Average Error: 14.5 → 10.5
Time: 16.5s
Precision: 64
\[x + \left(y - z\right) \cdot \frac{t - x}{a - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;a \le -3.6771152743398664 \cdot 10^{-164} \lor \neg \left(a \le 2.5546992440117739 \cdot 10^{-147}\right):\\ \;\;\;\;x + \left(\left(y - z\right) \cdot \frac{\sqrt[3]{t - x}}{\frac{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}}{\sqrt[3]{\sqrt[3]{t - x}} \cdot \sqrt[3]{\sqrt[3]{t - x}}}}\right) \cdot \frac{\sqrt[3]{t - x}}{\frac{\sqrt[3]{a - z}}{\sqrt[3]{\sqrt[3]{t - x}}}}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{x \cdot y}{z} + t\right) - \frac{t \cdot y}{z}\\ \end{array}\]
x + \left(y - z\right) \cdot \frac{t - x}{a - z}
↓
\begin{array}{l}
\mathbf{if}\;a \le -3.6771152743398664 \cdot 10^{-164} \lor \neg \left(a \le 2.5546992440117739 \cdot 10^{-147}\right):\\
\;\;\;\;x + \left(\left(y - z\right) \cdot \frac{\sqrt[3]{t - x}}{\frac{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}}{\sqrt[3]{\sqrt[3]{t - x}} \cdot \sqrt[3]{\sqrt[3]{t - x}}}}\right) \cdot \frac{\sqrt[3]{t - x}}{\frac{\sqrt[3]{a - z}}{\sqrt[3]{\sqrt[3]{t - x}}}}\\

\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 r155530 = x;
        double r155531 = y;
        double r155532 = z;
        double r155533 = r155531 - r155532;
        double r155534 = t;
        double r155535 = r155534 - r155530;
        double r155536 = a;
        double r155537 = r155536 - r155532;
        double r155538 = r155535 / r155537;
        double r155539 = r155533 * r155538;
        double r155540 = r155530 + r155539;
        return r155540;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r155541 = a;
        double r155542 = -3.6771152743398664e-164;
        bool r155543 = r155541 <= r155542;
        double r155544 = 2.554699244011774e-147;
        bool r155545 = r155541 <= r155544;
        double r155546 = !r155545;
        bool r155547 = r155543 || r155546;
        double r155548 = x;
        double r155549 = y;
        double r155550 = z;
        double r155551 = r155549 - r155550;
        double r155552 = t;
        double r155553 = r155552 - r155548;
        double r155554 = cbrt(r155553);
        double r155555 = r155541 - r155550;
        double r155556 = cbrt(r155555);
        double r155557 = r155556 * r155556;
        double r155558 = cbrt(r155554);
        double r155559 = r155558 * r155558;
        double r155560 = r155557 / r155559;
        double r155561 = r155554 / r155560;
        double r155562 = r155551 * r155561;
        double r155563 = r155556 / r155558;
        double r155564 = r155554 / r155563;
        double r155565 = r155562 * r155564;
        double r155566 = r155548 + r155565;
        double r155567 = r155548 * r155549;
        double r155568 = r155567 / r155550;
        double r155569 = r155568 + r155552;
        double r155570 = r155552 * r155549;
        double r155571 = r155570 / r155550;
        double r155572 = r155569 - r155571;
        double r155573 = r155547 ? r155566 : r155572;
        return r155573;
}

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 < -3.6771152743398664e-164 or 2.554699244011774e-147 < a

    1. Initial program 11.8

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

    3. Applied add-cube-cbrt12.3

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

    4. Applied associate-/l*12.3

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

    6. Applied add-cube-cbrt12.5

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

    7. Applied add-cube-cbrt12.6

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

    8. Applied times-frac12.6

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

    9. Applied times-frac12.6

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

    10. Applied associate-*r*9.8

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

    if -3.6771152743398664e-164 < a < 2.554699244011774e-147

    1. Initial program 24.5

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

    2. Taylor expanded around inf 13.0

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

  4. Final simplification10.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;a \le -3.6771152743398664 \cdot 10^{-164} \lor \neg \left(a \le 2.5546992440117739 \cdot 10^{-147}\right):\\ \;\;\;\;x + \left(\left(y - z\right) \cdot \frac{\sqrt[3]{t - x}}{\frac{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}}{\sqrt[3]{\sqrt[3]{t - x}} \cdot \sqrt[3]{\sqrt[3]{t - x}}}}\right) \cdot \frac{\sqrt[3]{t - x}}{\frac{\sqrt[3]{a - z}}{\sqrt[3]{\sqrt[3]{t - x}}}}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{x \cdot y}{z} + t\right) - \frac{t \cdot y}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020042 
(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)))))