Average Error: 7.5 → 0.4
Time: 25.2s
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 r28675823 = x;
        double r28675824 = y;
        double r28675825 = z;
        double r28675826 = r28675824 * r28675825;
        double r28675827 = r28675826 - r28675823;
        double r28675828 = t;
        double r28675829 = r28675828 * r28675825;
        double r28675830 = r28675829 - r28675823;
        double r28675831 = r28675827 / r28675830;
        double r28675832 = r28675823 + r28675831;
        double r28675833 = 1.0;
        double r28675834 = r28675823 + r28675833;
        double r28675835 = r28675832 / r28675834;
        return r28675835;
}
↓
double f(double x, double y, double z, double t) {
        double r28675836 = x;
        double r28675837 = y;
        double r28675838 = t;
        double r28675839 = z;
        double r28675840 = r28675836 / r28675839;
        double r28675841 = r28675838 - r28675840;
        double r28675842 = r28675837 / r28675841;
        double r28675843 = r28675838 * r28675839;
        double r28675844 = r28675843 - r28675836;
        double r28675845 = r28675836 / r28675844;
        double r28675846 = r28675842 - r28675845;
        double r28675847 = r28675836 + r28675846;
        double r28675848 = 1.0;
        double r28675849 = r28675848 + r28675836;
        double r28675850 = r28675847 / r28675849;
        return r28675850;
}

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
Target0.4
Herbie0.4
\[\frac{x + \left(\frac{y}{t - \frac{x}{z}} - \frac{x}{t \cdot z - x}\right)}{x + 1}\]

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. Simplified0.4

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

  9. Final simplification0.4

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

Reproduce

herbie shell --seed 2019169 +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)))