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

Percentage Accurate: 99.9% → 99.9%

Time: 8.9s

Alternatives: 8

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \left(x \cdot \log y - z\right) - y \end{array} \]

FPCore

(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;
}

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

Java

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

Julia

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(x \cdot \log y - z\right) - y \end{array} \]

FPCore

(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;
}

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

Java

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

Julia

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

Wolfram

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

Alternative 1: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\log y \cdot x - z\right) - y \end{array} \]

FPCore

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

C

double code(double x, double y, double z) {
	return ((log(y) * x) - 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 = ((log(y) * x) - z) - y
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

   \[\left(x \cdot \log y - z\right) - y \]
2. Add Preprocessing

3. Final simplification 99.9%

   \[\leadsto \left(\log y \cdot x - z\right) - y \]
4. Add Preprocessing

Alternative 2: 83.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.45 \cdot 10^{+41}:\\ \;\;\;\;\mathsf{fma}\left(\log y, x, -z\right)\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{-69}:\\ \;\;\;\;\left(-z\right) - y\\ \mathbf{else}:\\ \;\;\;\;\log y \cdot x - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -3.45e+41)
   (fma (log y) x (- z))
   (if (<= x 4.6e-69) (- (- z) y) (- (* (log y) x) z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -3.45e+41) {
		tmp = fma(log(y), x, -z);
	} else if (x <= 4.6e-69) {
		tmp = -z - y;
	} else {
		tmp = (log(y) * x) - z;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -3.45e+41)
		tmp = fma(log(y), x, Float64(-z));
	elseif (x <= 4.6e-69)
		tmp = Float64(Float64(-z) - y);
	else
		tmp = Float64(Float64(log(y) * x) - z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -3.45e+41], N[(N[Log[y], $MachinePrecision] * x + (-z)), $MachinePrecision], If[LessEqual[x, 4.6e-69], N[((-z) - y), $MachinePrecision], N[(N[(N[Log[y], $MachinePrecision] * x), $MachinePrecision] - z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.4500000000000001e41

   1. Initial program 99.8%

      \[\left(x \cdot \log y - z\right) - y \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift--.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-neg N/A

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

      4. associate--l+ N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower--.f64 N/A

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

      9. lower-neg.f64 99.8

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

   4. Applied rewrites 99.8%

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

   5. Taylor expanded in z around inf

      \[\leadsto \mathsf{fma}\left(\log y, x, \color{blue}{-1 \cdot z}\right) \]
   6. Step-by-step derivation

      1. mul-1-neg N/A

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

      2. lower-neg.f64 85.3

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

   7. Applied rewrites 85.3%

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

   if -3.4500000000000001e41 < x < 4.6000000000000001e-69

   1. Initial program 100.0%

      \[\left(x \cdot \log y - z\right) - y \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{-1 \cdot z} - y \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(z\right)\right)} - y \]

      2. lower-neg.f64 92.9

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

   5. Applied rewrites 92.9%

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

   if 4.6000000000000001e-69 < x

   1. Initial program 99.8%

      \[\left(x \cdot \log y - z\right) - y \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x \cdot \log y - z} \]
   4. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \color{blue}{x \cdot \log y - z} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{\log y \cdot x} - z \]

      3. lower-*.f64 N/A

         \[\leadsto \color{blue}{\log y \cdot x} - z \]

      4. lower-log.f64 86.0

         \[\leadsto \color{blue}{\log y} \cdot x - z \]

   5. Applied rewrites 86.0%

      \[\leadsto \color{blue}{\log y \cdot x - z} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 3: 83.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \log y \cdot x\\ \mathbf{if}\;x \leq -8.5 \cdot 10^{+74}:\\ \;\;\;\;t\_0 - y\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{-69}:\\ \;\;\;\;\left(-z\right) - y\\ \mathbf{else}:\\ \;\;\;\;t\_0 - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (log y) x)))
   (if (<= x -8.5e+74) (- t_0 y) (if (<= x 4.6e-69) (- (- z) y) (- t_0 z)))))

C

double code(double x, double y, double z) {
	double t_0 = log(y) * x;
	double tmp;
	if (x <= -8.5e+74) {
		tmp = t_0 - y;
	} else if (x <= 4.6e-69) {
		tmp = -z - y;
	} else {
		tmp = t_0 - z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = log(y) * x
    if (x <= (-8.5d+74)) then
        tmp = t_0 - y
    else if (x <= 4.6d-69) then
        tmp = -z - y
    else
        tmp = t_0 - z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = Math.log(y) * x;
	double tmp;
	if (x <= -8.5e+74) {
		tmp = t_0 - y;
	} else if (x <= 4.6e-69) {
		tmp = -z - y;
	} else {
		tmp = t_0 - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.log(y) * x
	tmp = 0
	if x <= -8.5e+74:
		tmp = t_0 - y
	elif x <= 4.6e-69:
		tmp = -z - y
	else:
		tmp = t_0 - z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(log(y) * x)
	tmp = 0.0
	if (x <= -8.5e+74)
		tmp = Float64(t_0 - y);
	elseif (x <= 4.6e-69)
		tmp = Float64(Float64(-z) - y);
	else
		tmp = Float64(t_0 - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = log(y) * x;
	tmp = 0.0;
	if (x <= -8.5e+74)
		tmp = t_0 - y;
	elseif (x <= 4.6e-69)
		tmp = -z - y;
	else
		tmp = t_0 - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Log[y], $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[x, -8.5e+74], N[(t$95$0 - y), $MachinePrecision], If[LessEqual[x, 4.6e-69], N[((-z) - y), $MachinePrecision], N[(t$95$0 - z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -8.50000000000000028e74

