Details

sample22.0ms

Algorithm

intervals

Results

11.0ms

269×

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: 25.2b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.2b	(+ (* x.re y.re) (* x.im y.im))
24.6b	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite20.0ms

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

series139.0ms

Counts

3 → 9

Calls

3 calls:

27.0ms	(+ (* y.re y.re) (* y.im y.im))
34.0ms	(+ (* x.re y.re) (* x.im y.im))
78.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify134.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 2 (30.0ms)

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

prune168.0ms

Filtered

62 candidates to 49 candidates (79.0%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	54	8	62
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	54	9	63

Merged error: 24.3b

Counts

63 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(+ (* x.re y.re) (* x.im y.im))
16.5b	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
26.3b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
26.3b	(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:

4.0ms	(+ (* 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)))

series222.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(+ (* x.re y.re) (* x.im y.im))
112.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
35.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
39.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify87.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (25.0ms)

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

prune256.0ms

Filtered

96 candidates to 74 candidates (77.1%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	93	3	96
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	94	11	105

Merged error: 22.0b

Counts

105 → 11

localize13.0ms

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)))))
16.5b	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
26.3b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
26.3b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite52.0ms

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:

26.0ms	(* (/ 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)))

series328.0ms

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)))))
111.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
36.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
37.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify82.0ms

Algorithm

egg-herbie

Counts

172 → 172

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	567	2505
1	3282	2242
2	5001	2117

prune375.0ms

Filtered

172 candidates to 111 candidates (64.5%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	172	0	172
Fresh	0	8	8
Picked	0	1	1
Done	0	2	2
Total	172	11	183

Merged error: 22.0b

Counts

183 → 11

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.2b	(+ (* x.re y.re) (* x.im y.im))
0.7b	(/ 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))))

rewrite31.0ms

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:

4.0ms	(+ (* 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)))
12.0ms	(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (+ (* y.re y.re) (* y.im y.im))))

series178.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(+ (* y.re y.re) (* y.im y.im))
31.0ms	(+ (* x.re y.re) (* x.im y.im))
42.0ms	(/ 1 (+ (* y.re y.re) (* y.im y.im)))
78.0ms	(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (+ (* y.re y.re) (* y.im y.im))))

simplify63.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 2 (48.0ms)

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

prune177.0ms

Filtered

109 candidates to 65 candidates (59.6%)

Pruning

11 alts after pruning (7 fresh and 4 done)

	Pruned	Kept	Total
New	109	0	109
Fresh	0	7	7
Picked	0	1	1
Done	0	3	3
Total	109	11	120

Merged error: 22.0b

Counts

120 → 11

regimes221.0ms

Accuracy

29.7% (2.1b remaining)

Error of 25.3b against oracle of 23.3b and baseline of 26.2b

bsearch2.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	25
1	22	25

end0.0ms

sample559.0ms

Algorithm

intervals

Results

353.0ms

8470×

body

valid

Details

sample22.0ms

simplify4.0ms

prune2.0ms

localize10.0ms

rewrite20.0ms

series139.0ms

simplify134.0ms

prune168.0ms

localize12.0ms

rewrite22.0ms

series222.0ms

simplify87.0ms

prune256.0ms

localize13.0ms

rewrite52.0ms

series328.0ms

simplify82.0ms

prune375.0ms

localize11.0ms

rewrite31.0ms

series178.0ms

simplify63.0ms

prune177.0ms

regimes221.0ms

bsearch2.0ms

simplify1.0ms

end0.0ms

sample559.0ms

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