Average Error: 4.9 → 0.5
Time: 5.7s
Precision: 64
\[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} - \frac{t}{1 - z} = -\infty:\\ \;\;\;\;\frac{x \cdot \left(y \cdot \left(\sqrt[3]{1 - z} \cdot \sqrt[3]{1 - z}\right) - z \cdot \left(1 \cdot \frac{t}{\sqrt[3]{1 - z}}\right)\right)}{z \cdot \left(\sqrt[3]{1 - z} \cdot \sqrt[3]{1 - z}\right)}\\ \mathbf{elif}\;\frac{y}{z} - \frac{t}{1 - z} \le -8.16649596119192336 \cdot 10^{-252}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right)\\ \mathbf{elif}\;\frac{y}{z} - \frac{t}{1 - z} \le 2.30370184373607733 \cdot 10^{-174}:\\ \;\;\;\;\frac{x \cdot y}{z} + \left(1 \cdot \frac{t \cdot x}{{z}^{2}} + \frac{t \cdot x}{z}\right)\\ \mathbf{elif}\;\frac{y}{z} - \frac{t}{1 - z} \le 5.3775524097820352 \cdot 10^{268}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y \cdot \left(\sqrt[3]{1 - z} \cdot \sqrt[3]{1 - z}\right) - z \cdot \left(1 \cdot \frac{t}{\sqrt[3]{1 - z}}\right)\right)}{z \cdot \left(\sqrt[3]{1 - z} \cdot \sqrt[3]{1 - z}\right)}\\ \end{array}\]
x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right)
↓
\begin{array}{l}
\mathbf{if}\;\frac{y}{z} - \frac{t}{1 - z} = -\infty:\\
\;\;\;\;\frac{x \cdot \left(y \cdot \left(\sqrt[3]{1 - z} \cdot \sqrt[3]{1 - z}\right) - z \cdot \left(1 \cdot \frac{t}{\sqrt[3]{1 - z}}\right)\right)}{z \cdot \left(\sqrt[3]{1 - z} \cdot \sqrt[3]{1 - z}\right)}\\

\mathbf{elif}\;\frac{y}{z} - \frac{t}{1 - z} \le -8.16649596119192336 \cdot 10^{-252}:\\
\;\;\;\;x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right)\\

\mathbf{elif}\;\frac{y}{z} - \frac{t}{1 - z} \le 2.30370184373607733 \cdot 10^{-174}:\\
\;\;\;\;\frac{x \cdot y}{z} + \left(1 \cdot \frac{t \cdot x}{{z}^{2}} + \frac{t \cdot x}{z}\right)\\

\mathbf{elif}\;\frac{y}{z} - \frac{t}{1 - z} \le 5.3775524097820352 \cdot 10^{268}:\\
\;\;\;\;x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right)\\

\mathbf{else}:\\
\;\;\;\;\frac{x \cdot \left(y \cdot \left(\sqrt[3]{1 - z} \cdot \sqrt[3]{1 - z}\right) - z \cdot \left(1 \cdot \frac{t}{\sqrt[3]{1 - z}}\right)\right)}{z \cdot \left(\sqrt[3]{1 - z} \cdot \sqrt[3]{1 - z}\right)}\\

\end{array}
double f(double x, double y, double z, double t) {
        double r378824 = x;
        double r378825 = y;
        double r378826 = z;
        double r378827 = r378825 / r378826;
        double r378828 = t;
        double r378829 = 1.0;
        double r378830 = r378829 - r378826;
        double r378831 = r378828 / r378830;
        double r378832 = r378827 - r378831;
        double r378833 = r378824 * r378832;
        return r378833;
}
↓
double f(double x, double y, double z, double t) {
        double r378834 = y;
        double r378835 = z;
        double r378836 = r378834 / r378835;
        double r378837 = t;
        double r378838 = 1.0;
        double r378839 = r378838 - r378835;
        double r378840 = r378837 / r378839;
        double r378841 = r378836 - r378840;
        double r378842 = -inf.0;
        bool r378843 = r378841 <= r378842;
        double r378844 = x;
        double r378845 = cbrt(r378839);
        double r378846 = r378845 * r378845;
        double r378847 = r378834 * r378846;
        double r378848 = 1.0;
        double r378849 = r378837 / r378845;
        double r378850 = r378848 * r378849;
        double r378851 = r378835 * r378850;
        double r378852 = r378847 - r378851;
        double r378853 = r378844 * r378852;
        double r378854 = r378835 * r378846;
        double r378855 = r378853 / r378854;
        double r378856 = -8.166495961191923e-252;
        bool r378857 = r378841 <= r378856;
        double r378858 = r378844 * r378841;
        double r378859 = 2.3037018437360773e-174;
        bool r378860 = r378841 <= r378859;
        double r378861 = r378844 * r378834;
        double r378862 = r378861 / r378835;
        double r378863 = r378837 * r378844;
        double r378864 = 2.0;
        double r378865 = pow(r378835, r378864);
        double r378866 = r378863 / r378865;
        double r378867 = r378838 * r378866;
        double r378868 = r378863 / r378835;
        double r378869 = r378867 + r378868;
        double r378870 = r378862 + r378869;
        double r378871 = 5.377552409782035e+268;
        bool r378872 = r378841 <= r378871;
        double r378873 = r378872 ? r378858 : r378855;
        double r378874 = r378860 ? r378870 : r378873;
        double r378875 = r378857 ? r378858 : r378874;
        double r378876 = r378843 ? r378855 : r378875;
        return r378876;
}

