Average Error: 6.2 → 0.4
Time: 2.6s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{a}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \le -1.8448302221257819 \cdot 10^{209}:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(z - t\right)\\ \mathbf{elif}\;y \cdot \left(z - t\right) \le 8.27775655163983859 \cdot 10^{192}:\\ \;\;\;\;x + \frac{y \cdot z + y \cdot \left(-t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \end{array}\]
x + \frac{y \cdot \left(z - t\right)}{a}
↓
\begin{array}{l}
\mathbf{if}\;y \cdot \left(z - t\right) \le -1.8448302221257819 \cdot 10^{209}:\\
\;\;\;\;x + \frac{y}{a} \cdot \left(z - t\right)\\

\mathbf{elif}\;y \cdot \left(z - t\right) \le 8.27775655163983859 \cdot 10^{192}:\\
\;\;\;\;x + \frac{y \cdot z + y \cdot \left(-t\right)}{a}\\

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

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r281373 = x;
        double r281374 = y;
        double r281375 = z;
        double r281376 = t;
        double r281377 = r281375 - r281376;
        double r281378 = r281374 * r281377;
        double r281379 = a;
        double r281380 = r281378 / r281379;
        double r281381 = r281373 + r281380;
        return r281381;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r281382 = y;
        double r281383 = z;
        double r281384 = t;
        double r281385 = r281383 - r281384;
        double r281386 = r281382 * r281385;
        double r281387 = -1.844830222125782e+209;
        bool r281388 = r281386 <= r281387;
        double r281389 = x;
        double r281390 = a;
        double r281391 = r281382 / r281390;
        double r281392 = r281391 * r281385;
        double r281393 = r281389 + r281392;
        double r281394 = 8.277756551639839e+192;
        bool r281395 = r281386 <= r281394;
        double r281396 = r281382 * r281383;
        double r281397 = -r281384;
        double r281398 = r281382 * r281397;
        double r281399 = r281396 + r281398;
        double r281400 = r281399 / r281390;
        double r281401 = r281389 + r281400;
        double r281402 = r281385 / r281390;
        double r281403 = r281382 * r281402;
        double r281404 = r281389 + r281403;
        double r281405 = r281395 ? r281401 : r281404;
        double r281406 = r281388 ? r281393 : r281405;
        return r281406;
}

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

Derivation

  1. Split input into 3 regimes

  2. if (* y (- z t)) < -1.844830222125782e+209

    1. Initial program 30.2

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

    3. Applied associate-/l*0.7

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

    5. Applied associate-/r/0.5

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

    if -1.844830222125782e+209 < (* y (- z t)) < 8.277756551639839e+192

    1. Initial program 0.3

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

    3. Applied sub-neg0.3

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

    4. Applied distribute-lft-in0.3

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

    if 8.277756551639839e+192 < (* y (- z t))

    1. Initial program 27.1

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

    3. Applied *-un-lft-identity27.1

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

    4. Applied times-frac1.0

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

    5. Simplified1.0

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

  4. Final simplification0.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \le -1.8448302221257819 \cdot 10^{209}:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(z - t\right)\\ \mathbf{elif}\;y \cdot \left(z - t\right) \le 8.27775655163983859 \cdot 10^{192}:\\ \;\;\;\;x + \frac{y \cdot z + y \cdot \left(-t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \end{array}\]

Reproduce

herbie shell --seed 2020036 
(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)))