Average Error: 0.0 → 0
Time: 2.2s
Precision: binary64
Cost: 6656
\[x - y \cdot y \]
↓
\[\mathsf{fma}\left(-y, y, x\right) \]
(FPCore (x y) :precision binary64 (- x (* y y)))
↓
(FPCore (x y) :precision binary64 (fma (- y) y x))
double code(double x, double y) {
	return x - (y * y);
}
↓
double code(double x, double y) {
	return fma(-y, y, x);
}

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

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

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

Error

Derivation

  1. Initial program 0.0

    \[x - y \cdot y \]

  2. Simplified0

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

Alternatives

Alternative 1
Error12.3
Cost1556
\[\begin{array}{l} t_0 := -y \cdot y\\ \mathbf{if}\;y \cdot y \leq 8.2 \cdot 10^{-112}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \cdot y \leq 1.9 \cdot 10^{-95}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \cdot y \leq 1.75 \cdot 10^{-26}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \cdot y \leq 9.8 \cdot 10^{+60}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \cdot y \leq 7.4 \cdot 10^{+123}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]
Alternative 2
Error0.0
Cost320
\[x - y \cdot y \]
Alternative 3
Error20.5
Cost64
\[x \]

Error

Reproduce

herbie shell --seed 2023010 
(FPCore (x y)
  :name "Graphics.Rasterific.Shading:$sradialGradientWithFocusShader from Rasterific-0.6.1"
  :precision binary64
  (- x (* y y)))