Average Error: 6.4 → 0.4
Time: 4.0s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{a}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \le -2.885127437985216706617229964801861933916 \cdot 10^{296} \lor \neg \left(y \cdot \left(z - t\right) \le 1.675666324185826084917217485128398230202 \cdot 10^{291}\right):\\ \;\;\;\;x + \frac{y}{a} \cdot \left(z - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \end{array}\]
x + \frac{y \cdot \left(z - t\right)}{a}
↓
\begin{array}{l}
\mathbf{if}\;y \cdot \left(z - t\right) \le -2.885127437985216706617229964801861933916 \cdot 10^{296} \lor \neg \left(y \cdot \left(z - t\right) \le 1.675666324185826084917217485128398230202 \cdot 10^{291}\right):\\
\;\;\;\;x + \frac{y}{a} \cdot \left(z - t\right)\\

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

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r360756 = x;
        double r360757 = y;
        double r360758 = z;
        double r360759 = t;
        double r360760 = r360758 - r360759;
        double r360761 = r360757 * r360760;
        double r360762 = a;
        double r360763 = r360761 / r360762;
        double r360764 = r360756 + r360763;
        return r360764;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r360765 = y;
        double r360766 = z;
        double r360767 = t;
        double r360768 = r360766 - r360767;
        double r360769 = r360765 * r360768;
        double r360770 = -2.8851274379852167e+296;
        bool r360771 = r360769 <= r360770;
        double r360772 = 1.675666324185826e+291;
        bool r360773 = r360769 <= r360772;
        double r360774 = !r360773;
        bool r360775 = r360771 || r360774;
        double r360776 = x;
        double r360777 = a;
        double r360778 = r360765 / r360777;
        double r360779 = r360778 * r360768;
        double r360780 = r360776 + r360779;
        double r360781 = r360769 / r360777;
        double r360782 = r360776 + r360781;
        double r360783 = r360775 ? r360780 : r360782;
        return r360783;
}

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
Herbie0.4
\[\begin{array}{l} \mathbf{if}\;y \lt -1.07612662163899753216593153715602325729 \cdot 10^{-10}:\\ \;\;\;\;x + \frac{1}{\frac{\frac{a}{z - t}}{y}}\\ \mathbf{elif}\;y \lt 2.894426862792089097262541964056085749132 \cdot 10^{-49}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (* y (- z t)) < -2.8851274379852167e+296 or 1.675666324185826e+291 < (* y (- z t))

    1. Initial program 57.2

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

    3. Applied associate-/l*0.2

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

    5. Applied associate-/r/0.2

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

    if -2.8851274379852167e+296 < (* y (- z t)) < 1.675666324185826e+291

    1. Initial program 0.4

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

    3. Applied associate-/l*6.2

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

    5. Applied associate-/r/2.9

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

    7. Applied associate-*l/0.4

      \[\leadsto x + \color{blue}{\frac{y \cdot \left(z - t\right)}{a}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \le -2.885127437985216706617229964801861933916 \cdot 10^{296} \lor \neg \left(y \cdot \left(z - t\right) \le 1.675666324185826084917217485128398230202 \cdot 10^{291}\right):\\ \;\;\;\;x + \frac{y}{a} \cdot \left(z - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \end{array}\]

Reproduce

herbie shell --seed 2020002 
(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)))