Average Error: 14.8 → 10.1
Time: 12.1s
Precision: 64
\[x + \left(y - z\right) \cdot \frac{t - x}{a - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -3.32143684010780844 \cdot 10^{165} \lor \neg \left(z \le 1.7200626204721968 \cdot 10^{178}\right):\\ \;\;\;\;\frac{y}{\frac{a - z}{t - x}} - -1 \cdot t\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \left(\sqrt[3]{t - x} \cdot \sqrt[3]{t - x}\right)\right) \cdot \frac{\sqrt[3]{y}}{\frac{a - z}{\sqrt[3]{t - x}}} - \left(\frac{z}{\frac{a - z}{t - x}} - x\right)\\ \end{array}\]
x + \left(y - z\right) \cdot \frac{t - x}{a - z}
↓
\begin{array}{l}
\mathbf{if}\;z \le -3.32143684010780844 \cdot 10^{165} \lor \neg \left(z \le 1.7200626204721968 \cdot 10^{178}\right):\\
\;\;\;\;\frac{y}{\frac{a - z}{t - x}} - -1 \cdot t\\

\mathbf{else}:\\
\;\;\;\;\left(\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \left(\sqrt[3]{t - x} \cdot \sqrt[3]{t - x}\right)\right) \cdot \frac{\sqrt[3]{y}}{\frac{a - z}{\sqrt[3]{t - x}}} - \left(\frac{z}{\frac{a - z}{t - x}} - x\right)\\

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r145579 = x;
        double r145580 = y;
        double r145581 = z;
        double r145582 = r145580 - r145581;
        double r145583 = t;
        double r145584 = r145583 - r145579;
        double r145585 = a;
        double r145586 = r145585 - r145581;
        double r145587 = r145584 / r145586;
        double r145588 = r145582 * r145587;
        double r145589 = r145579 + r145588;
        return r145589;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r145590 = z;
        double r145591 = -3.3214368401078084e+165;
        bool r145592 = r145590 <= r145591;
        double r145593 = 1.7200626204721968e+178;
        bool r145594 = r145590 <= r145593;
        double r145595 = !r145594;
        bool r145596 = r145592 || r145595;
        double r145597 = y;
        double r145598 = a;
        double r145599 = r145598 - r145590;
        double r145600 = t;
        double r145601 = x;
        double r145602 = r145600 - r145601;
        double r145603 = r145599 / r145602;
        double r145604 = r145597 / r145603;
        double r145605 = -1.0;
        double r145606 = r145605 * r145600;
        double r145607 = r145604 - r145606;
        double r145608 = cbrt(r145597);
        double r145609 = r145608 * r145608;
        double r145610 = cbrt(r145602);
        double r145611 = r145610 * r145610;
        double r145612 = r145609 * r145611;
        double r145613 = r145599 / r145610;
        double r145614 = r145608 / r145613;
        double r145615 = r145612 * r145614;
        double r145616 = r145590 / r145603;
        double r145617 = r145616 - r145601;
        double r145618 = r145615 - r145617;
        double r145619 = r145596 ? r145607 : r145618;
        return r145619;
}

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 z < -3.3214368401078084e+165 or 1.7200626204721968e+178 < z

    1. Initial program 28.7

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

    2. Simplified28.6

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)}\]
    3. Using strategy rm

    4. Applied clear-num28.9

      \[\leadsto \mathsf{fma}\left(y - z, \color{blue}{\frac{1}{\frac{a - z}{t - x}}}, x\right)\]
    5. Using strategy rm

    6. Applied fma-udef29.0

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

    7. Simplified29.0

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

    9. Applied div-sub29.0

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

    10. Applied associate-+l-24.9

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

    11. Taylor expanded around inf 14.8

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

    if -3.3214368401078084e+165 < z < 1.7200626204721968e+178

    1. Initial program 10.0

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

    2. Simplified10.0

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)}\]
    3. Using strategy rm

    4. Applied clear-num10.1

      \[\leadsto \mathsf{fma}\left(y - z, \color{blue}{\frac{1}{\frac{a - z}{t - x}}}, x\right)\]
    5. Using strategy rm

    6. Applied fma-udef10.2

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

    7. Simplified9.7

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

    9. Applied div-sub9.7

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

    10. Applied associate-+l-8.0

      \[\leadsto \color{blue}{\frac{y}{\frac{a - z}{t - x}} - \left(\frac{z}{\frac{a - z}{t - x}} - x\right)}\]
    11. Using strategy rm

    12. Applied add-cube-cbrt8.4

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

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

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

    14. Applied times-frac8.4

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

    15. Applied add-cube-cbrt8.5

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

    16. Applied times-frac8.5

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

    17. Simplified8.5

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

  4. Final simplification10.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -3.32143684010780844 \cdot 10^{165} \lor \neg \left(z \le 1.7200626204721968 \cdot 10^{178}\right):\\ \;\;\;\;\frac{y}{\frac{a - z}{t - x}} - -1 \cdot t\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \left(\sqrt[3]{t - x} \cdot \sqrt[3]{t - x}\right)\right) \cdot \frac{\sqrt[3]{y}}{\frac{a - z}{\sqrt[3]{t - x}}} - \left(\frac{z}{\frac{a - z}{t - x}} - x\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020018 +o rules:numerics
(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)))))