Average Error: 0.5 → 0.8
Time: 26.0s
Precision: 64
\[\frac{{p}^{t}}{{b}^{\left(\frac{t + 1}{2}\right)}}\]
\[\frac{{p}^{t}}{{\left(\sqrt[3]{b} \cdot \sqrt[3]{b}\right)}^{\left(\frac{t + 1}{2}\right)} \cdot {\left(\sqrt[3]{b}\right)}^{\left(\frac{t + 1}{2}\right)}}\]
\frac{{p}^{t}}{{b}^{\left(\frac{t + 1}{2}\right)}}
\frac{{p}^{t}}{{\left(\sqrt[3]{b} \cdot \sqrt[3]{b}\right)}^{\left(\frac{t + 1}{2}\right)} \cdot {\left(\sqrt[3]{b}\right)}^{\left(\frac{t + 1}{2}\right)}}
double f(double p, double t, double b) {
        double r3595508 = p;
        double r3595509 = t;
        double r3595510 = pow(r3595508, r3595509);
        double r3595511 = b;
        double r3595512 = 1.0;
        double r3595513 = r3595509 + r3595512;
        double r3595514 = 2.0;
        double r3595515 = r3595513 / r3595514;
        double r3595516 = pow(r3595511, r3595515);
        double r3595517 = r3595510 / r3595516;
        return r3595517;
}

double f(double p, double t, double b) {
        double r3595518 = p;
        double r3595519 = t;
        double r3595520 = pow(r3595518, r3595519);
        double r3595521 = b;
        double r3595522 = cbrt(r3595521);
        double r3595523 = r3595522 * r3595522;
        double r3595524 = 1.0;
        double r3595525 = r3595519 + r3595524;
        double r3595526 = 2.0;
        double r3595527 = r3595525 / r3595526;
        double r3595528 = pow(r3595523, r3595527);
        double r3595529 = pow(r3595522, r3595527);
        double r3595530 = r3595528 * r3595529;
        double r3595531 = r3595520 / r3595530;
        return r3595531;
}

Error

Bits error versus p

Bits error versus t

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.5

    \[\frac{{p}^{t}}{{b}^{\left(\frac{t + 1}{2}\right)}}\]
  2. Using strategy rm
  3. Applied add-cube-cbrt0.8

    \[\leadsto \frac{{p}^{t}}{{\color{blue}{\left(\left(\sqrt[3]{b} \cdot \sqrt[3]{b}\right) \cdot \sqrt[3]{b}\right)}}^{\left(\frac{t + 1}{2}\right)}}\]
  4. Applied unpow-prod-down0.8

    \[\leadsto \frac{{p}^{t}}{\color{blue}{{\left(\sqrt[3]{b} \cdot \sqrt[3]{b}\right)}^{\left(\frac{t + 1}{2}\right)} \cdot {\left(\sqrt[3]{b}\right)}^{\left(\frac{t + 1}{2}\right)}}}\]
  5. Final simplification0.8

    \[\leadsto \frac{{p}^{t}}{{\left(\sqrt[3]{b} \cdot \sqrt[3]{b}\right)}^{\left(\frac{t + 1}{2}\right)} \cdot {\left(\sqrt[3]{b}\right)}^{\left(\frac{t + 1}{2}\right)}}\]

Reproduce

herbie shell --seed 1 
(FPCore (p t b)
  :name "(p^t)/(b^((t+1)/2))"
  :precision binary64
  (/ (pow p t) (pow b (/ (+ t 1) 2))))