Average Error: 0.0 → 0
Time: 859.0ms
Precision: binary64
\[x \cdot \left(y + 1\right) \]
↓
\[\mathsf{fma}\left(x, y, x\right) \]
(FPCore (x y) :precision binary64 (* x (+ y 1.0)))
↓
(FPCore (x y) :precision binary64 (fma x y x))
double code(double x, double y) {
	return x * (y + 1.0);
}
↓
double code(double x, double y) {
	return fma(x, y, x);
}

function code(x, y)
	return Float64(x * Float64(y + 1.0))
end
↓
function code(x, y)
	return fma(x, y, x)
end

code[x_, y_] := N[(x * N[(y + 1.0), $MachinePrecision]), $MachinePrecision]
↓
code[x_, y_] := N[(x * y + x), $MachinePrecision]

x \cdot \left(y + 1\right)
↓
\mathsf{fma}\left(x, y, x\right)

Error

Bits error versus x

Bits error versus y

Target

Original0.0
Target0.0
Herbie0
\[x + x \cdot y \]

Derivation

  1. Initial program 0.0

    \[x \cdot \left(y + 1\right) \]

  2. Simplified0

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

  3. Final simplification0

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

Reproduce

herbie shell --seed 2022150 
(FPCore (x y)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, B"
  :precision binary64

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

  (* x (+ y 1.0)))