Average Error: 4.8 → 1.8
Time: 29.8s
Precision: 64
\[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} - \frac{t}{1 - z} \le -3.815360187890604728685296818871955976429 \cdot 10^{158} \lor \neg \left(\frac{y}{z} - \frac{t}{1 - z} \le 1.87103258485720813958555940057997964078 \cdot 10^{143}\right):\\ \;\;\;\;\frac{x \cdot y}{z} + x \cdot \left(-\frac{t}{1 - z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - \frac{1}{\frac{1 - z}{t}}\right)\\ \end{array}\]
x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right)
↓
\begin{array}{l}
\mathbf{if}\;\frac{y}{z} - \frac{t}{1 - z} \le -3.815360187890604728685296818871955976429 \cdot 10^{158} \lor \neg \left(\frac{y}{z} - \frac{t}{1 - z} \le 1.87103258485720813958555940057997964078 \cdot 10^{143}\right):\\
\;\;\;\;\frac{x \cdot y}{z} + x \cdot \left(-\frac{t}{1 - z}\right)\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r402844 = x;
        double r402845 = y;
        double r402846 = z;
        double r402847 = r402845 / r402846;
        double r402848 = t;
        double r402849 = 1.0;
        double r402850 = r402849 - r402846;
        double r402851 = r402848 / r402850;
        double r402852 = r402847 - r402851;
        double r402853 = r402844 * r402852;
        return r402853;
}
↓
double f(double x, double y, double z, double t) {
        double r402854 = y;
        double r402855 = z;
        double r402856 = r402854 / r402855;
        double r402857 = t;
        double r402858 = 1.0;
        double r402859 = r402858 - r402855;
        double r402860 = r402857 / r402859;
        double r402861 = r402856 - r402860;
        double r402862 = -3.8153601878906047e+158;
        bool r402863 = r402861 <= r402862;
        double r402864 = 1.8710325848572081e+143;
        bool r402865 = r402861 <= r402864;
        double r402866 = !r402865;
        bool r402867 = r402863 || r402866;
        double r402868 = x;
        double r402869 = r402868 * r402854;
        double r402870 = r402869 / r402855;
        double r402871 = -r402860;
        double r402872 = r402868 * r402871;
        double r402873 = r402870 + r402872;
        double r402874 = 1.0;
        double r402875 = r402859 / r402857;
        double r402876 = r402874 / r402875;
        double r402877 = r402856 - r402876;
        double r402878 = r402868 * r402877;
        double r402879 = r402867 ? r402873 : r402878;
        return r402879;
}

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

Original4.8
Target4.5
Herbie1.8
\[\begin{array}{l} \mathbf{if}\;x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \lt -7.623226303312042442144691872793570510727 \cdot 10^{-196}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t \cdot \frac{1}{1 - z}\right)\\ \mathbf{elif}\;x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \lt 1.413394492770230216018398633584271456447 \cdot 10^{-211}:\\ \;\;\;\;\frac{y \cdot x}{z} + \left(-\frac{t \cdot x}{1 - z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t \cdot \frac{1}{1 - z}\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (- (/ y z) (/ t (- 1.0 z))) < -3.8153601878906047e+158 or 1.8710325848572081e+143 < (- (/ y z) (/ t (- 1.0 z)))

    1. Initial program 14.0

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

    3. Applied sub-neg14.0

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

    4. Applied distribute-lft-in14.0

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

    5. Simplified1.7

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

    if -3.8153601878906047e+158 < (- (/ y z) (/ t (- 1.0 z))) < 1.8710325848572081e+143

    1. Initial program 1.7

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

    3. Applied clear-num1.8

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

  4. Final simplification1.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} - \frac{t}{1 - z} \le -3.815360187890604728685296818871955976429 \cdot 10^{158} \lor \neg \left(\frac{y}{z} - \frac{t}{1 - z} \le 1.87103258485720813958555940057997964078 \cdot 10^{143}\right):\\ \;\;\;\;\frac{x \cdot y}{z} + x \cdot \left(-\frac{t}{1 - z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - \frac{1}{\frac{1 - z}{t}}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019326 +o rules:numerics
(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)))))