Average Error: 4.9 → 0.6
Time: 4.1s
Precision: binary64
\[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} - \frac{t}{1 - z} \le -1.044749646739892 \cdot 10^{229}:\\ \;\;\;\;\frac{x \cdot \left(y \cdot \left(1 - z\right) - z \cdot t\right)}{z \cdot \left(1 - z\right)}\\ \mathbf{elif}\;\frac{y}{z} - \frac{t}{1 - z} \le -1.81094046641606889 \cdot 10^{-275}:\\ \;\;\;\;\frac{x}{\frac{z}{y - \frac{z}{\frac{1 - z}{t}}}}\\ \mathbf{elif}\;\frac{y}{z} - \frac{t}{1 - z} \le 4.67726574765448314 \cdot 10^{-292}:\\ \;\;\;\;\frac{\left(y \cdot \left(1 - z\right) - z \cdot t\right) \cdot \frac{x}{z}}{1 - z}\\ \mathbf{elif}\;\frac{y}{z} - \frac{t}{1 - z} \le 1.8997455834822073 \cdot 10^{244}:\\ \;\;\;\;\frac{x}{\frac{z}{y - \frac{z}{\frac{1 - z}{t}}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y \cdot \left(1 - z\right) - z \cdot t\right)}{z \cdot \left(1 - z\right)}\\ \end{array}\]
x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right)
↓
\begin{array}{l}
\mathbf{if}\;\frac{y}{z} - \frac{t}{1 - z} \le -1.044749646739892 \cdot 10^{229}:\\
\;\;\;\;\frac{x \cdot \left(y \cdot \left(1 - z\right) - z \cdot t\right)}{z \cdot \left(1 - z\right)}\\

\mathbf{elif}\;\frac{y}{z} - \frac{t}{1 - z} \le -1.81094046641606889 \cdot 10^{-275}:\\
\;\;\;\;\frac{x}{\frac{z}{y - \frac{z}{\frac{1 - z}{t}}}}\\

\mathbf{elif}\;\frac{y}{z} - \frac{t}{1 - z} \le 4.67726574765448314 \cdot 10^{-292}:\\
\;\;\;\;\frac{\left(y \cdot \left(1 - z\right) - z \cdot t\right) \cdot \frac{x}{z}}{1 - z}\\

\mathbf{elif}\;\frac{y}{z} - \frac{t}{1 - z} \le 1.8997455834822073 \cdot 10^{244}:\\
\;\;\;\;\frac{x}{\frac{z}{y - \frac{z}{\frac{1 - z}{t}}}}\\

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

\end{array}
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))))) <= -1.044749646739892e+229)) {
		VAR = (((double) (x * ((double) (((double) (y * ((double) (1.0 - z)))) - ((double) (z * t)))))) / ((double) (z * ((double) (1.0 - z)))));
	} else {
		double VAR_1;
		if ((((double) ((y / z) - (t / ((double) (1.0 - z))))) <= -1.810940466416069e-275)) {
			VAR_1 = (x / (z / ((double) (y - (z / (((double) (1.0 - z)) / t))))));
		} else {
			double VAR_2;
			if ((((double) ((y / z) - (t / ((double) (1.0 - z))))) <= 4.677265747654483e-292)) {
				VAR_2 = (((double) (((double) (((double) (y * ((double) (1.0 - z)))) - ((double) (z * t)))) * (x / z))) / ((double) (1.0 - z)));
			} else {
				double VAR_3;
				if ((((double) ((y / z) - (t / ((double) (1.0 - z))))) <= 1.8997455834822073e+244)) {
					VAR_3 = (x / (z / ((double) (y - (z / (((double) (1.0 - z)) / t))))));
				} else {
					VAR_3 = (((double) (x * ((double) (((double) (y * ((double) (1.0 - z)))) - ((double) (z * t)))))) / ((double) (z * ((double) (1.0 - z)))));
				}
				VAR_2 = VAR_3;
			}
			VAR_1 = VAR_2;
		}
		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
Target4.5
Herbie0.6
\[\begin{array}{l} \mathbf{if}\;x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \lt -7.62322630331204244 \cdot 10^{-196}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t \cdot \frac{1}{1 - z}\right)\\ \mathbf{elif}\;x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \lt 1.41339449277023022 \cdot 10^{-211}:\\ \;\;\;\;\frac{y \cdot x}{z} + \left(-\frac{t \cdot x}{1 - z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t \cdot \frac{1}{1 - z}\right)\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (- (/ y z) (/ t (- 1.0 z))) < -1.044749646739892e229 or 1.8997455834822073e244 < (- (/ y z) (/ t (- 1.0 z)))

    1. Initial program 26.8

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

    3. Applied frac-sub28.7

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

    4. Applied associate-*r/2.4

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

    if -1.044749646739892e229 < (- (/ y z) (/ t (- 1.0 z))) < -1.81094046641606889e-275 or 4.67726574765448314e-292 < (- (/ y z) (/ t (- 1.0 z))) < 1.8997455834822073e244

    1. Initial program 0.2

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

    3. Applied frac-sub23.3

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

    4. Applied associate-*r/28.4

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

    6. Applied associate-/l*23.3

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

    7. Simplified0.3

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

    if -1.81094046641606889e-275 < (- (/ y z) (/ t (- 1.0 z))) < 4.67726574765448314e-292

    1. Initial program 17.2

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

    3. Applied frac-sub22.8

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

    4. Applied associate-*r/20.2

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

    6. Applied associate-/r*10.9

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

    7. Simplified0.5

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

  4. Final simplification0.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} - \frac{t}{1 - z} \le -1.044749646739892 \cdot 10^{229}:\\ \;\;\;\;\frac{x \cdot \left(y \cdot \left(1 - z\right) - z \cdot t\right)}{z \cdot \left(1 - z\right)}\\ \mathbf{elif}\;\frac{y}{z} - \frac{t}{1 - z} \le -1.81094046641606889 \cdot 10^{-275}:\\ \;\;\;\;\frac{x}{\frac{z}{y - \frac{z}{\frac{1 - z}{t}}}}\\ \mathbf{elif}\;\frac{y}{z} - \frac{t}{1 - z} \le 4.67726574765448314 \cdot 10^{-292}:\\ \;\;\;\;\frac{\left(y \cdot \left(1 - z\right) - z \cdot t\right) \cdot \frac{x}{z}}{1 - z}\\ \mathbf{elif}\;\frac{y}{z} - \frac{t}{1 - z} \le 1.8997455834822073 \cdot 10^{244}:\\ \;\;\;\;\frac{x}{\frac{z}{y - \frac{z}{\frac{1 - z}{t}}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y \cdot \left(1 - z\right) - z \cdot t\right)}{z \cdot \left(1 - z\right)}\\ \end{array}\]

Reproduce

herbie shell --seed 2020182 
(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) (neg (/ (* t x) (- 1.0 z)))) (* x (- (/ y z) (* t (/ 1.0 (- 1.0 z)))))))

  (* x (- (/ y z) (/ t (- 1.0 z)))))