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

Percentage Accurate: 99.9% → 99.9%

Time: 10.0s

Alternatives: 9

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, 0.5× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. associate--l- 99.8%

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

   2. fma-neg 99.8%

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

   3. distribute-neg-in 99.8%

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

   4. +-commutative 99.8%

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

   5. sub-neg 99.8%

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

3. Simplified 99.8%

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

Alternative 2: 77.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \log y\\ t_1 := \left(-y\right) - z\\ \mathbf{if}\;x \leq -2.15 \cdot 10^{+55}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{-5}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{+19} \lor \neg \left(x \leq 2.6 \cdot 10^{+112} \lor \neg \left(x \leq 3 \cdot 10^{+202}\right) \land x \leq 1.1 \cdot 10^{+216}\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t\_1}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (log y))) (t_1 (- (- y) z)))
   (if (<= x -2.15e+55)
     t_0
     (if (<= x 4.5e-5)
       t_1
       (if (or (<= x 5.8e+19)
               (not
                (or (<= x 2.6e+112)
                    (and (not (<= x 3e+202)) (<= x 1.1e+216)))))
         t_0
         (* x (/ t_1 x)))))))

C

double code(double x, double y, double z) {
	double t_0 = x * log(y);
	double t_1 = -y - z;
	double tmp;
	if (x <= -2.15e+55) {
		tmp = t_0;
	} else if (x <= 4.5e-5) {
		tmp = t_1;
	} else if ((x <= 5.8e+19) || !((x <= 2.6e+112) || (!(x <= 3e+202) && (x <= 1.1e+216)))) {
		tmp = t_0;
	} else {
		tmp = x * (t_1 / x);
	}
	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) :: t_1
    real(8) :: tmp
    t_0 = x * log(y)
    t_1 = -y - z
    if (x <= (-2.15d+55)) then
        tmp = t_0
    else if (x <= 4.5d-5) then
        tmp = t_1
    else if ((x <= 5.8d+19) .or. (.not. (x <= 2.6d+112) .or. (.not. (x <= 3d+202)) .and. (x <= 1.1d+216))) then
        tmp = t_0
    else
        tmp = x * (t_1 / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * Math.log(y);
	double t_1 = -y - z;
	double tmp;
	if (x <= -2.15e+55) {
		tmp = t_0;
	} else if (x <= 4.5e-5) {
		tmp = t_1;
	} else if ((x <= 5.8e+19) || !((x <= 2.6e+112) || (!(x <= 3e+202) && (x <= 1.1e+216)))) {
		tmp = t_0;
	} else {
		tmp = x * (t_1 / x);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * math.log(y)
	t_1 = -y - z
	tmp = 0
	if x <= -2.15e+55:
		tmp = t_0
	elif x <= 4.5e-5:
		tmp = t_1
	elif (x <= 5.8e+19) or not ((x <= 2.6e+112) or (not (x <= 3e+202) and (x <= 1.1e+216))):
		tmp = t_0
	else:
		tmp = x * (t_1 / x)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * log(y))
	t_1 = Float64(Float64(-y) - z)
	tmp = 0.0
	if (x <= -2.15e+55)
		tmp = t_0;
	elseif (x <= 4.5e-5)
		tmp = t_1;
	elseif ((x <= 5.8e+19) || !((x <= 2.6e+112) || (!(x <= 3e+202) && (x <= 1.1e+216))))
		tmp = t_0;
	else
		tmp = Float64(x * Float64(t_1 / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * log(y);
	t_1 = -y - z;
	tmp = 0.0;
	if (x <= -2.15e+55)
		tmp = t_0;
	elseif (x <= 4.5e-5)
		tmp = t_1;
	elseif ((x <= 5.8e+19) || ~(((x <= 2.6e+112) || (~((x <= 3e+202)) && (x <= 1.1e+216)))))
		tmp = t_0;
	else
		tmp = x * (t_1 / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[((-y) - z), $MachinePrecision]}, If[LessEqual[x, -2.15e+55], t$95$0, If[LessEqual[x, 4.5e-5], t$95$1, If[Or[LessEqual[x, 5.8e+19], N[Not[Or[LessEqual[x, 2.6e+112], And[N[Not[LessEqual[x, 3e+202]], $MachinePrecision], LessEqual[x, 1.1e+216]]]], $MachinePrecision]], t$95$0, N[(x * N[(t$95$1 / x), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.1499999999999999e55 or 4.50000000000000028e-5 < x < 5.8e19 or 2.6000000000000001e112 < x < 3.0000000000000001e202 or 1.1e216 < x

