Average Error: 3.6 → 0.3
Time: 5.0s
Precision: 64
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \cdot 3 \le -6.370305939298982764420961800964263773328 \cdot 10^{-25} \lor \neg \left(z \cdot 3 \le 25217032.5919179953634738922119140625\right):\\ \;\;\;\;\left(x - \frac{\frac{y}{z}}{3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{1}{z}}{\frac{y}{\frac{t}{3}}}\\ \end{array}\]
\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 -6.370305939298982764420961800964263773328 \cdot 10^{-25} \lor \neg \left(z \cdot 3 \le 25217032.5919179953634738922119140625\right):\\
\;\;\;\;\left(x - \frac{\frac{y}{z}}{3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r922677 = x;
        double r922678 = y;
        double r922679 = z;
        double r922680 = 3.0;
        double r922681 = r922679 * r922680;
        double r922682 = r922678 / r922681;
        double r922683 = r922677 - r922682;
        double r922684 = t;
        double r922685 = r922681 * r922678;
        double r922686 = r922684 / r922685;
        double r922687 = r922683 + r922686;
        return r922687;
}
↓
double f(double x, double y, double z, double t) {
        double r922688 = z;
        double r922689 = 3.0;
        double r922690 = r922688 * r922689;
        double r922691 = -6.370305939298983e-25;
        bool r922692 = r922690 <= r922691;
        double r922693 = 25217032.591917995;
        bool r922694 = r922690 <= r922693;
        double r922695 = !r922694;
        bool r922696 = r922692 || r922695;
        double r922697 = x;
        double r922698 = y;
        double r922699 = r922698 / r922688;
        double r922700 = r922699 / r922689;
        double r922701 = r922697 - r922700;
        double r922702 = t;
        double r922703 = r922690 * r922698;
        double r922704 = r922702 / r922703;
        double r922705 = r922701 + r922704;
        double r922706 = r922698 / r922690;
        double r922707 = r922697 - r922706;
        double r922708 = 1.0;
        double r922709 = r922708 / r922688;
        double r922710 = r922702 / r922689;
        double r922711 = r922698 / r922710;
        double r922712 = r922709 / r922711;
        double r922713 = r922707 + r922712;
        double r922714 = r922696 ? r922705 : r922713;
        return r922714;
}

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

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

Derivation

  1. Split input into 2 regimes

  2. if (* z 3.0) < -6.370305939298983e-25 or 25217032.591917995 < (* z 3.0)

    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*0.4

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

    if -6.370305939298983e-25 < (* z 3.0) < 25217032.591917995

    1. Initial program 10.4

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

    3. Applied associate-/r*3.4

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

    5. Applied *-un-lft-identity3.4

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

    6. Applied times-frac3.4

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

    7. Applied associate-/l*0.3

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

  4. Final simplification0.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot 3 \le -6.370305939298982764420961800964263773328 \cdot 10^{-25} \lor \neg \left(z \cdot 3 \le 25217032.5919179953634738922119140625\right):\\ \;\;\;\;\left(x - \frac{\frac{y}{z}}{3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{1}{z}}{\frac{y}{\frac{t}{3}}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019362 +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))))