Average Error: 0.0 → 0.0
Time: 3.6s
Precision: 64
\[\sqrt{1.0 - x \cdot x}\]
↓
\[\sqrt{1.0 - x \cdot x}\]
\sqrt{1.0 - x \cdot x}
↓
\sqrt{1.0 - x \cdot x}
double f(double x) {
        double r2610140 = 1.0;
        double r2610141 = x;
        double r2610142 = r2610141 * r2610141;
        double r2610143 = r2610140 - r2610142;
        double r2610144 = sqrt(r2610143);
        return r2610144;
}
↓
double f(double x) {
        double r2610145 = 1.0;
        double r2610146 = x;
        double r2610147 = r2610146 * r2610146;
        double r2610148 = r2610145 - r2610147;
        double r2610149 = sqrt(r2610148);
        return r2610149;
}

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

    \[\sqrt{1.0 - x \cdot x}\]

  2. Final simplification0.0

    \[\leadsto \sqrt{1.0 - x \cdot x}\]

Reproduce

herbie shell --seed 2019156 +o rules:numerics
(FPCore (x)
  :name "Diagrams.TwoD.Ellipse:ellipse from diagrams-lib-1.3.0.3"
  (sqrt (- 1.0 (* x x))))