Average Error: 3.7 → 0.5
Time: 18.7s
Precision: 64
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \cdot 3 \le -8.11820399887137828533882369329874684639 \cdot 10^{-43}:\\ \;\;\;\;\frac{t}{z \cdot \left(y \cdot 3\right)} + \left(x - \frac{y}{z \cdot 3}\right)\\ \mathbf{elif}\;z \cdot 3 \le 2.832904502745671216655345975136535379116 \cdot 10^{-56}:\\ \;\;\;\;\frac{1}{z} \cdot \frac{\frac{t}{3}}{y} + \left(x - \frac{y}{z \cdot 3}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{z \cdot \left(y \cdot 3\right)} + \left(x - \frac{y}{z \cdot 3}\right)\\ \end{array}\]
\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 -8.11820399887137828533882369329874684639 \cdot 10^{-43}:\\
\;\;\;\;\frac{t}{z \cdot \left(y \cdot 3\right)} + \left(x - \frac{y}{z \cdot 3}\right)\\

\mathbf{elif}\;z \cdot 3 \le 2.832904502745671216655345975136535379116 \cdot 10^{-56}:\\
\;\;\;\;\frac{1}{z} \cdot \frac{\frac{t}{3}}{y} + \left(x - \frac{y}{z \cdot 3}\right)\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r37142639 = x;
        double r37142640 = y;
        double r37142641 = z;
        double r37142642 = 3.0;
        double r37142643 = r37142641 * r37142642;
        double r37142644 = r37142640 / r37142643;
        double r37142645 = r37142639 - r37142644;
        double r37142646 = t;
        double r37142647 = r37142643 * r37142640;
        double r37142648 = r37142646 / r37142647;
        double r37142649 = r37142645 + r37142648;
        return r37142649;
}
↓
double f(double x, double y, double z, double t) {
        double r37142650 = z;
        double r37142651 = 3.0;
        double r37142652 = r37142650 * r37142651;
        double r37142653 = -8.118203998871378e-43;
        bool r37142654 = r37142652 <= r37142653;
        double r37142655 = t;
        double r37142656 = y;
        double r37142657 = r37142656 * r37142651;
        double r37142658 = r37142650 * r37142657;
        double r37142659 = r37142655 / r37142658;
        double r37142660 = x;
        double r37142661 = r37142656 / r37142652;
        double r37142662 = r37142660 - r37142661;
        double r37142663 = r37142659 + r37142662;
        double r37142664 = 2.832904502745671e-56;
        bool r37142665 = r37142652 <= r37142664;
        double r37142666 = 1.0;
        double r37142667 = r37142666 / r37142650;
        double r37142668 = r37142655 / r37142651;
        double r37142669 = r37142668 / r37142656;
        double r37142670 = r37142667 * r37142669;
        double r37142671 = r37142670 + r37142662;
        double r37142672 = r37142665 ? r37142671 : r37142663;
        double r37142673 = r37142654 ? r37142663 : r37142672;
        return r37142673;
}

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
Herbie0.5
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z \cdot 3}}{y}\]

Derivation

  1. Split input into 2 regimes

  2. if (* z 3.0) < -8.118203998871378e-43 or 2.832904502745671e-56 < (* 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

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

    if -8.118203998871378e-43 < (* z 3.0) < 2.832904502745671e-56

    1. Initial program 13.5

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

    3. Applied associate-/r*3.6

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

    5. Applied *-un-lft-identity3.6

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

    6. Applied *-un-lft-identity3.6

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

    7. Applied times-frac3.6

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

    8. Applied times-frac0.3

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

    9. Simplified0.3

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

  4. Final simplification0.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot 3 \le -8.11820399887137828533882369329874684639 \cdot 10^{-43}:\\ \;\;\;\;\frac{t}{z \cdot \left(y \cdot 3\right)} + \left(x - \frac{y}{z \cdot 3}\right)\\ \mathbf{elif}\;z \cdot 3 \le 2.832904502745671216655345975136535379116 \cdot 10^{-56}:\\ \;\;\;\;\frac{1}{z} \cdot \frac{\frac{t}{3}}{y} + \left(x - \frac{y}{z \cdot 3}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{z \cdot \left(y \cdot 3\right)} + \left(x - \frac{y}{z \cdot 3}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019170 
(FPCore (x y z t)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, H"

  :herbie-target
  (+ (- x (/ y (* z 3.0))) (/ (/ t (* z 3.0)) y))

  (+ (- x (/ y (* z 3.0))) (/ t (* (* z 3.0) y))))