Average Error: 0.4 → 0.2
Time: 7.6s
Precision: 64
\[\frac{x \cdot 100}{x + y}\]
↓
\[\frac{100}{x + y} \cdot x\]
\frac{x \cdot 100}{x + y}
↓
\frac{100}{x + y} \cdot x
double f(double x, double y) {
        double r616603 = x;
        double r616604 = 100.0;
        double r616605 = r616603 * r616604;
        double r616606 = y;
        double r616607 = r616603 + r616606;
        double r616608 = r616605 / r616607;
        return r616608;
}
↓
double f(double x, double y) {
        double r616609 = 100.0;
        double r616610 = x;
        double r616611 = y;
        double r616612 = r616610 + r616611;
        double r616613 = r616609 / r616612;
        double r616614 = r616613 * r616610;
        return r616614;
}

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. Simplified0.2

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

  7. Final simplification0.2

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

Reproduce

herbie shell --seed 2019194 
(FPCore (x y)
  :name "Development.Shake.Progress:message from shake-0.15.5"

  :herbie-target
  (* (/ x 1.0) (/ 100.0 (+ x y)))

  (/ (* x 100.0) (+ x y)))