Average Error: 6.0 → 0.8
Time: 12.3s
Precision: 64
\[x - \frac{y \cdot \left(z - t\right)}{a}\]
↓
\[\begin{array}{l} \mathbf{if}\;a \le -1.598281406670949442324391521520754455565 \cdot 10^{-10}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - z}}\\ \mathbf{elif}\;a \le 2.399671998072701683137690037832409821452 \cdot 10^{-142}:\\ \;\;\;\;\left(x + \frac{t \cdot y}{a}\right) - \frac{y \cdot z}{a}\\ \mathbf{elif}\;a \le 2.181728582825251587184966617016023093761 \cdot 10^{52}:\\ \;\;\;\;x + \frac{\frac{y}{a}}{\frac{1}{t - z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - z}}\\ \end{array}\]
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}{t - z}}\\

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

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

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

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r826717 = x;
        double r826718 = y;
        double r826719 = z;
        double r826720 = t;
        double r826721 = r826719 - r826720;
        double r826722 = r826718 * r826721;
        double r826723 = a;
        double r826724 = r826722 / r826723;
        double r826725 = r826717 - r826724;
        return r826725;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r826726 = a;
        double r826727 = -1.5982814066709494e-10;
        bool r826728 = r826726 <= r826727;
        double r826729 = x;
        double r826730 = y;
        double r826731 = t;
        double r826732 = z;
        double r826733 = r826731 - r826732;
        double r826734 = r826726 / r826733;
        double r826735 = r826730 / r826734;
        double r826736 = r826729 + r826735;
        double r826737 = 2.3996719980727017e-142;
        bool r826738 = r826726 <= r826737;
        double r826739 = r826731 * r826730;
        double r826740 = r826739 / r826726;
        double r826741 = r826729 + r826740;
        double r826742 = r826730 * r826732;
        double r826743 = r826742 / r826726;
        double r826744 = r826741 - r826743;
        double r826745 = 2.1817285828252516e+52;
        bool r826746 = r826726 <= r826745;
        double r826747 = r826730 / r826726;
        double r826748 = 1.0;
        double r826749 = r826748 / r826733;
        double r826750 = r826747 / r826749;
        double r826751 = r826729 + r826750;
        double r826752 = r826746 ? r826751 : r826736;
        double r826753 = r826738 ? r826744 : r826752;
        double r826754 = r826728 ? r826736 : r826753;
        return r826754;
}

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. Simplified1.7

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

    4. Applied *-un-lft-identity1.7

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

    5. Applied *-un-lft-identity1.7

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

    6. Applied times-frac1.7

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

    7. Applied associate-*l*1.7

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

    8. Simplified0.5

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

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

    1. Initial program 1.1

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

    2. Simplified4.4

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

    4. Applied sub-neg4.4

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

    5. Applied distribute-lft-in4.4

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

    6. Simplified4.4

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

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

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

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

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

    10. Applied distribute-lft-out4.4

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

    11. Simplified1.1

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

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

    1. Initial program 1.1

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

    2. Simplified1.2

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

    4. Applied *-un-lft-identity1.2

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

    5. Applied *-un-lft-identity1.2

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

    6. Applied times-frac1.2

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

    7. Applied associate-*l*1.2

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

    8. Simplified5.2

      \[\leadsto x + \frac{1}{1} \cdot \color{blue}{\frac{y}{\frac{a}{t - z}}}\]
    9. Using strategy rm

    10. Applied div-inv5.3

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

    11. Applied associate-/r*1.3

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

  4. Final simplification0.8

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

Reproduce

herbie shell --seed 2019179 
(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)))