Average Error: 0.0 → 0.0
Time: 1.9s
Precision: binary64
\[\left(x + y\right) \cdot \left(z + 1\right) \]
↓
\[\mathsf{fma}\left(x, z + 1, \mathsf{fma}\left(y, z, y\right)\right) \]
(FPCore (x y z) :precision binary64 (* (+ x y) (+ z 1.0)))
↓
(FPCore (x y z) :precision binary64 (fma x (+ z 1.0) (fma y z y)))
double code(double x, double y, double z) {
	return (x + y) * (z + 1.0);
}
↓
double code(double x, double y, double z) {
	return fma(x, (z + 1.0), fma(y, z, y));
}

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

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

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

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

  1. Initial program 0.0

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

  2. Applied egg-rr0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(x, z + 1, y \cdot \left(z + 1\right)\right)} \]

  3. Taylor expanded in y around 0 0.0

    \[\leadsto \mathsf{fma}\left(x, z + 1, \color{blue}{y \cdot \left(1 + z\right)}\right) \]

  4. Simplified0.0

    \[\leadsto \mathsf{fma}\left(x, z + 1, \color{blue}{\mathsf{fma}\left(y, z, y\right)}\right) \]

  5. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(x, z + 1, \mathsf{fma}\left(y, z, y\right)\right) \]

Reproduce

herbie shell --seed 2022170 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, G"
  :precision binary64
  (* (+ x y) (+ z 1.0)))