Average Error: 12.0 → 2.3
Time: 14.1s
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 r32151871 = x;
        double r32151872 = y;
        double r32151873 = z;
        double r32151874 = r32151872 - r32151873;
        double r32151875 = r32151871 * r32151874;
        double r32151876 = t;
        double r32151877 = r32151876 - r32151873;
        double r32151878 = r32151875 / r32151877;
        return r32151878;
}
↓
double f(double x, double y, double z, double t) {
        double r32151879 = x;
        double r32151880 = y;
        double r32151881 = z;
        double r32151882 = r32151880 - r32151881;
        double r32151883 = t;
        double r32151884 = r32151883 - r32151881;
        double r32151885 = r32151882 / r32151884;
        double r32151886 = r32151879 * r32151885;
        return r32151886;
}

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
Target2.3
Herbie2.3
\[\frac{x}{\frac{t - z}{y - z}}\]

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-frac2.3

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

  5. Simplified2.3

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

  6. Final simplification2.3

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

Reproduce

herbie shell --seed 2019170 
(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)))