Average Error: 6.5 → 1.8
Time: 54.6s
Precision: 64
\[x - \frac{y \cdot \left(z - t\right)}{a}\]
↓
\[\begin{array}{l} \mathbf{if}\;a \le -1.7970758753613627 \cdot 10^{+105}:\\ \;\;\;\;x - y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;a \le 1.2591825253525602 \cdot 10^{-146}:\\ \;\;\;\;x - \frac{\left(z - t\right) \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\sqrt[3]{a} \cdot \sqrt[3]{a}} \cdot \frac{z - t}{\sqrt[3]{a}}\\ \end{array}\]
x - \frac{y \cdot \left(z - t\right)}{a}
↓
\begin{array}{l}
\mathbf{if}\;a \le -1.7970758753613627 \cdot 10^{+105}:\\
\;\;\;\;x - y \cdot \frac{z - t}{a}\\

\mathbf{elif}\;a \le 1.2591825253525602 \cdot 10^{-146}:\\
\;\;\;\;x - \frac{\left(z - t\right) \cdot y}{a}\\

\mathbf{else}:\\
\;\;\;\;x - \frac{y}{\sqrt[3]{a} \cdot \sqrt[3]{a}} \cdot \frac{z - t}{\sqrt[3]{a}}\\

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r15949676 = x;
        double r15949677 = y;
        double r15949678 = z;
        double r15949679 = t;
        double r15949680 = r15949678 - r15949679;
        double r15949681 = r15949677 * r15949680;
        double r15949682 = a;
        double r15949683 = r15949681 / r15949682;
        double r15949684 = r15949676 - r15949683;
        return r15949684;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r15949685 = a;
        double r15949686 = -1.7970758753613627e+105;
        bool r15949687 = r15949685 <= r15949686;
        double r15949688 = x;
        double r15949689 = y;
        double r15949690 = z;
        double r15949691 = t;
        double r15949692 = r15949690 - r15949691;
        double r15949693 = r15949692 / r15949685;
        double r15949694 = r15949689 * r15949693;
        double r15949695 = r15949688 - r15949694;
        double r15949696 = 1.2591825253525602e-146;
        bool r15949697 = r15949685 <= r15949696;
        double r15949698 = r15949692 * r15949689;
        double r15949699 = r15949698 / r15949685;
        double r15949700 = r15949688 - r15949699;
        double r15949701 = cbrt(r15949685);
        double r15949702 = r15949701 * r15949701;
        double r15949703 = r15949689 / r15949702;
        double r15949704 = r15949692 / r15949701;
        double r15949705 = r15949703 * r15949704;
        double r15949706 = r15949688 - r15949705;
        double r15949707 = r15949697 ? r15949700 : r15949706;
        double r15949708 = r15949687 ? r15949695 : r15949707;
        return r15949708;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original6.5
Target0.7
Herbie1.8
\[\begin{array}{l} \mathbf{if}\;y \lt -1.0761266216389975 \cdot 10^{-10}:\\ \;\;\;\;x - \frac{1.0}{\frac{\frac{a}{z - t}}{y}}\\ \mathbf{elif}\;y \lt 2.894426862792089 \cdot 10^{-49}:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if a < -1.7970758753613627e+105

    1. Initial program 11.8

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

    3. Applied *-un-lft-identity11.8

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

    4. Applied times-frac0.6

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

    5. Simplified0.6

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

    if -1.7970758753613627e+105 < a < 1.2591825253525602e-146

    1. Initial program 2.2

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

    if 1.2591825253525602e-146 < a

    1. Initial program 7.5

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

    3. Applied add-cube-cbrt7.9

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

    4. Applied times-frac2.1

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

  4. Final simplification1.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;a \le -1.7970758753613627 \cdot 10^{+105}:\\ \;\;\;\;x - y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;a \le 1.2591825253525602 \cdot 10^{-146}:\\ \;\;\;\;x - \frac{\left(z - t\right) \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\sqrt[3]{a} \cdot \sqrt[3]{a}} \cdot \frac{z - t}{\sqrt[3]{a}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019165 
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, F"

  :herbie-target
  (if (< y -1.0761266216389975e-10) (- x (/ 1.0 (/ (/ a (- z t)) y))) (if (< y 2.894426862792089e-49) (- x (/ (* y (- z t)) a)) (- x (/ y (/ a (- z t))))))

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