Details

sample59.0ms

Algorithm

intervals

Results

39.0ms

265×

body

valid

simplify123.0ms

Counts: 1 → 1

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.4b

localize41.0ms

Local error

Found 2 expressions with local error:

27.4b	(/ (- (* x.im y.re) (* x.re y.im)) (fma y.im y.im (* y.re y.re)))
0.6b	(- (* x.im y.re) (* x.re y.im))

rewrite47.0ms

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` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`expm1-log1p-u` `pow1` `flip3--` `insert-posit16` `log1p-expm1-u` `flip--` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `fma-neg` `diff-log` `div-sub` `div-exp` `prod-diff` `div-inv`

Counts

2 → 50

Calls

2 calls:

Slowest

32.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (fma y.im y.im (* y.re y.re)))
15.0ms	(- (* x.im y.re) (* x.re y.im))

series165.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

109.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (fma y.im y.im (* y.re y.re)))
56.0ms	(- (* x.im y.re) (* x.re y.im))

simplify1.2s

Counts: 56 → 56

prune590.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 26.9b

localize43.0ms

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)))
17.4b	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
0.6b	(- (* x.im y.re) (* x.re y.im))

rewrite33.0ms

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` `add-log-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3--` `pow1/2` `fma-udef` `hypot-def` `flip--` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `fma-neg` `diff-log` `div-sub` `div-exp` `prod-diff` `div-inv`

Counts

4 → 96

Calls

4 calls:

Slowest

16.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
13.0ms	(- (* x.im y.re) (* x.re y.im))
1.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
1.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

series390.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

178.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
91.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
70.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
51.0ms	(- (* x.im y.re) (* x.re y.im))

simplify918.0ms

Counts: 108 → 108

prune1.4s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 24.0b

localize40.0ms

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)))
17.5b	(* (- (* x.im y.re) (* x.re y.im)) (/ 1 (sqrt (fma y.im y.im (* y.re y.re)))))
0.6b	(- (* x.im y.re) (* x.re y.im))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
22×	`-un-lft-identity` `times-frac` `associate-r*`
20×	`add-cube-cbrt`
17×	`sqrt-prod`
13×	`add-exp-log`
9×	`add-cbrt-cube`
8×	`pow1`
6×	`add-log-exp`
5×	`unswap-sqr`
4×	`expm1-log1p-u` `prod-exp` `insert-posit16` `log1p-expm1-u`
3×	`flip3--` `associate-l` `flip--`
2×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `associate-*l/` `cbrt-unprod` `fma-udef` `hypot-def`
1×	`cbrt-undiv` `rec-exp` `sub-neg` `fma-neg` `diff-log` `1-exp` `prod-diff` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 105

Calls

4 calls:

Slowest

41.0ms	(* (- (* x.im y.re) (* x.re y.im)) (/ 1 (sqrt (fma y.im y.im (* y.re y.re)))))
10.0ms	(- (* x.im y.re) (* x.re y.im))
1.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
1.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

series317.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

143.0ms	(* (- (* x.im y.re) (* x.re y.im)) (/ 1 (sqrt (fma y.im y.im (* y.re y.re)))))
67.0ms	(- (* x.im y.re) (* x.re y.im))
60.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
48.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

simplify1.3s

Counts: 117 → 117

prune1.4s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 24.0b

localize35.0ms

Local error

Found 3 expressions with local error:

26.6b	(/ (fma y.im y.im (* y.re y.re)) (- (* x.im y.re) (* x.re y.im)))
1.0b	(/ 1 (/ (fma y.im y.im (* y.re y.re)) (- (* x.im y.re) (* x.re y.im))))
0.6b	(- (* x.im y.re) (* x.re y.im))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
55×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
18×	`associate-/r*`
16×	`add-exp-log`
11×	`associate-/r/`
10×	`add-cbrt-cube`
8×	`div-exp`
6×	`flip3--` `div-inv` `flip--` `associate-/l*`
5×	`add-log-exp`
4×	`pow1` `cbrt-undiv`
3×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
2×	`rec-exp` `clear-num` `frac-2neg` `1-exp`
1×	`sub-neg` `fma-neg` `diff-log` `prod-diff` `pow-flip` `inv-pow`

Counts

3 → 136

Calls

3 calls:

Slowest

15.0ms	(/ 1 (/ (fma y.im y.im (* y.re y.re)) (- (* x.im y.re) (* x.re y.im))))
14.0ms	(- (* x.im y.re) (* x.re y.im))
11.0ms	(/ (fma y.im y.im (* y.re y.re)) (- (* x.im y.re) (* x.re y.im)))

series391.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

235.0ms	(/ 1 (/ (fma y.im y.im (* y.re y.re)) (- (* x.im y.re) (* x.re y.im))))
95.0ms	(/ (fma y.im y.im (* y.re y.re)) (- (* x.im y.re) (* x.re y.im)))
61.0ms	(- (* x.im y.re) (* x.re y.im))

simplify1.8s

Counts: 145 → 145

prune1.7s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 14.7b

regimes285.0ms

Accuracy

-7.8% (2.6b remaining)

Error of 16.5b against oracle of 13.8b and baseline of 16.3b

bsearch186.0ms

end0.0ms

sample1.6s

Algorithm

intervals

Results

1.3s

8458×

body

valid