Average Error: 6.3 → 0.8
Time: 16.3s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{a}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -3.506169073250434556576682563271829432785 \cdot 10^{60} \lor \neg \left(y \le 5122316469.390033721923828125\right):\\ \;\;\;\;x - y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot \left(t - z\right)}{a}\\ \end{array}\]
x + \frac{y \cdot \left(z - t\right)}{a}
↓
\begin{array}{l}
\mathbf{if}\;y \le -3.506169073250434556576682563271829432785 \cdot 10^{60} \lor \neg \left(y \le 5122316469.390033721923828125\right):\\
\;\;\;\;x - y \cdot \frac{t - z}{a}\\

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

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r271839 = x;
        double r271840 = y;
        double r271841 = z;
        double r271842 = t;
        double r271843 = r271841 - r271842;
        double r271844 = r271840 * r271843;
        double r271845 = a;
        double r271846 = r271844 / r271845;
        double r271847 = r271839 + r271846;
        return r271847;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r271848 = y;
        double r271849 = -3.5061690732504346e+60;
        bool r271850 = r271848 <= r271849;
        double r271851 = 5122316469.390034;
        bool r271852 = r271848 <= r271851;
        double r271853 = !r271852;
        bool r271854 = r271850 || r271853;
        double r271855 = x;
        double r271856 = t;
        double r271857 = z;
        double r271858 = r271856 - r271857;
        double r271859 = a;
        double r271860 = r271858 / r271859;
        double r271861 = r271848 * r271860;
        double r271862 = r271855 - r271861;
        double r271863 = r271848 * r271858;
        double r271864 = r271863 / r271859;
        double r271865 = r271855 - r271864;
        double r271866 = r271854 ? r271862 : r271865;
        return r271866;
}

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

Original6.3
Target0.6
Herbie0.8
\[\begin{array}{l} \mathbf{if}\;y \lt -1.07612662163899753216593153715602325729 \cdot 10^{-10}:\\ \;\;\;\;x + \frac{1}{\frac{\frac{a}{z - t}}{y}}\\ \mathbf{elif}\;y \lt 2.894426862792089097262541964056085749132 \cdot 10^{-49}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -3.5061690732504346e+60 or 5122316469.390034 < y

    1. Initial program 18.0

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

    2. Simplified4.5

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

    4. Applied div-inv4.6

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

    5. Applied associate-*l*1.0

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

    6. Simplified0.9

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

    if -3.5061690732504346e+60 < y < 5122316469.390034

    1. Initial program 0.8

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

    2. Simplified1.7

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

    4. Applied add-cube-cbrt2.2

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

    5. Applied add-cube-cbrt2.3

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

    6. Applied times-frac2.3

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

    7. Applied associate-*l*0.8

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

    8. Simplified0.9

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

    10. Applied pow10.9

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

    11. Applied pow10.9

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

    12. Applied pow-prod-down0.9

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

    13. Simplified0.8

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

  4. Final simplification0.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -3.506169073250434556576682563271829432785 \cdot 10^{60} \lor \neg \left(y \le 5122316469.390033721923828125\right):\\ \;\;\;\;x - y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot \left(t - z\right)}{a}\\ \end{array}\]

Reproduce

herbie shell --seed 2019174 
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, E"

  :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)))