Average Error: 10.0 → 1.1
Time: 18.5s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{z - a}\]
↓
\[x + \frac{y}{\frac{z - a}{z - t}}\]
x + \frac{y \cdot \left(z - t\right)}{z - a}
↓
x + \frac{y}{\frac{z - a}{z - t}}
double f(double x, double y, double z, double t, double a) {
        double r30960773 = x;
        double r30960774 = y;
        double r30960775 = z;
        double r30960776 = t;
        double r30960777 = r30960775 - r30960776;
        double r30960778 = r30960774 * r30960777;
        double r30960779 = a;
        double r30960780 = r30960775 - r30960779;
        double r30960781 = r30960778 / r30960780;
        double r30960782 = r30960773 + r30960781;
        return r30960782;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r30960783 = x;
        double r30960784 = y;
        double r30960785 = z;
        double r30960786 = a;
        double r30960787 = r30960785 - r30960786;
        double r30960788 = t;
        double r30960789 = r30960785 - r30960788;
        double r30960790 = r30960787 / r30960789;
        double r30960791 = r30960784 / r30960790;
        double r30960792 = r30960783 + r30960791;
        return r30960792;
}

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

Original10.0
Target1.1
Herbie1.1
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Initial program 10.0

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

  3. Applied associate-/l*1.1

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

  4. Final simplification1.1

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

Reproduce

herbie shell --seed 2019162 
(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))))