Average Error: 0.1 → 0.1
Time: 1.2s
Precision: binary64
\[\mathsf{fma}\left(\cos x, \frac{1}{5 \cdot 10^{3}}, z\right)\]
↓
\[\mathsf{fma}\left(\cos x, \frac{1}{5 \cdot 10^{3}}, z\right)\]
\mathsf{fma}\left(\cos x, \frac{1}{5 \cdot 10^{3}}, z\right)
↓
\mathsf{fma}\left(\cos x, \frac{1}{5 \cdot 10^{3}}, z\right)
double code(double x, double z) {
	return ((double) fma(((double) cos(x)), ((double) (1.0 / 5000.0)), z));
}
↓
double code(double x, double z) {
	return ((double) fma(((double) cos(x)), ((double) (1.0 / 5000.0)), z));
}

Error

Bits error versus x

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[\mathsf{fma}\left(\cos x, \frac{1}{5 \cdot 10^{3}}, z\right)\]

  2. Final simplification0.1

    \[\leadsto \mathsf{fma}\left(\cos x, \frac{1}{5 \cdot 10^{3}}, z\right)\]

Reproduce

herbie shell --seed 2020153 
(FPCore (x z)
  :name "(fma (cos x) (/ 1.0 5000.0) z)"
  :precision binary64
  (fma (cos x) (/ 1.0 5000.0) z))