Details

sample25.0ms

Algorithm

intervals

Results

11.0ms

270×

body

valid

simplify2.0ms

Counts: 1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.2b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
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)))

rewrite58.0ms

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:

8.0ms	(+ (* y.re y.re) (* y.im y.im))
8.0ms	(+ (* x.re y.re) (* x.im y.im))
41.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series433.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(+ (* y.re y.re) (* y.im y.im))
35.0ms	(+ (* x.re y.re) (* x.im y.im))
361.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify141.0ms

Counts: 62 → 62

prune184.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 22.6b

localize15.0ms

Local error

Found 4 expressions with local error:

0.9b	(+ (* x.re y.re) (* x.im y.im))
12.5b	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
29.9b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.9b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite68.0ms

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))
41.0ms	(/ (+ (* 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)))

series240.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(+ (* x.re y.re) (* x.im y.im))
122.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
40.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
43.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify89.0ms

Counts: 96 → 96

prune284.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 21.6b

localize17.0ms

Local error

Found 4 expressions with local error:

0.9b	(+ (* x.re y.re) (* x.im y.im))
12.6b	(/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (+ (* x.re y.re) (* x.im y.im)))
29.9b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.9b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite53.0ms

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` `add-cbrt-cube` `associate-/l*` `add-log-exp`
5×	`flip3-+` `flip-+`
3×	`associate-/r*`
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:

13.0ms	(+ (* x.re y.re) (* x.im y.im))
22.0ms	(/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (+ (* x.re y.re) (* x.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)))

series204.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(+ (* x.re y.re) (* x.im y.im))
90.0ms	(/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (+ (* x.re y.re) (* x.im y.im)))
37.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
38.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify75.0ms

Counts: 96 → 96

prune295.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 21.6b

localize23.0ms

Local error

Found 4 expressions with local error:

12.6b	(/ (* (fabs (cbrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (cbrt (+ (* y.re y.re) (* y.im y.im))))) (+ (* x.re y.re) (* x.im y.im)))
29.9b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
30.9b	(cbrt (+ (* y.re y.re) (* y.im y.im)))
30.9b	(cbrt (+ (* y.re y.re) (* y.im y.im)))

rewrite50.0ms

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` `associate-/r*` `sqrt-prod`
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` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

4 → 66

Calls

4 calls:

24.0ms	(/ (* (fabs (cbrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (cbrt (+ (* y.re y.re) (* y.im y.im))))) (+ (* x.re y.re) (* x.im y.im)))
15.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
5.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))
5.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))

series479.0ms

Counts

4 → 12

Calls

4 calls:

241.0ms	(/ (* (fabs (cbrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (cbrt (+ (* y.re y.re) (* y.im y.im))))) (+ (* x.re y.re) (* x.im y.im)))
41.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
97.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))
98.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))

simplify39.0ms

Counts: 78 → 78

prune345.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 21.6b

regimes227.0ms

Accuracy

0% (2.7b remaining)

Error of 25.9b against oracle of 23.2b and baseline of 25.9b

bsearch0.0ms

simplify1.0ms

end0.0ms

sample828.0ms

Algorithm

intervals

Results

503.0ms

8498×

body

valid