Average Error: 3.8 → 0.4
Time: 3.5s
Precision: 64
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -5.63380401175012114 \cdot 10^{26} \lor \neg \left(t \le 142570936951662100\right):\\ \;\;\;\;\left(x - \frac{\frac{y}{z}}{3}\right) + 0.333333333333333315 \cdot \frac{t}{z \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{\frac{y}{z}}{3}\right) + \frac{\frac{1}{z}}{\frac{y}{\frac{t}{3}}}\\ \end{array}\]
\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}
↓
\begin{array}{l}
\mathbf{if}\;t \le -5.63380401175012114 \cdot 10^{26} \lor \neg \left(t \le 142570936951662100\right):\\
\;\;\;\;\left(x - \frac{\frac{y}{z}}{3}\right) + 0.333333333333333315 \cdot \frac{t}{z \cdot y}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r755431 = x;
        double r755432 = y;
        double r755433 = z;
        double r755434 = 3.0;
        double r755435 = r755433 * r755434;
        double r755436 = r755432 / r755435;
        double r755437 = r755431 - r755436;
        double r755438 = t;
        double r755439 = r755435 * r755432;
        double r755440 = r755438 / r755439;
        double r755441 = r755437 + r755440;
        return r755441;
}
↓
double f(double x, double y, double z, double t) {
        double r755442 = t;
        double r755443 = -5.633804011750121e+26;
        bool r755444 = r755442 <= r755443;
        double r755445 = 1.4257093695166208e+17;
        bool r755446 = r755442 <= r755445;
        double r755447 = !r755446;
        bool r755448 = r755444 || r755447;
        double r755449 = x;
        double r755450 = y;
        double r755451 = z;
        double r755452 = r755450 / r755451;
        double r755453 = 3.0;
        double r755454 = r755452 / r755453;
        double r755455 = r755449 - r755454;
        double r755456 = 0.3333333333333333;
        double r755457 = r755451 * r755450;
        double r755458 = r755442 / r755457;
        double r755459 = r755456 * r755458;
        double r755460 = r755455 + r755459;
        double r755461 = 1.0;
        double r755462 = r755461 / r755451;
        double r755463 = r755442 / r755453;
        double r755464 = r755450 / r755463;
        double r755465 = r755462 / r755464;
        double r755466 = r755455 + r755465;
        double r755467 = r755448 ? r755460 : r755466;
        return r755467;
}

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

Original3.8
Target1.8
Herbie0.4
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z \cdot 3}}{y}\]

Derivation

  1. Split input into 2 regimes

  2. if t < -5.633804011750121e+26 or 1.4257093695166208e+17 < t

    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*2.6

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

    5. Applied associate-/r*2.6

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

    6. Taylor expanded around 0 0.7

      \[\leadsto \left(x - \frac{\frac{y}{z}}{3}\right) + \color{blue}{0.333333333333333315 \cdot \frac{t}{z \cdot y}}\]

    if -5.633804011750121e+26 < t < 1.4257093695166208e+17

    1. Initial program 5.8

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

    3. Applied associate-/r*1.3

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

    5. Applied associate-/r*1.3

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

    7. Applied *-un-lft-identity1.3

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

    8. Applied times-frac1.3

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

    9. Applied associate-/l*0.3

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

  4. Final simplification0.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -5.63380401175012114 \cdot 10^{26} \lor \neg \left(t \le 142570936951662100\right):\\ \;\;\;\;\left(x - \frac{\frac{y}{z}}{3}\right) + 0.333333333333333315 \cdot \frac{t}{z \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{\frac{y}{z}}{3}\right) + \frac{\frac{1}{z}}{\frac{y}{\frac{t}{3}}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020036 
(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))))