Average Error: 4.8 → 1.7
Time: 4.2s
Precision: 64
\[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) = -\infty \lor \neg \left(x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \le 1.6877486553981596 \cdot 10^{287}\right):\\ \;\;\;\;\frac{x \cdot \left(y \cdot \left(1 - z\right) - z \cdot t\right)}{z \cdot \left(1 - z\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right)\\ \end{array}\]
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 \lor \neg \left(x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \le 1.6877486553981596 \cdot 10^{287}\right):\\
\;\;\;\;\frac{x \cdot \left(y \cdot \left(1 - z\right) - z \cdot t\right)}{z \cdot \left(1 - z\right)}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r399407 = x;
        double r399408 = y;
        double r399409 = z;
        double r399410 = r399408 / r399409;
        double r399411 = t;
        double r399412 = 1.0;
        double r399413 = r399412 - r399409;
        double r399414 = r399411 / r399413;
        double r399415 = r399410 - r399414;
        double r399416 = r399407 * r399415;
        return r399416;
}
↓
double f(double x, double y, double z, double t) {
        double r399417 = x;
        double r399418 = y;
        double r399419 = z;
        double r399420 = r399418 / r399419;
        double r399421 = t;
        double r399422 = 1.0;
        double r399423 = r399422 - r399419;
        double r399424 = r399421 / r399423;
        double r399425 = r399420 - r399424;
        double r399426 = r399417 * r399425;
        double r399427 = -inf.0;
        bool r399428 = r399426 <= r399427;
        double r399429 = 1.6877486553981596e+287;
        bool r399430 = r399426 <= r399429;
        double r399431 = !r399430;
        bool r399432 = r399428 || r399431;
        double r399433 = r399418 * r399423;
        double r399434 = r399419 * r399421;
        double r399435 = r399433 - r399434;
        double r399436 = r399417 * r399435;
        double r399437 = r399419 * r399423;
        double r399438 = r399436 / r399437;
        double r399439 = r399432 ? r399438 : r399426;
        return r399439;
}

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
Target4.3
Herbie1.7
\[\begin{array}{l} \mathbf{if}\;x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \lt -7.62322630331204244 \cdot 10^{-196}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t \cdot \frac{1}{1 - z}\right)\\ \mathbf{elif}\;x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \lt 1.41339449277023022 \cdot 10^{-211}:\\ \;\;\;\;\frac{y \cdot x}{z} + \left(-\frac{t \cdot x}{1 - z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t \cdot \frac{1}{1 - z}\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (* x (- (/ y z) (/ t (- 1.0 z)))) < -inf.0 or 1.6877486553981596e+287 < (* x (- (/ y z) (/ t (- 1.0 z))))

    1. Initial program 52.1

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

    3. Applied frac-sub54.8

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

    4. Applied associate-*r/4.9

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

    if -inf.0 < (* x (- (/ y z) (/ t (- 1.0 z)))) < 1.6877486553981596e+287

    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 simplification1.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) = -\infty \lor \neg \left(x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \le 1.6877486553981596 \cdot 10^{287}\right):\\ \;\;\;\;\frac{x \cdot \left(y \cdot \left(1 - z\right) - z \cdot t\right)}{z \cdot \left(1 - z\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020062 
(FPCore (x y z t)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, C"
  :precision binary64

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

  (* x (- (/ y z) (/ t (- 1 z)))))