Average Error: 0.0 → 0.0
Time: 10.8s
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 r8558475 = x;
        double r8558476 = y;
        double r8558477 = r8558475 * r8558476;
        double r8558478 = 1.0;
        double r8558479 = r8558475 - r8558478;
        double r8558480 = z;
        double r8558481 = r8558479 * r8558480;
        double r8558482 = r8558477 + r8558481;
        return r8558482;
}
↓
double f(double x, double y, double z) {
        double r8558483 = x;
        double r8558484 = y;
        double r8558485 = 1.0;
        double r8558486 = r8558483 - r8558485;
        double r8558487 = z;
        double r8558488 = r8558486 * r8558487;
        double r8558489 = fma(r8558483, r8558484, r8558488);
        return r8558489;
}

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 2019163 +o rules:numerics
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Drawing:drawTextsR from Chart-1.5.3"
  (+ (* x y) (* (- x 1.0) z)))