Average Error: 4.5 → 0.4
Time: 4.4s
Precision: binary64
\[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} - \frac{t}{1 - z} \leq -7.674361035406644 \cdot 10^{+306} \lor \neg \left(\frac{y}{z} - \frac{t}{1 - z} \leq -3.830574861523053 \cdot 10^{-303} \lor \neg \left(\frac{y}{z} - \frac{t}{1 - z} \leq 9.993403811868667 \cdot 10^{-209}\right) \land \frac{y}{z} - \frac{t}{1 - z} \leq 5.6561471375851743 \cdot 10^{+278}\right):\\ \;\;\;\;\frac{x}{z} \cdot \left(y - \frac{z \cdot t}{1 - z}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{y}{z} - \frac{t}{1 - z}\right) \cdot x\\ \end{array}\]
x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right)
↓
\begin{array}{l}
\mathbf{if}\;\frac{y}{z} - \frac{t}{1 - z} \leq -7.674361035406644 \cdot 10^{+306} \lor \neg \left(\frac{y}{z} - \frac{t}{1 - z} \leq -3.830574861523053 \cdot 10^{-303} \lor \neg \left(\frac{y}{z} - \frac{t}{1 - z} \leq 9.993403811868667 \cdot 10^{-209}\right) \land \frac{y}{z} - \frac{t}{1 - z} \leq 5.6561471375851743 \cdot 10^{+278}\right):\\
\;\;\;\;\frac{x}{z} \cdot \left(y - \frac{z \cdot t}{1 - z}\right)\\

\mathbf{else}:\\
\;\;\;\;\left(\frac{y}{z} - \frac{t}{1 - z}\right) \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 (or (<= (- (/ y z) (/ t (- 1.0 z))) -7.674361035406644e+306)
         (not
          (or (<= (- (/ y z) (/ t (- 1.0 z))) -3.830574861523053e-303)
              (and (not
                    (<= (- (/ y z) (/ t (- 1.0 z))) 9.993403811868667e-209))
                   (<= (- (/ y z) (/ t (- 1.0 z))) 5.6561471375851743e+278)))))
   (* (/ x z) (- y (/ (* z t) (- 1.0 z))))
   (* (- (/ y 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 tmp;
	if (((((double) ((y / z) - (t / ((double) (1.0 - z))))) <= -7.674361035406644e+306) || !((((double) ((y / z) - (t / ((double) (1.0 - z))))) <= -3.830574861523053e-303) || (!(((double) ((y / z) - (t / ((double) (1.0 - z))))) <= 9.993403811868667e-209) && (((double) ((y / z) - (t / ((double) (1.0 - z))))) <= 5.6561471375851743e+278))))) {
		tmp = ((double) ((x / z) * ((double) (y - (((double) (z * t)) / ((double) (1.0 - z)))))));
	} else {
		tmp = ((double) (((double) ((y / z) - (t / ((double) (1.0 - z))))) * x));
	}
	return tmp;
}

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
Herbie0.4
\[\begin{array}{l} \mathbf{if}\;x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) < -7.623226303312042 \cdot 10^{-196}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t \cdot \frac{1}{1 - z}\right)\\ \mathbf{elif}\;x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) < 1.4133944927702302 \cdot 10^{-211}:\\ \;\;\;\;\frac{y \cdot x}{z} + \left(-\frac{t \cdot x}{1 - z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t \cdot \frac{1}{1 - z}\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (-.f64 (/.f64 y z) (/.f64 t (-.f64 1.0 z))) < -7.6743610354066435e306 or -3.8305748615230528e-303 < (-.f64 (/.f64 y z) (/.f64 t (-.f64 1.0 z))) < 9.9934038118686668e-209 or 5.6561471375851743e278 < (-.f64 (/.f64 y z) (/.f64 t (-.f64 1.0 z)))

    1. Initial program 26.9

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

    3. Applied frac-sub_binary6434.1

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

    4. Applied associate-*r/_binary6413.2

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

    6. Applied times-frac_binary641.6

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

    7. Simplified1.1

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

    if -7.6743610354066435e306 < (-.f64 (/.f64 y z) (/.f64 t (-.f64 1.0 z))) < -3.8305748615230528e-303 or 9.9934038118686668e-209 < (-.f64 (/.f64 y z) (/.f64 t (-.f64 1.0 z))) < 5.6561471375851743e278

    1. Initial program 0.2

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

  4. Final simplification0.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} - \frac{t}{1 - z} \leq -7.674361035406644 \cdot 10^{+306} \lor \neg \left(\frac{y}{z} - \frac{t}{1 - z} \leq -3.830574861523053 \cdot 10^{-303} \lor \neg \left(\frac{y}{z} - \frac{t}{1 - z} \leq 9.993403811868667 \cdot 10^{-209}\right) \land \frac{y}{z} - \frac{t}{1 - z} \leq 5.6561471375851743 \cdot 10^{+278}\right):\\ \;\;\;\;\frac{x}{z} \cdot \left(y - \frac{z \cdot t}{1 - z}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{y}{z} - \frac{t}{1 - z}\right) \cdot x\\ \end{array}\]

Reproduce

herbie shell --seed 2020210 
(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)))))