Average Error: 14.7 → 11.0
Time: 21.0s
Precision: 64
\[x + \left(y - z\right) \cdot \frac{t - x}{a - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -1.278390233142496157723398389533109835581 \cdot 10^{241}:\\ \;\;\;\;\left(t + \frac{x \cdot y}{z}\right) - \frac{t \cdot y}{z}\\ \mathbf{elif}\;z \le 1.8327421093515108718227228606273223324 \cdot 10^{205}:\\ \;\;\;\;x + \frac{t - x}{\sqrt[3]{a - z}} \cdot \frac{y - z}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot y + \left(t - \frac{t}{\frac{z}{y}}\right)\\ \end{array}\]
x + \left(y - z\right) \cdot \frac{t - x}{a - z}
↓
\begin{array}{l}
\mathbf{if}\;z \le -1.278390233142496157723398389533109835581 \cdot 10^{241}:\\
\;\;\;\;\left(t + \frac{x \cdot y}{z}\right) - \frac{t \cdot y}{z}\\

\mathbf{elif}\;z \le 1.8327421093515108718227228606273223324 \cdot 10^{205}:\\
\;\;\;\;x + \frac{t - x}{\sqrt[3]{a - z}} \cdot \frac{y - z}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}}\\

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

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r103281 = x;
        double r103282 = y;
        double r103283 = z;
        double r103284 = r103282 - r103283;
        double r103285 = t;
        double r103286 = r103285 - r103281;
        double r103287 = a;
        double r103288 = r103287 - r103283;
        double r103289 = r103286 / r103288;
        double r103290 = r103284 * r103289;
        double r103291 = r103281 + r103290;
        return r103291;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r103292 = z;
        double r103293 = -1.2783902331424962e+241;
        bool r103294 = r103292 <= r103293;
        double r103295 = t;
        double r103296 = x;
        double r103297 = y;
        double r103298 = r103296 * r103297;
        double r103299 = r103298 / r103292;
        double r103300 = r103295 + r103299;
        double r103301 = r103295 * r103297;
        double r103302 = r103301 / r103292;
        double r103303 = r103300 - r103302;
        double r103304 = 1.8327421093515109e+205;
        bool r103305 = r103292 <= r103304;
        double r103306 = r103295 - r103296;
        double r103307 = a;
        double r103308 = r103307 - r103292;
        double r103309 = cbrt(r103308);
        double r103310 = r103306 / r103309;
        double r103311 = r103297 - r103292;
        double r103312 = r103309 * r103309;
        double r103313 = r103311 / r103312;
        double r103314 = r103310 * r103313;
        double r103315 = r103296 + r103314;
        double r103316 = r103296 / r103292;
        double r103317 = r103316 * r103297;
        double r103318 = r103292 / r103297;
        double r103319 = r103295 / r103318;
        double r103320 = r103295 - r103319;
        double r103321 = r103317 + r103320;
        double r103322 = r103305 ? r103315 : r103321;
        double r103323 = r103294 ? r103303 : r103322;
        return r103323;
}

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 z < -1.2783902331424962e+241

    1. Initial program 32.1

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

    2. Taylor expanded around inf 23.4

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

    if -1.2783902331424962e+241 < z < 1.8327421093515109e+205

    1. Initial program 11.3

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

    3. Applied add-cube-cbrt11.8

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

    4. Applied *-un-lft-identity11.8

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

    5. Applied times-frac11.8

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

    6. Applied associate-*r*9.7

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

    7. Simplified9.7

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

    if 1.8327421093515109e+205 < z

    1. Initial program 32.4

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

    3. Applied div-inv32.5

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

    4. Taylor expanded around inf 23.2

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

    5. Simplified14.6

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

  4. Final simplification11.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -1.278390233142496157723398389533109835581 \cdot 10^{241}:\\ \;\;\;\;\left(t + \frac{x \cdot y}{z}\right) - \frac{t \cdot y}{z}\\ \mathbf{elif}\;z \le 1.8327421093515108718227228606273223324 \cdot 10^{205}:\\ \;\;\;\;x + \frac{t - x}{\sqrt[3]{a - z}} \cdot \frac{y - z}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot y + \left(t - \frac{t}{\frac{z}{y}}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019194 
(FPCore (x y z t a)
  :name "Numeric.Signal:interpolate   from hsignal-0.2.7.1"
  (+ x (* (- y z) (/ (- t x) (- a z)))))