Average Error: 3.6 → 1.4
Time: 23.4s
Precision: 64
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -465104846371001377193813340330265673728:\\ \;\;\;\;\frac{t}{y \cdot \left(3 \cdot z\right)} + \left(x - \frac{\frac{y}{z}}{3}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\frac{t}{3}}{z}}{y} + \left(x - \frac{1}{z} \cdot \frac{y}{3}\right)\\ \end{array}\]
\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}
↓
\begin{array}{l}
\mathbf{if}\;y \le -465104846371001377193813340330265673728:\\
\;\;\;\;\frac{t}{y \cdot \left(3 \cdot z\right)} + \left(x - \frac{\frac{y}{z}}{3}\right)\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r28319178 = x;
        double r28319179 = y;
        double r28319180 = z;
        double r28319181 = 3.0;
        double r28319182 = r28319180 * r28319181;
        double r28319183 = r28319179 / r28319182;
        double r28319184 = r28319178 - r28319183;
        double r28319185 = t;
        double r28319186 = r28319182 * r28319179;
        double r28319187 = r28319185 / r28319186;
        double r28319188 = r28319184 + r28319187;
        return r28319188;
}
↓
double f(double x, double y, double z, double t) {
        double r28319189 = y;
        double r28319190 = -4.651048463710014e+38;
        bool r28319191 = r28319189 <= r28319190;
        double r28319192 = t;
        double r28319193 = 3.0;
        double r28319194 = z;
        double r28319195 = r28319193 * r28319194;
        double r28319196 = r28319189 * r28319195;
        double r28319197 = r28319192 / r28319196;
        double r28319198 = x;
        double r28319199 = r28319189 / r28319194;
        double r28319200 = r28319199 / r28319193;
        double r28319201 = r28319198 - r28319200;
        double r28319202 = r28319197 + r28319201;
        double r28319203 = r28319192 / r28319193;
        double r28319204 = r28319203 / r28319194;
        double r28319205 = r28319204 / r28319189;
        double r28319206 = 1.0;
        double r28319207 = r28319206 / r28319194;
        double r28319208 = r28319189 / r28319193;
        double r28319209 = r28319207 * r28319208;
        double r28319210 = r28319198 - r28319209;
        double r28319211 = r28319205 + r28319210;
        double r28319212 = r28319191 ? r28319202 : r28319211;
        return r28319212;
}

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

Original3.6
Target1.8
Herbie1.4
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z \cdot 3}}{y}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -4.651048463710014e+38

    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 associate-/r*0.5

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

    if -4.651048463710014e+38 < y

    1. Initial program 4.4

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

    3. Applied associate-/r*1.7

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

    5. Applied associate-/r*1.7

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

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

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

    8. Applied associate-/r*1.7

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

    9. Simplified1.7

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

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

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

    12. Applied times-frac1.7

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

  4. Final simplification1.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -465104846371001377193813340330265673728:\\ \;\;\;\;\frac{t}{y \cdot \left(3 \cdot z\right)} + \left(x - \frac{\frac{y}{z}}{3}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\frac{t}{3}}{z}}{y} + \left(x - \frac{1}{z} \cdot \frac{y}{3}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019172 +o rules:numerics
(FPCore (x y z t)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, H"

  :herbie-target
  (+ (- x (/ y (* z 3.0))) (/ (/ t (* z 3.0)) y))

  (+ (- x (/ y (* z 3.0))) (/ t (* (* z 3.0) y))))