Average Error: 16.3 → 10.1
Time: 6.5s
Precision: 64
\[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -2.1392755824805588 \cdot 10^{116} \lor \neg \left(t \le 1.01062669764849681 \cdot 10^{51}\right):\\ \;\;\;\;\frac{z \cdot y}{t} + x\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - \left(\frac{1}{\sqrt[3]{a - t}} \cdot \left(\frac{z - t}{\sqrt[3]{a - t}} \cdot \frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{\sqrt[3]{a - t}} \cdot \sqrt[3]{\sqrt[3]{a - t}}}\right)\right) \cdot \frac{\sqrt[3]{y}}{\sqrt[3]{\sqrt[3]{a - t}}}\\ \end{array}\]
\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}
↓
\begin{array}{l}
\mathbf{if}\;t \le -2.1392755824805588 \cdot 10^{116} \lor \neg \left(t \le 1.01062669764849681 \cdot 10^{51}\right):\\
\;\;\;\;\frac{z \cdot y}{t} + x\\

\mathbf{else}:\\
\;\;\;\;\left(x + y\right) - \left(\frac{1}{\sqrt[3]{a - t}} \cdot \left(\frac{z - t}{\sqrt[3]{a - t}} \cdot \frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{\sqrt[3]{a - t}} \cdot \sqrt[3]{\sqrt[3]{a - t}}}\right)\right) \cdot \frac{\sqrt[3]{y}}{\sqrt[3]{\sqrt[3]{a - t}}}\\

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r581746 = x;
        double r581747 = y;
        double r581748 = r581746 + r581747;
        double r581749 = z;
        double r581750 = t;
        double r581751 = r581749 - r581750;
        double r581752 = r581751 * r581747;
        double r581753 = a;
        double r581754 = r581753 - r581750;
        double r581755 = r581752 / r581754;
        double r581756 = r581748 - r581755;
        return r581756;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r581757 = t;
        double r581758 = -2.1392755824805588e+116;
        bool r581759 = r581757 <= r581758;
        double r581760 = 1.0106266976484968e+51;
        bool r581761 = r581757 <= r581760;
        double r581762 = !r581761;
        bool r581763 = r581759 || r581762;
        double r581764 = z;
        double r581765 = y;
        double r581766 = r581764 * r581765;
        double r581767 = r581766 / r581757;
        double r581768 = x;
        double r581769 = r581767 + r581768;
        double r581770 = r581768 + r581765;
        double r581771 = 1.0;
        double r581772 = a;
        double r581773 = r581772 - r581757;
        double r581774 = cbrt(r581773);
        double r581775 = r581771 / r581774;
        double r581776 = r581764 - r581757;
        double r581777 = r581776 / r581774;
        double r581778 = cbrt(r581765);
        double r581779 = r581778 * r581778;
        double r581780 = cbrt(r581774);
        double r581781 = r581780 * r581780;
        double r581782 = r581779 / r581781;
        double r581783 = r581777 * r581782;
        double r581784 = r581775 * r581783;
        double r581785 = r581778 / r581780;
        double r581786 = r581784 * r581785;
        double r581787 = r581770 - r581786;
        double r581788 = r581763 ? r581769 : r581787;
        return r581788;
}

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

Original16.3
Target8.6
Herbie10.1
\[\begin{array}{l} \mathbf{if}\;\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \lt -1.3664970889390727 \cdot 10^{-7}:\\ \;\;\;\;\left(y + x\right) - \left(\left(z - t\right) \cdot \frac{1}{a - t}\right) \cdot y\\ \mathbf{elif}\;\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \lt 1.47542934445772333 \cdot 10^{-239}:\\ \;\;\;\;\frac{y \cdot \left(a - z\right) - x \cdot t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;\left(y + x\right) - \left(\left(z - t\right) \cdot \frac{1}{a - t}\right) \cdot y\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if t < -2.1392755824805588e+116 or 1.0106266976484968e+51 < t

    1. Initial program 29.5

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

    2. Taylor expanded around inf 17.4

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

    if -2.1392755824805588e+116 < t < 1.0106266976484968e+51

    1. Initial program 7.7

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

    3. Applied add-cube-cbrt7.9

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

    4. Applied times-frac6.1

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

    6. Applied add-cube-cbrt6.2

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

    7. Applied add-cube-cbrt6.2

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

    8. Applied times-frac6.2

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

    9. Applied associate-*r*5.9

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

    11. Applied *-un-lft-identity5.9

      \[\leadsto \left(x + y\right) - \left(\frac{\color{blue}{1 \cdot \left(z - t\right)}}{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}} \cdot \frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{\sqrt[3]{a - t}} \cdot \sqrt[3]{\sqrt[3]{a - t}}}\right) \cdot \frac{\sqrt[3]{y}}{\sqrt[3]{\sqrt[3]{a - t}}}\]

    12. Applied times-frac5.9

      \[\leadsto \left(x + y\right) - \left(\color{blue}{\left(\frac{1}{\sqrt[3]{a - t}} \cdot \frac{z - t}{\sqrt[3]{a - t}}\right)} \cdot \frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{\sqrt[3]{a - t}} \cdot \sqrt[3]{\sqrt[3]{a - t}}}\right) \cdot \frac{\sqrt[3]{y}}{\sqrt[3]{\sqrt[3]{a - t}}}\]

    13. Applied associate-*l*5.3

      \[\leadsto \left(x + y\right) - \color{blue}{\left(\frac{1}{\sqrt[3]{a - t}} \cdot \left(\frac{z - t}{\sqrt[3]{a - t}} \cdot \frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{\sqrt[3]{a - t}} \cdot \sqrt[3]{\sqrt[3]{a - t}}}\right)\right)} \cdot \frac{\sqrt[3]{y}}{\sqrt[3]{\sqrt[3]{a - t}}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification10.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -2.1392755824805588 \cdot 10^{116} \lor \neg \left(t \le 1.01062669764849681 \cdot 10^{51}\right):\\ \;\;\;\;\frac{z \cdot y}{t} + x\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - \left(\frac{1}{\sqrt[3]{a - t}} \cdot \left(\frac{z - t}{\sqrt[3]{a - t}} \cdot \frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{\sqrt[3]{a - t}} \cdot \sqrt[3]{\sqrt[3]{a - t}}}\right)\right) \cdot \frac{\sqrt[3]{y}}{\sqrt[3]{\sqrt[3]{a - t}}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020024 
(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-07) (- (+ y x) (* (* (- z t) (/ 1 (- a t))) y)) (if (< (- (+ x y) (/ (* (- z t) y) (- a t))) 1.4754293444577233e-239) (/ (- (* y (- a z)) (* x t)) (- a t)) (- (+ y x) (* (* (- z t) (/ 1 (- a t))) y))))

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