Average Error: 3.8 → 0.4
Time: 18.2s
Precision: 64
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -3964198673573570831051653120 \lor \neg \left(t \le 2.882727162813425589307412170211595841217 \cdot 10^{-23}\right):\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{1}{\frac{\left(z \cdot 3\right) \cdot y}{t}}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{\frac{y}{z}}{3}\right) + \frac{1}{z} \cdot \frac{\frac{t}{3}}{y}\\ \end{array}\]
\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}
↓
\begin{array}{l}
\mathbf{if}\;t \le -3964198673573570831051653120 \lor \neg \left(t \le 2.882727162813425589307412170211595841217 \cdot 10^{-23}\right):\\
\;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{1}{\frac{\left(z \cdot 3\right) \cdot y}{t}}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r546035 = x;
        double r546036 = y;
        double r546037 = z;
        double r546038 = 3.0;
        double r546039 = r546037 * r546038;
        double r546040 = r546036 / r546039;
        double r546041 = r546035 - r546040;
        double r546042 = t;
        double r546043 = r546039 * r546036;
        double r546044 = r546042 / r546043;
        double r546045 = r546041 + r546044;
        return r546045;
}
↓
double f(double x, double y, double z, double t) {
        double r546046 = t;
        double r546047 = -3.964198673573571e+27;
        bool r546048 = r546046 <= r546047;
        double r546049 = 2.8827271628134256e-23;
        bool r546050 = r546046 <= r546049;
        double r546051 = !r546050;
        bool r546052 = r546048 || r546051;
        double r546053 = x;
        double r546054 = y;
        double r546055 = z;
        double r546056 = 3.0;
        double r546057 = r546055 * r546056;
        double r546058 = r546054 / r546057;
        double r546059 = r546053 - r546058;
        double r546060 = 1.0;
        double r546061 = r546057 * r546054;
        double r546062 = r546061 / r546046;
        double r546063 = r546060 / r546062;
        double r546064 = r546059 + r546063;
        double r546065 = r546054 / r546055;
        double r546066 = r546065 / r546056;
        double r546067 = r546053 - r546066;
        double r546068 = r546060 / r546055;
        double r546069 = r546046 / r546056;
        double r546070 = r546069 / r546054;
        double r546071 = r546068 * r546070;
        double r546072 = r546067 + r546071;
        double r546073 = r546052 ? r546064 : r546072;
        return r546073;
}

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
Target1.7
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 < -3.964198673573571e+27 or 2.8827271628134256e-23 < t

    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 clear-num0.5

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

    if -3.964198673573571e+27 < t < 2.8827271628134256e-23

    1. Initial program 6.1

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

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

    7. Applied *-un-lft-identity1.1

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

    8. Applied *-un-lft-identity1.1

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

    9. Applied times-frac1.1

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

    10. Applied times-frac0.3

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

    11. Simplified0.3

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

  4. Final simplification0.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -3964198673573570831051653120 \lor \neg \left(t \le 2.882727162813425589307412170211595841217 \cdot 10^{-23}\right):\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{1}{\frac{\left(z \cdot 3\right) \cdot y}{t}}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{\frac{y}{z}}{3}\right) + \frac{1}{z} \cdot \frac{\frac{t}{3}}{y}\\ \end{array}\]

Reproduce

herbie shell --seed 2019347 +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))))