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 72.7%

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

   if -2.1499999999999999e55 < x < 4.50000000000000028e-5

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 89.7%

      \[\leadsto \color{blue}{-1 \cdot \left(y + z\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 89.7%

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

      2. +-commutative 89.7%

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

      3. distribute-neg-in 89.7%

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

      4. sub-neg 89.7%

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

   5. Simplified 89.7%

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

   if 5.8e19 < x < 2.6000000000000001e112 or 3.0000000000000001e202 < x < 1.1e216

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 99.8%

      \[\leadsto \color{blue}{x \cdot \left(\log y + -1 \cdot \frac{y + z}{x}\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 99.8%

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

      2. unsub-neg 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in x around 0 73.7%

      \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \frac{y + z}{x}\right)} \]
   7. Step-by-step derivation

      1. associate-*r/ 73.7%

         \[\leadsto x \cdot \color{blue}{\frac{-1 \cdot \left(y + z\right)}{x}} \]

      2. +-commutative 73.7%

         \[\leadsto x \cdot \frac{-1 \cdot \color{blue}{\left(z + y\right)}}{x} \]

      3. distribute-lft-in 73.7%

         \[\leadsto x \cdot \frac{\color{blue}{-1 \cdot z + -1 \cdot y}}{x} \]

      4. mul-1-neg 73.7%

         \[\leadsto x \cdot \frac{-1 \cdot z + \color{blue}{\left(-y\right)}}{x} \]

      5. sub-neg 73.7%

         \[\leadsto x \cdot \frac{\color{blue}{-1 \cdot z - y}}{x} \]

      6. mul-1-neg 73.7%

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

   8. Simplified 73.7%

      \[\leadsto x \cdot \color{blue}{\frac{\left(-z\right) - y}{x}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.15 \cdot 10^{+55}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{-5}:\\ \;\;\;\;\left(-y\right) - z\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{+19} \lor \neg \left(x \leq 2.6 \cdot 10^{+112} \lor \neg \left(x \leq 3 \cdot 10^{+202}\right) \land x \leq 1.1 \cdot 10^{+216}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\left(-y\right) - z}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 83.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{-71} \lor \neg \left(x \leq 5.8 \cdot 10^{-6}\right):\\ \;\;\;\;x \cdot \log y - y\\ \mathbf{else}:\\ \;\;\;\;\left(-y\right) - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -8.5e-71) (not (<= x 5.8e-6))) (- (* x (log y)) y) (- (- y) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -8.5e-71) || !(x <= 5.8e-6)) {
		tmp = (x * log(y)) - y;
	} else {
		tmp = -y - 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) :: tmp
    if ((x <= (-8.5d-71)) .or. (.not. (x <= 5.8d-6))) then
        tmp = (x * log(y)) - y
    else
        tmp = -y - z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -8.5e-71) || !(x <= 5.8e-6)) {
		tmp = (x * Math.log(y)) - y;
	} else {
		tmp = -y - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -8.5e-71) or not (x <= 5.8e-6):
		tmp = (x * math.log(y)) - y
	else:
		tmp = -y - z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -8.5e-71) || !(x <= 5.8e-6))
		tmp = Float64(Float64(x * log(y)) - y);
	else
		tmp = Float64(Float64(-y) - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -8.5e-71) || ~((x <= 5.8e-6)))
		tmp = (x * log(y)) - y;
	else
		tmp = -y - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -8.5e-71], N[Not[LessEqual[x, 5.8e-6]], $MachinePrecision]], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision], N[((-y) - z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -8.49999999999999988e-71 or 5.8000000000000004e-6 < x

