Average Error: 0 → 0
Time: 809.0ms
Precision: binary64
\[x - \frac{y}{4} \]
↓
\[\mathsf{fma}\left(y, -0.25, x\right) \]
(FPCore (x y) :precision binary64 (- x (/ y 4.0)))
↓
(FPCore (x y) :precision binary64 (fma y -0.25 x))
double code(double x, double y) {
	return x - (y / 4.0);
}
↓
double code(double x, double y) {
	return fma(y, -0.25, x);
}

function code(x, y)
	return Float64(x - Float64(y / 4.0))
end
↓
function code(x, y)
	return fma(y, -0.25, x)
end

code[x_, y_] := N[(x - N[(y / 4.0), $MachinePrecision]), $MachinePrecision]
↓
code[x_, y_] := N[(y * -0.25 + x), $MachinePrecision]

x - \frac{y}{4}
↓
\mathsf{fma}\left(y, -0.25, x\right)

Error

Bits error versus x

Bits error versus y

Derivation

  1. Initial program 0

    \[x - \frac{y}{4} \]

  2. Simplified0

    \[\leadsto \color{blue}{\mathsf{fma}\left(y, -0.25, x\right)} \]

  3. Final simplification0

    \[\leadsto \mathsf{fma}\left(y, -0.25, x\right) \]

Reproduce

herbie shell --seed 2022150 
(FPCore (x y)
  :name "Diagrams.Solve.Polynomial:quartForm  from diagrams-solve-0.1, E"
  :precision binary64
  (- x (/ y 4.0)))