Average Error: 0.4 → 0.2
Time: 2.3s
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 r773524 = x;
        double r773525 = 100.0;
        double r773526 = r773524 * r773525;
        double r773527 = y;
        double r773528 = r773524 + r773527;
        double r773529 = r773526 / r773528;
        return r773529;
}
↓
double f(double x, double y) {
        double r773530 = x;
        double r773531 = y;
        double r773532 = r773530 + r773531;
        double r773533 = r773530 / r773532;
        double r773534 = 1.0;
        double r773535 = 100.0;
        double r773536 = r773534 / r773535;
        double r773537 = r773533 / r773536;
        return r773537;
}

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 2020047 +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)))