Average Error: 3.9 → 1.2
Time: 10.9s
Precision: 64
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le 1.5801305016597386 \cdot 10^{-18}:\\ \;\;\;\;\left(x - \frac{1}{\frac{z \cdot 3}{y}}\right) + \frac{\frac{t}{z \cdot 3}}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{1}{z} \cdot \frac{\frac{t}{3}}{y}\\ \end{array}\]
\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}
↓
\begin{array}{l}
\mathbf{if}\;y \le 1.5801305016597386 \cdot 10^{-18}:\\
\;\;\;\;\left(x - \frac{1}{\frac{z \cdot 3}{y}}\right) + \frac{\frac{t}{z \cdot 3}}{y}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r552390 = x;
        double r552391 = y;
        double r552392 = z;
        double r552393 = 3.0;
        double r552394 = r552392 * r552393;
        double r552395 = r552391 / r552394;
        double r552396 = r552390 - r552395;
        double r552397 = t;
        double r552398 = r552394 * r552391;
        double r552399 = r552397 / r552398;
        double r552400 = r552396 + r552399;
        return r552400;
}
↓
double f(double x, double y, double z, double t) {
        double r552401 = y;
        double r552402 = 1.5801305016597386e-18;
        bool r552403 = r552401 <= r552402;
        double r552404 = x;
        double r552405 = 1.0;
        double r552406 = z;
        double r552407 = 3.0;
        double r552408 = r552406 * r552407;
        double r552409 = r552408 / r552401;
        double r552410 = r552405 / r552409;
        double r552411 = r552404 - r552410;
        double r552412 = t;
        double r552413 = r552412 / r552408;
        double r552414 = r552413 / r552401;
        double r552415 = r552411 + r552414;
        double r552416 = r552401 / r552408;
        double r552417 = r552404 - r552416;
        double r552418 = r552405 / r552406;
        double r552419 = r552412 / r552407;
        double r552420 = r552419 / r552401;
        double r552421 = r552418 * r552420;
        double r552422 = r552417 + r552421;
        double r552423 = r552403 ? r552415 : r552422;
        return r552423;
}

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
Target1.6
Herbie1.2
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z \cdot 3}}{y}\]

Derivation

  1. Split input into 2 regimes

  2. if y < 1.5801305016597386e-18

    1. Initial program 5.1

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

    3. Applied associate-/r*1.6

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

    5. Applied clear-num1.6

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

    if 1.5801305016597386e-18 < y

    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*1.6

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

    5. Applied *-un-lft-identity1.6

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

    6. Applied *-un-lft-identity1.6

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

    7. Applied times-frac1.7

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

    8. Applied times-frac0.2

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

    9. Simplified0.2

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

  4. Final simplification1.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le 1.5801305016597386 \cdot 10^{-18}:\\ \;\;\;\;\left(x - \frac{1}{\frac{z \cdot 3}{y}}\right) + \frac{\frac{t}{z \cdot 3}}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{1}{z} \cdot \frac{\frac{t}{3}}{y}\\ \end{array}\]

Reproduce

herbie shell --seed 2019198 
(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))))