Average Error: 0.0 → 0.0
Time: 20.1s
Precision: 64
\[x \cdot y + \left(1 - x\right) \cdot z\]
↓
\[\mathsf{fma}\left(y, x, z \cdot \left(1 - x\right)\right)\]
x \cdot y + \left(1 - x\right) \cdot z
↓
\mathsf{fma}\left(y, x, z \cdot \left(1 - x\right)\right)
double f(double x, double y, double z) {
        double r10176941 = x;
        double r10176942 = y;
        double r10176943 = r10176941 * r10176942;
        double r10176944 = 1.0;
        double r10176945 = r10176944 - r10176941;
        double r10176946 = z;
        double r10176947 = r10176945 * r10176946;
        double r10176948 = r10176943 + r10176947;
        return r10176948;
}
↓
double f(double x, double y, double z) {
        double r10176949 = y;
        double r10176950 = x;
        double r10176951 = z;
        double r10176952 = 1.0;
        double r10176953 = r10176952 - r10176950;
        double r10176954 = r10176951 * r10176953;
        double r10176955 = fma(r10176949, r10176950, r10176954);
        return r10176955;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

  1. Initial program 0.0

    \[x \cdot y + \left(1 - x\right) \cdot z\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(1 - x, z, y \cdot x\right)}\]

  3. Taylor expanded around 0 0.0

    \[\leadsto \color{blue}{\left(1 \cdot z + x \cdot y\right) - x \cdot z}\]

  4. Simplified0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(y, x, \left(1 - x\right) \cdot z\right)}\]

  5. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(y, x, z \cdot \left(1 - x\right)\right)\]

Reproduce

herbie shell --seed 2019200 +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)))