Average Error: 4.7 → 1.6
Time: 8.3s
Precision: 64
\[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} - \frac{t}{1 - z} \le -8.7469245905233031 \cdot 10^{265}:\\ \;\;\;\;\frac{x \cdot y}{z} + \left(x \cdot \frac{t}{1 \cdot 1 - z \cdot z}\right) \cdot \left(-\left(1 + z\right)\right)\\ \mathbf{elif}\;\frac{y}{z} - \frac{t}{1 - z} \le 2.5905951762285947 \cdot 10^{176}:\\ \;\;\;\;\frac{x}{\frac{z}{y}} + x \cdot \left(-\frac{t}{1 - z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z} + \frac{x \cdot \left(-t\right)}{1 - z}\\ \end{array}\]
x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right)
↓
\begin{array}{l}
\mathbf{if}\;\frac{y}{z} - \frac{t}{1 - z} \le -8.7469245905233031 \cdot 10^{265}:\\
\;\;\;\;\frac{x \cdot y}{z} + \left(x \cdot \frac{t}{1 \cdot 1 - z \cdot z}\right) \cdot \left(-\left(1 + z\right)\right)\\

\mathbf{elif}\;\frac{y}{z} - \frac{t}{1 - z} \le 2.5905951762285947 \cdot 10^{176}:\\
\;\;\;\;\frac{x}{\frac{z}{y}} + x \cdot \left(-\frac{t}{1 - z}\right)\\

\mathbf{else}:\\
\;\;\;\;\frac{x \cdot y}{z} + \frac{x \cdot \left(-t\right)}{1 - z}\\

\end{array}
double f(double x, double y, double z, double t) {
        double r497766 = x;
        double r497767 = y;
        double r497768 = z;
        double r497769 = r497767 / r497768;
        double r497770 = t;
        double r497771 = 1.0;
        double r497772 = r497771 - r497768;
        double r497773 = r497770 / r497772;
        double r497774 = r497769 - r497773;
        double r497775 = r497766 * r497774;
        return r497775;
}
↓
double f(double x, double y, double z, double t) {
        double r497776 = y;
        double r497777 = z;
        double r497778 = r497776 / r497777;
        double r497779 = t;
        double r497780 = 1.0;
        double r497781 = r497780 - r497777;
        double r497782 = r497779 / r497781;
        double r497783 = r497778 - r497782;
        double r497784 = -8.746924590523303e+265;
        bool r497785 = r497783 <= r497784;
        double r497786 = x;
        double r497787 = r497786 * r497776;
        double r497788 = r497787 / r497777;
        double r497789 = r497780 * r497780;
        double r497790 = r497777 * r497777;
        double r497791 = r497789 - r497790;
        double r497792 = r497779 / r497791;
        double r497793 = r497786 * r497792;
        double r497794 = r497780 + r497777;
        double r497795 = -r497794;
        double r497796 = r497793 * r497795;
        double r497797 = r497788 + r497796;
        double r497798 = 2.5905951762285947e+176;
        bool r497799 = r497783 <= r497798;
        double r497800 = r497777 / r497776;
        double r497801 = r497786 / r497800;
        double r497802 = -r497782;
        double r497803 = r497786 * r497802;
        double r497804 = r497801 + r497803;
        double r497805 = -r497779;
        double r497806 = r497786 * r497805;
        double r497807 = r497806 / r497781;
        double r497808 = r497788 + r497807;
        double r497809 = r497799 ? r497804 : r497808;
        double r497810 = r497785 ? r497797 : r497809;
        return r497810;
}

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

Original4.7
Target4.3
Herbie1.6
\[\begin{array}{l} \mathbf{if}\;x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \lt -7.62322630331204244 \cdot 10^{-196}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t \cdot \frac{1}{1 - z}\right)\\ \mathbf{elif}\;x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \lt 1.41339449277023022 \cdot 10^{-211}:\\ \;\;\;\;\frac{y \cdot x}{z} + \left(-\frac{t \cdot x}{1 - z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t \cdot \frac{1}{1 - z}\right)\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (- (/ y z) (/ t (- 1.0 z))) < -8.746924590523303e+265

    1. Initial program 35.5

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

    3. Applied sub-neg35.5

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

    4. Applied distribute-lft-in35.5

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

    5. Simplified0.4

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

    7. Applied flip--0.4

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

    8. Applied associate-/r/0.4

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

    9. Applied distribute-rgt-neg-in0.4

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

    10. Applied associate-*r*0.4

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

    if -8.746924590523303e+265 < (- (/ y z) (/ t (- 1.0 z))) < 2.5905951762285947e+176

    1. Initial program 1.5

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

    3. Applied sub-neg1.5

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

    4. Applied distribute-lft-in1.5

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

    5. Simplified6.3

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

    7. Applied associate-/l*1.6

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

    if 2.5905951762285947e+176 < (- (/ y z) (/ t (- 1.0 z)))

    1. Initial program 16.9

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

    3. Applied sub-neg16.9

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

    4. Applied distribute-lft-in16.9

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

    5. Simplified1.1

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

    7. Applied distribute-neg-frac1.1

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

    8. Applied associate-*r/1.8

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

  4. Final simplification1.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} - \frac{t}{1 - z} \le -8.7469245905233031 \cdot 10^{265}:\\ \;\;\;\;\frac{x \cdot y}{z} + \left(x \cdot \frac{t}{1 \cdot 1 - z \cdot z}\right) \cdot \left(-\left(1 + z\right)\right)\\ \mathbf{elif}\;\frac{y}{z} - \frac{t}{1 - z} \le 2.5905951762285947 \cdot 10^{176}:\\ \;\;\;\;\frac{x}{\frac{z}{y}} + x \cdot \left(-\frac{t}{1 - z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z} + \frac{x \cdot \left(-t\right)}{1 - z}\\ \end{array}\]

Reproduce

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