Average Error: 14.8 → 7.4
Time: 6.5s
Precision: 64
\[x + \left(y - z\right) \cdot \frac{t - x}{a - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \le -3.7545844755986678 \cdot 10^{-296} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \le 0.0\right):\\ \;\;\;\;x + \left(\left(\left(y - z\right) \cdot \left|\frac{\sqrt[3]{t - x}}{\sqrt[3]{a - z}}\right|\right) \cdot \sqrt{\frac{\sqrt[3]{t - x} \cdot \sqrt[3]{t - x}}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}}}\right) \cdot \frac{\sqrt[3]{\sqrt[3]{t - x} \cdot \sqrt[3]{t - x}} \cdot \sqrt[3]{\sqrt[3]{t - x}}}{\sqrt[3]{a - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{x \cdot y}{z} + t\right) - \frac{t \cdot y}{z}\\ \end{array}\]
x + \left(y - z\right) \cdot \frac{t - x}{a - z}
↓
\begin{array}{l}
\mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \le -3.7545844755986678 \cdot 10^{-296} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \le 0.0\right):\\
\;\;\;\;x + \left(\left(\left(y - z\right) \cdot \left|\frac{\sqrt[3]{t - x}}{\sqrt[3]{a - z}}\right|\right) \cdot \sqrt{\frac{\sqrt[3]{t - x} \cdot \sqrt[3]{t - x}}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}}}\right) \cdot \frac{\sqrt[3]{\sqrt[3]{t - x} \cdot \sqrt[3]{t - x}} \cdot \sqrt[3]{\sqrt[3]{t - x}}}{\sqrt[3]{a - z}}\\

\mathbf{else}:\\
\;\;\;\;\left(\frac{x \cdot y}{z} + t\right) - \frac{t \cdot y}{z}\\

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r144815 = x;
        double r144816 = y;
        double r144817 = z;
        double r144818 = r144816 - r144817;
        double r144819 = t;
        double r144820 = r144819 - r144815;
        double r144821 = a;
        double r144822 = r144821 - r144817;
        double r144823 = r144820 / r144822;
        double r144824 = r144818 * r144823;
        double r144825 = r144815 + r144824;
        return r144825;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r144826 = x;
        double r144827 = y;
        double r144828 = z;
        double r144829 = r144827 - r144828;
        double r144830 = t;
        double r144831 = r144830 - r144826;
        double r144832 = a;
        double r144833 = r144832 - r144828;
        double r144834 = r144831 / r144833;
        double r144835 = r144829 * r144834;
        double r144836 = r144826 + r144835;
        double r144837 = -3.754584475598668e-296;
        bool r144838 = r144836 <= r144837;
        double r144839 = 0.0;
        bool r144840 = r144836 <= r144839;
        double r144841 = !r144840;
        bool r144842 = r144838 || r144841;
        double r144843 = cbrt(r144831);
        double r144844 = cbrt(r144833);
        double r144845 = r144843 / r144844;
        double r144846 = fabs(r144845);
        double r144847 = r144829 * r144846;
        double r144848 = r144843 * r144843;
        double r144849 = r144844 * r144844;
        double r144850 = r144848 / r144849;
        double r144851 = sqrt(r144850);
        double r144852 = r144847 * r144851;
        double r144853 = cbrt(r144848);
        double r144854 = cbrt(r144843);
        double r144855 = r144853 * r144854;
        double r144856 = r144855 / r144844;
        double r144857 = r144852 * r144856;
        double r144858 = r144826 + r144857;
        double r144859 = r144826 * r144827;
        double r144860 = r144859 / r144828;
        double r144861 = r144860 + r144830;
        double r144862 = r144830 * r144827;
        double r144863 = r144862 / r144828;
        double r144864 = r144861 - r144863;
        double r144865 = r144842 ? r144858 : r144864;
        return r144865;
}

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

Derivation

  1. Split input into 2 regimes

  2. if (+ x (* (- y z) (/ (- t x) (- a z)))) < -3.754584475598668e-296 or 0.0 < (+ x (* (- y z) (/ (- t x) (- a z))))

    1. Initial program 7.5

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

    3. Applied add-cube-cbrt8.2

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

    4. Applied add-cube-cbrt8.4

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

    5. Applied times-frac8.4

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

    6. Applied associate-*r*4.6

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

    8. Applied add-cube-cbrt4.6

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

    9. Applied cbrt-prod4.6

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

    11. Applied add-sqr-sqrt4.7

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

    12. Applied associate-*r*4.6

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

    13. Simplified4.6

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

    if -3.754584475598668e-296 < (+ x (* (- y z) (/ (- t x) (- a z)))) < 0.0

    1. Initial program 61.1

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

    2. Taylor expanded around inf 25.3

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

  4. Final simplification7.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \le -3.7545844755986678 \cdot 10^{-296} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \le 0.0\right):\\ \;\;\;\;x + \left(\left(\left(y - z\right) \cdot \left|\frac{\sqrt[3]{t - x}}{\sqrt[3]{a - z}}\right|\right) \cdot \sqrt{\frac{\sqrt[3]{t - x} \cdot \sqrt[3]{t - x}}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}}}\right) \cdot \frac{\sqrt[3]{\sqrt[3]{t - x} \cdot \sqrt[3]{t - x}} \cdot \sqrt[3]{\sqrt[3]{t - x}}}{\sqrt[3]{a - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{x \cdot y}{z} + t\right) - \frac{t \cdot y}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020060 
(FPCore (x y z t a)
  :name "Numeric.Signal:interpolate   from hsignal-0.2.7.1"
  :precision binary64
  (+ x (* (- y z) (/ (- t x) (- a z)))))