Details

sample70.0ms

Algorithm

intervals

Results

47.0ms

273×

body

valid

simplify38.0ms

Counts: 1 → 1

prune29.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.8b

localize41.0ms

Local error

Found 2 expressions with local error:

24.8b	(/ (fma x.re y.re (* x.im y.im)) (fma y.im y.im (* y.re y.re)))
0.0b	(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))

series167.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

109.0ms	(/ (fma x.re y.re (* x.im y.im)) (fma y.im y.im (* y.re y.re)))
58.0ms	(fma x.re y.re (* x.im y.im))

simplify1.2s

Counts: 47 → 47

prune797.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 24.4b

localize53.0ms

Local error

Found 4 expressions with local error:

28.6b	(sqrt (fma y.im y.im (* y.re y.re)))
28.6b	(sqrt (fma y.im y.im (* y.re y.re)))
15.7b	(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
0.1b	(/ (/ (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))))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 254

Calls

4 calls:

Slowest

13.0ms	(/ (/ (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))))
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)))

series408.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

162.0ms	(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
114.0ms	(/ (/ (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))))
68.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
63.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

simplify1.8s

Counts: 266 → 266

prune4.8s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 21.7b

localize56.0ms

Local error

Found 4 expressions with local error:

28.6b	(sqrt (fma y.im y.im (* y.re y.re)))
28.6b	(sqrt (fma y.im y.im (* y.re y.re)))
15.7b	(/ (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)) (sqrt (fma y.im y.im (* y.re y.re)))) (/ 1 (sqrt (fma y.im y.im (* y.re y.re)))))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

95×	`add-sqr-sqrt`
76×	`times-frac`
53×	`*-un-lft-identity`
47×	`add-cube-cbrt` `sqrt-prod`
28×	`add-exp-log`
22×	`associate-r` `associate-l`
18×	`add-cbrt-cube`
15×	`unswap-sqr`
9×	`div-exp`
8×	`pow1` `prod-exp`
6×	`associate-/r*`
5×	`cbrt-undiv`
4×	`expm1-log1p-u` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`div-inv` `associate-/l*`
2×	`rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `fma-udef` `hypot-def`
1×	`frac-times` `clear-num` `frac-2neg` `pow-prod-down` `associate-l/` `associate-r/` `un-div-inv` `*-commutative`

Counts

4 → 163

Calls

4 calls:

Slowest

29.0ms	(* (/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re)))) (/ 1 (sqrt (fma y.im y.im (* y.re 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)))
1.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

series466.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

187.0ms	(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
135.0ms	(* (/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re)))) (/ 1 (sqrt (fma y.im y.im (* y.re y.re)))))
74.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
69.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

simplify2.9s

Counts: 175 → 175

prune3.1s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 13.2b

localize30.0ms

Local error

Found 4 expressions with local error:

15.7b	(/ (fma y.re x.re (* y.im x.im)) (hypot y.im y.re))
0.1b	(/ (/ (fma y.re x.re (* y.im x.im)) (hypot y.im y.re)) (hypot y.im y.re))
0.0b	(fma y.re x.re (* y.im x.im))
0.0b	(hypot y.im y.re)

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 125

Calls

4 calls:

Slowest

16.0ms	(/ (/ (fma y.re x.re (* y.im x.im)) (hypot y.im y.re)) (hypot y.im y.re))
4.0ms	(/ (fma y.re x.re (* y.im x.im)) (hypot y.im y.re))
0.0ms	(fma y.re x.re (* y.im x.im))
0.0ms	(hypot y.im y.re)

series468.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

191.0ms	(/ (/ (fma y.re x.re (* y.im x.im)) (hypot y.im y.re)) (hypot y.im y.re))
139.0ms	(/ (fma y.re x.re (* y.im x.im)) (hypot y.im y.re))
76.0ms	(fma y.re x.re (* y.im x.im))
63.0ms	(hypot y.im y.re)

simplify1.2s

Counts: 137 → 137

prune2.3s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.9b

regimes574.0ms

Accuracy

35.3% (6.7b remaining)

Error of 12.6b against oracle of 5.9b and baseline of 16.2b

bsearch135.0ms

end0.0ms

sample2.1s

Algorithm

intervals

Results

1.7s

8498×

body

valid