Average Error: 7.0 → 3.2
Time: 4.6s
Precision: 64
\[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -1.2646983877022145 \cdot 10^{132} \lor \neg \left(z \le 3.75596125063527625 \cdot 10^{86}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \left(y \cdot z - x\right) \cdot \frac{1}{t \cdot z - x}}{x + 1}\\ \end{array}\]
\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}
↓
\begin{array}{l}
\mathbf{if}\;z \le -1.2646983877022145 \cdot 10^{132} \lor \neg \left(z \le 3.75596125063527625 \cdot 10^{86}\right):\\
\;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r669018 = x;
        double r669019 = y;
        double r669020 = z;
        double r669021 = r669019 * r669020;
        double r669022 = r669021 - r669018;
        double r669023 = t;
        double r669024 = r669023 * r669020;
        double r669025 = r669024 - r669018;
        double r669026 = r669022 / r669025;
        double r669027 = r669018 + r669026;
        double r669028 = 1.0;
        double r669029 = r669018 + r669028;
        double r669030 = r669027 / r669029;
        return r669030;
}
↓
double f(double x, double y, double z, double t) {
        double r669031 = z;
        double r669032 = -1.2646983877022145e+132;
        bool r669033 = r669031 <= r669032;
        double r669034 = 3.755961250635276e+86;
        bool r669035 = r669031 <= r669034;
        double r669036 = !r669035;
        bool r669037 = r669033 || r669036;
        double r669038 = x;
        double r669039 = y;
        double r669040 = t;
        double r669041 = r669039 / r669040;
        double r669042 = r669038 + r669041;
        double r669043 = 1.0;
        double r669044 = r669038 + r669043;
        double r669045 = r669042 / r669044;
        double r669046 = r669039 * r669031;
        double r669047 = r669046 - r669038;
        double r669048 = 1.0;
        double r669049 = r669040 * r669031;
        double r669050 = r669049 - r669038;
        double r669051 = r669048 / r669050;
        double r669052 = r669047 * r669051;
        double r669053 = r669038 + r669052;
        double r669054 = r669053 / r669044;
        double r669055 = r669037 ? r669045 : r669054;
        return r669055;
}

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

Original7.0
Target0.3
Herbie3.2
\[\frac{x + \left(\frac{y}{t - \frac{x}{z}} - \frac{x}{t \cdot z - x}\right)}{x + 1}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -1.2646983877022145e+132 or 3.755961250635276e+86 < z

    1. Initial program 19.7

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

    2. Taylor expanded around inf 7.2

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

    if -1.2646983877022145e+132 < z < 3.755961250635276e+86

    1. Initial program 1.3

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

    3. Applied div-inv1.3

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

  4. Final simplification3.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -1.2646983877022145 \cdot 10^{132} \lor \neg \left(z \le 3.75596125063527625 \cdot 10^{86}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \left(y \cdot z - x\right) \cdot \frac{1}{t \cdot z - x}}{x + 1}\\ \end{array}\]

Reproduce

herbie shell --seed 2020089 +o rules:numerics
(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)))