Average Error: 0.4 → 0.2
Time: 13.0s
Precision: 64
\[\frac{x \cdot 100}{x + y}\]
↓
\[\frac{\frac{x}{y + x}}{\frac{1}{100}}\]
\frac{x \cdot 100}{x + y}
↓
\frac{\frac{x}{y + x}}{\frac{1}{100}}
double f(double x, double y) {
        double r39462468 = x;
        double r39462469 = 100.0;
        double r39462470 = r39462468 * r39462469;
        double r39462471 = y;
        double r39462472 = r39462468 + r39462471;
        double r39462473 = r39462470 / r39462472;
        return r39462473;
}
↓
double f(double x, double y) {
        double r39462474 = x;
        double r39462475 = y;
        double r39462476 = r39462475 + r39462474;
        double r39462477 = r39462474 / r39462476;
        double r39462478 = 1.0;
        double r39462479 = 100.0;
        double r39462480 = r39462478 / r39462479;
        double r39462481 = r39462477 / r39462480;
        return r39462481;
}

Error

Bits error versus x

Bits error versus y

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Results

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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

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

Reproduce

herbie shell --seed 2019170 +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)))