Average Error: 0.4 → 0.2
Time: 5.6s
Precision: 64
\[\frac{x \cdot 100}{x + y}\]
↓
\[x \cdot \frac{100}{x + y}\]
\frac{x \cdot 100}{x + y}
↓
x \cdot \frac{100}{x + y}
double f(double x, double y) {
        double r780931 = x;
        double r780932 = 100.0;
        double r780933 = r780931 * r780932;
        double r780934 = y;
        double r780935 = r780931 + r780934;
        double r780936 = r780933 / r780935;
        return r780936;
}
↓
double f(double x, double y) {
        double r780937 = x;
        double r780938 = 100.0;
        double r780939 = y;
        double r780940 = r780937 + r780939;
        double r780941 = r780938 / r780940;
        double r780942 = r780937 * r780941;
        return r780942;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.4
Target0.2
Herbie0.2
\[\frac{x}{1} \cdot \frac{100}{x + y}\]

Derivation

  1. Initial program 0.4

    \[\frac{x \cdot 100}{x + y}\]
  2. Using strategy rm

  3. Applied *-un-lft-identity0.4

    \[\leadsto \frac{x \cdot 100}{\color{blue}{1 \cdot \left(x + y\right)}}\]

  4. Applied times-frac0.2

    \[\leadsto \color{blue}{\frac{x}{1} \cdot \frac{100}{x + y}}\]

  5. Simplified0.2

    \[\leadsto \color{blue}{x} \cdot \frac{100}{x + y}\]

  6. Final simplification0.2

    \[\leadsto x \cdot \frac{100}{x + y}\]

Reproduce

herbie shell --seed 2020046 +o rules:numerics
(FPCore (x y)
  :name "Development.Shake.Progress:message from shake-0.15.5"
  :precision binary64

  :herbie-target
  (* (/ x 1) (/ 100 (+ x y)))

  (/ (* x 100) (+ x y)))