Average Error: 0.9 → 0.6
Time: 23.8s
Precision: 64
• ## could not determine a ground truth for program body (more)

1. k = 1.3100436170095023e+65
2. x = -7.418868410425896e-99
$\frac{\sinh \left(k - k \cdot x\right)}{\sinh k}$
$\frac{-1}{3} \cdot \left(k \cdot \left(x \cdot k\right)\right) + \left(1 - x\right)$
\frac{\sinh \left(k - k \cdot x\right)}{\sinh k}
\frac{-1}{3} \cdot \left(k \cdot \left(x \cdot k\right)\right) + \left(1 - x\right)
double f(double k, double x) {
double r30034149 = k;
double r30034150 = x;
double r30034151 = r30034149 * r30034150;
double r30034152 = r30034149 - r30034151;
double r30034153 = sinh(r30034152);
double r30034154 = sinh(r30034149);
double r30034155 = r30034153 / r30034154;
return r30034155;
}


double f(double k, double x) {
double r30034156 = -0.3333333333333333;
double r30034157 = k;
double r30034158 = x;
double r30034159 = r30034158 * r30034157;
double r30034160 = r30034157 * r30034159;
double r30034161 = r30034156 * r30034160;
double r30034162 = 1.0;
double r30034163 = r30034162 - r30034158;
double r30034164 = r30034161 + r30034163;
return r30034164;
}



# Try it out

Results

 In Out
Enter valid numbers for all inputs

# Derivation

1. Initial program 0.9

$\frac{\sinh \left(k - k \cdot x\right)}{\sinh k}$
2. Taylor expanded around 0 0.6

$\leadsto \color{blue}{1 - \left(x + \frac{1}{3} \cdot \left(x \cdot {k}^{2}\right)\right)}$
3. Simplified0.6

$\leadsto \color{blue}{\left(1 - x\right) + \frac{-1}{3} \cdot \left(k \cdot \left(x \cdot k\right)\right)}$
4. Final simplification0.6

$\leadsto \frac{-1}{3} \cdot \left(k \cdot \left(x \cdot k\right)\right) + \left(1 - x\right)$

# Reproduce

herbie shell --seed 1
(FPCore (k x)
:name "sinh(k - k * x) / sinh(k)"
(/ (sinh (- k (* k x))) (sinh k)))