Average Error: 14.8 → 6.8
Time: 8.9s
Precision: 64
\[x + \left(y - z\right) \cdot \frac{t - x}{a - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \le -5.434803235903865600499221827993269409084 \cdot 10^{-306} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \le 0.0\right):\\ \;\;\;\;x + \left(\left(y - z\right) \cdot \frac{\left(\left(\sqrt[3]{\sqrt[3]{t - x}} \cdot \sqrt[3]{\sqrt[3]{t - x}}\right) \cdot \sqrt[3]{\sqrt[3]{t - x}}\right) \cdot \sqrt[3]{t - x}}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}}\right) \cdot \frac{\sqrt[3]{t - x}}{\sqrt[3]{a - z}}\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \left(\frac{x}{z} - \frac{t}{z}\right)\\ \end{array}\]
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 -5.434803235903865600499221827993269409084 \cdot 10^{-306} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \le 0.0\right):\\
\;\;\;\;x + \left(\left(y - z\right) \cdot \frac{\left(\left(\sqrt[3]{\sqrt[3]{t - x}} \cdot \sqrt[3]{\sqrt[3]{t - x}}\right) \cdot \sqrt[3]{\sqrt[3]{t - x}}\right) \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 r106807 = x;
        double r106808 = y;
        double r106809 = z;
        double r106810 = r106808 - r106809;
        double r106811 = t;
        double r106812 = r106811 - r106807;
        double r106813 = a;
        double r106814 = r106813 - r106809;
        double r106815 = r106812 / r106814;
        double r106816 = r106810 * r106815;
        double r106817 = r106807 + r106816;
        return r106817;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r106818 = x;
        double r106819 = y;
        double r106820 = z;
        double r106821 = r106819 - r106820;
        double r106822 = t;
        double r106823 = r106822 - r106818;
        double r106824 = a;
        double r106825 = r106824 - r106820;
        double r106826 = r106823 / r106825;
        double r106827 = r106821 * r106826;
        double r106828 = r106818 + r106827;
        double r106829 = -5.4348032359038656e-306;
        bool r106830 = r106828 <= r106829;
        double r106831 = 0.0;
        bool r106832 = r106828 <= r106831;
        double r106833 = !r106832;
        bool r106834 = r106830 || r106833;
        double r106835 = cbrt(r106823);
        double r106836 = cbrt(r106835);
        double r106837 = r106836 * r106836;
        double r106838 = r106837 * r106836;
        double r106839 = r106838 * r106835;
        double r106840 = cbrt(r106825);
        double r106841 = r106840 * r106840;
        double r106842 = r106839 / r106841;
        double r106843 = r106821 * r106842;
        double r106844 = r106835 / r106840;
        double r106845 = r106843 * r106844;
        double r106846 = r106818 + r106845;
        double r106847 = r106818 / r106820;
        double r106848 = r106822 / r106820;
        double r106849 = r106847 - r106848;
        double r106850 = r106819 * r106849;
        double r106851 = r106822 + r106850;
        double r106852 = r106834 ? r106846 : r106851;
        return r106852;
}

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)))) < -5.4348032359038656e-306 or 0.0 < (+ 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 add-cube-cbrt8.5

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

    5. Applied times-frac8.5

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

    6. Applied associate-*r*4.7

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

    8. Applied add-cube-cbrt4.9

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

    if -5.4348032359038656e-306 < (+ x (* (- y z) (/ (- t x) (- a z)))) < 0.0

    1. Initial program 61.8

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

    3. Applied add-cube-cbrt61.5

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

    4. Applied add-cube-cbrt61.5

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

    5. Applied times-frac61.4

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

    6. Applied associate-*r*61.2

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

    7. Taylor expanded around inf 24.8

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

    8. Simplified19.1

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

  4. Final simplification6.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \le -5.434803235903865600499221827993269409084 \cdot 10^{-306} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \le 0.0\right):\\ \;\;\;\;x + \left(\left(y - z\right) \cdot \frac{\left(\left(\sqrt[3]{\sqrt[3]{t - x}} \cdot \sqrt[3]{\sqrt[3]{t - x}}\right) \cdot \sqrt[3]{\sqrt[3]{t - x}}\right) \cdot \sqrt[3]{t - x}}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}}\right) \cdot \frac{\sqrt[3]{t - x}}{\sqrt[3]{a - z}}\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \left(\frac{x}{z} - \frac{t}{z}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 1978988140 
(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)))))