Statistics.Distribution.Poisson:$clogProbability from math-functions-0.1.5.2

Average Accuracy: 99.9% → 99.9%

Time: 7.9s

Precision: binary64

Cost: 6848

Math

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

↓

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

FPCore

(FPCore (x y z) :precision binary64 (- (- (* x (log y)) z) y))

↓

(FPCore (x y z) :precision binary64 (- (- (* x (log y)) z) y))

C

double code(double x, double y, double z) {
	return ((x * log(y)) - z) - y;
}

↓

double code(double x, double y, double z) {
	return ((x * log(y)) - z) - y;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = ((x * log(y)) - z) - y
end function

↓

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = ((x * log(y)) - z) - y
end function

Java

public static double code(double x, double y, double z) {
	return ((x * Math.log(y)) - z) - y;
}

↓

public static double code(double x, double y, double z) {
	return ((x * Math.log(y)) - z) - y;
}

Python

def code(x, y, z):
	return ((x * math.log(y)) - z) - y

↓

def code(x, y, z):
	return ((x * math.log(y)) - z) - y

Julia

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

↓

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

MATLAB

function tmp = code(x, y, z)
	tmp = ((x * log(y)) - z) - y;
end

↓

function tmp = code(x, y, z)
	tmp = ((x * log(y)) - z) - y;
end

Wolfram

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

↓

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

Derivation

1. Initial program 99.9%

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

2. Final simplification 99.9%

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

Alternatives

Alternative 1
Accuracy	78.0%
Cost	7122

\[\begin{array}{l} \mathbf{if}\;x \leq -8.2 \cdot 10^{+89} \lor \neg \left(x \leq 7.5 \cdot 10^{+106}\right) \land \left(x \leq 3.8 \cdot 10^{+142} \lor \neg \left(x \leq 7.9 \cdot 10^{+208}\right)\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - y\\ \end{array} \]

Alternative 2
Accuracy	85.4%
Cost	6985

\[\begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+62} \lor \neg \left(z \leq 1.1 \cdot 10^{+90}\right):\\ \;\;\;\;\left(-z\right) - y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y - y\\ \end{array} \]

Alternative 3
Accuracy	86.4%
Cost	6984

\[\begin{array}{l} t_0 := x \cdot \log y\\ \mathbf{if}\;y \leq 5.3 \cdot 10^{+26}:\\ \;\;\;\;t_0 - z\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+94}:\\ \;\;\;\;t_0 - y\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - y\\ \end{array} \]

Alternative 4
Accuracy	52.9%
Cost	260

\[\begin{array}{l} \mathbf{if}\;y \leq 4.8 \cdot 10^{+26}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \]

Alternative 5
Accuracy	66.7%
Cost	256

\[\left(-z\right) - y \]

Alternative 6
Accuracy	34.3%
Cost	128

\[-y \]

Alternative 7
Accuracy	2.3%
Cost	64

\[z \]

Reproduce

herbie shell --seed 2023141 
(FPCore (x y z)
  :name "Statistics.Distribution.Poisson:$clogProbability from math-functions-0.1.5.2"
  :precision binary64
  (- (- (* x (log y)) z) y))