Average Error: 0.0 → 0.0
Time: 999.0ms
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 r173477 = x;
        double r173478 = y;
        double r173479 = r173478 - r173477;
        double r173480 = z;
        double r173481 = r173479 * r173480;
        double r173482 = r173477 + r173481;
        return r173482;
}
↓
double f(double x, double y, double z) {
        double r173483 = z;
        double r173484 = y;
        double r173485 = x;
        double r173486 = r173484 - r173485;
        double r173487 = fma(r173483, r173486, r173485);
        return r173487;
}

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 2020100 +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)))