Average Error: 26.8 → 17.6
Time: 21.2s
Precision: 64
\[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -1.12340553540398282974395246595228861055 \cdot 10^{66}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{elif}\;y \le -1.472184673179024906311519965673653353206 \cdot 10^{-191}:\\ \;\;\;\;\left(\left(\left(x + y\right) \cdot z + a \cdot \left(y + t\right)\right) - y \cdot b\right) \cdot \frac{1}{x + \left(y + t\right)}\\ \mathbf{elif}\;y \le -1.624020243223143567434005918463591296748 \cdot 10^{-228}:\\ \;\;\;\;a\\ \mathbf{elif}\;y \le 0.001960496957535617142814876601164542080369:\\ \;\;\;\;\left(\left(\left(x + y\right) \cdot z + a \cdot \left(y + t\right)\right) - y \cdot b\right) \cdot \frac{1}{x + \left(y + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b\\ \end{array}\]
\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}\;y \le -1.12340553540398282974395246595228861055 \cdot 10^{66}:\\
\;\;\;\;\left(a + z\right) - b\\

\mathbf{elif}\;y \le -1.472184673179024906311519965673653353206 \cdot 10^{-191}:\\
\;\;\;\;\left(\left(\left(x + y\right) \cdot z + a \cdot \left(y + t\right)\right) - y \cdot b\right) \cdot \frac{1}{x + \left(y + t\right)}\\

\mathbf{elif}\;y \le -1.624020243223143567434005918463591296748 \cdot 10^{-228}:\\
\;\;\;\;a\\

\mathbf{elif}\;y \le 0.001960496957535617142814876601164542080369:\\
\;\;\;\;\left(\left(\left(x + y\right) \cdot z + a \cdot \left(y + t\right)\right) - y \cdot b\right) \cdot \frac{1}{x + \left(y + t\right)}\\

\mathbf{else}:\\
\;\;\;\;\left(a + z\right) - b\\

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r54298810 = x;
        double r54298811 = y;
        double r54298812 = r54298810 + r54298811;
        double r54298813 = z;
        double r54298814 = r54298812 * r54298813;
        double r54298815 = t;
        double r54298816 = r54298815 + r54298811;
        double r54298817 = a;
        double r54298818 = r54298816 * r54298817;
        double r54298819 = r54298814 + r54298818;
        double r54298820 = b;
        double r54298821 = r54298811 * r54298820;
        double r54298822 = r54298819 - r54298821;
        double r54298823 = r54298810 + r54298815;
        double r54298824 = r54298823 + r54298811;
        double r54298825 = r54298822 / r54298824;
        return r54298825;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r54298826 = y;
        double r54298827 = -1.1234055354039828e+66;
        bool r54298828 = r54298826 <= r54298827;
        double r54298829 = a;
        double r54298830 = z;
        double r54298831 = r54298829 + r54298830;
        double r54298832 = b;
        double r54298833 = r54298831 - r54298832;
        double r54298834 = -1.472184673179025e-191;
        bool r54298835 = r54298826 <= r54298834;
        double r54298836 = x;
        double r54298837 = r54298836 + r54298826;
        double r54298838 = r54298837 * r54298830;
        double r54298839 = t;
        double r54298840 = r54298826 + r54298839;
        double r54298841 = r54298829 * r54298840;
        double r54298842 = r54298838 + r54298841;
        double r54298843 = r54298826 * r54298832;
        double r54298844 = r54298842 - r54298843;
        double r54298845 = 1.0;
        double r54298846 = r54298836 + r54298840;
        double r54298847 = r54298845 / r54298846;
        double r54298848 = r54298844 * r54298847;
        double r54298849 = -1.6240202432231436e-228;
        bool r54298850 = r54298826 <= r54298849;
        double r54298851 = 0.001960496957535617;
        bool r54298852 = r54298826 <= r54298851;
        double r54298853 = r54298852 ? r54298848 : r54298833;
        double r54298854 = r54298850 ? r54298829 : r54298853;
        double r54298855 = r54298835 ? r54298848 : r54298854;
        double r54298856 = r54298828 ? r54298833 : r54298855;
        return r54298856;
}

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

Original26.8
Target11.6
Herbie17.6
\[\begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \lt -3.581311708415056427521064305370896655752 \cdot 10^{153}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \lt 1.228596430831560895857110658734089400289 \cdot 10^{82}:\\ \;\;\;\;\frac{1}{\frac{\left(x + t\right) + y}{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if y < -1.1234055354039828e+66 or 0.001960496957535617 < y

    1. Initial program 39.5

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

    2. Simplified39.5

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

    3. Taylor expanded around inf 16.5

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

    if -1.1234055354039828e+66 < y < -1.472184673179025e-191 or -1.6240202432231436e-228 < y < 0.001960496957535617

    1. Initial program 16.8

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

    2. Simplified16.8

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

    4. Applied div-inv16.9

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

    if -1.472184673179025e-191 < y < -1.6240202432231436e-228

    1. Initial program 17.9

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

    2. Simplified17.9

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

    4. Applied clear-num18.0

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

    5. Taylor expanded around 0 41.8

      \[\leadsto \color{blue}{a}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification17.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -1.12340553540398282974395246595228861055 \cdot 10^{66}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{elif}\;y \le -1.472184673179024906311519965673653353206 \cdot 10^{-191}:\\ \;\;\;\;\left(\left(\left(x + y\right) \cdot z + a \cdot \left(y + t\right)\right) - y \cdot b\right) \cdot \frac{1}{x + \left(y + t\right)}\\ \mathbf{elif}\;y \le -1.624020243223143567434005918463591296748 \cdot 10^{-228}:\\ \;\;\;\;a\\ \mathbf{elif}\;y \le 0.001960496957535617142814876601164542080369:\\ \;\;\;\;\left(\left(\left(x + y\right) \cdot z + a \cdot \left(y + t\right)\right) - y \cdot b\right) \cdot \frac{1}{x + \left(y + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b\\ \end{array}\]

Reproduce

herbie shell --seed 2019171 
(FPCore (x y z t a b)
  :name "AI.Clustering.Hierarchical.Internal:ward from clustering-0.2.1"

  :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) (/ 1.0 (/ (+ (+ 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)))