Details

sample57.0ms

Algorithm

intervals

Results

42.0ms

269×

body

valid

simplify24.0ms

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: 26.3b

localize16.0ms

Local error

Found 2 expressions with local error:

26.3b	(/ (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))

rewrite17.0ms

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

16.0ms	(/ (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))

series182.0ms

Calls

2 calls:

Slowest

113.0ms	(/ (fma x.re y.re (* x.im y.im)) (fma y.im y.im (* y.re y.re)))
69.0ms	(fma x.re y.re (* x.im y.im))

simplify1.2s

Calls

31 calls:

Slowest

424.0ms	(/ (* (* (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))))
93.0ms	(/ (* (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	(/ (sqrt (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)))))
43.0ms	(/ (* (cbrt (fma x.re y.re (* x.im y.im))) (cbrt (fma x.re y.re (* x.im y.im)))) 1)
40.0ms	(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))

prune661.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 25.8b

localize8.0ms

Local error

Found 4 expressions with local error:

27.4b	(sqrt (fma y.im y.im (* y.re y.re)))
27.4b	(sqrt (fma y.im y.im (* y.re y.re)))
16.7b	(/ (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))

rewrite12.0ms

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

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

series376.0ms

Calls

4 calls:

Slowest

159.0ms	(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
74.0ms	(fma x.re y.re (* x.im y.im))
72.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
71.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

simplify1.9s

Calls

68 calls:

Slowest

291.0ms	(/ (* (* (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))))))
58.0ms	(/ (* (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))))))
56.0ms	(/ (* (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)))))

prune1.3s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 24.4b

localize6.0ms

Local error

Found 4 expressions with local error:

27.4b	(sqrt (fma y.im y.im (* y.re y.re)))
16.7b	(/ (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))
0.1b	(/ (/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re)))) (hypot y.im y.re))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

156×	`times-frac`
99×	`add-sqr-sqrt`
98×	`*-un-lft-identity` `add-cube-cbrt`
54×	`sqrt-prod`
28×	`associate-/l*`
15×	`associate-/r*`
12×	`associate-/l/`
11×	`add-cbrt-cube` `add-exp-log`
6×	`div-inv`
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

10.0ms	(/ (/ (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))

series510.0ms

Calls

4 calls:

Slowest

234.0ms	(/ (/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re)))) (hypot y.im y.re))
173.0ms	(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
51.0ms	(fma x.re y.re (* x.im y.im))
51.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

simplify10.7s

Calls

233 calls:

Slowest

691.0ms	(/ (* (* (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)))))
263.0ms	(/ (/ (* (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))))
196.0ms	(/ (/ (* (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)))
193.0ms	(/ (/ (* (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))))) (* (cbrt (hypot y.im y.re)) (cbrt (hypot y.im y.re))))
167.0ms	(/ (/ (* (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))))) (* (cbrt (hypot y.im y.re)) (cbrt (hypot y.im y.re))))

prune2.7s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.9b

localize5.0ms

Local error

Found 4 expressions with local error:

16.7b	(/ (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))
0.0b	(hypot y.im y.re)

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

4 calls:

Slowest

8.0ms	(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re)) (hypot y.im y.re))
4.0ms	(/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re))
0.0ms	(hypot y.im y.re)
0.0ms	(fma x.re y.re (* x.im y.im))

series495.0ms

Calls

4 calls:

Slowest

196.0ms	(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re)) (hypot y.im y.re))
174.0ms	(/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re))
64.0ms	(fma x.re y.re (* x.im y.im))
60.0ms	(hypot y.im y.re)

simplify5.1s

Calls

141 calls:

Slowest

470.0ms	(/ (* (* (/ (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)))
320.0ms	(/ (* (* (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)))
147.0ms	(/ (/ (* (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 (hypot y.im y.re)))
147.0ms	(/ (/ (* (* (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)))
136.0ms	(/ (/ (* (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))))

prune1.6s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.9b

regimes363.0ms

Accuracy

31.5% (7.3b remaining)

Error of 13.3b against oracle of 6.0b and baseline of 16.7b

bsearch148.0ms

end0.0ms

sample1.4s

Algorithm

intervals

Results

1.1s

8487×

body

valid