Average Error: 3.3 → 2.5
Time: 11.7s
Precision: 64
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \cdot 3 \le 7.710678676523238637135715158350394310792 \cdot 10^{-280}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{0.3333333333333333148296162562473909929395}{\frac{y}{\frac{t}{z}}}\\ \mathbf{else}:\\ \;\;\;\;\left(x - 0.3333333333333333148296162562473909929395 \cdot \frac{y}{z}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\\ \end{array}\]
\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 7.710678676523238637135715158350394310792 \cdot 10^{-280}:\\
\;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{0.3333333333333333148296162562473909929395}{\frac{y}{\frac{t}{z}}}\\

\mathbf{else}:\\
\;\;\;\;\left(x - 0.3333333333333333148296162562473909929395 \cdot \frac{y}{z}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\\

\end{array}
double f(double x, double y, double z, double t) {
        double r593978 = x;
        double r593979 = y;
        double r593980 = z;
        double r593981 = 3.0;
        double r593982 = r593980 * r593981;
        double r593983 = r593979 / r593982;
        double r593984 = r593978 - r593983;
        double r593985 = t;
        double r593986 = r593982 * r593979;
        double r593987 = r593985 / r593986;
        double r593988 = r593984 + r593987;
        return r593988;
}
↓
double f(double x, double y, double z, double t) {
        double r593989 = z;
        double r593990 = 3.0;
        double r593991 = r593989 * r593990;
        double r593992 = 7.710678676523239e-280;
        bool r593993 = r593991 <= r593992;
        double r593994 = x;
        double r593995 = y;
        double r593996 = r593995 / r593991;
        double r593997 = r593994 - r593996;
        double r593998 = 0.3333333333333333;
        double r593999 = t;
        double r594000 = r593999 / r593989;
        double r594001 = r593995 / r594000;
        double r594002 = r593998 / r594001;
        double r594003 = r593997 + r594002;
        double r594004 = r593995 / r593989;
        double r594005 = r593998 * r594004;
        double r594006 = r593994 - r594005;
        double r594007 = r593991 * r593995;
        double r594008 = r593999 / r594007;
        double r594009 = r594006 + r594008;
        double r594010 = r593993 ? r594003 : r594009;
        return r594010;
}

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

Original3.3
Target1.8
Herbie2.5
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z \cdot 3}}{y}\]

Derivation

  1. Split input into 2 regimes

  2. if (* z 3.0) < 7.710678676523239e-280

    1. Initial program 3.7

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

    3. Applied associate-/r*1.9

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

    4. Taylor expanded around 0 1.9

      \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{\color{blue}{0.3333333333333333148296162562473909929395 \cdot \frac{t}{z}}}{y}\]
    5. Using strategy rm

    6. Applied associate-/l*1.9

      \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \color{blue}{\frac{0.3333333333333333148296162562473909929395}{\frac{y}{\frac{t}{z}}}}\]

    if 7.710678676523239e-280 < (* z 3.0)

    1. Initial program 3.0

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

    2. Taylor expanded around 0 3.1

      \[\leadsto \left(x - \color{blue}{0.3333333333333333148296162562473909929395 \cdot \frac{y}{z}}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification2.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot 3 \le 7.710678676523238637135715158350394310792 \cdot 10^{-280}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{0.3333333333333333148296162562473909929395}{\frac{y}{\frac{t}{z}}}\\ \mathbf{else}:\\ \;\;\;\;\left(x - 0.3333333333333333148296162562473909929395 \cdot \frac{y}{z}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\\ \end{array}\]

Reproduce

herbie shell --seed 2019294 
(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))))