Average Error: 10.9 → 1.3
Time: 19.9s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{z - a}\]
↓
\[x + \frac{y}{\frac{z}{z - t} - \frac{a}{z - t}}\]
x + \frac{y \cdot \left(z - t\right)}{z - a}
↓
x + \frac{y}{\frac{z}{z - t} - \frac{a}{z - t}}
double f(double x, double y, double z, double t, double a) {
        double r31017763 = x;
        double r31017764 = y;
        double r31017765 = z;
        double r31017766 = t;
        double r31017767 = r31017765 - r31017766;
        double r31017768 = r31017764 * r31017767;
        double r31017769 = a;
        double r31017770 = r31017765 - r31017769;
        double r31017771 = r31017768 / r31017770;
        double r31017772 = r31017763 + r31017771;
        return r31017772;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r31017773 = x;
        double r31017774 = y;
        double r31017775 = z;
        double r31017776 = t;
        double r31017777 = r31017775 - r31017776;
        double r31017778 = r31017775 / r31017777;
        double r31017779 = a;
        double r31017780 = r31017779 / r31017777;
        double r31017781 = r31017778 - r31017780;
        double r31017782 = r31017774 / r31017781;
        double r31017783 = r31017773 + r31017782;
        return r31017783;
}

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

Original10.9
Target1.3
Herbie1.3
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Initial program 10.9

    \[x + \frac{y \cdot \left(z - t\right)}{z - a}\]
  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-sub1.3

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

  6. Final simplification1.3

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

Reproduce

herbie shell --seed 2019171 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, A"

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

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