Average Error: 11.5 → 2.1
Time: 12.2s
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{t - z}\]
↓
\[\frac{x}{\frac{t}{y - z} - \frac{z}{y - z}}\]
\frac{x \cdot \left(y - z\right)}{t - z}
↓
\frac{x}{\frac{t}{y - z} - \frac{z}{y - z}}
double f(double x, double y, double z, double t) {
        double r390780 = x;
        double r390781 = y;
        double r390782 = z;
        double r390783 = r390781 - r390782;
        double r390784 = r390780 * r390783;
        double r390785 = t;
        double r390786 = r390785 - r390782;
        double r390787 = r390784 / r390786;
        return r390787;
}
↓
double f(double x, double y, double z, double t) {
        double r390788 = x;
        double r390789 = t;
        double r390790 = y;
        double r390791 = z;
        double r390792 = r390790 - r390791;
        double r390793 = r390789 / r390792;
        double r390794 = r390791 / r390792;
        double r390795 = r390793 - r390794;
        double r390796 = r390788 / r390795;
        return r390796;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original11.5
Target2.1
Herbie2.1
\[\frac{x}{\frac{t - z}{y - z}}\]

Derivation

  1. Initial program 11.5

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

  3. Applied associate-/l*2.1

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

  5. Applied div-sub2.1

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

  6. Final simplification2.1

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

Reproduce

herbie shell --seed 2019326 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Plot.AreaSpots:renderAreaSpots4D from Chart-1.5.3"
  :precision binary64

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

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