Average Error: 15.1 → 15.1
Time: 1.5s
Precision: binary64
\[\frac{1}{\sqrt{1 + {x}^{2}}} - 1\]
↓
\[\frac{1}{\sqrt{1 + {x}^{2}}} - 1\]
\frac{1}{\sqrt{1 + {x}^{2}}} - 1
↓
\frac{1}{\sqrt{1 + {x}^{2}}} - 1
double code(double x) {
	return ((double) (((double) (1.0 / ((double) sqrt(((double) (1.0 + ((double) pow(x, 2.0)))))))) - 1.0));
}
↓
double code(double x) {
	return ((double) (((double) (1.0 / ((double) sqrt(((double) (1.0 + ((double) pow(x, 2.0)))))))) - 1.0));
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 15.1

    \[\frac{1}{\sqrt{1 + {x}^{2}}} - 1\]

  2. Final simplification15.1

    \[\leadsto \frac{1}{\sqrt{1 + {x}^{2}}} - 1\]

Reproduce

herbie shell --seed 2020152 
(FPCore (x)
  :name "(- (/ 1 (sqrt (+ 1 (pow x 2)))) 1)"
  :precision binary64
  (- (/ 1.0 (sqrt (+ 1.0 (pow x 2.0)))) 1.0))