Average Error: 0.4 → 0.2
Time: 10.5s
Precision: 64
\[\frac{x \cdot 100}{x + y}\]
↓
\[\frac{\frac{x}{x + y}}{\frac{1}{100}}\]
\frac{x \cdot 100}{x + y}
↓
\frac{\frac{x}{x + y}}{\frac{1}{100}}
double f(double x, double y) {
        double r49523237 = x;
        double r49523238 = 100.0;
        double r49523239 = r49523237 * r49523238;
        double r49523240 = y;
        double r49523241 = r49523237 + r49523240;
        double r49523242 = r49523239 / r49523241;
        return r49523242;
}
↓
double f(double x, double y) {
        double r49523243 = x;
        double r49523244 = y;
        double r49523245 = r49523243 + r49523244;
        double r49523246 = r49523243 / r49523245;
        double r49523247 = 1.0;
        double r49523248 = 100.0;
        double r49523249 = r49523247 / r49523248;
        double r49523250 = r49523246 / r49523249;
        return r49523250;
}

Error

Bits error versus x

Bits error versus y

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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 associate-/l*0.2

    \[\leadsto \color{blue}{\frac{x}{\frac{x + y}{100}}}\]
  4. Using strategy rm

  5. Applied div-inv0.2

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

  6. Applied associate-/r*0.2

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

  7. Final simplification0.2

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

Reproduce

herbie shell --seed 2019174 +o rules:numerics
(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)))