Average Error: 4.5 → 1.2
Time: 5.4s
Precision: 64
\[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} - \frac{t}{1 - z} = -\infty \lor \neg \left(\frac{y}{z} - \frac{t}{1 - z} \le 1.10707959431727866 \cdot 10^{304}\right):\\ \;\;\;\;\frac{x \cdot \left(y \cdot \left(1 - z\right) - z \cdot t\right)}{z \cdot \left(1 - z\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right)\\ \end{array}\]
x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right)
↓
\begin{array}{l}
\mathbf{if}\;\frac{y}{z} - \frac{t}{1 - z} = -\infty \lor \neg \left(\frac{y}{z} - \frac{t}{1 - z} \le 1.10707959431727866 \cdot 10^{304}\right):\\
\;\;\;\;\frac{x \cdot \left(y \cdot \left(1 - z\right) - z \cdot t\right)}{z \cdot \left(1 - z\right)}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r392003 = x;
        double r392004 = y;
        double r392005 = z;
        double r392006 = r392004 / r392005;
        double r392007 = t;
        double r392008 = 1.0;
        double r392009 = r392008 - r392005;
        double r392010 = r392007 / r392009;
        double r392011 = r392006 - r392010;
        double r392012 = r392003 * r392011;
        return r392012;
}
↓
double f(double x, double y, double z, double t) {
        double r392013 = y;
        double r392014 = z;
        double r392015 = r392013 / r392014;
        double r392016 = t;
        double r392017 = 1.0;
        double r392018 = r392017 - r392014;
        double r392019 = r392016 / r392018;
        double r392020 = r392015 - r392019;
        double r392021 = -inf.0;
        bool r392022 = r392020 <= r392021;
        double r392023 = 1.1070795943172787e+304;
        bool r392024 = r392020 <= r392023;
        double r392025 = !r392024;
        bool r392026 = r392022 || r392025;
        double r392027 = x;
        double r392028 = r392013 * r392018;
        double r392029 = r392014 * r392016;
        double r392030 = r392028 - r392029;
        double r392031 = r392027 * r392030;
        double r392032 = r392014 * r392018;
        double r392033 = r392031 / r392032;
        double r392034 = r392027 * r392020;
        double r392035 = r392026 ? r392033 : r392034;
        return r392035;
}

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

Original4.5
Target4.2
Herbie1.2
\[\begin{array}{l} \mathbf{if}\;x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \lt -7.62322630331204244 \cdot 10^{-196}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t \cdot \frac{1}{1 - z}\right)\\ \mathbf{elif}\;x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \lt 1.41339449277023022 \cdot 10^{-211}:\\ \;\;\;\;\frac{y \cdot x}{z} + \left(-\frac{t \cdot x}{1 - z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t \cdot \frac{1}{1 - z}\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (- (/ y z) (/ t (- 1.0 z))) < -inf.0 or 1.1070795943172787e+304 < (- (/ y z) (/ t (- 1.0 z)))

    1. Initial program 61.8

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

    3. Applied frac-sub61.8

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

    4. Applied associate-*r/0.2

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

    if -inf.0 < (- (/ y z) (/ t (- 1.0 z))) < 1.1070795943172787e+304

    1. Initial program 1.2

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

  4. Final simplification1.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} - \frac{t}{1 - z} = -\infty \lor \neg \left(\frac{y}{z} - \frac{t}{1 - z} \le 1.10707959431727866 \cdot 10^{304}\right):\\ \;\;\;\;\frac{x \cdot \left(y \cdot \left(1 - z\right) - z \cdot t\right)}{z \cdot \left(1 - z\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020060 
(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)))))