Details

sample46.0ms

Algorithm

intervals

Results

22.0ms

270×

body

valid

simplify90.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	11	284
1	21	259
2	40	259
3	56	259
4	76	259
5	80	259
done	80	259

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.8b

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.7b	(- (* 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)))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
7×	`add-log-exp`
5×	`add-cbrt-cube` `add-exp-log`
3×	`expm1-log1p-u` `pow1` `associate-/r` `log1p-expm1-u` `associate-/l`
2×	`flip3-+` `flip3--` `associate-/r/` `flip-+` `flip--` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sum-log` `sub-neg` `fma-def` `frac-2neg` `fma-neg` `diff-log` `div-sub` `div-exp` `prod-diff` `div-inv`

Counts

3 → 64

Calls

3 calls:

6.0ms	(+ (* y.re y.re) (* y.im y.im))
19.0ms	(- (* 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)))

series257.0ms

Counts

3 → 9

Calls

3 calls:

50.0ms	(+ (* y.re y.re) (* y.im y.im))
59.0ms	(- (* x.im y.re) (* x.re y.im))
148.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify3.3s

Counts

73 → 73

Iterations

Useful iterations: 3 (2.0s)

Iter	Nodes	Cost
0	111	23523
1	324	19209
2	1241	18934
3	4942	18904
done	5000	18904

prune523.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 26.0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.7b	(- (* x.im y.re) (* x.re y.im))
16.8b	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
31.9b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
31.9b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
21×	`*-un-lft-identity` `add-cube-cbrt`
18×	`times-frac` `sqrt-prod`
6×	`pow1` `associate-/r*` `add-cbrt-cube` `sqrt-div` `add-exp-log` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`flip3-+` `flip-+` `associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3--` `pow1/2` `associate-/r/` `hypot-def` `flip--` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `fma-neg` `diff-log` `div-sub` `div-exp` `prod-diff` `div-inv`

Counts

4 → 98

Calls

4 calls:

10.0ms	(- (* x.im y.re) (* x.re y.im))
21.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
6.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
9.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series340.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(- (* x.im y.re) (* x.re y.im))
173.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
58.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
55.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify81.0ms

Iterations

Useful iterations: 0 (14.0ms)

Iter	Nodes	Cost
0	131	37737