Average Error: 14.1 → 10.4
Time: 27.9s
Precision: 64
\[x + \left(y - z\right) \cdot \frac{t - x}{a - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -2.287307948013401567659190226383170782569 \cdot 10^{143}:\\ \;\;\;\;t + \left(\frac{x}{z} - \frac{t}{z}\right) \cdot y\\ \mathbf{elif}\;z \le 3.524544795988202684293854966832494307064 \cdot 10^{220}:\\ \;\;\;\;\frac{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}}{\frac{\frac{\sqrt[3]{a - z}}{\sqrt[3]{\frac{t - x}{\sqrt[3]{a - z}}}} \cdot \frac{\sqrt[3]{a - z}}{\sqrt[3]{\frac{t - x}{\sqrt[3]{a - z}}}}}{\sqrt[3]{y - z}}} \cdot \sqrt[3]{\frac{t - x}{\sqrt[3]{a - z}}} + x\\ \mathbf{else}:\\ \;\;\;\;t + \left(\frac{x}{z} - \frac{t}{z}\right) \cdot y\\ \end{array}\]
x + \left(y - z\right) \cdot \frac{t - x}{a - z}
↓
\begin{array}{l}
\mathbf{if}\;z \le -2.287307948013401567659190226383170782569 \cdot 10^{143}:\\
\;\;\;\;t + \left(\frac{x}{z} - \frac{t}{z}\right) \cdot y\\

\mathbf{elif}\;z \le 3.524544795988202684293854966832494307064 \cdot 10^{220}:\\
\;\;\;\;\frac{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}}{\frac{\frac{\sqrt[3]{a - z}}{\sqrt[3]{\frac{t - x}{\sqrt[3]{a - z}}}} \cdot \frac{\sqrt[3]{a - z}}{\sqrt[3]{\frac{t - x}{\sqrt[3]{a - z}}}}}{\sqrt[3]{y - z}}} \cdot \sqrt[3]{\frac{t - x}{\sqrt[3]{a - z}}} + x\\

\mathbf{else}:\\
\;\;\;\;t + \left(\frac{x}{z} - \frac{t}{z}\right) \cdot y\\

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r5953615 = x;
        double r5953616 = y;
        double r5953617 = z;
        double r5953618 = r5953616 - r5953617;
        double r5953619 = t;
        double r5953620 = r5953619 - r5953615;
        double r5953621 = a;
        double r5953622 = r5953621 - r5953617;
        double r5953623 = r5953620 / r5953622;
        double r5953624 = r5953618 * r5953623;
        double r5953625 = r5953615 + r5953624;
        return r5953625;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r5953626 = z;
        double r5953627 = -2.2873079480134016e+143;
        bool r5953628 = r5953626 <= r5953627;
        double r5953629 = t;
        double r5953630 = x;
        double r5953631 = r5953630 / r5953626;
        double r5953632 = r5953629 / r5953626;
        double r5953633 = r5953631 - r5953632;
        double r5953634 = y;
        double r5953635 = r5953633 * r5953634;
        double r5953636 = r5953629 + r5953635;
        double r5953637 = 3.5245447959882027e+220;
        bool r5953638 = r5953626 <= r5953637;
        double r5953639 = r5953634 - r5953626;
        double r5953640 = cbrt(r5953639);
        double r5953641 = r5953640 * r5953640;
        double r5953642 = a;
        double r5953643 = r5953642 - r5953626;
        double r5953644 = cbrt(r5953643);
        double r5953645 = r5953629 - r5953630;
        double r5953646 = r5953645 / r5953644;
        double r5953647 = cbrt(r5953646);
        double r5953648 = r5953644 / r5953647;
        double r5953649 = r5953648 * r5953648;
        double r5953650 = r5953649 / r5953640;
        double r5953651 = r5953641 / r5953650;
        double r5953652 = r5953651 * r5953647;
        double r5953653 = r5953652 + r5953630;
        double r5953654 = r5953638 ? r5953653 : r5953636;
        double r5953655 = r5953628 ? r5953636 : r5953654;
        return r5953655;
}

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 z < -2.2873079480134016e+143 or 3.5245447959882027e+220 < z

    1. Initial program 26.8

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

    3. Applied add-cube-cbrt27.4

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

    4. Applied *-un-lft-identity27.4

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

    5. Applied times-frac27.4

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

    6. Applied associate-*r*22.5

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

    7. Simplified22.5

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

    9. Applied add-cube-cbrt22.7

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

    10. Applied associate-*l*22.7

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

    11. Taylor expanded around inf 25.1

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

    12. Simplified15.5

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

    if -2.2873079480134016e+143 < z < 3.5245447959882027e+220

    1. Initial program 10.2

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

    3. Applied add-cube-cbrt10.7

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

    4. Applied *-un-lft-identity10.7

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

    5. Applied times-frac10.7

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

    6. Applied associate-*r*8.6

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

    7. Simplified8.6

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

    9. Applied add-cube-cbrt8.7

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

    10. Applied associate-*r*8.7

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

    11. Simplified8.8

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

    13. Applied add-cube-cbrt8.8

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

    14. Applied associate-/l*8.8

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

  4. Final simplification10.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -2.287307948013401567659190226383170782569 \cdot 10^{143}:\\ \;\;\;\;t + \left(\frac{x}{z} - \frac{t}{z}\right) \cdot y\\ \mathbf{elif}\;z \le 3.524544795988202684293854966832494307064 \cdot 10^{220}:\\ \;\;\;\;\frac{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}}{\frac{\frac{\sqrt[3]{a - z}}{\sqrt[3]{\frac{t - x}{\sqrt[3]{a - z}}}} \cdot \frac{\sqrt[3]{a - z}}{\sqrt[3]{\frac{t - x}{\sqrt[3]{a - z}}}}}{\sqrt[3]{y - z}}} \cdot \sqrt[3]{\frac{t - x}{\sqrt[3]{a - z}}} + x\\ \mathbf{else}:\\ \;\;\;\;t + \left(\frac{x}{z} - \frac{t}{z}\right) \cdot y\\ \end{array}\]

Reproduce

herbie shell --seed 2019169 
(FPCore (x y z t a)
  :name "Numeric.Signal:interpolate   from hsignal-0.2.7.1"
  (+ x (* (- y z) (/ (- t x) (- a z)))))