Details

sample60.0ms

Algorithm

intervals

Results

40.0ms

271×

body

valid

simplify29.0ms

Counts: 1 → 1

prune34.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.4b

localize22.0ms

Local error

Found 2 expressions with local error:

23.4b	(/ (fma x.re y.re (* x.im y.im)) (fma y.im y.im (* y.re y.re)))
0.0b	(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:

Slowest

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

series173.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

110.0ms	(/ (fma x.re y.re (* x.im y.im)) (fma y.im y.im (* y.re y.re)))
63.0ms	(fma y.im y.im (* y.re y.re))

simplify918.0ms

Counts: 47 → 47

prune525.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 23.0b

localize21.0ms

Local error

Found 4 expressions with local error:

26.2b	(sqrt (fma y.im y.im (* y.re y.re)))
26.2b	(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))))
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))))

rewrite40.0ms

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:

Slowest

21.0ms	(/ (/ (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)))

series421.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

171.0ms	(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
90.0ms	(/ (/ (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))))
82.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
77.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

simplify2.0s

Counts: 266 → 266

prune3.6s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 21.3b

localize29.0ms

Local error

Found 4 expressions with local error:

26.2b	(sqrt (fma y.im y.im (* y.re y.re)))
26.2b	(sqrt (fma y.im y.im (* y.re y.re)))
14.2b	(/ (sqrt (fma y.im y.im (* y.re y.re))) (fma x.re y.re (* x.im y.im)))
0.2b	(/ 1 (/ (sqrt (fma y.im y.im (* y.re y.re))) (fma x.re y.re (* x.im y.im))))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

156×	`times-frac`
98×	`add-sqr-sqrt`
96×	`*-un-lft-identity` `add-cube-cbrt`
54×	`sqrt-prod`
25×	`associate-/r*`
17×	`add-exp-log`
11×	`add-cbrt-cube`
9×	`associate-/l*`
8×	`div-exp`
7×	`pow1`
6×	`div-inv`
4×	`expm1-log1p-u` `cbrt-undiv` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `rec-exp` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `1-exp` `fma-udef` `hypot-def`
1×	`associate-/r/` `pow-flip` `inv-pow`

Counts

4 → 191

Calls

4 calls:

Slowest

21.0ms	(/ 1 (/ (sqrt (fma y.im y.im (* y.re y.re))) (fma x.re y.re (* x.im y.im))))
10.0ms	(/ (sqrt (fma y.im y.im (* y.re y.re))) (fma x.re y.re (* x.im y.im)))
2.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
2.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

series444.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

209.0ms	(/ 1 (/ (sqrt (fma y.im y.im (* y.re y.re))) (fma x.re y.re (* x.im y.im))))
133.0ms	(/ (sqrt (fma y.im y.im (* y.re y.re))) (fma x.re y.re (* x.im y.im)))
51.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
51.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

simplify1.2s

Counts: 203 → 203

prune3.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 21.0b

localize55.0ms

Local error

Found 4 expressions with local error:

26.2b	(sqrt (fma y.im y.im (* y.re y.re)))
14.2b	(/ (hypot y.im y.re) (fma x.re y.re (* x.im y.im)))
0.2b	(/ 1 (/ (hypot y.im y.re) (fma x.re y.re (* x.im y.im))))
0.1b	(/ (/ 1 (/ (hypot y.im y.re) (fma x.re y.re (* x.im y.im)))) (sqrt (fma y.im y.im (* y.re y.re))))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

810×	`times-frac`
391×	`add-sqr-sqrt`
390×	`*-un-lft-identity` `add-cube-cbrt`
138×	`sqrt-prod`
50×	`associate-/l*`
36×	`add-exp-log`
35×	`div-inv`
22×	`associate-/r*` `div-exp`
20×	`add-cbrt-cube`
10×	`cbrt-undiv`
8×	`associate-/r/`
6×	`pow1`
4×	`expm1-log1p-u` `rec-exp` `1-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-udef` `hypot-def` `pow-flip` `inv-pow` `associate-/l/`

Counts

4 → 464

Calls

4 calls:

Slowest

19.0ms	(/ (/ 1 (/ (hypot y.im y.re) (fma x.re y.re (* x.im y.im)))) (sqrt (fma y.im y.im (* y.re y.re))))
6.0ms	(/ 1 (/ (hypot y.im y.re) (fma x.re y.re (* x.im y.im))))
4.0ms	(/ (hypot y.im y.re) (fma x.re y.re (* x.im y.im)))
1.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

series891.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

424.0ms	(/ (/ 1 (/ (hypot y.im y.re) (fma x.re y.re (* x.im y.im)))) (sqrt (fma y.im y.im (* y.re y.re))))
250.0ms	(/ 1 (/ (hypot y.im y.re) (fma x.re y.re (* x.im y.im))))
142.0ms	(/ (hypot y.im y.re) (fma x.re y.re (* x.im y.im)))
76.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

simplify1.1s

Counts: 476 → 476

prune7.3s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 12.5b

regimes310.0ms

Accuracy

0% (3.1b remaining)

Error of 16.8b against oracle of 13.7b and baseline of 16.8b

bsearch2.0ms

end0.0ms

sample1.6s

Algorithm

intervals

Results

1.2s

8474×

body

valid