Average Error: 3.6 → 2.0
Time: 13.7s
Precision: 64
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
↓
\[\left(x - \frac{-\left(\frac{\sqrt[3]{t} \cdot \sqrt[3]{t}}{z \cdot 3} \cdot \sqrt[3]{1}\right) \cdot \sqrt[3]{t}}{{\left(\sqrt[3]{y}\right)}^{3}}\right) - \frac{y}{z \cdot 3}\]
\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}
↓
\left(x - \frac{-\left(\frac{\sqrt[3]{t} \cdot \sqrt[3]{t}}{z \cdot 3} \cdot \sqrt[3]{1}\right) \cdot \sqrt[3]{t}}{{\left(\sqrt[3]{y}\right)}^{3}}\right) - \frac{y}{z \cdot 3}
double f(double x, double y, double z, double t) {
        double r493721 = x;
        double r493722 = y;
        double r493723 = z;
        double r493724 = 3.0;
        double r493725 = r493723 * r493724;
        double r493726 = r493722 / r493725;
        double r493727 = r493721 - r493726;
        double r493728 = t;
        double r493729 = r493725 * r493722;
        double r493730 = r493728 / r493729;
        double r493731 = r493727 + r493730;
        return r493731;
}
↓
double f(double x, double y, double z, double t) {
        double r493732 = x;
        double r493733 = t;
        double r493734 = cbrt(r493733);
        double r493735 = r493734 * r493734;
        double r493736 = z;
        double r493737 = 3.0;
        double r493738 = r493736 * r493737;
        double r493739 = r493735 / r493738;
        double r493740 = 1.0;
        double r493741 = cbrt(r493740);
        double r493742 = r493739 * r493741;
        double r493743 = r493742 * r493734;
        double r493744 = -r493743;
        double r493745 = y;
        double r493746 = cbrt(r493745);
        double r493747 = 3.0;
        double r493748 = pow(r493746, r493747);
        double r493749 = r493744 / r493748;
        double r493750 = r493732 - r493749;
        double r493751 = r493745 / r493738;
        double r493752 = r493750 - r493751;
        return r493752;
}

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

Original3.6
Target1.6
Herbie2.0
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z \cdot 3}}{y}\]

Derivation

  1. Initial program 3.6

    \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
  2. Using strategy rm

  3. Applied add-cube-cbrt3.8

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

  4. Applied times-frac1.5

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

  6. Applied add-cube-cbrt1.6

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

  7. Applied *-un-lft-identity1.6

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

  8. Applied cbrt-prod1.6

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

  9. Applied times-frac1.6

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

  10. Applied associate-*r*0.9

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

  11. Final simplification2.0

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

Reproduce

herbie shell --seed 2019298 
(FPCore (x y z t)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, H"
  :precision binary64

  :herbie-target
  (+ (- x (/ y (* z 3))) (/ (/ t (* z 3)) y))

  (+ (- x (/ y (* z 3))) (/ t (* (* z 3) y))))