Average Error: 14.9 → 8.0
Time: 32.8s
Precision: 64
\[x + \left(y - z\right) \cdot \frac{t - x}{a - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \le -1.274238033086374554639513675873894241359 \cdot 10^{-228} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \le 8.018705835666315962422253726065345135652 \cdot 10^{-282}\right):\\ \;\;\;\;x + \left(\left(y - z\right) \cdot \frac{\sqrt[3]{t - x} \cdot \sqrt[3]{t - x}}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}}\right) \cdot \frac{\sqrt[3]{t - x}}{\sqrt[3]{a - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{x \cdot y}{z} + t\right) - \frac{t \cdot y}{z}\\ \end{array}\]
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 -1.274238033086374554639513675873894241359 \cdot 10^{-228} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \le 8.018705835666315962422253726065345135652 \cdot 10^{-282}\right):\\
\;\;\;\;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]{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 r99753 = x;
        double r99754 = y;
        double r99755 = z;
        double r99756 = r99754 - r99755;
        double r99757 = t;
        double r99758 = r99757 - r99753;
        double r99759 = a;
        double r99760 = r99759 - r99755;
        double r99761 = r99758 / r99760;
        double r99762 = r99756 * r99761;
        double r99763 = r99753 + r99762;
        return r99763;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r99764 = x;
        double r99765 = y;
        double r99766 = z;
        double r99767 = r99765 - r99766;
        double r99768 = t;
        double r99769 = r99768 - r99764;
        double r99770 = a;
        double r99771 = r99770 - r99766;
        double r99772 = r99769 / r99771;
        double r99773 = r99767 * r99772;
        double r99774 = r99764 + r99773;
        double r99775 = -1.2742380330863746e-228;
        bool r99776 = r99774 <= r99775;
        double r99777 = 8.018705835666316e-282;
        bool r99778 = r99774 <= r99777;
        double r99779 = !r99778;
        bool r99780 = r99776 || r99779;
        double r99781 = cbrt(r99769);
        double r99782 = r99781 * r99781;
        double r99783 = cbrt(r99771);
        double r99784 = r99783 * r99783;
        double r99785 = r99782 / r99784;
        double r99786 = r99767 * r99785;
        double r99787 = r99781 / r99783;
        double r99788 = r99786 * r99787;
        double r99789 = r99764 + r99788;
        double r99790 = r99764 * r99765;
        double r99791 = r99790 / r99766;
        double r99792 = r99791 + r99768;
        double r99793 = r99768 * r99765;
        double r99794 = r99793 / r99766;
        double r99795 = r99792 - r99794;
        double r99796 = r99780 ? r99789 : r99795;
        return r99796;
}

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)))) < -1.2742380330863746e-228 or 8.018705835666316e-282 < (+ x (* (- y z) (/ (- t x) (- a z))))

    1. Initial program 7.1

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

    3. Applied add-cube-cbrt7.8

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

    4. Applied add-cube-cbrt7.9

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

    5. Applied times-frac7.9

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

    6. Applied associate-*r*4.7

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

    if -1.2742380330863746e-228 < (+ x (* (- y z) (/ (- t x) (- a z)))) < 8.018705835666316e-282

    1. Initial program 57.4

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

    2. Taylor expanded around inf 25.8

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

  4. Final simplification8.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \le -1.274238033086374554639513675873894241359 \cdot 10^{-228} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \le 8.018705835666315962422253726065345135652 \cdot 10^{-282}\right):\\ \;\;\;\;x + \left(\left(y - z\right) \cdot \frac{\sqrt[3]{t - x} \cdot \sqrt[3]{t - x}}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}}\right) \cdot \frac{\sqrt[3]{t - x}}{\sqrt[3]{a - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{x \cdot y}{z} + t\right) - \frac{t \cdot y}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2019325 
(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)))))