Average Error: 1.3 → 1.3
Time: 24.5s
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 r28002569 = x;
        double r28002570 = y;
        double r28002571 = z;
        double r28002572 = t;
        double r28002573 = r28002571 - r28002572;
        double r28002574 = a;
        double r28002575 = r28002571 - r28002574;
        double r28002576 = r28002573 / r28002575;
        double r28002577 = r28002570 * r28002576;
        double r28002578 = r28002569 + r28002577;
        return r28002578;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r28002579 = z;
        double r28002580 = t;
        double r28002581 = r28002579 - r28002580;
        double r28002582 = a;
        double r28002583 = r28002579 - r28002582;
        double r28002584 = r28002581 / r28002583;
        double r28002585 = y;
        double r28002586 = x;
        double r28002587 = fma(r28002584, r28002585, r28002586);
        return r28002587;
}

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)))))