Average Error: 0.0 → 0.0
Time: 7.2s
Precision: 64
\[x + \left(y - x\right) \cdot z\]
↓
\[\mathsf{fma}\left(z, y - x, x\right)\]
x + \left(y - x\right) \cdot z
↓
\mathsf{fma}\left(z, y - x, x\right)
double f(double x, double y, double z) {
        double r119049 = x;
        double r119050 = y;
        double r119051 = r119050 - r119049;
        double r119052 = z;
        double r119053 = r119051 * r119052;
        double r119054 = r119049 + r119053;
        return r119054;
}
↓
double f(double x, double y, double z) {
        double r119055 = z;
        double r119056 = y;
        double r119057 = x;
        double r119058 = r119056 - r119057;
        double r119059 = fma(r119055, r119058, r119057);
        return r119059;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019208 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, B"
  :precision binary64
  (+ x (* (- y x) z)))