Details

sample30.0ms

Algorithm

intervals

Results

20.0ms

267×

body

valid

simplify24.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

24.0ms

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

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.6b

localize18.0ms

Local error

Found 3 expressions with local error:

23.6b	(/ (fma x.re y.re (* x.im y.im)) (fma y.im y.im (* y.re y.re)))
0.5b	(fma x.re y.re (* x.im y.im))
0.0b	(fma y.im y.im (* y.re y.re))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
5×	`add-cbrt-cube` `add-exp-log`
3×	`expm1-log1p-u` `pow1` `associate-/r` `insert-posit16` `log1p-expm1-u` `associate-/l` `add-log-exp`
2×	`fma-udef`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv`

Counts

3 → 52

Calls

3 calls:

Slowest

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

series262.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

132.0ms	(/ (fma x.re y.re (* x.im y.im)) (fma y.im y.im (* y.re y.re)))
65.0ms	(fma x.re y.re (* x.im y.im))
64.0ms	(fma y.im y.im (* y.re y.re))

simplify1.1s

Counts

34 → 61

Calls

34 calls:

Slowest

399.0ms	(/ (* (* (fma x.re y.re (* x.im y.im)) (fma x.re y.re (* x.im y.im))) (fma x.re y.re (* x.im y.im))) (* (* (fma y.im y.im (* y.re y.re)) (fma y.im y.im (* y.re y.re))) (fma y.im y.im (* y.re y.re))))
63.0ms	(/ (* (cbrt (fma x.re y.re (* x.im y.im))) (cbrt (fma x.re y.re (* x.im y.im)))) (* (cbrt (fma y.im y.im (* y.re y.re))) (cbrt (fma y.im y.im (* y.re y.re)))))
48.0ms	(- (log (fma x.re y.re (* x.im y.im))) (log (fma y.im y.im (* y.re y.re))))
35.0ms	(/ (cbrt (fma x.re y.re (* x.im y.im))) (sqrt (fma y.im y.im (* y.re y.re))))
34.0ms	(/ (sqrt (fma x.re y.re (* x.im y.im))) (sqrt (fma y.im y.im (* y.re y.re))))

prune734.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 23.2b

localize55.0ms

Local error

Found 4 expressions with local error:

27.9b	(sqrt (fma y.im y.im (* y.re y.re)))
27.9b	(sqrt (fma y.im y.im (* y.re y.re)))
13.0b	(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
0.5b	(fma x.re y.re (* x.im y.im))

rewrite15.0ms

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

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

series304.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

143.0ms	(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
60.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
58.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
43.0ms	(fma x.re y.re (* x.im y.im))

simplify1.8s

Counts

68 → 99

Calls

68 calls:

Slowest

287.0ms	(/ (* (* (fma x.re y.re (* x.im y.im)) (fma x.re y.re (* x.im y.im))) (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)))) (sqrt (fma y.im y.im (* y.re y.re)))))
96.0ms	(/ (* (cbrt (fma x.re y.re (* x.im y.im))) (cbrt (fma x.re y.re (* x.im y.im)))) (* (cbrt (sqrt (fma y.im y.im (* y.re y.re)))) (cbrt (sqrt (fma y.im y.im (* y.re y.re))))))
65.0ms	(/ (* (cbrt (fma x.re y.re (* x.im y.im))) (cbrt (fma x.re y.re (* x.im y.im)))) (sqrt 1))
59.0ms	(/ (* (cbrt (fma x.re y.re (* x.im y.im))) (cbrt (fma x.re y.re (* x.im y.im)))) (sqrt (* (cbrt (fma y.im y.im (* y.re y.re))) (cbrt (fma y.im y.im (* y.re y.re))))))
52.0ms	(/ (sqrt (fma x.re y.re (* x.im y.im))) (* (cbrt (sqrt (fma y.im y.im (* y.re y.re)))) (cbrt (sqrt (fma y.im y.im (* y.re y.re))))))

prune1.0s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 21.6b

localize38.0ms

Local error

Found 4 expressions with local error:

