Details

sample41.0ms

Algorithm

intervals

Results

29.0ms

269×

body

valid

simplify8.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	21
2	21
1	17
0	11

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.8b

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma y.im y.im (* y.re y.re))
0.5b	(fma x.re y.re (* x.im y.im))
29.8b	(/ (fma x.re y.re (* x.im y.im)) (fma y.im y.im (* y.re y.re)))

rewrite8.0ms

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:

0.0ms	(fma y.im y.im (* y.re y.re))
0.0ms	(fma x.re y.re (* x.im y.im))
6.0ms	(/ (fma x.re y.re (* x.im y.im)) (fma y.im y.im (* y.re y.re)))

series248.0ms

Counts

3 → 9

Calls

3 calls:

45.0ms	(fma y.im y.im (* y.re y.re))
67.0ms	(fma x.re y.re (* x.im y.im))
136.0ms	(/ (fma x.re y.re (* x.im y.im)) (fma y.im y.im (* y.re y.re)))

simplify1.0s

Counts

61 → 61

Iterations

Iter	Nodes
done	2000
4	2000
3	787
2	257
1	117
0	76

prune726.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 29.4b

localize30.0ms

Local error

Found 4 expressions with local error:

0.5b	(fma x.re y.re (* x.im y.im))
16.8b	(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
31.8b	(sqrt (fma y.im y.im (* y.re y.re)))
31.8b	(sqrt (fma y.im y.im (* y.re y.re)))

rewrite9.0ms

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` `add-exp-log`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`fma-udef` `associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `hypot-def`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv`

Counts

4 → 87

Calls

4 calls:

0.0ms	(fma x.re y.re (* x.im y.im))
5.0ms	(/ (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)))
1.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

series329.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(fma x.re y.re (* x.im y.im))
141.0ms	(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
57.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
56.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

simplify947.0ms

Counts

99 → 99

Iterations

Iter	Nodes
done	2005
4	2005
3	857
2	304
1	143
0	93

prune1.3s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 27.0b

localize34.0ms

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)))) (hypot y.im y.re))
0.5b	(fma x.re y.re (* x.im y.im))
16.8b	(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
31.8b	(sqrt (fma y.im y.im (* y.re y.re)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

156×	`times-frac`
96×	`add-sqr-sqrt`
95×	`*-un-lft-identity` `add-cube-cbrt`
51×	`sqrt-prod`
25×	`associate-/l*`
11×	`add-cbrt-cube` `add-exp-log`
9×	`associate-/r*`
6×	`div-inv`
5×	`pow1`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`clear-num` `frac-2neg` `fma-udef`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `hypot-def` `associate-/l/`

Counts

4 → 179

Calls

4 calls:

11.0ms	(/ (/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re)))) (hypot y.im y.re))
0.0ms	(fma x.re y.re (* x.im y.im))
5.0ms	(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
1.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

series927.0ms

Counts

4 → 12

Calls

4 calls:

626.0ms	(/ (/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re)))) (hypot y.im y.re))
50.0ms	(fma x.re y.re (* x.im y.im))
159.0ms	(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
91.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

simplify1.3s

Counts

191 → 191

Iterations

Iter	Nodes
done	2025
3	2025
2	1099
1	479
0	233

prune2.5s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.9b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot y.im y.re)
0.1b	(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re)) (hypot y.im y.re))
0.5b	(fma x.re y.re (* x.im y.im))
16.8b	(/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re))

rewrite25.0ms

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` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`clear-num` `frac-2neg`
1×	`hypot-udef` `fma-udef` `associate-/l/`

Counts

4 → 125

Calls

4 calls:

0.0ms	(hypot y.im y.re)
13.0ms	(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re)) (hypot y.im y.re))
0.0ms	(fma x.re y.re (* x.im y.im))
8.0ms	(/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re))

series409.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(hypot y.im y.re)
136.0ms	(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re)) (hypot y.im y.re))
50.0ms	(fma x.re y.re (* x.im y.im))
156.0ms	(/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re))

simplify865.0ms

Counts

137 → 137

Iterations

Iter	Nodes
done	2002
3	2002
2	899
1	347
0	172

prune1.4s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.9b

regimes347.0ms

Accuracy

32.9% (7.2b remaining)

Error of 12.9b against oracle of 5.7b and baseline of 16.4b

bsearch108.0ms

Steps

Iters	Range		Point
9	1.6933955445897368e+221	1.4196464610458346e+230	1.7195081298008246e+221
9	-4.2516442886911883e+123	-3.786455365439721e+118	-1.8277997780989823e+123

simplify6.0ms

Iterations

Iter	Nodes
done	20
1	20
0	18

end0.0ms

sample1.4s

Algorithm

intervals

Results

1.1s

8488×

body

valid