Average Error: 14.5 → 6.5
Time: 26.7s
Precision: 64
\[x + \left(y - z\right) \cdot \frac{t - x}{a - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x + \frac{t - x}{a - z} \cdot \left(y - z\right) = -\infty:\\ \;\;\;\;\left(\left(y - z\right) \cdot \left(t - x\right)\right) \cdot \frac{1}{a - z} + x\\ \mathbf{elif}\;x + \frac{t - x}{a - z} \cdot \left(y - z\right) \le -1.539254624498238512905823682389083375771 \cdot 10^{-307}:\\ \;\;\;\;\frac{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}}{\sqrt[3]{a - z}} \cdot \left(\frac{\sqrt[3]{y - z}}{\sqrt[3]{a - z}} \cdot \frac{t - x}{\sqrt[3]{a - z}}\right) + x\\ \mathbf{elif}\;x + \frac{t - x}{a - z} \cdot \left(y - z\right) \le 0.0:\\ \;\;\;\;y \cdot \left(\frac{x}{z} - \frac{t}{z}\right) + t\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}}{\sqrt[3]{a - z}} \cdot \left(\frac{\sqrt[3]{y - z}}{\sqrt[3]{a - z}} \cdot \frac{t - x}{\sqrt[3]{a - z}}\right) + x\\ \end{array}\]
x + \left(y - z\right) \cdot \frac{t - x}{a - z}
↓
\begin{array}{l}
\mathbf{if}\;x + \frac{t - x}{a - z} \cdot \left(y - z\right) = -\infty:\\
\;\;\;\;\left(\left(y - z\right) \cdot \left(t - x\right)\right) \cdot \frac{1}{a - z} + x\\

\mathbf{elif}\;x + \frac{t - x}{a - z} \cdot \left(y - z\right) \le -1.539254624498238512905823682389083375771 \cdot 10^{-307}:\\
\;\;\;\;\frac{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}}{\sqrt[3]{a - z}} \cdot \left(\frac{\sqrt[3]{y - z}}{\sqrt[3]{a - z}} \cdot \frac{t - x}{\sqrt[3]{a - z}}\right) + x\\

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

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

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r6677773 = x;
        double r6677774 = y;
        double r6677775 = z;
        double r6677776 = r6677774 - r6677775;
        double r6677777 = t;
        double r6677778 = r6677777 - r6677773;
        double r6677779 = a;
        double r6677780 = r6677779 - r6677775;
        double r6677781 = r6677778 / r6677780;
        double r6677782 = r6677776 * r6677781;
        double r6677783 = r6677773 + r6677782;
        return r6677783;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r6677784 = x;
        double r6677785 = t;
        double r6677786 = r6677785 - r6677784;
        double r6677787 = a;
        double r6677788 = z;
        double r6677789 = r6677787 - r6677788;
        double r6677790 = r6677786 / r6677789;
        double r6677791 = y;
        double r6677792 = r6677791 - r6677788;
        double r6677793 = r6677790 * r6677792;
        double r6677794 = r6677784 + r6677793;
        double r6677795 = -inf.0;
        bool r6677796 = r6677794 <= r6677795;
        double r6677797 = r6677792 * r6677786;
        double r6677798 = 1.0;
        double r6677799 = r6677798 / r6677789;
        double r6677800 = r6677797 * r6677799;
        double r6677801 = r6677800 + r6677784;
        double r6677802 = -1.5392546244982385e-307;
        bool r6677803 = r6677794 <= r6677802;
        double r6677804 = cbrt(r6677792);
        double r6677805 = r6677804 * r6677804;
        double r6677806 = cbrt(r6677789);
        double r6677807 = r6677805 / r6677806;
        double r6677808 = r6677804 / r6677806;
        double r6677809 = r6677786 / r6677806;
        double r6677810 = r6677808 * r6677809;
        double r6677811 = r6677807 * r6677810;
        double r6677812 = r6677811 + r6677784;
        double r6677813 = 0.0;
        bool r6677814 = r6677794 <= r6677813;
        double r6677815 = r6677784 / r6677788;
        double r6677816 = r6677785 / r6677788;
        double r6677817 = r6677815 - r6677816;
        double r6677818 = r6677791 * r6677817;
        double r6677819 = r6677818 + r6677785;
        double r6677820 = r6677814 ? r6677819 : r6677812;
        double r6677821 = r6677803 ? r6677812 : r6677820;
        double r6677822 = r6677796 ? r6677801 : r6677821;
        return r6677822;
}

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)))) < -inf.0

    1. Initial program 64.0

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

    3. Applied div-inv64.0

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

    4. Applied associate-*r*13.8

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

    if -inf.0 < (+ x (* (- y z) (/ (- t x) (- a z)))) < -1.5392546244982385e-307 or 0.0 < (+ x (* (- y z) (/ (- t x) (- a z))))

    1. Initial program 6.2

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

    3. Applied add-cube-cbrt6.9

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

    4. Applied *-un-lft-identity6.9

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

    5. Applied times-frac6.9

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

    6. Applied associate-*r*4.8

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

    7. Simplified4.8

      \[\leadsto x + \color{blue}{\frac{y - z}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}}} \cdot \frac{t - x}{\sqrt[3]{a - z}}\]
    8. Using strategy rm

    9. Applied add-cube-cbrt4.7

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

    10. Applied times-frac4.7

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

    11. Applied associate-*l*4.3

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

    if -1.5392546244982385e-307 < (+ x (* (- y z) (/ (- t x) (- a z)))) < 0.0

    1. Initial program 61.9

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

    3. Applied add-cube-cbrt61.6

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

    4. Applied *-un-lft-identity61.6

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

    5. Applied times-frac61.5

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

    6. Applied associate-*r*61.5

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

    7. Simplified61.6

      \[\leadsto x + \color{blue}{\frac{y - z}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}}} \cdot \frac{t - x}{\sqrt[3]{a - z}}\]
    8. Using strategy rm

    9. Applied add-cube-cbrt61.8

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

    10. Applied times-frac61.8

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

    11. Applied associate-*l*61.8

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

    13. Applied add-cube-cbrt61.7

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

    14. Applied associate-*r*61.7

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

    15. Taylor expanded around inf 26.0

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

    16. Simplified19.9

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

  4. Final simplification6.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{t - x}{a - z} \cdot \left(y - z\right) = -\infty:\\ \;\;\;\;\left(\left(y - z\right) \cdot \left(t - x\right)\right) \cdot \frac{1}{a - z} + x\\ \mathbf{elif}\;x + \frac{t - x}{a - z} \cdot \left(y - z\right) \le -1.539254624498238512905823682389083375771 \cdot 10^{-307}:\\ \;\;\;\;\frac{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}}{\sqrt[3]{a - z}} \cdot \left(\frac{\sqrt[3]{y - z}}{\sqrt[3]{a - z}} \cdot \frac{t - x}{\sqrt[3]{a - z}}\right) + x\\ \mathbf{elif}\;x + \frac{t - x}{a - z} \cdot \left(y - z\right) \le 0.0:\\ \;\;\;\;y \cdot \left(\frac{x}{z} - \frac{t}{z}\right) + t\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}}{\sqrt[3]{a - z}} \cdot \left(\frac{\sqrt[3]{y - z}}{\sqrt[3]{a - z}} \cdot \frac{t - x}{\sqrt[3]{a - z}}\right) + x\\ \end{array}\]

Reproduce

herbie shell --seed 2019192 
(FPCore (x y z t a)
  :name "Numeric.Signal:interpolate   from hsignal-0.2.7.1"
  (+ x (* (- y z) (/ (- t x) (- a z)))))