Average Error: 26.0 → 17.8
Time: 13.3s
Precision: 64
\[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} = -\infty:\\ \;\;\;\;z\\ \mathbf{elif}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \le 3.00011947244809546 \cdot 10^{241}:\\ \;\;\;\;\left(\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b\right) \cdot \frac{1}{\left(x + t\right) + y}\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array}\]
\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:\\
\;\;\;\;z\\

\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 3.00011947244809546 \cdot 10^{241}:\\
\;\;\;\;\left(\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b\right) \cdot \frac{1}{\left(x + t\right) + y}\\

\mathbf{else}:\\
\;\;\;\;z\\

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r873210 = x;
        double r873211 = y;
        double r873212 = r873210 + r873211;
        double r873213 = z;
        double r873214 = r873212 * r873213;
        double r873215 = t;
        double r873216 = r873215 + r873211;
        double r873217 = a;
        double r873218 = r873216 * r873217;
        double r873219 = r873214 + r873218;
        double r873220 = b;
        double r873221 = r873211 * r873220;
        double r873222 = r873219 - r873221;
        double r873223 = r873210 + r873215;
        double r873224 = r873223 + r873211;
        double r873225 = r873222 / r873224;
        return r873225;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r873226 = x;
        double r873227 = y;
        double r873228 = r873226 + r873227;
        double r873229 = z;
        double r873230 = r873228 * r873229;
        double r873231 = t;
        double r873232 = r873231 + r873227;
        double r873233 = a;
        double r873234 = r873232 * r873233;
        double r873235 = r873230 + r873234;
        double r873236 = b;
        double r873237 = r873227 * r873236;
        double r873238 = r873235 - r873237;
        double r873239 = r873226 + r873231;
        double r873240 = r873239 + r873227;
        double r873241 = r873238 / r873240;
        double r873242 = -inf.0;
        bool r873243 = r873241 <= r873242;
        double r873244 = 3.0001194724480955e+241;
        bool r873245 = r873241 <= r873244;
        double r873246 = 1.0;
        double r873247 = r873246 / r873240;
        double r873248 = r873238 * r873247;
        double r873249 = r873245 ? r873248 : r873229;
        double r873250 = r873243 ? r873229 : r873249;
        return r873250;
}

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

Original26.0
Target11.3
Herbie17.8
\[\begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \lt -3.5813117084150564 \cdot 10^{153}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \lt 1.2285964308315609 \cdot 10^{82}:\\ \;\;\;\;\frac{1}{\frac{\left(x + t\right) + y}{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)) < -inf.0 or 3.0001194724480955e+241 < (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

    1. Initial program 60.8

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

    3. Applied div-inv60.8

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

    5. Applied *-un-lft-identity60.8

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

    6. Applied associate-*l*60.8

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

    7. Simplified60.8

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

    8. Taylor expanded around inf 41.5

      \[\leadsto 1 \cdot \color{blue}{z}\]

    if -inf.0 < (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)) < 3.0001194724480955e+241

    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 div-inv0.4

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

  4. Final simplification17.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} = -\infty:\\ \;\;\;\;z\\ \mathbf{elif}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \le 3.00011947244809546 \cdot 10^{241}:\\ \;\;\;\;\left(\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b\right) \cdot \frac{1}{\left(x + t\right) + y}\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array}\]

Reproduce

herbie shell --seed 2020045 
(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)))