Average Error: 6.5 → 1.3
Time: 3.5s
Precision: 64
\[x + \frac{\left(y - x\right) \cdot z}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot z}{t} = -\infty:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot z}{t} \le 1.34935661525439967 \cdot 10^{112}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array}\]
x + \frac{\left(y - x\right) \cdot z}{t}
↓
\begin{array}{l}
\mathbf{if}\;x + \frac{\left(y - x\right) \cdot z}{t} = -\infty:\\
\;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\

\mathbf{elif}\;x + \frac{\left(y - x\right) \cdot z}{t} \le 1.34935661525439967 \cdot 10^{112}:\\
\;\;\;\;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 r657610 = x;
        double r657611 = y;
        double r657612 = r657611 - r657610;
        double r657613 = z;
        double r657614 = r657612 * r657613;
        double r657615 = t;
        double r657616 = r657614 / r657615;
        double r657617 = r657610 + r657616;
        return r657617;
}
↓
double f(double x, double y, double z, double t) {
        double r657618 = x;
        double r657619 = y;
        double r657620 = r657619 - r657618;
        double r657621 = z;
        double r657622 = r657620 * r657621;
        double r657623 = t;
        double r657624 = r657622 / r657623;
        double r657625 = r657618 + r657624;
        double r657626 = -inf.0;
        bool r657627 = r657625 <= r657626;
        double r657628 = r657621 / r657623;
        double r657629 = r657620 * r657628;
        double r657630 = r657618 + r657629;
        double r657631 = 1.3493566152543997e+112;
        bool r657632 = r657625 <= r657631;
        double r657633 = r657623 / r657621;
        double r657634 = r657620 / r657633;
        double r657635 = r657618 + r657634;
        double r657636 = r657632 ? r657625 : r657635;
        double r657637 = r657627 ? r657630 : r657636;
        return r657637;
}

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

Original6.5
Target2.0
Herbie1.3
\[\begin{array}{l} \mathbf{if}\;x \lt -9.0255111955330046 \cdot 10^{-135}:\\ \;\;\;\;x - \frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{elif}\;x \lt 4.2750321637007147 \cdot 10^{-250}:\\ \;\;\;\;x + \frac{y - x}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array}\]

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 *-un-lft-identity64.0

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

    4. Applied times-frac0.2

      \[\leadsto x + \color{blue}{\frac{y - x}{1} \cdot \frac{z}{t}}\]

    5. Simplified0.2

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

    if -inf.0 < (+ x (/ (* (- y x) z) t)) < 1.3493566152543997e+112

    1. Initial program 1.0

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

    if 1.3493566152543997e+112 < (+ x (/ (* (- y x) z) t))

    1. Initial program 12.1

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

    3. Applied associate-/l*2.4

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

  4. Final simplification1.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot z}{t} = -\infty:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot z}{t} \le 1.34935661525439967 \cdot 10^{112}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020035 
(FPCore (x y z t)
  :name "Numeric.Histogram:binBounds from Chart-1.5.3"
  :precision binary64

  :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)))