Average Error: 12.0 → 2.1
Time: 32.5s
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{t - z}\]
↓
\[x \cdot \frac{y - z}{t - z}\]
\frac{x \cdot \left(y - z\right)}{t - z}
↓
x \cdot \frac{y - z}{t - z}
double f(double x, double y, double z, double t) {
        double r26599829 = x;
        double r26599830 = y;
        double r26599831 = z;
        double r26599832 = r26599830 - r26599831;
        double r26599833 = r26599829 * r26599832;
        double r26599834 = t;
        double r26599835 = r26599834 - r26599831;
        double r26599836 = r26599833 / r26599835;
        return r26599836;
}
↓
double f(double x, double y, double z, double t) {
        double r26599837 = x;
        double r26599838 = y;
        double r26599839 = z;
        double r26599840 = r26599838 - r26599839;
        double r26599841 = t;
        double r26599842 = r26599841 - r26599839;
        double r26599843 = r26599840 / r26599842;
        double r26599844 = r26599837 * r26599843;
        return r26599844;
}

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

Original12.0
Target2.1
Herbie2.1
\[\frac{x}{\frac{t - z}{y - z}}\]

Derivation

  1. Initial program 12.0

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

  3. Applied *-un-lft-identity12.0

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

  4. Applied times-frac2.1

    \[\leadsto \color{blue}{\frac{x}{1} \cdot \frac{y - z}{t - z}}\]

  5. Simplified2.1

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

  6. Final simplification2.1

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

Reproduce

herbie shell --seed 2019165 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Plot.AreaSpots:renderAreaSpots4D from Chart-1.5.3"

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

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