Average Error: 0.0 → 0.0
Time: 28.1s
Precision: 64
\[x \cdot y + \left(x - 1\right) \cdot z\]
↓
\[\mathsf{fma}\left(y, x, z \cdot \left(x - 1\right)\right)\]
x \cdot y + \left(x - 1\right) \cdot z
↓
\mathsf{fma}\left(y, x, z \cdot \left(x - 1\right)\right)
double f(double x, double y, double z) {
        double r8424206 = x;
        double r8424207 = y;
        double r8424208 = r8424206 * r8424207;
        double r8424209 = 1.0;
        double r8424210 = r8424206 - r8424209;
        double r8424211 = z;
        double r8424212 = r8424210 * r8424211;
        double r8424213 = r8424208 + r8424212;
        return r8424213;
}
↓
double f(double x, double y, double z) {
        double r8424214 = y;
        double r8424215 = x;
        double r8424216 = z;
        double r8424217 = 1.0;
        double r8424218 = r8424215 - r8424217;
        double r8424219 = r8424216 * r8424218;
        double r8424220 = fma(r8424214, r8424215, r8424219);
        return r8424220;
}

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

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

  3. Taylor expanded around 0 0.0

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

  4. Simplified0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019200 +o rules:numerics
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Drawing:drawTextsR from Chart-1.5.3"
  (+ (* x y) (* (- x 1.0) z)))