Average Error: 14.7 → 10.2
Time: 51.0s
Precision: 64
\[x + \left(y - z\right) \cdot \frac{t - x}{a - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;a \le -2.016722143479182721107069384915645128898 \cdot 10^{-79}:\\ \;\;\;\;x + \frac{\frac{y - z}{\sqrt[3]{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}}}}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}} \cdot \frac{t - x}{\sqrt[3]{\sqrt[3]{a - z}}}\\ \mathbf{elif}\;a \le 1.082916304047229047679075765793884594082 \cdot 10^{-175}:\\ \;\;\;\;\left(\frac{x}{z} - \frac{t}{z}\right) \cdot y + t\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt[3]{t - x}}{\sqrt[3]{a - z}} \cdot \frac{y - z}{\frac{\sqrt[3]{a - z}}{\sqrt[3]{t - x}} \cdot \frac{\sqrt[3]{a - z}}{\sqrt[3]{t - x}}} + x\\ \end{array}\]
x + \left(y - z\right) \cdot \frac{t - x}{a - z}
↓
\begin{array}{l}
\mathbf{if}\;a \le -2.016722143479182721107069384915645128898 \cdot 10^{-79}:\\
\;\;\;\;x + \frac{\frac{y - z}{\sqrt[3]{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}}}}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}} \cdot \frac{t - x}{\sqrt[3]{\sqrt[3]{a - z}}}\\

\mathbf{elif}\;a \le 1.082916304047229047679075765793884594082 \cdot 10^{-175}:\\
\;\;\;\;\left(\frac{x}{z} - \frac{t}{z}\right) \cdot y + t\\

\mathbf{else}:\\
\;\;\;\;\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}}} + x\\

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r7265009 = x;
        double r7265010 = y;
        double r7265011 = z;
        double r7265012 = r7265010 - r7265011;
        double r7265013 = t;
        double r7265014 = r7265013 - r7265009;
        double r7265015 = a;
        double r7265016 = r7265015 - r7265011;
        double r7265017 = r7265014 / r7265016;
        double r7265018 = r7265012 * r7265017;
        double r7265019 = r7265009 + r7265018;
        return r7265019;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r7265020 = a;
        double r7265021 = -2.0167221434791827e-79;
        bool r7265022 = r7265020 <= r7265021;
        double r7265023 = x;
        double r7265024 = y;
        double r7265025 = z;
        double r7265026 = r7265024 - r7265025;
        double r7265027 = r7265020 - r7265025;
        double r7265028 = cbrt(r7265027);
        double r7265029 = r7265028 * r7265028;
        double r7265030 = cbrt(r7265029);
        double r7265031 = r7265026 / r7265030;
        double r7265032 = r7265031 / r7265029;
        double r7265033 = t;
        double r7265034 = r7265033 - r7265023;
        double r7265035 = cbrt(r7265028);
        double r7265036 = r7265034 / r7265035;
        double r7265037 = r7265032 * r7265036;
        double r7265038 = r7265023 + r7265037;
        double r7265039 = 1.082916304047229e-175;
        bool r7265040 = r7265020 <= r7265039;
        double r7265041 = r7265023 / r7265025;
        double r7265042 = r7265033 / r7265025;
        double r7265043 = r7265041 - r7265042;
        double r7265044 = r7265043 * r7265024;
        double r7265045 = r7265044 + r7265033;
        double r7265046 = cbrt(r7265034);
        double r7265047 = r7265046 / r7265028;
        double r7265048 = r7265028 / r7265046;
        double r7265049 = r7265048 * r7265048;
        double r7265050 = r7265026 / r7265049;
        double r7265051 = r7265047 * r7265050;
        double r7265052 = r7265051 + r7265023;
        double r7265053 = r7265040 ? r7265045 : r7265052;
        double r7265054 = r7265022 ? r7265038 : r7265053;
        return r7265054;
}

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 < -2.0167221434791827e-79

    1. Initial program 10.3

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

    3. Applied add-cube-cbrt10.7

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

    4. Applied *-un-lft-identity10.7

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

    5. Applied times-frac10.7

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

    6. Applied associate-*r*8.6

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

    7. Simplified8.6

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

    9. Applied add-cube-cbrt8.6

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

    10. Applied cbrt-prod8.6

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

    11. Applied *-un-lft-identity8.6

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

    12. Applied times-frac8.7

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

    13. Applied associate-*r*8.4

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

    14. Simplified8.4

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

    if -2.0167221434791827e-79 < a < 1.082916304047229e-175

    1. Initial program 24.6

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

    3. Applied add-cube-cbrt25.3

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

    4. Applied add-cube-cbrt25.5

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

    5. Applied times-frac25.5

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

    6. Applied associate-*r*19.8

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

    7. Simplified19.8

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

    8. Taylor expanded around inf 15.4

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

    9. Simplified12.7

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

    if 1.082916304047229e-175 < a

    1. Initial program 12.1

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

    3. Applied add-cube-cbrt12.7

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

    4. Applied add-cube-cbrt12.8

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

    5. Applied times-frac12.8

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

    6. Applied associate-*r*10.1

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

    7. Simplified10.1

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

  4. Final simplification10.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;a \le -2.016722143479182721107069384915645128898 \cdot 10^{-79}:\\ \;\;\;\;x + \frac{\frac{y - z}{\sqrt[3]{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}}}}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}} \cdot \frac{t - x}{\sqrt[3]{\sqrt[3]{a - z}}}\\ \mathbf{elif}\;a \le 1.082916304047229047679075765793884594082 \cdot 10^{-175}:\\ \;\;\;\;\left(\frac{x}{z} - \frac{t}{z}\right) \cdot y + t\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt[3]{t - x}}{\sqrt[3]{a - z}} \cdot \frac{y - z}{\frac{\sqrt[3]{a - z}}{\sqrt[3]{t - x}} \cdot \frac{\sqrt[3]{a - z}}{\sqrt[3]{t - x}}} + x\\ \end{array}\]

Reproduce

herbie shell --seed 2019168 
(FPCore (x y z t a)
  :name "Numeric.Signal:interpolate   from hsignal-0.2.7.1"
  (+ x (* (- y z) (/ (- t x) (- a z)))))