Average Error: 3.7 → 1.7
Time: 13.0s
Precision: 64
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \cdot 3 \le 5.139606151127303520398748598797844304667 \cdot 10^{-106}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z \cdot 3}}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{\frac{y}{z}}{3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\\ \end{array}\]
\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}
↓
\begin{array}{l}
\mathbf{if}\;z \cdot 3 \le 5.139606151127303520398748598797844304667 \cdot 10^{-106}:\\
\;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z \cdot 3}}{y}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r1745531 = x;
        double r1745532 = y;
        double r1745533 = z;
        double r1745534 = 3.0;
        double r1745535 = r1745533 * r1745534;
        double r1745536 = r1745532 / r1745535;
        double r1745537 = r1745531 - r1745536;
        double r1745538 = t;
        double r1745539 = r1745535 * r1745532;
        double r1745540 = r1745538 / r1745539;
        double r1745541 = r1745537 + r1745540;
        return r1745541;
}
↓
double f(double x, double y, double z, double t) {
        double r1745542 = z;
        double r1745543 = 3.0;
        double r1745544 = r1745542 * r1745543;
        double r1745545 = 5.139606151127304e-106;
        bool r1745546 = r1745544 <= r1745545;
        double r1745547 = x;
        double r1745548 = y;
        double r1745549 = r1745548 / r1745544;
        double r1745550 = r1745547 - r1745549;
        double r1745551 = t;
        double r1745552 = r1745551 / r1745544;
        double r1745553 = r1745552 / r1745548;
        double r1745554 = r1745550 + r1745553;
        double r1745555 = r1745548 / r1745542;
        double r1745556 = r1745555 / r1745543;
        double r1745557 = r1745547 - r1745556;
        double r1745558 = r1745544 * r1745548;
        double r1745559 = r1745551 / r1745558;
        double r1745560 = r1745557 + r1745559;
        double r1745561 = r1745546 ? r1745554 : r1745560;
        return r1745561;
}

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
Target1.9
Herbie1.7
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z \cdot 3}}{y}\]

Derivation

  1. Split input into 2 regimes

  2. if (* z 3.0) < 5.139606151127304e-106

    1. Initial program 5.7

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

    3. Applied associate-/r*2.3

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

    if 5.139606151127304e-106 < (* z 3.0)

    1. Initial program 1.0

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

    3. Applied associate-/r*1.0

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

  4. Final simplification1.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot 3 \le 5.139606151127303520398748598797844304667 \cdot 10^{-106}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z \cdot 3}}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{\frac{y}{z}}{3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\\ \end{array}\]

Reproduce

herbie shell --seed 2019235 
(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))))