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

Original4.9
Target4.4
Herbie0.5
\[\begin{array}{l} \mathbf{if}\;x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \lt -7.62322630331204244 \cdot 10^{-196}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t \cdot \frac{1}{1 - z}\right)\\ \mathbf{elif}\;x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \lt 1.41339449277023022 \cdot 10^{-211}:\\ \;\;\;\;\frac{y \cdot x}{z} + \left(-\frac{t \cdot x}{1 - z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t \cdot \frac{1}{1 - z}\right)\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (- (/ y z) (/ t (- 1.0 z))) < -inf.0 or 5.377552409782035e+268 < (- (/ y z) (/ t (- 1.0 z)))

    1. Initial program 47.9

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right)\]
    2. Using strategy rm

    3. Applied add-cube-cbrt47.9

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

    4. Applied *-un-lft-identity47.9

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

    5. Applied times-frac47.9

      \[\leadsto x \cdot \left(\frac{y}{z} - \color{blue}{\frac{1}{\sqrt[3]{1 - z} \cdot \sqrt[3]{1 - z}} \cdot \frac{t}{\sqrt[3]{1 - z}}}\right)\]
    6. Using strategy rm

    7. Applied associate-*l/47.9

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

    8. Applied frac-sub48.8

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

    9. Applied associate-*r/1.2

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

    if -inf.0 < (- (/ y z) (/ t (- 1.0 z))) < -8.166495961191923e-252 or 2.3037018437360773e-174 < (- (/ y z) (/ t (- 1.0 z))) < 5.377552409782035e+268

    1. Initial program 0.2

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right)\]

    if -8.166495961191923e-252 < (- (/ y z) (/ t (- 1.0 z))) < 2.3037018437360773e-174

    1. Initial program 9.0

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right)\]
    2. Using strategy rm

    3. Applied add-cube-cbrt9.1

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

    4. Applied *-un-lft-identity9.1

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

    5. Applied times-frac9.1

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

    6. Taylor expanded around inf 1.9

      \[\leadsto \color{blue}{\frac{x \cdot y}{z} + \left(1 \cdot \frac{t \cdot x}{{z}^{2}} + \frac{t \cdot x}{z}\right)}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification0.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} - \frac{t}{1 - z} = -\infty:\\ \;\;\;\;\frac{x \cdot \left(y \cdot \left(\sqrt[3]{1 - z} \cdot \sqrt[3]{1 - z}\right) - z \cdot \left(1 \cdot \frac{t}{\sqrt[3]{1 - z}}\right)\right)}{z \cdot \left(\sqrt[3]{1 - z} \cdot \sqrt[3]{1 - z}\right)}\\ \mathbf{elif}\;\frac{y}{z} - \frac{t}{1 - z} \le -8.16649596119192336 \cdot 10^{-252}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right)\\ \mathbf{elif}\;\frac{y}{z} - \frac{t}{1 - z} \le 2.30370184373607733 \cdot 10^{-174}:\\ \;\;\;\;\frac{x \cdot y}{z} + \left(1 \cdot \frac{t \cdot x}{{z}^{2}} + \frac{t \cdot x}{z}\right)\\ \mathbf{elif}\;\frac{y}{z} - \frac{t}{1 - z} \le 5.3775524097820352 \cdot 10^{268}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y \cdot \left(\sqrt[3]{1 - z} \cdot \sqrt[3]{1 - z}\right) - z \cdot \left(1 \cdot \frac{t}{\sqrt[3]{1 - z}}\right)\right)}{z \cdot \left(\sqrt[3]{1 - z} \cdot \sqrt[3]{1 - z}\right)}\\ \end{array}\]

Reproduce

herbie shell --seed 2020081 
(FPCore (x y z t)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, C"
  :precision binary64

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

  (* x (- (/ y z) (/ t (- 1 z)))))