Average Error: 4.5 → 1.5
Time: 17.2s
Precision: 64
\[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} - \frac{t}{1 - z} = -\infty:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;\frac{y}{z} - \frac{t}{1 - z} \le 1.25948042757235515125902558255200611207 \cdot 10^{295}:\\ \;\;\;\;\left(\frac{y}{z} - \frac{t}{1 - z}\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array}\]
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 1.25948042757235515125902558255200611207 \cdot 10^{295}:\\
\;\;\;\;\left(\frac{y}{z} - \frac{t}{1 - z}\right) \cdot x\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r21325400 = x;
        double r21325401 = y;
        double r21325402 = z;
        double r21325403 = r21325401 / r21325402;
        double r21325404 = t;
        double r21325405 = 1.0;
        double r21325406 = r21325405 - r21325402;
        double r21325407 = r21325404 / r21325406;
        double r21325408 = r21325403 - r21325407;
        double r21325409 = r21325400 * r21325408;
        return r21325409;
}
↓
double f(double x, double y, double z, double t) {
        double r21325410 = y;
        double r21325411 = z;
        double r21325412 = r21325410 / r21325411;
        double r21325413 = t;
        double r21325414 = 1.0;
        double r21325415 = r21325414 - r21325411;
        double r21325416 = r21325413 / r21325415;
        double r21325417 = r21325412 - r21325416;
        double r21325418 = -inf.0;
        bool r21325419 = r21325417 <= r21325418;
        double r21325420 = x;
        double r21325421 = r21325410 * r21325420;
        double r21325422 = r21325421 / r21325411;
        double r21325423 = 1.2594804275723552e+295;
        bool r21325424 = r21325417 <= r21325423;
        double r21325425 = r21325417 * r21325420;
        double r21325426 = r21325424 ? r21325425 : r21325422;
        double r21325427 = r21325419 ? r21325422 : r21325426;
        return r21325427;
}

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

Original4.5
Target4.2
Herbie1.5
\[\begin{array}{l} \mathbf{if}\;x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \lt -7.623226303312042442144691872793570510727 \cdot 10^{-196}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t \cdot \frac{1}{1 - z}\right)\\ \mathbf{elif}\;x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \lt 1.413394492770230216018398633584271456447 \cdot 10^{-211}:\\ \;\;\;\;\frac{y \cdot x}{z} + \left(-\frac{t \cdot x}{1 - z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t \cdot \frac{1}{1 - z}\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (- (/ y z) (/ t (- 1.0 z))) < -inf.0 or 1.2594804275723552e+295 < (- (/ y z) (/ t (- 1.0 z)))

    1. Initial program 55.8

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

    2. Taylor expanded around 0 3.3

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

    if -inf.0 < (- (/ y z) (/ t (- 1.0 z))) < 1.2594804275723552e+295

    1. Initial program 1.4

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

  4. Final simplification1.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} - \frac{t}{1 - z} = -\infty:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;\frac{y}{z} - \frac{t}{1 - z} \le 1.25948042757235515125902558255200611207 \cdot 10^{295}:\\ \;\;\;\;\left(\frac{y}{z} - \frac{t}{1 - z}\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2019179 
(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)))))