Average Error: 0.6 → 0.4
Time: 7.7s
Precision: 64
$e^{1} - e^{x}$
$\left(\sqrt{e^{x}} + \sqrt{e^{1}}\right) \cdot \left(\sqrt{e^{1}} - \sqrt{e^{x}}\right)$
e^{1} - e^{x}
\left(\sqrt{e^{x}} + \sqrt{e^{1}}\right) \cdot \left(\sqrt{e^{1}} - \sqrt{e^{x}}\right)
double f(double x) {
double r6968355 = 1.0;
double r6968356 = exp(r6968355);
double r6968357 = x;
double r6968358 = exp(r6968357);
double r6968359 = r6968356 - r6968358;
return r6968359;
}


double f(double x) {
double r6968360 = x;
double r6968361 = exp(r6968360);
double r6968362 = sqrt(r6968361);
double r6968363 = 1.0;
double r6968364 = exp(r6968363);
double r6968365 = sqrt(r6968364);
double r6968366 = r6968362 + r6968365;
double r6968367 = r6968365 - r6968362;
double r6968368 = r6968366 * r6968367;
return r6968368;
}



# Try it out

Results

 In Out
Enter valid numbers for all inputs

# Derivation

1. Initial program 0.6

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

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

$\leadsto \color{blue}{\sqrt{e^{1}} \cdot \sqrt{e^{1}}} - \sqrt{e^{x}} \cdot \sqrt{e^{x}}$
5. Applied difference-of-squares0.4

$\leadsto \color{blue}{\left(\sqrt{e^{1}} + \sqrt{e^{x}}\right) \cdot \left(\sqrt{e^{1}} - \sqrt{e^{x}}\right)}$
6. Final simplification0.4

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

# Reproduce

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