Average Error: 2.2 → 1.6
Time: 14.9s
Precision: 64
\[\frac{x}{y} \cdot \left(z - t\right) + t\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -2.3965576020640518 \cdot 10^{99}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \mathbf{elif}\;y \le 1.47008867651433422 \cdot 10^{-30}:\\ \;\;\;\;\left(\frac{x \cdot z}{y} + \left(-\frac{t \cdot x}{y}\right)\right) + t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \end{array}\]
\frac{x}{y} \cdot \left(z - t\right) + t
↓
\begin{array}{l}
\mathbf{if}\;y \le -2.3965576020640518 \cdot 10^{99}:\\
\;\;\;\;x \cdot \frac{z - t}{y} + t\\

\mathbf{elif}\;y \le 1.47008867651433422 \cdot 10^{-30}:\\
\;\;\;\;\left(\frac{x \cdot z}{y} + \left(-\frac{t \cdot x}{y}\right)\right) + t\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r365160 = x;
        double r365161 = y;
        double r365162 = r365160 / r365161;
        double r365163 = z;
        double r365164 = t;
        double r365165 = r365163 - r365164;
        double r365166 = r365162 * r365165;
        double r365167 = r365166 + r365164;
        return r365167;
}
↓
double f(double x, double y, double z, double t) {
        double r365168 = y;
        double r365169 = -2.396557602064052e+99;
        bool r365170 = r365168 <= r365169;
        double r365171 = x;
        double r365172 = z;
        double r365173 = t;
        double r365174 = r365172 - r365173;
        double r365175 = r365174 / r365168;
        double r365176 = r365171 * r365175;
        double r365177 = r365176 + r365173;
        double r365178 = 1.4700886765143342e-30;
        bool r365179 = r365168 <= r365178;
        double r365180 = r365171 * r365172;
        double r365181 = r365180 / r365168;
        double r365182 = r365173 * r365171;
        double r365183 = r365182 / r365168;
        double r365184 = -r365183;
        double r365185 = r365181 + r365184;
        double r365186 = r365185 + r365173;
        double r365187 = r365171 / r365168;
        double r365188 = r365187 * r365174;
        double r365189 = r365188 + r365173;
        double r365190 = r365179 ? r365186 : r365189;
        double r365191 = r365170 ? r365177 : r365190;
        return r365191;
}

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
Target2.5
Herbie1.6
\[\begin{array}{l} \mathbf{if}\;z \lt 2.7594565545626922 \cdot 10^{-282}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{elif}\;z \lt 2.326994450874436 \cdot 10^{-110}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if y < -2.396557602064052e+99

    1. Initial program 1.4

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

    3. Applied div-inv1.4

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

    4. Applied associate-*l*1.2

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

    5. Simplified1.1

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

    if -2.396557602064052e+99 < y < 1.4700886765143342e-30

    1. Initial program 3.5

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

    3. Applied add-cube-cbrt4.2

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

    4. Applied *-un-lft-identity4.2

      \[\leadsto \frac{\color{blue}{1 \cdot x}}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}} \cdot \left(z - t\right) + t\]

    5. Applied times-frac4.2

      \[\leadsto \color{blue}{\left(\frac{1}{\sqrt[3]{y} \cdot \sqrt[3]{y}} \cdot \frac{x}{\sqrt[3]{y}}\right)} \cdot \left(z - t\right) + t\]

    6. Applied associate-*l*2.3

      \[\leadsto \color{blue}{\frac{1}{\sqrt[3]{y} \cdot \sqrt[3]{y}} \cdot \left(\frac{x}{\sqrt[3]{y}} \cdot \left(z - t\right)\right)} + t\]
    7. Using strategy rm

    8. Applied add-cbrt-cube2.4

      \[\leadsto \frac{1}{\sqrt[3]{y} \cdot \color{blue}{\sqrt[3]{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}}}} \cdot \left(\frac{x}{\sqrt[3]{y}} \cdot \left(z - t\right)\right) + t\]

    9. Simplified2.4

      \[\leadsto \frac{1}{\sqrt[3]{y} \cdot \sqrt[3]{\color{blue}{{\left(\sqrt[3]{y}\right)}^{3}}}} \cdot \left(\frac{x}{\sqrt[3]{y}} \cdot \left(z - t\right)\right) + t\]
    10. Using strategy rm

    11. Applied sub-neg2.4

      \[\leadsto \frac{1}{\sqrt[3]{y} \cdot \sqrt[3]{{\left(\sqrt[3]{y}\right)}^{3}}} \cdot \left(\frac{x}{\sqrt[3]{y}} \cdot \color{blue}{\left(z + \left(-t\right)\right)}\right) + t\]

    12. Applied distribute-lft-in2.4

      \[\leadsto \frac{1}{\sqrt[3]{y} \cdot \sqrt[3]{{\left(\sqrt[3]{y}\right)}^{3}}} \cdot \color{blue}{\left(\frac{x}{\sqrt[3]{y}} \cdot z + \frac{x}{\sqrt[3]{y}} \cdot \left(-t\right)\right)} + t\]

    13. Applied distribute-lft-in2.4

      \[\leadsto \color{blue}{\left(\frac{1}{\sqrt[3]{y} \cdot \sqrt[3]{{\left(\sqrt[3]{y}\right)}^{3}}} \cdot \left(\frac{x}{\sqrt[3]{y}} \cdot z\right) + \frac{1}{\sqrt[3]{y} \cdot \sqrt[3]{{\left(\sqrt[3]{y}\right)}^{3}}} \cdot \left(\frac{x}{\sqrt[3]{y}} \cdot \left(-t\right)\right)\right)} + t\]

    14. Simplified2.3

      \[\leadsto \left(\color{blue}{\frac{x \cdot z}{y}} + \frac{1}{\sqrt[3]{y} \cdot \sqrt[3]{{\left(\sqrt[3]{y}\right)}^{3}}} \cdot \left(\frac{x}{\sqrt[3]{y}} \cdot \left(-t\right)\right)\right) + t\]

    15. Simplified2.1

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

    if 1.4700886765143342e-30 < y

    1. Initial program 1.1

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

  4. Final simplification1.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -2.3965576020640518 \cdot 10^{99}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \mathbf{elif}\;y \le 1.47008867651433422 \cdot 10^{-30}:\\ \;\;\;\;\left(\frac{x \cdot z}{y} + \left(-\frac{t \cdot x}{y}\right)\right) + t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \end{array}\]

Reproduce

herbie shell --seed 2020046 
(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))