Average Error: 4.6 → 1.8
Time: 16.8s
Precision: 64
\[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) = -\infty:\\ \;\;\;\;\frac{x \cdot \left(\left(1 - z\right) \cdot y - t \cdot z\right)}{\left(1 - z\right) \cdot z}\\ \mathbf{elif}\;x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \le 5.365114686245201147953029381740708786098 \cdot 10^{265}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(\left(1 - z\right) \cdot y - t \cdot z\right)}{\left(1 - z\right) \cdot z}\\ \end{array}\]
x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right)
↓
\begin{array}{l}
\mathbf{if}\;x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) = -\infty:\\
\;\;\;\;\frac{x \cdot \left(\left(1 - z\right) \cdot y - t \cdot z\right)}{\left(1 - z\right) \cdot z}\\

\mathbf{elif}\;x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \le 5.365114686245201147953029381740708786098 \cdot 10^{265}:\\
\;\;\;\;x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right)\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r21600390 = x;
        double r21600391 = y;
        double r21600392 = z;
        double r21600393 = r21600391 / r21600392;
        double r21600394 = t;
        double r21600395 = 1.0;
        double r21600396 = r21600395 - r21600392;
        double r21600397 = r21600394 / r21600396;
        double r21600398 = r21600393 - r21600397;
        double r21600399 = r21600390 * r21600398;
        return r21600399;
}
↓
double f(double x, double y, double z, double t) {
        double r21600400 = x;
        double r21600401 = y;
        double r21600402 = z;
        double r21600403 = r21600401 / r21600402;
        double r21600404 = t;
        double r21600405 = 1.0;
        double r21600406 = r21600405 - r21600402;
        double r21600407 = r21600404 / r21600406;
        double r21600408 = r21600403 - r21600407;
        double r21600409 = r21600400 * r21600408;
        double r21600410 = -inf.0;
        bool r21600411 = r21600409 <= r21600410;
        double r21600412 = r21600406 * r21600401;
        double r21600413 = r21600404 * r21600402;
        double r21600414 = r21600412 - r21600413;
        double r21600415 = r21600400 * r21600414;
        double r21600416 = r21600406 * r21600402;
        double r21600417 = r21600415 / r21600416;
        double r21600418 = 5.365114686245201e+265;
        bool r21600419 = r21600409 <= r21600418;
        double r21600420 = r21600419 ? r21600409 : r21600417;
        double r21600421 = r21600411 ? r21600417 : r21600420;
        return r21600421;
}

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
Herbie1.8
\[\begin{array}{l} \mathbf{if}\;x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \lt -7.623226303312042442144691872793570510727 \cdot 10^{-196}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t \cdot \frac{1}{1 - z}\right)\\ \mathbf{elif}\;x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \lt 1.413394492770230216018398633584271456447 \cdot 10^{-211}:\\ \;\;\;\;\frac{y \cdot x}{z} + \left(-\frac{t \cdot x}{1 - z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t \cdot \frac{1}{1 - z}\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (* x (- (/ y z) (/ t (- 1.0 z)))) < -inf.0 or 5.365114686245201e+265 < (* x (- (/ y z) (/ t (- 1.0 z))))

    1. Initial program 43.1

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

    3. Applied frac-sub47.3

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

    4. Applied associate-*r/7.1

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

    if -inf.0 < (* x (- (/ y z) (/ t (- 1.0 z)))) < 5.365114686245201e+265

    1. Initial program 1.3

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

    3. Applied div-inv1.3

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

    5. Applied un-div-inv1.3

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

  4. Final simplification1.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) = -\infty:\\ \;\;\;\;\frac{x \cdot \left(\left(1 - z\right) \cdot y - t \cdot z\right)}{\left(1 - z\right) \cdot z}\\ \mathbf{elif}\;x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \le 5.365114686245201147953029381740708786098 \cdot 10^{265}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(\left(1 - z\right) \cdot y - t \cdot z\right)}{\left(1 - z\right) \cdot z}\\ \end{array}\]

Reproduce

herbie shell --seed 2019172 
(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)))))