?

Average Error: 44.6 → 0
Time: 4.2s
Precision: binary64
Cost: 64

?

\[\mathsf{fma}\left(x, y, z\right) - \left(1 + \left(x \cdot y + z\right)\right) \]
↓
\[-1 \]
(FPCore (x y z) :precision binary64 (- (fma x y z) (+ 1.0 (+ (* x y) z))))
↓
(FPCore (x y z) :precision binary64 -1.0)
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 -1.0;
}

function code(x, y, z)
	return Float64(fma(x, y, z) - Float64(1.0 + Float64(Float64(x * y) + z)))
end
↓
function code(x, y, z)
	return -1.0
end

code[x_, y_, z_] := N[(N[(x * y + z), $MachinePrecision] - N[(1.0 + N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
↓
code[x_, y_, z_] := -1.0

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

Error?

Target

Original44.6
Target0
Herbie0
\[-1 \]

Derivation?

  1. Initial program 44.6

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

  2. Simplified44.6

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

    [Start]44.6

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

    rational_best-simplify-1 [=>]44.6

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

    rational_best-simplify-43 [=>]44.6

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

  3. Taylor expanded in x around 0 0

    \[\leadsto \color{blue}{-1} \]

  4. Final simplification0

    \[\leadsto -1 \]

Reproduce?

herbie shell --seed 2023096 
(FPCore (x y z)
  :name "simple fma test"
  :precision binary64

  :herbie-target
  -1.0

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