Average Error: 0.0 → 0.0
Time: 1.1s
Precision: binary64
\[\sqrt{1 - x \cdot x}\]
↓
\[\sqrt{\left(\sqrt{1} + x\right) \cdot \left(\sqrt{1} - x\right)}\]
\sqrt{1 - x \cdot x}
↓
\sqrt{\left(\sqrt{1} + x\right) \cdot \left(\sqrt{1} - x\right)}
double code(double x) {
	return ((double) sqrt(((double) (1.0 - ((double) (x * x))))));
}
↓
double code(double x) {
	return ((double) sqrt(((double) (((double) (((double) sqrt(1.0)) + x)) * ((double) (((double) sqrt(1.0)) - x))))));
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[\sqrt{1 - x \cdot x}\]
  2. Using strategy rm

  3. Applied add-sqr-sqrt0.0

    \[\leadsto \sqrt{\color{blue}{\sqrt{1} \cdot \sqrt{1}} - x \cdot x}\]

  4. Applied difference-of-squares0.0

    \[\leadsto \sqrt{\color{blue}{\left(\sqrt{1} + x\right) \cdot \left(\sqrt{1} - x\right)}}\]

  5. Final simplification0.0

    \[\leadsto \sqrt{\left(\sqrt{1} + x\right) \cdot \left(\sqrt{1} - x\right)}\]

Reproduce

herbie shell --seed 2020148 
(FPCore (x)
  :name "Diagrams.TwoD.Ellipse:ellipse from diagrams-lib-1.3.0.3"
  :precision binary64
  (sqrt (- 1.0 (* x x))))