   1. Initial program 99.8%

      \[\left(x \cdot \log y - z\right) - y \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x \cdot \log y} - y \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\log y \cdot x} - y \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\log y \cdot x} - y \]

      3. lower-log.f64 89.1

         \[\leadsto \color{blue}{\log y} \cdot x - y \]

   5. Applied rewrites 89.1%

      \[\leadsto \color{blue}{\log y \cdot x} - y \]

   if -8.50000000000000028e74 < x < 4.6000000000000001e-69

   1. Initial program 100.0%

      \[\left(x \cdot \log y - z\right) - y \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{-1 \cdot z} - y \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(z\right)\right)} - y \]

      2. lower-neg.f64 90.8

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

   5. Applied rewrites 90.8%

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

   if 4.6000000000000001e-69 < x

   1. Initial program 99.8%

      \[\left(x \cdot \log y - z\right) - y \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x \cdot \log y - z} \]
   4. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \color{blue}{x \cdot \log y - z} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{\log y \cdot x} - z \]

      3. lower-*.f64 N/A

         \[\leadsto \color{blue}{\log y \cdot x} - z \]

      4. lower-log.f64 86.0

         \[\leadsto \color{blue}{\log y} \cdot x - z \]

   5. Applied rewrites 86.0%

      \[\leadsto \color{blue}{\log y \cdot x - z} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 4: 83.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \log y \cdot x - z\\ \mathbf{if}\;x \leq -3.45 \cdot 10^{+41}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{-69}:\\ \;\;\;\;\left(-z\right) - y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (* (log y) x) z)))
   (if (<= x -3.45e+41) t_0 (if (<= x 4.6e-69) (- (- z) y) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (log(y) * x) - z;
	double tmp;
	if (x <= -3.45e+41) {
		tmp = t_0;
	} else if (x <= 4.6e-69) {
		tmp = -z - y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (log(y) * x) - z
    if (x <= (-3.45d+41)) then
        tmp = t_0
    else if (x <= 4.6d-69) then
        tmp = -z - y
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (Math.log(y) * x) - z;
	double tmp;
	if (x <= -3.45e+41) {
		tmp = t_0;
	} else if (x <= 4.6e-69) {
		tmp = -z - y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (math.log(y) * x) - z
	tmp = 0
	if x <= -3.45e+41:
		tmp = t_0
	elif x <= 4.6e-69:
		tmp = -z - y
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(log(y) * x) - z)
	tmp = 0.0
	if (x <= -3.45e+41)
		tmp = t_0;
	elseif (x <= 4.6e-69)
		tmp = Float64(Float64(-z) - y);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (log(y) * x) - z;
	tmp = 0.0;
	if (x <= -3.45e+41)
		tmp = t_0;
	elseif (x <= 4.6e-69)
		tmp = -z - y;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[Log[y], $MachinePrecision] * x), $MachinePrecision] - z), $MachinePrecision]}, If[LessEqual[x, -3.45e+41], t$95$0, If[LessEqual[x, 4.6e-69], N[((-z) - y), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -3.4500000000000001e41 or 4.6000000000000001e-69 < x

   1. Initial program 99.8%

      \[\left(x \cdot \log y - z\right) - y \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x \cdot \log y - z} \]
   4. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \color{blue}{x \cdot \log y - z} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{\log y \cdot x} - z \]

      3. lower-*.f64 N/A

         \[\leadsto \color{blue}{\log y \cdot x} - z \]

      4. lower-log.f64 85.7

         \[\leadsto \color{blue}{\log y} \cdot x - z \]

   5. Applied rewrites 85.7%

      \[\leadsto \color{blue}{\log y \cdot x - z} \]

   if -3.4500000000000001e41 < x < 4.6000000000000001e-69

   1. Initial program 100.0%

      \[\left(x \cdot \log y - z\right) - y \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{-1 \cdot z} - y \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(z\right)\right)} - y \]

