Average Error: 4.6 → 1.5
Time: 15.6s
Precision: 64
\[x \cdot \left(\frac{y}{z} - \frac{t}{1.0 - z}\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} - \frac{t}{1.0 - z} \le -2.7487077635530947 \cdot 10^{+297}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;\frac{y}{z} - \frac{t}{1.0 - z} \le 1.828810479255877 \cdot 10^{+306}:\\ \;\;\;\;\left(\frac{y}{z} - \frac{t}{1.0 - z}\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array}\]
x \cdot \left(\frac{y}{z} - \frac{t}{1.0 - z}\right)
↓
\begin{array}{l}
\mathbf{if}\;\frac{y}{z} - \frac{t}{1.0 - z} \le -2.7487077635530947 \cdot 10^{+297}:\\
\;\;\;\;\frac{y \cdot x}{z}\\

\mathbf{elif}\;\frac{y}{z} - \frac{t}{1.0 - z} \le 1.828810479255877 \cdot 10^{+306}:\\
\;\;\;\;\left(\frac{y}{z} - \frac{t}{1.0 - z}\right) \cdot x\\

\mathbf{else}:\\
\;\;\;\;\frac{y \cdot x}{z}\\

\end{array}
double f(double x, double y, double z, double t) {
        double r19514532 = x;
        double r19514533 = y;
        double r19514534 = z;
        double r19514535 = r19514533 / r19514534;
        double r19514536 = t;
        double r19514537 = 1.0;
        double r19514538 = r19514537 - r19514534;
        double r19514539 = r19514536 / r19514538;
        double r19514540 = r19514535 - r19514539;
        double r19514541 = r19514532 * r19514540;
        return r19514541;
}
↓
double f(double x, double y, double z, double t) {
        double r19514542 = y;
        double r19514543 = z;
        double r19514544 = r19514542 / r19514543;
        double r19514545 = t;
        double r19514546 = 1.0;
        double r19514547 = r19514546 - r19514543;
        double r19514548 = r19514545 / r19514547;
        double r19514549 = r19514544 - r19514548;
        double r19514550 = -2.7487077635530947e+297;
        bool r19514551 = r19514549 <= r19514550;
        double r19514552 = x;
        double r19514553 = r19514542 * r19514552;
        double r19514554 = r19514553 / r19514543;
        double r19514555 = 1.828810479255877e+306;
        bool r19514556 = r19514549 <= r19514555;
        double r19514557 = r19514549 * r19514552;
        double r19514558 = r19514556 ? r19514557 : r19514554;
        double r19514559 = r19514551 ? r19514554 : r19514558;
        return r19514559;
}

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
Herbie1.5
\[\begin{array}{l} \mathbf{if}\;x \cdot \left(\frac{y}{z} - \frac{t}{1.0 - z}\right) \lt -7.623226303312042 \cdot 10^{-196}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t \cdot \frac{1}{1.0 - z}\right)\\ \mathbf{elif}\;x \cdot \left(\frac{y}{z} - \frac{t}{1.0 - z}\right) \lt 1.4133944927702302 \cdot 10^{-211}:\\ \;\;\;\;\frac{y \cdot x}{z} + \left(-\frac{t \cdot x}{1.0 - z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t \cdot \frac{1}{1.0 - z}\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (- (/ y z) (/ t (- 1.0 z))) < -2.7487077635530947e+297 or 1.828810479255877e+306 < (- (/ y z) (/ t (- 1.0 z)))

    1. Initial program 53.5

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1.0 - z}\right)\]

    2. Taylor expanded around 0 3.6

      \[\leadsto \color{blue}{\frac{x \cdot y}{z}}\]

    if -2.7487077635530947e+297 < (- (/ y z) (/ t (- 1.0 z))) < 1.828810479255877e+306

    1. Initial program 1.3

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1.0 - z}\right)\]
    2. Using strategy rm

    3. Applied *-commutative1.3

      \[\leadsto \color{blue}{\left(\frac{y}{z} - \frac{t}{1.0 - z}\right) \cdot x}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification1.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} - \frac{t}{1.0 - z} \le -2.7487077635530947 \cdot 10^{+297}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;\frac{y}{z} - \frac{t}{1.0 - z} \le 1.828810479255877 \cdot 10^{+306}:\\ \;\;\;\;\left(\frac{y}{z} - \frac{t}{1.0 - z}\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2019168 
(FPCore (x y z t)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, C"

  :herbie-target
  (if (< (* x (- (/ y z) (/ t (- 1.0 z)))) -7.623226303312042e-196) (* x (- (/ y z) (* t (/ 1 (- 1.0 z))))) (if (< (* x (- (/ y z) (/ t (- 1.0 z)))) 1.4133944927702302e-211) (+ (/ (* y x) z) (- (/ (* t x) (- 1.0 z)))) (* x (- (/ y z) (* t (/ 1 (- 1.0 z)))))))

  (* x (- (/ y z) (/ t (- 1.0 z)))))