Details

sample20.0ms

Algorithm

intervals

Results

9.0ms

273×

body

valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	7
1	15	7

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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: 28.5b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.0b	(+ (* x.re y.re) (* x.im y.im))
28.0b	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite19.0ms

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:

6.0ms	(+ (* 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)))

series143.0ms

Counts

3 → 9

Calls

3 calls:

27.0ms	(+ (* y.re y.re) (* y.im y.im))
36.0ms	(+ (* x.re y.re) (* x.im y.im))
79.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify133.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	272	527
1	1164	479
2	4451	477
3	5003	477

prune178.0ms

Filtered

62 candidates to 49 candidates (79.0%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	52	10	62
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	53	10	63

Merged error: 27.8b

Counts

63 → 10

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))) (/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im)))))
14.6b	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
31.4b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
31.4b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

95×	`add-sqr-sqrt`
76×	`times-frac`
53×	`*-un-lft-identity`
47×	`add-cube-cbrt` `sqrt-prod`
28×	`add-exp-log`
24×	`associate-r` `associate-l`
18×	`add-cbrt-cube`
15×	`unswap-sqr`
10×	`sqrt-div`
9×	`div-exp`
8×	`pow1` `prod-exp`
6×	`flip3-+` `associate-/r*` `associate-/r/` `flip-+`
5×	`cbrt-undiv`
4×	`cbrt-unprod` `add-log-exp`
3×	`div-inv` `associate-/l*`
2×	`rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `associate-/l/`
1×	`frac-times` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative`

Counts

4 → 160

Calls

4 calls:

28.0ms	(* (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))) (/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im)))))
9.0ms	(/ (+ (* 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)))

series326.0ms

Counts

4 → 12

Calls

4 calls:

143.0ms	(* (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))) (/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im)))))
107.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
41.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
36.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify78.0ms

Algorithm

egg-herbie

Counts

172 → 172

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	567	2507
1	3303	2242
2	5001	2117

prune415.0ms

Filtered

172 candidates to 113 candidates (65.7%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	167	5	172
Fresh	2	7	9
Picked	0	1	1
Done	0	0	0
Total	169	13	182

Merged error: 26.0b

Counts

182 → 13

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.0b	(+ (* x.re y.re) (* x.im y.im))
0.5b	(/ 1 (/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im))))
27.6b	(/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
56×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
18×	`associate-/r*`
17×	`add-exp-log`
11×	`associate-/r/` `add-cbrt-cube`
8×	`flip3-+` `div-exp` `flip-+` `add-log-exp`
6×	`div-inv` `associate-/l*`
5×	`pow1`
4×	`cbrt-undiv`
2×	`+-commutative` `rec-exp` `frac-2neg` `1-exp` `clear-num` `sum-log` `associate-/l/`
1×	`pow-flip` `inv-pow`

Counts

4 → 137

Calls

4 calls:

5.0ms	(+ (* y.re y.re) (* y.im y.im))
3.0ms	(+ (* x.re y.re) (* x.im y.im))
9.0ms	(/ 1 (/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im))))
8.0ms	(/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im)))

series298.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(+ (* y.re y.re) (* y.im y.im))
29.0ms	(+ (* x.re y.re) (* x.im y.im))
170.0ms	(/ 1 (/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im))))
74.0ms	(/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im)))

simplify69.0ms

Algorithm

egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	518	1821
1	2632	1656
2	5001	1569

prune295.0ms

Filtered

149 candidates to 85 candidates (57.0%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	148	1	149
Fresh	1	10	11
Picked	0	1	1
Done	0	1	1
Total	149	13	162

Merged error: 26.0b

Counts

162 → 13

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x.re y.re) (* x.im y.im))
0.5b	(/ 1 (* (+ (* y.re y.re) (* y.im y.im)) (/ 1 (+ (* x.re y.re) (* x.im y.im)))))
0.7b	(/ 1 (+ (* x.re y.re) (* x.im y.im)))
27.3b	(* (+ (* y.re y.re) (* y.im y.im)) (/ 1 (+ (* x.re y.re) (* x.im y.im))))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 130

Calls

4 calls:

3.0ms	(+ (* x.re y.re) (* x.im y.im))
11.0ms	(/ 1 (* (+ (* y.re y.re) (* y.im y.im)) (/ 1 (+ (* x.re y.re) (* x.im y.im)))))
5.0ms	(/ 1 (+ (* x.re y.re) (* x.im y.im)))
12.0ms	(* (+ (* y.re y.re) (* y.im y.im)) (/ 1 (+ (* x.re y.re) (* x.im y.im))))

series274.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(+ (* x.re y.re) (* x.im y.im))
152.0ms	(/ 1 (* (+ (* y.re y.re) (* y.im y.im)) (/ 1 (+ (* x.re y.re) (* x.im y.im)))))
26.0ms	(/ 1 (+ (* x.re y.re) (* x.im y.im)))
55.0ms	(* (+ (* y.re y.re) (* y.im y.im)) (/ 1 (+ (* x.re y.re) (* x.im y.im))))

simplify83.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 2 (67.0ms)

Iter	Nodes	Cost
0	489	1237
1	2362	1038
2	5002	998

prune207.0ms

Filtered

142 candidates to 79 candidates (55.6%)

Pruning

13 alts after pruning (10 fresh and 3 done)

	Pruned	Kept	Total
New	142	0	142
Fresh	0	10	10
Picked	0	1	1
Done	0	2	2
Total	142	13	155

Merged error: 26.0b

Counts

155 → 13

regimes284.0ms

Accuracy

25.7% (2.3b remaining)

Error of 25.6b against oracle of 23.3b and baseline of 26.4b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	27
1	28	27

end0.0ms

sample545.0ms

Algorithm

intervals

Results

312.0ms

8502×

body

valid

Details

sample20.0ms

simplify4.0ms

prune2.0ms

localize10.0ms

rewrite19.0ms

series143.0ms

simplify133.0ms

prune178.0ms

localize14.0ms

rewrite51.0ms

series326.0ms

simplify78.0ms

prune415.0ms

localize12.0ms

rewrite37.0ms

series298.0ms

simplify69.0ms

prune295.0ms

localize12.0ms

rewrite36.0ms

series274.0ms

simplify83.0ms

prune207.0ms

regimes284.0ms

bsearch2.0ms

simplify2.0ms

end0.0ms

sample545.0ms

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