      2. lower-neg.f64 92.9

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

   5. Applied rewrites 92.9%

      \[\leadsto \color{blue}{\left(-z\right)} - y \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 77.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \log y \cdot x\\ \mathbf{if}\;x \leq -5.8 \cdot 10^{+138}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{+29}:\\ \;\;\;\;\left(-z\right) - y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (log y) x)))
   (if (<= x -5.8e+138) t_0 (if (<= x 4.2e+29) (- (- z) y) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = log(y) * x;
	double tmp;
	if (x <= -5.8e+138) {
		tmp = t_0;
	} else if (x <= 4.2e+29) {
		tmp = -z - y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = log(y) * x
    if (x <= (-5.8d+138)) then
        tmp = t_0
    else if (x <= 4.2d+29) then
        tmp = -z - y
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = Math.log(y) * x;
	double tmp;
	if (x <= -5.8e+138) {
		tmp = t_0;
	} else if (x <= 4.2e+29) {
		tmp = -z - y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.log(y) * x
	tmp = 0
	if x <= -5.8e+138:
		tmp = t_0
	elif x <= 4.2e+29:
		tmp = -z - y
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(log(y) * x)
	tmp = 0.0
	if (x <= -5.8e+138)
		tmp = t_0;
	elseif (x <= 4.2e+29)
		tmp = Float64(Float64(-z) - y);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = log(y) * x;
	tmp = 0.0;
	if (x <= -5.8e+138)
		tmp = t_0;
	elseif (x <= 4.2e+29)
		tmp = -z - y;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Log[y], $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[x, -5.8e+138], t$95$0, If[LessEqual[x, 4.2e+29], N[((-z) - y), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -5.80000000000000019e138 or 4.2000000000000003e29 < x

   1. Initial program 99.8%

      \[\left(x \cdot \log y - z\right) - y \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \log y} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\log y \cdot x} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\log y \cdot x} \]

      3. lower-log.f64 73.8

         \[\leadsto \color{blue}{\log y} \cdot x \]

   5. Applied rewrites 73.8%

      \[\leadsto \color{blue}{\log y \cdot x} \]

   if -5.80000000000000019e138 < x < 4.2000000000000003e29

   1. Initial program 99.9%

      \[\left(x \cdot \log y - z\right) - y \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{-1 \cdot z} - y \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(z\right)\right)} - y \]

      2. lower-neg.f64 86.3

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

   5. Applied rewrites 86.3%

      \[\leadsto \color{blue}{\left(-z\right)} - y \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 52.2% accurate, 12.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 14:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= y 14.0) (- z) (- y)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 14.0) {
		tmp = -z;
	} else {
		tmp = -y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= 14.0d0) then
        tmp = -z
    else
        tmp = -y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 14.0) {
		tmp = -z;
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 14.0:
		tmp = -z
	else:
		tmp = -y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 14.0)
		tmp = Float64(-z);
	else
		tmp = Float64(-y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 14.0)
		tmp = -z;
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 14.0], (-z), (-y)]

Derivation

1. Split input into 2 regimes

2. if y < 14

   1. Initial program 99.8%

      \[\left(x \cdot \log y - z\right) - y \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{-1 \cdot z} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(z\right)} \]

      2. lower-neg.f64 44.1

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

   5. Applied rewrites 44.1%

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

   if 14 < y

   1. Initial program 99.9%

      \[\left(x \cdot \log y - z\right) - y \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{-1 \cdot y} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(y\right)} \]

      2. lower-neg.f64 57.6

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

   5. Applied rewrites 57.6%

      \[\leadsto \color{blue}{-y} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 65.9% accurate, 18.7× speedup

Math

\[\begin{array}{l} \\ \left(-z\right) - y \end{array} \]

FPCore

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

C

double code(double x, double y, double z) {
	return -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 = -z - y
end function

Java

public static double code(double x, double y, double z) {
	return -z - y;
}

Python

def code(x, y, z):
	return -z - y

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

   \[\left(x \cdot \log y - z\right) - y \]
2. Add Preprocessing

3. Taylor expanded in z around inf

   \[\leadsto \color{blue}{-1 \cdot z} - y \]
4. Step-by-step derivation

   1. mul-1-neg N/A

      \[\leadsto \color{blue}{\left(\mathsf{neg}\left(z\right)\right)} - y \]

   2. lower-neg.f64 64.3

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

5. Applied rewrites 64.3%

   \[\leadsto \color{blue}{\left(-z\right)} - y \]
6. Add Preprocessing

Alternative 8: 33.7% accurate, 37.3× speedup

Math

\[\begin{array}{l} \\ -y \end{array} \]

FPCore

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

C

double code(double x, double y, double z) {
	return -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 = -y
end function

Java

public static double code(double x, double y, double z) {
	return -y;
}

Python

def code(x, y, z):
	return -y

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := (-y)

Derivation

1. Initial program 99.9%

   \[\left(x \cdot \log y - z\right) - y \]
2. Add Preprocessing

3. Taylor expanded in y around inf

   \[\leadsto \color{blue}{-1 \cdot y} \]
4. Step-by-step derivation

   1. mul-1-neg N/A

      \[\leadsto \color{blue}{\mathsf{neg}\left(y\right)} \]

   2. lower-neg.f64 32.8

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

5. Applied rewrites 32.8%

   \[\leadsto \color{blue}{-y} \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024277 
(FPCore (x y z)
  :name "Statistics.Distribution.Poisson:$clogProbability from math-functions-0.1.5.2"
  :precision binary64
  (- (- (* x (log y)) z) y))