Average Error: 2.4 → 1.0
Time: 48.0s
Precision: 64
\[\log \left(\frac{1}{2} \cdot \left(\sqrt{4 \cdot {e}^{x} + 1} - 1\right)\right)\]
\[\sqrt[3]{\left(\log \left(\left(\sqrt{1 + 4 \cdot {e}^{x}} - 1\right) \cdot \frac{1}{2}\right) \cdot \log \left(\left(\sqrt{1 + 4 \cdot {e}^{x}} - 1\right) \cdot \frac{1}{2}\right)\right) \cdot \log \left(\left(\sqrt{1 + 4 \cdot {e}^{x}} - 1\right) \cdot \frac{1}{2}\right)}\]
\log \left(\frac{1}{2} \cdot \left(\sqrt{4 \cdot {e}^{x} + 1} - 1\right)\right)
\sqrt[3]{\left(\log \left(\left(\sqrt{1 + 4 \cdot {e}^{x}} - 1\right) \cdot \frac{1}{2}\right) \cdot \log \left(\left(\sqrt{1 + 4 \cdot {e}^{x}} - 1\right) \cdot \frac{1}{2}\right)\right) \cdot \log \left(\left(\sqrt{1 + 4 \cdot {e}^{x}} - 1\right) \cdot \frac{1}{2}\right)}
double f(double e, double x) {
        double r12866031 = 1.0;
        double r12866032 = 2.0;
        double r12866033 = r12866031 / r12866032;
        double r12866034 = 4.0;
        double r12866035 = e;
        double r12866036 = x;
        double r12866037 = pow(r12866035, r12866036);
        double r12866038 = r12866034 * r12866037;
        double r12866039 = r12866038 + r12866031;
        double r12866040 = sqrt(r12866039);
        double r12866041 = r12866040 - r12866031;
        double r12866042 = r12866033 * r12866041;
        double r12866043 = log(r12866042);
        return r12866043;
}

double f(double e, double x) {
        double r12866044 = 1.0;
        double r12866045 = 4.0;
        double r12866046 = e;
        double r12866047 = x;
        double r12866048 = pow(r12866046, r12866047);
        double r12866049 = r12866045 * r12866048;
        double r12866050 = r12866044 + r12866049;
        double r12866051 = sqrt(r12866050);
        double r12866052 = r12866051 - r12866044;
        double r12866053 = 2.0;
        double r12866054 = r12866044 / r12866053;
        double r12866055 = r12866052 * r12866054;
        double r12866056 = log(r12866055);
        double r12866057 = r12866056 * r12866056;
        double r12866058 = r12866057 * r12866056;
        double r12866059 = cbrt(r12866058);
        return r12866059;
}

Error

Bits error versus e

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 2.4

    \[\log \left(\frac{1}{2} \cdot \left(\sqrt{4 \cdot {e}^{x} + 1} - 1\right)\right)\]
  2. Using strategy rm
  3. Applied add-cbrt-cube1.0

    \[\leadsto \color{blue}{\sqrt[3]{\left(\log \left(\frac{1}{2} \cdot \left(\sqrt{4 \cdot {e}^{x} + 1} - 1\right)\right) \cdot \log \left(\frac{1}{2} \cdot \left(\sqrt{4 \cdot {e}^{x} + 1} - 1\right)\right)\right) \cdot \log \left(\frac{1}{2} \cdot \left(\sqrt{4 \cdot {e}^{x} + 1} - 1\right)\right)}}\]
  4. Final simplification1.0

    \[\leadsto \sqrt[3]{\left(\log \left(\left(\sqrt{1 + 4 \cdot {e}^{x}} - 1\right) \cdot \frac{1}{2}\right) \cdot \log \left(\left(\sqrt{1 + 4 \cdot {e}^{x}} - 1\right) \cdot \frac{1}{2}\right)\right) \cdot \log \left(\left(\sqrt{1 + 4 \cdot {e}^{x}} - 1\right) \cdot \frac{1}{2}\right)}\]

Reproduce

herbie shell --seed 1 
(FPCore (e x)
  :name "log(1/2 (sqrt(4 e^x + 1) - 1))"
  (log (* (/ 1.0 2.0) (- (sqrt (+ (* 4.0 (pow e x)) 1.0)) 1.0))))