Average Error: 0.0 → 0.0
Time: 1.4s
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 r14591 = 1.0;
        double r14592 = x;
        double r14593 = r14592 * r14592;
        double r14594 = r14591 - r14593;
        double r14595 = sqrt(r14594);
        return r14595;
}
↓
double f(double x) {
        double r14596 = 1.0;
        double r14597 = x;
        double r14598 = r14597 * r14597;
        double r14599 = r14596 - r14598;
        double r14600 = sqrt(r14599);
        return r14600;
}

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 2019310 
(FPCore (x)
  :name "Diagrams.TwoD.Ellipse:ellipse from diagrams-lib-1.3.0.3"
  :precision binary64
  (sqrt (- 1 (* x x))))