Average Error: 4.3 → 0.3
Time: 16.1s
Precision: 64
\[x \cdot \left(\frac{y}{z} - \frac{t}{1.0 - z}\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} - \frac{t}{1.0 - z} = -\infty:\\ \;\;\;\;\frac{x \cdot \left(y \cdot \left(\left(\sqrt[3]{\sqrt[3]{1.0 - z}} \cdot \sqrt[3]{\sqrt[3]{1.0 - z}}\right) \cdot \sqrt[3]{\sqrt[3]{1.0 - z}}\right) - \frac{t}{\sqrt[3]{1.0 - z} \cdot \sqrt[3]{1.0 - z}} \cdot z\right)}{z \cdot \left(\left(\sqrt[3]{\sqrt[3]{1.0 - z}} \cdot \sqrt[3]{\sqrt[3]{1.0 - z}}\right) \cdot \sqrt[3]{\sqrt[3]{1.0 - z}}\right)}\\ \mathbf{elif}\;\frac{y}{z} - \frac{t}{1.0 - z} \le -5.604253807165862 \cdot 10^{-286}:\\ \;\;\;\;\left(\frac{y}{z} - \frac{t}{1.0 - z}\right) \cdot x\\ \mathbf{elif}\;\frac{y}{z} - \frac{t}{1.0 - z} \le 0.0:\\ \;\;\;\;\frac{x \cdot t}{z} \cdot \left(\frac{1.0}{z} + 1\right) + \frac{y \cdot x}{z}\\ \mathbf{elif}\;\frac{y}{z} - \frac{t}{1.0 - z} \le 2.55312552975251 \cdot 10^{+287}:\\ \;\;\;\;\left(\frac{y}{z} - \frac{t}{1.0 - z}\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y \cdot \left(\left(\sqrt[3]{\sqrt[3]{1.0 - z}} \cdot \sqrt[3]{\sqrt[3]{1.0 - z}}\right) \cdot \sqrt[3]{\sqrt[3]{1.0 - z}}\right) - \frac{t}{\sqrt[3]{1.0 - z} \cdot \sqrt[3]{1.0 - z}} \cdot z\right)}{z \cdot \left(\left(\sqrt[3]{\sqrt[3]{1.0 - z}} \cdot \sqrt[3]{\sqrt[3]{1.0 - z}}\right) \cdot \sqrt[3]{\sqrt[3]{1.0 - z}}\right)}\\ \end{array}\]
x \cdot \left(\frac{y}{z} - \frac{t}{1.0 - z}\right)
↓
\begin{array}{l}
\mathbf{if}\;\frac{y}{z} - \frac{t}{1.0 - z} = -\infty:\\
\;\;\;\;\frac{x \cdot \left(y \cdot \left(\left(\sqrt[3]{\sqrt[3]{1.0 - z}} \cdot \sqrt[3]{\sqrt[3]{1.0 - z}}\right) \cdot \sqrt[3]{\sqrt[3]{1.0 - z}}\right) - \frac{t}{\sqrt[3]{1.0 - z} \cdot \sqrt[3]{1.0 - z}} \cdot z\right)}{z \cdot \left(\left(\sqrt[3]{\sqrt[3]{1.0 - z}} \cdot \sqrt[3]{\sqrt[3]{1.0 - z}}\right) \cdot \sqrt[3]{\sqrt[3]{1.0 - z}}\right)}\\

\mathbf{elif}\;\frac{y}{z} - \frac{t}{1.0 - z} \le -5.604253807165862 \cdot 10^{-286}:\\
\;\;\;\;\left(\frac{y}{z} - \frac{t}{1.0 - z}\right) \cdot x\\

\mathbf{elif}\;\frac{y}{z} - \frac{t}{1.0 - z} \le 0.0:\\
\;\;\;\;\frac{x \cdot t}{z} \cdot \left(\frac{1.0}{z} + 1\right) + \frac{y \cdot x}{z}\\

