Average Error: 4.6 → 4.6
Time: 4.0s
Precision: 64
\[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -1.77245517730717617 \cdot 10^{-293}:\\ \;\;\;\;\frac{x}{\sqrt[3]{z} \cdot \sqrt[3]{z}} \cdot \frac{y}{\sqrt[3]{z}} + x \cdot \left(-\frac{t}{1 - z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t \cdot \frac{1}{1 - z}\right)\\ \end{array}\]
x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right)
↓
\begin{array}{l}
\mathbf{if}\;x \le -1.77245517730717617 \cdot 10^{-293}:\\
\;\;\;\;\frac{x}{\sqrt[3]{z} \cdot \sqrt[3]{z}} \cdot \frac{y}{\sqrt[3]{z}} + x \cdot \left(-\frac{t}{1 - z}\right)\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r443977 = x;
        double r443978 = y;
        double r443979 = z;
        double r443980 = r443978 / r443979;
        double r443981 = t;
        double r443982 = 1.0;
        double r443983 = r443982 - r443979;
        double r443984 = r443981 / r443983;
        double r443985 = r443980 - r443984;
        double r443986 = r443977 * r443985;
        return r443986;
}
↓
double f(double x, double y, double z, double t) {
        double r443987 = x;
        double r443988 = -1.7724551773071762e-293;
        bool r443989 = r443987 <= r443988;
        double r443990 = z;
        double r443991 = cbrt(r443990);
        double r443992 = r443991 * r443991;
        double r443993 = r443987 / r443992;
        double r443994 = y;
        double r443995 = r443994 / r443991;
        double r443996 = r443993 * r443995;
        double r443997 = t;
        double r443998 = 1.0;
        double r443999 = r443998 - r443990;
        double r444000 = r443997 / r443999;
        double r444001 = -r444000;
        double r444002 = r443987 * r444001;
        double r444003 = r443996 + r444002;
        double r444004 = r443994 / r443990;
        double r444005 = 1.0;
        double r444006 = r444005 / r443999;
        double r444007 = r443997 * r444006;
        double r444008 = r444004 - r444007;
        double r444009 = r443987 * r444008;
        double r444010 = r443989 ? r444003 : r444009;
        return r444010;
}

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

Original4.6
Target4.2
Herbie4.6
\[\begin{array}{l} \mathbf{if}\;x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \lt -7.62322630331204244 \cdot 10^{-196}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t \cdot \frac{1}{1 - z}\right)\\ \mathbf{elif}\;x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \lt 1.41339449277023022 \cdot 10^{-211}:\\ \;\;\;\;\frac{y \cdot x}{z} + \left(-\frac{t \cdot x}{1 - z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t \cdot \frac{1}{1 - z}\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if x < -1.7724551773071762e-293

    1. Initial program 4.7

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

    3. Applied sub-neg4.7

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

    4. Applied distribute-lft-in4.7

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

    6. Applied add-cube-cbrt5.2

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

    7. Applied *-un-lft-identity5.2

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

    8. Applied times-frac5.2

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

    9. Applied associate-*r*4.7

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

    10. Simplified4.7

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

    if -1.7724551773071762e-293 < x

    1. Initial program 4.6

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

    3. Applied div-inv4.6

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

  4. Final simplification4.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -1.77245517730717617 \cdot 10^{-293}:\\ \;\;\;\;\frac{x}{\sqrt[3]{z} \cdot \sqrt[3]{z}} \cdot \frac{y}{\sqrt[3]{z}} + x \cdot \left(-\frac{t}{1 - z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t \cdot \frac{1}{1 - z}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020021 
(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)))))