Average Error: 23.4 → 23.4
Time: 815.0ms
Precision: binary64
\[\sqrt{x \cdot x + 99 \cdot 99} - x\]
↓
\[\sqrt{x \cdot x + 99 \cdot 99} - x\]
\sqrt{x \cdot x + 99 \cdot 99} - x
↓
\sqrt{x \cdot x + 99 \cdot 99} - x
double code(double x) {
	return ((double) (((double) sqrt(((double) (((double) (x * x)) + ((double) (99.0 * 99.0)))))) - x));
}
↓
double code(double x) {
	return ((double) (((double) sqrt(((double) (((double) (x * x)) + ((double) (99.0 * 99.0)))))) - x));
}

Error

Bits error versus x

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Results

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Derivation

  1. Initial program 23.4

    \[\sqrt{x \cdot x + 99 \cdot 99} - x\]

  2. Final simplification23.4

    \[\leadsto \sqrt{x \cdot x + 99 \cdot 99} - x\]

Reproduce

herbie shell --seed 2020152 
(FPCore (x)
  :name "(- (sqrt (+ (* x x) (* 99 99))) x)"
  :precision binary64
  (- (sqrt (+ (* x x) (* 99.0 99.0))) x))