Average Error: 3.7 → 0.9
Time: 5.7s
Precision: 64
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \cdot 3 \le -1.16964350915532777 \cdot 10^{116}:\\ \;\;\;\;\left(x - \frac{\frac{\frac{y}{z}}{\sqrt[3]{3} \cdot \sqrt[3]{3}}}{\sqrt[3]{3}}\right) + \frac{\frac{t}{z \cdot 3}}{y}\\ \mathbf{elif}\;z \cdot 3 \le 1.52241256667558003 \cdot 10^{-52}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{1}{z \cdot 3} \cdot \frac{t}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \left(3 \cdot y\right)}\\ \end{array}\]
\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 -1.16964350915532777 \cdot 10^{116}:\\
\;\;\;\;\left(x - \frac{\frac{\frac{y}{z}}{\sqrt[3]{3} \cdot \sqrt[3]{3}}}{\sqrt[3]{3}}\right) + \frac{\frac{t}{z \cdot 3}}{y}\\

\mathbf{elif}\;z \cdot 3 \le 1.52241256667558003 \cdot 10^{-52}:\\
\;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{1}{z \cdot 3} \cdot \frac{t}{y}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r699140 = x;
        double r699141 = y;
        double r699142 = z;
        double r699143 = 3.0;
        double r699144 = r699142 * r699143;
        double r699145 = r699141 / r699144;
        double r699146 = r699140 - r699145;
        double r699147 = t;
        double r699148 = r699144 * r699141;
        double r699149 = r699147 / r699148;
        double r699150 = r699146 + r699149;
        return r699150;
}
↓
double f(double x, double y, double z, double t) {
        double r699151 = z;
        double r699152 = 3.0;
        double r699153 = r699151 * r699152;
        double r699154 = -1.1696435091553278e+116;
        bool r699155 = r699153 <= r699154;
        double r699156 = x;
        double r699157 = y;
        double r699158 = r699157 / r699151;
        double r699159 = cbrt(r699152);
        double r699160 = r699159 * r699159;
        double r699161 = r699158 / r699160;
        double r699162 = r699161 / r699159;
        double r699163 = r699156 - r699162;
        double r699164 = t;
        double r699165 = r699164 / r699153;
        double r699166 = r699165 / r699157;
        double r699167 = r699163 + r699166;
        double r699168 = 1.52241256667558e-52;
        bool r699169 = r699153 <= r699168;
        double r699170 = r699157 / r699153;
        double r699171 = r699156 - r699170;
        double r699172 = 1.0;
        double r699173 = r699172 / r699153;
        double r699174 = r699164 / r699157;
        double r699175 = r699173 * r699174;
        double r699176 = r699171 + r699175;
        double r699177 = r699152 * r699157;
        double r699178 = r699151 * r699177;
        double r699179 = r699164 / r699178;
        double r699180 = r699171 + r699179;
        double r699181 = r699169 ? r699176 : r699180;
        double r699182 = r699155 ? r699167 : r699181;
        return r699182;
}

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
Target1.8
Herbie0.9
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z \cdot 3}}{y}\]

Derivation

  1. Split input into 3 regimes

  2. if (* z 3.0) < -1.1696435091553278e+116

    1. Initial program 0.7

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

    3. Applied associate-/r*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 add-cube-cbrt1.1

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

    8. Applied associate-/r*1.2

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

    if -1.1696435091553278e+116 < (* z 3.0) < 1.52241256667558e-52

    1. Initial program 8.3

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

    3. Applied *-un-lft-identity8.3

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

    4. Applied times-frac1.1

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

    if 1.52241256667558e-52 < (* z 3.0)

    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-*l*0.5

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

  4. Final simplification0.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot 3 \le -1.16964350915532777 \cdot 10^{116}:\\ \;\;\;\;\left(x - \frac{\frac{\frac{y}{z}}{\sqrt[3]{3} \cdot \sqrt[3]{3}}}{\sqrt[3]{3}}\right) + \frac{\frac{t}{z \cdot 3}}{y}\\ \mathbf{elif}\;z \cdot 3 \le 1.52241256667558003 \cdot 10^{-52}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{1}{z \cdot 3} \cdot \frac{t}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \left(3 \cdot y\right)}\\ \end{array}\]

Reproduce

herbie shell --seed 2020021 +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))))