Details

sample24.0ms

Algorithm

intervals

Results

11.0ms

266×

body

valid

simplify5.0ms

Counts: 1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.9b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.4b	(- (* x.im y.re) (* x.re y.im))
26.4b	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite53.0ms

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

Counts

3 → 55

Calls

3 calls:

8.0ms	(+ (* y.re y.re) (* y.im y.im))
8.0ms	(- (* x.im y.re) (* x.re y.im))
35.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series426.0ms

Counts

3 → 9

Calls

3 calls:

33.0ms	(+ (* y.re y.re) (* y.im y.im))
41.0ms	(- (* x.im y.re) (* x.re y.im))
352.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify38.0ms

Counts: 64 → 64

prune189.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 26.1b

localize14.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (* x.im y.re) (* x.re y.im))
16.3b	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
29.7b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.7b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite59.0ms

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:

8.0ms	(- (* 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)))

series241.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(- (* x.im y.re) (* x.re y.im))
121.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
39.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
37.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify100.0ms

Counts: 98 → 98

prune302.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 24.6b

localize18.0ms

Local error

Found 4 expressions with local error:

16.3b	(/ (- (* x.im y.re) (* x.re y.im)) (* (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im))))))
29.7b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.7b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.7b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

30×	`sqrt-div`
12×	`add-sqr-sqrt`
9×	`add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `flip3-+` `sqrt-prod` `add-cbrt-cube` `flip-+`
8×	`associate-/r/`
7×	`pow1`
4×	`frac-times` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `times-frac` `pow1/2` `associate-/l*`
2×	`cbrt-undiv` `associate-r/` `div-exp` `associate-l/` `associate-/l/`
1×	`flip3--` `frac-2neg` `div-sub` `prod-exp` `clear-num` `associate-/r*` `flip--` `cbrt-unprod` `div-inv`

Counts

4 → 77

Calls

4 calls:

51.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (* (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (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)))
9.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series244.0ms

Counts

4 → 12

Calls

4 calls:

125.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (* (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im))))))
38.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
38.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
43.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify76.0ms

Counts: 89 → 89

prune329.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 23.8b

localize19.0ms

Local error

Found 4 expressions with local error:

3.2b	(/ x.re (/ (sqrt (+ (* y.re y.re) (* y.im y.im))) y.im))
29.7b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.7b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.7b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
85×	`add-sqr-sqrt`
82×	`add-cube-cbrt` `*-un-lft-identity`
45×	`sqrt-prod`
22×	`associate-/r*`
9×	`add-exp-log` `add-cbrt-cube`
7×	`pow1`
6×	`sqrt-div`
5×	`div-inv`
4×	`add-log-exp`
3×	`cbrt-undiv` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `div-exp` `flip-+` `associate-/l*`
1×	`frac-2neg` `clear-num` `associate-/r/`

Counts

4 → 151

Calls

4 calls:

17.0ms	(/ x.re (/ (sqrt (+ (* y.re y.re) (* y.im y.im))) y.im))
8.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
16.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
8.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series184.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(/ x.re (/ (sqrt (+ (* y.re y.re) (* y.im y.im))) y.im))
38.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
38.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
44.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify54.0ms

Counts: 163 → 163

prune483.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 23.8b

regimes142.0ms

Accuracy

0% (0.4b remaining)

Error of 22.5b against oracle of 22.2b and baseline of 22.5b

bsearch0.0ms

simplify1.0ms

end0.0ms

sample890.0ms

Algorithm

intervals

Results

551.0ms

8476×

body

valid