Average Error: 6.0 → 0.8
Time: 18.9s
Precision: 64
\[x - \frac{y \cdot \left(z - t\right)}{a}\]
↓
\[\begin{array}{l} \mathbf{if}\;a \le -1.598281406670949442324391521520754455565 \cdot 10^{-10}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \mathbf{elif}\;a \le 2.399671998072701683137690037832409821452 \cdot 10^{-142}:\\ \;\;\;\;\left(\frac{t \cdot y}{a} + x\right) - \frac{y \cdot z}{a}\\ \mathbf{elif}\;a \le 2.181728582825251587184966617016023093761 \cdot 10^{52}:\\ \;\;\;\;x - \frac{\frac{y}{a}}{\frac{1}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \end{array}\]
x - \frac{y \cdot \left(z - t\right)}{a}
↓
\begin{array}{l}
\mathbf{if}\;a \le -1.598281406670949442324391521520754455565 \cdot 10^{-10}:\\
\;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\

\mathbf{elif}\;a \le 2.399671998072701683137690037832409821452 \cdot 10^{-142}:\\
\;\;\;\;\left(\frac{t \cdot y}{a} + x\right) - \frac{y \cdot z}{a}\\

\mathbf{elif}\;a \le 2.181728582825251587184966617016023093761 \cdot 10^{52}:\\
\;\;\;\;x - \frac{\frac{y}{a}}{\frac{1}{z - t}}\\

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

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r18830690 = x;
        double r18830691 = y;
        double r18830692 = z;
        double r18830693 = t;
        double r18830694 = r18830692 - r18830693;
        double r18830695 = r18830691 * r18830694;
        double r18830696 = a;
        double r18830697 = r18830695 / r18830696;
        double r18830698 = r18830690 - r18830697;
        return r18830698;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r18830699 = a;
        double r18830700 = -1.5982814066709494e-10;
        bool r18830701 = r18830699 <= r18830700;
        double r18830702 = x;
        double r18830703 = y;
        double r18830704 = z;
        double r18830705 = t;
        double r18830706 = r18830704 - r18830705;
        double r18830707 = r18830699 / r18830706;
        double r18830708 = r18830703 / r18830707;
        double r18830709 = r18830702 - r18830708;
        double r18830710 = 2.3996719980727017e-142;
        bool r18830711 = r18830699 <= r18830710;
        double r18830712 = r18830705 * r18830703;
        double r18830713 = r18830712 / r18830699;
        double r18830714 = r18830713 + r18830702;
        double r18830715 = r18830703 * r18830704;
        double r18830716 = r18830715 / r18830699;
        double r18830717 = r18830714 - r18830716;
        double r18830718 = 2.1817285828252516e+52;
        bool r18830719 = r18830699 <= r18830718;
        double r18830720 = r18830703 / r18830699;
        double r18830721 = 1.0;
        double r18830722 = r18830721 / r18830706;
        double r18830723 = r18830720 / r18830722;
        double r18830724 = r18830702 - r18830723;
        double r18830725 = r18830719 ? r18830724 : r18830709;
        double r18830726 = r18830711 ? r18830717 : r18830725;
        double r18830727 = r18830701 ? r18830709 : r18830726;
        return r18830727;
}

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

Original6.0
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 < -1.5982814066709494e-10 or 2.1817285828252516e+52 < a

    1. Initial program 9.6

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

    3. Applied associate-/l*0.5

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

    if -1.5982814066709494e-10 < a < 2.3996719980727017e-142

    1. Initial program 1.1

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

    3. Applied associate-/l*16.9

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

    4. Taylor expanded around 0 1.1

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

    if 2.3996719980727017e-142 < a < 2.1817285828252516e+52

    1. Initial program 1.1

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

    3. Applied associate-/l*5.2

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

    5. Applied div-inv5.3

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

    6. Applied associate-/r*1.3

      \[\leadsto x - \color{blue}{\frac{\frac{y}{a}}{\frac{1}{z - t}}}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification0.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;a \le -1.598281406670949442324391521520754455565 \cdot 10^{-10}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \mathbf{elif}\;a \le 2.399671998072701683137690037832409821452 \cdot 10^{-142}:\\ \;\;\;\;\left(\frac{t \cdot y}{a} + x\right) - \frac{y \cdot z}{a}\\ \mathbf{elif}\;a \le 2.181728582825251587184966617016023093761 \cdot 10^{52}:\\ \;\;\;\;x - \frac{\frac{y}{a}}{\frac{1}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019179 
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, F"

  :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)))