Average Error: 0.1 → 0.1
Time: 19.3s
Precision: binary64
Cost: 19712
\[\left(\left(x \cdot \log y - y\right) - z\right) + \log t \]
↓
\[\mathsf{fma}\left(x, \log y, -\left(y + z\right)\right) + \log t \]
(FPCore (x y z t) :precision binary64 (+ (- (- (* x (log y)) y) z) (log t)))
↓
(FPCore (x y z t) :precision binary64 (+ (fma x (log y) (- (+ y z))) (log t)))
double code(double x, double y, double z, double t) {
	return (((x * log(y)) - y) - z) + log(t);
}
↓
double code(double x, double y, double z, double t) {
	return fma(x, log(y), -(y + z)) + log(t);
}

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

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

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

Error

Derivation

  1. Initial program 0.1

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

  2. Simplified0.1

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

Alternatives

Alternative 1
Error0.4
Cost13380
\[\begin{array}{l} t_1 := \log y \cdot x\\ \mathbf{if}\;y \leq 480:\\ \;\;\;\;\left(t_1 + \log t\right) - z\\ \mathbf{else}:\\ \;\;\;\;t_1 - \left(y + z\right)\\ \end{array} \]
Alternative 2
Error0.1
Cost13376
\[\left(\left(x \cdot \log y - y\right) - z\right) + \log t \]
Alternative 3
Error19.8
Cost7516
\[\begin{array}{l} t_1 := \log y \cdot x\\ t_2 := -\left(y + z\right)\\ \mathbf{if}\;x \leq -6.4 \cdot 10^{+100}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -3.6 \cdot 10^{+27}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -320000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -2.5 \cdot 10^{-59}:\\ \;\;\;\;\log t - z\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-112}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 3.65 \cdot 10^{-59}:\\ \;\;\;\;\log t - y\\ \mathbf{elif}\;x \leq 1.475 \cdot 10^{+127}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 4
Error18.6
Cost7120
\[\begin{array}{l} t_1 := \log y \cdot x\\ t_2 := -\left(y + z\right)\\ \mathbf{if}\;x \leq -1.38 \cdot 10^{+101}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 6.4 \cdot 10^{-112}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{-59}:\\ \;\;\;\;\log t - y\\ \mathbf{elif}\;x \leq 1.475 \cdot 10^{+127}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 5
Error0.8
Cost7112
\[\begin{array}{l} t_1 := \log y \cdot x - \left(y + z\right)\\ \mathbf{if}\;x \leq -0.75:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{-32}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 6
Error0.8
Cost7112
\[\begin{array}{l} t_1 := \log y \cdot x\\ \mathbf{if}\;x \leq -0.28:\\ \;\;\;\;\left(-z\right) - \left(y - t_1\right)\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{-32}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;t_1 - \left(y + z\right)\\ \end{array} \]
Alternative 7
Error10.7
Cost6984
\[\begin{array}{l} t_1 := \log y \cdot x\\ \mathbf{if}\;x \leq -1.22 \cdot 10^{+101}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.475 \cdot 10^{+127}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 8
Error7.0
Cost6984
\[\begin{array}{l} t_1 := \log y \cdot x - y\\ \mathbf{if}\;x \leq -320000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{+53}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 9
Error18.3
Cost6856
\[\begin{array}{l} t_1 := \log y \cdot x\\ \mathbf{if}\;x \leq -3.1 \cdot 10^{+101}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.475 \cdot 10^{+127}:\\ \;\;\;\;-\left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 10
Error33.1
Cost260
\[\begin{array}{l} \mathbf{if}\;y \leq 5.5 \cdot 10^{+36}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \]
Alternative 11
Error26.6
Cost256
\[-\left(y + z\right) \]
Alternative 12
Error44.8
Cost128
\[-y \]

Error

Reproduce

herbie shell --seed 2023010 
(FPCore (x y z t)
  :name "Numeric.SpecFunctions:incompleteGamma from math-functions-0.1.5.2, A"
  :precision binary64
  (+ (- (- (* x (log y)) y) z) (log t)))