Details

sample31.0ms

Algorithm

intervals

Results

13.0ms

271×

body

valid

simplify6.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	21
2	21
1	17
0	11

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.0b

localize20.0ms

Local error

Found 1 expressions with local error:

22.6b

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

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

1 → 29

Calls

1 calls:

4.0ms

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

series106.0ms

Counts

1 → 3

Calls

1 calls:

106.0ms

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

simplify1.7s

Counts

32 → 32

Iterations

Iter	Nodes
done	5000
4	4396
3	906
2	240
1	95
0	58

prune178.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 22.3b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re)))) (sqrt (fma y.im y.im (* y.re y.re))))
14.2b	(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
27.1b	(sqrt (fma y.im y.im (* y.re y.re)))
27.1b	(sqrt (fma y.im y.im (* y.re y.re)))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

276×	`times-frac`
160×	`add-sqr-sqrt`
158×	`*-un-lft-identity` `add-cube-cbrt`
150×	`sqrt-prod`
25×	`associate-/l*`
12×	`associate-/r*`
11×	`add-cbrt-cube` `add-exp-log`
9×	`div-inv`
6×	`pow1`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-udef` `hypot-def`
1×	`associate-/l/`

Counts

4 → 250

Calls

4 calls:

23.0ms	(/ (/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re)))) (sqrt (fma y.im y.im (* y.re y.re))))
8.0ms	(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
2.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
2.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

series418.0ms

Counts

4 → 12

Calls

4 calls:

151.0ms	(/ (/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re)))) (sqrt (fma y.im y.im (* y.re y.re))))
138.0ms	(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
50.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
78.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

simplify1.4s

Counts

262 → 262

Iterations

Iter	Nodes
done	5000
2	2237
1	565
0	259

prune1.6s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 11.8b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot y.im y.re)
0.0b	(hypot y.im y.re)
0.1b	(/ (/ (fma y.re x.re (* x.im y.im)) (hypot y.im y.re)) (hypot y.im y.re))
14.2b	(/ (fma y.re x.re (* x.im y.im)) (hypot y.im y.re))

rewrite19.0ms

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

Counts

4 → 121

Calls

4 calls:

0.0ms	(hypot y.im y.re)
0.0ms	(hypot y.im y.re)
9.0ms	(/ (/ (fma y.re x.re (* x.im y.im)) (hypot y.im y.re)) (hypot y.im y.re))
6.0ms	(/ (fma y.re x.re (* x.im y.im)) (hypot y.im y.re))

series433.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(hypot y.im y.re)
56.0ms	(hypot y.im y.re)
162.0ms	(/ (/ (fma y.re x.re (* x.im y.im)) (hypot y.im y.re)) (hypot y.im y.re))
159.0ms	(/ (fma y.re x.re (* x.im y.im)) (hypot y.im y.re))

simplify1.0s

Counts

133 → 133

Iterations

Iter	Nodes
done	5000
2	1628
1	355
0	161

prune752.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 6.4b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot y.im y.re)
0.0b	(/ 1 (hypot y.im y.re))
0.3b	(* (/ (fma y.re x.re (* x.im y.im)) (hypot y.im y.re)) (/ 1 (hypot y.im y.re)))
14.2b	(/ (fma y.re x.re (* x.im y.im)) (hypot y.im y.re))

rewrite34.0ms

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` `hypot-udef` `pow-prod-down` `associate-l/` `associate-r/` `un-div-inv` `*-commutative` `pow-flip` `inv-pow`

Counts

4 → 131

Calls

4 calls:

0.0ms	(hypot y.im y.re)
5.0ms	(/ 1 (hypot y.im y.re))
21.0ms	(* (/ (fma y.re x.re (* x.im y.im)) (hypot y.im y.re)) (/ 1 (hypot y.im y.re)))
5.0ms	(/ (fma y.re x.re (* x.im y.im)) (hypot y.im y.re))

series404.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(hypot y.im y.re)
81.0ms	(/ 1 (hypot y.im y.re))
143.0ms	(* (/ (fma y.re x.re (* x.im y.im)) (hypot y.im y.re)) (/ 1 (hypot y.im y.re)))
120.0ms	(/ (fma y.re x.re (* x.im y.im)) (hypot y.im y.re))

simplify1.8s

Counts

143 → 143

Iterations

Iter	Nodes
done	5000
2	2636
1	398
0	153

prune883.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 6.4b

regimes552.0ms

Accuracy

34.8% (7.4b remaining)

Error of 13.4b against oracle of 6.0b and baseline of 17.3b

bsearch142.0ms

Steps

Iters	Range		Point
6	7.997843383138597e+191	8.056208352901572e+192	8.747123436813268e+191
10	-3.959953710600684e+125	-7.632284195501427e+113	-2.0458466692374305e+123

simplify13.0ms

Iterations

Iter	Nodes
done	40
3	40
2	38
1	29
0	22

end0.0ms

sample1.3s

Algorithm

intervals

Results

747.0ms

8463×

body

valid