Details

sample31.0ms

Algorithm

intervals

Results

12.0ms

278×

body

valid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	7
1	15	7

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: 28.3b

Counts

2 → 1

localize10.0ms

Local error

Found 2 expressions with local error:

1.2b	(+ (* x.re y.re) (* x.im y.im))
27.7b	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `associate-/r` `flip-+` `associate-/l`
2×	`pow1` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

2 → 42

Calls

2 calls:

3.0ms	(+ (* x.re y.re) (* x.im y.im))
7.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series37.0ms

Counts

2 → 6

Calls

2 calls:

12.0ms	(+ (* x.re y.re) (* x.im y.im))
25.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify81.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 2 (21.0ms)

Iter	Nodes	Cost
0	231	450
1	847	413
2	2837	412
3	5001	412

prune87.0ms

Filtered

38 candidates to 48 candidates (-26.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	42	6	48
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	42	7	49

Merged error: 27.5b

Counts

49 → 7

localize13.0ms

Local error

Found 4 expressions with local error:

1.2b	(+ (* x.re y.re) (* x.im y.im))
18.2b	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
31.0b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
31.0b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
21×	`add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac` `sqrt-prod`
6×	`pow1` `add-exp-log` `sqrt-div` `associate-/r*` `add-cbrt-cube` `add-log-exp`
5×	`flip3-+` `flip-+`
3×	`associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 84

Calls

4 calls:

3.0ms	(+ (* x.re y.re) (* x.im y.im))
10.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
3.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
3.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series52.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(+ (* x.re y.re) (* x.im y.im))
32.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
5.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
6.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify79.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (22.0ms)

Iter	Nodes	Cost
0	273	893
1	868	840
2	2679	828
3	5002	828

prune116.0ms

Filtered

74 candidates to 96 candidates (-29.7%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	91	5	96
Fresh	2	3	5
Picked	0	1	1
Done	0	1	1
Total	93	10	103

Merged error: 25.5b

Counts

103 → 10

localize17.0ms

Local error

Found 4 expressions with local error:

10.0b	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im)))))
31.0b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
31.0b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
31.0b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

45×	`sqrt-prod`
32×	`add-sqr-sqrt`
29×	`add-cube-cbrt` `*-un-lft-identity`
27×	`times-frac`
10×	`sqrt-div`
9×	`associate-/r*`
7×	`pow1`
6×	`add-exp-log` `add-cbrt-cube`
5×	`flip3-+` `flip-+`
4×	`add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/l*`
2×	`associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

4 → 100

Calls

4 calls:

10.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im)))))
3.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
3.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
3.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series91.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im)))))
5.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
5.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
6.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify85.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (23.0ms)

Iter	Nodes	Cost
0	330	1249
1	963	1178
2	2901	1143
3	5003	1143

prune124.0ms

Filtered

82 candidates to 112 candidates (-36.6%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	112	0	112
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	112	10	122

Merged error: 25.5b

Counts

122 → 10

localize14.0ms

Local error

Found 4 expressions with local error:

9.0b	(cbrt (/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im))))
27.7b	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))
27.7b	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))
27.7b	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

36×	`times-frac`
35×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
15×	`cbrt-prod`
10×	`add-exp-log` `add-cbrt-cube`
9×	`associate-/r` `associate-/l`
8×	`associate-/r/`
7×	`flip3-+` `flip-+`
6×	`associate-/l/`
4×	`pow1` `div-inv` `add-log-exp`
3×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num`
1×	`cbrt-div` `pow1/3`

Counts

4 → 117

Calls

4 calls:

5.0ms	(cbrt (/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im))))
8.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))
8.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))
8.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series138.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(cbrt (/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im))))
24.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))
24.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))
26.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify142.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	363	1556
1	1275	1448
2	4920	1437
3	5002	1437

prune131.0ms

Filtered

106 candidates to 129 candidates (-21.7%)

Pruning

10 alts after pruning (6 fresh and 4 done)

	Pruned	Kept	Total
New	129	0	129
Fresh	0	6	6
Picked	0	1	1
Done	0	3	3
Total	129	10	139

Merged error: 25.5b

Counts

139 → 10

regimes469.0ms

Accuracy

20.4% (2.3b remaining)

Error of 25.3b against oracle of 23.0b and baseline of 25.9b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	26
1	28	26
2	28	26

end0.0ms

sample689.0ms

Algorithm

intervals

Results

383.0ms

8471×

body

valid

Details

sample31.0ms

simplify3.0ms

prune3.0ms

localize10.0ms

rewrite12.0ms

series37.0ms

simplify81.0ms

prune87.0ms

localize13.0ms

rewrite22.0ms

series52.0ms

simplify79.0ms

prune116.0ms

localize17.0ms

rewrite23.0ms

series91.0ms

simplify85.0ms

prune124.0ms

localize14.0ms

rewrite32.0ms

series138.0ms

simplify142.0ms

prune131.0ms

regimes469.0ms

bsearch2.0ms

simplify2.0ms

end0.0ms

sample689.0ms

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