Details

sample26.0ms

Algorithm

intervals

Results

12.0ms

271×

body

valid

simplify9.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (2.0ms)

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

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.4b

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma x.re y.re (* x.im y.im))
27.9b	(/ (fma x.re y.re (* x.im y.im)) (fma y.re y.re (* y.im y.im)))

rewrite7.0ms

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:

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

series172.0ms

Counts

2 → 6

Calls

2 calls:

64.0ms	(fma x.re y.re (* x.im y.im))
108.0ms	(/ (fma x.re y.re (* x.im y.im)) (fma y.re y.re (* y.im y.im)))

simplify2.7s

Counts

45 → 45

Iterations

Useful iterations: 2 (48.0ms)

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

prune170.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 17.7b

localize18.0ms

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 (* y.im x.im)) (hypot y.re y.im)))
17.2b	(/ (fma y.re x.re (* y.im x.im)) (hypot y.re y.im))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 107

Calls

4 calls:

0.0ms	(hypot y.re y.im)
0.0ms	(hypot y.re y.im)
31.0ms	(* (/ 1 (hypot y.re y.im)) (/ (fma y.re x.re (* y.im x.im)) (hypot y.re y.im)))
5.0ms	(/ (fma y.re x.re (* y.im x.im)) (hypot y.re y.im))

series487.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(hypot y.re y.im)
78.0ms	(hypot y.re y.im)
217.0ms	(* (/ 1 (hypot y.re y.im)) (/ (fma y.re x.re (* y.im x.im)) (hypot y.re y.im)))
132.0ms	(/ (fma y.re x.re (* y.im x.im)) (hypot y.re y.im))

simplify3.3s

Counts

119 → 119

Iterations

Useful iterations: done (3.3s)

Iter	Nodes	Cost
0	140	1913
1	332	1779
2	1054	1543
3	3765	1543
done	5000	1510

prune439.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 7.7b

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 (* y.im x.im)) (hypot y.re y.im)) (hypot y.re y.im))
17.2b	(/ (fma y.re x.re (* y.im x.im)) (hypot y.re y.im))

rewrite32.0ms

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

Counts

4 → 121

Calls

4 calls:

0.0ms	(hypot y.re y.im)
0.0ms	(hypot y.re y.im)
17.0ms	(/ (/ (fma y.re x.re (* y.im x.im)) (hypot y.re y.im)) (hypot y.re y.im))
9.0ms	(/ (fma y.re x.re (* y.im x.im)) (hypot y.re y.im))

series507.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(hypot y.re y.im)
66.0ms	(hypot y.re y.im)
183.0ms	(/ (/ (fma y.re x.re (* y.im x.im)) (hypot y.re y.im)) (hypot y.re y.im))
187.0ms	(/ (fma y.re x.re (* y.im x.im)) (hypot y.re y.im))

simplify2.3s

Counts

133 → 133

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	161	2502
1	326	2439
2	698	2262
3	1998	2208
done	5000	2146

prune522.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 7.7b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot y.re y.im)
0.1b	(/ (/ (fma y.im x.im (* y.re x.re)) (hypot y.re y.im)) (hypot y.re y.im))
0.8b	(fma y.im x.im (* y.re x.re))
17.2b	(/ (fma y.im x.im (* y.re x.re)) (hypot y.re y.im))

rewrite41.0ms

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)
19.0ms	(/ (/ (fma y.im x.im (* y.re x.re)) (hypot y.re y.im)) (hypot y.re y.im))
1.0ms	(fma y.im x.im (* y.re x.re))
15.0ms	(/ (fma y.im x.im (* y.re x.re)) (hypot y.re y.im))

series440.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(hypot y.re y.im)
165.0ms	(/ (/ (fma y.im x.im (* y.re x.re)) (hypot y.re y.im)) (hypot y.re y.im))
53.0ms	(fma y.im x.im (* y.re x.re))
167.0ms	(/ (fma y.im x.im (* y.re x.re)) (hypot y.re y.im))

simplify2.3s

Counts

133 → 133

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	166	2544
1	332	2481
2	713	2298
3	2041	2244
done	5001	2182

prune552.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 3.3b

regimes356.0ms

Accuracy

26.8% (10.4b remaining)

Error of 13.0b against oracle of 2.6b and baseline of 16.8b

bsearch81.0ms

Steps

Iters	Range		Point
9	3.809265903266752e+94	8.632889513685064e+99	1.7771313591381173e+97
8	-3.105252758098682e+141	-1.049810621057281e+138	-2.3480882486675907e+140

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	33
1	20	33
done	20	33

end0.0ms

sample1.1s

Algorithm

intervals

Results

701.0ms

8500×

body

valid