Average Error: 15.0 → 12.5
Time: 27.5s
Precision: 64
\[x + \left(y - z\right) \cdot \frac{t - x}{a - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;a \le 2.656513054054775671758163824865311507001 \cdot 10^{-190} \lor \neg \left(a \le 6.918235825125439654113634070822670394678 \cdot 10^{-106}\right):\\ \;\;\;\;x + \left(\left(\frac{\sqrt[3]{t - x} \cdot \sqrt[3]{t - x}}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}} \cdot \left(\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}\right)\right) \cdot \sqrt[3]{y - z}\right) \cdot \frac{\sqrt[3]{t - x}}{\sqrt[3]{a - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{x \cdot y}{z} + t\right) - \frac{t \cdot y}{z}\\ \end{array}\]
x + \left(y - z\right) \cdot \frac{t - x}{a - z}
↓
\begin{array}{l}
\mathbf{if}\;a \le 2.656513054054775671758163824865311507001 \cdot 10^{-190} \lor \neg \left(a \le 6.918235825125439654113634070822670394678 \cdot 10^{-106}\right):\\
\;\;\;\;x + \left(\left(\frac{\sqrt[3]{t - x} \cdot \sqrt[3]{t - x}}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}} \cdot \left(\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}\right)\right) \cdot \sqrt[3]{y - 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 r96179 = x;
        double r96180 = y;
        double r96181 = z;
        double r96182 = r96180 - r96181;
        double r96183 = t;
        double r96184 = r96183 - r96179;
        double r96185 = a;
        double r96186 = r96185 - r96181;
        double r96187 = r96184 / r96186;
        double r96188 = r96182 * r96187;
        double r96189 = r96179 + r96188;
        return r96189;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r96190 = a;
        double r96191 = 2.6565130540547757e-190;
        bool r96192 = r96190 <= r96191;
        double r96193 = 6.91823582512544e-106;
        bool r96194 = r96190 <= r96193;
        double r96195 = !r96194;
        bool r96196 = r96192 || r96195;
        double r96197 = x;
        double r96198 = t;
        double r96199 = r96198 - r96197;
        double r96200 = cbrt(r96199);
        double r96201 = r96200 * r96200;
        double r96202 = z;
        double r96203 = r96190 - r96202;
        double r96204 = cbrt(r96203);
        double r96205 = r96204 * r96204;
        double r96206 = r96201 / r96205;
        double r96207 = y;
        double r96208 = r96207 - r96202;
        double r96209 = cbrt(r96208);
        double r96210 = r96209 * r96209;
        double r96211 = r96206 * r96210;
        double r96212 = r96211 * r96209;
        double r96213 = r96200 / r96204;
        double r96214 = r96212 * r96213;
        double r96215 = r96197 + r96214;
        double r96216 = r96197 * r96207;
        double r96217 = r96216 / r96202;
        double r96218 = r96217 + r96198;
        double r96219 = r96198 * r96207;
        double r96220 = r96219 / r96202;
        double r96221 = r96218 - r96220;
        double r96222 = r96196 ? r96215 : r96221;
        return r96222;
}

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 a < 2.6565130540547757e-190 or 6.91823582512544e-106 < a

    1. Initial program 14.4

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

    3. Applied add-cube-cbrt14.9

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

    4. Applied add-cube-cbrt15.1

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

    5. Applied times-frac15.1

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

    6. Applied associate-*r*11.8

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

    7. Simplified11.8

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

    9. Applied add-cube-cbrt11.8

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

    10. Applied associate-*r*11.8

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

    if 2.6565130540547757e-190 < a < 6.91823582512544e-106

    1. Initial program 24.9

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

    2. Taylor expanded around inf 23.8

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

  4. Final simplification12.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;a \le 2.656513054054775671758163824865311507001 \cdot 10^{-190} \lor \neg \left(a \le 6.918235825125439654113634070822670394678 \cdot 10^{-106}\right):\\ \;\;\;\;x + \left(\left(\frac{\sqrt[3]{t - x} \cdot \sqrt[3]{t - x}}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}} \cdot \left(\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}\right)\right) \cdot \sqrt[3]{y - z}\right) \cdot \frac{\sqrt[3]{t - x}}{\sqrt[3]{a - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{x \cdot y}{z} + t\right) - \frac{t \cdot y}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2019305 
(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)))))