Average Error: 20.1 → 20.1
Time: 2.4s
Precision: binary64
\[\frac{a \cdot x + b \cdot \sqrt{c + {x}^{2}}}{c}\]
↓
\[\frac{a \cdot x + b \cdot \sqrt{c + {x}^{2}}}{c}\]
\frac{a \cdot x + b \cdot \sqrt{c + {x}^{2}}}{c}
↓
\frac{a \cdot x + b \cdot \sqrt{c + {x}^{2}}}{c}
double code(double a, double x, double b, double c) {
	return ((double) (((double) (((double) (a * x)) + ((double) (b * ((double) sqrt(((double) (c + ((double) pow(x, 2.0)))))))))) / c));
}
↓
double code(double a, double x, double b, double c) {
	return ((double) (((double) (((double) (a * x)) + ((double) (b * ((double) sqrt(((double) (c + ((double) pow(x, 2.0)))))))))) / c));
}

Error

Bits error versus a

Bits error versus x

Bits error versus b

Bits error versus c

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 20.1

    \[\frac{a \cdot x + b \cdot \sqrt{c + {x}^{2}}}{c}\]

  2. Final simplification20.1

    \[\leadsto \frac{a \cdot x + b \cdot \sqrt{c + {x}^{2}}}{c}\]

Reproduce

herbie shell --seed 2020152 
(FPCore (a x b c)
  :name "(/ (+ (* a x) (* b (sqrt (+ c (pow x 2))))) c)"
  :precision binary64
  (/ (+ (* a x) (* b (sqrt (+ c (pow x 2.0))))) c))