Average Error: 0.0 → 0.0
Time: 5.6s
Precision: 64
\[x \cdot y + \left(1.0 - x\right) \cdot z\]
↓
\[\mathsf{fma}\left(1.0 - x, z, x \cdot y\right)\]
x \cdot y + \left(1.0 - x\right) \cdot z
↓
\mathsf{fma}\left(1.0 - x, z, x \cdot y\right)
double f(double x, double y, double z) {
        double r8536783 = x;
        double r8536784 = y;
        double r8536785 = r8536783 * r8536784;
        double r8536786 = 1.0;
        double r8536787 = r8536786 - r8536783;
        double r8536788 = z;
        double r8536789 = r8536787 * r8536788;
        double r8536790 = r8536785 + r8536789;
        return r8536790;
}
↓
double f(double x, double y, double z) {
        double r8536791 = 1.0;
        double r8536792 = x;
        double r8536793 = r8536791 - r8536792;
        double r8536794 = z;
        double r8536795 = y;
        double r8536796 = r8536792 * r8536795;
        double r8536797 = fma(r8536793, r8536794, r8536796);
        return r8536797;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

  1. Initial program 0.0

    \[x \cdot y + \left(1.0 - x\right) \cdot z\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(1.0 - x, z, y \cdot x\right)}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(1.0 - x, z, x \cdot y\right)\]

Reproduce

herbie shell --seed 2019164 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.Backend.Rasterific:$crender from diagrams-rasterific-1.3.1.3"
  (+ (* x y) (* (- 1.0 x) z)))