Average Error: 27.0 → 7.8
Time: 19.5s
Precision: 64
\[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \le -8.416712259254574092270707749732520074762 \cdot 10^{242}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{elif}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \le 7.307468158284447910195168497396941423128 \cdot 10^{286}:\\ \;\;\;\;\frac{1}{\frac{x + \left(t + y\right)}{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}}\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b\\ \end{array}\]
\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}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \le -8.416712259254574092270707749732520074762 \cdot 10^{242}:\\
\;\;\;\;\left(a + z\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} \le 7.307468158284447910195168497396941423128 \cdot 10^{286}:\\
\;\;\;\;\frac{1}{\frac{x + \left(t + y\right)}{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}}\\

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

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r62722808 = x;
        double r62722809 = y;
        double r62722810 = r62722808 + r62722809;
        double r62722811 = z;
        double r62722812 = r62722810 * r62722811;
        double r62722813 = t;
        double r62722814 = r62722813 + r62722809;
        double r62722815 = a;
        double r62722816 = r62722814 * r62722815;
        double r62722817 = r62722812 + r62722816;
        double r62722818 = b;
        double r62722819 = r62722809 * r62722818;
        double r62722820 = r62722817 - r62722819;
        double r62722821 = r62722808 + r62722813;
        double r62722822 = r62722821 + r62722809;
        double r62722823 = r62722820 / r62722822;
        return r62722823;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r62722824 = x;
        double r62722825 = y;
        double r62722826 = r62722824 + r62722825;
        double r62722827 = z;
        double r62722828 = r62722826 * r62722827;
        double r62722829 = t;
        double r62722830 = r62722829 + r62722825;
        double r62722831 = a;
        double r62722832 = r62722830 * r62722831;
        double r62722833 = r62722828 + r62722832;
        double r62722834 = b;
        double r62722835 = r62722825 * r62722834;
        double r62722836 = r62722833 - r62722835;
        double r62722837 = r62722824 + r62722829;
        double r62722838 = r62722837 + r62722825;
        double r62722839 = r62722836 / r62722838;
        double r62722840 = -8.416712259254574e+242;
        bool r62722841 = r62722839 <= r62722840;
        double r62722842 = r62722831 + r62722827;
        double r62722843 = r62722842 - r62722834;
        double r62722844 = 7.307468158284448e+286;
        bool r62722845 = r62722839 <= r62722844;
        double r62722846 = 1.0;
        double r62722847 = r62722824 + r62722830;
        double r62722848 = r62722847 / r62722836;
        double r62722849 = r62722846 / r62722848;
        double r62722850 = r62722845 ? r62722849 : r62722843;
        double r62722851 = r62722841 ? r62722843 : r62722850;
        return r62722851;
}

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

Original27.0
Target11.3
Herbie7.8
\[\begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \lt -3.581311708415056427521064305370896655752 \cdot 10^{153}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \lt 1.228596430831560895857110658734089400289 \cdot 10^{82}:\\ \;\;\;\;\frac{1}{\frac{\left(x + t\right) + y}{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)) < -8.416712259254574e+242 or 7.307468158284448e+286 < (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

    1. Initial program 61.5

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

    3. Applied clear-num61.5

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

    4. Simplified61.5

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

    5. Taylor expanded around 0 17.4

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

    if -8.416712259254574e+242 < (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)) < 7.307468158284448e+286

    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. Simplified0.5

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

  4. Final simplification7.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \le -8.416712259254574092270707749732520074762 \cdot 10^{242}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{elif}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \le 7.307468158284447910195168497396941423128 \cdot 10^{286}:\\ \;\;\;\;\frac{1}{\frac{x + \left(t + y\right)}{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}}\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b\\ \end{array}\]

Reproduce

herbie shell --seed 2019174 
(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)))