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 r131605 = 1.0;
        double r131606 = x;
        double r131607 = r131606 * r131606;
        double r131608 = r131605 - r131607;
        double r131609 = sqrt(r131608);
        return r131609;
}
↓
double f(double x) {
        double r131610 = 1.0;
        double r131611 = x;
        double r131612 = r131611 * r131611;
        double r131613 = r131610 - r131612;
        double r131614 = sqrt(r131613);
        return r131614;
}

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 2019198 +o rules:numerics
(FPCore (x)
  :name "Diagrams.TwoD.Ellipse:ellipse from diagrams-lib-1.3.0.3"
  (sqrt (- 1.0 (* x x))))