Details

sample60.0ms

Algorithm

intervals

Results

43.0ms

278×

body

valid

simplify24.0ms

Calls

1 calls:

Slowest

23.0ms

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

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 28.1b

localize17.0ms

Local error

Found 2 expressions with local error:

28.1b	(/ (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`

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))

series184.0ms

Calls

2 calls:

Slowest

116.0ms	(/ (fma x.re y.re (* x.im y.im)) (fma y.im y.im (* y.re y.re)))
68.0ms	(fma x.re y.re (* x.im y.im))

simplify1.1s

Calls

31 calls:

Slowest

341.0ms	(/ (* (* (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))))
69.0ms	(/ (* (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))))
45.0ms	(/ (* (cbrt (fma x.re y.re (* x.im y.im))) (cbrt (fma x.re y.re (* x.im y.im)))) 1)
45.0ms	(/ (cbrt (fma x.re y.re (* x.im y.im))) (cbrt (fma y.im y.im (* y.re y.re))))

prune569.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 27.6b

localize9.0ms

Local error

Found 4 expressions with local error:

32.0b	(sqrt (fma y.im y.im (* y.re y.re)))
32.0b	(sqrt (fma y.im y.im (* y.re y.re)))
15.0b	(/ (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))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

4 calls:

Slowest

4.0ms	(/ (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))

series256.0ms

Calls

4 calls:

Slowest

122.0ms	(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
47.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
45.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
41.0ms	(fma x.re y.re (* x.im y.im))

simplify1.9s

Calls

66 calls:

Slowest

295.0ms	(/ (* (* (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)))))
53.0ms	(/ (* (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))))))
50.0ms	(/ (sqrt (fma x.re y.re (* x.im y.im))) (sqrt (cbrt (fma y.im y.im (* y.re y.re)))))
48.0ms	(/ (* (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)))))
46.0ms	(/ (sqrt (fma x.re y.re (* x.im y.im))) (sqrt (sqrt (fma y.im y.im (* y.re y.re)))))

prune1.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 26.2b

localize9.0ms

Local error

Found 4 expressions with local error:

32.0b	(sqrt (fma y.im y.im (* y.re y.re)))
15.0b	(/ (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))
0.0b	(/ (/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re)))) (hypot y.im y.re))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

4 calls:

Slowest

12.0ms	(/ (/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re)))) (hypot y.im 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)))
0.0ms	(fma x.re y.re (* x.im y.im))

series485.0ms

Calls

4 calls:

Slowest

237.0ms	(/ (/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re)))) (hypot y.im y.re))
147.0ms	(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
57.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
44.0ms	(fma x.re y.re (* x.im y.im))

simplify10.7s

Calls

223 calls:

Slowest

423.0ms	(/ (/ (cbrt (fma x.re y.re (* x.im y.im))) (sqrt (cbrt (fma y.im y.im (* y.re y.re))))) (sqrt (hypot y.im y.re)))
356.0ms	(/ (* (* (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)))))
244.0ms	(/ (/ (* (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)))))) (* (cbrt (hypot y.im y.re)) (cbrt (hypot y.im y.re))))
202.0ms	(/ (/ (* (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)))))) (sqrt (hypot y.im y.re)))
185.0ms	(/ (/ (* (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)))))) (* (cbrt (hypot y.im y.re)) (cbrt (hypot y.im y.re))))

prune2.6s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.3b

localize15.0ms

Local error

Found 3 expressions with local error:

15.0b	(/ (fma y.im x.im (* x.re y.re)) (hypot y.im y.re))
0.0b	(/ (* 1 (/ (fma y.im x.im (* x.re y.re)) (hypot y.im y.re))) (hypot y.im y.re))
0.0b	(fma y.im x.im (* x.re y.re))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

3 calls:

Slowest

5.0ms	(/ (* 1 (/ (fma y.im x.im (* x.re y.re)) (hypot y.im y.re))) (hypot y.im y.re))
4.0ms	(/ (fma y.im x.im (* x.re y.re)) (hypot y.im y.re))
0.0ms	(fma y.im x.im (* x.re y.re))

series335.0ms

Calls

3 calls:

Slowest

133.0ms	(/ (* 1 (/ (fma y.im x.im (* x.re y.re)) (hypot y.im y.re))) (hypot y.im y.re))
127.0ms	(/ (fma y.im x.im (* x.re y.re)) (hypot y.im y.re))
75.0ms	(fma y.im x.im (* x.re y.re))

simplify2.0s

Calls

46 calls:

Slowest

713.0ms	(/ (* (* (* 1 (/ (fma y.im x.im (* x.re y.re)) (hypot y.im y.re))) (* 1 (/ (fma y.im x.im (* x.re y.re)) (hypot y.im y.re)))) (* 1 (/ (fma y.im x.im (* x.re y.re)) (hypot y.im y.re)))) (* (* (hypot y.im y.re) (hypot y.im y.re)) (hypot y.im y.re)))
317.0ms	(/ (* (* (fma y.im x.im (* x.re y.re)) (fma y.im x.im (* x.re y.re))) (fma y.im x.im (* x.re y.re))) (* (* (hypot y.im y.re) (hypot y.im y.re)) (hypot y.im y.re)))
203.0ms	(- (log (* 1 (/ (fma y.im x.im (* x.re y.re)) (hypot y.im y.re)))) (log (hypot y.im y.re)))
78.0ms	(/ (* (cbrt (fma y.im x.im (* x.re y.re))) (cbrt (fma y.im x.im (* x.re y.re)))) (* (cbrt (hypot y.im y.re)) (cbrt (hypot y.im y.re))))
44.0ms	(/ (* (cbrt (fma y.im x.im (* x.re y.re))) (cbrt (fma y.im x.im (* x.re y.re)))) 1)

prune839.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 2.8b

regimes299.0ms

Accuracy

25.7% (10.0b remaining)

Error of 12.5b against oracle of 2.5b and baseline of 15.9b

bsearch148.0ms

end0.0ms

sample1.5s

Algorithm

intervals

Results

1.2s

8476×

body

valid