Average Error: 15.0 → 8.9
Time: 31.9s
Precision: 64
\[x + \left(y - z\right) \cdot \frac{t - x}{a - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \le -3.00144295601552635 \cdot 10^{-245}:\\ \;\;\;\;\left(\frac{\frac{\sqrt[3]{y - z}}{\sqrt[3]{a - z}}}{\sqrt[3]{a - z}} \cdot \frac{t - x}{\sqrt[3]{a - z}}\right) \cdot \left(\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}\right) + x\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \le 0.0:\\ \;\;\;\;\left(\frac{x \cdot y}{z} + t\right) - \frac{t \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{y - z}{\sqrt[3]{a - z}}}{\sqrt[3]{a - z}} \cdot \frac{t - x}{\sqrt[3]{a - z}}\\ \end{array}\]
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 -3.00144295601552635 \cdot 10^{-245}:\\
\;\;\;\;\left(\frac{\frac{\sqrt[3]{y - z}}{\sqrt[3]{a - z}}}{\sqrt[3]{a - z}} \cdot \frac{t - x}{\sqrt[3]{a - z}}\right) \cdot \left(\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}\right) + x\\

\mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \le 0.0:\\
\;\;\;\;\left(\frac{x \cdot y}{z} + t\right) - \frac{t \cdot y}{z}\\

\mathbf{else}:\\
\;\;\;\;x + \frac{\frac{y - z}{\sqrt[3]{a - z}}}{\sqrt[3]{a - z}} \cdot \frac{t - x}{\sqrt[3]{a - z}}\\

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r127477 = x;
        double r127478 = y;
        double r127479 = z;
        double r127480 = r127478 - r127479;
        double r127481 = t;
        double r127482 = r127481 - r127477;
        double r127483 = a;
        double r127484 = r127483 - r127479;
        double r127485 = r127482 / r127484;
        double r127486 = r127480 * r127485;
        double r127487 = r127477 + r127486;
        return r127487;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r127488 = x;
        double r127489 = y;
        double r127490 = z;
        double r127491 = r127489 - r127490;
        double r127492 = t;
        double r127493 = r127492 - r127488;
        double r127494 = a;
        double r127495 = r127494 - r127490;
        double r127496 = r127493 / r127495;
        double r127497 = r127491 * r127496;
        double r127498 = r127488 + r127497;
        double r127499 = -3.0014429560155264e-245;
        bool r127500 = r127498 <= r127499;
        double r127501 = cbrt(r127491);
        double r127502 = cbrt(r127495);
        double r127503 = r127501 / r127502;
        double r127504 = r127503 / r127502;
        double r127505 = r127493 / r127502;
        double r127506 = r127504 * r127505;
        double r127507 = r127501 * r127501;
        double r127508 = r127506 * r127507;
        double r127509 = r127508 + r127488;
        double r127510 = 0.0;
        bool r127511 = r127498 <= r127510;
        double r127512 = r127488 * r127489;
        double r127513 = r127512 / r127490;
        double r127514 = r127513 + r127492;
        double r127515 = r127492 * r127489;
        double r127516 = r127515 / r127490;
        double r127517 = r127514 - r127516;
        double r127518 = r127491 / r127502;
        double r127519 = r127518 / r127502;
        double r127520 = r127519 * r127505;
        double r127521 = r127488 + r127520;
        double r127522 = r127511 ? r127517 : r127521;
        double r127523 = r127500 ? r127509 : r127522;
        return r127523;
}

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 (+ x (* (- y z) (/ (- t x) (- a z)))) < -3.0014429560155264e-245

    1. Initial program 6.8

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

    3. Applied add-cube-cbrt7.5

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

    4. Applied *-un-lft-identity7.5

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

    5. Applied times-frac7.5

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

    6. Applied associate-*r*5.2

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

    7. Simplified5.2

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

    9. Applied *-un-lft-identity5.2

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

    10. Applied *-un-lft-identity5.2

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

    11. Applied cbrt-prod5.2

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

    12. Applied add-cube-cbrt5.1

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

    13. Applied times-frac5.1

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

    14. Applied times-frac5.1

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

    15. Applied associate-*l*5.5

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

    if -3.0014429560155264e-245 < (+ x (* (- y z) (/ (- t x) (- a z)))) < 0.0

    1. Initial program 58.6

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

    2. Taylor expanded around inf 27.9

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

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

    1. Initial program 7.7

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

    3. Applied add-cube-cbrt8.4

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

    4. Applied *-un-lft-identity8.4

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

    5. Applied times-frac8.4

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

    6. Applied associate-*r*5.5

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

    7. Simplified5.5

      \[\leadsto x + \color{blue}{\frac{\frac{y - z}{\sqrt[3]{a - z}}}{\sqrt[3]{a - z}}} \cdot \frac{t - x}{\sqrt[3]{a - z}}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification8.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \le -3.00144295601552635 \cdot 10^{-245}:\\ \;\;\;\;\left(\frac{\frac{\sqrt[3]{y - z}}{\sqrt[3]{a - z}}}{\sqrt[3]{a - z}} \cdot \frac{t - x}{\sqrt[3]{a - z}}\right) \cdot \left(\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}\right) + x\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \le 0.0:\\ \;\;\;\;\left(\frac{x \cdot y}{z} + t\right) - \frac{t \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{y - z}{\sqrt[3]{a - z}}}{\sqrt[3]{a - z}} \cdot \frac{t - x}{\sqrt[3]{a - z}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019199 
(FPCore (x y z t a)
  :name "Numeric.Signal:interpolate   from hsignal-0.2.7.1"
  (+ x (* (- y z) (/ (- t x) (- a z)))))