Average Error: 6.4 → 0.5
Time: 4.3s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{a}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \le -2.689959535719968 \cdot 10^{288}:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(z - t\right)\\ \mathbf{elif}\;y \cdot \left(z - t\right) \le 3.12395947034459992 \cdot 10^{186}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \end{array}\]
x + \frac{y \cdot \left(z - t\right)}{a}
↓
\begin{array}{l}
\mathbf{if}\;y \cdot \left(z - t\right) \le -2.689959535719968 \cdot 10^{288}:\\
\;\;\;\;x + \frac{y}{a} \cdot \left(z - t\right)\\

\mathbf{elif}\;y \cdot \left(z - t\right) \le 3.12395947034459992 \cdot 10^{186}:\\
\;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\

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

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r308089 = x;
        double r308090 = y;
        double r308091 = z;
        double r308092 = t;
        double r308093 = r308091 - r308092;
        double r308094 = r308090 * r308093;
        double r308095 = a;
        double r308096 = r308094 / r308095;
        double r308097 = r308089 + r308096;
        return r308097;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r308098 = y;
        double r308099 = z;
        double r308100 = t;
        double r308101 = r308099 - r308100;
        double r308102 = r308098 * r308101;
        double r308103 = -2.689959535719968e+288;
        bool r308104 = r308102 <= r308103;
        double r308105 = x;
        double r308106 = a;
        double r308107 = r308098 / r308106;
        double r308108 = r308107 * r308101;
        double r308109 = r308105 + r308108;
        double r308110 = 3.1239594703446e+186;
        bool r308111 = r308102 <= r308110;
        double r308112 = r308102 / r308106;
        double r308113 = r308105 + r308112;
        double r308114 = r308106 / r308101;
        double r308115 = r308098 / r308114;
        double r308116 = r308105 + r308115;
        double r308117 = r308111 ? r308113 : r308116;
        double r308118 = r308104 ? r308109 : r308117;
        return r308118;
}

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
Target0.8
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)) < -2.689959535719968e+288

    1. Initial program 54.0

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

    3. Applied clear-num54.0

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

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

    8. Applied add-cube-cbrt0.4

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

    9. Applied times-frac0.4

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

    10. Simplified0.3

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

    11. Simplified0.2

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

    if -2.689959535719968e+288 < (* y (- z t)) < 3.1239594703446e+186

    1. Initial program 0.5

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

    if 3.1239594703446e+186 < (* y (- z t))

    1. Initial program 26.6

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

    3. Applied associate-/l*1.1

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

  4. Final simplification0.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \le -2.689959535719968 \cdot 10^{288}:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(z - t\right)\\ \mathbf{elif}\;y \cdot \left(z - t\right) \le 3.12395947034459992 \cdot 10^{186}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020081 
(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)))