Average Error: 16.1 → 9.3
Time: 9.0s
Precision: 64
\[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -1.91570009620441830670906157024910521968 \cdot 10^{107} \lor \neg \left(t \le 3.351252885723445614738514992744822267851 \cdot 10^{128}\right):\\ \;\;\;\;\frac{z \cdot y}{t} + x\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - \frac{\sqrt[3]{z - t} \cdot \left(\sqrt[3]{\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}} \cdot \sqrt[3]{\sqrt[3]{z - t}}\right)}{\sqrt[3]{a - t}} \cdot \left(\frac{\sqrt[3]{z - t}}{\sqrt[3]{a - t}} \cdot \frac{y}{\sqrt[3]{a - t}}\right)\right)\\ \end{array}\]
\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}
↓
\begin{array}{l}
\mathbf{if}\;t \le -1.91570009620441830670906157024910521968 \cdot 10^{107} \lor \neg \left(t \le 3.351252885723445614738514992744822267851 \cdot 10^{128}\right):\\
\;\;\;\;\frac{z \cdot y}{t} + x\\

\mathbf{else}:\\
\;\;\;\;x + \left(y - \frac{\sqrt[3]{z - t} \cdot \left(\sqrt[3]{\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}} \cdot \sqrt[3]{\sqrt[3]{z - t}}\right)}{\sqrt[3]{a - t}} \cdot \left(\frac{\sqrt[3]{z - t}}{\sqrt[3]{a - t}} \cdot \frac{y}{\sqrt[3]{a - t}}\right)\right)\\

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r584716 = x;
        double r584717 = y;
        double r584718 = r584716 + r584717;
        double r584719 = z;
        double r584720 = t;
        double r584721 = r584719 - r584720;
        double r584722 = r584721 * r584717;
        double r584723 = a;
        double r584724 = r584723 - r584720;
        double r584725 = r584722 / r584724;
        double r584726 = r584718 - r584725;
        return r584726;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r584727 = t;
        double r584728 = -1.9157000962044183e+107;
        bool r584729 = r584727 <= r584728;
        double r584730 = 3.3512528857234456e+128;
        bool r584731 = r584727 <= r584730;
        double r584732 = !r584731;
        bool r584733 = r584729 || r584732;
        double r584734 = z;
        double r584735 = y;
        double r584736 = r584734 * r584735;
        double r584737 = r584736 / r584727;
        double r584738 = x;
        double r584739 = r584737 + r584738;
        double r584740 = r584734 - r584727;
        double r584741 = cbrt(r584740);
        double r584742 = r584741 * r584741;
        double r584743 = cbrt(r584742);
        double r584744 = cbrt(r584741);
        double r584745 = r584743 * r584744;
        double r584746 = r584741 * r584745;
        double r584747 = a;
        double r584748 = r584747 - r584727;
        double r584749 = cbrt(r584748);
        double r584750 = r584746 / r584749;
        double r584751 = r584741 / r584749;
        double r584752 = r584735 / r584749;
        double r584753 = r584751 * r584752;
        double r584754 = r584750 * r584753;
        double r584755 = r584735 - r584754;
        double r584756 = r584738 + r584755;
        double r584757 = r584733 ? r584739 : r584756;
        return r584757;
}

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

Original16.1
Target8.1
Herbie9.3
\[\begin{array}{l} \mathbf{if}\;\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \lt -1.366497088939072697550672266103566343531 \cdot 10^{-7}:\\ \;\;\;\;\left(y + x\right) - \left(\left(z - t\right) \cdot \frac{1}{a - t}\right) \cdot y\\ \mathbf{elif}\;\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \lt 1.475429344457723334351036314450840066235 \cdot 10^{-239}:\\ \;\;\;\;\frac{y \cdot \left(a - z\right) - x \cdot t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;\left(y + x\right) - \left(\left(z - t\right) \cdot \frac{1}{a - t}\right) \cdot y\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if t < -1.9157000962044183e+107 or 3.3512528857234456e+128 < t

    1. Initial program 29.7

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

    2. Taylor expanded around inf 17.3

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

    if -1.9157000962044183e+107 < t < 3.3512528857234456e+128

    1. Initial program 9.1

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

    3. Applied add-cube-cbrt9.3

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

    4. Applied times-frac6.4

      \[\leadsto \left(x + y\right) - \color{blue}{\frac{z - t}{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}} \cdot \frac{y}{\sqrt[3]{a - t}}}\]
    5. Using strategy rm

    6. Applied add-cube-cbrt6.4

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

    7. Applied times-frac6.4

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

    8. Applied associate-*l*5.6

      \[\leadsto \left(x + y\right) - \color{blue}{\frac{\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}}{\sqrt[3]{a - t}} \cdot \left(\frac{\sqrt[3]{z - t}}{\sqrt[3]{a - t}} \cdot \frac{y}{\sqrt[3]{a - t}}\right)}\]
    9. Using strategy rm

    10. Applied associate--l+4.5

      \[\leadsto \color{blue}{x + \left(y - \frac{\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}}{\sqrt[3]{a - t}} \cdot \left(\frac{\sqrt[3]{z - t}}{\sqrt[3]{a - t}} \cdot \frac{y}{\sqrt[3]{a - t}}\right)\right)}\]
    11. Using strategy rm

    12. Applied add-cube-cbrt4.8

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

    13. Applied cbrt-prod5.1

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

  4. Final simplification9.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -1.91570009620441830670906157024910521968 \cdot 10^{107} \lor \neg \left(t \le 3.351252885723445614738514992744822267851 \cdot 10^{128}\right):\\ \;\;\;\;\frac{z \cdot y}{t} + x\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - \frac{\sqrt[3]{z - t} \cdot \left(\sqrt[3]{\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}} \cdot \sqrt[3]{\sqrt[3]{z - t}}\right)}{\sqrt[3]{a - t}} \cdot \left(\frac{\sqrt[3]{z - t}}{\sqrt[3]{a - t}} \cdot \frac{y}{\sqrt[3]{a - t}}\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019304 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, B"
  :precision binary64

  :herbie-target
  (if (< (- (+ x y) (/ (* (- z t) y) (- a t))) -1.3664970889390727e-7) (- (+ y x) (* (* (- z t) (/ 1 (- a t))) y)) (if (< (- (+ x y) (/ (* (- z t) y) (- a t))) 1.47542934445772333e-239) (/ (- (* y (- a z)) (* x t)) (- a t)) (- (+ y x) (* (* (- z t) (/ 1 (- a t))) y))))

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