Details

sample21.0ms

Algorithm

intervals

Results

8.0ms

268×

body

valid

simplify3.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	7
1	15	7
done	15	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.3b

localize9.0ms

Local error

Found 2 expressions with local error:

0.9b	(+ (* x.re y.re) (* x.im y.im))
22.9b	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 42

Calls

2 calls:

7.0ms	(+ (* x.re y.re) (* x.im y.im))
33.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series116.0ms

Counts

2 → 6

Calls

2 calls:

33.0ms	(+ (* x.re y.re) (* x.im y.im))
83.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify78.0ms

Counts

48 → 48

Iterations

Useful iterations: 2 (21.0ms)

Iter	Nodes	Cost
0	231	450
1	847	413
2	2851	412
3	5003	412
done	5003	412

prune131.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 22.6b

localize12.0ms

Local error

Found 4 expressions with local error:

0.9b	(+ (* x.re y.re) (* x.im y.im))
14.4b	(/ (+ (* 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)))

rewrite60.0ms

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:

8.0ms	(+ (* 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))))
8.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
8.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series254.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(+ (* x.re y.re) (* x.im y.im))
129.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
57.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
36.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify76.0ms

Counts

96 → 96

Iterations

Useful iterations: 2 (21.0ms)

Iter	Nodes	Cost
0	273	893
1	868	840
2	2693	828
3	5001	828
done	5001	828

prune253.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 20.4b

localize14.0ms

Local error

Found 4 expressions with local error:

11.6b	(cbrt (/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im))))
22.9b	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))
22.9b	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))
22.9b	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite107.0ms

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:

9.0ms	(cbrt (/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im))))
32.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))
30.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))
33.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series451.0ms

Counts

4 → 12

Calls

4 calls:

196.0ms	(cbrt (/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im))))
84.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))
84.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))
86.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify139.0ms

Counts

129 → 129

Iterations

Useful iterations: 3 (126.0ms)

Iter	Nodes	Cost
0	353	1546
1	1221	1439
2	4480	1430
3	5002	1425
done	5002	1425

prune409.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 20.4b

localize16.0ms

Local error

Found 4 expressions with local error:

15.0b	(cbrt (+ (* x.re y.re) (* x.im y.im)))
15.0b	(cbrt (+ (* x.re y.re) (* x.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)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `cbrt-prod` `sqrt-prod`
4×	`add-exp-log` `cbrt-div` `flip3-+` `sqrt-div` `add-cbrt-cube` `flip-+` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow1/3`

Counts

4 → 56

Calls

4 calls:

4.0ms	(cbrt (+ (* x.re y.re) (* x.im y.im)))
5.0ms	(cbrt (+ (* x.re y.re) (* x.im y.im)))
10.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
8.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series296.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(cbrt (+ (* x.re y.re) (* x.im y.im)))
115.0ms	(cbrt (+ (* x.re y.re) (* x.im y.im)))
37.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
35.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify121.0ms

Counts

68 → 68

Iterations

Useful iterations: 4 (116.0ms)

Iter	Nodes	Cost
0	254	480
1	655	456
2	1709	444
3	4133	440
4	5001	438
done	5001	438

prune238.0ms

Pruning

10 alts after pruning (6 fresh and 4 done)

Merged error: 20.4b

regimes187.0ms

Accuracy

0% (3.1b remaining)

Error of 26.5b against oracle of 23.3b and baseline of 26.5b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	13
1	17	13
done	17	13

end0.0ms

sample573.0ms

Algorithm

intervals

Results

275.0ms

8487×

body

valid