Average Error: 0.0 → 0.0
Time: 9.4s
Precision: 64
\[x + \left(y - x\right) \cdot z\]
↓
\[\mathsf{fma}\left(y - x, z, x\right)\]
x + \left(y - x\right) \cdot z
↓
\mathsf{fma}\left(y - x, z, x\right)
double f(double x, double y, double z) {
        double r8401318 = x;
        double r8401319 = y;
        double r8401320 = r8401319 - r8401318;
        double r8401321 = z;
        double r8401322 = r8401320 * r8401321;
        double r8401323 = r8401318 + r8401322;
        return r8401323;
}
↓
double f(double x, double y, double z) {
        double r8401324 = y;
        double r8401325 = x;
        double r8401326 = r8401324 - r8401325;
        double r8401327 = z;
        double r8401328 = fma(r8401326, r8401327, r8401325);
        return r8401328;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2019163 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, B"
  (+ x (* (- y x) z)))