Details

sample57.0ms

Algorithm

intervals

Results

39.0ms

267×

body

valid

simplify29.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

29.0ms

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

prune25.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 22.7b

localize18.0ms

Local error

Found 2 expressions with local error:

22.7b	(/ (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))

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))

series194.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

134.0ms	(/ (fma x.re y.re (* x.im y.im)) (fma y.im y.im (* y.re y.re)))
60.0ms	(fma x.re y.re (* x.im y.im))

simplify1.1s

Counts

31 → 47

Calls

31 calls:

Slowest

422.0ms	(/ (* (* (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))))
72.0ms	(/ (* (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)))))
47.0ms	(- (log (fma x.re y.re (* x.im y.im))) (log (fma y.im y.im (* y.re y.re))))
40.0ms	(/ (cbrt (fma x.re y.re (* x.im y.im))) (cbrt (fma y.im y.im (* y.re y.re))))
35.0ms	(/ (fma x.re y.re (* x.im y.im)) (cbrt (fma y.im y.im (* y.re y.re))))

prune498.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 22.3b

localize30.0ms

Local error

Found 4 expressions with local error:

29.2b	(sqrt (fma y.im y.im (* y.re y.re)))
29.2b	(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))))
0.5b	(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

9.0ms	(/ (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))

series390.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

176.0ms	(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
75.0ms	(fma x.re y.re (* x.im y.im))
70.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
69.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

simplify2.0s

Counts

68 → 99

Calls

68 calls:

Slowest

303.0ms	(/ (* (* (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)))))
77.0ms	(/ (* (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))
65.0ms	(/ (* (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))))))
48.0ms	(/ (cbrt (fma x.re y.re (* x.im y.im))) (sqrt (cbrt (fma y.im y.im (* y.re y.re)))))

prune1.3s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 18.8b

localize16.0ms

Local error

Found 2 expressions with local error:

22.7b	(/ (fma y.im x.im (* y.re x.re)) (fma y.im y.im (* y.re y.re)))
0.3b	(fma y.im x.im (* y.re x.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 y.im x.im (* y.re x.re)) (fma y.im y.im (* y.re y.re)))
0.0ms	(fma y.im x.im (* y.re x.re))

series204.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

132.0ms	(/ (fma y.im x.im (* y.re x.re)) (fma y.im y.im (* y.re y.re)))
71.0ms	(fma y.im x.im (* y.re x.re))

simplify1.2s

Counts

31 → 47

Calls

31 calls:

Slowest

422.0ms	(/ (* (* (fma y.im x.im (* y.re x.re)) (fma y.im x.im (* y.re x.re))) (fma y.im x.im (* y.re x.re))) (* (* (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))))
67.0ms	(/ (* (cbrt (fma y.im x.im (* y.re x.re))) (cbrt (fma y.im x.im (* y.re x.re)))) (* (cbrt (fma y.im y.im (* y.re y.re))) (cbrt (fma y.im y.im (* y.re y.re)))))
54.0ms	(/ (sqrt (fma y.im x.im (* y.re x.re))) (* (cbrt (fma y.im y.im (* y.re y.re))) (cbrt (fma y.im y.im (* y.re y.re)))))
46.0ms	(- (log (fma y.im x.im (* y.re x.re))) (log (fma y.im y.im (* y.re y.re))))
44.0ms	(/ (sqrt (fma y.im x.im (* y.re x.re))) (sqrt (fma y.im y.im (* y.re y.re))))

prune607.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 18.8b

localize24.0ms

Local error

Found 4 expressions with local error:

29.2b	(sqrt (fma y.im y.im (* y.re y.re)))
29.2b	(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))))
0.5b	(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

9.0ms	(/ (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)))
1.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
0.0ms	(fma x.re y.re (* x.im y.im))

series356.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

164.0ms	(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
93.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
55.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
43.0ms	(fma x.re y.re (* x.im y.im))

simplify1.9s

Counts

68 → 99

Calls

68 calls:

Slowest

266.0ms	(/ (* (* (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)))))
62.0ms	(/ (* (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))))))
53.0ms	(/ (* (cbrt (fma x.re y.re (* x.im y.im))) (cbrt (fma x.re y.re (* x.im y.im)))) (sqrt (sqrt (fma y.im y.im (* y.re y.re)))))
50.0ms	(/ (sqrt (fma x.re y.re (* x.im y.im))) (sqrt (sqrt (fma y.im y.im (* y.re y.re)))))
50.0ms	(- (log (fma x.re y.re (* x.im y.im))) (log (sqrt (fma y.im y.im (* y.re y.re)))))

prune1.5s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 18.8b

regimes329.0ms

Accuracy

4% (2.7b remaining)

Error of 25.6b against oracle of 22.8b and baseline of 25.7b

bsearch95.0ms

end0.0ms

sample1.8s

Algorithm

intervals

Results

1.5s

8464×

body

valid