Average Error: 24.9 → 24.9
Time: 702.0ms
Precision: binary64
\[\frac{x}{\sqrt{d \cdot d + x \cdot x}}\]
↓
\[\frac{x}{\sqrt{d \cdot d + x \cdot x}}\]
\frac{x}{\sqrt{d \cdot d + x \cdot x}}
↓
\frac{x}{\sqrt{d \cdot d + x \cdot x}}
double code(double x, double d) {
	return ((double) (x / ((double) sqrt(((double) (((double) (d * d)) + ((double) (x * x))))))));
}
↓
double code(double x, double d) {
	return ((double) (x / ((double) sqrt(((double) (((double) (d * d)) + ((double) (x * x))))))));
}

Error

Bits error versus x

Bits error versus d

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 24.9

    \[\frac{x}{\sqrt{d \cdot d + x \cdot x}}\]

  2. Final simplification24.9

    \[\leadsto \frac{x}{\sqrt{d \cdot d + x \cdot x}}\]

Reproduce

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