Average Error: 4.7 → 4.6
Time: 7.4s
Precision: 64
\[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le 9.1825479463819844 \cdot 10^{88}:\\ \;\;\;\;\frac{x}{\frac{z}{y}} + x \cdot \left(-\frac{t}{1 - z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z} + \frac{x \cdot \left(-t\right)}{1 - z}\\ \end{array}\]
x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right)
↓
\begin{array}{l}
\mathbf{if}\;y \le 9.1825479463819844 \cdot 10^{88}:\\
\;\;\;\;\frac{x}{\frac{z}{y}} + x \cdot \left(-\frac{t}{1 - z}\right)\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r494101 = x;
        double r494102 = y;
        double r494103 = z;
        double r494104 = r494102 / r494103;
        double r494105 = t;
        double r494106 = 1.0;
        double r494107 = r494106 - r494103;
        double r494108 = r494105 / r494107;
        double r494109 = r494104 - r494108;
        double r494110 = r494101 * r494109;
        return r494110;
}
↓
double f(double x, double y, double z, double t) {
        double r494111 = y;
        double r494112 = 9.182547946381984e+88;
        bool r494113 = r494111 <= r494112;
        double r494114 = x;
        double r494115 = z;
        double r494116 = r494115 / r494111;
        double r494117 = r494114 / r494116;
        double r494118 = t;
        double r494119 = 1.0;
        double r494120 = r494119 - r494115;
        double r494121 = r494118 / r494120;
        double r494122 = -r494121;
        double r494123 = r494114 * r494122;
        double r494124 = r494117 + r494123;
        double r494125 = r494114 * r494111;
        double r494126 = r494125 / r494115;
        double r494127 = -r494118;
        double r494128 = r494114 * r494127;
        double r494129 = r494128 / r494120;
        double r494130 = r494126 + r494129;
        double r494131 = r494113 ? r494124 : r494130;
        return r494131;
}

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

Original4.7
Target4.3
Herbie4.6
\[\begin{array}{l} \mathbf{if}\;x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \lt -7.62322630331204244 \cdot 10^{-196}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t \cdot \frac{1}{1 - z}\right)\\ \mathbf{elif}\;x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \lt 1.41339449277023022 \cdot 10^{-211}:\\ \;\;\;\;\frac{y \cdot x}{z} + \left(-\frac{t \cdot x}{1 - z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t \cdot \frac{1}{1 - z}\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if y < 9.182547946381984e+88

    1. Initial program 3.7

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

    3. Applied sub-neg3.7

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

    4. Applied distribute-lft-in3.7

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

    5. Simplified4.5

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

    7. Applied clear-num4.7

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

    9. Applied *-un-lft-identity4.7

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

    10. Applied add-cube-cbrt4.7

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

    11. Applied times-frac4.7

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

    12. Simplified4.7

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

    13. Simplified3.6

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

    if 9.182547946381984e+88 < y

    1. Initial program 10.5

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

    3. Applied sub-neg10.5

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

    4. Applied distribute-lft-in10.5

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

    5. Simplified9.8

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

    7. Applied distribute-neg-frac9.8

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

    8. Applied associate-*r/10.6

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

  4. Final simplification4.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le 9.1825479463819844 \cdot 10^{88}:\\ \;\;\;\;\frac{x}{\frac{z}{y}} + x \cdot \left(-\frac{t}{1 - z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z} + \frac{x \cdot \left(-t\right)}{1 - z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020045 
(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)))))