Details

analyze507.0ms

Algorithm: search

sample23.0ms

Algorithm

intervals

Results

11.0ms	256×	body	80	valid
1.0ms	13×	body	80	invalid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	7
1	15	7

prune4.0ms

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: 24.9b

Counts

2 → 1

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.4b	(+ (* x.re y.re) (* x.im y.im))
24.4b	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 53

Calls

3 calls:

3.0ms	(+ (* y.re y.re) (* y.im y.im))
3.0ms	(+ (* x.re y.re) (* x.im y.im))
8.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series39.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(+ (* y.re y.re) (* y.im y.im))
9.0ms	(+ (* 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)))

simplify130.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	272	527
1	1164	479
2	4437	477
3	5002	477

prune101.0ms

Filtered

49 candidates to 62 candidates (-26.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	57	5	62
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	57	6	63

Merged error: 24.2b

Counts

63 → 6

localize11.0ms

Local error

Found 4 expressions with local error:

0.4b	(+ (* x.re y.re) (* x.im y.im))
15.0b	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
28.3b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
28.3b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite20.0ms

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))
8.0ms	(/ (+ (* 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)))

series54.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(+ (* x.re y.re) (* x.im y.im))
34.0ms	(/ (+ (* 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)))

simplify78.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (21.0ms)

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

prune120.0ms

Filtered

74 candidates to 96 candidates (-29.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	92	4	96
Fresh	1	3	4
Picked	0	1	1
Done	1	0	1
Total	94	8	102

Merged error: 21.9b

Counts

102 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

0.4b	(+ (* x.re y.re) (* x.im y.im))
15.1b	(/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (+ (* x.re y.re) (* x.im y.im)))
28.3b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
28.3b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite20.0ms

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` `add-cbrt-cube` `associate-/l*` `add-log-exp`
5×	`flip3-+` `flip-+`
3×	`associate-/r*`
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))
8.0ms	(/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (+ (* x.re y.re) (* x.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)))

series44.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(+ (* x.re y.re) (* x.im y.im))
24.0ms	(/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (+ (* x.re y.re) (* x.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)))

simplify69.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (20.0ms)

Iter	Nodes	Cost
0	263	883
1	831	838
2	2287	833
3	5001	833

prune115.0ms

Filtered

74 candidates to 96 candidates (-29.7%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	96	0	96
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	96	8	104

Merged error: 21.9b

Counts

104 → 8

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.4b	(+ (* x.re y.re) (* x.im y.im))
0.6b	(/ 1 (+ (* y.re y.re) (* y.im y.im)))
24.0b	(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (+ (* y.re y.re) (* y.im y.im))))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
20×	`add-cube-cbrt` `times-frac`
17×	`add-exp-log`
15×	`associate-r`
11×	`add-cbrt-cube`
8×	`add-log-exp`
7×	`pow1`
6×	`flip3-+` `flip-+`
4×	`div-exp` `prod-exp` `associate-/r/`
3×	`associate-l` `associate-/r` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `+-commutative` `frac-times` `rec-exp` `1-exp` `associate-*l/` `sum-log` `cbrt-unprod` `div-inv`
1×	`pow-flip` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `un-div-inv` `-commutative` `inv-pow`

Counts

4 → 97

Calls

4 calls:

3.0ms	(+ (* y.re y.re) (* y.im y.im))
3.0ms	(+ (* x.re y.re) (* x.im y.im))
5.0ms	(/ 1 (+ (* y.re y.re) (* y.im y.im)))
11.0ms	(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (+ (* y.re y.re) (* y.im y.im))))

series46.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(+ (* y.re y.re) (* y.im y.im))
9.0ms	(+ (* x.re y.re) (* x.im y.im))
6.0ms	(/ 1 (+ (* y.re y.re) (* y.im y.im)))
25.0ms	(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (+ (* y.re y.re) (* y.im y.im))))

simplify51.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	393	851
1	2037	747
2	5003	718

prune91.0ms

Filtered

69 candidates to 109 candidates (-58.0%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	109	0	109
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	109	8	117

Merged error: 21.9b

Counts

117 → 8

regimes323.0ms

Accuracy

0% (3.0b remaining)

Error of 26.1b against oracle of 23.1b and baseline of 26.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	13
1	17	13

end0.0ms

analyze695.0ms

Algorithm: search

sample619.0ms

Algorithm

intervals

Results

361.0ms	8000×	body	80	valid
22.0ms	491×	body	80	invalid

Details

analyze507.0ms

sample23.0ms

simplify3.0ms

prune4.0ms

localize13.0ms

rewrite15.0ms

series39.0ms

simplify130.0ms

prune101.0ms

localize11.0ms

rewrite20.0ms

series54.0ms

simplify78.0ms

prune120.0ms

localize13.0ms

rewrite20.0ms

series44.0ms

simplify69.0ms

prune115.0ms

localize10.0ms

rewrite25.0ms

series46.0ms

simplify51.0ms

prune91.0ms

regimes323.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

analyze695.0ms

sample619.0ms

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