Average Error: 6.4 → 0.5
Time: 4.3s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{a}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) = -\infty:\\ \;\;\;\;x + \frac{1}{\frac{a}{y} \cdot \frac{1}{z - t}}\\ \mathbf{elif}\;y \cdot \left(z - t\right) \le 8.39997312975099039 \cdot 10^{198}:\\ \;\;\;\;x + \frac{1}{a} \cdot \left(y \cdot \left(z - t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \end{array}\]
x + \frac{y \cdot \left(z - t\right)}{a}
↓
\begin{array}{l}
\mathbf{if}\;y \cdot \left(z - t\right) = -\infty:\\
\;\;\;\;x + \frac{1}{\frac{a}{y} \cdot \frac{1}{z - t}}\\

\mathbf{elif}\;y \cdot \left(z - t\right) \le 8.39997312975099039 \cdot 10^{198}:\\
\;\;\;\;x + \frac{1}{a} \cdot \left(y \cdot \left(z - t\right)\right)\\

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

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r385250 = x;
        double r385251 = y;
        double r385252 = z;
        double r385253 = t;
        double r385254 = r385252 - r385253;
        double r385255 = r385251 * r385254;
        double r385256 = a;
        double r385257 = r385255 / r385256;
        double r385258 = r385250 + r385257;
        return r385258;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r385259 = y;
        double r385260 = z;
        double r385261 = t;
        double r385262 = r385260 - r385261;
        double r385263 = r385259 * r385262;
        double r385264 = -inf.0;
        bool r385265 = r385263 <= r385264;
        double r385266 = x;
        double r385267 = 1.0;
        double r385268 = a;
        double r385269 = r385268 / r385259;
        double r385270 = r385267 / r385262;
        double r385271 = r385269 * r385270;
        double r385272 = r385267 / r385271;
        double r385273 = r385266 + r385272;
        double r385274 = 8.39997312975099e+198;
        bool r385275 = r385263 <= r385274;
        double r385276 = r385267 / r385268;
        double r385277 = r385276 * r385263;
        double r385278 = r385266 + r385277;
        double r385279 = r385268 / r385262;
        double r385280 = r385259 / r385279;
        double r385281 = r385266 + r385280;
        double r385282 = r385275 ? r385278 : r385281;
        double r385283 = r385265 ? r385273 : r385282;
        return r385283;
}

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

Original6.4
Target0.7
Herbie0.5
\[\begin{array}{l} \mathbf{if}\;y \lt -1.07612662163899753 \cdot 10^{-10}:\\ \;\;\;\;x + \frac{1}{\frac{\frac{a}{z - t}}{y}}\\ \mathbf{elif}\;y \lt 2.8944268627920891 \cdot 10^{-49}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (* y (- z t)) < -inf.0

    1. Initial program 64.0

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

    3. Applied clear-num64.0

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

    5. Applied associate-/r*0.3

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

    7. Applied div-inv0.4

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

    if -inf.0 < (* y (- z t)) < 8.39997312975099e+198

    1. Initial program 0.4

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

    3. Applied clear-num0.5

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

    5. Applied div-inv0.6

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

    6. Applied add-cube-cbrt0.6

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

    7. Applied times-frac0.5

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

    8. Simplified0.5

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

    9. Simplified0.5

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

    if 8.39997312975099e+198 < (* y (- z t))

    1. Initial program 29.4

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

    3. Applied associate-/l*1.0

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

  4. Final simplification0.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) = -\infty:\\ \;\;\;\;x + \frac{1}{\frac{a}{y} \cdot \frac{1}{z - t}}\\ \mathbf{elif}\;y \cdot \left(z - t\right) \le 8.39997312975099039 \cdot 10^{198}:\\ \;\;\;\;x + \frac{1}{a} \cdot \left(y \cdot \left(z - t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020060 
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, E"
  :precision binary64

  :herbie-target
  (if (< y -1.0761266216389975e-10) (+ x (/ 1 (/ (/ a (- z t)) y))) (if (< y 2.894426862792089e-49) (+ x (/ (* y (- z t)) a)) (+ x (/ y (/ a (- z t))))))

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