Average Error: 0.6 → 0.0
Time: 8.8s
Precision: 64
• ## could not determine a ground truth for program body (more)

1. x = 1.3100436170095023e+65
$e^{x + 1} - e^{x}$
$\left(\sqrt{e^{x}} \cdot \sqrt{e^{1}} - \sqrt{e^{x}}\right) \cdot \left(\sqrt{e^{x}} + \sqrt{e^{x + 1}}\right)$
e^{x + 1} - e^{x}
\left(\sqrt{e^{x}} \cdot \sqrt{e^{1}} - \sqrt{e^{x}}\right) \cdot \left(\sqrt{e^{x}} + \sqrt{e^{x + 1}}\right)
double f(double x) {
double r7748974 = x;
double r7748975 = 1.0;
double r7748976 = r7748974 + r7748975;
double r7748977 = exp(r7748976);
double r7748978 = exp(r7748974);
double r7748979 = r7748977 - r7748978;
return r7748979;
}


double f(double x) {
double r7748980 = x;
double r7748981 = exp(r7748980);
double r7748982 = sqrt(r7748981);
double r7748983 = 1.0;
double r7748984 = exp(r7748983);
double r7748985 = sqrt(r7748984);
double r7748986 = r7748982 * r7748985;
double r7748987 = r7748986 - r7748982;
double r7748988 = r7748980 + r7748983;
double r7748989 = exp(r7748988);
double r7748990 = sqrt(r7748989);
double r7748991 = r7748982 + r7748990;
double r7748992 = r7748987 * r7748991;
return r7748992;
}



# Try it out

Results

 In Out
Enter valid numbers for all inputs

# Derivation

1. Initial program 0.6

$e^{x + 1} - e^{x}$
2. Using strategy rm

$\leadsto e^{x + 1} - \color{blue}{\sqrt{e^{x}} \cdot \sqrt{e^{x}}}$

$\leadsto \color{blue}{\sqrt{e^{x + 1}} \cdot \sqrt{e^{x + 1}}} - \sqrt{e^{x}} \cdot \sqrt{e^{x}}$
5. Applied difference-of-squares0.0

$\leadsto \color{blue}{\left(\sqrt{e^{x + 1}} + \sqrt{e^{x}}\right) \cdot \left(\sqrt{e^{x + 1}} - \sqrt{e^{x}}\right)}$
6. Using strategy rm
7. Applied exp-sum0.0

$\leadsto \left(\sqrt{e^{x + 1}} + \sqrt{e^{x}}\right) \cdot \left(\sqrt{\color{blue}{e^{x} \cdot e^{1}}} - \sqrt{e^{x}}\right)$
8. Applied sqrt-prod0.0

$\leadsto \left(\sqrt{e^{x + 1}} + \sqrt{e^{x}}\right) \cdot \left(\color{blue}{\sqrt{e^{x}} \cdot \sqrt{e^{1}}} - \sqrt{e^{x}}\right)$
9. Final simplification0.0

$\leadsto \left(\sqrt{e^{x}} \cdot \sqrt{e^{1}} - \sqrt{e^{x}}\right) \cdot \left(\sqrt{e^{x}} + \sqrt{e^{x + 1}}\right)$

# Reproduce

herbie shell --seed 1
(FPCore (x)
:name "exp(x+1)-exp(x)"
(- (exp (+ x 1.0)) (exp x)))