Average Error: 4.4 → 4.2
Time: 4.9s
Precision: 64
\[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -9.1091683703358591 \cdot 10^{90} \lor \neg \left(t \le 1.0875462656188573 \cdot 10^{151}\right):\\ \;\;\;\;\frac{x \cdot y}{z} + x \cdot \left(-\frac{t}{1 - z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z} + \frac{x}{1 - z} \cdot \left(-t\right)\\ \end{array}\]
x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right)
↓
\begin{array}{l}
\mathbf{if}\;t \le -9.1091683703358591 \cdot 10^{90} \lor \neg \left(t \le 1.0875462656188573 \cdot 10^{151}\right):\\
\;\;\;\;\frac{x \cdot y}{z} + x \cdot \left(-\frac{t}{1 - z}\right)\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r383232 = x;
        double r383233 = y;
        double r383234 = z;
        double r383235 = r383233 / r383234;
        double r383236 = t;
        double r383237 = 1.0;
        double r383238 = r383237 - r383234;
        double r383239 = r383236 / r383238;
        double r383240 = r383235 - r383239;
        double r383241 = r383232 * r383240;
        return r383241;
}
↓
double f(double x, double y, double z, double t) {
        double r383242 = t;
        double r383243 = -9.10916837033586e+90;
        bool r383244 = r383242 <= r383243;
        double r383245 = 1.0875462656188573e+151;
        bool r383246 = r383242 <= r383245;
        double r383247 = !r383246;
        bool r383248 = r383244 || r383247;
        double r383249 = x;
        double r383250 = y;
        double r383251 = r383249 * r383250;
        double r383252 = z;
        double r383253 = r383251 / r383252;
        double r383254 = 1.0;
        double r383255 = r383254 - r383252;
        double r383256 = r383242 / r383255;
        double r383257 = -r383256;
        double r383258 = r383249 * r383257;
        double r383259 = r383253 + r383258;
        double r383260 = r383250 / r383252;
        double r383261 = r383249 * r383260;
        double r383262 = r383249 / r383255;
        double r383263 = -r383242;
        double r383264 = r383262 * r383263;
        double r383265 = r383261 + r383264;
        double r383266 = r383248 ? r383259 : r383265;
        return r383266;
}

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

Original4.4
Target4.0
Herbie4.2
\[\begin{array}{l} \mathbf{if}\;x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \lt -7.62322630331204244 \cdot 10^{-196}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t \cdot \frac{1}{1 - z}\right)\\ \mathbf{elif}\;x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \lt 1.41339449277023022 \cdot 10^{-211}:\\ \;\;\;\;\frac{y \cdot x}{z} + \left(-\frac{t \cdot x}{1 - z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t \cdot \frac{1}{1 - z}\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if t < -9.10916837033586e+90 or 1.0875462656188573e+151 < t

    1. Initial program 3.8

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

    3. Applied sub-neg3.8

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

    4. Applied distribute-lft-in3.8

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

    6. Applied associate-*r/3.5

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

    if -9.10916837033586e+90 < t < 1.0875462656188573e+151

    1. Initial program 4.6

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

    3. Applied sub-neg4.6

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

    4. Applied distribute-lft-in4.6

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

    6. Applied clear-num4.6

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

    8. Applied associate-/r/4.6

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

    9. Applied distribute-rgt-neg-in4.6

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

    10. Applied associate-*r*4.4

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

    11. Simplified4.4

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

  4. Final simplification4.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -9.1091683703358591 \cdot 10^{90} \lor \neg \left(t \le 1.0875462656188573 \cdot 10^{151}\right):\\ \;\;\;\;\frac{x \cdot y}{z} + x \cdot \left(-\frac{t}{1 - z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z} + \frac{x}{1 - z} \cdot \left(-t\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020039 
(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)))))