Average Error: 0.0 → 0.0
Time: 3.3s
Precision: binary64
\[x + \left(y - x\right) \cdot z \]
↓
\[\mathsf{fma}\left(y, z, x\right) - z \cdot x \]
x + \left(y - x\right) \cdot z
↓
\mathsf{fma}\left(y, z, x\right) - z \cdot x

(FPCore (x y z) :precision binary64 (+ x (* (- y x) z)))
↓
(FPCore (x y z) :precision binary64 (- (fma y z x) (* z x)))
double code(double x, double y, double z) {
	return x + ((y - x) * z);
}
↓
double code(double x, double y, double z) {
	return fma(y, z, x) - (z * x);
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

  1. Initial program 0.0

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

  2. Simplified0.0

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

  3. Taylor expanded in y around 0 0.0

    \[\leadsto \color{blue}{\left(y \cdot z + x\right) - z \cdot x} \]

  4. Applied fma-def_binary640.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2022067 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, B"
  :precision binary64
  (+ x (* (- y x) z)))