Average Error: 4.6 → 1.3
Time: 5.3s
Precision: binary64
\[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} - \frac{t}{1 - z} \le -7.4025841227585561 \cdot 10^{260} \lor \neg \left(\frac{y}{z} - \frac{t}{1 - z} \le 5.7350153978038753 \cdot 10^{288}\right):\\ \;\;\;\;\frac{x \cdot \left(y \cdot \left(\left(\sqrt[3]{1 - z} \cdot \sqrt[3]{1 - z}\right) \cdot \sqrt[3]{1 - z}\right) - z \cdot \left(1 \cdot t\right)\right)}{z \cdot \left(\left(\sqrt[3]{1 - z} \cdot \sqrt[3]{1 - z}\right) \cdot \sqrt[3]{1 - z}\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right)\\ \end{array}\]
x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right)
↓
\begin{array}{l}
\mathbf{if}\;\frac{y}{z} - \frac{t}{1 - z} \le -7.4025841227585561 \cdot 10^{260} \lor \neg \left(\frac{y}{z} - \frac{t}{1 - z} \le 5.7350153978038753 \cdot 10^{288}\right):\\
\;\;\;\;\frac{x \cdot \left(y \cdot \left(\left(\sqrt[3]{1 - z} \cdot \sqrt[3]{1 - z}\right) \cdot \sqrt[3]{1 - z}\right) - z \cdot \left(1 \cdot t\right)\right)}{z \cdot \left(\left(\sqrt[3]{1 - z} \cdot \sqrt[3]{1 - z}\right) \cdot \sqrt[3]{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 ((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) (((double) (y / z)) - ((double) (t / ((double) (1.0 - z)))))) <= -7.402584122758556e+260) || !(((double) (((double) (y / z)) - ((double) (t / ((double) (1.0 - z)))))) <= 5.735015397803875e+288))) {
		VAR = ((double) (((double) (x * ((double) (((double) (y * ((double) (((double) (((double) cbrt(((double) (1.0 - z)))) * ((double) cbrt(((double) (1.0 - z)))))) * ((double) cbrt(((double) (1.0 - z)))))))) - ((double) (z * ((double) (1.0 * t)))))))) / ((double) (z * ((double) (((double) (((double) cbrt(((double) (1.0 - z)))) * ((double) cbrt(((double) (1.0 - z)))))) * ((double) cbrt(((double) (1.0 - z))))))))));
	} else {
		VAR = ((double) (x * ((double) (((double) (y / z)) - ((double) (t / ((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

Original4.6
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 (- (/ y z) (/ t (- 1.0 z))) < -7.4025841227585561e260 or 5.7350153978038753e288 < (- (/ y z) (/ t (- 1.0 z)))

    1. Initial program 39.5

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

    3. Applied add-cube-cbrt39.5

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

    4. Applied *-un-lft-identity39.5

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

    5. Applied times-frac39.5

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

    7. Applied frac-times39.5

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

    8. Applied frac-sub40.4

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

    9. Applied associate-*r/1.3

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

    if -7.4025841227585561e260 < (- (/ y z) (/ t (- 1.0 z))) < 5.7350153978038753e288

    1. Initial program 1.3

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

  4. Final simplification1.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} - \frac{t}{1 - z} \le -7.4025841227585561 \cdot 10^{260} \lor \neg \left(\frac{y}{z} - \frac{t}{1 - z} \le 5.7350153978038753 \cdot 10^{288}\right):\\ \;\;\;\;\frac{x \cdot \left(y \cdot \left(\left(\sqrt[3]{1 - z} \cdot \sqrt[3]{1 - z}\right) \cdot \sqrt[3]{1 - z}\right) - z \cdot \left(1 \cdot t\right)\right)}{z \cdot \left(\left(\sqrt[3]{1 - z} \cdot \sqrt[3]{1 - z}\right) \cdot \sqrt[3]{1 - z}\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020150 
(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)))))