Average Error: 15.3 → 7.0
Time: 6.3s
Precision: 64
\[x + \left(y - z\right) \cdot \frac{t - x}{a - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \le -2.4340653570962097 \cdot 10^{-278} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \le 1.8831324269033737 \cdot 10^{-303}\right):\\ \;\;\;\;x + \frac{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}}{\sqrt[3]{a - z}} \cdot \left(\frac{\sqrt[3]{y - z}}{\sqrt[3]{a - z}} \cdot \frac{t - x}{\sqrt[3]{a - z}}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\frac{x}{z} - \frac{t}{z}\right) + t\\ \end{array}\]
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 -2.4340653570962097 \cdot 10^{-278} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \le 1.8831324269033737 \cdot 10^{-303}\right):\\
\;\;\;\;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 \frac{t - x}{\sqrt[3]{a - z}}\right)\\

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

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r107576 = x;
        double r107577 = y;
        double r107578 = z;
        double r107579 = r107577 - r107578;
        double r107580 = t;
        double r107581 = r107580 - r107576;
        double r107582 = a;
        double r107583 = r107582 - r107578;
        double r107584 = r107581 / r107583;
        double r107585 = r107579 * r107584;
        double r107586 = r107576 + r107585;
        return r107586;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r107587 = x;
        double r107588 = y;
        double r107589 = z;
        double r107590 = r107588 - r107589;
        double r107591 = t;
        double r107592 = r107591 - r107587;
        double r107593 = a;
        double r107594 = r107593 - r107589;
        double r107595 = r107592 / r107594;
        double r107596 = r107590 * r107595;
        double r107597 = r107587 + r107596;
        double r107598 = -2.4340653570962097e-278;
        bool r107599 = r107597 <= r107598;
        double r107600 = 1.8831324269033737e-303;
        bool r107601 = r107597 <= r107600;
        double r107602 = !r107601;
        bool r107603 = r107599 || r107602;
        double r107604 = cbrt(r107590);
        double r107605 = r107604 * r107604;
        double r107606 = cbrt(r107594);
        double r107607 = r107605 / r107606;
        double r107608 = r107604 / r107606;
        double r107609 = r107592 / r107606;
        double r107610 = r107608 * r107609;
        double r107611 = r107607 * r107610;
        double r107612 = r107587 + r107611;
        double r107613 = r107587 / r107589;
        double r107614 = r107591 / r107589;
        double r107615 = r107613 - r107614;
        double r107616 = r107588 * r107615;
        double r107617 = r107616 + r107591;
        double r107618 = r107603 ? r107612 : r107617;
        return r107618;
}

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)))) < -2.4340653570962097e-278 or 1.8831324269033737e-303 < (+ x (* (- y z) (/ (- t x) (- a z))))

    1. Initial program 7.7

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

    3. Applied add-cube-cbrt8.3

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

    4. Applied *-un-lft-identity8.3

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

    5. Applied times-frac8.3

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

    6. Applied associate-*r*5.2

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

    7. Simplified5.2

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

    9. Applied add-cube-cbrt5.0

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

    10. Applied times-frac5.0

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

    11. Applied associate-*l*4.7

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

    if -2.4340653570962097e-278 < (+ x (* (- y z) (/ (- t x) (- a z)))) < 1.8831324269033737e-303

    1. Initial program 60.6

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

    3. Applied add-cube-cbrt60.4

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

    4. Applied *-un-lft-identity60.4

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

    5. Applied times-frac60.4

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

    6. Applied associate-*r*59.1

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

    7. Simplified59.0

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

    9. Applied add-cube-cbrt59.3

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

    10. Applied times-frac59.2

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

    11. Applied associate-*l*59.2

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

    12. Taylor expanded around inf 25.6

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

    13. Simplified20.1

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

  4. Final simplification7.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \le -2.4340653570962097 \cdot 10^{-278} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \le 1.8831324269033737 \cdot 10^{-303}\right):\\ \;\;\;\;x + \frac{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}}{\sqrt[3]{a - z}} \cdot \left(\frac{\sqrt[3]{y - z}}{\sqrt[3]{a - z}} \cdot \frac{t - x}{\sqrt[3]{a - z}}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\frac{x}{z} - \frac{t}{z}\right) + t\\ \end{array}\]

Reproduce

herbie shell --seed 2020049 
(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)))))