Average Error: 11.4 → 1.0
Time: 3.7s
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{t - z}\]
↓
\[\left(x \cdot \frac{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}}{\sqrt[3]{t - z} \cdot \sqrt[3]{t - z}}\right) \cdot \frac{\sqrt[3]{y - z}}{\sqrt[3]{t - z}}\]
\frac{x \cdot \left(y - z\right)}{t - z}
↓
\left(x \cdot \frac{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}}{\sqrt[3]{t - z} \cdot \sqrt[3]{t - z}}\right) \cdot \frac{\sqrt[3]{y - z}}{\sqrt[3]{t - z}}
double f(double x, double y, double z, double t) {
        double r656226 = x;
        double r656227 = y;
        double r656228 = z;
        double r656229 = r656227 - r656228;
        double r656230 = r656226 * r656229;
        double r656231 = t;
        double r656232 = r656231 - r656228;
        double r656233 = r656230 / r656232;
        return r656233;
}
↓
double f(double x, double y, double z, double t) {
        double r656234 = x;
        double r656235 = y;
        double r656236 = z;
        double r656237 = r656235 - r656236;
        double r656238 = cbrt(r656237);
        double r656239 = r656238 * r656238;
        double r656240 = t;
        double r656241 = r656240 - r656236;
        double r656242 = cbrt(r656241);
        double r656243 = r656242 * r656242;
        double r656244 = r656239 / r656243;
        double r656245 = r656234 * r656244;
        double r656246 = r656238 / r656242;
        double r656247 = r656245 * r656246;
        return r656247;
}

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

Original11.4
Target2.0
Herbie1.0
\[\frac{x}{\frac{t - z}{y - z}}\]

Derivation

  1. Initial program 11.4

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

  3. Applied *-un-lft-identity11.4

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

  4. Applied times-frac2.0

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

  5. Simplified2.0

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

  7. Applied add-cube-cbrt3.0

    \[\leadsto x \cdot \frac{y - z}{\color{blue}{\left(\sqrt[3]{t - z} \cdot \sqrt[3]{t - z}\right) \cdot \sqrt[3]{t - z}}}\]

  8. Applied add-cube-cbrt2.7

    \[\leadsto x \cdot \frac{\color{blue}{\left(\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}\right) \cdot \sqrt[3]{y - z}}}{\left(\sqrt[3]{t - z} \cdot \sqrt[3]{t - z}\right) \cdot \sqrt[3]{t - z}}\]

  9. Applied times-frac2.7

    \[\leadsto x \cdot \color{blue}{\left(\frac{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}}{\sqrt[3]{t - z} \cdot \sqrt[3]{t - z}} \cdot \frac{\sqrt[3]{y - z}}{\sqrt[3]{t - z}}\right)}\]

  10. Applied associate-*r*1.0

    \[\leadsto \color{blue}{\left(x \cdot \frac{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}}{\sqrt[3]{t - z} \cdot \sqrt[3]{t - z}}\right) \cdot \frac{\sqrt[3]{y - z}}{\sqrt[3]{t - z}}}\]

  11. Final simplification1.0

    \[\leadsto \left(x \cdot \frac{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}}{\sqrt[3]{t - z} \cdot \sqrt[3]{t - z}}\right) \cdot \frac{\sqrt[3]{y - z}}{\sqrt[3]{t - z}}\]

Reproduce

herbie shell --seed 2020034 
(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)))