Average Error: 0.0 → 0.0
Time: 6.3s
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 r7442086 = 1.0;
        double r7442087 = x;
        double r7442088 = r7442087 * r7442087;
        double r7442089 = r7442086 - r7442088;
        double r7442090 = sqrt(r7442089);
        return r7442090;
}
↓
double f(double x) {
        double r7442091 = 1.0;
        double r7442092 = x;
        double r7442093 = r7442092 * r7442092;
        double r7442094 = r7442091 - r7442093;
        double r7442095 = sqrt(r7442094);
        return r7442095;
}

Error

Bits error versus x

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Results

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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 2019165 
(FPCore (x)
  :name "Diagrams.TwoD.Ellipse:ellipse from diagrams-lib-1.3.0.3"
  (sqrt (- 1.0 (* x x))))