Average Error: 6.4 → 1.8
Time: 15.1s
Precision: 64
\[x + \frac{\left(y - x\right) \cdot z}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -1.47437460621894122515597907358401131123 \cdot 10^{-73}:\\ \;\;\;\;x + \frac{y - x}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\ \end{array}\]
x + \frac{\left(y - x\right) \cdot z}{t}
↓
\begin{array}{l}
\mathbf{if}\;z \le -1.47437460621894122515597907358401131123 \cdot 10^{-73}:\\
\;\;\;\;x + \frac{y - x}{t} \cdot z\\

\mathbf{else}:\\
\;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\

\end{array}
double f(double x, double y, double z, double t) {
        double r22418807 = x;
        double r22418808 = y;
        double r22418809 = r22418808 - r22418807;
        double r22418810 = z;
        double r22418811 = r22418809 * r22418810;
        double r22418812 = t;
        double r22418813 = r22418811 / r22418812;
        double r22418814 = r22418807 + r22418813;
        return r22418814;
}
↓
double f(double x, double y, double z, double t) {
        double r22418815 = z;
        double r22418816 = -1.4743746062189412e-73;
        bool r22418817 = r22418815 <= r22418816;
        double r22418818 = x;
        double r22418819 = y;
        double r22418820 = r22418819 - r22418818;
        double r22418821 = t;
        double r22418822 = r22418820 / r22418821;
        double r22418823 = r22418822 * r22418815;
        double r22418824 = r22418818 + r22418823;
        double r22418825 = r22418815 / r22418821;
        double r22418826 = r22418820 * r22418825;
        double r22418827 = r22418818 + r22418826;
        double r22418828 = r22418817 ? r22418824 : r22418827;
        return r22418828;
}

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
Target1.9
Herbie1.8
\[\begin{array}{l} \mathbf{if}\;x \lt -9.025511195533004570453352523209034680317 \cdot 10^{-135}:\\ \;\;\;\;x - \frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{elif}\;x \lt 4.275032163700714748507147332551979944314 \cdot 10^{-250}:\\ \;\;\;\;x + \frac{y - x}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -1.4743746062189412e-73

    1. Initial program 11.2

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

    3. Applied associate-/l*2.5

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

    5. Applied associate-/r/2.1

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

    if -1.4743746062189412e-73 < z

    1. Initial program 4.8

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

    3. Applied *-un-lft-identity4.8

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

    4. Applied times-frac1.8

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

    5. Simplified1.8

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

  4. Final simplification1.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -1.47437460621894122515597907358401131123 \cdot 10^{-73}:\\ \;\;\;\;x + \frac{y - x}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\ \end{array}\]

Reproduce

herbie shell --seed 2019179 
(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)))