Average Error: 26.4 → 7.5
Time: 15.3s
Precision: 64
\[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} = -\infty \lor \neg \left(\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \le 1.3789470957892983 \cdot 10^{302}\right):\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(\left(t + y\right) \cdot a - y \cdot b\right) + \left(x + y\right) \cdot z}{\left(x + t\right) + y}\\ \end{array}\]
\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}
↓
\begin{array}{l}
\mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} = -\infty \lor \neg \left(\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \le 1.3789470957892983 \cdot 10^{302}\right):\\
\;\;\;\;\left(a + z\right) - b\\

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

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r951834 = x;
        double r951835 = y;
        double r951836 = r951834 + r951835;
        double r951837 = z;
        double r951838 = r951836 * r951837;
        double r951839 = t;
        double r951840 = r951839 + r951835;
        double r951841 = a;
        double r951842 = r951840 * r951841;
        double r951843 = r951838 + r951842;
        double r951844 = b;
        double r951845 = r951835 * r951844;
        double r951846 = r951843 - r951845;
        double r951847 = r951834 + r951839;
        double r951848 = r951847 + r951835;
        double r951849 = r951846 / r951848;
        return r951849;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r951850 = x;
        double r951851 = y;
        double r951852 = r951850 + r951851;
        double r951853 = z;
        double r951854 = r951852 * r951853;
        double r951855 = t;
        double r951856 = r951855 + r951851;
        double r951857 = a;
        double r951858 = r951856 * r951857;
        double r951859 = r951854 + r951858;
        double r951860 = b;
        double r951861 = r951851 * r951860;
        double r951862 = r951859 - r951861;
        double r951863 = r951850 + r951855;
        double r951864 = r951863 + r951851;
        double r951865 = r951862 / r951864;
        double r951866 = -inf.0;
        bool r951867 = r951865 <= r951866;
        double r951868 = 1.3789470957892983e+302;
        bool r951869 = r951865 <= r951868;
        double r951870 = !r951869;
        bool r951871 = r951867 || r951870;
        double r951872 = r951857 + r951853;
        double r951873 = r951872 - r951860;
        double r951874 = r951858 - r951861;
        double r951875 = r951874 + r951854;
        double r951876 = r951875 / r951864;
        double r951877 = r951871 ? r951873 : r951876;
        return r951877;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original26.4
Target11.3
Herbie7.5
\[\begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \lt -3.5813117084150564 \cdot 10^{153}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \lt 1.2285964308315609 \cdot 10^{82}:\\ \;\;\;\;\frac{1}{\frac{\left(x + t\right) + y}{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)) < -inf.0 or 1.3789470957892983e+302 < (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

    1. Initial program 63.8

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

    3. Applied clear-num63.8

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

    4. Taylor expanded around 0 17.9

      \[\leadsto \color{blue}{\left(a + z\right) - b}\]

    if -inf.0 < (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)) < 1.3789470957892983e+302

    1. Initial program 0.3

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

    3. Applied clear-num0.5

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

    5. Applied inv-pow0.5

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

    7. Applied div-inv0.6

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

    8. Applied unpow-prod-down0.6

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

    9. Simplified0.5

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

    11. Applied *-un-lft-identity0.5

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

    12. Applied associate-*l*0.5

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

    13. Simplified0.3

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

  4. Final simplification7.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} = -\infty \lor \neg \left(\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \le 1.3789470957892983 \cdot 10^{302}\right):\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(\left(t + y\right) \cdot a - y \cdot b\right) + \left(x + y\right) \cdot z}{\left(x + t\right) + y}\\ \end{array}\]

Reproduce

herbie shell --seed 2020047 
(FPCore (x y z t a b)
  :name "AI.Clustering.Hierarchical.Internal:ward from clustering-0.2.1"
  :precision binary64

  :herbie-target
  (if (< (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)) -3.5813117084150564e+153) (- (+ z a) b) (if (< (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)) 1.2285964308315609e+82) (/ 1 (/ (+ (+ x t) y) (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)))) (- (+ z a) b)))

  (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)))