Details

sample28.0ms

Algorithm

intervals

Results

12.0ms

283×

body

valid

simplify7.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	21
2	21
1	17
0	11

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 25.1b

localize22.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma x.re y.re (* x.im y.im))
24.7b	(/ (fma x.re y.re (* x.im y.im)) (fma y.im y.im (* y.re y.re)))

rewrite5.0ms

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

series185.0ms

Counts

2 → 6

Calls

2 calls:

44.0ms	(fma x.re y.re (* x.im y.im))
141.0ms	(/ (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	5002
3	2442
2	402
1	104
0	65

prune301.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 15.1b

localize25.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma x.re y.re (* x.im y.im))
0.3b	(* (/ 1 (hypot y.im y.re)) (/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re)))
14.7b	(/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 97

Calls

3 calls:

0.0ms	(fma x.re y.re (* x.im y.im))
21.0ms	(* (/ 1 (hypot y.im y.re)) (/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re)))
4.0ms	(/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re))

series510.0ms

Counts

3 → 9

Calls

3 calls:

58.0ms	(fma x.re y.re (* x.im y.im))
271.0ms	(* (/ 1 (hypot y.im y.re)) (/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re)))
180.0ms	(/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re))

simplify2.2s

Counts

106 → 106

Iterations

Iter	Nodes
done	5000
2	2979
1	373
0	140

prune706.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.4b

localize29.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma x.im y.im (* x.re y.re))
0.1b	(/ (/ (fma x.im y.im (* x.re y.re)) (hypot y.im y.re)) (hypot y.im y.re))
14.7b	(/ (fma x.im y.im (* x.re y.re)) (hypot y.im y.re))

rewrite37.0ms

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

Counts

3 → 111

Calls

3 calls:

1.0ms	(fma x.im y.im (* x.re y.re))
20.0ms	(/ (/ (fma x.im y.im (* x.re y.re)) (hypot y.im y.re)) (hypot y.im y.re))
9.0ms	(/ (fma x.im y.im (* x.re y.re)) (hypot y.im y.re))

series441.0ms

Counts

3 → 9

Calls

3 calls:

62.0ms	(fma x.im y.im (* x.re y.re))
207.0ms	(/ (/ (fma x.im y.im (* x.re y.re)) (hypot y.im y.re)) (hypot y.im y.re))
171.0ms	(/ (fma x.im y.im (* x.re y.re)) (hypot y.im y.re))

simplify865.0ms

Counts

120 → 120

Iterations

Iter	Nodes
done	5001
2	1676
1	351
0	161

prune809.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 1.3b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma y.re x.re (* x.im y.im))
0.1b	(/ (/ 1 (/ (hypot y.im y.re) (fma y.re x.re (* x.im y.im)))) (hypot y.im y.re))
0.2b	(/ 1 (/ (hypot y.im y.re) (fma y.re x.re (* x.im y.im))))
14.7b	(/ (hypot y.im y.re) (fma y.re x.re (* x.im y.im)))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

480×	`times-frac`
239×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
50×	`associate-/l*`
36×	`add-exp-log`
23×	`div-inv`
22×	`div-exp`
20×	`add-cbrt-cube`
19×	`associate-/r*`
10×	`cbrt-undiv`
5×	`pow1` `associate-/r/`
4×	`expm1-log1p-u` `rec-exp` `1-exp` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg`
1×	`fma-udef` `pow-flip` `inv-pow` `associate-/l/`

Counts

4 → 319

Calls

4 calls:

0.0ms	(fma y.re x.re (* x.im y.im))
33.0ms	(/ (/ 1 (/ (hypot y.im y.re) (fma y.re x.re (* x.im y.im)))) (hypot y.im y.re))
15.0ms	(/ 1 (/ (hypot y.im y.re) (fma y.re x.re (* x.im y.im))))
8.0ms	(/ (hypot y.im y.re) (fma y.re x.re (* x.im y.im)))

series702.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(fma y.re x.re (* x.im y.im))
254.0ms	(/ (/ 1 (/ (hypot y.im y.re) (fma y.re x.re (* x.im y.im)))) (hypot y.im y.re))
257.0ms	(/ 1 (/ (hypot y.im y.re) (fma y.re x.re (* x.im y.im))))
122.0ms	(/ (hypot y.im y.re) (fma y.re x.re (* x.im y.im)))

simplify980.0ms

Counts

331 → 331

Iterations

Iter	Nodes
done	5001
1	1310
0	458

prune1.4s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 1.3b

regimes420.0ms

Accuracy

30.1% (9.7b remaining)

Error of 12.0b against oracle of 2.2b and baseline of 16.1b

bsearch106.0ms

Steps

Iters	Range		Point
6	8.846670165818639e+179	1.1670387656327415e+181	1.7216921703264507e+180
8	-4.194746639390341e+188	-1.186401832632246e+184	-2.328453055309953e+184

simplify10.0ms

Iterations

Iter	Nodes
done	34
3	34
2	30
1	26
0	20

end0.0ms

sample1.2s

Algorithm

intervals

Results

747.0ms

8478×

body

valid