Average Error: 7.5 → 0.3
Time: 59.5s
Precision: 64
\[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\]
↓
\[\frac{x + \left(\frac{y}{t - \frac{x}{z}} - \frac{x}{t \cdot z - x}\right)}{1 + x}\]
\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}
↓
\frac{x + \left(\frac{y}{t - \frac{x}{z}} - \frac{x}{t \cdot z - x}\right)}{1 + x}
double f(double x, double y, double z, double t) {
        double r34111828 = x;
        double r34111829 = y;
        double r34111830 = z;
        double r34111831 = r34111829 * r34111830;
        double r34111832 = r34111831 - r34111828;
        double r34111833 = t;
        double r34111834 = r34111833 * r34111830;
        double r34111835 = r34111834 - r34111828;
        double r34111836 = r34111832 / r34111835;
        double r34111837 = r34111828 + r34111836;
        double r34111838 = 1.0;
        double r34111839 = r34111828 + r34111838;
        double r34111840 = r34111837 / r34111839;
        return r34111840;
}
↓
double f(double x, double y, double z, double t) {
        double r34111841 = x;
        double r34111842 = y;
        double r34111843 = t;
        double r34111844 = z;
        double r34111845 = r34111841 / r34111844;
        double r34111846 = r34111843 - r34111845;
        double r34111847 = r34111842 / r34111846;
        double r34111848 = r34111843 * r34111844;
        double r34111849 = r34111848 - r34111841;
        double r34111850 = r34111841 / r34111849;
        double r34111851 = r34111847 - r34111850;
        double r34111852 = r34111841 + r34111851;
        double r34111853 = 1.0;
        double r34111854 = r34111853 + r34111841;
        double r34111855 = r34111852 / r34111854;
        return r34111855;
}

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

Original7.5
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 7.5

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

  3. Applied div-sub7.5

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

  5. Applied associate-/l*2.4

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

  7. Applied div-sub2.4

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

  8. Simplified0.3

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

  9. Final simplification0.3

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

Reproduce

herbie shell --seed 2019168 +o rules:numerics
(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)))