Details

analyze513.0ms

Algorithm: search

sample24.0ms

Algorithm

intervals

Results

13.0ms	256×	body	80	valid
0.0ms	4×	body	80	invalid

simplify4.0ms

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: 27.3b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.3b	(+ (* x.re y.re) (* x.im y.im))
26.8b	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite16.0ms

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)))

series42.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(+ (* y.re y.re) (* y.im y.im))
11.0ms	(+ (* x.re y.re) (* x.im y.im))
26.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify135.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 2 (28.0ms)

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

prune103.0ms

Filtered

49 candidates to 62 candidates (-26.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	55	7	62
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	56	7	63

Merged error: 26.6b

Counts

63 → 7

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(+ (* x.re y.re) (* x.im y.im))
15.4b	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
30.0b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
30.0b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite21.0ms

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))
9.0ms	(/ (+ (* 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)))

series55.0ms

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))))
6.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
6.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify84.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (24.0ms)

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

prune119.0ms

Filtered

74 candidates to 96 candidates (-29.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	91	5	96
Fresh	3	3	6
Picked	0	1	1
Done	0	0	0
Total	94	9	103

Merged error: 24.1b

Counts

103 → 9

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.3b	(+ (* x.re y.re) (* x.im y.im))
0.8b	(/ 1 (+ (* y.re y.re) (* y.im y.im)))
26.3b	(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (+ (* y.re y.re) (* y.im y.im))))

rewrite26.0ms

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))))

series47.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(+ (* y.re y.re) (* y.im y.im))
10.0ms	(+ (* x.re y.re) (* x.im y.im))
6.0ms	(/ 1 (+ (* y.re y.re) (* y.im y.im)))
27.0ms	(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (+ (* y.re y.re) (* y.im y.im))))

simplify56.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 2 (45.0ms)

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

prune110.0ms

Filtered

69 candidates to 109 candidates (-58.0%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	109	0	109
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	109	9	118

Merged error: 24.1b

Counts

118 → 9

localize17.0ms

Local error

Found 4 expressions with local error:

9.7b	(cbrt (/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im))))
26.8b	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))
26.8b	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))
26.8b	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite34.0ms

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:

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

series151.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(cbrt (/ (+ (* 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)))
29.0ms	(/ (+ (* 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)))

simplify148.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 2 (32.0ms)

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

prune134.0ms

Filtered

106 candidates to 129 candidates (-21.7%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	129	0	129
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	129	9	138

Merged error: 24.1b

Counts

138 → 9

regimes416.0ms

Accuracy

0% (3.0b remaining)

Error of 25.8b against oracle of 22.9b and baseline of 25.8b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	13
1	17	13

end0.0ms

analyze511.0ms

Algorithm: search

sample613.0ms

Algorithm

intervals

Results

375.0ms	8000×	body	80	valid
21.0ms	471×	body	80	invalid

Details

analyze513.0ms

sample24.0ms

simplify4.0ms

prune3.0ms

localize10.0ms

rewrite16.0ms

series42.0ms

simplify135.0ms

prune103.0ms

localize14.0ms

rewrite21.0ms

series55.0ms

simplify84.0ms

prune119.0ms

localize11.0ms

rewrite26.0ms

series47.0ms

simplify56.0ms

prune110.0ms

localize17.0ms

rewrite34.0ms

series151.0ms

simplify148.0ms

prune134.0ms

regimes416.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

analyze511.0ms

sample613.0ms

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