Average Error: 0.0 → 0.0
Time: 882.0ms
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 r136076 = x;
        double r136077 = y;
        double r136078 = r136077 - r136076;
        double r136079 = z;
        double r136080 = r136078 * r136079;
        double r136081 = r136076 + r136080;
        return r136081;
}
↓
double f(double x, double y, double z) {
        double r136082 = z;
        double r136083 = y;
        double r136084 = x;
        double r136085 = r136083 - r136084;
        double r136086 = fma(r136082, r136085, r136084);
        return r136086;
}

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 2020034 +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)))