Average Error: 14.8 → 6.8
Time: 6.8s
Precision: 64
\[x + \left(y - z\right) \cdot \frac{t - x}{a - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \le -3.5146774546459616 \cdot 10^{-282} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \le 3.33709759619623259 \cdot 10^{-306}\right):\\ \;\;\;\;x + \left(\left(y - z\right) \cdot \frac{\sqrt[3]{t - x} \cdot \sqrt[3]{t - x}}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}}\right) \cdot \frac{\sqrt[3]{t - x}}{\sqrt[3]{a - z}}\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \left(\frac{x}{z} - \frac{t}{z}\right)\\ \end{array}\]
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 -3.5146774546459616 \cdot 10^{-282} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \le 3.33709759619623259 \cdot 10^{-306}\right):\\
\;\;\;\;x + \left(\left(y - z\right) \cdot \frac{\sqrt[3]{t - x} \cdot \sqrt[3]{t - x}}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}}\right) \cdot \frac{\sqrt[3]{t - x}}{\sqrt[3]{a - z}}\\

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

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r137522 = x;
        double r137523 = y;
        double r137524 = z;
        double r137525 = r137523 - r137524;
        double r137526 = t;
        double r137527 = r137526 - r137522;
        double r137528 = a;
        double r137529 = r137528 - r137524;
        double r137530 = r137527 / r137529;
        double r137531 = r137525 * r137530;
        double r137532 = r137522 + r137531;
        return r137532;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r137533 = x;
        double r137534 = y;
        double r137535 = z;
        double r137536 = r137534 - r137535;
        double r137537 = t;
        double r137538 = r137537 - r137533;
        double r137539 = a;
        double r137540 = r137539 - r137535;
        double r137541 = r137538 / r137540;
        double r137542 = r137536 * r137541;
        double r137543 = r137533 + r137542;
        double r137544 = -3.514677454645962e-282;
        bool r137545 = r137543 <= r137544;
        double r137546 = 3.3370975961962326e-306;
        bool r137547 = r137543 <= r137546;
        double r137548 = !r137547;
        bool r137549 = r137545 || r137548;
        double r137550 = cbrt(r137538);
        double r137551 = r137550 * r137550;
        double r137552 = cbrt(r137540);
        double r137553 = r137552 * r137552;
        double r137554 = r137551 / r137553;
        double r137555 = r137536 * r137554;
        double r137556 = r137550 / r137552;
        double r137557 = r137555 * r137556;
        double r137558 = r137533 + r137557;
        double r137559 = r137533 / r137535;
        double r137560 = r137537 / r137535;
        double r137561 = r137559 - r137560;
        double r137562 = r137534 * r137561;
        double r137563 = r137537 + r137562;
        double r137564 = r137549 ? r137558 : r137563;
        return r137564;
}

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)))) < -3.514677454645962e-282 or 3.3370975961962326e-306 < (+ x (* (- y z) (/ (- t x) (- a z))))

    1. Initial program 7.6

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

    3. Applied add-cube-cbrt8.2

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

    4. Applied add-cube-cbrt8.4

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

    5. Applied times-frac8.4

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

    6. Applied associate-*r*4.4

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

    if -3.514677454645962e-282 < (+ x (* (- y z) (/ (- t x) (- a z)))) < 3.3370975961962326e-306

    1. Initial program 60.5

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

    3. Applied add-cube-cbrt60.3

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

    4. Applied add-cube-cbrt60.3

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

    5. Applied times-frac60.3

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

    6. Applied associate-*r*59.2

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

    7. Taylor expanded around inf 26.8

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

    8. Simplified21.5

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

  4. Final simplification6.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \le -3.5146774546459616 \cdot 10^{-282} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \le 3.33709759619623259 \cdot 10^{-306}\right):\\ \;\;\;\;x + \left(\left(y - z\right) \cdot \frac{\sqrt[3]{t - x} \cdot \sqrt[3]{t - x}}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}}\right) \cdot \frac{\sqrt[3]{t - x}}{\sqrt[3]{a - z}}\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \left(\frac{x}{z} - \frac{t}{z}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020018 
(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)))))