Average Error: 6.0 → 0.8
Time: 16.7s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{a}\]
↓
\[\begin{array}{l} \mathbf{if}\;a \le -1.598281406670949442324391521520754455565 \cdot 10^{-10}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \mathbf{elif}\;a \le 2.399671998072701683137690037832409821452 \cdot 10^{-142}:\\ \;\;\;\;x + \left(\frac{y \cdot z}{a} - \frac{t \cdot y}{a}\right)\\ \mathbf{elif}\;a \le 2.181728582825251587184966617016023093761 \cdot 10^{52}:\\ \;\;\;\;x + \frac{\frac{y}{a}}{\frac{1}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \end{array}\]
x + \frac{y \cdot \left(z - t\right)}{a}
↓
\begin{array}{l}
\mathbf{if}\;a \le -1.598281406670949442324391521520754455565 \cdot 10^{-10}:\\
\;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\

\mathbf{elif}\;a \le 2.399671998072701683137690037832409821452 \cdot 10^{-142}:\\
\;\;\;\;x + \left(\frac{y \cdot z}{a} - \frac{t \cdot y}{a}\right)\\

\mathbf{elif}\;a \le 2.181728582825251587184966617016023093761 \cdot 10^{52}:\\
\;\;\;\;x + \frac{\frac{y}{a}}{\frac{1}{z - t}}\\

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

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r19935679 = x;
        double r19935680 = y;
        double r19935681 = z;
        double r19935682 = t;
        double r19935683 = r19935681 - r19935682;
        double r19935684 = r19935680 * r19935683;
        double r19935685 = a;
        double r19935686 = r19935684 / r19935685;
        double r19935687 = r19935679 + r19935686;
        return r19935687;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r19935688 = a;
        double r19935689 = -1.5982814066709494e-10;
        bool r19935690 = r19935688 <= r19935689;
        double r19935691 = x;
        double r19935692 = y;
        double r19935693 = z;
        double r19935694 = t;
        double r19935695 = r19935693 - r19935694;
        double r19935696 = r19935688 / r19935695;
        double r19935697 = r19935692 / r19935696;
        double r19935698 = r19935691 + r19935697;
        double r19935699 = 2.3996719980727017e-142;
        bool r19935700 = r19935688 <= r19935699;
        double r19935701 = r19935692 * r19935693;
        double r19935702 = r19935701 / r19935688;
        double r19935703 = r19935694 * r19935692;
        double r19935704 = r19935703 / r19935688;
        double r19935705 = r19935702 - r19935704;
        double r19935706 = r19935691 + r19935705;
        double r19935707 = 2.1817285828252516e+52;
        bool r19935708 = r19935688 <= r19935707;
        double r19935709 = r19935692 / r19935688;
        double r19935710 = 1.0;
        double r19935711 = r19935710 / r19935695;
        double r19935712 = r19935709 / r19935711;
        double r19935713 = r19935691 + r19935712;
        double r19935714 = r19935708 ? r19935713 : r19935698;
        double r19935715 = r19935700 ? r19935706 : r19935714;
        double r19935716 = r19935690 ? r19935698 : r19935715;
        return r19935716;
}

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

Original6.0
Target0.7
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 3 regimes

  2. if a < -1.5982814066709494e-10 or 2.1817285828252516e+52 < a

    1. Initial program 9.6

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

    3. Applied associate-/l*0.5

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

    if -1.5982814066709494e-10 < a < 2.3996719980727017e-142

    1. Initial program 1.1

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

    2. Taylor expanded around 0 1.1

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

    3. Simplified4.4

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

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

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

    6. Applied add-cube-cbrt5.1

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

    7. Applied times-frac5.1

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

    8. Applied associate-*l*12.6

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

    9. Taylor expanded around 0 1.1

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

    if 2.3996719980727017e-142 < a < 2.1817285828252516e+52

    1. Initial program 1.1

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

    3. Applied associate-/l*5.2

      \[\leadsto x + \color{blue}{\frac{y}{\frac{a}{z - t}}}\]
    4. Using strategy rm

    5. Applied div-inv5.3

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

    6. Applied associate-/r*1.3

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

  4. Final simplification0.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;a \le -1.598281406670949442324391521520754455565 \cdot 10^{-10}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \mathbf{elif}\;a \le 2.399671998072701683137690037832409821452 \cdot 10^{-142}:\\ \;\;\;\;x + \left(\frac{y \cdot z}{a} - \frac{t \cdot y}{a}\right)\\ \mathbf{elif}\;a \le 2.181728582825251587184966617016023093761 \cdot 10^{52}:\\ \;\;\;\;x + \frac{\frac{y}{a}}{\frac{1}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019179 
(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)))