Details

sample46.0ms

Algorithm

intervals

Results

21.0ms

271×

body

valid

simplify8.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	11	15
1	17	13
2	21	13
done	21	13

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.7b

localize11.0ms

Local error

Found 2 expressions with local error:

0.8b	(fma x.re y.re (* x.im y.im))
24.2b	(/ (fma x.re y.re (* x.im y.im)) (fma y.re y.re (* y.im y.im)))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 39

Calls

2 calls:

1.0ms	(fma x.re y.re (* x.im y.im))
11.0ms	(/ (fma x.re y.re (* x.im y.im)) (fma y.re y.re (* y.im y.im)))

series207.0ms

Counts

2 → 6

Calls

2 calls:

56.0ms	(fma x.re y.re (* x.im y.im))
151.0ms	(/ (fma x.re y.re (* x.im y.im)) (fma y.re y.re (* y.im y.im)))

simplify3.1s

Counts

45 → 45

Iterations

Useful iterations: 2 (76.0ms)

Iter	Nodes	Cost
0	65	725
1	101	714
2	250	622
3	726	622
4	2199	622
done	5001	622

prune208.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 16.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (hypot y.re y.im))
0.3b	(* (/ 1 (hypot y.re y.im)) (/ (fma y.re x.re (* y.im x.im)) (hypot y.re y.im)))
0.8b	(fma y.re x.re (* y.im x.im))
15.7b	(/ (fma y.re x.re (* y.im x.im)) (hypot y.re y.im))

rewrite46.0ms

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×	`frac-2neg` `clear-num`
1×	`frac-times` `pow-flip` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `fma-udef` `inv-pow`

Counts

4 → 130

Calls

4 calls:

11.0ms	(/ 1 (hypot y.re y.im))
24.0ms	(* (/ 1 (hypot y.re y.im)) (/ (fma y.re x.re (* y.im x.im)) (hypot y.re y.im)))
0.0ms	(fma y.re x.re (* y.im x.im))
5.0ms	(/ (fma y.re x.re (* y.im x.im)) (hypot y.re y.im))

series518.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(/ 1 (hypot y.re y.im))
275.0ms	(* (/ 1 (hypot y.re y.im)) (/ (fma y.re x.re (* y.im x.im)) (hypot y.re y.im)))
46.0ms	(fma y.re x.re (* y.im x.im))
128.0ms	(/ (fma y.re x.re (* y.im x.im)) (hypot y.re y.im))

simplify3.1s

Counts

142 → 142

Iterations

Useful iterations: done (3.1s)

Iter	Nodes	Cost
0	152	2192
1	349	2009
2	1089	1759
3	3938	1759
done	5000	1726

prune628.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 6.5b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot y.re y.im)
0.1b	(/ (/ (fma y.re x.re (* y.im x.im)) (hypot y.re y.im)) (hypot y.re y.im))
0.8b	(fma y.re x.re (* y.im x.im))
15.7b	(/ (fma y.re x.re (* y.im x.im)) (hypot y.re y.im))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
54×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
16×	`associate-/l*`
11×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r*` `div-inv`
4×	`pow1` `cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u` `add-log-exp`
2×	`frac-2neg` `clear-num`
1×	`hypot-udef` `fma-udef` `associate-/l/`

Counts

4 → 121

Calls

4 calls:

0.0ms	(hypot y.re y.im)
12.0ms	(/ (/ (fma y.re x.re (* y.im x.im)) (hypot y.re y.im)) (hypot y.re y.im))
0.0ms	(fma y.re x.re (* y.im x.im))
6.0ms	(/ (fma y.re x.re (* y.im x.im)) (hypot y.re y.im))

series522.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(hypot y.re y.im)
197.0ms	(/ (/ (fma y.re x.re (* y.im x.im)) (hypot y.re y.im)) (hypot y.re y.im))
80.0ms	(fma y.re x.re (* y.im x.im))
178.0ms	(/ (fma y.re x.re (* y.im x.im)) (hypot y.re y.im))

simplify2.1s

Counts

133 → 133

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	166	2544
1	331	2481
2	717	2298
3	2050	2244
done	5000	2182

prune616.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 6.5b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ 1 (/ (hypot y.re y.im) (fma y.re x.re (* y.im x.im)))) (hypot y.re y.im))
0.2b	(/ 1 (/ (hypot y.re y.im) (fma y.re x.re (* y.im x.im))))
0.8b	(fma y.re x.re (* y.im x.im))
15.8b	(/ (hypot y.re y.im) (fma y.re x.re (* y.im x.im)))

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

480×	`times-frac`
239×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
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×	`frac-2neg` `clear-num`
1×	`pow-flip` `fma-udef` `associate-/l/` `inv-pow`

Counts

4 → 319

Calls

4 calls:

43.0ms	(/ (/ 1 (/ (hypot y.re y.im) (fma y.re x.re (* y.im x.im)))) (hypot y.re y.im))
20.0ms	(/ 1 (/ (hypot y.re y.im) (fma y.re x.re (* y.im x.im))))
1.0ms	(fma y.re x.re (* y.im x.im))
10.0ms	(/ (hypot y.re y.im) (fma y.re x.re (* y.im x.im)))

series661.0ms

Counts

4 → 12

Calls

4 calls:

292.0ms	(/ (/ 1 (/ (hypot y.re y.im) (fma y.re x.re (* y.im x.im)))) (hypot y.re y.im))
176.0ms	(/ 1 (/ (hypot y.re y.im) (fma y.re x.re (* y.im x.im))))
67.0ms	(fma y.re x.re (* y.im x.im))
126.0ms	(/ (hypot y.re y.im) (fma y.re x.re (* y.im x.im)))

simplify1.9s

Counts

331 → 331

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	457	8797
1	1011	7708
2	1898	7150
done	5000	6968

prune904.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 6.5b

regimes363.0ms

Accuracy

35.7% (7.0b remaining)

Error of 13.0b against oracle of 6.0b and baseline of 16.9b

bsearch175.0ms

Steps

Iters	Range		Point
9	5.148798436504621e+206	6.633447625029813e+211	1.0368644268796637e+207
10	-3.1661596442426373e+173	-4.4874797001979404e+160	-1.2861841180889815e+163

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	35
1	24	35
done	24	35

end0.0ms

sample1.7s

Algorithm

intervals

Results

1.2s

8494×

body

valid