Average Error: 14.8 → 8.6
Time: 24.2s
Precision: 64
\[x + \left(y - z\right) \cdot \frac{t - x}{a - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} = -\infty:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \le -4.873433303661003277629103595829393437488 \cdot 10^{-297} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \le 0.0\right):\\ \;\;\;\;x + \left(\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}\right) \cdot \left(\frac{\sqrt[3]{y - z}}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}} \cdot \frac{t - x}{\sqrt[3]{a - z}}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{x \cdot y}{z} + t\right) - \frac{t \cdot y}{z}\\ \end{array}\]
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} = -\infty:\\
\;\;\;\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\

\mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \le -4.873433303661003277629103595829393437488 \cdot 10^{-297} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \le 0.0\right):\\
\;\;\;\;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]{a - z}} \cdot \frac{t - x}{\sqrt[3]{a - z}}\right)\\

\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 r96595 = x;
        double r96596 = y;
        double r96597 = z;
        double r96598 = r96596 - r96597;
        double r96599 = t;
        double r96600 = r96599 - r96595;
        double r96601 = a;
        double r96602 = r96601 - r96597;
        double r96603 = r96600 / r96602;
        double r96604 = r96598 * r96603;
        double r96605 = r96595 + r96604;
        return r96605;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r96606 = x;
        double r96607 = y;
        double r96608 = z;
        double r96609 = r96607 - r96608;
        double r96610 = t;
        double r96611 = r96610 - r96606;
        double r96612 = a;
        double r96613 = r96612 - r96608;
        double r96614 = r96611 / r96613;
        double r96615 = r96609 * r96614;
        double r96616 = r96606 + r96615;
        double r96617 = -inf.0;
        bool r96618 = r96616 <= r96617;
        double r96619 = r96609 * r96611;
        double r96620 = r96619 / r96613;
        double r96621 = r96606 + r96620;
        double r96622 = -4.873433303661003e-297;
        bool r96623 = r96616 <= r96622;
        double r96624 = 0.0;
        bool r96625 = r96616 <= r96624;
        double r96626 = !r96625;
        bool r96627 = r96623 || r96626;
        double r96628 = cbrt(r96609);
        double r96629 = r96628 * r96628;
        double r96630 = cbrt(r96613);
        double r96631 = r96630 * r96630;
        double r96632 = r96628 / r96631;
        double r96633 = r96611 / r96630;
        double r96634 = r96632 * r96633;
        double r96635 = r96629 * r96634;
        double r96636 = r96606 + r96635;
        double r96637 = r96606 * r96607;
        double r96638 = r96637 / r96608;
        double r96639 = r96638 + r96610;
        double r96640 = r96610 * r96607;
        double r96641 = r96640 / r96608;
        double r96642 = r96639 - r96641;
        double r96643 = r96627 ? r96636 : r96642;
        double r96644 = r96618 ? r96621 : r96643;
        return r96644;
}

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 3 regimes

  2. if (+ x (* (- y z) (/ (- t x) (- a z)))) < -inf.0

    1. Initial program 64.0

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

    3. Applied associate-*r/12.1

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

    if -inf.0 < (+ x (* (- y z) (/ (- t x) (- a z)))) < -4.873433303661003e-297 or 0.0 < (+ x (* (- y z) (/ (- t x) (- a z))))

    1. Initial program 6.4

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

    3. Applied add-cube-cbrt7.0

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

    4. Applied associate-*l*7.0

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

    6. Applied add-cube-cbrt7.0

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

    7. Applied *-un-lft-identity7.0

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

    8. Applied times-frac7.0

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

    9. Applied associate-*r*5.4

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

    10. Simplified5.4

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

    if -4.873433303661003e-297 < (+ x (* (- y z) (/ (- t x) (- a z)))) < 0.0

    1. Initial program 61.5

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

    2. Taylor expanded around inf 28.0

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

  4. Final simplification8.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} = -\infty:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \le -4.873433303661003277629103595829393437488 \cdot 10^{-297} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \le 0.0\right):\\ \;\;\;\;x + \left(\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}\right) \cdot \left(\frac{\sqrt[3]{y - z}}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}} \cdot \frac{t - x}{\sqrt[3]{a - z}}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{x \cdot y}{z} + t\right) - \frac{t \cdot y}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2019208 
(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)))))