Details

sample26.0ms

Algorithm

intervals

Results

12.0ms

269×

body

valid

simplify3.0ms

Counts: 1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.8b

localize12.0ms

Local error

Found 2 expressions with local error:

0.7b	(- (* x.im y.re) (* x.re y.im))
24.4b	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite46.0ms

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×	`associate-/r` `associate-/l`
2×	`pow1` `flip3--` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-sub` `div-exp` `clear-num` `flip-+` `div-inv`

Counts

2 → 44

Calls

2 calls:

8.0ms	(- (* x.im y.re) (* x.re y.im))
37.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series145.0ms

Counts

2 → 6

Calls

2 calls:

43.0ms	(- (* x.im y.re) (* x.re y.im))
102.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify77.0ms

Counts: 50 → 50

prune157.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 24.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.7b	(- (* x.im y.re) (* x.re y.im))
16.1b	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
30.1b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
30.1b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite64.0ms

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`
3×	`flip3-+` `flip-+` `associate-/l*`
2×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

4 → 86

Calls

4 calls:

10.0ms	(- (* x.im y.re) (* x.re y.im))
33.0ms	(/ (- (* x.im y.re) (* x.re 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)))

series353.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(- (* x.im y.re) (* x.re y.im))
182.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
62.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
57.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify93.0ms

Counts: 98 → 98

prune406.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 22.1b

localize23.0ms

Local error

Found 4 expressions with local error:

0.7b	(- (* x.im y.re) (* x.re y.im))
16.1b	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
30.1b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
30.1b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite81.0ms

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`
3×	`flip3-+` `flip-+` `associate-/l*`
2×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

4 → 86

Calls

4 calls:

13.0ms	(- (* x.im y.re) (* x.re y.im))
42.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
14.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
8.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series326.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(- (* x.im y.re) (* x.re y.im))
170.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
54.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
55.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify73.0ms

Counts: 98 → 98

prune352.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 22.1b

localize18.0ms

Local error

Found 3 expressions with local error:

0.4b	(/ 1 (/ (+ (* y.re y.re) (* y.im y.im)) (- (* x.im y.re) (* x.re y.im))))
0.7b	(- (* x.im y.re) (* x.re y.im))
24.1b	(/ (+ (* y.re y.re) (* y.im y.im)) (- (* x.im y.re) (* x.re y.im)))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
55×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
18×	`associate-/r*`
16×	`add-exp-log`
11×	`associate-/r/`
10×	`add-cbrt-cube`
8×	`div-exp`
6×	`flip3--` `flip--` `div-inv` `associate-/l*`
5×	`add-log-exp`
4×	`pow1` `cbrt-undiv`
2×	`rec-exp` `frac-2neg` `1-exp` `clear-num` `associate-/l/`
1×	`sub-neg` `pow-flip` `flip3-+` `diff-log` `flip-+` `inv-pow`

Counts

3 → 127

Calls

3 calls:

36.0ms	(/ 1 (/ (+ (* y.re y.re) (* y.im y.im)) (- (* x.im y.re) (* x.re y.im))))
8.0ms	(- (* x.im y.re) (* x.re y.im))
33.0ms	(/ (+ (* y.re y.re) (* y.im y.im)) (- (* x.im y.re) (* x.re y.im)))

series378.0ms

Counts

3 → 9

Calls

3 calls:

224.0ms	(/ 1 (/ (+ (* y.re y.re) (* y.im y.im)) (- (* x.im y.re) (* x.re y.im))))
58.0ms	(- (* x.im y.re) (* x.re y.im))
95.0ms	(/ (+ (* y.re y.re) (* y.im y.im)) (- (* x.im y.re) (* x.re y.im)))

simplify60.0ms

Counts: 136 → 136

prune368.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 22.1b

regimes204.0ms

Accuracy

24.6% (2.5b remaining)

Error of 25.3b against oracle of 22.8b and baseline of 26.1b

bsearch2.0ms

simplify4.0ms

end0.0ms

sample1.2s

Algorithm

intervals

Results

720.0ms

8494×

body

valid