Details

sample19.0ms

Algorithm

intervals

Results

9.0ms

264×

body

valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	15
1	15	15
done	15	15

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.0b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.6b	(+ (* x.re y.re) (* x.im y.im))
26.5b	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite18.0ms

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))
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:

30.0ms	(+ (* y.re y.re) (* y.im y.im))
30.0ms	(+ (* x.re y.re) (* x.im y.im))
80.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify1.4s

Counts

62 → 62

Iterations

Useful iterations: 2 (91.0ms)

Iter	Nodes	Cost
0	99	1090
1	270	1067
2	932	951
3	3230	951
done	5001	951

prune181.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 26.2b

localize15.0ms

Local error

Found 4 expressions with local error:

0.6b	(+ (* x.re y.re) (* x.im y.im))
17.5b	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
29.0b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.0b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite24.0ms

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:

2.0ms	(+ (* x.re y.re) (* x.im y.im))
12.0ms	(/ (+ (* 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)))
4.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series207.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(+ (* x.re y.re) (* x.im y.im))
104.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
39.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
35.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify1.1s

Counts

96 → 96

Iterations

Useful iterations: 3 (347.0ms)

Iter	Nodes	Cost
0	117	1780
1	274	1649
2	751	1541
3	2033	1525
done	5001	1525

prune275.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 23.4b

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b	(+ (* x.re y.re) (* x.im y.im))
17.5b	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
29.0b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.0b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite27.0ms

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

series204.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(+ (* x.re y.re) (* x.im y.im))
103.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
38.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
34.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify1.1s

Counts

96 → 96

Iterations

Useful iterations: 3 (358.0ms)

Iter	Nodes	Cost
0	117	1780
1	274	1649
2	751	1541
3	2033	1525
done	5001	1525

prune310.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 23.4b

localize33.0ms

Local error

Found 4 expressions with local error:

17.5b	(/ (+ (* x.re y.re) (* x.im y.im)) (* (fabs (cbrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (cbrt (+ (* y.re y.re) (* y.im y.im))))))
29.0b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.9b	(cbrt (+ (* y.re y.re) (* y.im y.im)))
29.9b	(cbrt (+ (* y.re y.re) (* y.im y.im)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
6×	`cbrt-prod` `cbrt-div`
5×	`pow1` `flip3-+` `flip-+`
4×	`sqrt-div` `add-log-exp`
3×	`times-frac` `sqrt-prod` `associate-/l*`
2×	`cbrt-undiv` `pow1/3` `associate-*r/` `div-exp` `associate-/r/` `associate-/l/`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 66

Calls

4 calls:

15.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (* (fabs (cbrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (cbrt (+ (* y.re y.re) (* y.im y.im))))))
6.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
4.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))
8.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))

series544.0ms

Counts

4 → 12

Calls

4 calls:

326.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (* (fabs (cbrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (cbrt (+ (* y.re y.re) (* y.im y.im))))))
34.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
92.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))
92.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))

simplify1.6s

Counts

78 → 78

Iterations

Useful iterations: 3 (716.0ms)

Iter	Nodes	Cost
0	158	1722
1	398	1625
2	1272	1387
3	4668	1381
done	5000	1381

prune363.0ms

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 23.4b

regimes265.0ms

Accuracy

0.1% (3.0b remaining)

Error of 26.3b against oracle of 23.3b and baseline of 26.3b

bsearch36.0ms

Steps

Iters	Range		Point
8	1.5974682383539887e+61	1.4744290377191018e+65	1.4473657936297032e+65

simplify5.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	29
1	20	29
done	20	29

end0.0ms

sample701.0ms

Algorithm

intervals

Results

487.0ms

8511×

body

valid