Average Error: 6.4 → 1.1
Time: 49.6s
Precision: 64
\[x + \frac{\left(y - x\right) \cdot z}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot z}{t} = -\infty:\\ \;\;\;\;\frac{y - x}{t} \cdot z + x\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot z}{t} \le -2.715106235456037737959438890335298524578 \cdot 10^{-132}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array}\]
x + \frac{\left(y - x\right) \cdot z}{t}
↓
\begin{array}{l}
\mathbf{if}\;x + \frac{\left(y - x\right) \cdot z}{t} = -\infty:\\
\;\;\;\;\frac{y - x}{t} \cdot z + x\\

\mathbf{elif}\;x + \frac{\left(y - x\right) \cdot z}{t} \le -2.715106235456037737959438890335298524578 \cdot 10^{-132}:\\
\;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\

\mathbf{else}:\\
\;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\

\end{array}
double f(double x, double y, double z, double t) {
        double r24424612 = x;
        double r24424613 = y;
        double r24424614 = r24424613 - r24424612;
        double r24424615 = z;
        double r24424616 = r24424614 * r24424615;
        double r24424617 = t;
        double r24424618 = r24424616 / r24424617;
        double r24424619 = r24424612 + r24424618;
        return r24424619;
}
↓
double f(double x, double y, double z, double t) {
        double r24424620 = x;
        double r24424621 = y;
        double r24424622 = r24424621 - r24424620;
        double r24424623 = z;
        double r24424624 = r24424622 * r24424623;
        double r24424625 = t;
        double r24424626 = r24424624 / r24424625;
        double r24424627 = r24424620 + r24424626;
        double r24424628 = -inf.0;
        bool r24424629 = r24424627 <= r24424628;
        double r24424630 = r24424622 / r24424625;
        double r24424631 = r24424630 * r24424623;
        double r24424632 = r24424631 + r24424620;
        double r24424633 = -2.7151062354560377e-132;
        bool r24424634 = r24424627 <= r24424633;
        double r24424635 = r24424625 / r24424623;
        double r24424636 = r24424622 / r24424635;
        double r24424637 = r24424620 + r24424636;
        double r24424638 = r24424634 ? r24424627 : r24424637;
        double r24424639 = r24424629 ? r24424632 : r24424638;
        return r24424639;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original6.4
Target2.1
Herbie1.1
\[\begin{array}{l} \mathbf{if}\;x \lt -9.025511195533004570453352523209034680317 \cdot 10^{-135}:\\ \;\;\;\;x - \frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{elif}\;x \lt 4.275032163700714748507147332551979944314 \cdot 10^{-250}:\\ \;\;\;\;x + \frac{y - x}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (+ x (/ (* (- y x) z) t)) < -inf.0

    1. Initial program 64.0

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

    3. Applied associate-/l*0.3

      \[\leadsto x + \color{blue}{\frac{y - x}{\frac{t}{z}}}\]
    4. Using strategy rm

    5. Applied associate-/r/0.2

      \[\leadsto x + \color{blue}{\frac{y - x}{t} \cdot z}\]

    if -inf.0 < (+ x (/ (* (- y x) z) t)) < -2.7151062354560377e-132

    1. Initial program 0.2

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

    if -2.7151062354560377e-132 < (+ x (/ (* (- y x) z) t))

    1. Initial program 6.4

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

    3. Applied associate-/l*1.7

      \[\leadsto x + \color{blue}{\frac{y - x}{\frac{t}{z}}}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification1.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot z}{t} = -\infty:\\ \;\;\;\;\frac{y - x}{t} \cdot z + x\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot z}{t} \le -2.715106235456037737959438890335298524578 \cdot 10^{-132}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019200 
(FPCore (x y z t)
  :name "Numeric.Histogram:binBounds from Chart-1.5.3"

  :herbie-target
  (if (< x -9.025511195533005e-135) (- x (* (/ z t) (- x y))) (if (< x 4.275032163700715e-250) (+ x (* (/ (- y x) t) z)) (+ x (/ (- y x) (/ t z)))))

  (+ x (/ (* (- y x) z) t)))