Average Error: 1.3 → 1.3
Time: 27.9s
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 r25783608 = x;
        double r25783609 = y;
        double r25783610 = z;
        double r25783611 = t;
        double r25783612 = r25783610 - r25783611;
        double r25783613 = a;
        double r25783614 = r25783610 - r25783613;
        double r25783615 = r25783612 / r25783614;
        double r25783616 = r25783609 * r25783615;
        double r25783617 = r25783608 + r25783616;
        return r25783617;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r25783618 = z;
        double r25783619 = t;
        double r25783620 = r25783618 - r25783619;
        double r25783621 = a;
        double r25783622 = r25783618 - r25783621;
        double r25783623 = r25783620 / r25783622;
        double r25783624 = y;
        double r25783625 = x;
        double r25783626 = fma(r25783623, r25783624, r25783625);
        return r25783626;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original1.3
Target1.3
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 2019172 +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)))))