Average Error: 0.0 → 0.0
Time: 5.7s
Precision: 64
\[x + \left(y - x\right) \cdot z\]
↓
\[\mathsf{fma}\left(y - x, z, x\right)\]
x + \left(y - x\right) \cdot z
↓
\mathsf{fma}\left(y - x, z, x\right)
double f(double x, double y, double z) {
        double r3029128 = x;
        double r3029129 = y;
        double r3029130 = r3029129 - r3029128;
        double r3029131 = z;
        double r3029132 = r3029130 * r3029131;
        double r3029133 = r3029128 + r3029132;
        return r3029133;
}
↓
double f(double x, double y, double z) {
        double r3029134 = y;
        double r3029135 = x;
        double r3029136 = r3029134 - r3029135;
        double r3029137 = z;
        double r3029138 = fma(r3029136, r3029137, r3029135);
        return r3029138;
}

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

    \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, z, x\right)}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(y - x, z, x\right)\]

Reproduce

herbie shell --seed 2019156 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, B"
  (+ x (* (- y x) z)))