Average Error: 0.0 → 0.0
Time: 3.0s
Precision: binary64
\[x \cdot y + \left(x - 1\right) \cdot z \]
↓
\[\mathsf{fma}\left(y + z, x, -z\right) \]
(FPCore (x y z) :precision binary64 (+ (* x y) (* (- x 1.0) z)))
↓
(FPCore (x y z) :precision binary64 (fma (+ y z) x (- z)))
double code(double x, double y, double z) {
	return (x * y) + ((x - 1.0) * z);
}
↓
double code(double x, double y, double z) {
	return fma((y + z), x, -z);
}

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

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

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

Error

Derivation

  1. Initial program 0.0

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

  2. Simplified0.0

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

  3. Taylor expanded in x around 0 0.0

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

  4. Simplified0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2022210 
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Drawing:drawTextsR from Chart-1.5.3"
  :precision binary64
  (+ (* x y) (* (- x 1.0) z)))