Average Error: 0.6 → 0.2
Time: 6.5s
Precision: 64
\[\frac{1.0}{x \cdot x}\]
↓
\[\frac{\frac{1.0}{x}}{x}\]
\frac{1.0}{x \cdot x}
↓
\frac{\frac{1.0}{x}}{x}
double f(double x) {
        double r6910963 = 1.0;
        double r6910964 = x;
        double r6910965 = r6910964 * r6910964;
        double r6910966 = r6910963 / r6910965;
        return r6910966;
}
↓
double f(double x) {
        double r6910967 = 1.0;
        double r6910968 = x;
        double r6910969 = r6910967 / r6910968;
        double r6910970 = r6910969 / r6910968;
        return r6910970;
}

Error

Bits error versus x

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Results

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Target

Original0.6
Target0.2
Herbie0.2
\[\frac{\frac{1.0}{x}}{x}\]

Derivation

  1. Initial program 0.6

    \[\frac{1.0}{x \cdot x}\]
  2. Using strategy rm

  3. Applied associate-/r*0.2

    \[\leadsto \color{blue}{\frac{\frac{1.0}{x}}{x}}\]

  4. Final simplification0.2

    \[\leadsto \frac{\frac{1.0}{x}}{x}\]

Reproduce

herbie shell --seed 2019156 +o rules:numerics
(FPCore (x)
  :name "Numeric.SpecFunctions:$slogFactorial from math-functions-0.1.5.2, A"

  :herbie-target
  (/ (/ 1.0 x) x)

  (/ 1.0 (* x x)))