Average Error: 0.0 → 0.0
Time: 4.4s
Precision: binary64
\[\left(x + y\right) \cdot \left(1 - z\right) \]
↓
\[\mathsf{fma}\left(z, \left(-x\right) - y, x + y\right) \]
(FPCore (x y z) :precision binary64 (* (+ x y) (- 1.0 z)))
↓
(FPCore (x y z) :precision binary64 (fma z (- (- x) y) (+ x y)))
double code(double x, double y, double z) {
	return (x + y) * (1.0 - z);
}
↓
double code(double x, double y, double z) {
	return fma(z, (-x - y), (x + y));
}

function code(x, y, z)
	return Float64(Float64(x + y) * Float64(1.0 - z))
end
↓
function code(x, y, z)
	return fma(z, Float64(Float64(-x) - y), Float64(x + y))
end

code[x_, y_, z_] := N[(N[(x + y), $MachinePrecision] * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]
↓
code[x_, y_, z_] := N[(z * N[((-x) - y), $MachinePrecision] + N[(x + y), $MachinePrecision]), $MachinePrecision]

\left(x + y\right) \cdot \left(1 - z\right)
↓
\mathsf{fma}\left(z, \left(-x\right) - y, x + y\right)

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

  1. Initial program 0.0

    \[\left(x + y\right) \cdot \left(1 - z\right) \]

  2. Applied egg-rr0.0

    \[\leadsto \color{blue}{\left(x + y\right) + \left(-z\right) \cdot \left(x + y\right)} \]

  3. Applied egg-rr0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(z, -\left(x + y\right), x + y\right)} \]

  4. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(z, \left(-x\right) - y, x + y\right) \]

Reproduce

herbie shell --seed 2022160 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, H"
  :precision binary64
  (* (+ x y) (- 1.0 z)))