Average Error: 3.5 → 1.0
Time: 5.1s
Precision: 64
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \cdot 3 \le -1.5357642338074745 \cdot 10^{112}:\\ \;\;\;\;\left(x - \frac{1}{\frac{z \cdot 3}{y}}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\\ \mathbf{elif}\;z \cdot 3 \le 3.513750229300045 \cdot 10^{89}:\\ \;\;\;\;\left(x - \frac{1}{z} \cdot \frac{y}{3}\right) + \frac{\frac{1}{z}}{\frac{y}{\frac{t}{3}}}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{\frac{1}{z}}{\sqrt[3]{3} \cdot \sqrt[3]{3}} \cdot \frac{y}{\sqrt[3]{3}}\right) + \frac{\frac{t}{z \cdot 3}}{y}\\ \end{array}\]
\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}
↓
\begin{array}{l}
\mathbf{if}\;z \cdot 3 \le -1.5357642338074745 \cdot 10^{112}:\\
\;\;\;\;\left(x - \frac{1}{\frac{z \cdot 3}{y}}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\\

\mathbf{elif}\;z \cdot 3 \le 3.513750229300045 \cdot 10^{89}:\\
\;\;\;\;\left(x - \frac{1}{z} \cdot \frac{y}{3}\right) + \frac{\frac{1}{z}}{\frac{y}{\frac{t}{3}}}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r873423 = x;
        double r873424 = y;
        double r873425 = z;
        double r873426 = 3.0;
        double r873427 = r873425 * r873426;
        double r873428 = r873424 / r873427;
        double r873429 = r873423 - r873428;
        double r873430 = t;
        double r873431 = r873427 * r873424;
        double r873432 = r873430 / r873431;
        double r873433 = r873429 + r873432;
        return r873433;
}
↓
double f(double x, double y, double z, double t) {
        double r873434 = z;
        double r873435 = 3.0;
        double r873436 = r873434 * r873435;
        double r873437 = -1.5357642338074745e+112;
        bool r873438 = r873436 <= r873437;
        double r873439 = x;
        double r873440 = 1.0;
        double r873441 = y;
        double r873442 = r873436 / r873441;
        double r873443 = r873440 / r873442;
        double r873444 = r873439 - r873443;
        double r873445 = t;
        double r873446 = r873436 * r873441;
        double r873447 = r873445 / r873446;
        double r873448 = r873444 + r873447;
        double r873449 = 3.513750229300045e+89;
        bool r873450 = r873436 <= r873449;
        double r873451 = r873440 / r873434;
        double r873452 = r873441 / r873435;
        double r873453 = r873451 * r873452;
        double r873454 = r873439 - r873453;
        double r873455 = r873445 / r873435;
        double r873456 = r873441 / r873455;
        double r873457 = r873451 / r873456;
        double r873458 = r873454 + r873457;
        double r873459 = cbrt(r873435);
        double r873460 = r873459 * r873459;
        double r873461 = r873451 / r873460;
        double r873462 = r873441 / r873459;
        double r873463 = r873461 * r873462;
        double r873464 = r873439 - r873463;
        double r873465 = r873445 / r873436;
        double r873466 = r873465 / r873441;
        double r873467 = r873464 + r873466;
        double r873468 = r873450 ? r873458 : r873467;
        double r873469 = r873438 ? r873448 : r873468;
        return r873469;
}

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

Original3.5
Target1.6
Herbie1.0
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z \cdot 3}}{y}\]

Derivation

  1. Split input into 3 regimes

  2. if (* z 3.0) < -1.5357642338074745e+112

    1. Initial program 0.8

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

    3. Applied clear-num0.8

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

    if -1.5357642338074745e+112 < (* z 3.0) < 3.513750229300045e+89

    1. Initial program 5.9

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

    3. Applied associate-/r*1.9

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

    5. Applied *-un-lft-identity1.9

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

    6. Applied times-frac1.9

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

    8. Applied *-un-lft-identity1.9

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

    9. Applied times-frac1.9

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

    10. Applied associate-/l*1.0

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

    if 3.513750229300045e+89 < (* z 3.0)

    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*1.1

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

    5. Applied *-un-lft-identity1.1

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

    6. Applied times-frac1.1

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

    8. Applied add-cube-cbrt1.1

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

    9. Applied *-un-lft-identity1.1

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

    10. Applied times-frac1.2

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

    11. Applied associate-*r*1.2

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

    12. Simplified1.2

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

  4. Final simplification1.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot 3 \le -1.5357642338074745 \cdot 10^{112}:\\ \;\;\;\;\left(x - \frac{1}{\frac{z \cdot 3}{y}}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\\ \mathbf{elif}\;z \cdot 3 \le 3.513750229300045 \cdot 10^{89}:\\ \;\;\;\;\left(x - \frac{1}{z} \cdot \frac{y}{3}\right) + \frac{\frac{1}{z}}{\frac{y}{\frac{t}{3}}}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{\frac{1}{z}}{\sqrt[3]{3} \cdot \sqrt[3]{3}} \cdot \frac{y}{\sqrt[3]{3}}\right) + \frac{\frac{t}{z \cdot 3}}{y}\\ \end{array}\]

Reproduce

herbie shell --seed 2020057 +o rules:numerics
(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))))