Average Error: 0.5 → 0.8
Time: 26.0s
Precision: 64
• ## could not determine a ground truth for program body (more)

1. p = -3.5576636605408446e-78
2. t = 1.1871905687471456e+288
3. b = 3.081677227826355e-259
$\frac{{p}^{t}}{{b}^{\left(\frac{t + 1}{2}\right)}}$
$\frac{{p}^{t}}{{\left(\sqrt[3]{b} \cdot \sqrt[3]{b}\right)}^{\left(\frac{t + 1}{2}\right)} \cdot {\left(\sqrt[3]{b}\right)}^{\left(\frac{t + 1}{2}\right)}}$
\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;
}



# Try it out

Results

 In Out
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

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