Average Error: 12.1 → 12.1
Time: 5.3s
Precision: binary64
\[\left(\frac{x}{{a}^{2}} + \frac{y}{{b}^{2}}\right) + \frac{z}{{b}^{c}}\]
↓
\[\left(\frac{x}{{a}^{2}} + \frac{y}{{b}^{2}}\right) + \frac{z}{{b}^{c}}\]
\left(\frac{x}{{a}^{2}} + \frac{y}{{b}^{2}}\right) + \frac{z}{{b}^{c}}
↓
\left(\frac{x}{{a}^{2}} + \frac{y}{{b}^{2}}\right) + \frac{z}{{b}^{c}}
double code(double x, double a, double y, double b, double z, double c) {
	return ((double) (((double) (((double) (x / ((double) pow(a, 2.0)))) + ((double) (y / ((double) pow(b, 2.0)))))) + ((double) (z / ((double) pow(b, c))))));
}
↓
double code(double x, double a, double y, double b, double z, double c) {
	return ((double) (((double) (((double) (x / ((double) pow(a, 2.0)))) + ((double) (y / ((double) pow(b, 2.0)))))) + ((double) (z / ((double) pow(b, c))))));
}

Error

Bits error versus x

Bits error versus a

Bits error versus y

Bits error versus b

Bits error versus z

Bits error versus c

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 12.1

    \[\left(\frac{x}{{a}^{2}} + \frac{y}{{b}^{2}}\right) + \frac{z}{{b}^{c}}\]

  2. Final simplification12.1

    \[\leadsto \left(\frac{x}{{a}^{2}} + \frac{y}{{b}^{2}}\right) + \frac{z}{{b}^{c}}\]

Reproduce

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