Average Error: 0.0 → 0.0
Time: 1.8s
Precision: binary64
\[x + \left(y - x\right) \cdot z \]
↓
\[\mathsf{fma}\left(-x, z, \mathsf{fma}\left(y, z, x\right)\right) \]
(FPCore (x y z) :precision binary64 (+ x (* (- y x) z)))
↓
(FPCore (x y z) :precision binary64 (fma (- x) z (fma y z x)))
double code(double x, double y, double z) {
	return x + ((y - x) * z);
}
↓
double code(double x, double y, double z) {
	return fma(-x, z, fma(y, z, x));
}

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

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

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

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

  1. Initial program 0.0

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

  2. Simplified0.0

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

  3. Taylor expanded in y around 0 0.0

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

  4. Applied egg-rr0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2022153 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, B"
  :precision binary64
  (+ x (* (- y x) z)))