Average Error: 0.0 → 0.0
Time: 2.4s
Precision: 64
\[\sqrt{1 - x \cdot x}\]
↓
\[\sqrt{1 - x \cdot x}\]
\sqrt{1 - x \cdot x}
↓
\sqrt{1 - x \cdot x}
double f(double x) {
        double r119117 = 1.0;
        double r119118 = x;
        double r119119 = r119118 * r119118;
        double r119120 = r119117 - r119119;
        double r119121 = sqrt(r119120);
        return r119121;
}
↓
double f(double x) {
        double r119122 = 1.0;
        double r119123 = x;
        double r119124 = r119123 * r119123;
        double r119125 = r119122 - r119124;
        double r119126 = sqrt(r119125);
        return r119126;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[\sqrt{1 - x \cdot x}\]

  2. Final simplification0.0

    \[\leadsto \sqrt{1 - x \cdot x}\]

Reproduce

herbie shell --seed 2020034 +o rules:numerics
(FPCore (x)
  :name "Diagrams.TwoD.Ellipse:ellipse from diagrams-lib-1.3.0.3"
  :precision binary64
  (sqrt (- 1 (* x x))))