Average Error: 11.6 → 1.4
Time: 8.9s
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{t - z}\]
↓
\[\left(x \cdot \frac{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}}{\sqrt[3]{t - z} \cdot \sqrt[3]{t - z}}\right) \cdot \frac{\sqrt[3]{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}} \cdot \sqrt[3]{\sqrt[3]{y - z}}}{\sqrt[3]{t - z}}\]
\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]{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}} \cdot \sqrt[3]{\sqrt[3]{y - z}}}{\sqrt[3]{t - z}}
double f(double x, double y, double z, double t) {
        double r439092 = x;
        double r439093 = y;
        double r439094 = z;
        double r439095 = r439093 - r439094;
        double r439096 = r439092 * r439095;
        double r439097 = t;
        double r439098 = r439097 - r439094;
        double r439099 = r439096 / r439098;
        return r439099;
}
↓
double f(double x, double y, double z, double t) {
        double r439100 = x;
        double r439101 = y;
        double r439102 = z;
        double r439103 = r439101 - r439102;
        double r439104 = cbrt(r439103);
        double r439105 = r439104 * r439104;
        double r439106 = t;
        double r439107 = r439106 - r439102;
        double r439108 = cbrt(r439107);
        double r439109 = r439108 * r439108;
        double r439110 = r439105 / r439109;
        double r439111 = r439100 * r439110;
        double r439112 = cbrt(r439105);
        double r439113 = cbrt(r439104);
        double r439114 = r439112 * r439113;
        double r439115 = r439114 / r439108;
        double r439116 = r439111 * r439115;
        return r439116;
}

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

Original11.6
Target2.2
Herbie1.4
\[\frac{x}{\frac{t - z}{y - z}}\]

Derivation

  1. Initial program 11.6

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

  3. Applied *-un-lft-identity11.6

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

  4. Applied times-frac2.2

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

  5. Simplified2.2

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

  7. Applied add-cube-cbrt3.2

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

  8. Applied add-cube-cbrt2.9

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

  9. Applied times-frac2.9

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

  10. Applied associate-*r*1.1

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

  12. Applied add-cube-cbrt1.2

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

  13. Applied cbrt-prod1.4

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

  14. Final simplification1.4

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

Reproduce

herbie shell --seed 2019208 
(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)))