Details

sample36.0ms

Algorithm

intervals

Results

24.0ms

265×

body

valid

simplify14.0ms

Counts: 1 → 1

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.6b

localize26.0ms

Local error

Found 2 expressions with local error:

27.6b	(/ (fma x.re y.re (* x.im y.im)) (fma y.im y.im (* y.re y.re)))
0.8b	(fma x.re y.re (* x.im y.im))

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

series163.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

109.0ms	(/ (fma x.re y.re (* x.im y.im)) (fma y.im y.im (* y.re y.re)))
54.0ms	(fma x.re y.re (* x.im y.im))

simplify1.1s

Counts: 47 → 47

prune473.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 27.2b

localize29.0ms

Local error

Found 4 expressions with local error:

31.6b	(sqrt (fma y.im y.im (* y.re y.re)))
31.6b	(sqrt (fma y.im y.im (* y.re y.re)))
15.5b	(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
0.8b	(fma x.re y.re (* x.im y.im))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
21×	`*-un-lft-identity` `add-cube-cbrt`
18×	`times-frac` `sqrt-prod`
6×	`pow1` `associate-/r*` `add-cbrt-cube` `add-exp-log`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`fma-udef` `associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `hypot-def`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv`

Counts

4 → 87

Calls

4 calls:

Slowest

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

series342.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

131.0ms	(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
84.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
67.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
59.0ms	(fma x.re y.re (* x.im y.im))

simplify1.4s

Counts: 99 → 99

prune1.3s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 26.4b

localize27.0ms

Local error

Found 4 expressions with local error:

31.6b	(sqrt (fma y.im y.im (* y.re y.re)))
31.6b	(sqrt (fma y.im y.im (* y.re y.re)))
15.6b	(/ (sqrt (fma y.im y.im (* y.re y.re))) (fma x.re y.re (* x.im y.im)))
0.8b	(fma x.re y.re (* x.im y.im))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
21×	`*-un-lft-identity` `add-cube-cbrt`
18×	`times-frac` `sqrt-prod`
6×	`pow1` `add-cbrt-cube` `add-exp-log` `associate-/l*`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r*` `fma-udef`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `hypot-def`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv`

Counts

4 → 87

Calls

4 calls:

Slowest

5.0ms	(/ (sqrt (fma y.im y.im (* y.re y.re))) (fma x.re y.re (* x.im y.im)))
1.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
1.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
0.0ms	(fma x.re y.re (* x.im y.im))

series352.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

118.0ms	(/ (sqrt (fma y.im y.im (* y.re y.re))) (fma x.re y.re (* x.im y.im)))
85.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
83.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
66.0ms	(fma x.re y.re (* x.im y.im))

simplify739.0ms

Counts: 99 → 99

prune1.2s

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 26.4b

localize38.0ms

Local error

Found 3 expressions with local error:

27.2b	(* (fma x.re y.re (* x.im y.im)) (/ 1 (fma y.im y.im (* y.re y.re))))
0.8b	(fma x.re y.re (* x.im y.im))
0.7b	(/ 1 (fma y.im y.im (* y.re y.re)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
20×	`*-un-lft-identity` `times-frac`
19×	`add-cube-cbrt`
16×	`add-exp-log`
13×	`associate-r`
10×	`add-cbrt-cube`
6×	`pow1`
4×	`div-exp` `prod-exp`
3×	`expm1-log1p-u` `associate-/r` `associate-l` `insert-posit16` `log1p-expm1-u` `associate-/l` `add-log-exp` `unswap-sqr`
2×	`cbrt-undiv` `rec-exp` `1-exp` `cbrt-unprod` `div-inv`
1×	`clear-num` `frac-2neg` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `fma-udef` `pow-flip` `inv-pow`

Counts

3 → 84

Calls

3 calls:

Slowest

13.0ms	(* (fma x.re y.re (* x.im y.im)) (/ 1 (fma y.im y.im (* y.re y.re))))
4.0ms	(/ 1 (fma y.im y.im (* y.re y.re)))
0.0ms	(fma x.re y.re (* x.im y.im))

series222.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

112.0ms	(* (fma x.re y.re (* x.im y.im)) (/ 1 (fma y.im y.im (* y.re y.re))))
61.0ms	(/ 1 (fma y.im y.im (* y.re y.re)))
49.0ms	(fma x.re y.re (* x.im y.im))

simplify851.0ms

Counts: 93 → 93

prune872.0ms

Pruning

11 alts after pruning (7 fresh and 4 done)

Merged error: 26.4b

regimes395.0ms

Accuracy

0% (2.6b remaining)

Error of 25.6b against oracle of 23.0b and baseline of 25.6b

bsearch3.0ms

end0.0ms

sample1.5s

Algorithm

intervals

Results

1.1s

8497×

body

valid