Average Error: 31.2 → 31.2
Time: 1.4s
Precision: binary64
\[\sqrt{1 + {x}^{2}} - 1\]
↓
\[\sqrt{1 + {x}^{2}} - 1\]
\sqrt{1 + {x}^{2}} - 1
↓
\sqrt{1 + {x}^{2}} - 1
double code(double x) {
	return ((double) (((double) sqrt(((double) (1.0 + ((double) pow(x, 2.0)))))) - 1.0));
}
↓
double code(double x) {
	return ((double) (((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

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Derivation

  1. Initial program 31.2

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

  2. Final simplification31.2

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

Reproduce

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