Average Error: 0.0 → 0.0
Time: 7.6s
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 r6335571 = x;
        double r6335572 = y;
        double r6335573 = r6335571 * r6335572;
        double r6335574 = 1.0;
        double r6335575 = r6335571 - r6335574;
        double r6335576 = z;
        double r6335577 = r6335575 * r6335576;
        double r6335578 = r6335573 + r6335577;
        return r6335578;
}
↓
double f(double x, double y, double z) {
        double r6335579 = x;
        double r6335580 = 1.0;
        double r6335581 = r6335579 - r6335580;
        double r6335582 = z;
        double r6335583 = y;
        double r6335584 = r6335583 * r6335579;
        double r6335585 = fma(r6335581, r6335582, r6335584);
        return r6335585;
}

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 2019179 +o rules:numerics
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Drawing:drawTextsR from Chart-1.5.3"
  (+ (* x y) (* (- x 1.0) z)))