Average Error: 0.0 → 0.0
Time: 1.3s
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 r118078 = 1.0;
        double r118079 = x;
        double r118080 = r118079 * r118079;
        double r118081 = r118078 - r118080;
        double r118082 = sqrt(r118081);
        return r118082;
}
↓
double f(double x) {
        double r118083 = 1.0;
        double r118084 = x;
        double r118085 = r118084 * r118084;
        double r118086 = r118083 - r118085;
        double r118087 = sqrt(r118086);
        return r118087;
}

Error

Bits error versus x

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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 2019196 +o rules:numerics
(FPCore (x)
  :name "Diagrams.TwoD.Ellipse:ellipse from diagrams-lib-1.3.0.3"
  (sqrt (- 1.0 (* x x))))