Average Error: 14.7 → 7.1
Time: 23.3s
Precision: 64
\[x + \left(y - z\right) \cdot \frac{t - x}{a - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \le -1.325586496596394733118592144672022611 \cdot 10^{-299}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot \left(t - x\right)\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \le 0.0:\\ \;\;\;\;\left(\frac{x \cdot y}{z} + t\right) - \frac{t \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{\sqrt[3]{t - x} \cdot \sqrt[3]{t - x}}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}} \cdot \left(y - z\right)\right) \cdot \frac{\sqrt[3]{t - x}}{\sqrt[3]{a - z}}\\ \end{array}\]
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 -1.325586496596394733118592144672022611 \cdot 10^{-299}:\\
\;\;\;\;x + \frac{y - z}{a - z} \cdot \left(t - x\right)\\

\mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \le 0.0:\\
\;\;\;\;\left(\frac{x \cdot y}{z} + t\right) - \frac{t \cdot y}{z}\\

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

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r89781 = x;
        double r89782 = y;
        double r89783 = z;
        double r89784 = r89782 - r89783;
        double r89785 = t;
        double r89786 = r89785 - r89781;
        double r89787 = a;
        double r89788 = r89787 - r89783;
        double r89789 = r89786 / r89788;
        double r89790 = r89784 * r89789;
        double r89791 = r89781 + r89790;
        return r89791;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r89792 = x;
        double r89793 = y;
        double r89794 = z;
        double r89795 = r89793 - r89794;
        double r89796 = t;
        double r89797 = r89796 - r89792;
        double r89798 = a;
        double r89799 = r89798 - r89794;
        double r89800 = r89797 / r89799;
        double r89801 = r89795 * r89800;
        double r89802 = r89792 + r89801;
        double r89803 = -1.3255864965963947e-299;
        bool r89804 = r89802 <= r89803;
        double r89805 = r89795 / r89799;
        double r89806 = r89805 * r89797;
        double r89807 = r89792 + r89806;
        double r89808 = 0.0;
        bool r89809 = r89802 <= r89808;
        double r89810 = r89792 * r89793;
        double r89811 = r89810 / r89794;
        double r89812 = r89811 + r89796;
        double r89813 = r89796 * r89793;
        double r89814 = r89813 / r89794;
        double r89815 = r89812 - r89814;
        double r89816 = cbrt(r89797);
        double r89817 = r89816 * r89816;
        double r89818 = cbrt(r89799);
        double r89819 = r89818 * r89818;
        double r89820 = r89817 / r89819;
        double r89821 = r89820 * r89795;
        double r89822 = r89816 / r89818;
        double r89823 = r89821 * r89822;
        double r89824 = r89792 + r89823;
        double r89825 = r89809 ? r89815 : r89824;
        double r89826 = r89804 ? r89807 : r89825;
        return r89826;
}

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 3 regimes

  2. if (+ x (* (- y z) (/ (- t x) (- a z)))) < -1.3255864965963947e-299

    1. Initial program 7.0

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

    3. Applied clear-num7.3

      \[\leadsto x + \left(y - z\right) \cdot \color{blue}{\frac{1}{\frac{a - z}{t - x}}}\]
    4. Using strategy rm

    5. Applied associate-/r/7.1

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

    6. Applied associate-*r*3.7

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

    7. Simplified3.7

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

    if -1.3255864965963947e-299 < (+ x (* (- y z) (/ (- t x) (- a z)))) < 0.0

    1. Initial program 61.5

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

    2. Taylor expanded around inf 24.9

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

    if 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-cbrt8.1

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

    4. Applied add-cube-cbrt8.3

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

    5. Applied times-frac8.3

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

    6. Applied associate-*r*4.8

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

    7. Simplified4.8

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

  4. Final simplification7.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \le -1.325586496596394733118592144672022611 \cdot 10^{-299}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot \left(t - x\right)\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \le 0.0:\\ \;\;\;\;\left(\frac{x \cdot y}{z} + t\right) - \frac{t \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{\sqrt[3]{t - x} \cdot \sqrt[3]{t - x}}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}} \cdot \left(y - z\right)\right) \cdot \frac{\sqrt[3]{t - x}}{\sqrt[3]{a - z}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019212 
(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)))))