Details

sample26.0ms

Algorithm

intervals

Results

12.0ms

272×

body

valid

simplify51.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	94
6	94
5	90
4	76
3	56
2	40
1	21
0	11

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.7b

localize15.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma (- y.im) x.re (* x.im y.re))
23.2b	(/ (fma (- y.im) x.re (* x.im y.re)) (fma y.im y.im (* y.re y.re)))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 39

Calls

2 calls:

0.0ms	(fma (- y.im) x.re (* x.im y.re))
4.0ms	(/ (fma (- y.im) x.re (* x.im y.re)) (fma y.im y.im (* y.re y.re)))

series168.0ms

Counts

2 → 6

Calls

2 calls:

63.0ms	(fma (- y.im) x.re (* x.im y.re))
104.0ms	(/ (fma (- y.im) x.re (* x.im y.re)) (fma y.im y.im (* y.re y.re)))

simplify909.0ms

Counts

45 → 45

Iterations

Iter	Nodes
done	5001
3	1390
2	268
1	106
0	66

prune331.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 15.1b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (hypot y.re y.im))
0.0b	(fma y.im (- x.re) (* x.im y.re))
0.3b	(* (/ 1 (hypot y.re y.im)) (/ (fma y.im (- x.re) (* x.im y.re)) (hypot y.re y.im)))
14.8b	(/ (fma y.im (- x.re) (* x.im y.re)) (hypot y.re y.im))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
43×	`times-frac`
36×	`*-un-lft-identity`
34×	`add-cube-cbrt`
32×	`add-exp-log`
20×	`add-cbrt-cube`
13×	`associate-r` `associate-l`
11×	`div-exp`
8×	`prod-exp`
7×	`pow1`
6×	`cbrt-undiv` `associate-/r` `associate-/l` `unswap-sqr`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`rec-exp` `1-exp`
2×	`clear-num` `frac-2neg`
1×	`frac-times` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `fma-udef` `pow-flip` `inv-pow`

Counts

4 → 130

Calls

4 calls:

4.0ms	(/ 1 (hypot y.re y.im))
0.0ms	(fma y.im (- x.re) (* x.im y.re))
18.0ms	(* (/ 1 (hypot y.re y.im)) (/ (fma y.im (- x.re) (* x.im y.re)) (hypot y.re y.im)))
4.0ms	(/ (fma y.im (- x.re) (* x.im y.re)) (hypot y.re y.im))

series484.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(/ 1 (hypot y.re y.im))
66.0ms	(fma y.im (- x.re) (* x.im y.re))
229.0ms	(* (/ 1 (hypot y.re y.im)) (/ (fma y.im (- x.re) (* x.im y.re)) (hypot y.re y.im)))
114.0ms	(/ (fma y.im (- x.re) (* x.im y.re)) (hypot y.re y.im))

simplify1.6s

Counts

142 → 142

Iterations

Iter	Nodes
done	5002
2	2894
1	407
0	155

prune722.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.2b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot y.re y.im)
0.0b	(- (* x.im y.re) (* y.im x.re))
0.1b	(/ (/ (- (* x.im y.re) (* y.im x.re)) (hypot y.re y.im)) (hypot y.re y.im))
14.8b	(/ (- (* x.im y.re) (* y.im x.re)) (hypot y.re y.im))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
54×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
16×	`associate-/l*`
11×	`add-cbrt-cube` `add-exp-log`
6×	`associate-/r*` `div-inv` `add-log-exp`
4×	`expm1-log1p-u` `pow1` `cbrt-undiv` `div-exp` `log1p-expm1-u`
3×	`div-sub` `associate-/l/`
2×	`clear-num` `frac-2neg` `flip3--` `flip--`
1×	`hypot-udef` `sub-neg` `fma-neg` `diff-log` `prod-diff`

Counts

4 → 131

Calls

4 calls:

0.0ms	(hypot y.re y.im)
6.0ms	(- (* x.im y.re) (* y.im x.re))
19.0ms	(/ (/ (- (* x.im y.re) (* y.im x.re)) (hypot y.re y.im)) (hypot y.re y.im))
14.0ms	(/ (- (* x.im y.re) (* y.im x.re)) (hypot y.re y.im))

series481.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(hypot y.re y.im)
44.0ms	(- (* x.im y.re) (* y.im x.re))
198.0ms	(/ (/ (- (* x.im y.re) (* y.im x.re)) (hypot y.re y.im)) (hypot y.re y.im))
174.0ms	(/ (- (* x.im y.re) (* y.im x.re)) (hypot y.re y.im))

simplify864.0ms

Counts

143 → 143

Iterations

Iter	Nodes
done	5001
2	2307
1	488
0	194

prune1.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.5b

localize36.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (hypot y.re y.im) x.re)
0.1b	(/ (- (/ (* x.im y.re) (hypot y.re y.im)) (/ y.im (/ (hypot y.re y.im) x.re))) (hypot y.re y.im))
6.9b	(/ (* x.im y.re) (hypot y.re y.im))
9.0b	(/ y.im (/ (hypot y.re y.im) x.re))

rewrite174.0ms

Algorithm

rewrite-expression-head

Rules

120×	`times-frac`
104×	`add-sqr-sqrt`
76×	`*-un-lft-identity`
68×	`add-cube-cbrt`
22×	`associate-/r*`
18×	`add-cbrt-cube` `add-exp-log`
14×	`associate-/l*`
12×	`difference-of-squares`
8×	`div-inv`
7×	`cbrt-undiv` `div-exp`
4×	`expm1-log1p-u` `pow1` `clear-num` `frac-2neg` `log1p-expm1-u` `distribute-lft-out--` `add-log-exp`
3×	`associate-/l/`
1×	`flip3--` `div-sub` `prod-exp` `associate-/r/` `frac-sub` `cbrt-unprod` `flip--`

Counts

4 → 173

Calls

4 calls:

7.0ms	(/ (hypot y.re y.im) x.re)
146.0ms	(/ (- (/ (* x.im y.re) (hypot y.re y.im)) (/ y.im (/ (hypot y.re y.im) x.re))) (hypot y.re y.im))
8.0ms	(/ (* x.im y.re) (hypot y.re y.im))
7.0ms	(/ y.im (/ (hypot y.re y.im) x.re))

series640.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(/ (hypot y.re y.im) x.re)
326.0ms	(/ (- (/ (* x.im y.re) (hypot y.re y.im)) (/ y.im (/ (hypot y.re y.im) x.re))) (hypot y.re y.im))
116.0ms	(/ (* x.im y.re) (hypot y.re y.im))
120.0ms	(/ y.im (/ (hypot y.re y.im) x.re))

simplify1.3s

Counts

185 → 185

Iterations

Iter	Nodes
done	5001
2	3585
1	704
0	282

prune1.5s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

regimes412.0ms

Accuracy

0% (1.1b remaining)

Error of 1.1b against oracle of 0.0b and baseline of 1.1b

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	20
2	20
1	18
0	15

end0.0ms

sample1.5s

Algorithm

intervals

Results

1.1s

8438×

body

valid