Average Error: 14.6 → 7.4
Time: 20.7s
Precision: 64
\[x + \left(y - z\right) \cdot \frac{t - x}{a - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x + \frac{t - x}{a - z} \cdot \left(y - z\right) \le -1.435093340274830611665799903700831981469 \cdot 10^{-291} \lor \neg \left(x + \frac{t - x}{a - z} \cdot \left(y - z\right) \le 4.239988548410316393693334801140591712737 \cdot 10^{-282}\right):\\ \;\;\;\;\frac{y - z}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}} \cdot \frac{t - x}{\sqrt[3]{a - z}} + x\\ \mathbf{else}:\\ \;\;\;\;t + \left(\frac{y}{\frac{z}{x}} - y \cdot \frac{t}{z}\right)\\ \end{array}\]
x + \left(y - z\right) \cdot \frac{t - x}{a - z}
↓
\begin{array}{l}
\mathbf{if}\;x + \frac{t - x}{a - z} \cdot \left(y - z\right) \le -1.435093340274830611665799903700831981469 \cdot 10^{-291} \lor \neg \left(x + \frac{t - x}{a - z} \cdot \left(y - z\right) \le 4.239988548410316393693334801140591712737 \cdot 10^{-282}\right):\\
\;\;\;\;\frac{y - z}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}} \cdot \frac{t - x}{\sqrt[3]{a - z}} + x\\

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

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r102741 = x;
        double r102742 = y;
        double r102743 = z;
        double r102744 = r102742 - r102743;
        double r102745 = t;
        double r102746 = r102745 - r102741;
        double r102747 = a;
        double r102748 = r102747 - r102743;
        double r102749 = r102746 / r102748;
        double r102750 = r102744 * r102749;
        double r102751 = r102741 + r102750;
        return r102751;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r102752 = x;
        double r102753 = t;
        double r102754 = r102753 - r102752;
        double r102755 = a;
        double r102756 = z;
        double r102757 = r102755 - r102756;
        double r102758 = r102754 / r102757;
        double r102759 = y;
        double r102760 = r102759 - r102756;
        double r102761 = r102758 * r102760;
        double r102762 = r102752 + r102761;
        double r102763 = -1.4350933402748306e-291;
        bool r102764 = r102762 <= r102763;
        double r102765 = 4.2399885484103164e-282;
        bool r102766 = r102762 <= r102765;
        double r102767 = !r102766;
        bool r102768 = r102764 || r102767;
        double r102769 = cbrt(r102757);
        double r102770 = r102769 * r102769;
        double r102771 = r102760 / r102770;
        double r102772 = r102754 / r102769;
        double r102773 = r102771 * r102772;
        double r102774 = r102773 + r102752;
        double r102775 = r102756 / r102752;
        double r102776 = r102759 / r102775;
        double r102777 = r102753 / r102756;
        double r102778 = r102759 * r102777;
        double r102779 = r102776 - r102778;
        double r102780 = r102753 + r102779;
        double r102781 = r102768 ? r102774 : r102780;
        return r102781;
}

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)))) < -1.4350933402748306e-291 or 4.2399885484103164e-282 < (+ x (* (- y z) (/ (- t x) (- a z))))

    1. Initial program 7.1

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

    3. Applied add-cube-cbrt7.8

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

    4. Applied *-un-lft-identity7.8

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

    5. Applied times-frac7.8

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

    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

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

    if -1.4350933402748306e-291 < (+ x (* (- y z) (/ (- t x) (- a z)))) < 4.2399885484103164e-282

    1. Initial program 60.0

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

    3. Applied add-cube-cbrt59.7

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

    4. Applied *-un-lft-identity59.7

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

    5. Applied times-frac59.7

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

    6. Applied associate-*r*57.9

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

    7. Simplified58.0

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

    8. Taylor expanded around inf 27.0

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

    9. Simplified21.4

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

  4. Final simplification7.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{t - x}{a - z} \cdot \left(y - z\right) \le -1.435093340274830611665799903700831981469 \cdot 10^{-291} \lor \neg \left(x + \frac{t - x}{a - z} \cdot \left(y - z\right) \le 4.239988548410316393693334801140591712737 \cdot 10^{-282}\right):\\ \;\;\;\;\frac{y - z}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}} \cdot \frac{t - x}{\sqrt[3]{a - z}} + x\\ \mathbf{else}:\\ \;\;\;\;t + \left(\frac{y}{\frac{z}{x}} - y \cdot \frac{t}{z}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019196 
(FPCore (x y z t a)
  :name "Numeric.Signal:interpolate   from hsignal-0.2.7.1"
  (+ x (* (- y z) (/ (- t x) (- a z)))))