\mathbf{elif}\;\frac{y}{z} - \frac{t}{1.0 - z} \le 2.55312552975251 \cdot 10^{+287}:\\
\;\;\;\;\left(\frac{y}{z} - \frac{t}{1.0 - z}\right) \cdot x\\

\mathbf{else}:\\
\;\;\;\;\frac{x \cdot \left(y \cdot \left(\left(\sqrt[3]{\sqrt[3]{1.0 - z}} \cdot \sqrt[3]{\sqrt[3]{1.0 - z}}\right) \cdot \sqrt[3]{\sqrt[3]{1.0 - z}}\right) - \frac{t}{\sqrt[3]{1.0 - z} \cdot \sqrt[3]{1.0 - z}} \cdot z\right)}{z \cdot \left(\left(\sqrt[3]{\sqrt[3]{1.0 - z}} \cdot \sqrt[3]{\sqrt[3]{1.0 - z}}\right) \cdot \sqrt[3]{\sqrt[3]{1.0 - z}}\right)}\\

\end{array}
double f(double x, double y, double z, double t) {
        double r17041747 = x;
        double r17041748 = y;
        double r17041749 = z;
        double r17041750 = r17041748 / r17041749;
        double r17041751 = t;
        double r17041752 = 1.0;
        double r17041753 = r17041752 - r17041749;
        double r17041754 = r17041751 / r17041753;
        double r17041755 = r17041750 - r17041754;
        double r17041756 = r17041747 * r17041755;
        return r17041756;
}
↓
double f(double x, double y, double z, double t) {
        double r17041757 = y;
        double r17041758 = z;
        double r17041759 = r17041757 / r17041758;
        double r17041760 = t;
        double r17041761 = 1.0;
        double r17041762 = r17041761 - r17041758;
        double r17041763 = r17041760 / r17041762;
        double r17041764 = r17041759 - r17041763;
        double r17041765 = -inf.0;
        bool r17041766 = r17041764 <= r17041765;
        double r17041767 = x;
        double r17041768 = cbrt(r17041762);
        double r17041769 = cbrt(r17041768);
        double r17041770 = r17041769 * r17041769;
        double r17041771 = r17041770 * r17041769;
        double r17041772 = r17041757 * r17041771;
        double r17041773 = r17041768 * r17041768;
        double r17041774 = r17041760 / r17041773;
        double r17041775 = r17041774 * r17041758;
        double r17041776 = r17041772 - r17041775;
        double r17041777 = r17041767 * r17041776;
        double r17041778 = r17041758 * r17041771;
        double r17041779 = r17041777 / r17041778;
        double r17041780 = -5.604253807165862e-286;
        bool r17041781 = r17041764 <= r17041780;
        double r17041782 = r17041764 * r17041767;
        double r17041783 = 0.0;
        bool r17041784 = r17041764 <= r17041783;
        double r17041785 = r17041767 * r17041760;
        double r17041786 = r17041785 / r17041758;
        double r17041787 = r17041761 / r17041758;
        double r17041788 = 1.0;
        double r17041789 = r17041787 + r17041788;
        double r17041790 = r17041786 * r17041789;
        double r17041791 = r17041757 * r17041767;
        double r17041792 = r17041791 / r17041758;
        double r17041793 = r17041790 + r17041792;
        double r17041794 = 2.55312552975251e+287;
        bool r17041795 = r17041764 <= r17041794;
        double r17041796 = r17041795 ? r17041782 : r17041779;
        double r17041797 = r17041784 ? r17041793 : r17041796;
        double r17041798 = r17041781 ? r17041782 : r17041797;
        double r17041799 = r17041766 ? r17041779 : r17041798;
        return r17041799;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original4.3
Target3.9
Herbie0.3
\[\begin{array}{l} \mathbf{if}\;x \cdot \left(\frac{y}{z} - \frac{t}{1.0 - z}\right) \lt -7.623226303312042 \cdot 10^{-196}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t \cdot \frac{1}{1.0 - z}\right)\\ \mathbf{elif}\;x \cdot \left(\frac{y}{z} - \frac{t}{1.0 - z}\right) \lt 1.4133944927702302 \cdot 10^{-211}:\\ \;\;\;\;\frac{y \cdot x}{z} + \left(-\frac{t \cdot x}{1.0 - z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t \cdot \frac{1}{1.0 - z}\right)\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (- (/ y z) (/ t (- 1.0 z))) < -inf.0 or 2.55312552975251e+287 < (- (/ y z) (/ t (- 1.0 z)))

