?

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

↓

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

(FPCore (x y z) :precision binary64 (- (* (* x 3.0) y) z))

↓

(FPCore (x y z) :precision binary64 (fma 3.0 (* y x) (- 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(3.0, (y * x), -z);
}

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

↓

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

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

↓

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

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

↓

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

Original	0.2
Target	0.2
Herbie	0.1

Derivation?

Initial program 0.2
\[\left(x \cdot 3\right) \cdot y - z \]
Taylor expanded in x around 0 0.1
\[\leadsto \color{blue}{3 \cdot \left(y \cdot x\right) + -1 \cdot z} \]

Simplified0.1

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

Proof

[Start]0.1	\[ 3 \cdot \left(y \cdot x\right) + -1 \cdot z \]
mul-1-neg [=>]0.1	\[ 3 \cdot \left(y \cdot x\right) + \color{blue}{\left(-z\right)} \]
fma-def [=>]0.1	\[ \color{blue}{\mathsf{fma}\left(3, y \cdot x, -z\right)} \]

Final simplification0.1
\[\leadsto \mathsf{fma}\left(3, y \cdot x, -z\right) \]

Alternatives

Alternative 1
Error	23.6
Cost	1380

\[\begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{+119} \lor \neg \left(x \leq -1.45 \cdot 10^{+112} \lor \neg \left(x \leq -4 \cdot 10^{+79}\right) \land \left(x \leq -1.35 \cdot 10^{+67} \lor \neg \left(x \leq -4.3 \cdot 10^{+41}\right) \land \left(x \leq -8 \cdot 10^{-98} \lor \neg \left(x \leq -3.4 \cdot 10^{-139}\right) \land x \leq 1.8 \cdot 10^{-117}\right)\right)\right):\\ \;\;\;\;3 \cdot \left(y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 2
Error	23.7
Cost	1376

\[\begin{array}{l} t_0 := 3 \cdot \left(y \cdot x\right)\\ t_1 := x \cdot \left(3 \cdot y\right)\\ \mathbf{if}\;x \leq -4.8 \cdot 10^{+119}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -4 \cdot 10^{+114}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq -1.35 \cdot 10^{+80}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{+67}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq -4.8 \cdot 10^{+41}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{-97}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq -3.4 \cdot 10^{-139}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{-117}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 3
Error	0.2
Cost	448

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

Alternative 4
Error	26.8
Cost	128

\[-z \]

Reproduce?

herbie shell --seed 2023041 
(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))

?

?

Error?

Target

Derivation?

Alternatives

Error

Reproduce?