Average Error: 0.0 → 0.0
Time: 16.0s
Precision: 64
\[x \cdot y + \left(1 - x\right) \cdot z\]
↓
\[\mathsf{fma}\left(x, y, \left(1 - x\right) \cdot z\right)\]
x \cdot y + \left(1 - x\right) \cdot z
↓
\mathsf{fma}\left(x, y, \left(1 - x\right) \cdot z\right)
double f(double x, double y, double z) {
        double r160072 = x;
        double r160073 = y;
        double r160074 = r160072 * r160073;
        double r160075 = 1.0;
        double r160076 = r160075 - r160072;
        double r160077 = z;
        double r160078 = r160076 * r160077;
        double r160079 = r160074 + r160078;
        return r160079;
}
↓
double f(double x, double y, double z) {
        double r160080 = x;
        double r160081 = y;
        double r160082 = 1.0;
        double r160083 = r160082 - r160080;
        double r160084 = z;
        double r160085 = r160083 * r160084;
        double r160086 = fma(r160080, r160081, r160085);
        return r160086;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019198 +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)))