Average Error: 0.0 → 0.0
Time: 6.9s
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 r13220075 = x;
        double r13220076 = y;
        double r13220077 = r13220076 - r13220075;
        double r13220078 = z;
        double r13220079 = r13220077 * r13220078;
        double r13220080 = r13220075 + r13220079;
        return r13220080;
}
↓
double f(double x, double y, double z) {
        double r13220081 = y;
        double r13220082 = x;
        double r13220083 = r13220081 - r13220082;
        double r13220084 = z;
        double r13220085 = fma(r13220083, r13220084, r13220082);
        return r13220085;
}

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 2019170 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, B"
  (+ x (* (- y x) z)))