Average Error: 27.3 → 8.0
Time: 6.3s
Precision: 64
\[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} = -\infty \lor \neg \left(\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \le 2.334828876963019126638500573266416450503 \cdot 10^{262}\right):\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\left(\left(x + t\right) + y\right) \cdot \frac{1}{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}}\\ \end{array}\]
\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 2.334828876963019126638500573266416450503 \cdot 10^{262}\right):\\
\;\;\;\;\left(a + z\right) - b\\

\mathbf{else}:\\
\;\;\;\;\frac{1}{\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}}\\

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r887026 = x;
        double r887027 = y;
        double r887028 = r887026 + r887027;
        double r887029 = z;
        double r887030 = r887028 * r887029;
        double r887031 = t;
        double r887032 = r887031 + r887027;
        double r887033 = a;
        double r887034 = r887032 * r887033;
        double r887035 = r887030 + r887034;
        double r887036 = b;
        double r887037 = r887027 * r887036;
        double r887038 = r887035 - r887037;
        double r887039 = r887026 + r887031;
        double r887040 = r887039 + r887027;
        double r887041 = r887038 / r887040;
        return r887041;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r887042 = x;
        double r887043 = y;
        double r887044 = r887042 + r887043;
        double r887045 = z;
        double r887046 = r887044 * r887045;
        double r887047 = t;
        double r887048 = r887047 + r887043;
        double r887049 = a;
        double r887050 = r887048 * r887049;
        double r887051 = r887046 + r887050;
        double r887052 = b;
        double r887053 = r887043 * r887052;
        double r887054 = r887051 - r887053;
        double r887055 = r887042 + r887047;
        double r887056 = r887055 + r887043;
        double r887057 = r887054 / r887056;
        double r887058 = -inf.0;
        bool r887059 = r887057 <= r887058;
        double r887060 = 2.334828876963019e+262;
        bool r887061 = r887057 <= r887060;
        double r887062 = !r887061;
        bool r887063 = r887059 || r887062;
        double r887064 = r887049 + r887045;
        double r887065 = r887064 - r887052;
        double r887066 = 1.0;
        double r887067 = r887066 / r887054;
        double r887068 = r887056 * r887067;
        double r887069 = r887066 / r887068;
        double r887070 = r887063 ? r887065 : r887069;
        return r887070;
}

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

Original27.3
Target11.4
Herbie8.0
\[\begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \lt -3.581311708415056427521064305370896655752 \cdot 10^{153}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \lt 1.228596430831560895857110658734089400289 \cdot 10^{82}:\\ \;\;\;\;\frac{1}{\frac{\left(x + t\right) + y}{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)) < -inf.0 or 2.334828876963019e+262 < (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

    1. Initial program 62.5

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

    3. Applied clear-num62.5

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

    4. Taylor expanded around 0 17.6

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

    if -inf.0 < (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)) < 2.334828876963019e+262

    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 div-inv0.6

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

  4. Final simplification8.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} = -\infty \lor \neg \left(\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \le 2.334828876963019126638500573266416450503 \cdot 10^{262}\right):\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\left(\left(x + t\right) + y\right) \cdot \frac{1}{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019353 
(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)))