Average Error: 4.8 → 0.3
Time: 7.7s
Precision: 64
\[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} - \frac{t}{1 - z} \le -2.2592621423955549 \cdot 10^{306}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{y \cdot \left(1 - z\right) - z \cdot t}{1 - z}\\ \mathbf{elif}\;\frac{y}{z} - \frac{t}{1 - z} \le -4.7536441784100923 \cdot 10^{-305}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t \cdot \frac{1}{1 - z}\right)\\ \mathbf{elif}\;\frac{y}{z} - \frac{t}{1 - z} \le -0.0:\\ \;\;\;\;\frac{x}{z} \cdot \frac{y \cdot \left(1 - z\right) - z \cdot t}{1 - z}\\ \mathbf{elif}\;\frac{y}{z} - \frac{t}{1 - z} \le 3.1420396255810733 \cdot 10^{257}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t \cdot \frac{1}{1 - z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x \cdot \left(y \cdot \left(1 - z\right) - z \cdot t\right)}{z}}{1 - z}\\ \end{array}\]
x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right)
↓
\begin{array}{l}
\mathbf{if}\;\frac{y}{z} - \frac{t}{1 - z} \le -2.2592621423955549 \cdot 10^{306}:\\
\;\;\;\;\frac{x}{z} \cdot \frac{y \cdot \left(1 - z\right) - z \cdot t}{1 - z}\\

\mathbf{elif}\;\frac{y}{z} - \frac{t}{1 - z} \le -4.7536441784100923 \cdot 10^{-305}:\\
\;\;\;\;x \cdot \left(\frac{y}{z} - t \cdot \frac{1}{1 - z}\right)\\

\mathbf{elif}\;\frac{y}{z} - \frac{t}{1 - z} \le -0.0:\\
\;\;\;\;\frac{x}{z} \cdot \frac{y \cdot \left(1 - z\right) - z \cdot t}{1 - z}\\

\mathbf{elif}\;\frac{y}{z} - \frac{t}{1 - z} \le 3.1420396255810733 \cdot 10^{257}:\\
\;\;\;\;x \cdot \left(\frac{y}{z} - t \cdot \frac{1}{1 - z}\right)\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r564693 = x;
        double r564694 = y;
        double r564695 = z;
        double r564696 = r564694 / r564695;
        double r564697 = t;
        double r564698 = 1.0;
        double r564699 = r564698 - r564695;
        double r564700 = r564697 / r564699;
        double r564701 = r564696 - r564700;
        double r564702 = r564693 * r564701;
        return r564702;
}
↓
double f(double x, double y, double z, double t) {
        double r564703 = y;
        double r564704 = z;
        double r564705 = r564703 / r564704;
        double r564706 = t;
        double r564707 = 1.0;
        double r564708 = r564707 - r564704;
        double r564709 = r564706 / r564708;
        double r564710 = r564705 - r564709;
        double r564711 = -2.259262142395555e+306;
        bool r564712 = r564710 <= r564711;
        double r564713 = x;
        double r564714 = r564713 / r564704;
        double r564715 = r564703 * r564708;
        double r564716 = r564704 * r564706;
        double r564717 = r564715 - r564716;
        double r564718 = r564717 / r564708;
        double r564719 = r564714 * r564718;
        double r564720 = -4.753644178410092e-305;
        bool r564721 = r564710 <= r564720;
        double r564722 = 1.0;
        double r564723 = r564722 / r564708;
        double r564724 = r564706 * r564723;
        double r564725 = r564705 - r564724;
        double r564726 = r564713 * r564725;
        double r564727 = -0.0;
        bool r564728 = r564710 <= r564727;
        double r564729 = 3.142039625581073e+257;
        bool r564730 = r564710 <= r564729;
        double r564731 = r564713 * r564717;
        double r564732 = r564731 / r564704;
        double r564733 = r564732 / r564708;
        double r564734 = r564730 ? r564726 : r564733;
        double r564735 = r564728 ? r564719 : r564734;
        double r564736 = r564721 ? r564726 : r564735;
        double r564737 = r564712 ? r564719 : r564736;
        return r564737;
}

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
Target4.3
Herbie0.3
\[\begin{array}{l} \mathbf{if}\;x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \lt -7.62322630331204244 \cdot 10^{-196}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t \cdot \frac{1}{1 - z}\right)\\ \mathbf{elif}\;x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \lt 1.41339449277023022 \cdot 10^{-211}:\\ \;\;\;\;\frac{y \cdot x}{z} + \left(-\frac{t \cdot x}{1 - z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t \cdot \frac{1}{1 - z}\right)\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (- (/ y z) (/ t (- 1.0 z))) < -2.259262142395555e+306 or -4.753644178410092e-305 < (- (/ y z) (/ t (- 1.0 z))) < -0.0

    1. Initial program 37.0

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

    3. Applied frac-sub37.8

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

    4. Applied associate-*r/12.8

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

    6. Applied times-frac0.1

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

    if -2.259262142395555e+306 < (- (/ y z) (/ t (- 1.0 z))) < -4.753644178410092e-305 or -0.0 < (- (/ y z) (/ t (- 1.0 z))) < 3.142039625581073e+257

    1. Initial program 0.3

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

    3. Applied div-inv0.3

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

    if 3.142039625581073e+257 < (- (/ y z) (/ t (- 1.0 z)))

    1. Initial program 36.2

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

    3. Applied frac-sub37.6

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

    4. Applied associate-*r/1.7

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

    6. Applied associate-/r*1.7

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

  4. Final simplification0.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} - \frac{t}{1 - z} \le -2.2592621423955549 \cdot 10^{306}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{y \cdot \left(1 - z\right) - z \cdot t}{1 - z}\\ \mathbf{elif}\;\frac{y}{z} - \frac{t}{1 - z} \le -4.7536441784100923 \cdot 10^{-305}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t \cdot \frac{1}{1 - z}\right)\\ \mathbf{elif}\;\frac{y}{z} - \frac{t}{1 - z} \le -0.0:\\ \;\;\;\;\frac{x}{z} \cdot \frac{y \cdot \left(1 - z\right) - z \cdot t}{1 - z}\\ \mathbf{elif}\;\frac{y}{z} - \frac{t}{1 - z} \le 3.1420396255810733 \cdot 10^{257}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t \cdot \frac{1}{1 - z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x \cdot \left(y \cdot \left(1 - z\right) - z \cdot t\right)}{z}}{1 - z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020046 
(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)))))