Average Error: 0.0 → 0.0
Time: 2.7s
Precision: 64
\[x \cdot y + \left(x - 1\right) \cdot z\]
↓
\[\mathsf{fma}\left(x, y, \left(x - 1\right) \cdot z\right)\]
x \cdot y + \left(x - 1\right) \cdot z
↓
\mathsf{fma}\left(x, y, \left(x - 1\right) \cdot z\right)
double f(double x, double y, double z) {
        double r139948 = x;
        double r139949 = y;
        double r139950 = r139948 * r139949;
        double r139951 = 1.0;
        double r139952 = r139948 - r139951;
        double r139953 = z;
        double r139954 = r139952 * r139953;
        double r139955 = r139950 + r139954;
        return r139955;
}
↓
double f(double x, double y, double z) {
        double r139956 = x;
        double r139957 = y;
        double r139958 = 1.0;
        double r139959 = r139956 - r139958;
        double r139960 = z;
        double r139961 = r139959 * r139960;
        double r139962 = fma(r139956, r139957, r139961);
        return r139962;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019353 +o rules:numerics
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Drawing:drawTextsR from Chart-1.5.3"
  :precision binary64
  (+ (* x y) (* (- x 1) z)))