Average Error: 14.5 → 8.0
Time: 16.6s
Precision: 64
\[x + \left(y - z\right) \cdot \frac{t - x}{a - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \le -5.6326949207991802 \cdot 10^{-206}:\\ \;\;\;\;x + \left(\left(y - z\right) \cdot \frac{\sqrt[3]{t - x}}{a - z}\right) \cdot \frac{\sqrt[3]{t - x}}{\frac{1}{\sqrt[3]{t - x}}}\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \le 0.0:\\ \;\;\;\;\left(\frac{x \cdot y}{z} + t\right) - \frac{t \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(y - z\right) \cdot \frac{\sqrt[3]{t - x}}{\frac{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}}{\sqrt[3]{\sqrt[3]{t - x}} \cdot \sqrt[3]{\sqrt[3]{t - x}}}}\right) \cdot \frac{\sqrt[3]{t - x}}{\frac{\sqrt[3]{a - z}}{\sqrt[3]{\sqrt[3]{t - x}}}}\\ \end{array}\]
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 -5.6326949207991802 \cdot 10^{-206}:\\
\;\;\;\;x + \left(\left(y - z\right) \cdot \frac{\sqrt[3]{t - x}}{a - z}\right) \cdot \frac{\sqrt[3]{t - x}}{\frac{1}{\sqrt[3]{t - 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 + \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}}}}\\

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r154713 = x;
        double r154714 = y;
        double r154715 = z;
        double r154716 = r154714 - r154715;
        double r154717 = t;
        double r154718 = r154717 - r154713;
        double r154719 = a;
        double r154720 = r154719 - r154715;
        double r154721 = r154718 / r154720;
        double r154722 = r154716 * r154721;
        double r154723 = r154713 + r154722;
        return r154723;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r154724 = x;
        double r154725 = y;
        double r154726 = z;
        double r154727 = r154725 - r154726;
        double r154728 = t;
        double r154729 = r154728 - r154724;
        double r154730 = a;
        double r154731 = r154730 - r154726;
        double r154732 = r154729 / r154731;
        double r154733 = r154727 * r154732;
        double r154734 = r154724 + r154733;
        double r154735 = -5.63269492079918e-206;
        bool r154736 = r154734 <= r154735;
        double r154737 = cbrt(r154729);
        double r154738 = r154737 / r154731;
        double r154739 = r154727 * r154738;
        double r154740 = 1.0;
        double r154741 = r154740 / r154737;
        double r154742 = r154737 / r154741;
        double r154743 = r154739 * r154742;
        double r154744 = r154724 + r154743;
        double r154745 = 0.0;
        bool r154746 = r154734 <= r154745;
        double r154747 = r154724 * r154725;
        double r154748 = r154747 / r154726;
        double r154749 = r154748 + r154728;
        double r154750 = r154728 * r154725;
        double r154751 = r154750 / r154726;
        double r154752 = r154749 - r154751;
        double r154753 = cbrt(r154731);
        double r154754 = r154753 * r154753;
        double r154755 = cbrt(r154737);
        double r154756 = r154755 * r154755;
        double r154757 = r154754 / r154756;
        double r154758 = r154737 / r154757;
        double r154759 = r154727 * r154758;
        double r154760 = r154753 / r154755;
        double r154761 = r154737 / r154760;
        double r154762 = r154759 * r154761;
        double r154763 = r154724 + r154762;
        double r154764 = r154746 ? r154752 : r154763;
        double r154765 = r154736 ? r154744 : r154764;
        return r154765;
}

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)))) < -5.63269492079918e-206

    1. Initial program 5.9

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

    3. Applied add-cube-cbrt6.7

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

    4. Applied associate-/l*6.6

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

    6. Applied div-inv6.7

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

    7. Applied times-frac6.6

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

    8. Applied associate-*r*4.8

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

    if -5.63269492079918e-206 < (+ x (* (- y z) (/ (- t x) (- a z)))) < 0.0

    1. Initial program 57.4

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

    2. Taylor expanded around inf 27.5

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

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

    1. Initial program 7.4

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

    3. Applied add-cube-cbrt8.1

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

    4. Applied associate-/l*8.1

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

    6. Applied add-cube-cbrt8.4

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

    7. Applied add-cube-cbrt8.5

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

    8. Applied times-frac8.5

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

    9. Applied times-frac8.4

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

    10. Applied associate-*r*4.1

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

  4. Final simplification8.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \le -5.6326949207991802 \cdot 10^{-206}:\\ \;\;\;\;x + \left(\left(y - z\right) \cdot \frac{\sqrt[3]{t - x}}{a - z}\right) \cdot \frac{\sqrt[3]{t - x}}{\frac{1}{\sqrt[3]{t - x}}}\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \le 0.0:\\ \;\;\;\;\left(\frac{x \cdot y}{z} + t\right) - \frac{t \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(y - z\right) \cdot \frac{\sqrt[3]{t - x}}{\frac{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}}{\sqrt[3]{\sqrt[3]{t - x}} \cdot \sqrt[3]{\sqrt[3]{t - x}}}}\right) \cdot \frac{\sqrt[3]{t - x}}{\frac{\sqrt[3]{a - z}}{\sqrt[3]{\sqrt[3]{t - x}}}}\\ \end{array}\]

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)))))