Average Error: 4.8 → 1.4
Time: 5.4s
Precision: 64
\[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} - \frac{t}{1 - z} \le -1.1814149006083051 \cdot 10^{300} \lor \neg \left(\frac{y}{z} - \frac{t}{1 - z} \le 6.5045101283005079 \cdot 10^{295}\right):\\ \;\;\;\;\frac{x \cdot \left(y \cdot \left(1 - z\right) - z \cdot t\right)}{z \cdot \left(1 - z\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right)\\ \end{array}\]
x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right)
↓
\begin{array}{l}
\mathbf{if}\;\frac{y}{z} - \frac{t}{1 - z} \le -1.1814149006083051 \cdot 10^{300} \lor \neg \left(\frac{y}{z} - \frac{t}{1 - z} \le 6.5045101283005079 \cdot 10^{295}\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 code(double x, double y, double z, double t) {
	return (x * ((y / z) - (t / (1.0 - z))));
}
↓
double code(double x, double y, double z, double t) {
	double VAR;
	if (((((y / z) - (t / (1.0 - z))) <= -1.181414900608305e+300) || !(((y / z) - (t / (1.0 - z))) <= 6.504510128300508e+295))) {
		VAR = ((x * ((y * (1.0 - z)) - (z * t))) / (z * (1.0 - z)));
	} else {
		VAR = (x * ((y / z) - (t / (1.0 - z))));
	}
	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

Original4.8
Target4.3
Herbie1.4
\[\begin{array}{l} \mathbf{if}\;x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \lt -7.62322630331204244 \cdot 10^{-196}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t \cdot \frac{1}{1 - z}\right)\\ \mathbf{elif}\;x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \lt 1.41339449277023022 \cdot 10^{-211}:\\ \;\;\;\;\frac{y \cdot x}{z} + \left(-\frac{t \cdot x}{1 - z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t \cdot \frac{1}{1 - z}\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (- (/ y z) (/ t (- 1.0 z))) < -1.181414900608305e+300 or 6.504510128300508e+295 < (- (/ y z) (/ t (- 1.0 z)))

    1. Initial program 53.4

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

    3. Applied frac-sub53.5

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

    4. Applied associate-*r/0.4

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

    if -1.181414900608305e+300 < (- (/ y z) (/ t (- 1.0 z))) < 6.504510128300508e+295

    1. Initial program 1.5

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

  4. Final simplification1.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} - \frac{t}{1 - z} \le -1.1814149006083051 \cdot 10^{300} \lor \neg \left(\frac{y}{z} - \frac{t}{1 - z} \le 6.5045101283005079 \cdot 10^{295}\right):\\ \;\;\;\;\frac{x \cdot \left(y \cdot \left(1 - z\right) - z \cdot t\right)}{z \cdot \left(1 - z\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020078 
(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)))))