Average Error: 3.7 → 0.6
Time: 13.9s
Precision: 64
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \cdot 3 \le -650340682119.03857421875:\\ \;\;\;\;\left(x - \frac{\frac{y}{z}}{3}\right) + \frac{\frac{t}{z \cdot 3}}{y}\\ \mathbf{elif}\;z \cdot 3 \le 5.531250664679463187888177829139671400627 \cdot 10^{-59}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{1}{z \cdot 3} \cdot \frac{t}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \left(3 \cdot y\right)}\\ \end{array}\]
\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 -650340682119.03857421875:\\
\;\;\;\;\left(x - \frac{\frac{y}{z}}{3}\right) + \frac{\frac{t}{z \cdot 3}}{y}\\

\mathbf{elif}\;z \cdot 3 \le 5.531250664679463187888177829139671400627 \cdot 10^{-59}:\\
\;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{1}{z \cdot 3} \cdot \frac{t}{y}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r521661 = x;
        double r521662 = y;
        double r521663 = z;
        double r521664 = 3.0;
        double r521665 = r521663 * r521664;
        double r521666 = r521662 / r521665;
        double r521667 = r521661 - r521666;
        double r521668 = t;
        double r521669 = r521665 * r521662;
        double r521670 = r521668 / r521669;
        double r521671 = r521667 + r521670;
        return r521671;
}
↓
double f(double x, double y, double z, double t) {
        double r521672 = z;
        double r521673 = 3.0;
        double r521674 = r521672 * r521673;
        double r521675 = -650340682119.0386;
        bool r521676 = r521674 <= r521675;
        double r521677 = x;
        double r521678 = y;
        double r521679 = r521678 / r521672;
        double r521680 = r521679 / r521673;
        double r521681 = r521677 - r521680;
        double r521682 = t;
        double r521683 = r521682 / r521674;
        double r521684 = r521683 / r521678;
        double r521685 = r521681 + r521684;
        double r521686 = 5.531250664679463e-59;
        bool r521687 = r521674 <= r521686;
        double r521688 = r521678 / r521674;
        double r521689 = r521677 - r521688;
        double r521690 = 1.0;
        double r521691 = r521690 / r521674;
        double r521692 = r521682 / r521678;
        double r521693 = r521691 * r521692;
        double r521694 = r521689 + r521693;
        double r521695 = r521673 * r521678;
        double r521696 = r521672 * r521695;
        double r521697 = r521682 / r521696;
        double r521698 = r521689 + r521697;
        double r521699 = r521687 ? r521694 : r521698;
        double r521700 = r521676 ? r521685 : r521699;
        return r521700;
}

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
Target1.8
Herbie0.6
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z \cdot 3}}{y}\]

Derivation

  1. Split input into 3 regimes

  2. if (* z 3.0) < -650340682119.0386

    1. Initial program 0.4

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
    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 associate-/r*1.1

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

    if -650340682119.0386 < (* z 3.0) < 5.531250664679463e-59

    1. Initial program 11.8

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

    3. Applied *-un-lft-identity11.8

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

    4. Applied times-frac0.3

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

    if 5.531250664679463e-59 < (* z 3.0)

    1. Initial program 0.5

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

    3. Applied associate-*l*0.5

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

  4. Final simplification0.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot 3 \le -650340682119.03857421875:\\ \;\;\;\;\left(x - \frac{\frac{y}{z}}{3}\right) + \frac{\frac{t}{z \cdot 3}}{y}\\ \mathbf{elif}\;z \cdot 3 \le 5.531250664679463187888177829139671400627 \cdot 10^{-59}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{1}{z \cdot 3} \cdot \frac{t}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \left(3 \cdot y\right)}\\ \end{array}\]

Reproduce

herbie shell --seed 2019212 
(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))))