Average Error: 0.2 → 0.2
Time: 6.3s
Precision: binary64
\[\mathsf{fma}\left(x, y, z\right) - \frac{\sqrt{x} + \sqrt{y}}{\sqrt{z}}\]
↓
\[\mathsf{fma}\left(x, y, z\right) - \frac{\sqrt{x} + \sqrt{y}}{\sqrt{z}}\]
\mathsf{fma}\left(x, y, z\right) - \frac{\sqrt{x} + \sqrt{y}}{\sqrt{z}}
↓
\mathsf{fma}\left(x, y, z\right) - \frac{\sqrt{x} + \sqrt{y}}{\sqrt{z}}
double code(double x, double y, double z) {
	return ((double) (((double) fma(x, y, z)) - ((double) (((double) (((double) sqrt(x)) + ((double) sqrt(y)))) / ((double) sqrt(z))))));
}
↓
double code(double x, double y, double z) {
	return ((double) (((double) fma(x, y, z)) - ((double) (((double) (((double) sqrt(x)) + ((double) sqrt(y)))) / ((double) sqrt(z))))));
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.2

    \[\mathsf{fma}\left(x, y, z\right) - \frac{\sqrt{x} + \sqrt{y}}{\sqrt{z}}\]

  2. Final simplification0.2

    \[\leadsto \mathsf{fma}\left(x, y, z\right) - \frac{\sqrt{x} + \sqrt{y}}{\sqrt{z}}\]

Reproduce

herbie shell --seed 2020153 
(FPCore (x y z)
  :name "(- (fma x y z) (/ (+ (sqrt x) (sqrt y)) (sqrt z)))"
  :precision binary64
  (- (fma x y z) (/ (+ (sqrt x) (sqrt y)) (sqrt z))))