Average Error: 7.2 → 2.3
Time: 12.8s
Precision: 64
\[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\]
↓
\[\frac{x + \left(y \cdot \frac{1}{\frac{t \cdot z - x}{z}} - \frac{x}{t \cdot z - x}\right)}{x + 1}\]
\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}
↓
\frac{x + \left(y \cdot \frac{1}{\frac{t \cdot z - x}{z}} - \frac{x}{t \cdot z - x}\right)}{x + 1}
double f(double x, double y, double z, double t) {
        double r759023 = x;
        double r759024 = y;
        double r759025 = z;
        double r759026 = r759024 * r759025;
        double r759027 = r759026 - r759023;
        double r759028 = t;
        double r759029 = r759028 * r759025;
        double r759030 = r759029 - r759023;
        double r759031 = r759027 / r759030;
        double r759032 = r759023 + r759031;
        double r759033 = 1.0;
        double r759034 = r759023 + r759033;
        double r759035 = r759032 / r759034;
        return r759035;
}
↓
double f(double x, double y, double z, double t) {
        double r759036 = x;
        double r759037 = y;
        double r759038 = 1.0;
        double r759039 = t;
        double r759040 = z;
        double r759041 = r759039 * r759040;
        double r759042 = r759041 - r759036;
        double r759043 = r759042 / r759040;
        double r759044 = r759038 / r759043;
        double r759045 = r759037 * r759044;
        double r759046 = r759036 / r759042;
        double r759047 = r759045 - r759046;
        double r759048 = r759036 + r759047;
        double r759049 = 1.0;
        double r759050 = r759036 + r759049;
        double r759051 = r759048 / r759050;
        return r759051;
}

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

Original7.2
Target0.3
Herbie2.3
\[\frac{x + \left(\frac{y}{t - \frac{x}{z}} - \frac{x}{t \cdot z - x}\right)}{x + 1}\]

Derivation

  1. Initial program 7.2

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

  3. Applied div-sub7.2

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

  4. Simplified2.3

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

  6. Applied clear-num2.3

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

  7. Final simplification2.3

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

Reproduce

herbie shell --seed 2020042 
(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)))