Average Error: 7.4 → 3.4
Time: 25.9s
Precision: 64
\[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -7.466575650945099720574707422047672473328 \cdot 10^{79}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{elif}\;z \le 8.602497059991938743425250288839984899656 \cdot 10^{114}:\\ \;\;\;\;\frac{\frac{\frac{1}{t \cdot z - x}}{\frac{1}{y \cdot z - x}} + x}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array}\]
\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}
↓
\begin{array}{l}
\mathbf{if}\;z \le -7.466575650945099720574707422047672473328 \cdot 10^{79}:\\
\;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\

\mathbf{elif}\;z \le 8.602497059991938743425250288839984899656 \cdot 10^{114}:\\
\;\;\;\;\frac{\frac{\frac{1}{t \cdot z - x}}{\frac{1}{y \cdot z - x}} + x}{x + 1}\\

\mathbf{else}:\\
\;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\

\end{array}
double f(double x, double y, double z, double t) {
        double r31604098 = x;
        double r31604099 = y;
        double r31604100 = z;
        double r31604101 = r31604099 * r31604100;
        double r31604102 = r31604101 - r31604098;
        double r31604103 = t;
        double r31604104 = r31604103 * r31604100;
        double r31604105 = r31604104 - r31604098;
        double r31604106 = r31604102 / r31604105;
        double r31604107 = r31604098 + r31604106;
        double r31604108 = 1.0;
        double r31604109 = r31604098 + r31604108;
        double r31604110 = r31604107 / r31604109;
        return r31604110;
}
↓
double f(double x, double y, double z, double t) {
        double r31604111 = z;
        double r31604112 = -7.4665756509451e+79;
        bool r31604113 = r31604111 <= r31604112;
        double r31604114 = x;
        double r31604115 = y;
        double r31604116 = t;
        double r31604117 = r31604115 / r31604116;
        double r31604118 = r31604114 + r31604117;
        double r31604119 = 1.0;
        double r31604120 = r31604114 + r31604119;
        double r31604121 = r31604118 / r31604120;
        double r31604122 = 8.602497059991939e+114;
        bool r31604123 = r31604111 <= r31604122;
        double r31604124 = 1.0;
        double r31604125 = r31604116 * r31604111;
        double r31604126 = r31604125 - r31604114;
        double r31604127 = r31604124 / r31604126;
        double r31604128 = r31604115 * r31604111;
        double r31604129 = r31604128 - r31604114;
        double r31604130 = r31604124 / r31604129;
        double r31604131 = r31604127 / r31604130;
        double r31604132 = r31604131 + r31604114;
        double r31604133 = r31604132 / r31604120;
        double r31604134 = r31604123 ? r31604133 : r31604121;
        double r31604135 = r31604113 ? r31604121 : r31604134;
        return r31604135;
}

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
Target0.3
Herbie3.4
\[\frac{x + \left(\frac{y}{t - \frac{x}{z}} - \frac{x}{t \cdot z - x}\right)}{x + 1}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -7.4665756509451e+79 or 8.602497059991939e+114 < z

    1. Initial program 19.4

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

    2. Taylor expanded around inf 7.5

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

    if -7.4665756509451e+79 < z < 8.602497059991939e+114

    1. Initial program 1.3

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

    3. Applied clear-num1.3

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

    5. Applied div-inv1.4

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

    6. Applied associate-/r*1.3

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

  4. Final simplification3.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -7.466575650945099720574707422047672473328 \cdot 10^{79}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{elif}\;z \le 8.602497059991938743425250288839984899656 \cdot 10^{114}:\\ \;\;\;\;\frac{\frac{\frac{1}{t \cdot z - x}}{\frac{1}{y \cdot z - x}} + x}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array}\]

Reproduce

herbie shell --seed 2019170 
(FPCore (x y z t)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, A"

  :herbie-target
  (/ (+ x (- (/ y (- t (/ x z))) (/ x (- (* t z) x)))) (+ x 1.0))

  (/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0)))