Average Error: 0.0 → 0.0
Time: 5.9s
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 r152670 = x;
        double r152671 = y;
        double r152672 = r152671 - r152670;
        double r152673 = z;
        double r152674 = r152672 * r152673;
        double r152675 = r152670 + r152674;
        return r152675;
}
↓
double f(double x, double y, double z) {
        double r152676 = z;
        double r152677 = y;
        double r152678 = x;
        double r152679 = r152677 - r152678;
        double r152680 = fma(r152676, r152679, r152678);
        return r152680;
}

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 2019303 +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)))