Average Error: 0.0 → 0.0
Time: 11.7s
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 r7791819 = 1.0;
        double r7791820 = x;
        double r7791821 = r7791820 * r7791820;
        double r7791822 = r7791819 - r7791821;
        double r7791823 = sqrt(r7791822);
        return r7791823;
}
↓
double f(double x) {
        double r7791824 = 1.0;
        double r7791825 = x;
        double r7791826 = r7791825 * r7791825;
        double r7791827 = r7791824 - r7791826;
        double r7791828 = sqrt(r7791827);
        return r7791828;
}

Error

Bits error versus x

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Results

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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 2019168 +o rules:numerics
(FPCore (x)
  :name "Diagrams.TwoD.Ellipse:ellipse from diagrams-lib-1.3.0.3"
  (sqrt (- 1.0 (* x x))))