Average Error: 26.4 → 7.5
Time: 7.5s
Precision: 64
\[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} = -\infty \lor \neg \left(\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \le 1.3789470957892983 \cdot 10^{302}\right):\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;1 \cdot \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\\ \end{array}\]
\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}:\\
\;\;\;\;1 \cdot \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\\

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r882351 = x;
        double r882352 = y;
        double r882353 = r882351 + r882352;
        double r882354 = z;
        double r882355 = r882353 * r882354;
        double r882356 = t;
        double r882357 = r882356 + r882352;
        double r882358 = a;
        double r882359 = r882357 * r882358;
        double r882360 = r882355 + r882359;
        double r882361 = b;
        double r882362 = r882352 * r882361;
        double r882363 = r882360 - r882362;
        double r882364 = r882351 + r882356;
        double r882365 = r882364 + r882352;
        double r882366 = r882363 / r882365;
        return r882366;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r882367 = x;
        double r882368 = y;
        double r882369 = r882367 + r882368;
        double r882370 = z;
        double r882371 = r882369 * r882370;
        double r882372 = t;
        double r882373 = r882372 + r882368;
        double r882374 = a;
        double r882375 = r882373 * r882374;
        double r882376 = r882371 + r882375;
        double r882377 = b;
        double r882378 = r882368 * r882377;
        double r882379 = r882376 - r882378;
        double r882380 = r882367 + r882372;
        double r882381 = r882380 + r882368;
        double r882382 = r882379 / r882381;
        double r882383 = -inf.0;
        bool r882384 = r882382 <= r882383;
        double r882385 = 1.3789470957892983e+302;
        bool r882386 = r882382 <= r882385;
        double r882387 = !r882386;
        bool r882388 = r882384 || r882387;
        double r882389 = r882374 + r882370;
        double r882390 = r882389 - r882377;
        double r882391 = 1.0;
        double r882392 = r882391 * r882382;
        double r882393 = r882388 ? r882390 : r882392;
        return r882393;
}

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 sub-neg0.5

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

    7. Applied associate-/r/0.5

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

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

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

    10. Applied associate-*l*0.5

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

    11. Simplified0.3

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

  4. Final simplification7.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} = -\infty \lor \neg \left(\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \le 1.3789470957892983 \cdot 10^{302}\right):\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;1 \cdot \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\\ \end{array}\]

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)))