Average Error: 3.7 → 0.9
Time: 3.9s
Precision: 64
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -2.171528493507656670283271706692623069358 \cdot 10^{-57} \lor \neg \left(z \le 1.594003072049920579576627778635528875032 \cdot 10^{76}\right):\\ \;\;\;\;\left(x - \frac{\frac{y}{z}}{3}\right) + \frac{\frac{t}{z \cdot 3}}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{\frac{y}{3}}{z}\right) + \frac{1}{z} \cdot \frac{\frac{t}{3}}{y}\\ \end{array}\]
\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}
↓
\begin{array}{l}
\mathbf{if}\;z \le -2.171528493507656670283271706692623069358 \cdot 10^{-57} \lor \neg \left(z \le 1.594003072049920579576627778635528875032 \cdot 10^{76}\right):\\
\;\;\;\;\left(x - \frac{\frac{y}{z}}{3}\right) + \frac{\frac{t}{z \cdot 3}}{y}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r734153 = x;
        double r734154 = y;
        double r734155 = z;
        double r734156 = 3.0;
        double r734157 = r734155 * r734156;
        double r734158 = r734154 / r734157;
        double r734159 = r734153 - r734158;
        double r734160 = t;
        double r734161 = r734157 * r734154;
        double r734162 = r734160 / r734161;
        double r734163 = r734159 + r734162;
        return r734163;
}
↓
double f(double x, double y, double z, double t) {
        double r734164 = z;
        double r734165 = -2.1715284935076567e-57;
        bool r734166 = r734164 <= r734165;
        double r734167 = 1.5940030720499206e+76;
        bool r734168 = r734164 <= r734167;
        double r734169 = !r734168;
        bool r734170 = r734166 || r734169;
        double r734171 = x;
        double r734172 = y;
        double r734173 = r734172 / r734164;
        double r734174 = 3.0;
        double r734175 = r734173 / r734174;
        double r734176 = r734171 - r734175;
        double r734177 = t;
        double r734178 = r734164 * r734174;
        double r734179 = r734177 / r734178;
        double r734180 = r734179 / r734172;
        double r734181 = r734176 + r734180;
        double r734182 = r734172 / r734174;
        double r734183 = r734182 / r734164;
        double r734184 = r734171 - r734183;
        double r734185 = 1.0;
        double r734186 = r734185 / r734164;
        double r734187 = r734177 / r734174;
        double r734188 = r734187 / r734172;
        double r734189 = r734186 * r734188;
        double r734190 = r734184 + r734189;
        double r734191 = r734170 ? r734181 : r734190;
        return r734191;
}

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

Derivation

  1. Split input into 2 regimes

  2. if z < -2.1715284935076567e-57 or 1.5940030720499206e+76 < z

    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*1.0

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

    5. Applied *-un-lft-identity1.0

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

    6. Applied times-frac1.0

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

    8. Applied associate-*r/1.0

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

    9. Simplified1.0

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

    if -2.1715284935076567e-57 < z < 1.5940030720499206e+76

    1. Initial program 9.1

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

    3. Applied associate-/r*2.7

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

    5. Applied *-un-lft-identity2.7

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

    6. Applied times-frac2.7

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

    8. Applied associate-*l/2.7

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

    9. Simplified2.7

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

    11. Applied *-un-lft-identity2.7

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

    12. Applied *-un-lft-identity2.7

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

    13. Applied times-frac2.7

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

    14. Applied times-frac0.7

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

    15. Simplified0.7

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

  4. Final simplification0.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -2.171528493507656670283271706692623069358 \cdot 10^{-57} \lor \neg \left(z \le 1.594003072049920579576627778635528875032 \cdot 10^{76}\right):\\ \;\;\;\;\left(x - \frac{\frac{y}{z}}{3}\right) + \frac{\frac{t}{z \cdot 3}}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{\frac{y}{3}}{z}\right) + \frac{1}{z} \cdot \frac{\frac{t}{3}}{y}\\ \end{array}\]

Reproduce

herbie shell --seed 2020001 
(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))))