Average Error: 0.1 → 0.1
Time: 2.5s
Precision: binary64
\[\left(x \cdot \log y - z\right) - y \]
↓
\[\mathsf{fma}\left(\log y, x, -z\right) - y \]
(FPCore (x y z) :precision binary64 (- (- (* x (log y)) z) y))
↓
(FPCore (x y z) :precision binary64 (- (fma (log y) x (- z)) y))
double code(double x, double y, double z) {
	return ((x * log(y)) - z) - y;
}
↓
double code(double x, double y, double z) {
	return fma(log(y), x, -z) - y;
}

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

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

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

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

  1. Initial program 0.1

    \[\left(x \cdot \log y - z\right) - y \]

  2. Taylor expanded in x around 0 0.1

    \[\leadsto \color{blue}{\left(\log y \cdot x - z\right)} - y \]

  3. Simplified0.1

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2022162 
(FPCore (x y z)
  :name "Statistics.Distribution.Poisson:$clogProbability from math-functions-0.1.5.2"
  :precision binary64
  (- (- (* x (log y)) z) y))