    1. Initial program 50.0

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1.0 - z}\right)\]
    2. Using strategy rm

    3. Applied add-cube-cbrt50.0

      \[\leadsto x \cdot \left(\frac{y}{z} - \frac{t}{\color{blue}{\left(\sqrt[3]{1.0 - z} \cdot \sqrt[3]{1.0 - z}\right) \cdot \sqrt[3]{1.0 - z}}}\right)\]

    4. Applied associate-/r*50.0

      \[\leadsto x \cdot \left(\frac{y}{z} - \color{blue}{\frac{\frac{t}{\sqrt[3]{1.0 - z} \cdot \sqrt[3]{1.0 - z}}}{\sqrt[3]{1.0 - z}}}\right)\]
    5. Using strategy rm

    6. Applied add-cube-cbrt50.0

      \[\leadsto x \cdot \left(\frac{y}{z} - \frac{\frac{t}{\sqrt[3]{1.0 - z} \cdot \sqrt[3]{1.0 - z}}}{\color{blue}{\left(\sqrt[3]{\sqrt[3]{1.0 - z}} \cdot \sqrt[3]{\sqrt[3]{1.0 - z}}\right) \cdot \sqrt[3]{\sqrt[3]{1.0 - z}}}}\right)\]
    7. Using strategy rm

    8. Applied frac-sub50.0

      \[\leadsto x \cdot \color{blue}{\frac{y \cdot \left(\left(\sqrt[3]{\sqrt[3]{1.0 - z}} \cdot \sqrt[3]{\sqrt[3]{1.0 - z}}\right) \cdot \sqrt[3]{\sqrt[3]{1.0 - z}}\right) - z \cdot \frac{t}{\sqrt[3]{1.0 - z} \cdot \sqrt[3]{1.0 - z}}}{z \cdot \left(\left(\sqrt[3]{\sqrt[3]{1.0 - z}} \cdot \sqrt[3]{\sqrt[3]{1.0 - z}}\right) \cdot \sqrt[3]{\sqrt[3]{1.0 - z}}\right)}}\]

    9. Applied associate-*r/0.3

      \[\leadsto \color{blue}{\frac{x \cdot \left(y \cdot \left(\left(\sqrt[3]{\sqrt[3]{1.0 - z}} \cdot \sqrt[3]{\sqrt[3]{1.0 - z}}\right) \cdot \sqrt[3]{\sqrt[3]{1.0 - z}}\right) - z \cdot \frac{t}{\sqrt[3]{1.0 - z} \cdot \sqrt[3]{1.0 - z}}\right)}{z \cdot \left(\left(\sqrt[3]{\sqrt[3]{1.0 - z}} \cdot \sqrt[3]{\sqrt[3]{1.0 - z}}\right) \cdot \sqrt[3]{\sqrt[3]{1.0 - z}}\right)}}\]

    if -inf.0 < (- (/ y z) (/ t (- 1.0 z))) < -5.604253807165862e-286 or 0.0 < (- (/ y z) (/ t (- 1.0 z))) < 2.55312552975251e+287

    1. Initial program 0.3

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1.0 - z}\right)\]
    2. Using strategy rm

