Average Error: 4.6 → 1.4
Time: 14.6s
Precision: 64
\[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} - \frac{t}{1 - z} = -\infty:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;\frac{y}{z} - \frac{t}{1 - z} \le 5.734750356785414350135318053971508775162 \cdot 10^{301}:\\ \;\;\;\;\left(\frac{y}{z} - \frac{1}{\frac{1 - z}{t}}\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array}\]
x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right)
↓
\begin{array}{l}
\mathbf{if}\;\frac{y}{z} - \frac{t}{1 - z} = -\infty:\\
\;\;\;\;\frac{y \cdot x}{z}\\

\mathbf{elif}\;\frac{y}{z} - \frac{t}{1 - z} \le 5.734750356785414350135318053971508775162 \cdot 10^{301}:\\
\;\;\;\;\left(\frac{y}{z} - \frac{1}{\frac{1 - z}{t}}\right) \cdot x\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r20503927 = x;
        double r20503928 = y;
        double r20503929 = z;
        double r20503930 = r20503928 / r20503929;
        double r20503931 = t;
        double r20503932 = 1.0;
        double r20503933 = r20503932 - r20503929;
        double r20503934 = r20503931 / r20503933;
        double r20503935 = r20503930 - r20503934;
        double r20503936 = r20503927 * r20503935;
        return r20503936;
}
↓
double f(double x, double y, double z, double t) {
        double r20503937 = y;
        double r20503938 = z;
        double r20503939 = r20503937 / r20503938;
        double r20503940 = t;
        double r20503941 = 1.0;
        double r20503942 = r20503941 - r20503938;
        double r20503943 = r20503940 / r20503942;
        double r20503944 = r20503939 - r20503943;
        double r20503945 = -inf.0;
        bool r20503946 = r20503944 <= r20503945;
        double r20503947 = x;
        double r20503948 = r20503937 * r20503947;
        double r20503949 = r20503948 / r20503938;
        double r20503950 = 5.734750356785414e+301;
        bool r20503951 = r20503944 <= r20503950;
        double r20503952 = 1.0;
        double r20503953 = r20503942 / r20503940;
        double r20503954 = r20503952 / r20503953;
        double r20503955 = r20503939 - r20503954;
        double r20503956 = r20503955 * r20503947;
        double r20503957 = r20503951 ? r20503956 : r20503949;
        double r20503958 = r20503946 ? r20503949 : r20503957;
        return r20503958;
}

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
Target4.5
Herbie1.4
\[\begin{array}{l} \mathbf{if}\;x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \lt -7.623226303312042442144691872793570510727 \cdot 10^{-196}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t \cdot \frac{1}{1 - z}\right)\\ \mathbf{elif}\;x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \lt 1.413394492770230216018398633584271456447 \cdot 10^{-211}:\\ \;\;\;\;\frac{y \cdot x}{z} + \left(-\frac{t \cdot x}{1 - z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t \cdot \frac{1}{1 - z}\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (- (/ y z) (/ t (- 1.0 z))) < -inf.0 or 5.734750356785414e+301 < (- (/ y z) (/ t (- 1.0 z)))

    1. Initial program 60.8

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

    2. Taylor expanded around 0 1.3

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

    if -inf.0 < (- (/ y z) (/ t (- 1.0 z))) < 5.734750356785414e+301

    1. Initial program 1.3

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

    3. Applied clear-num1.4

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

  4. Final simplification1.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} - \frac{t}{1 - z} = -\infty:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;\frac{y}{z} - \frac{t}{1 - z} \le 5.734750356785414350135318053971508775162 \cdot 10^{301}:\\ \;\;\;\;\left(\frac{y}{z} - \frac{1}{\frac{1 - z}{t}}\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2019192 
(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 (/ 1.0 (- 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 (/ 1.0 (- 1.0 z)))))))

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