Details

sample28.0ms

Algorithm

intervals

Results

11.0ms

266×

body

valid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	15	15
1	15	15

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: 25.6b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.7b	(+ (* x.re y.re) (* x.im y.im))
25.1b	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite17.0ms

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:

4.0ms	(+ (* y.re y.re) (* y.im y.im))
4.0ms	(+ (* x.re y.re) (* x.im y.im))
9.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series45.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(+ (* y.re y.re) (* y.im y.im))
10.0ms	(+ (* x.re y.re) (* x.im y.im))
30.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify29.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5430	951

prune118.0ms

Filtered

48 candidates to 62 candidates (-29.2%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	51	11	62
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	51	12	63

Merged error: 24.8b

Counts

63 → 12

localize12.0ms

Local error

Found 4 expressions with local error:

0.7b	(+ (* x.re y.re) (* x.im y.im))
16.1b	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
29.1b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.1b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite23.0ms

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

series56.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(+ (* x.re y.re) (* x.im y.im))
35.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
6.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
6.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify40.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5070	1525

prune131.0ms

Filtered

76 candidates to 96 candidates (-26.3%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	90	6	96
Fresh	6	4	10
Picked	0	1	1
Done	0	1	1
Total	96	12	108

Merged error: 22.0b

Counts

108 → 12

localize13.0ms

Local error

Found 4 expressions with local error:

0.7b	(+ (* y.re x.re) (* y.im x.im))
16.1b	(/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (+ (* y.re x.re) (* y.im x.im)))
29.1b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.1b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite23.0ms

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:

5.0ms	(+ (* y.re x.re) (* y.im x.im))
8.0ms	(/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (+ (* y.re x.re) (* y.im x.im)))
3.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
3.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series43.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(+ (* y.re x.re) (* y.im x.im))
23.0ms	(/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (+ (* y.re x.re) (* y.im x.im)))
6.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
6.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify47.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5015	1540

prune118.0ms

Filtered

73 candidates to 96 candidates (-31.5%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	96	0	96
Fresh	0	9	9
Picked	0	1	1
Done	0	2	2
Total	96	12	108

Merged error: 22.0b

Counts

108 → 12

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.5b	(/ 1 (+ (* y.re y.re) (* y.im y.im)))
0.7b	(+ (* x.re y.re) (* x.im y.im))
24.8b	(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (+ (* y.re y.re) (* y.im y.im))))

rewrite28.0ms

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))
7.0ms	(/ 1 (+ (* y.re y.re) (* y.im y.im)))
3.0ms	(+ (* x.re y.re) (* x.im y.im))
11.0ms	(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (+ (* y.re y.re) (* y.im y.im))))

series45.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify48.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5477	1453

prune88.0ms

Filtered

70 candidates to 109 candidates (-55.7%)

Pruning

12 alts after pruning (8 fresh and 4 done)

	Pruned	Kept	Total
New	109	0	109
Fresh	0	8	8
Picked	0	1	1
Done	0	3	3
Total	109	12	121

Merged error: 22.0b

Counts

121 → 12

regimes480.0ms

Accuracy

23.2% (2.2b remaining)

Error of 25.6b against oracle of 23.5b and baseline of 26.3b

bsearch2.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	53
1	22	53

end0.0ms

sample737.0ms

Algorithm

intervals

Results

367.0ms

8495×

body

valid

Details

sample28.0ms

simplify3.0ms

prune4.0ms

localize10.0ms

rewrite17.0ms

series45.0ms

simplify29.0ms

prune118.0ms

localize12.0ms

rewrite23.0ms

series56.0ms

simplify40.0ms

prune131.0ms

localize13.0ms

rewrite23.0ms

series43.0ms

simplify47.0ms

prune118.0ms

localize10.0ms

rewrite28.0ms

series45.0ms

simplify48.0ms

prune88.0ms

regimes480.0ms

bsearch2.0ms

simplify1.0ms

end0.0ms

sample737.0ms

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