Average Error: 4.9 → 1.6
Time: 4.9s
Precision: binary64
\[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} - \frac{t}{1 - z} \leq -7.635757019929209 \cdot 10^{+191}:\\ \;\;\;\;\frac{y \cdot x}{z} - \frac{t}{1 - z} \cdot x\\ \mathbf{elif}\;\frac{y}{z} - \frac{t}{1 - z} \leq 7.337745091788642 \cdot 10^{+306}:\\ \;\;\;\;\frac{y}{z} \cdot x - \frac{t}{1 - z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot x\right) \cdot \frac{1}{z} - \frac{t}{1 - z} \cdot x\\ \end{array}\]
x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right)
↓
\begin{array}{l}
\mathbf{if}\;\frac{y}{z} - \frac{t}{1 - z} \leq -7.635757019929209 \cdot 10^{+191}:\\
\;\;\;\;\frac{y \cdot x}{z} - \frac{t}{1 - z} \cdot x\\

\mathbf{elif}\;\frac{y}{z} - \frac{t}{1 - z} \leq 7.337745091788642 \cdot 10^{+306}:\\
\;\;\;\;\frac{y}{z} \cdot x - \frac{t}{1 - z} \cdot x\\

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

\end{array}
(FPCore (x y z t) :precision binary64 (* x (- (/ y z) (/ t (- 1.0 z)))))
↓
(FPCore (x y z t)
 :precision binary64
 (if (<= (- (/ y z) (/ t (- 1.0 z))) -7.635757019929209e+191)
   (- (/ (* y x) z) (* (/ t (- 1.0 z)) x))
   (if (<= (- (/ y z) (/ t (- 1.0 z))) 7.337745091788642e+306)
     (- (* (/ y z) x) (* (/ t (- 1.0 z)) x))
     (- (* (* y x) (/ 1.0 z)) (* (/ t (- 1.0 z)) x)))))
double code(double x, double y, double z, double t) {
	return ((double) (x * ((double) ((y / z) - (t / ((double) (1.0 - z)))))));
}
↓
double code(double x, double y, double z, double t) {
	double VAR;
	if ((((double) ((y / z) - (t / ((double) (1.0 - z))))) <= -7.635757019929209e+191)) {
		VAR = ((double) ((((double) (y * x)) / z) - ((double) ((t / ((double) (1.0 - z))) * x))));
	} else {
		double VAR_1;
		if ((((double) ((y / z) - (t / ((double) (1.0 - z))))) <= 7.337745091788642e+306)) {
			VAR_1 = ((double) (((double) ((y / z) * x)) - ((double) ((t / ((double) (1.0 - z))) * x))));
		} else {
			VAR_1 = ((double) (((double) (((double) (y * x)) * (1.0 / z))) - ((double) ((t / ((double) (1.0 - z))) * x))));
		}
		VAR = VAR_1;
	}
	return VAR;
}

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

Original4.9
Target4.4
Herbie1.6
\[\begin{array}{l} \mathbf{if}\;x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) < -7.623226303312042 \cdot 10^{-196}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t \cdot \frac{1}{1 - z}\right)\\ \mathbf{elif}\;x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) < 1.4133944927702302 \cdot 10^{-211}:\\ \;\;\;\;\frac{y \cdot x}{z} + \left(-\frac{t \cdot x}{1 - z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t \cdot \frac{1}{1 - z}\right)\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (- (/ y z) (/ t (- 1.0 z))) < -7.63575701992920881e191

    1. Initial program 19.6

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

    3. Applied sub-neg19.6

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

    4. Applied distribute-lft-in19.6

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

    5. Simplified19.6

      \[\leadsto x \cdot \frac{y}{z} + \color{blue}{x \cdot \frac{-t}{1 - z}}\]
    6. Using strategy rm

    7. Applied distribute-frac-neg19.6

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

    8. Applied distribute-rgt-neg-out19.6

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

    9. Applied unsub-neg19.6

      \[\leadsto \color{blue}{x \cdot \frac{y}{z} - x \cdot \frac{t}{1 - z}}\]
    10. Using strategy rm

    11. Applied associate-*r/0.9

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

    if -7.63575701992920881e191 < (- (/ y z) (/ t (- 1.0 z))) < 7.33774509178864222e306

    1. Initial program 1.7

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

    3. Applied sub-neg1.7

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

    4. Applied distribute-lft-in1.7

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

    5. Simplified1.7

      \[\leadsto x \cdot \frac{y}{z} + \color{blue}{x \cdot \frac{-t}{1 - z}}\]
    6. Using strategy rm

    7. Applied distribute-frac-neg1.7

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

    8. Applied distribute-rgt-neg-out1.7

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

    9. Applied unsub-neg1.7

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

    if 7.33774509178864222e306 < (- (/ y z) (/ t (- 1.0 z)))

    1. Initial program 62.7

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

    3. Applied sub-neg62.7

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

    4. Applied distribute-lft-in62.7

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

    5. Simplified62.7

      \[\leadsto x \cdot \frac{y}{z} + \color{blue}{x \cdot \frac{-t}{1 - z}}\]
    6. Using strategy rm

    7. Applied distribute-frac-neg62.7

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

    8. Applied distribute-rgt-neg-out62.7

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

    9. Applied unsub-neg62.7

      \[\leadsto \color{blue}{x \cdot \frac{y}{z} - x \cdot \frac{t}{1 - z}}\]
    10. Using strategy rm

    11. Applied div-inv62.7

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

    12. Applied associate-*r*0.6

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

  4. Final simplification1.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} - \frac{t}{1 - z} \leq -7.635757019929209 \cdot 10^{+191}:\\ \;\;\;\;\frac{y \cdot x}{z} - \frac{t}{1 - z} \cdot x\\ \mathbf{elif}\;\frac{y}{z} - \frac{t}{1 - z} \leq 7.337745091788642 \cdot 10^{+306}:\\ \;\;\;\;\frac{y}{z} \cdot x - \frac{t}{1 - z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot x\right) \cdot \frac{1}{z} - \frac{t}{1 - z} \cdot x\\ \end{array}\]

Reproduce

herbie shell --seed 2020198 
(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 (- 1.0 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)))))