Average Error: 6.2 → 0.4
Time: 3.0s
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 r333662 = x;
        double r333663 = y;
        double r333664 = z;
        double r333665 = t;
        double r333666 = r333664 - r333665;
        double r333667 = r333663 * r333666;
        double r333668 = a;
        double r333669 = r333667 / r333668;
        double r333670 = r333662 + r333669;
        return r333670;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r333671 = y;
        double r333672 = z;
        double r333673 = t;
        double r333674 = r333672 - r333673;
        double r333675 = r333671 * r333674;
        double r333676 = -1.844830222125782e+209;
        bool r333677 = r333675 <= r333676;
        double r333678 = x;
        double r333679 = a;
        double r333680 = r333671 / r333679;
        double r333681 = r333680 * r333674;
        double r333682 = r333678 + r333681;
        double r333683 = 8.277756551639839e+192;
        bool r333684 = r333675 <= r333683;
        double r333685 = r333671 * r333672;
        double r333686 = -r333673;
        double r333687 = r333671 * r333686;
        double r333688 = r333685 + r333687;
        double r333689 = r333688 / r333679;
        double r333690 = r333678 + r333689;
        double r333691 = r333674 / r333679;
        double r333692 = r333671 * r333691;
        double r333693 = r333678 + r333692;
        double r333694 = r333684 ? r333690 : r333693;
        double r333695 = r333677 ? r333682 : r333694;
        return r333695;
}

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)))