Details

sample65.0ms

Algorithm

intervals

Results

46.0ms

271×

body

valid

simplify16.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	21
2	21
1	17
0	11

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.6b

localize32.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma x.re y.re (* x.im y.im))
27.6b	(/ (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

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` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `fma-udef` `div-inv`

Counts

2 → 41

Calls

2 calls:

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

series171.0ms

Counts

2 → 6

Calls

2 calls:

50.0ms	(fma x.re y.re (* x.im y.im))
120.0ms	(/ (fma x.re y.re (* x.im y.im)) (fma y.im y.im (* y.re y.re)))

simplify1.6s

Counts

47 → 47

Iterations

Iter	Nodes
4	3206
3	937
2	297
1	105
0	67

prune534.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 27.2b

localize26.0ms

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))))
15.2b	(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
29.2b	(sqrt (fma y.im y.im (* y.re y.re)))
29.2b	(sqrt (fma y.im y.im (* y.re y.re)))

rewrite22.0ms

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` `insert-posit16` `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 → 254

Calls

4 calls:

10.0ms	(/ (/ (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))))
5.0ms	(/ (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)))

series417.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(/ (/ (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))))
168.0ms	(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
73.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
63.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

simplify1.8s

Counts

266 → 266

Iterations

Iter	Nodes
3	4174
2	1184
1	542
0	262

prune3.9s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 13.0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (hypot y.im y.re) (/ (fma x.im y.im (* y.re x.re)) (hypot y.im y.re)))
0.5b	(fma x.im y.im (* y.re x.re))
0.5b	(/ 1 (/ (hypot y.im y.re) (/ (fma x.im y.im (* y.re x.re)) (hypot y.im y.re))))
15.2b	(/ (fma x.im y.im (* y.re x.re)) (hypot y.im y.re))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

480×	`times-frac`
239×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
60×	`associate-/r*`
32×	`add-exp-log`
23×	`div-inv`
20×	`add-cbrt-cube`
19×	`div-exp`
10×	`cbrt-undiv`
9×	`associate-/l*`
6×	`associate-/r/`
5×	`pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`rec-exp` `clear-num` `frac-2neg` `1-exp`
1×	`fma-udef` `pow-flip` `inv-pow`

Counts

4 → 321

Calls

4 calls:

7.0ms	(/ (hypot y.im y.re) (/ (fma x.im y.im (* y.re x.re)) (hypot y.im y.re)))
0.0ms	(fma x.im y.im (* y.re x.re))
9.0ms	(/ 1 (/ (hypot y.im y.re) (/ (fma x.im y.im (* y.re x.re)) (hypot y.im y.re))))
6.0ms	(/ (fma x.im y.im (* y.re x.re)) (hypot y.im y.re))

series688.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(/ (hypot y.im y.re) (/ (fma x.im y.im (* y.re x.re)) (hypot y.im y.re)))
70.0ms	(fma x.im y.im (* y.re x.re))
338.0ms	(/ 1 (/ (hypot y.im y.re) (/ (fma x.im y.im (* y.re x.re)) (hypot y.im y.re))))
153.0ms	(/ (fma x.im y.im (* y.re x.re)) (hypot y.im y.re))

simplify6.9s

Counts

333 → 333

Iterations

Iter	Nodes
2	3041
1	1161
0	442

prune4.3s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.1b

localize26.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (* 1 (/ (fma x.im y.im (* y.re x.re)) (hypot y.im y.re))) (hypot y.im y.re))
0.5b	(fma x.im y.im (* y.re x.re))
15.2b	(/ (fma x.im y.im (* y.re x.re)) (hypot y.im y.re))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-exp-log`
14×	`add-cbrt-cube`
13×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
12×	`times-frac`
8×	`div-exp`
6×	`associate-/r*`
5×	`cbrt-undiv`
4×	`prod-exp` `associate-/l*`
3×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`clear-num` `frac-2neg` `1-exp` `cbrt-unprod` `div-inv`
1×	`associate-*r/` `fma-udef` `associate-/l/`

Counts

3 → 70

Calls

3 calls:

22.0ms	(/ (* 1 (/ (fma x.im y.im (* y.re x.re)) (hypot y.im y.re))) (hypot y.im y.re))
0.0ms	(fma x.im y.im (* y.re x.re))
5.0ms	(/ (fma x.im y.im (* y.re x.re)) (hypot y.im y.re))

series365.0ms

Counts

3 → 9

Calls

3 calls:

152.0ms	(/ (* 1 (/ (fma x.im y.im (* y.re x.re)) (hypot y.im y.re))) (hypot y.im y.re))
53.0ms	(fma x.im y.im (* y.re x.re))
161.0ms	(/ (fma x.im y.im (* y.re x.re)) (hypot y.im y.re))

simplify1.9s

Counts

79 → 79

Iterations

Iter	Nodes
3	3553
2	673
1	229
0	108

prune1.1s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 4.0b

regimes527.0ms

Accuracy

31.9% (7.9b remaining)

Error of 12.9b against oracle of 5.0b and baseline of 16.6b

bsearch154.0ms

Steps

Iters	Range		Point
7	3.7011672301607764e+92	1.3693909217968502e+94	1.3523719097356063e+94
9	-1.3356149600874886e+175	-3.871831131797674e+167	-3.146721494979391e+170

simplify24.0ms

Iterations

Iter	Nodes
7	52
6	52
5	44
4	40
3	38
2	32
1	30
0	25

end0.0ms

sample1.9s

Algorithm

intervals

Results

1.6s

8497×

body

valid