Average Error: 3.9 → 0.9
Time: 10.3s
Precision: 64
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \cdot 3 \le -1.679549677934962912371060912947000332007 \cdot 10^{-9}:\\ \;\;\;\;\left(x - 0.3333333333333333148296162562473909929395 \cdot \frac{y}{z}\right) + \frac{\frac{t}{3}}{z \cdot y}\\ \mathbf{elif}\;z \cdot 3 \le 1.988546582597582853711732660366369539647 \cdot 10^{129}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{1}{z \cdot 3} \cdot \frac{t}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z \cdot 3}}{y}\\ \end{array}\]
\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}
↓
\begin{array}{l}
\mathbf{if}\;z \cdot 3 \le -1.679549677934962912371060912947000332007 \cdot 10^{-9}:\\
\;\;\;\;\left(x - 0.3333333333333333148296162562473909929395 \cdot \frac{y}{z}\right) + \frac{\frac{t}{3}}{z \cdot y}\\

\mathbf{elif}\;z \cdot 3 \le 1.988546582597582853711732660366369539647 \cdot 10^{129}:\\
\;\;\;\;\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{\frac{t}{z \cdot 3}}{y}\\

\end{array}
double f(double x, double y, double z, double t) {
        double r503128 = x;
        double r503129 = y;
        double r503130 = z;
        double r503131 = 3.0;
        double r503132 = r503130 * r503131;
        double r503133 = r503129 / r503132;
        double r503134 = r503128 - r503133;
        double r503135 = t;
        double r503136 = r503132 * r503129;
        double r503137 = r503135 / r503136;
        double r503138 = r503134 + r503137;
        return r503138;
}
↓
double f(double x, double y, double z, double t) {
        double r503139 = z;
        double r503140 = 3.0;
        double r503141 = r503139 * r503140;
        double r503142 = -1.679549677934963e-09;
        bool r503143 = r503141 <= r503142;
        double r503144 = x;
        double r503145 = 0.3333333333333333;
        double r503146 = y;
        double r503147 = r503146 / r503139;
        double r503148 = r503145 * r503147;
        double r503149 = r503144 - r503148;
        double r503150 = t;
        double r503151 = r503150 / r503140;
        double r503152 = r503139 * r503146;
        double r503153 = r503151 / r503152;
        double r503154 = r503149 + r503153;
        double r503155 = 1.988546582597583e+129;
        bool r503156 = r503141 <= r503155;
        double r503157 = r503146 / r503141;
        double r503158 = r503144 - r503157;
        double r503159 = 1.0;
        double r503160 = r503159 / r503141;
        double r503161 = r503150 / r503146;
        double r503162 = r503160 * r503161;
        double r503163 = r503158 + r503162;
        double r503164 = r503150 / r503141;
        double r503165 = r503164 / r503146;
        double r503166 = r503158 + r503165;
        double r503167 = r503156 ? r503163 : r503166;
        double r503168 = r503143 ? r503154 : r503167;
        return r503168;
}

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

Original3.9
Target1.7
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) < -1.679549677934963e-09

    1. Initial program 0.5

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

    2. Taylor expanded around 0 0.5

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

    4. Applied associate-/r*0.5

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

    5. Taylor expanded around 0 0.5

      \[\leadsto \left(x - \color{blue}{0.3333333333333333148296162562473909929395 \cdot \frac{y}{z}}\right) + \frac{\frac{t}{3}}{z \cdot y}\]

    if -1.679549677934963e-09 < (* z 3.0) < 1.988546582597583e+129

    1. Initial program 7.9

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

    3. Applied *-un-lft-identity7.9

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

    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 1.988546582597583e+129 < (* 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*1.5

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

  4. Final simplification0.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot 3 \le -1.679549677934962912371060912947000332007 \cdot 10^{-9}:\\ \;\;\;\;\left(x - 0.3333333333333333148296162562473909929395 \cdot \frac{y}{z}\right) + \frac{\frac{t}{3}}{z \cdot y}\\ \mathbf{elif}\;z \cdot 3 \le 1.988546582597582853711732660366369539647 \cdot 10^{129}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{1}{z \cdot 3} \cdot \frac{t}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z \cdot 3}}{y}\\ \end{array}\]

Reproduce

herbie shell --seed 2019325 
(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))))