Average Error: 3.7 → 0.9
Time: 3.8s
Precision: 64
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -2.171528493507656670283271706692623069358 \cdot 10^{-57} \lor \neg \left(z \le 1.594003072049920579576627778635528875032 \cdot 10^{76}\right):\\ \;\;\;\;\left(x - \frac{\frac{y}{z}}{3}\right) + \frac{\frac{t}{z \cdot 3}}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{1} \cdot \frac{\frac{y}{3}}{z}\right) + \frac{1}{z} \cdot \frac{\frac{t}{3}}{y}\\ \end{array}\]
\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}
↓
\begin{array}{l}
\mathbf{if}\;z \le -2.171528493507656670283271706692623069358 \cdot 10^{-57} \lor \neg \left(z \le 1.594003072049920579576627778635528875032 \cdot 10^{76}\right):\\
\;\;\;\;\left(x - \frac{\frac{y}{z}}{3}\right) + \frac{\frac{t}{z \cdot 3}}{y}\\

\mathbf{else}:\\
\;\;\;\;\left(x - \frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{1} \cdot \frac{\frac{y}{3}}{z}\right) + \frac{1}{z} \cdot \frac{\frac{t}{3}}{y}\\

\end{array}
double f(double x, double y, double z, double t) {
        double r798293 = x;
        double r798294 = y;
        double r798295 = z;
        double r798296 = 3.0;
        double r798297 = r798295 * r798296;
        double r798298 = r798294 / r798297;
        double r798299 = r798293 - r798298;
        double r798300 = t;
        double r798301 = r798297 * r798294;
        double r798302 = r798300 / r798301;
        double r798303 = r798299 + r798302;
        return r798303;
}
↓
double f(double x, double y, double z, double t) {
        double r798304 = z;
        double r798305 = -2.1715284935076567e-57;
        bool r798306 = r798304 <= r798305;
        double r798307 = 1.5940030720499206e+76;
        bool r798308 = r798304 <= r798307;
        double r798309 = !r798308;
        bool r798310 = r798306 || r798309;
        double r798311 = x;
        double r798312 = y;
        double r798313 = r798312 / r798304;
        double r798314 = 3.0;
        double r798315 = r798313 / r798314;
        double r798316 = r798311 - r798315;
        double r798317 = t;
        double r798318 = r798304 * r798314;
        double r798319 = r798317 / r798318;
        double r798320 = r798319 / r798312;
        double r798321 = r798316 + r798320;
        double r798322 = 1.0;
        double r798323 = cbrt(r798322);
        double r798324 = r798323 * r798323;
        double r798325 = r798324 / r798322;
        double r798326 = r798312 / r798314;
        double r798327 = r798326 / r798304;
        double r798328 = r798325 * r798327;
        double r798329 = r798311 - r798328;
        double r798330 = r798322 / r798304;
        double r798331 = r798317 / r798314;
        double r798332 = r798331 / r798312;
        double r798333 = r798330 * r798332;
        double r798334 = r798329 + r798333;
        double r798335 = r798310 ? r798321 : r798334;
        return r798335;
}

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

Original3.7
Target1.6
Herbie0.9
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z \cdot 3}}{y}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -2.1715284935076567e-57 or 1.5940030720499206e+76 < z

    1. Initial program 0.6

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

    3. Applied associate-/r*1.0

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

    5. Applied *-un-lft-identity1.0

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

    6. Applied times-frac1.0

      \[\leadsto \left(x - \color{blue}{\frac{1}{z} \cdot \frac{y}{3}}\right) + \frac{\frac{t}{z \cdot 3}}{y}\]
    7. Using strategy rm

    8. Applied associate-*r/1.0

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

    9. Simplified1.0

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

    if -2.1715284935076567e-57 < z < 1.5940030720499206e+76

    1. Initial program 9.1

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

    3. Applied associate-/r*2.7

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

    5. Applied *-un-lft-identity2.7

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

    6. Applied times-frac2.7

      \[\leadsto \left(x - \color{blue}{\frac{1}{z} \cdot \frac{y}{3}}\right) + \frac{\frac{t}{z \cdot 3}}{y}\]
    7. Using strategy rm

    8. Applied *-un-lft-identity2.7

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

    9. Applied add-cube-cbrt2.7

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

    10. Applied times-frac2.7

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

    11. Applied associate-*l*2.7

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

    12. Simplified2.7

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

    14. Applied *-un-lft-identity2.7

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

    15. Applied *-un-lft-identity2.7

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

    16. Applied times-frac2.7

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

    17. Applied times-frac0.7

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

    18. Simplified0.7

      \[\leadsto \left(x - \frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{1} \cdot \frac{\frac{y}{3}}{z}\right) + \color{blue}{\frac{1}{z}} \cdot \frac{\frac{t}{3}}{y}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -2.171528493507656670283271706692623069358 \cdot 10^{-57} \lor \neg \left(z \le 1.594003072049920579576627778635528875032 \cdot 10^{76}\right):\\ \;\;\;\;\left(x - \frac{\frac{y}{z}}{3}\right) + \frac{\frac{t}{z \cdot 3}}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{1} \cdot \frac{\frac{y}{3}}{z}\right) + \frac{1}{z} \cdot \frac{\frac{t}{3}}{y}\\ \end{array}\]

Reproduce

herbie shell --seed 2020001 
(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))))