Average Error: 14.4 → 7.8
Time: 50.7s
Precision: 64
\[x + \left(y - z\right) \cdot \frac{t - x}{a - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \le -1.728574168981643158068947885483381777474 \cdot 10^{-279} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \le 0.0\right):\\ \;\;\;\;x + \frac{\frac{y - z}{\sqrt[3]{a - z}}}{\sqrt[3]{a - z}} \cdot \frac{t - x}{\sqrt[3]{a - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{x \cdot y}{z} + t\right) - \frac{t \cdot y}{z}\\ \end{array}\]
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 -1.728574168981643158068947885483381777474 \cdot 10^{-279} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \le 0.0\right):\\
\;\;\;\;x + \frac{\frac{y - z}{\sqrt[3]{a - z}}}{\sqrt[3]{a - z}} \cdot \frac{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 r178574 = x;
        double r178575 = y;
        double r178576 = z;
        double r178577 = r178575 - r178576;
        double r178578 = t;
        double r178579 = r178578 - r178574;
        double r178580 = a;
        double r178581 = r178580 - r178576;
        double r178582 = r178579 / r178581;
        double r178583 = r178577 * r178582;
        double r178584 = r178574 + r178583;
        return r178584;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r178585 = x;
        double r178586 = y;
        double r178587 = z;
        double r178588 = r178586 - r178587;
        double r178589 = t;
        double r178590 = r178589 - r178585;
        double r178591 = a;
        double r178592 = r178591 - r178587;
        double r178593 = r178590 / r178592;
        double r178594 = r178588 * r178593;
        double r178595 = r178585 + r178594;
        double r178596 = -1.7285741689816432e-279;
        bool r178597 = r178595 <= r178596;
        double r178598 = 0.0;
        bool r178599 = r178595 <= r178598;
        double r178600 = !r178599;
        bool r178601 = r178597 || r178600;
        double r178602 = cbrt(r178592);
        double r178603 = r178588 / r178602;
        double r178604 = r178603 / r178602;
        double r178605 = r178590 / r178602;
        double r178606 = r178604 * r178605;
        double r178607 = r178585 + r178606;
        double r178608 = r178585 * r178586;
        double r178609 = r178608 / r178587;
        double r178610 = r178609 + r178589;
        double r178611 = r178589 * r178586;
        double r178612 = r178611 / r178587;
        double r178613 = r178610 - r178612;
        double r178614 = r178601 ? r178607 : r178613;
        return r178614;
}

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)))) < -1.7285741689816432e-279 or 0.0 < (+ x (* (- y z) (/ (- t x) (- a z))))

    1. Initial program 7.1

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

    3. Applied add-cube-cbrt7.8

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

    4. Applied *-un-lft-identity7.8

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

    5. Applied times-frac7.8

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

    6. Applied associate-*r*5.1

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

    7. Simplified5.1

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

    if -1.7285741689816432e-279 < (+ x (* (- y z) (/ (- t x) (- a z)))) < 0.0

    1. Initial program 60.9

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

    2. Taylor expanded around inf 24.8

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

  4. Final simplification7.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \le -1.728574168981643158068947885483381777474 \cdot 10^{-279} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \le 0.0\right):\\ \;\;\;\;x + \frac{\frac{y - z}{\sqrt[3]{a - z}}}{\sqrt[3]{a - z}} \cdot \frac{t - x}{\sqrt[3]{a - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{x \cdot y}{z} + t\right) - \frac{t \cdot y}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2019209 
(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)))))