Average Error: 30.6 → 30.6
Time: 1.5s
Precision: binary64
\[\frac{\cos^{-1} \left(\frac{x}{y}\right)}{\sqrt{y \cdot y - x \cdot x}}\]
↓
\[\frac{\cos^{-1} \left(\frac{x}{y}\right)}{\sqrt{y \cdot y - x \cdot x}}\]
\frac{\cos^{-1} \left(\frac{x}{y}\right)}{\sqrt{y \cdot y - x \cdot x}}
↓
\frac{\cos^{-1} \left(\frac{x}{y}\right)}{\sqrt{y \cdot y - x \cdot x}}
double code(double x, double y) {
	return ((double) (((double) acos(((double) (x / y)))) / ((double) sqrt(((double) (((double) (y * y)) - ((double) (x * x))))))));
}
↓
double code(double x, double y) {
	return ((double) (((double) acos(((double) (x / y)))) / ((double) sqrt(((double) (((double) (y * y)) - ((double) (x * x))))))));
}

Error

Bits error versus x

Bits error versus y

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Results

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Derivation

  1. Initial program 30.6

    \[\frac{\cos^{-1} \left(\frac{x}{y}\right)}{\sqrt{y \cdot y - x \cdot x}}\]

  2. Final simplification30.6

    \[\leadsto \frac{\cos^{-1} \left(\frac{x}{y}\right)}{\sqrt{y \cdot y - x \cdot x}}\]

Reproduce

herbie shell --seed 2020153 
(FPCore (x y)
  :name "(/ (acos (/ x y)) (sqrt (- (* y y) (* x x))))"
  :precision binary64
  (/ (acos (/ x y)) (sqrt (- (* y y) (* x x)))))