Average Error: 14.8 → 8.1
Time: 53.8s
Precision: 64
\[x + \left(y - z\right) \cdot \frac{t - x}{a - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \le -1.914088505242243065504529285746814231003 \cdot 10^{-230} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \le 0.0\right):\\ \;\;\;\;x + \left(\left(y - z\right) \cdot \frac{\sqrt[3]{t - x} \cdot \sqrt[3]{t - x}}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}}\right) \cdot \frac{\sqrt[3]{t - x}}{\sqrt[3]{a - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{x \cdot y}{z} + t\right) - \frac{t \cdot y}{z}\\ \end{array}\]
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 -1.914088505242243065504529285746814231003 \cdot 10^{-230} \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}:\\
\;\;\;\;\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 r157128 = x;
        double r157129 = y;
        double r157130 = z;
        double r157131 = r157129 - r157130;
        double r157132 = t;
        double r157133 = r157132 - r157128;
        double r157134 = a;
        double r157135 = r157134 - r157130;
        double r157136 = r157133 / r157135;
        double r157137 = r157131 * r157136;
        double r157138 = r157128 + r157137;
        return r157138;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r157139 = x;
        double r157140 = y;
        double r157141 = z;
        double r157142 = r157140 - r157141;
        double r157143 = t;
        double r157144 = r157143 - r157139;
        double r157145 = a;
        double r157146 = r157145 - r157141;
        double r157147 = r157144 / r157146;
        double r157148 = r157142 * r157147;
        double r157149 = r157139 + r157148;
        double r157150 = -1.914088505242243e-230;
        bool r157151 = r157149 <= r157150;
        double r157152 = 0.0;
        bool r157153 = r157149 <= r157152;
        double r157154 = !r157153;
        bool r157155 = r157151 || r157154;
        double r157156 = cbrt(r157144);
        double r157157 = r157156 * r157156;
        double r157158 = cbrt(r157146);
        double r157159 = r157158 * r157158;
        double r157160 = r157157 / r157159;
        double r157161 = r157142 * r157160;
        double r157162 = r157156 / r157158;
        double r157163 = r157161 * r157162;
        double r157164 = r157139 + r157163;
        double r157165 = r157139 * r157140;
        double r157166 = r157165 / r157141;
        double r157167 = r157166 + r157143;
        double r157168 = r157143 * r157140;
        double r157169 = r157168 / r157141;
        double r157170 = r157167 - r157169;
        double r157171 = r157155 ? r157164 : r157170;
        return r157171;
}

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)))) < -1.914088505242243e-230 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-cbrt8.1

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

    5. Applied times-frac8.1

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

    6. Applied associate-*r*4.8

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

    if -1.914088505242243e-230 < (+ x (* (- y z) (/ (- t x) (- a z)))) < 0.0

    1. Initial program 57.9

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

    2. Taylor expanded around inf 27.1

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

  4. Final simplification8.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \le -1.914088505242243065504529285746814231003 \cdot 10^{-230} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \le 0.0\right):\\ \;\;\;\;x + \left(\left(y - z\right) \cdot \frac{\sqrt[3]{t - x} \cdot \sqrt[3]{t - x}}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}}\right) \cdot \frac{\sqrt[3]{t - x}}{\sqrt[3]{a - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{x \cdot y}{z} + t\right) - \frac{t \cdot y}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2019353 
(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)))))