Average Error: 0.0 → 0.0
Time: 15.9s
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 r6731573 = x;
        double r6731574 = y;
        double r6731575 = r6731573 * r6731574;
        double r6731576 = 1.0;
        double r6731577 = r6731573 - r6731576;
        double r6731578 = z;
        double r6731579 = r6731577 * r6731578;
        double r6731580 = r6731575 + r6731579;
        return r6731580;
}
↓
double f(double x, double y, double z) {
        double r6731581 = x;
        double r6731582 = 1.0;
        double r6731583 = r6731581 - r6731582;
        double r6731584 = z;
        double r6731585 = y;
        double r6731586 = r6731585 * r6731581;
        double r6731587 = fma(r6731583, r6731584, r6731586);
        return r6731587;
}

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 2019174 +o rules:numerics
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Drawing:drawTextsR from Chart-1.5.3"
  (+ (* x y) (* (- x 1.0) z)))