Average Error: 0.6 → 0.0
Time: 12.9s
Precision: 64
• could not determine a ground truth for program body (more)

1. x = 1.3100436170095023e+65
$e^{x} - e^{x + 1}$
$\left(\sqrt{e^{x}} + \sqrt{e^{1 + x}}\right) \cdot \left(\sqrt{e^{x}} - \sqrt{e^{1 + x}}\right)$
e^{x} - e^{x + 1}
\left(\sqrt{e^{x}} + \sqrt{e^{1 + x}}\right) \cdot \left(\sqrt{e^{x}} - \sqrt{e^{1 + x}}\right)
double f(double x) {
double r8587751 = x;
double r8587752 = exp(r8587751);
double r8587753 = 1.0;
double r8587754 = r8587751 + r8587753;
double r8587755 = exp(r8587754);
double r8587756 = r8587752 - r8587755;
return r8587756;
}

double f(double x) {
double r8587757 = x;
double r8587758 = exp(r8587757);
double r8587759 = sqrt(r8587758);
double r8587760 = 1.0;
double r8587761 = r8587760 + r8587757;
double r8587762 = exp(r8587761);
double r8587763 = sqrt(r8587762);
double r8587764 = r8587759 + r8587763;
double r8587765 = r8587759 - r8587763;
double r8587766 = r8587764 * r8587765;
return r8587766;
}

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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. Final simplification0.0

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

Reproduce

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