Average Error: 10.7 → 1.4
Time: 3.1s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{z - a}\]
↓
\[x + y \cdot \frac{z - t}{z - a}\]
x + \frac{y \cdot \left(z - t\right)}{z - a}
↓
x + y \cdot \frac{z - t}{z - a}
double f(double x, double y, double z, double t, double a) {
        double r674777 = x;
        double r674778 = y;
        double r674779 = z;
        double r674780 = t;
        double r674781 = r674779 - r674780;
        double r674782 = r674778 * r674781;
        double r674783 = a;
        double r674784 = r674779 - r674783;
        double r674785 = r674782 / r674784;
        double r674786 = r674777 + r674785;
        return r674786;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r674787 = x;
        double r674788 = y;
        double r674789 = z;
        double r674790 = t;
        double r674791 = r674789 - r674790;
        double r674792 = a;
        double r674793 = r674789 - r674792;
        double r674794 = r674791 / r674793;
        double r674795 = r674788 * r674794;
        double r674796 = r674787 + r674795;
        return r674796;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original10.7
Target1.3
Herbie1.4
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Initial program 10.7

    \[x + \frac{y \cdot \left(z - t\right)}{z - a}\]
  2. Using strategy rm

  3. Applied associate-/l*1.3

    \[\leadsto x + \color{blue}{\frac{y}{\frac{z - a}{z - t}}}\]
  4. Using strategy rm

  5. Applied div-inv1.3

    \[\leadsto x + \frac{y}{\color{blue}{\left(z - a\right) \cdot \frac{1}{z - t}}}\]
  6. Using strategy rm

  7. Applied div-inv1.5

    \[\leadsto x + \color{blue}{y \cdot \frac{1}{\left(z - a\right) \cdot \frac{1}{z - t}}}\]

  8. Simplified1.4

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

  9. Final simplification1.4

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

Reproduce

herbie shell --seed 2020062 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, A"
  :precision binary64

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

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