Average Error: 3.8 → 0.4
Time: 6.0s
Precision: 64
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -5.63380401175012114 \cdot 10^{26} \lor \neg \left(t \le 142570936951662100\right):\\ \;\;\;\;\left(x - \frac{\frac{y}{z}}{3}\right) + 0.333333333333333315 \cdot \frac{t}{z \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{\frac{y}{z}}{3}\right) + \frac{\frac{1}{z}}{\frac{y}{\frac{t}{3}}}\\ \end{array}\]
\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}
↓
\begin{array}{l}
\mathbf{if}\;t \le -5.63380401175012114 \cdot 10^{26} \lor \neg \left(t \le 142570936951662100\right):\\
\;\;\;\;\left(x - \frac{\frac{y}{z}}{3}\right) + 0.333333333333333315 \cdot \frac{t}{z \cdot y}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r727169 = x;
        double r727170 = y;
        double r727171 = z;
        double r727172 = 3.0;
        double r727173 = r727171 * r727172;
        double r727174 = r727170 / r727173;
        double r727175 = r727169 - r727174;
        double r727176 = t;
        double r727177 = r727173 * r727170;
        double r727178 = r727176 / r727177;
        double r727179 = r727175 + r727178;
        return r727179;
}
↓
double f(double x, double y, double z, double t) {
        double r727180 = t;
        double r727181 = -5.633804011750121e+26;
        bool r727182 = r727180 <= r727181;
        double r727183 = 1.4257093695166208e+17;
        bool r727184 = r727180 <= r727183;
        double r727185 = !r727184;
        bool r727186 = r727182 || r727185;
        double r727187 = x;
        double r727188 = y;
        double r727189 = z;
        double r727190 = r727188 / r727189;
        double r727191 = 3.0;
        double r727192 = r727190 / r727191;
        double r727193 = r727187 - r727192;
        double r727194 = 0.3333333333333333;
        double r727195 = r727189 * r727188;
        double r727196 = r727180 / r727195;
        double r727197 = r727194 * r727196;
        double r727198 = r727193 + r727197;
        double r727199 = 1.0;
        double r727200 = r727199 / r727189;
        double r727201 = r727180 / r727191;
        double r727202 = r727188 / r727201;
        double r727203 = r727200 / r727202;
        double r727204 = r727193 + r727203;
        double r727205 = r727186 ? r727198 : r727204;
        return r727205;
}

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

Original3.8
Target1.8
Herbie0.4
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z \cdot 3}}{y}\]

Derivation

  1. Split input into 2 regimes

  2. if t < -5.633804011750121e+26 or 1.4257093695166208e+17 < t

    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*2.6

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

    5. Applied associate-/r*2.6

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

    6. Taylor expanded around 0 0.7

      \[\leadsto \left(x - \frac{\frac{y}{z}}{3}\right) + \color{blue}{0.333333333333333315 \cdot \frac{t}{z \cdot y}}\]

    if -5.633804011750121e+26 < t < 1.4257093695166208e+17

    1. Initial program 5.8

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

    3. Applied associate-/r*1.3

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

    5. Applied associate-/r*1.3

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

    7. Applied *-un-lft-identity1.3

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

    8. Applied times-frac1.3

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

    9. Applied associate-/l*0.3

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

  4. Final simplification0.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -5.63380401175012114 \cdot 10^{26} \lor \neg \left(t \le 142570936951662100\right):\\ \;\;\;\;\left(x - \frac{\frac{y}{z}}{3}\right) + 0.333333333333333315 \cdot \frac{t}{z \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{\frac{y}{z}}{3}\right) + \frac{\frac{1}{z}}{\frac{y}{\frac{t}{3}}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020036 +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))))