Average Error: 0.0 → 0.0
Time: 5.3s
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 r187801 = x;
        double r187802 = y;
        double r187803 = r187802 - r187801;
        double r187804 = z;
        double r187805 = r187803 * r187804;
        double r187806 = r187801 + r187805;
        return r187806;
}
↓
double f(double x, double y, double z) {
        double r187807 = z;
        double r187808 = y;
        double r187809 = x;
        double r187810 = r187808 - r187809;
        double r187811 = fma(r187807, r187810, r187809);
        return r187811;
}

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 2019325 +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)))