Average Error: 6.8 → 3.2
Time: 3.2s
Precision: 64
\[x + \frac{\left(y - x\right) \cdot z}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot z}{t} \le 5.7276462089243311 \cdot 10^{203}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{t} \cdot z\\ \end{array}\]
x + \frac{\left(y - x\right) \cdot z}{t}
↓
\begin{array}{l}
\mathbf{if}\;x + \frac{\left(y - x\right) \cdot z}{t} \le 5.7276462089243311 \cdot 10^{203}:\\
\;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r448126 = x;
        double r448127 = y;
        double r448128 = r448127 - r448126;
        double r448129 = z;
        double r448130 = r448128 * r448129;
        double r448131 = t;
        double r448132 = r448130 / r448131;
        double r448133 = r448126 + r448132;
        return r448133;
}
↓
double f(double x, double y, double z, double t) {
        double r448134 = x;
        double r448135 = y;
        double r448136 = r448135 - r448134;
        double r448137 = z;
        double r448138 = r448136 * r448137;
        double r448139 = t;
        double r448140 = r448138 / r448139;
        double r448141 = r448134 + r448140;
        double r448142 = 5.727646208924331e+203;
        bool r448143 = r448141 <= r448142;
        double r448144 = r448137 / r448139;
        double r448145 = r448136 * r448144;
        double r448146 = r448134 + r448145;
        double r448147 = r448136 / r448139;
        double r448148 = r448147 * r448137;
        double r448149 = r448134 + r448148;
        double r448150 = r448143 ? r448146 : r448149;
        return r448150;
}

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

Original6.8
Target2.1
Herbie3.2
\[\begin{array}{l} \mathbf{if}\;x \lt -9.0255111955330046 \cdot 10^{-135}:\\ \;\;\;\;x - \frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{elif}\;x \lt 4.2750321637007147 \cdot 10^{-250}:\\ \;\;\;\;x + \frac{y - x}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (+ x (/ (* (- y x) z) t)) < 5.727646208924331e+203

    1. Initial program 4.7

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

    3. Applied *-un-lft-identity4.7

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

    4. Applied times-frac1.7

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

    5. Simplified1.7

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

    if 5.727646208924331e+203 < (+ x (/ (* (- y x) z) t))

    1. Initial program 19.2

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

    3. Applied associate-/l*3.3

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

    5. Applied associate-/r/12.2

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

  4. Final simplification3.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot z}{t} \le 5.7276462089243311 \cdot 10^{203}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{t} \cdot z\\ \end{array}\]

Reproduce

herbie shell --seed 2020034 
(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)))