Average Error: 2.0 → 2.0
Time: 5.3s
Precision: 64
\[\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]
↓
\[\left({k}^{m} \cdot \frac{1}{k \cdot \left(10 + k\right) + 1}\right) \cdot a\]
\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}
↓
\left({k}^{m} \cdot \frac{1}{k \cdot \left(10 + k\right) + 1}\right) \cdot a
double f(double a, double k, double m) {
        double r192111 = a;
        double r192112 = k;
        double r192113 = m;
        double r192114 = pow(r192112, r192113);
        double r192115 = r192111 * r192114;
        double r192116 = 1.0;
        double r192117 = 10.0;
        double r192118 = r192117 * r192112;
        double r192119 = r192116 + r192118;
        double r192120 = r192112 * r192112;
        double r192121 = r192119 + r192120;
        double r192122 = r192115 / r192121;
        return r192122;
}
↓
double f(double a, double k, double m) {
        double r192123 = k;
        double r192124 = m;
        double r192125 = pow(r192123, r192124);
        double r192126 = 1.0;
        double r192127 = 10.0;
        double r192128 = r192127 + r192123;
        double r192129 = r192123 * r192128;
        double r192130 = 1.0;
        double r192131 = r192129 + r192130;
        double r192132 = r192126 / r192131;
        double r192133 = r192125 * r192132;
        double r192134 = a;
        double r192135 = r192133 * r192134;
        return r192135;
}

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. Simplified2.0

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

  4. Applied div-inv2.0

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

  5. Final simplification2.0

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

Reproduce

herbie shell --seed 2020002 
(FPCore (a k m)
  :name "Falkner and Boettcher, Appendix A"
  :precision binary64
  (/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k))))