Average Error: 7.4 → 2.3
Time: 4.7s
Precision: 64
\[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} = -\infty \lor \neg \left(\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \le 1.17519594851290092 \cdot 10^{297}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{1}{\left(t \cdot z - x\right) \cdot \frac{1}{y \cdot z - x}}}{x + 1}\\ \end{array}\]
\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}
↓
\begin{array}{l}
\mathbf{if}\;\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} = -\infty \lor \neg \left(\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \le 1.17519594851290092 \cdot 10^{297}\right):\\
\;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r830109 = x;
        double r830110 = y;
        double r830111 = z;
        double r830112 = r830110 * r830111;
        double r830113 = r830112 - r830109;
        double r830114 = t;
        double r830115 = r830114 * r830111;
        double r830116 = r830115 - r830109;
        double r830117 = r830113 / r830116;
        double r830118 = r830109 + r830117;
        double r830119 = 1.0;
        double r830120 = r830109 + r830119;
        double r830121 = r830118 / r830120;
        return r830121;
}
↓
double f(double x, double y, double z, double t) {
        double r830122 = x;
        double r830123 = y;
        double r830124 = z;
        double r830125 = r830123 * r830124;
        double r830126 = r830125 - r830122;
        double r830127 = t;
        double r830128 = r830127 * r830124;
        double r830129 = r830128 - r830122;
        double r830130 = r830126 / r830129;
        double r830131 = r830122 + r830130;
        double r830132 = 1.0;
        double r830133 = r830122 + r830132;
        double r830134 = r830131 / r830133;
        double r830135 = -inf.0;
        bool r830136 = r830134 <= r830135;
        double r830137 = 1.1751959485129009e+297;
        bool r830138 = r830134 <= r830137;
        double r830139 = !r830138;
        bool r830140 = r830136 || r830139;
        double r830141 = r830123 / r830127;
        double r830142 = r830122 + r830141;
        double r830143 = r830142 / r830133;
        double r830144 = 1.0;
        double r830145 = r830144 / r830126;
        double r830146 = r830129 * r830145;
        double r830147 = r830144 / r830146;
        double r830148 = r830122 + r830147;
        double r830149 = r830148 / r830133;
        double r830150 = r830140 ? r830143 : r830149;
        return r830150;
}

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

Original7.4
Target0.4
Herbie2.3
\[\frac{x + \left(\frac{y}{t - \frac{x}{z}} - \frac{x}{t \cdot z - x}\right)}{x + 1}\]

Derivation

  1. Split input into 2 regimes

  2. if (/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0)) < -inf.0 or 1.1751959485129009e+297 < (/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0))

    1. Initial program 63.5

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

    2. Taylor expanded around inf 14.8

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

    if -inf.0 < (/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0)) < 1.1751959485129009e+297

    1. Initial program 0.7

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\]
    2. Using strategy rm

    3. Applied clear-num0.8

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

    5. Applied div-inv0.8

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

  4. Final simplification2.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} = -\infty \lor \neg \left(\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \le 1.17519594851290092 \cdot 10^{297}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{1}{\left(t \cdot z - x\right) \cdot \frac{1}{y \cdot z - x}}}{x + 1}\\ \end{array}\]

Reproduce

herbie shell --seed 2020100 
(FPCore (x y z t)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, A"
  :precision binary64

  :herbie-target
  (/ (+ x (- (/ y (- t (/ x z))) (/ x (- (* t z) x)))) (+ x 1))

  (/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1)))