Average Error: 3.1 → 1.2
Time: 14.2s
Precision: 64
\[\left(x - \frac{y}{z \cdot 3.0}\right) + \frac{t}{\left(z \cdot 3.0\right) \cdot y}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -3.4470093223023695 \cdot 10^{-06}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3.0}\right) + \frac{1}{\frac{z \cdot y}{\frac{t}{3.0}}}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3.0}\right) + \frac{\frac{\frac{t}{z}}{3.0}}{y}\\ \end{array}\]
\left(x - \frac{y}{z \cdot 3.0}\right) + \frac{t}{\left(z \cdot 3.0\right) \cdot y}
↓
\begin{array}{l}
\mathbf{if}\;y \le -3.4470093223023695 \cdot 10^{-06}:\\
\;\;\;\;\left(x - \frac{y}{z \cdot 3.0}\right) + \frac{1}{\frac{z \cdot y}{\frac{t}{3.0}}}\\

\mathbf{else}:\\
\;\;\;\;\left(x - \frac{y}{z \cdot 3.0}\right) + \frac{\frac{\frac{t}{z}}{3.0}}{y}\\

\end{array}
double f(double x, double y, double z, double t) {
        double r31486232 = x;
        double r31486233 = y;
        double r31486234 = z;
        double r31486235 = 3.0;
        double r31486236 = r31486234 * r31486235;
        double r31486237 = r31486233 / r31486236;
        double r31486238 = r31486232 - r31486237;
        double r31486239 = t;
        double r31486240 = r31486236 * r31486233;
        double r31486241 = r31486239 / r31486240;
        double r31486242 = r31486238 + r31486241;
        return r31486242;
}
↓
double f(double x, double y, double z, double t) {
        double r31486243 = y;
        double r31486244 = -3.4470093223023695e-06;
        bool r31486245 = r31486243 <= r31486244;
        double r31486246 = x;
        double r31486247 = z;
        double r31486248 = 3.0;
        double r31486249 = r31486247 * r31486248;
        double r31486250 = r31486243 / r31486249;
        double r31486251 = r31486246 - r31486250;
        double r31486252 = 1.0;
        double r31486253 = r31486247 * r31486243;
        double r31486254 = t;
        double r31486255 = r31486254 / r31486248;
        double r31486256 = r31486253 / r31486255;
        double r31486257 = r31486252 / r31486256;
        double r31486258 = r31486251 + r31486257;
        double r31486259 = r31486254 / r31486247;
        double r31486260 = r31486259 / r31486248;
        double r31486261 = r31486260 / r31486243;
        double r31486262 = r31486251 + r31486261;
        double r31486263 = r31486245 ? r31486258 : r31486262;
        return r31486263;
}

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

Original3.1
Target1.6
Herbie1.2
\[\left(x - \frac{y}{z \cdot 3.0}\right) + \frac{\frac{t}{z \cdot 3.0}}{y}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -3.4470093223023695e-06

    1. Initial program 0.5

      \[\left(x - \frac{y}{z \cdot 3.0}\right) + \frac{t}{\left(z \cdot 3.0\right) \cdot y}\]
    2. Using strategy rm

    3. Applied associate-/r*1.9

      \[\leadsto \left(x - \frac{y}{z \cdot 3.0}\right) + \color{blue}{\frac{\frac{t}{z \cdot 3.0}}{y}}\]
    4. Using strategy rm

    5. Applied clear-num1.9

      \[\leadsto \left(x - \frac{y}{z \cdot 3.0}\right) + \color{blue}{\frac{1}{\frac{y}{\frac{t}{z \cdot 3.0}}}}\]
    6. Using strategy rm

    7. Applied *-un-lft-identity1.9

      \[\leadsto \left(x - \frac{y}{z \cdot 3.0}\right) + \frac{1}{\frac{y}{\frac{\color{blue}{1 \cdot t}}{z \cdot 3.0}}}\]

    8. Applied times-frac1.9

      \[\leadsto \left(x - \frac{y}{z \cdot 3.0}\right) + \frac{1}{\frac{y}{\color{blue}{\frac{1}{z} \cdot \frac{t}{3.0}}}}\]

    9. Applied associate-/r*0.5

      \[\leadsto \left(x - \frac{y}{z \cdot 3.0}\right) + \frac{1}{\color{blue}{\frac{\frac{y}{\frac{1}{z}}}{\frac{t}{3.0}}}}\]

    10. Simplified0.5

      \[\leadsto \left(x - \frac{y}{z \cdot 3.0}\right) + \frac{1}{\frac{\color{blue}{z \cdot y}}{\frac{t}{3.0}}}\]

    if -3.4470093223023695e-06 < y

    1. Initial program 4.1

      \[\left(x - \frac{y}{z \cdot 3.0}\right) + \frac{t}{\left(z \cdot 3.0\right) \cdot y}\]
    2. Using strategy rm

    3. Applied associate-/r*1.5

      \[\leadsto \left(x - \frac{y}{z \cdot 3.0}\right) + \color{blue}{\frac{\frac{t}{z \cdot 3.0}}{y}}\]
    4. Using strategy rm

    5. Applied associate-/r*1.5

      \[\leadsto \left(x - \frac{y}{z \cdot 3.0}\right) + \frac{\color{blue}{\frac{\frac{t}{z}}{3.0}}}{y}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification1.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -3.4470093223023695 \cdot 10^{-06}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3.0}\right) + \frac{1}{\frac{z \cdot y}{\frac{t}{3.0}}}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3.0}\right) + \frac{\frac{\frac{t}{z}}{3.0}}{y}\\ \end{array}\]

Reproduce

herbie shell --seed 2019165 
(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))))