Average Error: 0.0 → 0.0
Time: 1.7s
Precision: binary64
\[\left(1 - x\right) \cdot y + x \cdot z \]
↓
\[\mathsf{fma}\left(x, z - y, y\right) \]
(FPCore (x y z) :precision binary64 (+ (* (- 1.0 x) y) (* x z)))
↓
(FPCore (x y z) :precision binary64 (fma x (- z y) y))
double code(double x, double y, double z) {
	return ((1.0 - x) * y) + (x * z);
}
↓
double code(double x, double y, double z) {
	return fma(x, (z - y), y);
}

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

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

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

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original0.0
Target0.0
Herbie0.0
\[y - x \cdot \left(y - z\right) \]

Derivation

  1. Initial program 0.0

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

  2. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2022131 
(FPCore (x y z)
  :name "Diagrams.Color.HSV:lerp  from diagrams-contrib-1.3.0.5"
  :precision binary64

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

  (+ (* (- 1.0 x) y) (* x z)))