Average Error: 14.6 → 10.5
Time: 41.5s
Precision: 64
\[x + \left(y - z\right) \cdot \frac{t - x}{a - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;a \le -1.997543300824516967451174039616744917242 \cdot 10^{-131} \lor \neg \left(a \le 3.148145590460313919036522755186967820726 \cdot 10^{-195}\right):\\ \;\;\;\;\frac{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}}{\sqrt[3]{a - z}} \cdot \left(1 \cdot \left(\frac{t - x}{\sqrt[3]{a - z}} \cdot \frac{\sqrt[3]{y - z}}{\sqrt[3]{a - z}}\right)\right) + x\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{x \cdot y}{z} + t\right) - \frac{t \cdot y}{z}\\ \end{array}\]
x + \left(y - z\right) \cdot \frac{t - x}{a - z}
↓
\begin{array}{l}
\mathbf{if}\;a \le -1.997543300824516967451174039616744917242 \cdot 10^{-131} \lor \neg \left(a \le 3.148145590460313919036522755186967820726 \cdot 10^{-195}\right):\\
\;\;\;\;\frac{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}}{\sqrt[3]{a - z}} \cdot \left(1 \cdot \left(\frac{t - x}{\sqrt[3]{a - z}} \cdot \frac{\sqrt[3]{y - z}}{\sqrt[3]{a - z}}\right)\right) + x\\

\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 r155593 = x;
        double r155594 = y;
        double r155595 = z;
        double r155596 = r155594 - r155595;
        double r155597 = t;
        double r155598 = r155597 - r155593;
        double r155599 = a;
        double r155600 = r155599 - r155595;
        double r155601 = r155598 / r155600;
        double r155602 = r155596 * r155601;
        double r155603 = r155593 + r155602;
        return r155603;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r155604 = a;
        double r155605 = -1.997543300824517e-131;
        bool r155606 = r155604 <= r155605;
        double r155607 = 3.148145590460314e-195;
        bool r155608 = r155604 <= r155607;
        double r155609 = !r155608;
        bool r155610 = r155606 || r155609;
        double r155611 = y;
        double r155612 = z;
        double r155613 = r155611 - r155612;
        double r155614 = cbrt(r155613);
        double r155615 = r155614 * r155614;
        double r155616 = r155604 - r155612;
        double r155617 = cbrt(r155616);
        double r155618 = r155615 / r155617;
        double r155619 = 1.0;
        double r155620 = t;
        double r155621 = x;
        double r155622 = r155620 - r155621;
        double r155623 = r155622 / r155617;
        double r155624 = r155614 / r155617;
        double r155625 = r155623 * r155624;
        double r155626 = r155619 * r155625;
        double r155627 = r155618 * r155626;
        double r155628 = r155627 + r155621;
        double r155629 = r155621 * r155611;
        double r155630 = r155629 / r155612;
        double r155631 = r155630 + r155620;
        double r155632 = r155620 * r155611;
        double r155633 = r155632 / r155612;
        double r155634 = r155631 - r155633;
        double r155635 = r155610 ? r155628 : r155634;
        return r155635;
}

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 a < -1.997543300824517e-131 or 3.148145590460314e-195 < a

    1. Initial program 11.8

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

    3. Applied add-cube-cbrt12.3

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

    4. Applied *-un-lft-identity12.3

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

    5. Applied times-frac12.3

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

    6. Applied associate-*r*10.1

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

    7. Simplified10.1

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

    9. Applied add-cube-cbrt10.1

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

    10. Applied times-frac10.1

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

    11. Applied associate-*l*9.8

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

    13. Applied *-un-lft-identity9.8

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

    14. Applied cbrt-prod9.8

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

    15. Applied *-un-lft-identity9.8

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

    16. Applied times-frac9.8

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

    17. Applied associate-*l*9.8

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

    18. Simplified9.8

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

    if -1.997543300824517e-131 < a < 3.148145590460314e-195

    1. Initial program 25.5

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

    2. Taylor expanded around inf 13.3

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

  4. Final simplification10.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;a \le -1.997543300824516967451174039616744917242 \cdot 10^{-131} \lor \neg \left(a \le 3.148145590460313919036522755186967820726 \cdot 10^{-195}\right):\\ \;\;\;\;\frac{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}}{\sqrt[3]{a - z}} \cdot \left(1 \cdot \left(\frac{t - x}{\sqrt[3]{a - z}} \cdot \frac{\sqrt[3]{y - z}}{\sqrt[3]{a - z}}\right)\right) + x\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{x \cdot y}{z} + t\right) - \frac{t \cdot y}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2019323 
(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)))))