Average Error: 14.9 → 8.0
Time: 32.2s
Precision: 64
\[x + \left(y - z\right) \cdot \frac{t - x}{a - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \le -1.274238033086374554639513675873894241359 \cdot 10^{-228} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \le 8.018705835666315962422253726065345135652 \cdot 10^{-282}\right):\\ \;\;\;\;x + \left(\left(y - z\right) \cdot \frac{\sqrt[3]{t - x} \cdot \sqrt[3]{t - x}}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}}\right) \cdot \frac{\sqrt[3]{t - x}}{\sqrt[3]{a - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{x \cdot y}{z} + t\right) - \frac{t \cdot y}{z}\\ \end{array}\]
x + \left(y - z\right) \cdot \frac{t - x}{a - z}
↓
\begin{array}{l}
\mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \le -1.274238033086374554639513675873894241359 \cdot 10^{-228} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \le 8.018705835666315962422253726065345135652 \cdot 10^{-282}\right):\\
\;\;\;\;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}}\\

\mathbf{else}:\\
\;\;\;\;\left(\frac{x \cdot y}{z} + t\right) - \frac{t \cdot y}{z}\\

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r100024 = x;
        double r100025 = y;
        double r100026 = z;
        double r100027 = r100025 - r100026;
        double r100028 = t;
        double r100029 = r100028 - r100024;
        double r100030 = a;
        double r100031 = r100030 - r100026;
        double r100032 = r100029 / r100031;
        double r100033 = r100027 * r100032;
        double r100034 = r100024 + r100033;
        return r100034;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r100035 = x;
        double r100036 = y;
        double r100037 = z;
        double r100038 = r100036 - r100037;
        double r100039 = t;
        double r100040 = r100039 - r100035;
        double r100041 = a;
        double r100042 = r100041 - r100037;
        double r100043 = r100040 / r100042;
        double r100044 = r100038 * r100043;
        double r100045 = r100035 + r100044;
        double r100046 = -1.2742380330863746e-228;
        bool r100047 = r100045 <= r100046;
        double r100048 = 8.018705835666316e-282;
        bool r100049 = r100045 <= r100048;
        double r100050 = !r100049;
        bool r100051 = r100047 || r100050;
        double r100052 = cbrt(r100040);
        double r100053 = r100052 * r100052;
        double r100054 = cbrt(r100042);
        double r100055 = r100054 * r100054;
        double r100056 = r100053 / r100055;
        double r100057 = r100038 * r100056;
        double r100058 = r100052 / r100054;
        double r100059 = r100057 * r100058;
        double r100060 = r100035 + r100059;
        double r100061 = r100035 * r100036;
        double r100062 = r100061 / r100037;
        double r100063 = r100062 + r100039;
        double r100064 = r100039 * r100036;
        double r100065 = r100064 / r100037;
        double r100066 = r100063 - r100065;
        double r100067 = r100051 ? r100060 : r100066;
        return r100067;
}

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 2 regimes

  2. if (+ x (* (- y z) (/ (- t x) (- a z)))) < -1.2742380330863746e-228 or 8.018705835666316e-282 < (+ 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 add-cube-cbrt7.9

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

    5. Applied times-frac7.9

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

    6. Applied associate-*r*4.7

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

    if -1.2742380330863746e-228 < (+ x (* (- y z) (/ (- t x) (- a z)))) < 8.018705835666316e-282

    1. Initial program 57.4

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

    2. Taylor expanded around inf 25.8

      \[\leadsto \color{blue}{\left(\frac{x \cdot y}{z} + t\right) - \frac{t \cdot y}{z}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification8.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \le -1.274238033086374554639513675873894241359 \cdot 10^{-228} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \le 8.018705835666315962422253726065345135652 \cdot 10^{-282}\right):\\ \;\;\;\;x + \left(\left(y - z\right) \cdot \frac{\sqrt[3]{t - x} \cdot \sqrt[3]{t - x}}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}}\right) \cdot \frac{\sqrt[3]{t - x}}{\sqrt[3]{a - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{x \cdot y}{z} + t\right) - \frac{t \cdot y}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2019325 
(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)))))