Details

sample38.0ms

Algorithm

intervals

Results

20.0ms

271×

body

valid

simplify10.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	21
2	21
1	17
0	11

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.0b

localize26.0ms

Local error

Found 2 expressions with local error:

0.2b	(+ (* x.re y.re) (* x.im y.im))
22.6b	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite58.0ms

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` `add-log-exp`
3×	`associate-/r` `flip3-+` `flip-+` `associate-/l`
2×	`expm1-log1p-u` `pow1` `associate-/r/` `log1p-expm1-u` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sum-log` `fma-def` `frac-2neg` `div-exp` `div-inv`

Counts

2 → 47

Calls

2 calls:

16.0ms	(+ (* x.re y.re) (* x.im y.im))
40.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series179.0ms

Counts

2 → 6

Calls

2 calls:

54.0ms	(+ (* x.re y.re) (* x.im y.im))
125.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify733.0ms

Counts

53 → 53

Iterations

Iter	Nodes
done	5000
2	1059
1	248
0	90

prune326.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 14.5b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot y.re y.im)
0.0b	(/ 1 (hypot y.re y.im))
0.3b	(* (/ 1 (hypot y.re y.im)) (/ (fma y.re x.re (* x.im y.im)) (hypot y.re y.im)))
14.2b	(/ (fma y.re x.re (* x.im y.im)) (hypot y.re y.im))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 130

Calls

4 calls:

0.0ms	(hypot y.re y.im)
6.0ms	(/ 1 (hypot y.re y.im))
25.0ms	(* (/ 1 (hypot y.re y.im)) (/ (fma y.re x.re (* x.im y.im)) (hypot y.re y.im)))
6.0ms	(/ (fma y.re x.re (* x.im y.im)) (hypot y.re y.im))

series494.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(hypot y.re y.im)
65.0ms	(/ 1 (hypot y.re y.im))
215.0ms	(* (/ 1 (hypot y.re y.im)) (/ (fma y.re x.re (* x.im y.im)) (hypot y.re y.im)))
146.0ms	(/ (fma y.re x.re (* x.im y.im)) (hypot y.re y.im))

simplify1.8s

Counts

142 → 142

Iterations

Iter	Nodes
done	5000
2	2850
1	407
0	154

prune735.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.4b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot y.re y.im)
0.0b	(hypot y.re y.im)
0.1b	(/ (/ (fma y.re x.re (* x.im y.im)) (hypot y.re y.im)) (hypot y.re y.im))
14.2b	(/ (fma y.re x.re (* x.im y.im)) (hypot y.re y.im))

rewrite21.0ms

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

Counts

4 → 121

Calls

4 calls:

0.0ms	(hypot y.re y.im)
0.0ms	(hypot y.re y.im)
9.0ms	(/ (/ (fma y.re x.re (* x.im y.im)) (hypot y.re y.im)) (hypot y.re y.im))
8.0ms	(/ (fma y.re x.re (* x.im y.im)) (hypot y.re y.im))

series375.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(hypot y.re y.im)
50.0ms	(hypot y.re y.im)
153.0ms	(/ (/ (fma y.re x.re (* x.im y.im)) (hypot y.re y.im)) (hypot y.re y.im))
115.0ms	(/ (fma y.re x.re (* x.im y.im)) (hypot y.re y.im))

simplify681.0ms

Counts

133 → 133

Iterations

Iter	Nodes
done	5000
2	1628
1	355
0	161

prune932.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 6.4b

localize35.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot y.re y.im)
0.0b	(hypot y.re y.im)
0.3b	(* (/ 1 (hypot y.re y.im)) (* (fma y.re x.re (* x.im y.im)) (/ 1 (hypot y.re y.im))))
14.4b	(* (fma y.re x.re (* x.im y.im)) (/ 1 (hypot y.re y.im)))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

78×	`add-exp-log`
40×	`prod-exp`
30×	`add-cbrt-cube`
26×	`add-sqr-sqrt`
20×	`*-un-lft-identity` `times-frac` `div-exp`
19×	`add-cube-cbrt`
16×	`associate-l`
14×	`associate-r`
12×	`cbrt-unprod`
11×	`pow1`
10×	`rec-exp` `1-exp`
6×	`cbrt-undiv`
5×	`associate-*r/`
4×	`expm1-log1p-u` `pow-prod-down` `log1p-expm1-u` `add-log-exp`
3×	`un-div-inv` `unswap-sqr`
2×	`frac-times` `hypot-udef` `*-commutative` `div-inv`
1×	`associate-*l/`

Counts

4 → 115

Calls

4 calls:

0.0ms	(hypot y.re y.im)
0.0ms	(hypot y.re y.im)
34.0ms	(* (/ 1 (hypot y.re y.im)) (* (fma y.re x.re (* x.im y.im)) (/ 1 (hypot y.re y.im))))
17.0ms	(* (fma y.re x.re (* x.im y.im)) (/ 1 (hypot y.re y.im)))

series528.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(hypot y.re y.im)
49.0ms	(hypot y.re y.im)
270.0ms	(* (/ 1 (hypot y.re y.im)) (* (fma y.re x.re (* x.im y.im)) (/ 1 (hypot y.re y.im))))
156.0ms	(* (fma y.re x.re (* x.im y.im)) (/ 1 (hypot y.re y.im)))

simplify6.8s

Counts

127 → 127

Iterations

Iter	Nodes
done	5001
2	4265
1	433
0	145

prune674.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 6.4b

regimes614.0ms

Accuracy

34.8% (7.4b remaining)

Error of 13.4b against oracle of 6.0b and baseline of 17.3b

bsearch123.0ms

Steps

Iters	Range		Point
6	7.997843383138597e+191	8.056208352901572e+192	8.747123436813268e+191
10	-3.959953710600684e+125	-7.632284195501427e+113	-2.0458466692374305e+123

simplify7.0ms

Iterations

Iter	Nodes
done	26
1	26
0	22

end0.0ms

sample1.4s

Algorithm

intervals

Results

1.1s

8463×

body

valid