Average Error: 14.7 → 7.4
Time: 24.2s
Precision: 64
\[x + \left(y - z\right) \cdot \frac{t - x}{a - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x + \frac{t - x}{a - z} \cdot \left(y - z\right) = -\infty:\\ \;\;\;\;\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} + x\\ \mathbf{elif}\;x + \frac{t - x}{a - z} \cdot \left(y - z\right) \le -1.110560608770146688603763352924655798649 \cdot 10^{-181}:\\ \;\;\;\;x + \frac{t - x}{a - z} \cdot \left(y - z\right)\\ \mathbf{elif}\;x + \frac{t - x}{a - z} \cdot \left(y - z\right) \le -3.956280165893758193874340988906388103674 \cdot 10^{-277}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} + x\\ \mathbf{elif}\;x + \frac{t - x}{a - z} \cdot \left(y - z\right) \le 0.0:\\ \;\;\;\;\left(t + \frac{x \cdot y}{z}\right) - \frac{y \cdot t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\sqrt[3]{\sqrt[3]{a - z}}} \cdot \frac{y - z}{\sqrt[3]{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}} \cdot \left(\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}\right)}\\ \end{array}\]
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) = -\infty:\\
\;\;\;\;\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} + x\\

\mathbf{elif}\;x + \frac{t - x}{a - z} \cdot \left(y - z\right) \le -1.110560608770146688603763352924655798649 \cdot 10^{-181}:\\
\;\;\;\;x + \frac{t - x}{a - z} \cdot \left(y - z\right)\\

\mathbf{elif}\;x + \frac{t - x}{a - z} \cdot \left(y - z\right) \le -3.956280165893758193874340988906388103674 \cdot 10^{-277}:\\
\;\;\;\;\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} + x\\

\mathbf{elif}\;x + \frac{t - x}{a - z} \cdot \left(y - z\right) \le 0.0:\\
\;\;\;\;\left(t + \frac{x \cdot y}{z}\right) - \frac{y \cdot t}{z}\\

\mathbf{else}:\\
\;\;\;\;x + \frac{t - x}{\sqrt[3]{\sqrt[3]{a - z}}} \cdot \frac{y - z}{\sqrt[3]{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}} \cdot \left(\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}\right)}\\

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r7652741 = x;
        double r7652742 = y;
        double r7652743 = z;
        double r7652744 = r7652742 - r7652743;
        double r7652745 = t;
        double r7652746 = r7652745 - r7652741;
        double r7652747 = a;
        double r7652748 = r7652747 - r7652743;
        double r7652749 = r7652746 / r7652748;
        double r7652750 = r7652744 * r7652749;
        double r7652751 = r7652741 + r7652750;
        return r7652751;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r7652752 = x;
        double r7652753 = t;
        double r7652754 = r7652753 - r7652752;
        double r7652755 = a;
        double r7652756 = z;
        double r7652757 = r7652755 - r7652756;
        double r7652758 = r7652754 / r7652757;
        double r7652759 = y;
        double r7652760 = r7652759 - r7652756;
        double r7652761 = r7652758 * r7652760;
        double r7652762 = r7652752 + r7652761;
        double r7652763 = -inf.0;
        bool r7652764 = r7652762 <= r7652763;
        double r7652765 = r7652760 * r7652754;
        double r7652766 = r7652765 / r7652757;
        double r7652767 = r7652766 + r7652752;
        double r7652768 = -1.1105606087701467e-181;
        bool r7652769 = r7652762 <= r7652768;
        double r7652770 = -3.956280165893758e-277;
        bool r7652771 = r7652762 <= r7652770;
        double r7652772 = 0.0;
        bool r7652773 = r7652762 <= r7652772;
        double r7652774 = r7652752 * r7652759;
        double r7652775 = r7652774 / r7652756;
        double r7652776 = r7652753 + r7652775;
        double r7652777 = r7652759 * r7652753;
        double r7652778 = r7652777 / r7652756;
        double r7652779 = r7652776 - r7652778;
        double r7652780 = cbrt(r7652757);
        double r7652781 = cbrt(r7652780);
        double r7652782 = r7652754 / r7652781;
        double r7652783 = r7652780 * r7652780;
        double r7652784 = cbrt(r7652783);
        double r7652785 = r7652784 * r7652783;
        double r7652786 = r7652760 / r7652785;
        double r7652787 = r7652782 * r7652786;
        double r7652788 = r7652752 + r7652787;
        double r7652789 = r7652773 ? r7652779 : r7652788;
        double r7652790 = r7652771 ? r7652767 : r7652789;
        double r7652791 = r7652769 ? r7652762 : r7652790;
        double r7652792 = r7652764 ? r7652767 : r7652791;
        return r7652792;
}

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 4 regimes

  2. if (+ x (* (- y z) (/ (- t x) (- a z)))) < -inf.0 or -1.1105606087701467e-181 < (+ x (* (- y z) (/ (- t x) (- a z)))) < -3.956280165893758e-277

    1. Initial program 39.7

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

    3. Applied associate-*r/8.3

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

    if -inf.0 < (+ x (* (- y z) (/ (- t x) (- a z)))) < -1.1105606087701467e-181

    1. Initial program 3.3

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

    if -3.956280165893758e-277 < (+ x (* (- y z) (/ (- t x) (- a z)))) < 0.0

    1. Initial program 60.6

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

    2. Taylor expanded around inf 26.2

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

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

    1. Initial program 8.2

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

    3. Applied add-cube-cbrt8.8

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

    4. Applied *-un-lft-identity8.8

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

    5. Applied times-frac8.9

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

    6. Applied associate-*r*5.3

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

    7. Simplified5.3

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

    9. Applied add-cube-cbrt5.3

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

    10. Applied cbrt-prod5.4

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

    11. Applied *-un-lft-identity5.4

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

    12. Applied times-frac5.4

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

    13. Applied associate-*r*4.9

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

    14. Simplified4.9

      \[\leadsto x + \color{blue}{\frac{y - z}{\sqrt[3]{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}} \cdot \left(\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}\right)}} \cdot \frac{t - x}{\sqrt[3]{\sqrt[3]{a - z}}}\]
  3. Recombined 4 regimes into one program.

  4. Final simplification7.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{t - x}{a - z} \cdot \left(y - z\right) = -\infty:\\ \;\;\;\;\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} + x\\ \mathbf{elif}\;x + \frac{t - x}{a - z} \cdot \left(y - z\right) \le -1.110560608770146688603763352924655798649 \cdot 10^{-181}:\\ \;\;\;\;x + \frac{t - x}{a - z} \cdot \left(y - z\right)\\ \mathbf{elif}\;x + \frac{t - x}{a - z} \cdot \left(y - z\right) \le -3.956280165893758193874340988906388103674 \cdot 10^{-277}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} + x\\ \mathbf{elif}\;x + \frac{t - x}{a - z} \cdot \left(y - z\right) \le 0.0:\\ \;\;\;\;\left(t + \frac{x \cdot y}{z}\right) - \frac{y \cdot t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\sqrt[3]{\sqrt[3]{a - z}}} \cdot \frac{y - z}{\sqrt[3]{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}} \cdot \left(\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}\right)}\\ \end{array}\]

Reproduce

herbie shell --seed 2019174 
(FPCore (x y z t a)
  :name "Numeric.Signal:interpolate   from hsignal-0.2.7.1"
  (+ x (* (- y z) (/ (- t x) (- a z)))))