Average Error: 3.7 → 1.7
Time: 20.2s
Precision: 64
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \cdot 3 \le 5.139606151127303520398748598797844304667 \cdot 10^{-106}:\\ \;\;\;\;x - \left(\frac{\frac{y}{3}}{z} - \frac{\frac{t}{z \cdot 3}}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{t}{\left(z \cdot 3\right) \cdot y} - \frac{\frac{y}{z}}{3}\right)\\ \end{array}\]
\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 5.139606151127303520398748598797844304667 \cdot 10^{-106}:\\
\;\;\;\;x - \left(\frac{\frac{y}{3}}{z} - \frac{\frac{t}{z \cdot 3}}{y}\right)\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r1217674 = x;
        double r1217675 = y;
        double r1217676 = z;
        double r1217677 = 3.0;
        double r1217678 = r1217676 * r1217677;
        double r1217679 = r1217675 / r1217678;
        double r1217680 = r1217674 - r1217679;
        double r1217681 = t;
        double r1217682 = r1217678 * r1217675;
        double r1217683 = r1217681 / r1217682;
        double r1217684 = r1217680 + r1217683;
        return r1217684;
}
↓
double f(double x, double y, double z, double t) {
        double r1217685 = z;
        double r1217686 = 3.0;
        double r1217687 = r1217685 * r1217686;
        double r1217688 = 5.139606151127304e-106;
        bool r1217689 = r1217687 <= r1217688;
        double r1217690 = x;
        double r1217691 = y;
        double r1217692 = r1217691 / r1217686;
        double r1217693 = r1217692 / r1217685;
        double r1217694 = t;
        double r1217695 = r1217694 / r1217687;
        double r1217696 = r1217695 / r1217691;
        double r1217697 = r1217693 - r1217696;
        double r1217698 = r1217690 - r1217697;
        double r1217699 = r1217687 * r1217691;
        double r1217700 = r1217694 / r1217699;
        double r1217701 = r1217691 / r1217685;
        double r1217702 = r1217701 / r1217686;
        double r1217703 = r1217700 - r1217702;
        double r1217704 = r1217690 + r1217703;
        double r1217705 = r1217689 ? r1217698 : r1217704;
        return r1217705;
}

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
Target1.9
Herbie1.7
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z \cdot 3}}{y}\]

Derivation

  1. Split input into 2 regimes

  2. if (* z 3.0) < 5.139606151127304e-106

    1. Initial program 5.7

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

    3. Applied associate-/r*2.3

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

    5. Applied associate-+l-2.3

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

    6. Simplified2.3

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

    if 5.139606151127304e-106 < (* z 3.0)

    1. Initial program 1.0

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

    3. Applied sub-neg1.0

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

    4. Applied associate-+l+1.0

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

    5. Simplified1.0

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

  4. Final simplification1.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot 3 \le 5.139606151127303520398748598797844304667 \cdot 10^{-106}:\\ \;\;\;\;x - \left(\frac{\frac{y}{3}}{z} - \frac{\frac{t}{z \cdot 3}}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{t}{\left(z \cdot 3\right) \cdot y} - \frac{\frac{y}{z}}{3}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019235 +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))))