Details

sample35.0ms

Algorithm

intervals

Results

19.0ms

271×

body

valid

simplify2.0ms

Counts: 1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.7b

localize12.0ms

Local error

Found 2 expressions with local error:

0.4b	(+ (* x.re y.re) (* x.im y.im))
25.2b	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite74.0ms

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:

24.0ms	(+ (* x.re y.re) (* x.im y.im))
48.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series153.0ms

Counts

2 → 6

Calls

2 calls:

46.0ms	(+ (* x.re y.re) (* x.im y.im))
107.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify80.0ms

Counts: 48 → 48

prune166.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 25.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.4b	(+ (* x.re y.re) (* x.im y.im))
14.0b	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
28.6b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
28.6b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite84.0ms

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:

14.0ms	(+ (* x.re y.re) (* x.im y.im))
45.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
11.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
11.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series275.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(+ (* x.re y.re) (* x.im y.im))
144.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
48.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
49.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify64.0ms

Counts: 96 → 96

prune406.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 22.5b

localize34.0ms

Local error

Found 4 expressions with local error:

14.0b	(/ (+ (* 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))))))
28.6b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.5b	(cbrt (+ (* y.re y.re) (* y.im y.im)))
29.5b	(cbrt (+ (* y.re y.re) (* y.im y.im)))

rewrite81.0ms

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:

54.0ms	(/ (+ (* 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))))))
11.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
7.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))
7.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))

series783.0ms

Counts

4 → 12

Calls

4 calls:

478.0ms	(/ (+ (* 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))))))
48.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
128.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))
128.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))

simplify47.0ms

Counts: 78 → 78

prune512.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 22.5b

localize23.0ms

Local error

Found 4 expressions with local error:

14.5b	(cbrt (+ (* x.re y.re) (* x.im y.im)))
14.5b	(cbrt (+ (* x.re y.re) (* x.im y.im)))
14.5b	(cbrt (+ (* x.re y.re) (* x.im y.im)))
14.9b	(/ (* (cbrt (+ (* x.re y.re) (* x.im y.im))) (cbrt (+ (* x.re y.re) (* x.im y.im)))) (/ (+ (* y.re y.re) (* y.im y.im)) (cbrt (+ (* x.re y.re) (* x.im y.im)))))

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

60×	`times-frac`
33×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
27×	`cbrt-prod`
24×	`associate-/r*`
22×	`cbrt-div`
16×	`add-exp-log`
11×	`flip3-+` `flip-+`
10×	`add-cbrt-cube`
8×	`associate-/l/`
6×	`cbrt-undiv` `div-exp`
5×	`associate-/r/`
4×	`pow1` `frac-times` `add-log-exp`
3×	`pow1/3` `div-inv`
2×	`associate-r/` `associate-l/` `prod-exp` `cbrt-unprod`
1×	`frac-2neg` `clear-num` `associate-/l*`

Counts

4 → 115

Calls

4 calls:

5.0ms	(cbrt (+ (* x.re y.re) (* x.im y.im)))
5.0ms	(cbrt (+ (* x.re y.re) (* x.im y.im)))
5.0ms	(cbrt (+ (* x.re y.re) (* x.im y.im)))
69.0ms	(/ (* (cbrt (+ (* x.re y.re) (* x.im y.im))) (cbrt (+ (* x.re y.re) (* x.im y.im)))) (/ (+ (* y.re y.re) (* y.im y.im)) (cbrt (+ (* x.re y.re) (* x.im y.im)))))

series528.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(cbrt (+ (* x.re y.re) (* x.im y.im)))
127.0ms	(cbrt (+ (* x.re y.re) (* x.im y.im)))
164.0ms	(cbrt (+ (* x.re y.re) (* x.im y.im)))
122.0ms	(/ (* (cbrt (+ (* x.re y.re) (* x.im y.im))) (cbrt (+ (* x.re y.re) (* x.im y.im)))) (/ (+ (* y.re y.re) (* y.im y.im)) (cbrt (+ (* x.re y.re) (* x.im y.im)))))

simplify50.0ms

Counts: 127 → 127

prune469.0ms

Pruning

11 alts after pruning (7 fresh and 4 done)

Merged error: 22.5b

regimes307.0ms

Accuracy

-2.1% (3.0b remaining)

Error of 26.2b against oracle of 23.2b and baseline of 26.1b

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.1s

Algorithm

intervals

Results

622.0ms

8495×

body

valid