Average Error: 14.6 → 6.4
Time: 5.7s
Precision: 64
\[x + \left(y - z\right) \cdot \frac{t - x}{a - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \le -6.297250090481523301886445910737257463116 \cdot 10^{-305} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \le 0.0\right):\\ \;\;\;\;x + \left(\left(y - z\right) \cdot \frac{\sqrt[3]{t - x} \cdot \sqrt[3]{t - x}}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}}\right) \cdot \frac{\sqrt[3]{t - x}}{\sqrt[3]{a - z}}\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \left(\frac{x}{z} - \frac{t}{z}\right)\\ \end{array}\]
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 -6.297250090481523301886445910737257463116 \cdot 10^{-305} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \le 0.0\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}:\\
\;\;\;\;t + y \cdot \left(\frac{x}{z} - \frac{t}{z}\right)\\

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r106073 = x;
        double r106074 = y;
        double r106075 = z;
        double r106076 = r106074 - r106075;
        double r106077 = t;
        double r106078 = r106077 - r106073;
        double r106079 = a;
        double r106080 = r106079 - r106075;
        double r106081 = r106078 / r106080;
        double r106082 = r106076 * r106081;
        double r106083 = r106073 + r106082;
        return r106083;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r106084 = x;
        double r106085 = y;
        double r106086 = z;
        double r106087 = r106085 - r106086;
        double r106088 = t;
        double r106089 = r106088 - r106084;
        double r106090 = a;
        double r106091 = r106090 - r106086;
        double r106092 = r106089 / r106091;
        double r106093 = r106087 * r106092;
        double r106094 = r106084 + r106093;
        double r106095 = -6.297250090481523e-305;
        bool r106096 = r106094 <= r106095;
        double r106097 = 0.0;
        bool r106098 = r106094 <= r106097;
        double r106099 = !r106098;
        bool r106100 = r106096 || r106099;
        double r106101 = cbrt(r106089);
        double r106102 = r106101 * r106101;
        double r106103 = cbrt(r106091);
        double r106104 = r106103 * r106103;
        double r106105 = r106102 / r106104;
        double r106106 = r106087 * r106105;
        double r106107 = r106101 / r106103;
        double r106108 = r106106 * r106107;
        double r106109 = r106084 + r106108;
        double r106110 = r106084 / r106086;
        double r106111 = r106088 / r106086;
        double r106112 = r106110 - r106111;
        double r106113 = r106085 * r106112;
        double r106114 = r106088 + r106113;
        double r106115 = r106100 ? r106109 : r106114;
        return r106115;
}

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)))) < -6.297250090481523e-305 or 0.0 < (+ x (* (- y z) (/ (- t x) (- a z))))

    1. Initial program 7.2

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

    3. Applied add-cube-cbrt7.9

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

    4. Applied add-cube-cbrt8.0

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

    5. Applied times-frac8.0

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

    6. Applied associate-*r*4.4

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

    if -6.297250090481523e-305 < (+ x (* (- y z) (/ (- t x) (- a z)))) < 0.0

    1. Initial program 61.8

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

    3. Applied add-cube-cbrt61.5

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

    4. Applied add-cube-cbrt61.5

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

    5. Applied times-frac61.5

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

    6. Applied associate-*r*61.4

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

    7. Taylor expanded around inf 24.8

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

    8. Simplified18.9

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

  4. Final simplification6.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \le -6.297250090481523301886445910737257463116 \cdot 10^{-305} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \le 0.0\right):\\ \;\;\;\;x + \left(\left(y - z\right) \cdot \frac{\sqrt[3]{t - x} \cdot \sqrt[3]{t - x}}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}}\right) \cdot \frac{\sqrt[3]{t - x}}{\sqrt[3]{a - z}}\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \left(\frac{x}{z} - \frac{t}{z}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019356 
(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)))))