Average Error: 6.8 → 3.6
Time: 5.1s
Precision: 64
\[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -3.7159402059423155 \cdot 10^{84} \lor \neg \left(z \le 9.3558992132836225 \cdot 10^{148}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \left(\sqrt[3]{\left(y \cdot z - x\right) \cdot \frac{1}{t \cdot z - x}} \cdot \sqrt[3]{\left(y \cdot z - x\right) \cdot \frac{1}{t \cdot z - x}}\right) \cdot \sqrt[3]{\left(y \cdot z - x\right) \cdot \frac{1}{t \cdot z - x}}}{x + 1}\\ \end{array}\]
\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}
↓
\begin{array}{l}
\mathbf{if}\;z \le -3.7159402059423155 \cdot 10^{84} \lor \neg \left(z \le 9.3558992132836225 \cdot 10^{148}\right):\\
\;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r942966 = x;
        double r942967 = y;
        double r942968 = z;
        double r942969 = r942967 * r942968;
        double r942970 = r942969 - r942966;
        double r942971 = t;
        double r942972 = r942971 * r942968;
        double r942973 = r942972 - r942966;
        double r942974 = r942970 / r942973;
        double r942975 = r942966 + r942974;
        double r942976 = 1.0;
        double r942977 = r942966 + r942976;
        double r942978 = r942975 / r942977;
        return r942978;
}
↓
double f(double x, double y, double z, double t) {
        double r942979 = z;
        double r942980 = -3.7159402059423155e+84;
        bool r942981 = r942979 <= r942980;
        double r942982 = 9.355899213283623e+148;
        bool r942983 = r942979 <= r942982;
        double r942984 = !r942983;
        bool r942985 = r942981 || r942984;
        double r942986 = x;
        double r942987 = y;
        double r942988 = t;
        double r942989 = r942987 / r942988;
        double r942990 = r942986 + r942989;
        double r942991 = 1.0;
        double r942992 = r942986 + r942991;
        double r942993 = r942990 / r942992;
        double r942994 = r942987 * r942979;
        double r942995 = r942994 - r942986;
        double r942996 = 1.0;
        double r942997 = r942988 * r942979;
        double r942998 = r942997 - r942986;
        double r942999 = r942996 / r942998;
        double r943000 = r942995 * r942999;
        double r943001 = cbrt(r943000);
        double r943002 = r943001 * r943001;
        double r943003 = r943002 * r943001;
        double r943004 = r942986 + r943003;
        double r943005 = r943004 / r942992;
        double r943006 = r942985 ? r942993 : r943005;
        return r943006;
}

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

Original6.8
Target0.3
Herbie3.6
\[\frac{x + \left(\frac{y}{t - \frac{x}{z}} - \frac{x}{t \cdot z - x}\right)}{x + 1}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -3.7159402059423155e+84 or 9.355899213283623e+148 < z

    1. Initial program 19.2

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\]

    2. Taylor expanded around inf 7.6

      \[\leadsto \frac{x + \color{blue}{\frac{y}{t}}}{x + 1}\]

    if -3.7159402059423155e+84 < z < 9.355899213283623e+148

    1. Initial program 1.5

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\]
    2. Using strategy rm

    3. Applied div-inv1.6

      \[\leadsto \frac{x + \color{blue}{\left(y \cdot z - x\right) \cdot \frac{1}{t \cdot z - x}}}{x + 1}\]
    4. Using strategy rm

    5. Applied add-cube-cbrt1.8

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

  4. Final simplification3.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -3.7159402059423155 \cdot 10^{84} \lor \neg \left(z \le 9.3558992132836225 \cdot 10^{148}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \left(\sqrt[3]{\left(y \cdot z - x\right) \cdot \frac{1}{t \cdot z - x}} \cdot \sqrt[3]{\left(y \cdot z - x\right) \cdot \frac{1}{t \cdot z - x}}\right) \cdot \sqrt[3]{\left(y \cdot z - x\right) \cdot \frac{1}{t \cdot z - x}}}{x + 1}\\ \end{array}\]

Reproduce

herbie shell --seed 2020035 
(FPCore (x y z t)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, A"
  :precision binary64

  :herbie-target
  (/ (+ x (- (/ y (- t (/ x z))) (/ x (- (* t z) x)))) (+ x 1))

  (/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1)))