Average Error: 6.2 → 1.1
Time: 18.0s
Precision: 64
\[x + \frac{\left(y - x\right) \cdot z}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot z}{t} = -\infty:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot z}{t} \le 2.4829011027507563 \cdot 10^{+286}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - x}{t} \cdot z + x\\ \end{array}\]
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 2.4829011027507563 \cdot 10^{+286}:\\
\;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r22919107 = x;
        double r22919108 = y;
        double r22919109 = r22919108 - r22919107;
        double r22919110 = z;
        double r22919111 = r22919109 * r22919110;
        double r22919112 = t;
        double r22919113 = r22919111 / r22919112;
        double r22919114 = r22919107 + r22919113;
        return r22919114;
}
↓
double f(double x, double y, double z, double t) {
        double r22919115 = x;
        double r22919116 = y;
        double r22919117 = r22919116 - r22919115;
        double r22919118 = z;
        double r22919119 = r22919117 * r22919118;
        double r22919120 = t;
        double r22919121 = r22919119 / r22919120;
        double r22919122 = r22919115 + r22919121;
        double r22919123 = -inf.0;
        bool r22919124 = r22919122 <= r22919123;
        double r22919125 = r22919118 / r22919120;
        double r22919126 = r22919117 * r22919125;
        double r22919127 = r22919115 + r22919126;
        double r22919128 = 2.4829011027507563e+286;
        bool r22919129 = r22919122 <= r22919128;
        double r22919130 = r22919117 / r22919120;
        double r22919131 = r22919130 * r22919118;
        double r22919132 = r22919131 + r22919115;
        double r22919133 = r22919129 ? r22919122 : r22919132;
        double r22919134 = r22919124 ? r22919127 : r22919133;
        return r22919134;
}

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

Original6.2
Target2.0
Herbie1.1
\[\begin{array}{l} \mathbf{if}\;x \lt -9.025511195533005 \cdot 10^{-135}:\\ \;\;\;\;x - \frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{elif}\;x \lt 4.275032163700715 \cdot 10^{-250}:\\ \;\;\;\;x + \frac{y - x}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

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

    1. Initial program 60.3

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

    3. Applied *-un-lft-identity60.3

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

    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)) < 2.4829011027507563e+286

    1. Initial program 0.8

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

    if 2.4829011027507563e+286 < (+ x (/ (* (- y x) z) t))

    1. Initial program 42.6

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

    3. Applied associate-/l*2.0

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

    5. Applied associate-/r/6.1

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

  4. Final simplification1.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot z}{t} = -\infty:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot z}{t} \le 2.4829011027507563 \cdot 10^{+286}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - x}{t} \cdot z + x\\ \end{array}\]

Reproduce

herbie shell --seed 2019158 
(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)))