Average Error: 6.2 → 0.8
Time: 30.6s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{a}\]
↓
\[\begin{array}{l} \mathbf{if}\;a \le -4.858733342956042121945166421427989828942 \cdot 10^{-60}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \mathbf{elif}\;a \le 73718650226315457682472960:\\ \;\;\;\;x + \frac{1}{\frac{a}{y \cdot \left(z - t\right)}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(\frac{z}{a} - \frac{t}{a}\right)\\ \end{array}\]
x + \frac{y \cdot \left(z - t\right)}{a}
↓
\begin{array}{l}
\mathbf{if}\;a \le -4.858733342956042121945166421427989828942 \cdot 10^{-60}:\\
\;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\

\mathbf{elif}\;a \le 73718650226315457682472960:\\
\;\;\;\;x + \frac{1}{\frac{a}{y \cdot \left(z - t\right)}}\\

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

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r66323209 = x;
        double r66323210 = y;
        double r66323211 = z;
        double r66323212 = t;
        double r66323213 = r66323211 - r66323212;
        double r66323214 = r66323210 * r66323213;
        double r66323215 = a;
        double r66323216 = r66323214 / r66323215;
        double r66323217 = r66323209 + r66323216;
        return r66323217;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r66323218 = a;
        double r66323219 = -4.858733342956042e-60;
        bool r66323220 = r66323218 <= r66323219;
        double r66323221 = x;
        double r66323222 = y;
        double r66323223 = z;
        double r66323224 = t;
        double r66323225 = r66323223 - r66323224;
        double r66323226 = r66323218 / r66323225;
        double r66323227 = r66323222 / r66323226;
        double r66323228 = r66323221 + r66323227;
        double r66323229 = 7.371865022631546e+25;
        bool r66323230 = r66323218 <= r66323229;
        double r66323231 = 1.0;
        double r66323232 = r66323222 * r66323225;
        double r66323233 = r66323218 / r66323232;
        double r66323234 = r66323231 / r66323233;
        double r66323235 = r66323221 + r66323234;
        double r66323236 = r66323223 / r66323218;
        double r66323237 = r66323224 / r66323218;
        double r66323238 = r66323236 - r66323237;
        double r66323239 = r66323222 * r66323238;
        double r66323240 = r66323221 + r66323239;
        double r66323241 = r66323230 ? r66323235 : r66323240;
        double r66323242 = r66323220 ? r66323228 : r66323241;
        return r66323242;
}

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

Original6.2
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 < -4.858733342956042e-60

    1. Initial program 8.6

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

    3. Applied associate-/l*0.6

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

    if -4.858733342956042e-60 < a < 7.371865022631546e+25

    1. Initial program 1.0

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

    3. Applied clear-num1.1

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

    if 7.371865022631546e+25 < a

    1. Initial program 9.6

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

    3. Applied add-cube-cbrt9.9

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

    4. Applied times-frac1.3

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

    5. Taylor expanded around 0 9.6

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

    6. Simplified0.6

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

  4. Final simplification0.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;a \le -4.858733342956042121945166421427989828942 \cdot 10^{-60}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \mathbf{elif}\;a \le 73718650226315457682472960:\\ \;\;\;\;x + \frac{1}{\frac{a}{y \cdot \left(z - t\right)}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(\frac{z}{a} - \frac{t}{a}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019173 
(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)))