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 r120085 = 1.0;
        double r120086 = x;
        double r120087 = r120086 * r120086;
        double r120088 = r120085 - r120087;
        double r120089 = sqrt(r120088);
        return r120089;
}
↓
double f(double x) {
        double r120090 = 1.0;
        double r120091 = x;
        double r120092 = r120091 * r120091;
        double r120093 = r120090 - r120092;
        double r120094 = sqrt(r120093);
        return r120094;
}

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 2019325 
(FPCore (x)
  :name "Diagrams.TwoD.Ellipse:ellipse from diagrams-lib-1.3.0.3"
  :precision binary64
  (sqrt (- 1 (* x x))))