Details

sample29.0ms

Algorithm

intervals

Results

12.0ms

270×

body

valid

simplify7.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	21
2	21
1	17
0	11

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.1b

localize18.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.5b	(+ (* x.re y.re) (* x.im y.im))
24.6b	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
7×	`add-log-exp`
5×	`add-cbrt-cube` `add-exp-log`
4×	`flip3-+` `flip-+`
3×	`expm1-log1p-u` `pow1` `associate-/r` `log1p-expm1-u` `associate-/l`
2×	`+-commutative` `sum-log` `fma-def` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv`

Counts

3 → 61

Calls

3 calls:

10.0ms	(+ (* y.re y.re) (* y.im y.im))
6.0ms	(+ (* x.re y.re) (* x.im y.im))
24.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series202.0ms

Counts

3 → 9

Calls

3 calls:

30.0ms	(+ (* y.re y.re) (* y.im y.im))
40.0ms	(+ (* x.re y.re) (* x.im y.im))
131.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify786.0ms

Counts

70 → 70

Iterations

Iter	Nodes
done	5000
2	1598
1	307
0	104

prune461.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 16.7b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (hypot y.im y.re))
0.3b	(* (/ 1 (hypot y.im y.re)) (/ (fma x.re y.re (* y.im x.im)) (hypot y.im y.re)))
0.5b	(fma x.re y.re (* y.im x.im))
16.4b	(/ (fma x.re y.re (* y.im x.im)) (hypot y.im y.re))

rewrite43.0ms

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` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `fma-udef` `pow-flip` `inv-pow`

Counts

4 → 130

Calls

4 calls:

6.0ms	(/ 1 (hypot y.im y.re))
26.0ms	(* (/ 1 (hypot y.im y.re)) (/ (fma x.re y.re (* y.im x.im)) (hypot y.im y.re)))
0.0ms	(fma x.re y.re (* y.im x.im))
5.0ms	(/ (fma x.re y.re (* y.im x.im)) (hypot y.im y.re))

series562.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(/ 1 (hypot y.im y.re))
249.0ms	(* (/ 1 (hypot y.im y.re)) (/ (fma x.re y.re (* y.im x.im)) (hypot y.im y.re)))
53.0ms	(fma x.re y.re (* y.im x.im))
192.0ms	(/ (fma x.re y.re (* y.im x.im)) (hypot y.im y.re))

simplify1.5s

Counts

142 → 142

Iterations

Iter	Nodes
done	5000
2	3184
1	404
0	153

prune766.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.2b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot y.im y.re)
0.0b	(fma y.im x.im (* x.re y.re))
0.1b	(/ (/ (fma y.im x.im (* x.re y.re)) (hypot y.im y.re)) (hypot y.im y.re))
16.4b	(/ (fma y.im x.im (* x.re y.re)) (hypot y.im y.re))

rewrite22.0ms

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×	`clear-num` `frac-2neg`
1×	`hypot-udef` `fma-udef` `associate-/l/`

Counts

4 → 121

Calls

4 calls:

0.0ms	(hypot y.im y.re)
0.0ms	(fma y.im x.im (* x.re y.re))
12.0ms	(/ (/ (fma y.im x.im (* x.re y.re)) (hypot y.im y.re)) (hypot y.im y.re))
4.0ms	(/ (fma y.im x.im (* x.re y.re)) (hypot y.im y.re))

series378.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(hypot y.im y.re)
56.0ms	(fma y.im x.im (* x.re y.re))
133.0ms	(/ (/ (fma y.im x.im (* x.re y.re)) (hypot y.im y.re)) (hypot y.im y.re))
119.0ms	(/ (fma y.im x.im (* x.re y.re)) (hypot y.im y.re))

simplify607.0ms

Counts

133 → 133

Iterations

Iter	Nodes
done	5002
2	1748
1	364
0	167

prune883.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 2.8b

localize39.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (sqrt (/ 1 (hypot y.im y.re))) (sqrt (/ 1 (hypot y.im y.re)))) (/ (fma x.re y.re (* y.im x.im)) (hypot y.im y.re)))
0.5b	(fma x.re y.re (* y.im x.im))
0.5b	(* (sqrt (/ 1 (hypot y.im y.re))) (sqrt (/ 1 (hypot y.im y.re))))
16.4b	(/ (fma x.re y.re (* y.im x.im)) (hypot y.im y.re))

rewrite137.0ms

Algorithm

rewrite-expression-head

Rules

98×	`add-sqr-sqrt`
82×	`sqrt-prod`
71×	`times-frac`
61×	`*-un-lft-identity`
51×	`add-cube-cbrt`
32×	`pow1`
29×	`associate-r`
24×	`sqrt-pow1`
20×	`add-cbrt-cube` `swap-sqr` `add-exp-log`
18×	`unswap-sqr`
17×	`associate-l`
12×	`sqrt-div`
9×	`pow-prod-up`
8×	`pow1/2` `pow-prod-down` `div-inv` `pow-flip` `inv-pow`
7×	`prod-exp` `cbrt-unprod`
6×	`frac-times` `associate-*l/`
5×	`pow-sqr`
4×	`expm1-log1p-u` `associate-*r/` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `associate-/r` `div-exp` `associate-/l`
2×	`*-commutative`
1×	`pow2` `clear-num` `rem-square-sqrt` `frac-2neg` `pow-plus` `sqrt-unprod` `fma-udef`

Counts

4 → 188

Calls

4 calls:

81.0ms	(* (* (sqrt (/ 1 (hypot y.im y.re))) (sqrt (/ 1 (hypot y.im y.re)))) (/ (fma x.re y.re (* y.im x.im)) (hypot y.im y.re)))
0.0ms	(fma x.re y.re (* y.im x.im))
44.0ms	(* (sqrt (/ 1 (hypot y.im y.re))) (sqrt (/ 1 (hypot y.im y.re))))
4.0ms	(/ (fma x.re y.re (* y.im x.im)) (hypot y.im y.re))

series567.0ms

Counts

4 → 12

Calls

4 calls:

259.0ms	(* (* (sqrt (/ 1 (hypot y.im y.re))) (sqrt (/ 1 (hypot y.im y.re)))) (/ (fma x.re y.re (* y.im x.im)) (hypot y.im y.re)))
58.0ms	(fma x.re y.re (* y.im x.im))
74.0ms	(* (sqrt (/ 1 (hypot y.im y.re))) (sqrt (/ 1 (hypot y.im y.re))))
175.0ms	(/ (fma x.re y.re (* y.im x.im)) (hypot y.im y.re))

simplify2.6s

Counts

200 → 200

Iterations

Iter	Nodes
done	5000
2	3801
1	517
0	234

prune940.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 2.8b

regimes631.0ms

Accuracy

30.9% (10.0b remaining)

Error of 12.2b against oracle of 2.2b and baseline of 16.7b

bsearch101.0ms

Steps

Iters	Range		Point
10	2.835236500018992e+172	4.906219376410612e+188	1.2832757285292212e+179
6	-1.2608308818293039e+154	-1.5171851739610474e+153	-5.555678636173395e+153

simplify3.0ms

Iterations

Iter	Nodes
done	26
1	26
0	22

end0.0ms

sample1.4s

Algorithm

intervals

Results

970.0ms

8493×

body

valid