Average Error: 4.6 → 5.2
Time: 9.1s
Precision: 64
\[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le 1.49434769304270387 \cdot 10^{-284} \lor \neg \left(t \le 2.4975741639943097 \cdot 10^{91}\right):\\ \;\;\;\;\frac{x}{z} \cdot y + x \cdot \left(-\frac{t}{1 - z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z} + \left(t \cdot x\right) \cdot \left(-\frac{1}{1 - z}\right)\\ \end{array}\]
x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right)
↓
\begin{array}{l}
\mathbf{if}\;t \le 1.49434769304270387 \cdot 10^{-284} \lor \neg \left(t \le 2.4975741639943097 \cdot 10^{91}\right):\\
\;\;\;\;\frac{x}{z} \cdot y + x \cdot \left(-\frac{t}{1 - z}\right)\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r579788 = x;
        double r579789 = y;
        double r579790 = z;
        double r579791 = r579789 / r579790;
        double r579792 = t;
        double r579793 = 1.0;
        double r579794 = r579793 - r579790;
        double r579795 = r579792 / r579794;
        double r579796 = r579791 - r579795;
        double r579797 = r579788 * r579796;
        return r579797;
}
↓
double f(double x, double y, double z, double t) {
        double r579798 = t;
        double r579799 = 1.494347693042704e-284;
        bool r579800 = r579798 <= r579799;
        double r579801 = 2.4975741639943097e+91;
        bool r579802 = r579798 <= r579801;
        double r579803 = !r579802;
        bool r579804 = r579800 || r579803;
        double r579805 = x;
        double r579806 = z;
        double r579807 = r579805 / r579806;
        double r579808 = y;
        double r579809 = r579807 * r579808;
        double r579810 = 1.0;
        double r579811 = r579810 - r579806;
        double r579812 = r579798 / r579811;
        double r579813 = -r579812;
        double r579814 = r579805 * r579813;
        double r579815 = r579809 + r579814;
        double r579816 = r579805 * r579808;
        double r579817 = r579816 / r579806;
        double r579818 = r579798 * r579805;
        double r579819 = 1.0;
        double r579820 = r579819 / r579811;
        double r579821 = -r579820;
        double r579822 = r579818 * r579821;
        double r579823 = r579817 + r579822;
        double r579824 = r579804 ? r579815 : r579823;
        return r579824;
}

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
Target4.1
Herbie5.2
\[\begin{array}{l} \mathbf{if}\;x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \lt -7.62322630331204244 \cdot 10^{-196}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t \cdot \frac{1}{1 - z}\right)\\ \mathbf{elif}\;x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \lt 1.41339449277023022 \cdot 10^{-211}:\\ \;\;\;\;\frac{y \cdot x}{z} + \left(-\frac{t \cdot x}{1 - z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t \cdot \frac{1}{1 - z}\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if t < 1.494347693042704e-284 or 2.4975741639943097e+91 < t

    1. Initial program 4.4

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

    3. Applied sub-neg4.4

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

    4. Applied distribute-lft-in4.4

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

    5. Simplified4.6

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

    7. Applied associate-/l*4.2

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

    9. Applied associate-/r/5.0

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

    if 1.494347693042704e-284 < t < 2.4975741639943097e+91

    1. Initial program 4.9

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

    3. Applied sub-neg4.9

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

    4. Applied distribute-lft-in4.9

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

    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 div-inv6.3

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

    8. Applied distribute-rgt-neg-in6.3

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

    9. Applied associate-*r*5.7

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

    10. Simplified5.7

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

  4. Final simplification5.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le 1.49434769304270387 \cdot 10^{-284} \lor \neg \left(t \le 2.4975741639943097 \cdot 10^{91}\right):\\ \;\;\;\;\frac{x}{z} \cdot y + x \cdot \left(-\frac{t}{1 - z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z} + \left(t \cdot x\right) \cdot \left(-\frac{1}{1 - z}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020043 
(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)))))