Average Error: 1.1 → 1.1
Time: 3.1s
Precision: binary64
\[\frac{\sqrt{a + b}}{{\left(c \cdot b\right)}^{2}} - \frac{b}{2} \cdot a\]
↓
\[\frac{\sqrt{a + b}}{{\left(c \cdot b\right)}^{2}} - \frac{b}{2} \cdot a\]
\frac{\sqrt{a + b}}{{\left(c \cdot b\right)}^{2}} - \frac{b}{2} \cdot a
↓
\frac{\sqrt{a + b}}{{\left(c \cdot b\right)}^{2}} - \frac{b}{2} \cdot a
double code(double a, double b, double c) {
	return ((double) (((double) (((double) sqrt(((double) (a + b)))) / ((double) pow(((double) (c * b)), 2.0)))) - ((double) (((double) (b / 2.0)) * a))));
}
↓
double code(double a, double b, double c) {
	return ((double) (((double) (((double) sqrt(((double) (a + b)))) / ((double) pow(((double) (c * b)), 2.0)))) - ((double) (((double) (b / 2.0)) * a))));
}

Error

Bits error versus a

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 1.1

    \[\frac{\sqrt{a + b}}{{\left(c \cdot b\right)}^{2}} - \frac{b}{2} \cdot a\]

  2. Final simplification1.1

    \[\leadsto \frac{\sqrt{a + b}}{{\left(c \cdot b\right)}^{2}} - \frac{b}{2} \cdot a\]

Reproduce

herbie shell --seed 2020153 
(FPCore (a b c)
  :name "(- (/ (sqrt (+ a b)) (pow (* c b) 2)) (* (/ b 2) a))"
  :precision binary64
  (- (/ (sqrt (+ a b)) (pow (* c b) 2.0)) (* (/ b 2.0) a)))