Average Error: 44.9 → 44.9
Time: 10.4s
Precision: binary64
\[\mathsf{fma}\left(x, y, z\right) - \left(1 + \left(x \cdot y + z\right)\right)\]
↓
\[\left(\mathsf{fma}\left(x, y, z\right) + -1\right) - \left(z + x \cdot y\right)\]
\mathsf{fma}\left(x, y, z\right) - \left(1 + \left(x \cdot y + z\right)\right)
↓
\left(\mathsf{fma}\left(x, y, z\right) + -1\right) - \left(z + x \cdot y\right)
(FPCore (x y z) :precision binary64 (- (fma x y z) (+ 1.0 (+ (* x y) z))))
↓
(FPCore (x y z) :precision binary64 (- (+ (fma x y z) -1.0) (+ z (* x y))))
double code(double x, double y, double z) {
	return fma(x, y, z) - (1.0 + ((x * y) + z));
}
↓
double code(double x, double y, double z) {
	return (fma(x, y, z) + -1.0) - (z + (x * y));
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original44.9
Target0
Herbie44.9
\[-1\]

Derivation

  1. Initial program 44.9

    \[\mathsf{fma}\left(x, y, z\right) - \left(1 + \left(x \cdot y + z\right)\right)\]
  2. Using strategy rm

  3. Applied associate--r+_binary64_206044.9

    \[\leadsto \color{blue}{\left(\mathsf{fma}\left(x, y, z\right) - 1\right) - \left(x \cdot y + z\right)}\]

  4. Simplified44.9

    \[\leadsto \color{blue}{\left(\mathsf{fma}\left(x, y, z\right) + -1\right)} - \left(x \cdot y + z\right)\]

  5. Final simplification44.9

    \[\leadsto \left(\mathsf{fma}\left(x, y, z\right) + -1\right) - \left(z + x \cdot y\right)\]

Reproduce

herbie shell --seed 2021044 
(FPCore (x y z)
  :name "simple fma test"
  :precision binary64

  :herbie-target
  -1.0

  (- (fma x y z) (+ 1.0 (+ (* x y) z))))