Average Error: 14.8 → 10.6
Time: 5.9s
Precision: 64
\[x + \left(y - z\right) \cdot \frac{t - x}{a - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;a \le -5.8776542829972293 \cdot 10^{-231}:\\ \;\;\;\;x + \left(\left(y - z\right) \cdot \frac{\sqrt[3]{t - x} \cdot \sqrt[3]{t - x}}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}}\right) \cdot \frac{\sqrt[3]{t - x}}{\sqrt[3]{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}} \cdot \sqrt[3]{\sqrt[3]{a - z}}}\\ \mathbf{elif}\;a \le 1.20471099826735273 \cdot 10^{-174}:\\ \;\;\;\;\left(\frac{x \cdot y}{z} + t\right) - \frac{t \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(y - z\right) \cdot \frac{\sqrt[3]{t - x} \cdot \sqrt[3]{t - x}}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}}\right) \cdot \frac{\sqrt[3]{t - x}}{\sqrt[3]{a - z}}\\ \end{array}\]
x + \left(y - z\right) \cdot \frac{t - x}{a - z}
↓
\begin{array}{l}
\mathbf{if}\;a \le -5.8776542829972293 \cdot 10^{-231}:\\
\;\;\;\;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]{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}} \cdot \sqrt[3]{\sqrt[3]{a - z}}}\\

\mathbf{elif}\;a \le 1.20471099826735273 \cdot 10^{-174}:\\
\;\;\;\;\left(\frac{x \cdot y}{z} + t\right) - \frac{t \cdot y}{z}\\

\mathbf{else}:\\
\;\;\;\;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}}\\

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r84662 = x;
        double r84663 = y;
        double r84664 = z;
        double r84665 = r84663 - r84664;
        double r84666 = t;
        double r84667 = r84666 - r84662;
        double r84668 = a;
        double r84669 = r84668 - r84664;
        double r84670 = r84667 / r84669;
        double r84671 = r84665 * r84670;
        double r84672 = r84662 + r84671;
        return r84672;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r84673 = a;
        double r84674 = -5.877654282997229e-231;
        bool r84675 = r84673 <= r84674;
        double r84676 = x;
        double r84677 = y;
        double r84678 = z;
        double r84679 = r84677 - r84678;
        double r84680 = t;
        double r84681 = r84680 - r84676;
        double r84682 = cbrt(r84681);
        double r84683 = r84682 * r84682;
        double r84684 = r84673 - r84678;
        double r84685 = cbrt(r84684);
        double r84686 = r84685 * r84685;
        double r84687 = r84683 / r84686;
        double r84688 = r84679 * r84687;
        double r84689 = cbrt(r84686);
        double r84690 = cbrt(r84685);
        double r84691 = r84689 * r84690;
        double r84692 = r84682 / r84691;
        double r84693 = r84688 * r84692;
        double r84694 = r84676 + r84693;
        double r84695 = 1.2047109982673527e-174;
        bool r84696 = r84673 <= r84695;
        double r84697 = r84676 * r84677;
        double r84698 = r84697 / r84678;
        double r84699 = r84698 + r84680;
        double r84700 = r84680 * r84677;
        double r84701 = r84700 / r84678;
        double r84702 = r84699 - r84701;
        double r84703 = r84682 / r84685;
        double r84704 = r84688 * r84703;
        double r84705 = r84676 + r84704;
        double r84706 = r84696 ? r84702 : r84705;
        double r84707 = r84675 ? r84694 : r84706;
        return r84707;
}

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 a < -5.877654282997229e-231

    1. Initial program 13.2

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

    3. Applied add-cube-cbrt13.7

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

    4. Applied add-cube-cbrt13.9

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

    5. Applied times-frac13.9

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

    6. Applied associate-*r*11.1

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

    8. Applied add-cube-cbrt11.1

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

    9. Applied cbrt-prod11.1

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

    if -5.877654282997229e-231 < a < 1.2047109982673527e-174

    1. Initial program 25.5

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

    2. Taylor expanded around inf 10.4

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

    if 1.2047109982673527e-174 < a

    1. Initial program 12.5

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

    3. Applied add-cube-cbrt12.9

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

    4. Applied add-cube-cbrt13.1

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

    5. Applied times-frac13.1

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

    6. Applied associate-*r*10.1

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

  4. Final simplification10.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;a \le -5.8776542829972293 \cdot 10^{-231}:\\ \;\;\;\;x + \left(\left(y - z\right) \cdot \frac{\sqrt[3]{t - x} \cdot \sqrt[3]{t - x}}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}}\right) \cdot \frac{\sqrt[3]{t - x}}{\sqrt[3]{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}} \cdot \sqrt[3]{\sqrt[3]{a - z}}}\\ \mathbf{elif}\;a \le 1.20471099826735273 \cdot 10^{-174}:\\ \;\;\;\;\left(\frac{x \cdot y}{z} + t\right) - \frac{t \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(y - z\right) \cdot \frac{\sqrt[3]{t - x} \cdot \sqrt[3]{t - x}}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}}\right) \cdot \frac{\sqrt[3]{t - x}}{\sqrt[3]{a - z}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020025 
(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)))))