Average Error: 3.4 → 0.6
Time: 5.8s
Precision: 64
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -487590429957737517416448:\\ \;\;\;\;\left(x - 0.3333333333333333148296162562473909929395 \cdot \frac{y}{z}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\\ \mathbf{elif}\;t \le 5.180963650856014659509226956777421915555 \cdot 10^{-113}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{y}}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + 0.3333333333333333148296162562473909929395 \cdot \frac{t}{z \cdot y}\\ \end{array}\]
\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}
↓
\begin{array}{l}
\mathbf{if}\;t \le -487590429957737517416448:\\
\;\;\;\;\left(x - 0.3333333333333333148296162562473909929395 \cdot \frac{y}{z}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\\

\mathbf{elif}\;t \le 5.180963650856014659509226956777421915555 \cdot 10^{-113}:\\
\;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{y}}{z \cdot 3}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r517979 = x;
        double r517980 = y;
        double r517981 = z;
        double r517982 = 3.0;
        double r517983 = r517981 * r517982;
        double r517984 = r517980 / r517983;
        double r517985 = r517979 - r517984;
        double r517986 = t;
        double r517987 = r517983 * r517980;
        double r517988 = r517986 / r517987;
        double r517989 = r517985 + r517988;
        return r517989;
}
↓
double f(double x, double y, double z, double t) {
        double r517990 = t;
        double r517991 = -4.875904299577375e+23;
        bool r517992 = r517990 <= r517991;
        double r517993 = x;
        double r517994 = 0.3333333333333333;
        double r517995 = y;
        double r517996 = z;
        double r517997 = r517995 / r517996;
        double r517998 = r517994 * r517997;
        double r517999 = r517993 - r517998;
        double r518000 = 3.0;
        double r518001 = r517996 * r518000;
        double r518002 = r518001 * r517995;
        double r518003 = r517990 / r518002;
        double r518004 = r517999 + r518003;
        double r518005 = 5.1809636508560147e-113;
        bool r518006 = r517990 <= r518005;
        double r518007 = r517995 / r518001;
        double r518008 = r517993 - r518007;
        double r518009 = r517990 / r517995;
        double r518010 = r518009 / r518001;
        double r518011 = r518008 + r518010;
        double r518012 = r517996 * r517995;
        double r518013 = r517990 / r518012;
        double r518014 = r517994 * r518013;
        double r518015 = r518008 + r518014;
        double r518016 = r518006 ? r518011 : r518015;
        double r518017 = r517992 ? r518004 : r518016;
        return r518017;
}

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

Original3.4
Target1.6
Herbie0.6
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z \cdot 3}}{y}\]

Derivation

  1. Split input into 3 regimes

  2. if t < -4.875904299577375e+23

    1. Initial program 0.3

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

    2. Taylor expanded around 0 0.4

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

    if -4.875904299577375e+23 < t < 5.1809636508560147e-113

    1. Initial program 5.9

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

    3. Applied add-cube-cbrt6.0

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

    4. Applied times-frac0.8

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

    6. Applied associate-*l/0.4

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

    7. Simplified0.2

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

    if 5.1809636508560147e-113 < t

    1. Initial program 1.4

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

    2. Taylor expanded around 0 1.4

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

  4. Final simplification0.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -487590429957737517416448:\\ \;\;\;\;\left(x - 0.3333333333333333148296162562473909929395 \cdot \frac{y}{z}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\\ \mathbf{elif}\;t \le 5.180963650856014659509226956777421915555 \cdot 10^{-113}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{y}}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + 0.3333333333333333148296162562473909929395 \cdot \frac{t}{z \cdot y}\\ \end{array}\]

Reproduce

herbie shell --seed 1978988140 
(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))))