Details

sample55.0ms

Algorithm

intervals

Results

40.0ms

269×

body

valid

simplify29.0ms

Calls

1 calls:

Slowest

29.0ms

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

prune33.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.6b

localize33.0ms

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)))
0.3b	(fma x.re y.re (* x.im y.im))

rewrite10.0ms

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`

Calls

2 calls:

Slowest

9.0ms	(/ (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))

series193.0ms

Calls

2 calls:

Slowest

131.0ms	(/ (fma x.re y.re (* x.im y.im)) (fma y.im y.im (* y.re y.re)))
62.0ms	(fma x.re y.re (* x.im y.im))

simplify1.0s

Calls

31 calls:

Slowest

368.0ms	(/ (* (* (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))))
57.0ms	(/ (* (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)))))
46.0ms	(/ (* (cbrt (fma x.re y.re (* x.im y.im))) (cbrt (fma x.re y.re (* x.im y.im)))) (sqrt (fma y.im y.im (* y.re y.re))))
45.0ms	(- (log (fma x.re y.re (* x.im y.im))) (log (fma y.im y.im (* y.re y.re))))
39.0ms	(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))

prune627.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 27.1b

localize26.0ms

Local error

Found 4 expressions with local error:

30.8b	(sqrt (fma y.im y.im (* y.re y.re)))
30.8b	(sqrt (fma y.im y.im (* y.re y.re)))
17.7b	(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
0.3b	(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` `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`

Calls

4 calls:

Slowest

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

series367.0ms

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))))
71.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
71.0ms	(fma x.re y.re (* x.im y.im))
54.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

simplify2.0s

Calls

68 calls:

Slowest

334.0ms	(/ (* (* (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)))))
95.0ms	(/ (* (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))))))
64.0ms	(/ (* (cbrt (fma x.re y.re (* x.im y.im))) (cbrt (fma x.re y.re (* x.im y.im)))) (sqrt 1))
53.0ms	(/ (sqrt (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))))))
51.0ms	(- (log (fma x.re y.re (* x.im y.im))) (log (sqrt (fma y.im y.im (* y.re y.re)))))

prune1.5s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 25.0b

localize55.0ms

Local error

Found 4 expressions with local error:

30.8b	(sqrt (fma y.im y.im (* y.re y.re)))
17.7b	(/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re))
0.3b	(fma x.re y.re (* x.im y.im))
0.1b	(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re)) (sqrt (fma y.im y.im (* y.re y.re))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

150×	`times-frac`
93×	`add-sqr-sqrt`
92×	`*-un-lft-identity` `add-cube-cbrt`
45×	`sqrt-prod`
19×	`associate-/l*`
12×	`associate-/r*`
11×	`add-cbrt-cube` `add-exp-log`
9×	`div-inv` `associate-/l/`
5×	`pow1`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg`
2×	`fma-udef`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `hypot-def`

Calls

4 calls:

Slowest

15.0ms	(/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re))
10.0ms	(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re)) (sqrt (fma y.im y.im (* y.re y.re))))
3.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
0.0ms	(fma x.re y.re (* x.im y.im))

series514.0ms

Calls

4 calls:

Slowest

204.0ms	(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re)) (sqrt (fma y.im y.im (* y.re y.re))))
183.0ms	(/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re))
67.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
61.0ms	(fma x.re y.re (* x.im y.im))

simplify11.2s

Calls

227 calls:

Slowest

451.0ms	(/ (cbrt (/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re))) (cbrt (sqrt (fma y.im y.im (* y.re y.re)))))
358.0ms	(/ (/ (* (cbrt (fma x.re y.re (* x.im y.im))) (cbrt (fma x.re y.re (* x.im y.im)))) (* (cbrt (hypot y.im y.re)) (cbrt (hypot y.im y.re)))) (* (cbrt (sqrt (fma y.im y.im (* y.re y.re)))) (cbrt (sqrt (fma y.im y.im (* y.re y.re))))))
307.0ms	(/ (* (* (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))) (* (* (hypot y.im y.re) (hypot y.im y.re)) (hypot y.im y.re)))
218.0ms	(/ (/ (* (cbrt (fma x.re y.re (* x.im y.im))) (cbrt (fma x.re y.re (* x.im y.im)))) (* (cbrt (hypot y.im y.re)) (cbrt (hypot y.im y.re)))) (sqrt (* (cbrt (fma y.im y.im (* y.re y.re))) (cbrt (fma y.im y.im (* y.re y.re))))))
185.0ms	(/ (/ (* (cbrt (fma x.re y.re (* x.im y.im))) (cbrt (fma x.re y.re (* x.im y.im)))) (* (cbrt (hypot y.im y.re)) (cbrt (hypot y.im y.re)))) (sqrt (sqrt (fma y.im y.im (* y.re y.re)))))

prune2.7s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 15.9b

localize38.0ms

Local error

Found 3 expressions with local error:

17.7b	(/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re))
0.3b	(fma x.re y.re (* x.im y.im))
0.1b	(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re)) (hypot y.im y.re))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

3 calls:

Slowest

18.0ms	(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re)) (hypot y.im y.re))
9.0ms	(/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re))
0.0ms	(fma x.re y.re (* x.im y.im))

series349.0ms

Calls

3 calls:

Slowest

160.0ms	(/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re))
133.0ms	(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re)) (hypot y.im y.re))
55.0ms	(fma x.re y.re (* x.im y.im))

simplify5.8s

Calls

138 calls:

Slowest

446.0ms	(/ (* (* (/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re)) (/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re))) (/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re))) (* (* (hypot y.im y.re) (hypot y.im y.re)) (hypot y.im y.re)))
240.0ms	(/ (* (* (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))) (* (* (hypot y.im y.re) (hypot y.im y.re)) (hypot y.im y.re)))
222.0ms	(/ (/ (* (cbrt (fma x.re y.re (* x.im y.im))) (cbrt (fma x.re y.re (* x.im y.im)))) (* (cbrt (hypot y.im y.re)) (cbrt (hypot y.im y.re)))) (* (cbrt (hypot y.im y.re)) (cbrt (hypot y.im y.re))))
199.0ms	(/ (/ (* (* (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))) (* (* (hypot y.im y.re) (hypot y.im y.re)) (hypot y.im y.re))) (* (* (hypot y.im y.re) (hypot y.im y.re)) (hypot y.im y.re)))
193.0ms	(/ (/ (* (cbrt (fma x.re y.re (* x.im y.im))) (cbrt (fma x.re y.re (* x.im y.im)))) (sqrt (hypot y.im y.re))) (* (cbrt (hypot y.im y.re)) (cbrt (hypot y.im y.re))))

prune1.6s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 7.1b

regimes349.0ms

Accuracy

35.5% (7.0b remaining)

Error of 12.7b against oracle of 5.7b and baseline of 16.5b

bsearch160.0ms

end0.0ms

sample1.3s

Algorithm

intervals

Results

1.1s

8413×

body

valid