Details

sample27.0ms

Algorithm

intervals

Results

11.0ms

268×

body

valid

simplify15.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	21
2	21
1	17
0	11

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.1b

localize17.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma x.re y.re (* x.im y.im))
27.6b	(/ (fma x.re y.re (* x.im y.im)) (fma y.im y.im (* y.re y.re)))

rewrite9.0ms

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 x.re y.re (* x.im y.im))
7.0ms	(/ (fma x.re y.re (* x.im y.im)) (fma y.im y.im (* y.re y.re)))

series208.0ms

Counts

2 → 6

Calls

2 calls:

58.0ms	(fma x.re y.re (* x.im y.im))
150.0ms	(/ (fma x.re y.re (* x.im y.im)) (fma y.im y.im (* y.re y.re)))

simplify1.9s

Counts

45 → 45

Iterations

Iter	Nodes
done	5001
4	2350
3	700
2	244
1	104
0	65

prune296.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 27.3b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re)))) (sqrt (fma y.im y.im (* y.re y.re))))
17.2b	(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
28.8b	(sqrt (fma y.im y.im (* y.re y.re)))
28.8b	(sqrt (fma y.im y.im (* y.re y.re)))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

276×	`times-frac`
160×	`add-sqr-sqrt`
158×	`*-un-lft-identity` `add-cube-cbrt`
150×	`sqrt-prod`
25×	`associate-/l*`
12×	`associate-/r*`
11×	`add-cbrt-cube` `add-exp-log`
9×	`div-inv`
6×	`pow1`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-udef` `hypot-def`
1×	`associate-/l/`

Counts

4 → 250

Calls

4 calls:

29.0ms	(/ (/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re)))) (sqrt (fma y.im y.im (* y.re y.re))))
10.0ms	(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
2.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
2.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

series461.0ms

Counts

4 → 12

Calls

4 calls:

149.0ms	(/ (/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re)))) (sqrt (fma y.im y.im (* y.re y.re))))
182.0ms	(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
79.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
51.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

simplify2.3s

Counts

262 → 262

Iterations

Iter	Nodes
done	5000
3	3674
2	1121
1	549
0	259

prune1.8s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 14.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot y.im y.re)
0.0b	(hypot y.im y.re)
0.1b	(/ (/ (fma y.re x.re (* x.im y.im)) (hypot y.im y.re)) (hypot y.im y.re))
17.2b	(/ (fma y.re x.re (* x.im y.im)) (hypot y.im y.re))

rewrite22.0ms

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`
4×	`expm1-log1p-u` `pow1` `cbrt-undiv` `div-exp` `log1p-expm1-u` `add-log-exp`
2×	`hypot-udef` `clear-num` `frac-2neg`
1×	`associate-/l/`

Counts

4 → 121

Calls

4 calls:

0.0ms	(hypot y.im y.re)
0.0ms	(hypot y.im y.re)
14.0ms	(/ (/ (fma y.re x.re (* x.im y.im)) (hypot y.im y.re)) (hypot y.im y.re))
4.0ms	(/ (fma y.re x.re (* x.im y.im)) (hypot y.im y.re))

series432.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(hypot y.im y.re)
59.0ms	(hypot y.im y.re)
149.0ms	(/ (/ (fma y.re x.re (* x.im y.im)) (hypot y.im y.re)) (hypot y.im y.re))
154.0ms	(/ (fma y.re x.re (* x.im y.im)) (hypot y.im y.re))

simplify2.2s

Counts

133 → 133

Iterations

Iter	Nodes
done	5279
3	3422
2	864
1	335
0	161

prune904.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.9b

localize36.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma y.re x.re (* x.im y.im))
0.0b	(/ 1 (hypot y.im y.re))
0.2b	(* (/ (fma y.re x.re (* x.im y.im)) (hypot y.im y.re)) (/ 1 (hypot y.im y.re)))
17.2b	(/ (fma y.re x.re (* x.im y.im)) (hypot y.im y.re))

rewrite41.0ms

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/` `un-div-inv` `*-commutative` `fma-udef` `pow-flip` `inv-pow`

Counts

4 → 131

Calls

4 calls:

0.0ms	(fma y.re x.re (* x.im y.im))
4.0ms	(/ 1 (hypot y.im y.re))
29.0ms	(* (/ (fma y.re x.re (* x.im y.im)) (hypot y.im y.re)) (/ 1 (hypot y.im y.re)))
4.0ms	(/ (fma y.re x.re (* x.im y.im)) (hypot y.im y.re))

series400.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(fma y.re x.re (* x.im y.im))
70.0ms	(/ 1 (hypot y.im y.re))
153.0ms	(* (/ (fma y.re x.re (* x.im y.im)) (hypot y.im y.re)) (/ 1 (hypot y.im y.re)))
131.0ms	(/ (fma y.re x.re (* x.im y.im)) (hypot y.im y.re))

simplify3.1s

Counts

143 → 143

Iterations

Iter	Nodes
done	5013
3	3770
2	1398
1	380
0	152

prune836.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 5.9b

regimes605.0ms

Accuracy

33% (7.7b remaining)

Error of 13.8b against oracle of 6.2b and baseline of 17.6b

bsearch122.0ms

Steps

Iters	Range		Point
10	1.1063855308468765e+219	1.1167816988421008e+230	1.118997009957087e+219
7	-1.2513451800241158e+129	-6.14118040551932e+127	-1.089461735547702e+128

simplify13.0ms

Iterations

Iter	Nodes
done	33
3	33
2	32
1	29
0	22

end0.0ms

sample1.2s

Algorithm

intervals

Results

778.0ms

8480×

body

valid