    3. Applied *-commutative0.3

      \[\leadsto \color{blue}{\left(\frac{y}{z} - \frac{t}{1.0 - z}\right) \cdot x}\]

    if -5.604253807165862e-286 < (- (/ y z) (/ t (- 1.0 z))) < 0.0

    1. Initial program 19.7

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1.0 - z}\right)\]
    2. Using strategy rm

    3. Applied *-commutative19.7

      \[\leadsto \color{blue}{\left(\frac{y}{z} - \frac{t}{1.0 - z}\right) \cdot x}\]

    4. Taylor expanded around inf 0.1

      \[\leadsto \color{blue}{\frac{x \cdot y}{z} + \left(1.0 \cdot \frac{t \cdot x}{{z}^{2}} + \frac{t \cdot x}{z}\right)}\]

    5. Simplified0.1

      \[\leadsto \color{blue}{\frac{x \cdot y}{z} + \left(\frac{1.0}{z} + 1\right) \cdot \frac{t \cdot x}{z}}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification0.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} - \frac{t}{1.0 - z} = -\infty:\\ \;\;\;\;\frac{x \cdot \left(y \cdot \left(\left(\sqrt[3]{\sqrt[3]{1.0 - z}} \cdot \sqrt[3]{\sqrt[3]{1.0 - z}}\right) \cdot \sqrt[3]{\sqrt[3]{1.0 - z}}\right) - \frac{t}{\sqrt[3]{1.0 - z} \cdot \sqrt[3]{1.0 - z}} \cdot z\right)}{z \cdot \left(\left(\sqrt[3]{\sqrt[3]{1.0 - z}} \cdot \sqrt[3]{\sqrt[3]{1.0 - z}}\right) \cdot \sqrt[3]{\sqrt[3]{1.0 - z}}\right)}\\ \mathbf{elif}\;\frac{y}{z} - \frac{t}{1.0 - z} \le -5.604253807165862 \cdot 10^{-286}:\\ \;\;\;\;\left(\frac{y}{z} - \frac{t}{1.0 - z}\right) \cdot x\\ \mathbf{elif}\;\frac{y}{z} - \frac{t}{1.0 - z} \le 0.0:\\ \;\;\;\;\frac{x \cdot t}{z} \cdot \left(\frac{1.0}{z} + 1\right) + \frac{y \cdot x}{z}\\ \mathbf{elif}\;\frac{y}{z} - \frac{t}{1.0 - z} \le 2.55312552975251 \cdot 10^{+287}:\\ \;\;\;\;\left(\frac{y}{z} - \frac{t}{1.0 - z}\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y \cdot \left(\left(\sqrt[3]{\sqrt[3]{1.0 - z}} \cdot \sqrt[3]{\sqrt[3]{1.0 - z}}\right) \cdot \sqrt[3]{\sqrt[3]{1.0 - z}}\right) - \frac{t}{\sqrt[3]{1.0 - z} \cdot \sqrt[3]{1.0 - z}} \cdot z\right)}{z \cdot \left(\left(\sqrt[3]{\sqrt[3]{1.0 - z}} \cdot \sqrt[3]{\sqrt[3]{1.0 - z}}\right) \cdot \sqrt[3]{\sqrt[3]{1.0 - z}}\right)}\\ \end{array}\]

Reproduce

herbie shell --seed 2019162 
(FPCore (x y z t)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, C"

  :herbie-target
  (if (< (* x (- (/ y z) (/ t (- 1.0 z)))) -7.623226303312042e-196) (* x (- (/ y z) (* t (/ 1 (- 1.0 z))))) (if (< (* x (- (/ y z) (/ t (- 1.0 z)))) 1.4133944927702302e-211) (+ (/ (* y x) z) (- (/ (* t x) (- 1.0 z)))) (* x (- (/ y z) (* t (/ 1 (- 1.0 z)))))))

  (* x (- (/ y z) (/ t (- 1.0 z)))))