Average Error: 0.0 → 0.0
Time: 10.2s
Precision: 64
\[x \cdot y + \left(x - 1.0\right) \cdot z\]
↓
\[\mathsf{fma}\left(x, y, \left(x - 1.0\right) \cdot z\right)\]
x \cdot y + \left(x - 1.0\right) \cdot z
↓
\mathsf{fma}\left(x, y, \left(x - 1.0\right) \cdot z\right)
double f(double x, double y, double z) {
        double r7123255 = x;
        double r7123256 = y;
        double r7123257 = r7123255 * r7123256;
        double r7123258 = 1.0;
        double r7123259 = r7123255 - r7123258;
        double r7123260 = z;
        double r7123261 = r7123259 * r7123260;
        double r7123262 = r7123257 + r7123261;
        return r7123262;
}
↓
double f(double x, double y, double z) {
        double r7123263 = x;
        double r7123264 = y;
        double r7123265 = 1.0;
        double r7123266 = r7123263 - r7123265;
        double r7123267 = z;
        double r7123268 = r7123266 * r7123267;
        double r7123269 = fma(r7123263, r7123264, r7123268);
        return r7123269;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

  1. Initial program 0.0

    \[x \cdot y + \left(x - 1.0\right) \cdot z\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \left(x - 1.0\right) \cdot z\right)}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(x, y, \left(x - 1.0\right) \cdot z\right)\]

Reproduce

herbie shell --seed 2019164 +o rules:numerics
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Drawing:drawTextsR from Chart-1.5.3"
  (+ (* x y) (* (- x 1.0) z)))