Average Error: 0.2 → 0.2
Time: 6.3s
Precision: binary64
Cost: 6784
\[\left(x \cdot 3\right) \cdot y - z \]
↓
\[\mathsf{fma}\left(x \cdot 3, y, -z\right) \]
(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

Target

Original0.2
Target0.2
Herbie0.2
\[x \cdot \left(3 \cdot y\right) - z \]

Derivation

  1. Initial program 0.2

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

  2. Simplified0.2

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

    [Start]0.2

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

    fma-neg [=>]0.2

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

  3. Final simplification0.2

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

Alternatives

Alternative 1
Error16.9
Cost584
\[\begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{-53}:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-104}:\\ \;\;\;\;3 \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
Alternative 2
Error16.8
Cost584
\[\begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{-56}:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-104}:\\ \;\;\;\;\left(x \cdot 3\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
Alternative 3
Error16.8
Cost584
\[\begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{-57}:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-104}:\\ \;\;\;\;x \cdot \left(3 \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
Alternative 4
Error0.2
Cost448
\[x \cdot \left(3 \cdot y\right) - z \]
Alternative 5
Error0.2
Cost448
\[\left(x \cdot 3\right) \cdot y - z \]
Alternative 6
Error27.6
Cost128
\[-z \]
Alternative 7
Error62.5
Cost64
\[z \]

Error

Reproduce

herbie shell --seed 2023010 
(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))