Average Error: 3.4 → 0.2
Time: 5.2s
Precision: 64
$0.9899999999999999911182158029987476766109 \lt e \lt 1$
$\sqrt{1 - e \cdot e}$
$\sqrt{\left(\sqrt{1} + e\right) \cdot \left(\sqrt{1} - e\right)}$
\sqrt{1 - e \cdot e}
\sqrt{\left(\sqrt{1} + e\right) \cdot \left(\sqrt{1} - e\right)}
double f(double e) {
double r901120 = 1.0;
double r901121 = e;
double r901122 = r901121 * r901121;
double r901123 = r901120 - r901122;
double r901124 = sqrt(r901123);
return r901124;
}


double f(double e) {
double r901125 = 1.0;
double r901126 = sqrt(r901125);
double r901127 = e;
double r901128 = r901126 + r901127;
double r901129 = r901126 - r901127;
double r901130 = r901128 * r901129;
double r901131 = sqrt(r901130);
return r901131;
}



# Try it out

Results

 In Out
Enter valid numbers for all inputs

# Derivation

1. Initial program 3.4

$\sqrt{1 - e \cdot e}$
2. Using strategy rm

$\leadsto \sqrt{\color{blue}{\sqrt{1} \cdot \sqrt{1}} - e \cdot e}$
4. Applied difference-of-squares0.2

$\leadsto \sqrt{\color{blue}{\left(\sqrt{1} + e\right) \cdot \left(\sqrt{1} - e\right)}}$
5. Final simplification0.2

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

# Reproduce

herbie shell --seed 1
(FPCore (e)
:name "sqrt(1-e*e)"
:precision binary64
:pre (< 0.98999999999999999 e 1)
(sqrt (- 1 (* e e))))