Average Error: 2.0 → 2.0
Time: 18.9s
Precision: 64
\[\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]
↓
\[\frac{\sqrt{{k}^{m}} \cdot \left(\sqrt{{k}^{m}} \cdot a\right)}{k \cdot k + \left(10 \cdot k + 1\right)}\]
\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}
↓
\frac{\sqrt{{k}^{m}} \cdot \left(\sqrt{{k}^{m}} \cdot a\right)}{k \cdot k + \left(10 \cdot k + 1\right)}
double f(double a, double k, double m) {
        double r7636063 = a;
        double r7636064 = k;
        double r7636065 = m;
        double r7636066 = pow(r7636064, r7636065);
        double r7636067 = r7636063 * r7636066;
        double r7636068 = 1.0;
        double r7636069 = 10.0;
        double r7636070 = r7636069 * r7636064;
        double r7636071 = r7636068 + r7636070;
        double r7636072 = r7636064 * r7636064;
        double r7636073 = r7636071 + r7636072;
        double r7636074 = r7636067 / r7636073;
        return r7636074;
}
↓
double f(double a, double k, double m) {
        double r7636075 = k;
        double r7636076 = m;
        double r7636077 = pow(r7636075, r7636076);
        double r7636078 = sqrt(r7636077);
        double r7636079 = a;
        double r7636080 = r7636078 * r7636079;
        double r7636081 = r7636078 * r7636080;
        double r7636082 = r7636075 * r7636075;
        double r7636083 = 10.0;
        double r7636084 = r7636083 * r7636075;
        double r7636085 = 1.0;
        double r7636086 = r7636084 + r7636085;
        double r7636087 = r7636082 + r7636086;
        double r7636088 = r7636081 / r7636087;
        return r7636088;
}

Error

Bits error versus a

Bits error versus k

Bits error versus m

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 2.0

    \[\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]
  2. Using strategy rm

  3. Applied add-sqr-sqrt2.0

    \[\leadsto \frac{a \cdot \color{blue}{\left(\sqrt{{k}^{m}} \cdot \sqrt{{k}^{m}}\right)}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]

  4. Applied associate-*r*2.0

    \[\leadsto \frac{\color{blue}{\left(a \cdot \sqrt{{k}^{m}}\right) \cdot \sqrt{{k}^{m}}}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]

  5. Final simplification2.0

    \[\leadsto \frac{\sqrt{{k}^{m}} \cdot \left(\sqrt{{k}^{m}} \cdot a\right)}{k \cdot k + \left(10 \cdot k + 1\right)}\]

Reproduce

herbie shell --seed 2019162 +o rules:numerics
(FPCore (a k m)
  :name "Falkner and Boettcher, Appendix A"
  (/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k))))