Average Error: 0.4 → 0.2
Time: 13.1s
Precision: 64
\[\frac{x \cdot 100}{x + y}\]
↓
\[\frac{x}{\frac{x + y}{100}}\]
\frac{x \cdot 100}{x + y}
↓
\frac{x}{\frac{x + y}{100}}
double f(double x, double y) {
        double r419946 = x;
        double r419947 = 100.0;
        double r419948 = r419946 * r419947;
        double r419949 = y;
        double r419950 = r419946 + r419949;
        double r419951 = r419948 / r419950;
        return r419951;
}
↓
double f(double x, double y) {
        double r419952 = x;
        double r419953 = y;
        double r419954 = r419952 + r419953;
        double r419955 = 100.0;
        double r419956 = r419954 / r419955;
        double r419957 = r419952 / r419956;
        return r419957;
}

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. Final simplification0.2

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

Reproduce

herbie shell --seed 2019323 +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)))