Average Error: 0.1 → 0.1
Time: 21.8s
Precision: binary64
Cost: 13184
\[\left(x \cdot \log y - z\right) - y \]
↓
\[\mathsf{fma}\left(x, \log y, -\left(z + y\right)\right) \]
(FPCore (x y z) :precision binary64 (- (- (* x (log y)) z) y))
↓
(FPCore (x y z) :precision binary64 (fma x (log y) (- (+ 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(x, log(y), -(z + y));
}

function code(x, y, z)
	return Float64(Float64(Float64(x * log(y)) - z) - y)
end
↓
function code(x, y, z)
	return fma(x, log(y), Float64(-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[(x * N[Log[y], $MachinePrecision] + (-N[(z + y), $MachinePrecision])), $MachinePrecision]

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

Error

Derivation

  1. Initial program 0.1

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

  2. Simplified0.1

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

Alternatives

Alternative 1
Error9.6
Cost6984
\[\begin{array}{l} t_0 := \left(-z\right) - y\\ \mathbf{if}\;z \leq -8.6 \cdot 10^{+67}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{-39}:\\ \;\;\;\;\log y \cdot x - y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]
Alternative 2
Error12.5
Cost6856
\[\begin{array}{l} t_0 := \log y \cdot x\\ \mathbf{if}\;x \leq -1.34 \cdot 10^{+129}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{+125}:\\ \;\;\;\;\left(-z\right) - y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]
Alternative 3
Error0.1
Cost6848
\[\left(x \cdot \log y - z\right) - y \]
Alternative 4
Error30.7
Cost260
\[\begin{array}{l} \mathbf{if}\;y \leq 4.5 \cdot 10^{+92}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \]
Alternative 5
Error21.1
Cost256
\[\left(-z\right) - y \]
Alternative 6
Error41.9
Cost128
\[-y \]

Error

Reproduce

herbie shell --seed 2023010 
(FPCore (x y z)
  :name "Statistics.Distribution.Poisson:$clogProbability from math-functions-0.1.5.2"
  :precision binary64
  (- (- (* x (log y)) z) y))