Average Error: 14.7 → 6.9
Time: 24.4s
Precision: 64
\[x + \left(y - z\right) \cdot \frac{t - x}{a - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x + \frac{t - x}{a - z} \cdot \left(y - z\right) \le -1.3435650229451346 \cdot 10^{-276}:\\ \;\;\;\;x + \frac{\sqrt[3]{t - x}}{\sqrt[3]{a - z}} \cdot \frac{y - z}{\frac{\sqrt[3]{a - z}}{\sqrt[3]{t - x}} \cdot \frac{\sqrt[3]{a - z}}{\sqrt[3]{t - x}}}\\ \mathbf{elif}\;x + \frac{t - x}{a - z} \cdot \left(y - z\right) \le 0.0:\\ \;\;\;\;y \cdot \left(\frac{x}{z} - \frac{t}{z}\right) + t\\ \mathbf{else}:\\ \;\;\;\;\frac{t - x}{\sqrt[3]{a - z}} \cdot \frac{y - z}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}} + x\\ \end{array}\]
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 -1.3435650229451346 \cdot 10^{-276}:\\
\;\;\;\;x + \frac{\sqrt[3]{t - x}}{\sqrt[3]{a - z}} \cdot \frac{y - z}{\frac{\sqrt[3]{a - z}}{\sqrt[3]{t - x}} \cdot \frac{\sqrt[3]{a - z}}{\sqrt[3]{t - x}}}\\

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

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

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r6853993 = x;
        double r6853994 = y;
        double r6853995 = z;
        double r6853996 = r6853994 - r6853995;
        double r6853997 = t;
        double r6853998 = r6853997 - r6853993;
        double r6853999 = a;
        double r6854000 = r6853999 - r6853995;
        double r6854001 = r6853998 / r6854000;
        double r6854002 = r6853996 * r6854001;
        double r6854003 = r6853993 + r6854002;
        return r6854003;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r6854004 = x;
        double r6854005 = t;
        double r6854006 = r6854005 - r6854004;
        double r6854007 = a;
        double r6854008 = z;
        double r6854009 = r6854007 - r6854008;
        double r6854010 = r6854006 / r6854009;
        double r6854011 = y;
        double r6854012 = r6854011 - r6854008;
        double r6854013 = r6854010 * r6854012;
        double r6854014 = r6854004 + r6854013;
        double r6854015 = -1.3435650229451346e-276;
        bool r6854016 = r6854014 <= r6854015;
        double r6854017 = cbrt(r6854006);
        double r6854018 = cbrt(r6854009);
        double r6854019 = r6854017 / r6854018;
        double r6854020 = r6854018 / r6854017;
        double r6854021 = r6854020 * r6854020;
        double r6854022 = r6854012 / r6854021;
        double r6854023 = r6854019 * r6854022;
        double r6854024 = r6854004 + r6854023;
        double r6854025 = 0.0;
        bool r6854026 = r6854014 <= r6854025;
        double r6854027 = r6854004 / r6854008;
        double r6854028 = r6854005 / r6854008;
        double r6854029 = r6854027 - r6854028;
        double r6854030 = r6854011 * r6854029;
        double r6854031 = r6854030 + r6854005;
        double r6854032 = r6854006 / r6854018;
        double r6854033 = r6854018 * r6854018;
        double r6854034 = r6854012 / r6854033;
        double r6854035 = r6854032 * r6854034;
        double r6854036 = r6854035 + r6854004;
        double r6854037 = r6854026 ? r6854031 : r6854036;
        double r6854038 = r6854016 ? r6854024 : r6854037;
        return r6854038;
}

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)))) < -1.3435650229451346e-276

    1. Initial program 6.9

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

    3. Applied add-cube-cbrt7.6

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

    4. Applied *-un-lft-identity7.6

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

    5. Applied times-frac7.6

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

    6. Applied associate-*r*5.0

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

    7. Simplified5.0

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

    9. Applied *-un-lft-identity5.0

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

    10. Applied cbrt-prod5.0

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

    11. Applied add-cube-cbrt5.2

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

    12. Applied times-frac5.2

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

    13. Applied associate-*r*4.6

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

    14. Simplified4.6

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

    if -1.3435650229451346e-276 < (+ 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. Using strategy rm

    3. Applied add-cube-cbrt60.5

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

    4. Applied *-un-lft-identity60.5

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

    5. Applied times-frac60.4

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

    6. Applied associate-*r*59.3

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

    7. Simplified59.3

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

    9. Applied add-cube-cbrt59.2

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

    10. Applied associate-*l*59.2

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

    11. Taylor expanded around inf 24.7

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

    12. Simplified20.3

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

    if 0.0 < (+ 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*4.8

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

    7. Simplified4.8

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

  4. Final simplification6.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{t - x}{a - z} \cdot \left(y - z\right) \le -1.3435650229451346 \cdot 10^{-276}:\\ \;\;\;\;x + \frac{\sqrt[3]{t - x}}{\sqrt[3]{a - z}} \cdot \frac{y - z}{\frac{\sqrt[3]{a - z}}{\sqrt[3]{t - x}} \cdot \frac{\sqrt[3]{a - z}}{\sqrt[3]{t - x}}}\\ \mathbf{elif}\;x + \frac{t - x}{a - z} \cdot \left(y - z\right) \le 0.0:\\ \;\;\;\;y \cdot \left(\frac{x}{z} - \frac{t}{z}\right) + t\\ \mathbf{else}:\\ \;\;\;\;\frac{t - x}{\sqrt[3]{a - z}} \cdot \frac{y - z}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}} + x\\ \end{array}\]

Reproduce

herbie shell --seed 2019162 
(FPCore (x y z t a)
  :name "Numeric.Signal:interpolate   from hsignal-0.2.7.1"
  (+ x (* (- y z) (/ (- t x) (- a z)))))