Average Error: 0.1 → 0.1
Time: 1.9s
Precision: binary64
\[\left(x \cdot 3\right) \cdot y - z \]
↓
\[\mathsf{fma}\left(x \cdot 3, y, -z\right) \]
(FPCore (x y z) :precision binary64 (- (* (* x 3.0) y) z))
↓
(FPCore (x y z) :precision binary64 (fma (* x 3.0) y (- z)))
double code(double x, double y, double z) {
	return ((x * 3.0) * y) - z;
}
↓
double code(double x, double y, double z) {
	return fma((x * 3.0), y, -z);
}

function code(x, y, z)
	return Float64(Float64(Float64(x * 3.0) * y) - z)
end
↓
function code(x, y, z)
	return fma(Float64(x * 3.0), y, Float64(-z))
end

code[x_, y_, z_] := N[(N[(N[(x * 3.0), $MachinePrecision] * y), $MachinePrecision] - z), $MachinePrecision]
↓
code[x_, y_, z_] := N[(N[(x * 3.0), $MachinePrecision] * y + (-z)), $MachinePrecision]

\left(x \cdot 3\right) \cdot y - z
↓
\mathsf{fma}\left(x \cdot 3, y, -z\right)

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original0.1
Target0.1
Herbie0.1
\[x \cdot \left(3 \cdot y\right) - z \]

Derivation

  1. Initial program 0.1

    \[\left(x \cdot 3\right) \cdot y - z \]

  2. Applied fma-neg_binary640.1

    \[\leadsto \color{blue}{\mathsf{fma}\left(x \cdot 3, y, -z\right)} \]

  3. Final simplification0.1

    \[\leadsto \mathsf{fma}\left(x \cdot 3, y, -z\right) \]

Reproduce

herbie shell --seed 2022131 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, B"
  :precision binary64

  :herbie-target
  (- (* x (* 3.0 y)) z)

  (- (* (* x 3.0) y) z))