Average Error: 15.2 → 8.3
Time: 7.7s
Precision: 64
\[x + \left(y - z\right) \cdot \frac{t - x}{a - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \le -9.1253472310740824 \cdot 10^{-302} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \le 0.0\right):\\ \;\;\;\;x + \frac{y - z}{\sqrt[3]{a - z} \cdot \left(\sqrt[3]{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}} \cdot \sqrt[3]{\sqrt[3]{a - z}}\right)} \cdot \frac{t - x}{\sqrt[3]{a - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{x \cdot y}{z} + t\right) - \frac{t \cdot y}{z}\\ \end{array}\]
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 -9.1253472310740824 \cdot 10^{-302} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \le 0.0\right):\\
\;\;\;\;x + \frac{y - z}{\sqrt[3]{a - z} \cdot \left(\sqrt[3]{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}} \cdot \sqrt[3]{\sqrt[3]{a - z}}\right)} \cdot \frac{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 r171567 = x;
        double r171568 = y;
        double r171569 = z;
        double r171570 = r171568 - r171569;
        double r171571 = t;
        double r171572 = r171571 - r171567;
        double r171573 = a;
        double r171574 = r171573 - r171569;
        double r171575 = r171572 / r171574;
        double r171576 = r171570 * r171575;
        double r171577 = r171567 + r171576;
        return r171577;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r171578 = x;
        double r171579 = y;
        double r171580 = z;
        double r171581 = r171579 - r171580;
        double r171582 = t;
        double r171583 = r171582 - r171578;
        double r171584 = a;
        double r171585 = r171584 - r171580;
        double r171586 = r171583 / r171585;
        double r171587 = r171581 * r171586;
        double r171588 = r171578 + r171587;
        double r171589 = -9.125347231074082e-302;
        bool r171590 = r171588 <= r171589;
        double r171591 = 0.0;
        bool r171592 = r171588 <= r171591;
        double r171593 = !r171592;
        bool r171594 = r171590 || r171593;
        double r171595 = cbrt(r171585);
        double r171596 = r171595 * r171595;
        double r171597 = cbrt(r171596);
        double r171598 = cbrt(r171595);
        double r171599 = r171597 * r171598;
        double r171600 = r171595 * r171599;
        double r171601 = r171581 / r171600;
        double r171602 = r171583 / r171595;
        double r171603 = r171601 * r171602;
        double r171604 = r171578 + r171603;
        double r171605 = r171578 * r171579;
        double r171606 = r171605 / r171580;
        double r171607 = r171606 + r171582;
        double r171608 = r171582 * r171579;
        double r171609 = r171608 / r171580;
        double r171610 = r171607 - r171609;
        double r171611 = r171594 ? r171604 : r171610;
        return r171611;
}

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)))) < -9.125347231074082e-302 or 0.0 < (+ x (* (- y z) (/ (- t x) (- a z))))

    1. Initial program 8.0

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

    3. Applied add-cube-cbrt8.6

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

    4. Applied associate-*l*8.6

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

    6. Applied add-cube-cbrt8.6

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

    7. Applied *-un-lft-identity8.6

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

    8. Applied times-frac8.6

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

    9. Applied associate-*r*6.7

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

    10. Simplified6.7

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

    12. Applied add-cube-cbrt6.7

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

    13. Applied cbrt-prod6.8

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

    15. Applied associate-*r*5.5

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

    16. Simplified5.6

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

    if -9.125347231074082e-302 < (+ x (* (- y z) (/ (- t x) (- a z)))) < 0.0

    1. Initial program 61.4

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

    2. Taylor expanded around inf 25.9

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

  4. Final simplification8.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \le -9.1253472310740824 \cdot 10^{-302} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \le 0.0\right):\\ \;\;\;\;x + \frac{y - z}{\sqrt[3]{a - z} \cdot \left(\sqrt[3]{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}} \cdot \sqrt[3]{\sqrt[3]{a - z}}\right)} \cdot \frac{t - x}{\sqrt[3]{a - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{x \cdot y}{z} + t\right) - \frac{t \cdot y}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020065 
(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)))))