Average Error: 0.0 → 0.0
Time: 18.1s
Precision: 64
\[x \cdot y + \left(x - 1\right) \cdot z\]
↓
\[\mathsf{fma}\left(x - 1, z, y \cdot x\right)\]
x \cdot y + \left(x - 1\right) \cdot z
↓
\mathsf{fma}\left(x - 1, z, y \cdot x\right)
double f(double x, double y, double z) {
        double r6207092 = x;
        double r6207093 = y;
        double r6207094 = r6207092 * r6207093;
        double r6207095 = 1.0;
        double r6207096 = r6207092 - r6207095;
        double r6207097 = z;
        double r6207098 = r6207096 * r6207097;
        double r6207099 = r6207094 + r6207098;
        return r6207099;
}
↓
double f(double x, double y, double z) {
        double r6207100 = x;
        double r6207101 = 1.0;
        double r6207102 = r6207100 - r6207101;
        double r6207103 = z;
        double r6207104 = y;
        double r6207105 = r6207104 * r6207100;
        double r6207106 = fma(r6207102, r6207103, r6207105);
        return r6207106;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

  1. Initial program 0.0

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

  2. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019171 +o rules:numerics
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Drawing:drawTextsR from Chart-1.5.3"
  (+ (* x y) (* (- x 1.0) z)))