Details

sample46.0ms

Algorithm

intervals

Results

16.0ms

269×

body

valid

simplify42.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	21
2	21
1	17
0	11

prune23.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.7b

localize31.0ms

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)))

rewrite13.0ms

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:

1.0ms	(fma x.re y.re (* x.im y.im))
10.0ms	(/ (fma x.re y.re (* x.im y.im)) (fma y.im y.im (* y.re y.re)))

series285.0ms

Counts

2 → 6

Calls

2 calls:

79.0ms	(fma x.re y.re (* x.im y.im))
206.0ms	(/ (fma x.re y.re (* x.im y.im)) (fma y.im y.im (* y.re y.re)))

simplify4.2s

Counts

47 → 47

Iterations

Iter	Nodes
done	5000
4	3183
3	863
2	289
1	105
0	67

prune845.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 25.0b

localize54.0ms

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)))

rewrite30.0ms

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:

1.0ms	(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))))
10.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
6.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

series536.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(fma x.re y.re (* x.im y.im))
302.0ms	(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
83.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
72.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

simplify4.6s

Counts

99 → 99

Iterations

Iter	Nodes
done	5004
4	2590
3	854
2	304
1	143
0	93

prune1.7s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 22.3b

localize71.0ms

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)))

rewrite76.0ms

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:

22.0ms	(/ (/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re)))) (hypot y.im y.re))
1.0ms	(fma x.re y.re (* x.im y.im))
15.0ms	(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
6.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

series984.0ms

Counts

4 → 12

Calls

4 calls:

510.0ms	(/ (/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re)))) (hypot y.im y.re))
74.0ms	(fma x.re y.re (* x.im y.im))
302.0ms	(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
99.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

simplify6.4s

Counts

191 → 191

Iterations

Iter	Nodes
done	5026
3	4046
2	1027
1	482
0	233

prune2.8s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.6b

localize40.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (/ (fma x.im y.im (* y.re x.re)) (hypot y.im y.re)) (hypot y.im y.re))
0.5b	(fma x.im y.im (* y.re x.re))
14.5b	(/ (fma x.im y.im (* y.re x.re)) (hypot y.im y.re))

rewrite64.0ms

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:

30.0ms	(/ (/ (fma x.im y.im (* y.re x.re)) (hypot y.im y.re)) (hypot y.im y.re))
2.0ms	(fma x.im y.im (* y.re x.re))
13.0ms	(/ (fma x.im y.im (* y.re x.re)) (hypot y.im y.re))

series759.0ms

Counts

3 → 9

Calls

3 calls:

355.0ms	(/ (/ (fma x.im y.im (* y.re x.re)) (hypot y.im y.re)) (hypot y.im y.re))
69.0ms	(fma x.im y.im (* y.re x.re))
335.0ms	(/ (fma x.im y.im (* y.re x.re)) (hypot y.im y.re))

simplify6.2s

Counts

123 → 123

Iterations

Iter	Nodes
done	5353
3	3556
2	907
1	339
0	163

prune1.7s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 3.0b

regimes1.4s

Accuracy

27.9% (10.7b remaining)

Error of 13.2b against oracle of 2.6b and baseline of 17.4b

bsearch115.0ms

Steps

Iters	Range		Point
9	4.230872522382776e+160	1.60249842060193e+167	2.4763280442388167e+164
7	-7.223268975160798e+166	-1.971781211500644e+165	-1.258889379708196e+166

simplify7.0ms

Iterations

Iter	Nodes
done	25
1	25
0	20

end0.0ms

sample1.2s

Algorithm

intervals

Results

729.0ms

8499×

body

valid