Average Error: 0.0 → 0.0
Time: 2.2s
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 r199943 = x;
        double r199944 = y;
        double r199945 = r199943 * r199944;
        double r199946 = 1.0;
        double r199947 = r199946 - r199943;
        double r199948 = z;
        double r199949 = r199947 * r199948;
        double r199950 = r199945 + r199949;
        return r199950;
}
↓
double f(double x, double y, double z) {
        double r199951 = x;
        double r199952 = y;
        double r199953 = 1.0;
        double r199954 = r199953 - r199951;
        double r199955 = z;
        double r199956 = r199954 * r199955;
        double r199957 = fma(r199951, r199952, r199956);
        return r199957;
}

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 2020035 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.Backend.Rasterific:$crender from diagrams-rasterific-1.3.1.3"
  :precision binary64
  (+ (* x y) (* (- 1 x) z)))