Average Error: 0.6 → 0.0
Time: 11.9s
Precision: 64
• ## could not determine a ground truth for program body (more)

1. x = 1.3100436170095023e+65
$e^{x} - e^{x + 1}$
$\left(\sqrt{e^{x}} + \sqrt{e^{x + 1}}\right) \cdot \left(\sqrt{e^{x}} - \sqrt{e^{x}} \cdot \sqrt{e^{1}}\right)$
e^{x} - e^{x + 1}
\left(\sqrt{e^{x}} + \sqrt{e^{x + 1}}\right) \cdot \left(\sqrt{e^{x}} - \sqrt{e^{x}} \cdot \sqrt{e^{1}}\right)
double f(double x) {
double r1609764 = x;
double r1609765 = exp(r1609764);
double r1609766 = 1.0;
double r1609767 = r1609764 + r1609766;
double r1609768 = exp(r1609767);
double r1609769 = r1609765 - r1609768;
return r1609769;
}


double f(double x) {
double r1609770 = x;
double r1609771 = exp(r1609770);
double r1609772 = sqrt(r1609771);
double r1609773 = 1.0;
double r1609774 = r1609770 + r1609773;
double r1609775 = exp(r1609774);
double r1609776 = sqrt(r1609775);
double r1609777 = r1609772 + r1609776;
double r1609778 = exp(r1609773);
double r1609779 = sqrt(r1609778);
double r1609780 = r1609772 * r1609779;
double r1609781 = r1609772 - r1609780;
double r1609782 = r1609777 * r1609781;
return r1609782;
}



# Try it out

Results

 In Out
Enter valid numbers for all inputs

# Derivation

1. Initial program 0.6

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

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

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

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

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

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

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

# Reproduce

herbie shell --seed 1
(FPCore (x)
:name "exp(x)-exp(x+1)"
:precision binary64
(- (exp x) (exp (+ x 1))))