Details

sample43.0ms

Algorithm

intervals

Results

21.0ms

263×

body

valid

simplify49.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	21
2	21
1	17
0	11

prune36.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 27.8b

localize96.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma y.im y.im (* y.re y.re))
0.0b	(fma x.re y.re (* x.im y.im))
27.3b	(/ (fma x.re y.re (* x.im y.im)) (fma y.im y.im (* y.re y.re)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
5×	`add-cbrt-cube` `add-exp-log`
3×	`expm1-log1p-u` `pow1` `associate-/r` `insert-posit16` `log1p-expm1-u` `associate-/l` `add-log-exp`
2×	`fma-udef`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv`

Counts

3 → 52

Calls

3 calls:

1.0ms	(fma y.im y.im (* y.re y.re))
2.0ms	(fma x.re y.re (* x.im y.im))
17.0ms	(/ (fma x.re y.re (* x.im y.im)) (fma y.im y.im (* y.re y.re)))

series412.0ms

Counts

3 → 9

Calls

3 calls:

64.0ms	(fma y.im y.im (* y.re y.re))
77.0ms	(fma x.re y.re (* x.im y.im))
271.0ms	(/ (fma x.re y.re (* x.im y.im)) (fma y.im y.im (* y.re y.re)))

simplify5.2s

Counts

61 → 61

Iterations

Iter	Nodes
done	5016
4	2378
3	676
2	255
1	117
0	76

prune958.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 27.0b

localize103.0ms

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))))
18.4b	(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
28.3b	(sqrt (fma y.im y.im (* y.re y.re)))
28.3b	(sqrt (fma y.im y.im (* y.re y.re)))

rewrite97.0ms

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` `insert-posit16` `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 → 254

Calls

4 calls:

40.0ms	(/ (/ (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))))
16.0ms	(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
7.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
6.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

series598.0ms

Counts

4 → 12

Calls

4 calls:

209.0ms	(/ (/ (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))))
236.0ms	(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
80.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
73.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

simplify7.7s

Counts

266 → 266

Iterations

Iter	Nodes
done	5022
3	4606
2	1144
1	547
0	262

prune3.7s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 17.0b

localize123.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (hypot y.im y.re) (fma x.im y.im (* y.re x.re))) (hypot y.im y.re))
0.3b	(/ 1 (* (/ (hypot y.im y.re) (fma x.im y.im (* y.re x.re))) (hypot y.im y.re)))
0.8b	(fma x.im y.im (* y.re x.re))
18.5b	(/ (hypot y.im y.re) (fma x.im y.im (* y.re x.re)))

rewrite110.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-exp-log`
27×	`add-sqr-sqrt`
22×	`*-un-lft-identity` `times-frac` `add-cube-cbrt`
20×	`add-cbrt-cube`
13×	`associate-l`
11×	`div-exp`
9×	`pow1`
8×	`prod-exp`
6×	`cbrt-undiv` `associate-/l*`
4×	`expm1-log1p-u` `associate-/r*` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`rec-exp` `1-exp` `associate-r` `div-inv`
2×	`clear-num` `frac-2neg` `pow-prod-down` `associate-*l/` `pow-flip` `unswap-sqr`
1×	`associate-/r/` `*-commutative` `fma-udef` `inv-pow`

Counts

4 → 112

Calls

4 calls:

39.0ms	(* (/ (hypot y.im y.re) (fma x.im y.im (* y.re x.re))) (hypot y.im y.re))
46.0ms	(/ 1 (* (/ (hypot y.im y.re) (fma x.im y.im (* y.re x.re))) (hypot y.im y.re)))
1.0ms	(fma x.im y.im (* y.re x.re))
18.0ms	(/ (hypot y.im y.re) (fma x.im y.im (* y.re x.re)))

series902.0ms

Counts

4 → 12

Calls

4 calls:

186.0ms	(* (/ (hypot y.im y.re) (fma x.im y.im (* y.re x.re))) (hypot y.im y.re))
402.0ms	(/ 1 (* (/ (hypot y.im y.re) (fma x.im y.im (* y.re x.re))) (hypot y.im y.re)))
82.0ms	(fma x.im y.im (* y.re x.re))
231.0ms	(/ (hypot y.im y.re) (fma x.im y.im (* y.re x.re)))

simplify7.5s

Counts

124 → 124

Iterations

Iter	Nodes
done	5000
3	3354
2	1101
1	310
0	137

prune1.7s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 16.9b

localize94.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma x.re y.re (* x.im y.im))
0.1b	(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re)) (hypot y.im y.re))
18.4b	(/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re))

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
53×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
16×	`associate-/l*`
10×	`add-cbrt-cube` `add-exp-log`
6×	`associate-/r*` `div-inv`
4×	`cbrt-undiv` `div-exp`
3×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`clear-num` `frac-2neg`
1×	`fma-udef` `associate-/l/`

Counts

3 → 114

Calls

3 calls:

3.0ms	(fma x.re y.re (* x.im y.im))
47.0ms	(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re)) (hypot y.im y.re))
22.0ms	(/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re))

series669.0ms

Counts

3 → 9

Calls

3 calls:

83.0ms	(fma x.re y.re (* x.im y.im))
312.0ms	(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re)) (hypot y.im y.re))
274.0ms	(/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re))

simplify6.0s

Counts

123 → 123

Iterations

Iter	Nodes
done	5013
3	3153
2	865
1	328
0	164

prune1.8s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 6.6b

regimes1.3s

Accuracy

31.8% (7.8b remaining)

Error of 13.9b against oracle of 6.2b and baseline of 17.6b

bsearch158.0ms

Steps

Iters	Range		Point
10	4.331297687208775e+156	9.47206348113385e+174	2.1006973305354477e+171
8	-1.194776095236265e+88	-9.69756663765047e+83	-1.0930594930595556e+87

simplify17.0ms

Iterations

Iter	Nodes
done	20
1	20
0	18

end0.0ms

sample1.5s

Algorithm

intervals

Results

858.0ms

8425×

body

valid