Average Error: 14.4 → 7.9
Time: 25.7s
Precision: 64
\[x + \left(y - z\right) \cdot \frac{t - x}{a - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x + \frac{t - x}{a - z} \cdot \left(y - z\right) \le -1.923994883449214 \cdot 10^{-303}:\\ \;\;\;\;x + \frac{t - x}{a - z} \cdot \left(y - z\right)\\ \mathbf{elif}\;x + \frac{t - x}{a - z} \cdot \left(y - z\right) \le 0.0:\\ \;\;\;\;\left(t - \frac{t}{\frac{z}{y}}\right) + \frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\sqrt[3]{\frac{t - x}{\sqrt[3]{a - z}}} \cdot \left(\left(\sqrt[3]{\frac{t - x}{\sqrt[3]{a - z}}} \cdot \sqrt[3]{\frac{t - x}{\sqrt[3]{a - z}}}\right) \cdot \frac{y - z}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}}\right) + x\\ \end{array}\]
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 -1.923994883449214 \cdot 10^{-303}:\\
\;\;\;\;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 0.0:\\
\;\;\;\;\left(t - \frac{t}{\frac{z}{y}}\right) + \frac{x}{\frac{z}{y}}\\

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

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r6752983 = x;
        double r6752984 = y;
        double r6752985 = z;
        double r6752986 = r6752984 - r6752985;
        double r6752987 = t;
        double r6752988 = r6752987 - r6752983;
        double r6752989 = a;
        double r6752990 = r6752989 - r6752985;
        double r6752991 = r6752988 / r6752990;
        double r6752992 = r6752986 * r6752991;
        double r6752993 = r6752983 + r6752992;
        return r6752993;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r6752994 = x;
        double r6752995 = t;
        double r6752996 = r6752995 - r6752994;
        double r6752997 = a;
        double r6752998 = z;
        double r6752999 = r6752997 - r6752998;
        double r6753000 = r6752996 / r6752999;
        double r6753001 = y;
        double r6753002 = r6753001 - r6752998;
        double r6753003 = r6753000 * r6753002;
        double r6753004 = r6752994 + r6753003;
        double r6753005 = -1.923994883449214e-303;
        bool r6753006 = r6753004 <= r6753005;
        double r6753007 = 0.0;
        bool r6753008 = r6753004 <= r6753007;
        double r6753009 = r6752998 / r6753001;
        double r6753010 = r6752995 / r6753009;
        double r6753011 = r6752995 - r6753010;
        double r6753012 = r6752994 / r6753009;
        double r6753013 = r6753011 + r6753012;
        double r6753014 = cbrt(r6752999);
        double r6753015 = r6752996 / r6753014;
        double r6753016 = cbrt(r6753015);
        double r6753017 = r6753016 * r6753016;
        double r6753018 = r6753014 * r6753014;
        double r6753019 = r6753002 / r6753018;
        double r6753020 = r6753017 * r6753019;
        double r6753021 = r6753016 * r6753020;
        double r6753022 = r6753021 + r6752994;
        double r6753023 = r6753008 ? r6753013 : r6753022;
        double r6753024 = r6753006 ? r6753004 : r6753023;
        return r6753024;
}

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)))) < -1.923994883449214e-303

    1. Initial program 6.7

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

    if -1.923994883449214e-303 < (+ x (* (- y z) (/ (- t x) (- a z)))) < 0.0

    1. Initial program 61.7

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

    3. Applied add-cube-cbrt61.4

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

    4. Applied *-un-lft-identity61.4

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

    5. Applied times-frac61.3

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

    6. Applied associate-*r*61.2

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

    7. Simplified61.3

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

    9. Applied add-cube-cbrt61.2

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

    10. Applied associate-*r*61.2

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

    11. Taylor expanded around inf 25.5

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

    12. Simplified19.6

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

    if 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-cbrt8.4

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

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

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

    5. Applied times-frac8.4

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

    6. Applied associate-*r*5.5

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

    7. Simplified5.4

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

    9. Applied add-cube-cbrt5.7

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

    10. Applied associate-*r*5.7

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

  4. Final simplification7.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{t - x}{a - z} \cdot \left(y - z\right) \le -1.923994883449214 \cdot 10^{-303}:\\ \;\;\;\;x + \frac{t - x}{a - z} \cdot \left(y - z\right)\\ \mathbf{elif}\;x + \frac{t - x}{a - z} \cdot \left(y - z\right) \le 0.0:\\ \;\;\;\;\left(t - \frac{t}{\frac{z}{y}}\right) + \frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\sqrt[3]{\frac{t - x}{\sqrt[3]{a - z}}} \cdot \left(\left(\sqrt[3]{\frac{t - x}{\sqrt[3]{a - z}}} \cdot \sqrt[3]{\frac{t - x}{\sqrt[3]{a - z}}}\right) \cdot \frac{y - z}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}}\right) + x\\ \end{array}\]

Reproduce

herbie shell --seed 2019164 
(FPCore (x y z t a)
  :name "Numeric.Signal:interpolate   from hsignal-0.2.7.1"
  (+ x (* (- y z) (/ (- t x) (- a z)))))