Details

sample30.0ms

Algorithm

intervals

Results

15.0ms

277×

body

valid

simplify7.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	21
2	21
1	17
0	11

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.1b

localize29.0ms

Local error

Found 2 expressions with local error:

0.5b	(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)))

rewrite7.0ms

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))
6.0ms	(/ (fma x.re y.re (* x.im y.im)) (fma y.im y.im (* y.re y.re)))

series182.0ms

Counts

2 → 6

Calls

2 calls:

57.0ms	(fma x.re y.re (* x.im y.im))
125.0ms	(/ (fma x.re y.re (* x.im y.im)) (fma y.im y.im (* y.re y.re)))

simplify1.7s

Counts

45 → 45

Iterations

Iter	Nodes
done	5002
3	2442
2	402
1	104
0	65

prune213.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 24.3b

localize22.0ms

Local error

Found 4 expressions with local error:

0.5b	(fma x.re y.re (* x.im y.im))
16.6b	(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
29.1b	(sqrt (fma y.im y.im (* y.re y.re)))
29.1b	(sqrt (fma y.im y.im (* y.re y.re)))

rewrite12.0ms

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` `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 → 83

Calls

4 calls:

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

series327.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(fma x.re y.re (* x.im y.im))
154.0ms	(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
58.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
64.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

simplify1.1s

Counts

95 → 95

Iterations

Iter	Nodes
done	5000
3	1259
2	375
1	138
0	90

prune476.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 21.7b

localize25.0ms

Local error

Found 3 expressions with local error:

0.4b	(/ 1 (/ (fma y.im y.im (* y.re y.re)) (fma x.re y.re (* x.im y.im))))
0.5b	(fma x.re y.re (* x.im y.im))
24.4b	(/ (fma y.im y.im (* y.re y.re)) (fma x.re y.re (* x.im y.im)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
53×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
16×	`associate-/r*` `add-exp-log`
10×	`add-cbrt-cube`
8×	`div-exp`
6×	`div-inv` `associate-/l*`
4×	`pow1` `cbrt-undiv`
3×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`rec-exp` `clear-num` `frac-2neg` `1-exp`
1×	`associate-/r/` `fma-udef` `pow-flip` `inv-pow`

Counts

3 → 117

Calls

3 calls:

9.0ms	(/ 1 (/ (fma y.im y.im (* y.re y.re)) (fma x.re y.re (* x.im y.im))))
0.0ms	(fma x.re y.re (* x.im y.im))
5.0ms	(/ (fma y.im y.im (* y.re y.re)) (fma x.re y.re (* x.im y.im)))

series330.0ms

Counts

3 → 9

Calls

3 calls:

182.0ms	(/ 1 (/ (fma y.im y.im (* y.re y.re)) (fma x.re y.re (* x.im y.im))))
56.0ms	(fma x.re y.re (* x.im y.im))
92.0ms	(/ (fma y.im y.im (* y.re y.re)) (fma x.re y.re (* x.im y.im)))

simplify1.2s

Counts

126 → 126

Iterations

Iter	Nodes
done	5002
2	1806
1	366
0	163

prune817.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 14.3b

localize18.0ms

Local error

Found 3 expressions with local error:

0.2b	(* (/ 1 (hypot y.im y.re)) (/ (fma y.im x.im (* y.re x.re)) (hypot y.im y.re)))
0.8b	(fma y.im x.im (* y.re x.re))
16.6b	(/ (fma y.im x.im (* y.re x.re)) (hypot y.im y.re))

rewrite26.0ms

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:

19.0ms	(* (/ 1 (hypot y.im y.re)) (/ (fma y.im x.im (* y.re x.re)) (hypot y.im y.re)))
0.0ms	(fma y.im x.im (* y.re x.re))
4.0ms	(/ (fma y.im x.im (* y.re x.re)) (hypot y.im y.re))

series358.0ms

Counts

3 → 9

Calls

3 calls:

195.0ms	(* (/ 1 (hypot y.im y.re)) (/ (fma y.im x.im (* y.re x.re)) (hypot y.im y.re)))
42.0ms	(fma y.im x.im (* y.re x.re))
121.0ms	(/ (fma y.im x.im (* y.re x.re)) (hypot y.im y.re))

simplify1.8s

Counts

106 → 106

Iterations

Iter	Nodes
done	5000
2	2408
1	382
0	138

prune634.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 5.1b

regimes494.0ms

Accuracy

18.3% (9.6b remaining)

Error of 14.8b against oracle of 5.3b and baseline of 17.0b

bsearch46.0ms

Steps

Iters	Range		Point
9	5.46867282370483e+131	8.999209221712282e+139	7.643741764178764e+138

simplify3.0ms

Iterations

Iter	Nodes
done	19
1	19
0	15

end0.0ms

sample1.4s

Algorithm

intervals

Results

1.0s

8465×

body

valid