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
7.0ms	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
5.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify47.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	267	1096
1	974	974
2	5001	950

prune134.0ms

Filtered

74 candidates to 136 candidates (-83.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	132	4	136
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	134	8	142

Merged error: 20.6b

Counts

142 → 8

localize18.0ms

Local error

Found 4 expressions with local error:

0.7b	(pow (sqrt (sqrt (sqrt (+ (* re re) (* im im))))) 3)
12.4b	(+ (* (pow (sqrt (sqrt (sqrt (+ (* re re) (* im im))))) 3) (sqrt (sqrt (sqrt (+ (* re re) (* im im)))))) re)
29.3b	(sqrt (+ (* re re) (* im im)))
29.3b	(sqrt (+ (* re re) (* im im)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

42×	`sqrt-prod`
17×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
12×	`unpow-prod-down` `cube-prod`
11×	`sqrt-pow1`
10×	`pow1` `sqrt-div`
7×	`pow-pow`
6×	`add-log-exp`
5×	`add-exp-log` `pow1/2` `add-cbrt-cube`
4×	`flip3-+` `flip-+`
3×	`pow-unpow`
2×	`cube-div` `rem-sqrt-square`
1×	`+-commutative` `cube-mult` `pow-to-exp` `unpow3` `pow-exp` `sum-log` `sqrt-pow2` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 91

Calls

4 calls:

7.0ms	(pow (sqrt (sqrt (sqrt (+ (* re re) (* im im))))) 3)
15.0ms	(+ (* (pow (sqrt (sqrt (sqrt (+ (* re re) (* im im))))) 3) (sqrt (sqrt (sqrt (+ (* re re) (* im im)))))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series50.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(pow (sqrt (sqrt (sqrt (+ (* re re) (* im im))))) 3)
7.0ms	(+ (* (pow (sqrt (sqrt (sqrt (+ (* re re) (* im im))))) 3) (sqrt (sqrt (sqrt (+ (* re re) (* im im)))))) re)
5.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify56.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	438	1011
1	1505	897
2	5001	864

prune152.0ms

Filtered

66 candidates to 103 candidates (-56.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	101	2	103
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	103	8	111

Merged error: 20.6b

Counts

111 → 8

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (pow (sqrt (+ (* re re) (* im im))) 3/4) (sqrt (sqrt (sqrt (+ (* re re) (* im im))))))
5.4b	(+ (* (pow (sqrt (+ (* re re) (* im im))) 3/4) (sqrt (sqrt (sqrt (+ (* re re) (* im im)))))) re)
29.3b	(sqrt (+ (* re re) (* im im)))
29.3b	(sqrt (+ (* re re) (* im im)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

55×	`sqrt-prod`
43×	`add-sqr-sqrt`
16×	`unswap-sqr`
14×	`unpow-prod-down`
13×	`add-cube-cbrt` `*-un-lft-identity`
12×	`associate-r`
10×	`sqrt-div` `associate-l`
9×	`add-exp-log`
7×	`pow1`
6×	`add-cbrt-cube` `add-log-exp`
5×	`sqrt-pow1` `sqr-pow`
4×	`flip3-+` `flip-+`
3×	`pow1/2` `prod-exp`
2×	`rem-sqrt-square` `associate-*r/` `pow-prod-up`
1×	`+-commutative` `pow-to-exp` `pow-exp` `sum-log` `*-commutative` `cbrt-unprod`

Counts

4 → 95

Calls

4 calls:

15.0ms	(* (pow (sqrt (+ (* re re) (* im im))) 3/4) (sqrt (sqrt (sqrt (+ (* re re) (* im im))))))
12.0ms	(+ (* (pow (sqrt (+ (* re re) (* im im))) 3/4) (sqrt (sqrt (sqrt (+ (* re re) (* im im)))))) re)
3.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series24.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(* (pow (sqrt (+ (* re re) (* im im))) 3/4) (sqrt (sqrt (sqrt (+ (* re re) (* im im))))))
7.0ms	(+ (* (pow (sqrt (+ (* re re) (* im im))) 3/4) (sqrt (sqrt (sqrt (+ (* re re) (* im im)))))) re)
5.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify132.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	276	1353
1	876	1309
2	4525	1293
3	5001	1293

prune135.0ms

Filtered

71 candidates to 107 candidates (-50.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	106	1	107
Fresh	0	7	7
Picked	1	0	1
Done	0	0	0
Total	107	8	115

Merged error: 20.6b

Counts

115 → 8

regimes257.0ms

Accuracy

57.3% (9.2b remaining)

Error of 26.9b against oracle of 17.7b and baseline of 39.2b

bsearch33.0ms

Steps

Iters	Range		Point
7	430474635.760152	8049369413.927381	7977722365.3892355
7	-2.250103559887549e-299	-4.137910899764001e-301	-4.222125489978646e-301

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	42
1	48	42

end0.0ms

sample1.0s

Algorithm

intervals

Results

291.0ms	6023×	body	80	valid
202.0ms	723×	body	2560	valid
116.0ms	501×	body	1280	valid
92.0ms	278×	body	5120	valid
46.0ms	252×	body	640	valid
23.0ms	156×	body	320	valid
6.0ms	67×	body	160	valid

Details

sample76.0ms

simplify5.0ms

prune3.0ms

localize10.0ms

rewrite21.0ms

series41.0ms

simplify92.0ms

prune115.0ms

localize12.0ms

rewrite41.0ms

series24.0ms

simplify47.0ms

prune134.0ms

localize18.0ms

rewrite32.0ms

series50.0ms

simplify56.0ms

prune152.0ms

localize22.0ms

rewrite38.0ms

series24.0ms

simplify132.0ms

prune135.0ms

regimes257.0ms

bsearch33.0ms

simplify2.0ms

end0.0ms

sample1.0s

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