Average Error: 2.0 → 2.0
Time: 20.3s
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 r8765370 = a;
        double r8765371 = k;
        double r8765372 = m;
        double r8765373 = pow(r8765371, r8765372);
        double r8765374 = r8765370 * r8765373;
        double r8765375 = 1.0;
        double r8765376 = 10.0;
        double r8765377 = r8765376 * r8765371;
        double r8765378 = r8765375 + r8765377;
        double r8765379 = r8765371 * r8765371;
        double r8765380 = r8765378 + r8765379;
        double r8765381 = r8765374 / r8765380;
        return r8765381;
}
↓
double f(double a, double k, double m) {
        double r8765382 = k;
        double r8765383 = m;
        double r8765384 = pow(r8765382, r8765383);
        double r8765385 = sqrt(r8765384);
        double r8765386 = a;
        double r8765387 = r8765385 * r8765386;
        double r8765388 = r8765385 * r8765387;
        double r8765389 = r8765382 * r8765382;
        double r8765390 = 10.0;
        double r8765391 = r8765390 * r8765382;
        double r8765392 = 1.0;
        double r8765393 = r8765391 + r8765392;
        double r8765394 = r8765389 + r8765393;
        double r8765395 = r8765388 / r8765394;
        return r8765395;
}

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))))