Average Error: 6.5 → 1.0
Time: 18.0s
Precision: 64
\[x + \frac{y \cdot \left(z - x\right)}{t}\]
↓
\[x + \frac{\sqrt[3]{z - x} \cdot \sqrt[3]{z - x}}{\frac{\sqrt[3]{t} \cdot \sqrt[3]{t}}{\sqrt[3]{y} \cdot \sqrt[3]{y}}} \cdot \frac{\sqrt[3]{z - x}}{\frac{\sqrt[3]{t}}{\sqrt[3]{y}}}\]
x + \frac{y \cdot \left(z - x\right)}{t}
↓
x + \frac{\sqrt[3]{z - x} \cdot \sqrt[3]{z - x}}{\frac{\sqrt[3]{t} \cdot \sqrt[3]{t}}{\sqrt[3]{y} \cdot \sqrt[3]{y}}} \cdot \frac{\sqrt[3]{z - x}}{\frac{\sqrt[3]{t}}{\sqrt[3]{y}}}
double f(double x, double y, double z, double t) {
        double r221842 = x;
        double r221843 = y;
        double r221844 = z;
        double r221845 = r221844 - r221842;
        double r221846 = r221843 * r221845;
        double r221847 = t;
        double r221848 = r221846 / r221847;
        double r221849 = r221842 + r221848;
        return r221849;
}
↓
double f(double x, double y, double z, double t) {
        double r221850 = x;
        double r221851 = z;
        double r221852 = r221851 - r221850;
        double r221853 = cbrt(r221852);
        double r221854 = r221853 * r221853;
        double r221855 = t;
        double r221856 = cbrt(r221855);
        double r221857 = r221856 * r221856;
        double r221858 = y;
        double r221859 = cbrt(r221858);
        double r221860 = r221859 * r221859;
        double r221861 = r221857 / r221860;
        double r221862 = r221854 / r221861;
        double r221863 = r221856 / r221859;
        double r221864 = r221853 / r221863;
        double r221865 = r221862 * r221864;
        double r221866 = r221850 + r221865;
        return r221866;
}

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

Original6.5
Target2.0
Herbie1.0
\[x - \left(x \cdot \frac{y}{t} + \left(-z\right) \cdot \frac{y}{t}\right)\]

Derivation

  1. Initial program 6.5

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

  3. Applied clear-num6.5

    \[\leadsto x + \color{blue}{\frac{1}{\frac{t}{y \cdot \left(z - x\right)}}}\]
  4. Using strategy rm

  5. Applied *-un-lft-identity6.5

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

  6. Applied *-un-lft-identity6.5

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

  7. Applied distribute-lft-out6.5

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

  8. Simplified1.9

    \[\leadsto 1 \cdot \color{blue}{\left(x + \frac{z - x}{\frac{t}{y}}\right)}\]
  9. Using strategy rm

  10. Applied add-cube-cbrt2.5

    \[\leadsto 1 \cdot \left(x + \frac{z - x}{\frac{t}{\color{blue}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}}}}\right)\]

  11. Applied add-cube-cbrt2.6

    \[\leadsto 1 \cdot \left(x + \frac{z - x}{\frac{\color{blue}{\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \sqrt[3]{t}}}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}}}\right)\]

  12. Applied times-frac2.6

    \[\leadsto 1 \cdot \left(x + \frac{z - x}{\color{blue}{\frac{\sqrt[3]{t} \cdot \sqrt[3]{t}}{\sqrt[3]{y} \cdot \sqrt[3]{y}} \cdot \frac{\sqrt[3]{t}}{\sqrt[3]{y}}}}\right)\]

  13. Applied add-cube-cbrt2.7

    \[\leadsto 1 \cdot \left(x + \frac{\color{blue}{\left(\sqrt[3]{z - x} \cdot \sqrt[3]{z - x}\right) \cdot \sqrt[3]{z - x}}}{\frac{\sqrt[3]{t} \cdot \sqrt[3]{t}}{\sqrt[3]{y} \cdot \sqrt[3]{y}} \cdot \frac{\sqrt[3]{t}}{\sqrt[3]{y}}}\right)\]

  14. Applied times-frac1.0

    \[\leadsto 1 \cdot \left(x + \color{blue}{\frac{\sqrt[3]{z - x} \cdot \sqrt[3]{z - x}}{\frac{\sqrt[3]{t} \cdot \sqrt[3]{t}}{\sqrt[3]{y} \cdot \sqrt[3]{y}}} \cdot \frac{\sqrt[3]{z - x}}{\frac{\sqrt[3]{t}}{\sqrt[3]{y}}}}\right)\]

  15. Final simplification1.0

    \[\leadsto x + \frac{\sqrt[3]{z - x} \cdot \sqrt[3]{z - x}}{\frac{\sqrt[3]{t} \cdot \sqrt[3]{t}}{\sqrt[3]{y} \cdot \sqrt[3]{y}}} \cdot \frac{\sqrt[3]{z - x}}{\frac{\sqrt[3]{t}}{\sqrt[3]{y}}}\]

Reproduce

herbie shell --seed 2019304 
(FPCore (x y z t)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, D"
  :precision binary64

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

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