Average Error: 2.2 → 1.7
Time: 16.9s
Precision: 64
\[\frac{x}{y} \cdot \left(z - t\right) + t\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le 1185186617532904803707928969216:\\ \;\;\;\;\left(\frac{z}{\frac{y}{x}} - \frac{t}{\frac{y}{x}}\right) + t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y}{z - t}} + t\\ \end{array}\]
\frac{x}{y} \cdot \left(z - t\right) + t
↓
\begin{array}{l}
\mathbf{if}\;x \le 1185186617532904803707928969216:\\
\;\;\;\;\left(\frac{z}{\frac{y}{x}} - \frac{t}{\frac{y}{x}}\right) + t\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r351669 = x;
        double r351670 = y;
        double r351671 = r351669 / r351670;
        double r351672 = z;
        double r351673 = t;
        double r351674 = r351672 - r351673;
        double r351675 = r351671 * r351674;
        double r351676 = r351675 + r351673;
        return r351676;
}
↓
double f(double x, double y, double z, double t) {
        double r351677 = x;
        double r351678 = 1.1851866175329048e+30;
        bool r351679 = r351677 <= r351678;
        double r351680 = z;
        double r351681 = y;
        double r351682 = r351681 / r351677;
        double r351683 = r351680 / r351682;
        double r351684 = t;
        double r351685 = r351684 / r351682;
        double r351686 = r351683 - r351685;
        double r351687 = r351686 + r351684;
        double r351688 = r351680 - r351684;
        double r351689 = r351681 / r351688;
        double r351690 = r351677 / r351689;
        double r351691 = r351690 + r351684;
        double r351692 = r351679 ? r351687 : r351691;
        return r351692;
}

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
Herbie1.7
\[\begin{array}{l} \mathbf{if}\;z \lt 2.759456554562692182563154937894909044548 \cdot 10^{-282}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{elif}\;z \lt 2.32699445087443595687739933019129648094 \cdot 10^{-110}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if x < 1.1851866175329048e+30

    1. Initial program 1.7

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

    3. Applied add-cube-cbrt2.2

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

    4. Applied associate-*r*2.2

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

    5. Taylor expanded around 0 4.3

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

    6. Simplified1.7

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

    if 1.1851866175329048e+30 < x

    1. Initial program 4.6

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

    3. Applied *-un-lft-identity4.6

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

    4. Applied associate-*l*4.6

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

    5. Simplified1.8

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

  4. Final simplification1.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le 1185186617532904803707928969216:\\ \;\;\;\;\left(\frac{z}{\frac{y}{x}} - \frac{t}{\frac{y}{x}}\right) + t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y}{z - t}} + t\\ \end{array}\]

Reproduce

herbie shell --seed 2019195 
(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))