Average Error: 6.1 → 1.3
Time: 15.9s
Precision: 64
\[x - \frac{y \cdot \left(z - t\right)}{a}\]
↓
\[\begin{array}{l} \mathbf{if}\;a \le -1.0435501163087303 \cdot 10^{-16}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \mathbf{elif}\;a \le 1.3920873544366965 \cdot 10^{-146}:\\ \;\;\;\;x - \frac{1}{\frac{a}{\left(z - t\right) \cdot y}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\sqrt[3]{a} \cdot \sqrt[3]{a}} \cdot \frac{z - t}{\sqrt[3]{a}}\\ \end{array}\]
x - \frac{y \cdot \left(z - t\right)}{a}
↓
\begin{array}{l}
\mathbf{if}\;a \le -1.0435501163087303 \cdot 10^{-16}:\\
\;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\

\mathbf{elif}\;a \le 1.3920873544366965 \cdot 10^{-146}:\\
\;\;\;\;x - \frac{1}{\frac{a}{\left(z - t\right) \cdot y}}\\

\mathbf{else}:\\
\;\;\;\;x - \frac{y}{\sqrt[3]{a} \cdot \sqrt[3]{a}} \cdot \frac{z - t}{\sqrt[3]{a}}\\

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r19495005 = x;
        double r19495006 = y;
        double r19495007 = z;
        double r19495008 = t;
        double r19495009 = r19495007 - r19495008;
        double r19495010 = r19495006 * r19495009;
        double r19495011 = a;
        double r19495012 = r19495010 / r19495011;
        double r19495013 = r19495005 - r19495012;
        return r19495013;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r19495014 = a;
        double r19495015 = -1.0435501163087303e-16;
        bool r19495016 = r19495014 <= r19495015;
        double r19495017 = x;
        double r19495018 = y;
        double r19495019 = z;
        double r19495020 = t;
        double r19495021 = r19495019 - r19495020;
        double r19495022 = r19495014 / r19495021;
        double r19495023 = r19495018 / r19495022;
        double r19495024 = r19495017 - r19495023;
        double r19495025 = 1.3920873544366965e-146;
        bool r19495026 = r19495014 <= r19495025;
        double r19495027 = 1.0;
        double r19495028 = r19495021 * r19495018;
        double r19495029 = r19495014 / r19495028;
        double r19495030 = r19495027 / r19495029;
        double r19495031 = r19495017 - r19495030;
        double r19495032 = cbrt(r19495014);
        double r19495033 = r19495032 * r19495032;
        double r19495034 = r19495018 / r19495033;
        double r19495035 = r19495021 / r19495032;
        double r19495036 = r19495034 * r19495035;
        double r19495037 = r19495017 - r19495036;
        double r19495038 = r19495026 ? r19495031 : r19495037;
        double r19495039 = r19495016 ? r19495024 : r19495038;
        return r19495039;
}

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

Original6.1
Target0.6
Herbie1.3
\[\begin{array}{l} \mathbf{if}\;y \lt -1.0761266216389975 \cdot 10^{-10}:\\ \;\;\;\;x - \frac{1}{\frac{\frac{a}{z - t}}{y}}\\ \mathbf{elif}\;y \lt 2.894426862792089 \cdot 10^{-49}:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if a < -1.0435501163087303e-16

    1. Initial program 8.9

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

    3. Applied associate-/l*0.5

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

    if -1.0435501163087303e-16 < a < 1.3920873544366965e-146

    1. Initial program 0.8

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

    3. Applied clear-num0.9

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

    if 1.3920873544366965e-146 < a

    1. Initial program 7.1

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

    3. Applied add-cube-cbrt7.5

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

    4. Applied times-frac2.1

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

  4. Final simplification1.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;a \le -1.0435501163087303 \cdot 10^{-16}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \mathbf{elif}\;a \le 1.3920873544366965 \cdot 10^{-146}:\\ \;\;\;\;x - \frac{1}{\frac{a}{\left(z - t\right) \cdot y}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\sqrt[3]{a} \cdot \sqrt[3]{a}} \cdot \frac{z - t}{\sqrt[3]{a}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019165 
(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 (/ (/ a (- z t)) y))) (if (< y 2.894426862792089e-49) (- x (/ (* y (- z t)) a)) (- x (/ y (/ a (- z t))))))

  (- x (/ (* y (- z t)) a)))