Average Error: 2.0 → 1.8
Time: 17.1s
Precision: 64
\[\frac{x}{y} \cdot \left(z - t\right) + t\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -1.0528328207751368 \cdot 10^{+116}:\\ \;\;\;\;\frac{z - t}{y} \cdot x + t\\ \mathbf{elif}\;x \le 1.0663057389610308 \cdot 10^{+80}:\\ \;\;\;\;t + \left(\frac{z \cdot x}{y} - \frac{1}{\frac{\frac{y}{x}}{t}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z - t}{y} \cdot x + t\\ \end{array}\]
\frac{x}{y} \cdot \left(z - t\right) + t
↓
\begin{array}{l}
\mathbf{if}\;x \le -1.0528328207751368 \cdot 10^{+116}:\\
\;\;\;\;\frac{z - t}{y} \cdot x + t\\

\mathbf{elif}\;x \le 1.0663057389610308 \cdot 10^{+80}:\\
\;\;\;\;t + \left(\frac{z \cdot x}{y} - \frac{1}{\frac{\frac{y}{x}}{t}}\right)\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r24417042 = x;
        double r24417043 = y;
        double r24417044 = r24417042 / r24417043;
        double r24417045 = z;
        double r24417046 = t;
        double r24417047 = r24417045 - r24417046;
        double r24417048 = r24417044 * r24417047;
        double r24417049 = r24417048 + r24417046;
        return r24417049;
}
↓
double f(double x, double y, double z, double t) {
        double r24417050 = x;
        double r24417051 = -1.0528328207751368e+116;
        bool r24417052 = r24417050 <= r24417051;
        double r24417053 = z;
        double r24417054 = t;
        double r24417055 = r24417053 - r24417054;
        double r24417056 = y;
        double r24417057 = r24417055 / r24417056;
        double r24417058 = r24417057 * r24417050;
        double r24417059 = r24417058 + r24417054;
        double r24417060 = 1.0663057389610308e+80;
        bool r24417061 = r24417050 <= r24417060;
        double r24417062 = r24417053 * r24417050;
        double r24417063 = r24417062 / r24417056;
        double r24417064 = 1.0;
        double r24417065 = r24417056 / r24417050;
        double r24417066 = r24417065 / r24417054;
        double r24417067 = r24417064 / r24417066;
        double r24417068 = r24417063 - r24417067;
        double r24417069 = r24417054 + r24417068;
        double r24417070 = r24417061 ? r24417069 : r24417059;
        double r24417071 = r24417052 ? r24417059 : r24417070;
        return r24417071;
}

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

Original2.0
Target2.2
Herbie1.8
\[\begin{array}{l} \mathbf{if}\;z \lt 2.759456554562692 \cdot 10^{-282}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{elif}\;z \lt 2.326994450874436 \cdot 10^{-110}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if x < -1.0528328207751368e+116 or 1.0663057389610308e+80 < x

    1. Initial program 5.9

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

    3. Applied div-inv6.0

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

    4. Applied associate-*l*3.0

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

    5. Simplified2.9

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

    if -1.0528328207751368e+116 < x < 1.0663057389610308e+80

    1. Initial program 1.0

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

    2. Taylor expanded around 0 2.0

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

    4. Applied associate-/l*1.4

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

    6. Applied clear-num1.4

      \[\leadsto \left(\frac{x \cdot z}{y} - \color{blue}{\frac{1}{\frac{\frac{y}{x}}{t}}}\right) + t\]
  3. Recombined 2 regimes into one program.

  4. Final simplification1.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -1.0528328207751368 \cdot 10^{+116}:\\ \;\;\;\;\frac{z - t}{y} \cdot x + t\\ \mathbf{elif}\;x \le 1.0663057389610308 \cdot 10^{+80}:\\ \;\;\;\;t + \left(\frac{z \cdot x}{y} - \frac{1}{\frac{\frac{y}{x}}{t}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z - t}{y} \cdot x + t\\ \end{array}\]

Reproduce

herbie shell --seed 2019158 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cget from hsignal-0.2.7.1"

  :herbie-target
  (if (< z 2.759456554562692e-282) (+ (* (/ x y) (- z t)) t) (if (< z 2.326994450874436e-110) (+ (* x (/ (- z t) y)) t) (+ (* (/ x y) (- z t)) t)))

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