Average Error: 4.5 → 4.3
Time: 4.7s
Precision: 64
\[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -4.3574788430707297 \cdot 10^{-179} \lor \neg \left(z \le 8.4759760965436472 \cdot 10^{-78}\right):\\ \;\;\;\;\left(\sqrt[3]{x \cdot \left(\frac{y}{z} - \frac{1}{\frac{1 - z}{t}}\right)} \cdot \sqrt[3]{x \cdot \left(\frac{y}{z} - \frac{1}{\frac{1 - z}{t}}\right)}\right) \cdot \sqrt[3]{x \cdot \left(\frac{y}{z} - \frac{1}{\frac{1 - z}{t}}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y \cdot \left(1 - z\right) - z \cdot t\right)}{z \cdot \left(1 - z\right)}\\ \end{array}\]
x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right)
↓
\begin{array}{l}
\mathbf{if}\;z \le -4.3574788430707297 \cdot 10^{-179} \lor \neg \left(z \le 8.4759760965436472 \cdot 10^{-78}\right):\\
\;\;\;\;\left(\sqrt[3]{x \cdot \left(\frac{y}{z} - \frac{1}{\frac{1 - z}{t}}\right)} \cdot \sqrt[3]{x \cdot \left(\frac{y}{z} - \frac{1}{\frac{1 - z}{t}}\right)}\right) \cdot \sqrt[3]{x \cdot \left(\frac{y}{z} - \frac{1}{\frac{1 - z}{t}}\right)}\\

\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 f(double x, double y, double z, double t) {
        double r503393 = x;
        double r503394 = y;
        double r503395 = z;
        double r503396 = r503394 / r503395;
        double r503397 = t;
        double r503398 = 1.0;
        double r503399 = r503398 - r503395;
        double r503400 = r503397 / r503399;
        double r503401 = r503396 - r503400;
        double r503402 = r503393 * r503401;
        return r503402;
}
↓
double f(double x, double y, double z, double t) {
        double r503403 = z;
        double r503404 = -4.35747884307073e-179;
        bool r503405 = r503403 <= r503404;
        double r503406 = 8.475976096543647e-78;
        bool r503407 = r503403 <= r503406;
        double r503408 = !r503407;
        bool r503409 = r503405 || r503408;
        double r503410 = x;
        double r503411 = y;
        double r503412 = r503411 / r503403;
        double r503413 = 1.0;
        double r503414 = 1.0;
        double r503415 = r503414 - r503403;
        double r503416 = t;
        double r503417 = r503415 / r503416;
        double r503418 = r503413 / r503417;
        double r503419 = r503412 - r503418;
        double r503420 = r503410 * r503419;
        double r503421 = cbrt(r503420);
        double r503422 = r503421 * r503421;
        double r503423 = r503422 * r503421;
        double r503424 = r503411 * r503415;
        double r503425 = r503403 * r503416;
        double r503426 = r503424 - r503425;
        double r503427 = r503410 * r503426;
        double r503428 = r503403 * r503415;
        double r503429 = r503427 / r503428;
        double r503430 = r503409 ? r503423 : r503429;
        return r503430;
}

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

Original4.5
Target4.1
Herbie4.3
\[\begin{array}{l} \mathbf{if}\;x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \lt -7.62322630331204244 \cdot 10^{-196}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t \cdot \frac{1}{1 - z}\right)\\ \mathbf{elif}\;x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \lt 1.41339449277023022 \cdot 10^{-211}:\\ \;\;\;\;\frac{y \cdot x}{z} + \left(-\frac{t \cdot x}{1 - z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t \cdot \frac{1}{1 - z}\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -4.35747884307073e-179 or 8.475976096543647e-78 < z

    1. Initial program 2.6

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

    3. Applied clear-num2.7

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

    5. Applied add-cube-cbrt3.6

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

    if -4.35747884307073e-179 < z < 8.475976096543647e-78

    1. Initial program 11.6

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

    3. Applied frac-sub11.7

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

    4. Applied associate-*r/7.1

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

  4. Final simplification4.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -4.3574788430707297 \cdot 10^{-179} \lor \neg \left(z \le 8.4759760965436472 \cdot 10^{-78}\right):\\ \;\;\;\;\left(\sqrt[3]{x \cdot \left(\frac{y}{z} - \frac{1}{\frac{1 - z}{t}}\right)} \cdot \sqrt[3]{x \cdot \left(\frac{y}{z} - \frac{1}{\frac{1 - z}{t}}\right)}\right) \cdot \sqrt[3]{x \cdot \left(\frac{y}{z} - \frac{1}{\frac{1 - z}{t}}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y \cdot \left(1 - z\right) - z \cdot t\right)}{z \cdot \left(1 - z\right)}\\ \end{array}\]

Reproduce

herbie shell --seed 2020027 
(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)))))