Average Error: 2.2 → 0.6
Time: 4.9s
Precision: 64
\[\frac{x}{y} \cdot \left(z - t\right) + t\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{x}{y} \le -6.04867663875874172 \cdot 10^{150}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \mathbf{elif}\;\frac{x}{y} \le -1.36244919224433305 \cdot 10^{-224}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{elif}\;\frac{x}{y} \le 1.05256307658924449 \cdot 10^{-154}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \mathbf{elif}\;\frac{x}{y} \le 1.1652646933472875 \cdot 10^{195}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{x \cdot z}{y} - \frac{t \cdot x}{y}\right) + t\\ \end{array}\]
\frac{x}{y} \cdot \left(z - t\right) + t
↓
\begin{array}{l}
\mathbf{if}\;\frac{x}{y} \le -6.04867663875874172 \cdot 10^{150}:\\
\;\;\;\;x \cdot \frac{z - t}{y} + t\\

\mathbf{elif}\;\frac{x}{y} \le -1.36244919224433305 \cdot 10^{-224}:\\
\;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\

\mathbf{elif}\;\frac{x}{y} \le 1.05256307658924449 \cdot 10^{-154}:\\
\;\;\;\;x \cdot \frac{z - t}{y} + t\\

\mathbf{elif}\;\frac{x}{y} \le 1.1652646933472875 \cdot 10^{195}:\\
\;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r494119 = x;
        double r494120 = y;
        double r494121 = r494119 / r494120;
        double r494122 = z;
        double r494123 = t;
        double r494124 = r494122 - r494123;
        double r494125 = r494121 * r494124;
        double r494126 = r494125 + r494123;
        return r494126;
}
↓
double f(double x, double y, double z, double t) {
        double r494127 = x;
        double r494128 = y;
        double r494129 = r494127 / r494128;
        double r494130 = -6.048676638758742e+150;
        bool r494131 = r494129 <= r494130;
        double r494132 = z;
        double r494133 = t;
        double r494134 = r494132 - r494133;
        double r494135 = r494134 / r494128;
        double r494136 = r494127 * r494135;
        double r494137 = r494136 + r494133;
        double r494138 = -1.362449192244333e-224;
        bool r494139 = r494129 <= r494138;
        double r494140 = r494129 * r494134;
        double r494141 = r494140 + r494133;
        double r494142 = 1.0525630765892445e-154;
        bool r494143 = r494129 <= r494142;
        double r494144 = 1.1652646933472875e+195;
        bool r494145 = r494129 <= r494144;
        double r494146 = r494127 * r494132;
        double r494147 = r494146 / r494128;
        double r494148 = r494133 * r494127;
        double r494149 = r494148 / r494128;
        double r494150 = r494147 - r494149;
        double r494151 = r494150 + r494133;
        double r494152 = r494145 ? r494141 : r494151;
        double r494153 = r494143 ? r494137 : r494152;
        double r494154 = r494139 ? r494141 : r494153;
        double r494155 = r494131 ? r494137 : r494154;
        return r494155;
}

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

Original2.2
Target2.3
Herbie0.6
\[\begin{array}{l} \mathbf{if}\;z \lt 2.7594565545626922 \cdot 10^{-282}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{elif}\;z \lt 2.326994450874436 \cdot 10^{-110}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (/ x y) < -6.048676638758742e+150 or -1.362449192244333e-224 < (/ x y) < 1.0525630765892445e-154

    1. Initial program 3.7

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

    3. Applied div-inv3.7

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

    4. Applied associate-*l*1.1

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

    5. Simplified1.1

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

    if -6.048676638758742e+150 < (/ x y) < -1.362449192244333e-224 or 1.0525630765892445e-154 < (/ x y) < 1.1652646933472875e+195

    1. Initial program 0.2

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

    if 1.1652646933472875e+195 < (/ x y)

    1. Initial program 18.5

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

    3. Applied add-cube-cbrt19.2

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

    4. Applied associate-*r*19.2

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

    5. Taylor expanded around 0 1.5

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

  4. Final simplification0.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \le -6.04867663875874172 \cdot 10^{150}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \mathbf{elif}\;\frac{x}{y} \le -1.36244919224433305 \cdot 10^{-224}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{elif}\;\frac{x}{y} \le 1.05256307658924449 \cdot 10^{-154}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \mathbf{elif}\;\frac{x}{y} \le 1.1652646933472875 \cdot 10^{195}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{x \cdot z}{y} - \frac{t \cdot x}{y}\right) + t\\ \end{array}\]

Reproduce

herbie shell --seed 2020003 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cget from hsignal-0.2.7.1"
  :precision binary64

  :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))