Average Error: 0.0 → 0.0
Time: 9.9s
Precision: 64
\[x \cdot y + \left(1.0 - x\right) \cdot z\]
↓
\[\mathsf{fma}\left(x, y - z, 1.0 \cdot z\right)\]
x \cdot y + \left(1.0 - x\right) \cdot z
↓
\mathsf{fma}\left(x, y - z, 1.0 \cdot z\right)
double f(double x, double y, double z) {
        double r10683662 = x;
        double r10683663 = y;
        double r10683664 = r10683662 * r10683663;
        double r10683665 = 1.0;
        double r10683666 = r10683665 - r10683662;
        double r10683667 = z;
        double r10683668 = r10683666 * r10683667;
        double r10683669 = r10683664 + r10683668;
        return r10683669;
}
↓
double f(double x, double y, double z) {
        double r10683670 = x;
        double r10683671 = y;
        double r10683672 = z;
        double r10683673 = r10683671 - r10683672;
        double r10683674 = 1.0;
        double r10683675 = r10683674 * r10683672;
        double r10683676 = fma(r10683670, r10683673, r10683675);
        return r10683676;
}

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

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

  3. Taylor expanded around 0 0.0

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

  4. Simplified0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019163 +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)))