Details

sample24.0ms

Algorithm

intervals

Results

12.0ms

270×

body

valid

simplify89.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	284
1	19	284
2	36	284
3	48	284
4	66	284
5	70	284
done	70	284

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.8b

localize30.0ms

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)))

rewrite40.0ms

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

Counts

3 → 55

Calls

3 calls:

11.0ms	(+ (* y.re y.re) (* y.im y.im))
6.0ms	(- (* x.im y.re) (* x.re y.im))
20.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series270.0ms

Counts

3 → 9

Calls

3 calls:

49.0ms	(+ (* y.re y.re) (* y.im y.im))
53.0ms	(- (* x.im y.re) (* x.re y.im))
168.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify3.6s

Counts

64 → 64

Iterations

Useful iterations: 3 (1.7s)

Iter	Nodes	Cost
0	101	21625
1	304	19486
2	1132	19286
3	4560	19206
done	5066	19206

prune492.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 26.0b

localize52.0ms

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)))

rewrite65.0ms

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

Counts

4 → 86

Calls

4 calls:

6.0ms	(- (* x.im y.re) (* x.re y.im))
32.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
12.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
12.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series298.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(- (* x.im y.re) (* x.re y.im))
156.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
40.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
51.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify96.0ms

Iterations

Useful iterations: 0 (16.0ms)

Iter	Nodes	Cost
0	121	35195