Average Error: 7.7 → 0.3
Time: 6.6s
Precision: 64
\[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\]
↓
\[\frac{x + \frac{y}{\frac{t}{1} - \frac{x}{z}}}{x + 1} - \frac{\frac{1}{\frac{t \cdot z - x}{x}}}{x + 1}\]
\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}
↓
\frac{x + \frac{y}{\frac{t}{1} - \frac{x}{z}}}{x + 1} - \frac{\frac{1}{\frac{t \cdot z - x}{x}}}{x + 1}
double f(double x, double y, double z, double t) {
        double r757948 = x;
        double r757949 = y;
        double r757950 = z;
        double r757951 = r757949 * r757950;
        double r757952 = r757951 - r757948;
        double r757953 = t;
        double r757954 = r757953 * r757950;
        double r757955 = r757954 - r757948;
        double r757956 = r757952 / r757955;
        double r757957 = r757948 + r757956;
        double r757958 = 1.0;
        double r757959 = r757948 + r757958;
        double r757960 = r757957 / r757959;
        return r757960;
}
↓
double f(double x, double y, double z, double t) {
        double r757961 = x;
        double r757962 = y;
        double r757963 = t;
        double r757964 = 1.0;
        double r757965 = r757963 / r757964;
        double r757966 = z;
        double r757967 = r757961 / r757966;
        double r757968 = r757965 - r757967;
        double r757969 = r757962 / r757968;
        double r757970 = r757961 + r757969;
        double r757971 = 1.0;
        double r757972 = r757961 + r757971;
        double r757973 = r757970 / r757972;
        double r757974 = r757963 * r757966;
        double r757975 = r757974 - r757961;
        double r757976 = r757975 / r757961;
        double r757977 = r757964 / r757976;
        double r757978 = r757977 / r757972;
        double r757979 = r757973 - r757978;
        return r757979;
}

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

Original7.7
Target0.3
Herbie0.3
\[\frac{x + \left(\frac{y}{t - \frac{x}{z}} - \frac{x}{t \cdot z - x}\right)}{x + 1}\]

Derivation

  1. Initial program 7.7

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

  3. Applied div-sub7.7

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

  4. Applied associate-+r-7.7

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

  5. Applied div-sub7.7

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

  7. Applied associate-/l*2.2

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

  9. Applied div-sub2.2

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

  10. Simplified0.3

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

  12. Applied clear-num0.3

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

  13. Final simplification0.3

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

Reproduce

herbie shell --seed 2019322 
(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)))