Details

sample37.0ms

Algorithm

intervals

Results

23.0ms

270×

body

valid

simplify17.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	11	15
1	17	13
2	21	13
done	21	13

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.1b

localize25.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.7b	(+ (* x.re y.re) (* x.im y.im))
24.7b	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite78.0ms

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` `expm1-log1p-u` `associate-/r` `log1p-expm1-u` `associate-/l`
2×	`+-commutative` `fma-def` `sum-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

3 → 61

Calls

3 calls:

8.0ms	(+ (* y.re y.re) (* y.im y.im))
14.0ms	(+ (* x.re y.re) (* x.im y.im))
54.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series194.0ms

Counts

3 → 9

Calls

3 calls:

32.0ms	(+ (* y.re y.re) (* y.im y.im))
42.0ms	(+ (* x.re y.re) (* x.im y.im))
120.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify2.2s

Counts

70 → 70

Iterations

Useful iterations: 2 (276.0ms)

Iter	Nodes	Cost
0	105	1154
1	288	969
2	955	867
3	2981	867
done	5001	867

prune355.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 15.0b

localize12.0ms

Local error

Found 3 expressions with local error:

0.3b	(* (/ 1 (hypot y.re y.im)) (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)))
0.5b	(fma x.re y.re (* x.im y.im))
14.7b	(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

42×	`add-sqr-sqrt`
34×	`times-frac`
27×	`add-exp-log` `*-un-lft-identity`
25×	`add-cube-cbrt`
17×	`add-cbrt-cube`
13×	`associate-r` `associate-l`
9×	`div-exp`
8×	`prod-exp`
6×	`unswap-sqr`
5×	`pow1` `cbrt-undiv`
4×	`cbrt-unprod`
3×	`expm1-log1p-u` `associate-/r` `log1p-expm1-u` `div-inv` `associate-/l` `add-log-exp`
2×	`rec-exp` `1-exp`
1×	`frac-times` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative` `fma-udef`

Counts

3 → 97

Calls

3 calls:

35.0ms	(* (/ 1 (hypot y.re y.im)) (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)))
0.0ms	(fma x.re y.re (* x.im y.im))
5.0ms	(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

series456.0ms

Counts

3 → 9

Calls

3 calls:

236.0ms	(* (/ 1 (hypot y.re y.im)) (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)))
69.0ms	(fma x.re y.re (* x.im y.im))
151.0ms	(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

simplify4.6s

Counts

106 → 106

Iterations

Useful iterations: done (4.6s)

Iter	Nodes	Cost
0	140	1895
1	328	1763
2	1068	1527
3	3979	1527
done	5000	1494

prune424.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.1b

localize16.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)) (hypot y.re y.im))
0.5b	(fma x.re y.re (* x.im y.im))
14.7b	(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
53×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
16×	`associate-/l*`
10×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r*` `div-inv`
4×	`cbrt-undiv` `div-exp`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`frac-2neg` `clear-num`
1×	`fma-udef` `associate-/l/`

Counts

3 → 111

Calls

3 calls:

24.0ms	(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)) (hypot y.re y.im))
0.0ms	(fma x.re y.re (* x.im y.im))
5.0ms	(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

series435.0ms

Counts

3 → 9

Calls

3 calls:

203.0ms	(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)) (hypot y.re y.im))
46.0ms	(fma x.re y.re (* x.im y.im))
187.0ms	(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

simplify2.3s

Counts

120 → 120

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	161	2484
1	322	2423
2	703	2246
3	2030	2192
done	5000	2130

prune588.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im))))
0.3b	(* (/ 1 (hypot y.re y.im)) (/ 1 (/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im)))))
0.5b	(fma x.re y.re (* x.im y.im))
14.8b	(/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im)))

rewrite106.0ms

Algorithm

rewrite-expression-head

Rules

187×	`times-frac`
143×	`add-sqr-sqrt`
107×	`*-un-lft-identity`
100×	`add-exp-log`
96×	`add-cube-cbrt`
50×	`div-exp`
44×	`associate-r`
32×	`add-cbrt-cube`
28×	`prod-exp`
17×	`rec-exp` `1-exp`
16×	`associate-/r*`
15×	`unswap-sqr`
13×	`cbrt-undiv` `associate-l`
11×	`div-inv`
9×	`pow1`
6×	`cbrt-unprod` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-flip` `pow-prod-down` `inv-pow`
2×	`frac-2neg` `clear-num` `associate-/r/`
1×	`frac-times` `associate-r/` `associate-l/` `un-div-inv` `*-commutative` `fma-udef`

Counts

4 → 240

Calls

4 calls:

10.0ms	(/ 1 (/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im))))
78.0ms	(* (/ 1 (hypot y.re y.im)) (/ 1 (/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im)))))
0.0ms	(fma x.re y.re (* x.im y.im))
6.0ms	(/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im)))

series702.0ms

Counts

4 → 12

Calls

4 calls:

172.0ms	(/ 1 (/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im))))
296.0ms	(* (/ 1 (hypot y.re y.im)) (/ 1 (/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im)))))
81.0ms	(fma x.re y.re (* x.im y.im))
153.0ms	(/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im)))

simplify4.1s

Counts

252 → 252

Iterations

Useful iterations: done (4.1s)

Iter	Nodes	Cost
0	292	5363
1	722	4687
2	1535	4048
3	4311	4030
done	5001	3953

prune748.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 4.1b

Details

sample37.0ms

simplify17.0ms

prune10.0ms

localize25.0ms

rewrite78.0ms

series194.0ms

simplify2.2s

prune355.0ms

localize12.0ms

rewrite47.0ms

series456.0ms

simplify4.6s

prune424.0ms

localize16.0ms

rewrite40.0ms

series435.0ms

simplify2.3s

prune588.0ms

localize13.0ms

rewrite106.0ms

series702.0ms

simplify4.1s

prune748.0ms

regimes310.0ms

bsearch3.0ms