Average Error: 1.3 → 1.3
Time: 26.0s
Precision: 64
\[x + y \cdot \frac{z - t}{z - a}\]
↓
\[\mathsf{fma}\left(\frac{z - t}{z - a}, y, x\right)\]
x + y \cdot \frac{z - t}{z - a}
↓
\mathsf{fma}\left(\frac{z - t}{z - a}, y, x\right)
double f(double x, double y, double z, double t, double a) {
        double r26371749 = x;
        double r26371750 = y;
        double r26371751 = z;
        double r26371752 = t;
        double r26371753 = r26371751 - r26371752;
        double r26371754 = a;
        double r26371755 = r26371751 - r26371754;
        double r26371756 = r26371753 / r26371755;
        double r26371757 = r26371750 * r26371756;
        double r26371758 = r26371749 + r26371757;
        return r26371758;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r26371759 = z;
        double r26371760 = t;
        double r26371761 = r26371759 - r26371760;
        double r26371762 = a;
        double r26371763 = r26371759 - r26371762;
        double r26371764 = r26371761 / r26371763;
        double r26371765 = y;
        double r26371766 = x;
        double r26371767 = fma(r26371764, r26371765, r26371766);
        return r26371767;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original1.3
Target1.2
Herbie1.3
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Initial program 1.3

    \[x + y \cdot \frac{z - t}{z - a}\]

  2. Simplified1.3

    \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{z - a}, y, x\right)}\]

  3. Final simplification1.3

    \[\leadsto \mathsf{fma}\left(\frac{z - t}{z - a}, y, x\right)\]

Reproduce

herbie shell --seed 2019163 +o rules:numerics
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, A"

  :herbie-target
  (+ x (/ y (/ (- z a) (- z t))))

  (+ x (* y (/ (- z t) (- z a)))))