Average Error: 4.8 → 1.3
Time: 5.5s
Precision: binary64
\[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) = -inf.0 \lor \neg \left(x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \le 4.1429700509756861 \cdot 10^{305}\right):\\ \;\;\;\;\frac{x \cdot \left(y \cdot \sqrt[3]{1 - z} - z \cdot \frac{t}{\sqrt[3]{1 - z} \cdot \sqrt[3]{1 - z}}\right)}{z \cdot \sqrt[3]{1 - z}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} + t \cdot \frac{-1}{1 - z}\right)\\ \end{array}\]
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) = -inf.0 \lor \neg \left(x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \le 4.1429700509756861 \cdot 10^{305}\right):\\
\;\;\;\;\frac{x \cdot \left(y \cdot \sqrt[3]{1 - z} - z \cdot \frac{t}{\sqrt[3]{1 - z} \cdot \sqrt[3]{1 - z}}\right)}{z \cdot \sqrt[3]{1 - z}}\\

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

\end{array}
double code(double x, double y, double z, double t) {
	return ((double) (x * ((double) (((double) (y / z)) - ((double) (t / ((double) (1.0 - z))))))));
}
↓
double code(double x, double y, double z, double t) {
	double VAR;
	if (((((double) (x * ((double) (((double) (y / z)) - ((double) (t / ((double) (1.0 - z)))))))) <= -inf.0) || !(((double) (x * ((double) (((double) (y / z)) - ((double) (t / ((double) (1.0 - z)))))))) <= 4.142970050975686e+305))) {
		VAR = ((double) (((double) (x * ((double) (((double) (y * ((double) cbrt(((double) (1.0 - z)))))) - ((double) (z * ((double) (t / ((double) (((double) cbrt(((double) (1.0 - z)))) * ((double) cbrt(((double) (1.0 - z)))))))))))))) / ((double) (z * ((double) cbrt(((double) (1.0 - z))))))));
	} else {
		VAR = ((double) (x * ((double) (((double) (y / z)) + ((double) (t * ((double) (-1.0 / ((double) (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
Herbie1.3
\[\begin{array}{l} \mathbf{if}\;x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \lt -7.62322630331204244 \cdot 10^{-196}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t \cdot \frac{1}{1 - z}\right)\\ \mathbf{elif}\;x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \lt 1.41339449277023022 \cdot 10^{-211}:\\ \;\;\;\;\frac{y \cdot x}{z} + \left(-\frac{t \cdot x}{1 - z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t \cdot \frac{1}{1 - z}\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (* x (- (/ y z) (/ t (- 1.0 z)))) < -inf.0 or 4.1429700509756861e305 < (* x (- (/ y z) (/ t (- 1.0 z))))

    1. Initial program 62.8

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

    3. Applied add-cube-cbrt62.8

      \[\leadsto x \cdot \left(\frac{y}{z} - \frac{t}{\color{blue}{\left(\sqrt[3]{1 - z} \cdot \sqrt[3]{1 - z}\right) \cdot \sqrt[3]{1 - z}}}\right)\]

    4. Applied associate-/r*62.8

      \[\leadsto x \cdot \left(\frac{y}{z} - \color{blue}{\frac{\frac{t}{\sqrt[3]{1 - z} \cdot \sqrt[3]{1 - z}}}{\sqrt[3]{1 - z}}}\right)\]
    5. Using strategy rm

    6. Applied frac-sub62.8

      \[\leadsto x \cdot \color{blue}{\frac{y \cdot \sqrt[3]{1 - z} - z \cdot \frac{t}{\sqrt[3]{1 - z} \cdot \sqrt[3]{1 - z}}}{z \cdot \sqrt[3]{1 - z}}}\]

    7. Applied associate-*r/0.4

      \[\leadsto \color{blue}{\frac{x \cdot \left(y \cdot \sqrt[3]{1 - z} - z \cdot \frac{t}{\sqrt[3]{1 - z} \cdot \sqrt[3]{1 - z}}\right)}{z \cdot \sqrt[3]{1 - z}}}\]

    if -inf.0 < (* x (- (/ y z) (/ t (- 1.0 z)))) < 4.1429700509756861e305

    1. Initial program 1.4

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

    3. Applied div-inv1.4

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

  4. Final simplification1.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) = -inf.0 \lor \neg \left(x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \le 4.1429700509756861 \cdot 10^{305}\right):\\ \;\;\;\;\frac{x \cdot \left(y \cdot \sqrt[3]{1 - z} - z \cdot \frac{t}{\sqrt[3]{1 - z} \cdot \sqrt[3]{1 - z}}\right)}{z \cdot \sqrt[3]{1 - z}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} + t \cdot \frac{-1}{1 - z}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020185 
(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)))))