Details

sample26.0ms

Algorithm

intervals

Results

12.0ms

273×

body

valid

simplify15.0ms

Counts: 1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.8b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.5b	(+ (* x.re y.re) (* x.im y.im))
23.4b	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite75.0ms

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:

12.0ms	(+ (* y.re y.re) (* y.im y.im))
12.0ms	(+ (* 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)))

series194.0ms

Counts

3 → 9

Calls

3 calls:

40.0ms	(+ (* y.re y.re) (* y.im y.im))
47.0ms	(+ (* 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)))

simplify1.6s

Counts: 62 → 62

prune225.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 23.1b

localize27.0ms

Local error

Found 4 expressions with local error:

0.5b	(+ (* x.re y.re) (* x.im y.im))
15.5b	(/ (+ (* 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)))

rewrite93.0ms

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:

13.0ms	(+ (* x.re y.re) (* x.im y.im))
60.0ms	(/ (+ (* 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)))
9.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series294.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(+ (* x.re y.re) (* x.im y.im))
151.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
47.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
51.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify1.4s

Counts: 96 → 96

prune353.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 21.3b

localize31.0ms

Local error

Found 4 expressions with local error:

0.5b	(+ (* x.re y.re) (* x.im y.im))
15.5b	(/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (+ (* x.re y.re) (* x.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)))

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` `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:

12.0ms	(+ (* x.re y.re) (* x.im y.im))
30.0ms	(/ (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)))
15.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series231.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(+ (* x.re y.re) (* x.im y.im))
104.0ms	(/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (+ (* x.re y.re) (* x.im y.im)))
47.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
45.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify1.1s

Counts: 96 → 96

prune465.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 21.3b

localize30.0ms

Local error

Found 4 expressions with local error:

0.5b	(+ (* x.re y.re) (* x.im y.im))
15.5b	(/ (+ (* 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)))

rewrite65.0ms

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:

11.0ms	(+ (* x.re y.re) (* x.im y.im))
35.0ms	(/ (+ (* 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)))
9.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series304.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(+ (* x.re y.re) (* x.im y.im))
147.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
56.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
44.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify1.4s

Counts: 96 → 96

prune375.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 21.3b

regimes243.0ms

Accuracy

-0.6% (3.1b remaining)

Error of 26.0b against oracle of 22.8b and baseline of 26.0b

bsearch0.0ms

simplify821.0ms

end0.0ms

sample1.6s

Algorithm

intervals

Results

1.1s

8467×

body

valid