Details

sample56.0ms

Algorithm

intervals

Results

40.0ms

271×

body

valid

simplify91.0ms

Counts: 1 → 1

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.6b

localize34.0ms

Local error

Found 3 expressions with local error:

24.6b	(/ (- (* x.im y.re) (* x.re y.im)) (fma y.im y.im (* y.re y.re)))
1.0b	(- (* x.im y.re) (* x.re y.im))
0.0b	(fma y.im y.im (* y.re y.re))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
5×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`expm1-log1p-u` `pow1` `associate-/r` `insert-posit16` `log1p-expm1-u` `associate-/l`
2×	`flip3--` `flip--` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `fma-neg` `diff-log` `div-sub` `div-exp` `prod-diff` `fma-udef` `div-inv`

Counts

3 → 61

Calls

3 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))
0.0ms	(fma y.im y.im (* y.re y.re))

series240.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

121.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (fma y.im y.im (* y.re y.re)))
66.0ms	(- (* x.im y.re) (* x.re y.im))
53.0ms	(fma y.im y.im (* y.re y.re))

simplify1.2s

Counts: 70 → 70

prune885.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 24.1b

localize29.0ms

Local error

Found 4 expressions with local error:

27.8b	(sqrt (fma y.im y.im (* y.re y.re)))
27.8b	(sqrt (fma y.im y.im (* y.re y.re)))
16.1b	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
1.0b	(- (* x.im y.re) (* x.re y.im))

rewrite47.0ms

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

29.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
14.0ms	(- (* 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)))

series338.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

162.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
61.0ms	(- (* x.im y.re) (* x.re y.im))
60.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
55.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

simplify897.0ms

Counts: 108 → 108

prune1.4s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 22.0b

localize54.0ms

Local error

Found 4 expressions with local error:

27.8b	(sqrt (fma y.im y.im (* y.re y.re)))
27.8b	(sqrt (fma y.im y.im (* y.re y.re)))
16.1b	(/ (- (* y.re x.im) (* y.im x.re)) (sqrt (fma y.im y.im (* y.re y.re))))
1.0b	(- (* y.re x.im) (* y.im x.re))

rewrite27.0ms

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	(/ (- (* y.re x.im) (* y.im x.re)) (sqrt (fma y.im y.im (* y.re y.re))))
8.0ms	(- (* y.re x.im) (* y.im x.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)))

series322.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

125.0ms	(/ (- (* y.re x.im) (* y.im x.re)) (sqrt (fma y.im y.im (* y.re y.re))))
69.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
68.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
60.0ms	(- (* y.re x.im) (* y.im x.re))

simplify870.0ms

Counts: 108 → 108

prune1.3s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 22.0b

localize26.0ms

Local error

Found 4 expressions with local error:

24.1b	(/ (fma y.im y.im (* y.re y.re)) (- (* x.im y.re) (* x.re y.im)))
1.0b	(- (* x.im y.re) (* x.re y.im))
0.9b	(/ 1 (/ (fma y.im y.im (* y.re y.re)) (- (* x.im y.re) (* x.re y.im))))
0.0b	(fma y.im y.im (* y.re y.re))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 147

Calls

4 calls:

Slowest

28.0ms	(/ 1 (/ (fma y.im y.im (* y.re y.re)) (- (* x.im y.re) (* x.re y.im))))
16.0ms	(- (* x.im y.re) (* x.re y.im))
15.0ms	(/ (fma y.im y.im (* y.re y.re)) (- (* x.im y.re) (* x.re y.im)))
0.0ms	(fma y.im y.im (* y.re y.re))

series421.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

229.0ms	(/ 1 (/ (fma y.im y.im (* y.re y.re)) (- (* x.im y.re) (* x.re y.im))))
86.0ms	(/ (fma y.im y.im (* y.re y.re)) (- (* x.im y.re) (* x.re y.im)))
55.0ms	(fma y.im y.im (* y.re y.re))
51.0ms	(- (* x.im y.re) (* x.re y.im))

simplify2.0s

Counts: 159 → 159

prune1.9s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 14.2b

regimes328.0ms

Accuracy

0% (2.5b remaining)

Error of 16.1b against oracle of 13.6b and baseline of 16.1b

bsearch3.0ms

end0.0ms

sample1.7s

Algorithm

intervals

Results

1.5s

8461×

body

valid