Details

sample37.0ms

Algorithm

intervals

Results

20.0ms

269×

body

valid

simplify13.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	21
2	21
1	17
0	11

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.2b

localize39.0ms

Local error

Found 2 expressions with local error:

0.3b	(fma x.re y.re (* x.im y.im))
25.2b	(/ (fma x.re y.re (* x.im y.im)) (fma y.im y.im (* y.re y.re)))

rewrite10.0ms

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` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `fma-udef` `div-inv`

Counts

2 → 41

Calls

2 calls:

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

series199.0ms

Counts

2 → 6

Calls

2 calls:

61.0ms	(fma x.re y.re (* x.im y.im))
138.0ms	(/ (fma x.re y.re (* x.im y.im)) (fma y.im y.im (* y.re y.re)))

simplify2.1s

Counts

47 → 47

Iterations

Iter	Nodes
done	5000
4	3356
3	936
2	296
1	106
0	67

prune264.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 24.8b

localize28.0ms

Local error

Found 4 expressions with local error:

0.3b	(fma x.re y.re (* x.im y.im))
14.5b	(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
29.5b	(sqrt (fma y.im y.im (* y.re y.re)))
29.5b	(sqrt (fma y.im y.im (* y.re y.re)))

rewrite20.0ms

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))
9.0ms	(/ (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)))

series302.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(fma x.re y.re (* x.im y.im))
136.0ms	(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
51.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
60.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

simplify2.1s

Counts

99 → 99

Iterations

Iter	Nodes
done	5000
4	2629
3	857
2	304
1	143
0	93

prune467.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 22.2b

localize24.0ms

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))
0.3b	(fma x.re y.re (* x.im y.im))
14.5b	(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
29.5b	(sqrt (fma y.im y.im (* y.re y.re)))

rewrite33.0ms

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:

18.0ms	(/ (/ (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))
6.0ms	(/ (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)))

series460.0ms

Counts

4 → 12

Calls

4 calls:

205.0ms	(/ (/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re)))) (hypot y.im y.re))
41.0ms	(fma x.re y.re (* x.im y.im))
154.0ms	(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
60.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

simplify1.8s

Counts

191 → 191

Iterations

Iter	Nodes
done	5433
3	4138
2	1099
1	479
0	233

prune901.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.6b

localize21.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re)) (hypot y.im y.re))
0.3b	(fma x.re y.re (* x.im y.im))
14.5b	(/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re))

rewrite28.0ms

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:

12.0ms	(/ (/ (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))
10.0ms	(/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re))

series415.0ms

Counts

3 → 9

Calls

3 calls:

178.0ms	(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re)) (hypot y.im y.re))
68.0ms	(fma x.re y.re (* x.im y.im))
169.0ms	(/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re))

simplify2.1s

Counts

123 → 123

Iterations

Iter	Nodes
done	5937
3	3512
2	886
1	335
0	164

prune630.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 5.6b

regimes256.0ms

Accuracy

18.7% (8.9b remaining)

Error of 14.7b against oracle of 5.8b and baseline of 16.8b

bsearch42.0ms

Steps

Iters	Range		Point
9	4.230872522382776e+160	1.60249842060193e+167	9.842459121637509e+163

simplify2.0ms

Iterations

Iter	Nodes
done	14
1	14
0	13

end0.0ms

sample1.3s

Algorithm

intervals

Results

1.0s

8499×

body

valid