Average Error: 0.0 → 0.0
Time: 839.0ms
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 r187404 = x;
        double r187405 = y;
        double r187406 = r187405 - r187404;
        double r187407 = z;
        double r187408 = r187406 * r187407;
        double r187409 = r187404 + r187408;
        return r187409;
}
↓
double f(double x, double y, double z) {
        double r187410 = z;
        double r187411 = y;
        double r187412 = x;
        double r187413 = r187411 - r187412;
        double r187414 = fma(r187410, r187413, r187412);
        return r187414;
}

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 2020062 +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)))