Details

sample37.0ms

Algorithm

intervals

Results

25.0ms

267×

body

valid

simplify50.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	80
5	80
4	76
3	56
2	40
1	21
0	11

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.1b

localize34.0ms

Local error

Found 2 expressions with local error:

0.5b	(- (* x.im y.re) (* x.re y.im))
24.1b	(/ (- (* x.im y.re) (* x.re y.im)) (fma y.im y.im (* y.re y.re)))

rewrite30.0ms

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` `associate-/l`
2×	`expm1-log1p-u` `pow1` `flip3--` `insert-posit16` `log1p-expm1-u` `flip--` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `fma-neg` `diff-log` `div-sub` `div-exp` `prod-diff` `div-inv`

Counts

2 → 50

Calls

2 calls:

8.0ms	(- (* x.im y.re) (* x.re y.im))
21.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (fma y.im y.im (* y.re y.re)))

series184.0ms

Counts

2 → 6

Calls

2 calls:

59.0ms	(- (* x.im y.re) (* x.re y.im))
125.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (fma y.im y.im (* y.re y.re)))

simplify498.0ms

Counts

56 → 56

Iterations

Iter	Nodes
done	2000
2	716
1	223
0	90

prune330.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 23.6b

localize33.0ms

Local error

Found 4 expressions with local error:

0.5b	(- (* x.im y.re) (* x.re y.im))
15.9b	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
31.0b	(sqrt (fma y.im y.im (* y.re y.re)))
31.0b	(sqrt (fma y.im y.im (* y.re y.re)))

rewrite33.0ms

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` `add-log-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3--` `pow1/2` `fma-udef` `hypot-def` `flip--` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `fma-neg` `diff-log` `div-sub` `div-exp` `prod-diff` `div-inv`

Counts

4 → 96

Calls

4 calls:

8.0ms	(- (* x.im y.re) (* x.re y.im))
21.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
1.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
1.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

series297.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(- (* x.im y.re) (* x.re y.im))
132.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
58.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
59.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

simplify538.0ms

Counts

108 → 108

Iterations

Iter	Nodes
done	2002
2	759
1	270
0	117

prune700.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 22.4b

localize46.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.im y.re)) (sqrt (fma y.im y.im (* y.re y.re))))
0.5b	(- (* x.im y.re) (* x.re y.im))
15.9b	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.im y.re))
31.0b	(sqrt (fma y.im y.im (* y.re y.re)))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

150×	`times-frac`
91×	`add-sqr-sqrt`
90×	`*-un-lft-identity` `add-cube-cbrt`
45×	`sqrt-prod`
16×	`associate-/l*`
11×	`add-cbrt-cube` `add-exp-log`
9×	`associate-/r*` `div-inv`
6×	`add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `insert-posit16` `log1p-expm1-u`
3×	`div-sub` `associate-/l/`
2×	`clear-num` `frac-2neg` `flip3--` `flip--`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff` `fma-udef` `hypot-def`

Counts

4 → 183

Calls

4 calls:

22.0ms	(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.im y.re)) (sqrt (fma y.im y.im (* y.re y.re))))
12.0ms	(- (* x.im y.re) (* x.re y.im))
25.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.im y.re))
2.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

series443.0ms

Counts

4 → 12

Calls

4 calls:

194.0ms	(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.im y.re)) (sqrt (fma y.im y.im (* y.re y.re))))
54.0ms	(- (* x.im y.re) (* x.re y.im))
127.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.im y.re))
68.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

simplify758.0ms

Counts

195 → 195

Iterations

Iter	Nodes
done	2011
2	1622
1	596
0	258

prune1.2s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 14.9b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot y.im y.re)
0.1b	(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.im y.re)) (hypot y.im y.re))
0.5b	(- (* x.im y.re) (* x.re y.im))
15.9b	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.im y.re))

rewrite48.0ms

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` `add-log-exp`
4×	`expm1-log1p-u` `pow1` `cbrt-undiv` `div-exp` `insert-posit16` `log1p-expm1-u`
3×	`div-sub` `associate-/l/`
2×	`clear-num` `frac-2neg` `flip3--` `flip--`
1×	`hypot-udef` `sub-neg` `fma-neg` `diff-log` `prod-diff`

Counts

4 → 135

Calls

4 calls:

0.0ms	(hypot y.im y.re)
14.0ms	(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.im y.re)) (hypot y.im y.re))
14.0ms	(- (* x.im y.re) (* x.re y.im))
18.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.im y.re))

series418.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(hypot y.im y.re)
147.0ms	(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.im y.re)) (hypot y.im y.re))
50.0ms	(- (* x.im y.re) (* x.re y.im))
159.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.im y.re))

simplify732.0ms

Counts

147 → 147

Iterations

Iter	Nodes
done	2019
2	1479
1	473
0	198

prune752.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 7.1b

regimes418.0ms

Accuracy

37.1% (6.8b remaining)

Error of 13.0b against oracle of 6.2b and baseline of 17.0b

bsearch86.0ms

Steps

Iters	Range		Point
8	5.358739737127594e+138	3.125027152050763e+142	7.75132925369235e+139
6	-1.0929779358508971e+146	-8.954837193749603e+144	-6.603705426560988e+145

simplify3.0ms

Iterations

Iter	Nodes
done	22
1	22
0	19

end0.0ms

sample1.4s

Algorithm

intervals

Results

1.0s

8493×

body

valid