Average Error: 0.0 → 0.0
Time: 6.4s
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 r11603136 = 1.0;
        double r11603137 = x;
        double r11603138 = r11603137 * r11603137;
        double r11603139 = r11603136 - r11603138;
        double r11603140 = sqrt(r11603139);
        return r11603140;
}
↓
double f(double x) {
        double r11603141 = 1.0;
        double r11603142 = x;
        double r11603143 = r11603142 * r11603142;
        double r11603144 = r11603141 - r11603143;
        double r11603145 = sqrt(r11603144);
        return r11603145;
}

Error

Bits error versus x

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