Average Error: 4.8 → 1.5
Time: 18.9s
Precision: 64
\[x \cdot \left(\frac{y}{z} - \frac{t}{1.0 - z}\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} - \frac{t}{1.0 - z} \le -1.133138390126253 \cdot 10^{+295}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;\frac{y}{z} - \frac{t}{1.0 - z} \le 5.770308615374242 \cdot 10^{+303}:\\ \;\;\;\;\left(\frac{y}{z} - \frac{t}{1.0 - z}\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array}\]
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 -1.133138390126253 \cdot 10^{+295}:\\
\;\;\;\;\frac{y \cdot x}{z}\\

\mathbf{elif}\;\frac{y}{z} - \frac{t}{1.0 - z} \le 5.770308615374242 \cdot 10^{+303}:\\
\;\;\;\;\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 r22359412 = x;
        double r22359413 = y;
        double r22359414 = z;
        double r22359415 = r22359413 / r22359414;
        double r22359416 = t;
        double r22359417 = 1.0;
        double r22359418 = r22359417 - r22359414;
        double r22359419 = r22359416 / r22359418;
        double r22359420 = r22359415 - r22359419;
        double r22359421 = r22359412 * r22359420;
        return r22359421;
}
↓
double f(double x, double y, double z, double t) {
        double r22359422 = y;
        double r22359423 = z;
        double r22359424 = r22359422 / r22359423;
        double r22359425 = t;
        double r22359426 = 1.0;
        double r22359427 = r22359426 - r22359423;
        double r22359428 = r22359425 / r22359427;
        double r22359429 = r22359424 - r22359428;
        double r22359430 = -1.133138390126253e+295;
        bool r22359431 = r22359429 <= r22359430;
        double r22359432 = x;
        double r22359433 = r22359422 * r22359432;
        double r22359434 = r22359433 / r22359423;
        double r22359435 = 5.770308615374242e+303;
        bool r22359436 = r22359429 <= r22359435;
        double r22359437 = r22359429 * r22359432;
        double r22359438 = r22359436 ? r22359437 : r22359434;
        double r22359439 = r22359431 ? r22359434 : r22359438;
        return r22359439;
}

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
Target4.5
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))) < -1.133138390126253e+295 or 5.770308615374242e+303 < (- (/ y z) (/ t (- 1.0 z)))

    1. Initial program 51.2

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

    2. Taylor expanded around 0 3.9

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

    if -1.133138390126253e+295 < (- (/ y z) (/ t (- 1.0 z))) < 5.770308615374242e+303

    1. Initial program 1.3

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

  4. Final simplification1.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} - \frac{t}{1.0 - z} \le -1.133138390126253 \cdot 10^{+295}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;\frac{y}{z} - \frac{t}{1.0 - z} \le 5.770308615374242 \cdot 10^{+303}:\\ \;\;\;\;\left(\frac{y}{z} - \frac{t}{1.0 - z}\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2019158 
(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)))))