Average Error: 2.3 → 2.3
Time: 4.9s
Precision: 64
\[\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]
↓
\[\left(a \cdot {k}^{m}\right) \cdot \frac{\frac{1}{\sqrt{1 + k \cdot \left(10 + k\right)}}}{\sqrt{1 + k \cdot \left(10 + k\right)}}\]
\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}
↓
\left(a \cdot {k}^{m}\right) \cdot \frac{\frac{1}{\sqrt{1 + k \cdot \left(10 + k\right)}}}{\sqrt{1 + k \cdot \left(10 + k\right)}}
double f(double a, double k, double m) {
        double r239190 = a;
        double r239191 = k;
        double r239192 = m;
        double r239193 = pow(r239191, r239192);
        double r239194 = r239190 * r239193;
        double r239195 = 1.0;
        double r239196 = 10.0;
        double r239197 = r239196 * r239191;
        double r239198 = r239195 + r239197;
        double r239199 = r239191 * r239191;
        double r239200 = r239198 + r239199;
        double r239201 = r239194 / r239200;
        return r239201;
}
↓
double f(double a, double k, double m) {
        double r239202 = a;
        double r239203 = k;
        double r239204 = m;
        double r239205 = pow(r239203, r239204);
        double r239206 = r239202 * r239205;
        double r239207 = 1.0;
        double r239208 = 1.0;
        double r239209 = 10.0;
        double r239210 = r239209 + r239203;
        double r239211 = r239203 * r239210;
        double r239212 = r239208 + r239211;
        double r239213 = sqrt(r239212);
        double r239214 = r239207 / r239213;
        double r239215 = r239214 / r239213;
        double r239216 = r239206 * r239215;
        return r239216;
}

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 2.3

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

  3. Applied div-inv2.3

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

  4. Simplified2.2

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

  6. Applied add-sqr-sqrt2.3

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

  7. Applied associate-/r*2.3

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

  8. Final simplification2.3

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

Reproduce

herbie shell --seed 2020024 
(FPCore (a k m)
  :name "Falkner and Boettcher, Appendix A"
  :precision binary64
  (/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k))))