Average Error: 44.7 → 44.7
Time: 4.6s
Precision: binary64
\[\mathsf{fma}\left(x, y, z\right) - \left(1 + \left(x \cdot y + z\right)\right)\]
↓
\[\mathsf{fma}\left(x, y, z\right) - \left(1 + \left(z + x \cdot y\right)\right)\]
\mathsf{fma}\left(x, y, z\right) - \left(1 + \left(x \cdot y + z\right)\right)
↓
\mathsf{fma}\left(x, y, z\right) - \left(1 + \left(z + x \cdot y\right)\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

Original44.7
Target0
Herbie44.7
\[-1\]

Derivation

  1. Initial program 44.7

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

  2. Final simplification44.7

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

Reproduce

herbie shell --seed 2020233 
(FPCore (x y z)
  :name "simple fma test"
  :precision binary64

  :herbie-target
  -1.0

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