Average Error: 0.0 → 0
Time: 2.0s
Precision: binary64
Cost: 6656
\[x - y \cdot z \]
↓
\[\mathsf{fma}\left(y, -z, x\right) \]
(FPCore (x y z) :precision binary64 (- x (* y z)))
↓
(FPCore (x y z) :precision binary64 (fma y (- z) x))
double code(double x, double y, double z) {
	return x - (y * z);
}
↓
double code(double x, double y, double z) {
	return fma(y, -z, x);
}

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

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

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

Error

Target

Original0.0
Target0.0
Herbie0
\[\frac{x + y \cdot z}{\frac{x + y \cdot z}{x - y \cdot z}} \]

Derivation

  1. Initial program 0.0

    \[x - y \cdot z \]

  2. Simplified0

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

Alternatives

Alternative 1
Error16.8
Cost1816
\[\begin{array}{l} t_0 := -y \cdot z\\ \mathbf{if}\;y \cdot z \leq -2.05 \cdot 10^{+36}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \cdot z \leq 3.6 \cdot 10^{-118}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \cdot z \leq 6.8 \cdot 10^{-97}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \cdot z \leq 4.3 \cdot 10^{-77}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \cdot z \leq 1.2 \cdot 10^{-23}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \cdot z \leq 6.8 \cdot 10^{+98}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]
Alternative 2
Error0.0
Cost320
\[x - y \cdot z \]
Alternative 3
Error26.6
Cost64
\[x \]

Error

Reproduce

herbie shell --seed 2023010 
(FPCore (x y z)
  :name "Diagrams.Solve.Tridiagonal:solveTriDiagonal from diagrams-solve-0.1, C"
  :precision binary64

  :herbie-target
  (/ (+ x (* y z)) (/ (+ x (* y z)) (- x (* y z))))

  (- x (* y z)))