27.9b	(sqrt (fma y.im y.im (* y.re y.re)))
27.9b	(sqrt (fma y.im y.im (* y.re y.re)))
13.2b	(/ (sqrt (fma y.im y.im (* y.re y.re))) (fma x.re y.re (* x.im y.im)))
0.5b	(fma x.re y.re (* x.im y.im))

rewrite10.0ms

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

6.0ms	(/ (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)))
1.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
0.0ms	(fma x.re y.re (* x.im y.im))

series260.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

113.0ms	(/ (sqrt (fma y.im y.im (* y.re y.re))) (fma x.re y.re (* x.im y.im)))
56.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
47.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
45.0ms	(fma x.re y.re (* x.im y.im))

simplify1.6s

Counts

68 → 99

Calls

68 calls:

Slowest

266.0ms	(/ (* (* (sqrt (fma y.im y.im (* y.re y.re))) (sqrt (fma y.im y.im (* y.re y.re)))) (sqrt (fma y.im y.im (* y.re y.re)))) (* (* (fma x.re y.re (* x.im y.im)) (fma x.re y.re (* x.im y.im))) (fma x.re y.re (* x.im y.im))))
60.0ms	(/ (* (cbrt (sqrt (fma y.im y.im (* y.re y.re)))) (cbrt (sqrt (fma y.im y.im (* y.re y.re))))) (* (cbrt (fma x.re y.re (* x.im y.im))) (cbrt (fma x.re y.re (* x.im y.im)))))
48.0ms	(/ (cbrt (sqrt (fma y.im y.im (* y.re y.re)))) (cbrt (fma x.re y.re (* x.im y.im))))
39.0ms	(/ (sqrt (fma y.im y.im (* y.re y.re))) (fma x.re y.re (* x.im y.im)))
37.0ms	(/ (sqrt (cbrt (fma y.im y.im (* y.re y.re)))) (cbrt (fma x.re y.re (* x.im y.im))))

prune1.2s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 21.6b

localize20.0ms

Local error

Found 4 expressions with local error:

23.3b	(* (fma x.re y.re (* x.im y.im)) (/ 1 (fma y.im y.im (* y.re y.re))))
0.5b	(fma x.re y.re (* x.im y.im))
0.5b	(/ 1 (fma y.im y.im (* y.re y.re)))
0.0b	(fma y.im y.im (* y.re y.re))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 95

Calls

4 calls:

Slowest

17.0ms	(* (fma x.re y.re (* x.im y.im)) (/ 1 (fma y.im y.im (* y.re y.re))))
8.0ms	(/ 1 (fma y.im y.im (* y.re y.re)))
0.0ms	(fma y.im y.im (* y.re y.re))
0.0ms	(fma x.re y.re (* x.im y.im))

series262.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

106.0ms	(* (fma x.re y.re (* x.im y.im)) (/ 1 (fma y.im y.im (* y.re y.re))))
63.0ms	(fma x.re y.re (* x.im y.im))
55.0ms	(/ 1 (fma y.im y.im (* y.re y.re)))
39.0ms	(fma y.im y.im (* y.re y.re))

simplify3.0s

Counts

69 → 107

Calls

69 calls:

Slowest

665.0ms	(* (* (* (fma x.re y.re (* x.im y.im)) (fma x.re y.re (* x.im y.im))) (fma x.re y.re (* x.im y.im))) (* (* (/ 1 (fma y.im y.im (* y.re y.re))) (/ 1 (fma y.im y.im (* y.re y.re)))) (/ 1 (fma y.im y.im (* y.re y.re)))))
338.0ms	(/ (cbrt 1) (sqrt (fma y.im y.im (* y.re y.re))))
189.0ms	(/ (* (* 1 1) 1) (* (* (fma y.im y.im (* y.re y.re)) (fma y.im y.im (* y.re y.re))) (fma y.im y.im (* y.re y.re))))
139.0ms	(* (* (* (fma x.re y.re (* x.im y.im)) (fma x.re y.re (* x.im y.im))) (fma x.re y.re (* x.im y.im))) (/ (* (* 1 1) 1) (* (* (fma y.im y.im (* y.re y.re)) (fma y.im y.im (* y.re y.re))) (fma y.im y.im (* y.re y.re)))))
119.0ms	(* (fma x.re y.re (* x.im y.im)) (/ 1 (fma y.im y.im (* y.re y.re))))

prune1.3s

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 21.6b

regimes360.0ms

Accuracy

0% (2.6b remaining)

Error of 26.1b against oracle of 23.5b and baseline of 26.1b

bsearch2.0ms

end0.0ms

sample1.3s

Algorithm

intervals

Results

1.1s

8449×

body

valid