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 0 79.3%

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

   if -8.49999999999999988e-71 < x < 5.8000000000000004e-6

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 94.9%

      \[\leadsto \color{blue}{-1 \cdot \left(y + z\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 94.9%

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

      2. +-commutative 94.9%

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

      3. distribute-neg-in 94.9%

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

      4. sub-neg 94.9%

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

   5. Simplified 94.9%

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

4. Final simplification 86.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{-71} \lor \neg \left(x \leq 5.8 \cdot 10^{-6}\right):\\ \;\;\;\;x \cdot \log y - y\\ \mathbf{else}:\\ \;\;\;\;\left(-y\right) - z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \log y\\ \mathbf{if}\;y \leq 1.55 \cdot 10^{+95}:\\ \;\;\;\;t\_0 - z\\ \mathbf{else}:\\ \;\;\;\;t\_0 - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (log y)))) (if (<= y 1.55e+95) (- t_0 z) (- t_0 y))))

C

double code(double x, double y, double z) {
	double t_0 = x * log(y);
	double tmp;
	if (y <= 1.55e+95) {
		tmp = t_0 - z;
	} else {
		tmp = t_0 - 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) :: t_0
    real(8) :: tmp
    t_0 = x * log(y)
    if (y <= 1.55d+95) then
        tmp = t_0 - z
    else
        tmp = t_0 - y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * Math.log(y);
	double tmp;
	if (y <= 1.55e+95) {
		tmp = t_0 - z;
	} else {
		tmp = t_0 - y;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * math.log(y)
	tmp = 0
	if y <= 1.55e+95:
		tmp = t_0 - z
	else:
		tmp = t_0 - y
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * log(y))
	tmp = 0.0
	if (y <= 1.55e+95)
		tmp = Float64(t_0 - z);
	else
		tmp = Float64(t_0 - y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * log(y);
	tmp = 0.0;
	if (y <= 1.55e+95)
		tmp = t_0 - z;
	else
		tmp = t_0 - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, 1.55e+95], N[(t$95$0 - z), $MachinePrecision], N[(t$95$0 - y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < 1.5500000000000001e95

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 89.5%

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

   if 1.5500000000000001e95 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 85.4%

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

Alternative 5: 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]

Derivation

1. Initial program 99.8%

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

Alternative 6: 52.2% accurate, 15.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 8 \cdot 10^{+94}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= y 8e+94) (- z) (- y)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 8e+94) {
		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 <= 8d+94) 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 <= 8e+94) {
		tmp = -z;
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 8e+94:
		tmp = -z
	else:
		tmp = -y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 8e+94)
		tmp = Float64(-z);
	else
		tmp = Float64(-y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 8e+94)
		tmp = -z;
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 8e+94], (-z), (-y)]

Derivation

1. Split input into 2 regimes

2. if y < 8.0000000000000002e94

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf 42.9%

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

      1. neg-mul-1 42.9%

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

   5. Simplified 42.9%

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

   if 8.0000000000000002e94 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 68.0%

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

      1. mul-1-neg 68.0%

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

   5. Simplified 68.0%

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

Alternative 7: 66.6% accurate, 26.8× speedup

Math

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

FPCore

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

C

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

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 - z
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

3. Taylor expanded in x around 0 63.0%

   \[\leadsto \color{blue}{-1 \cdot \left(y + z\right)} \]
4. Step-by-step derivation

   1. mul-1-neg 63.0%

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

   2. +-commutative 63.0%

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

   3. distribute-neg-in 63.0%

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

   4. sub-neg 63.0%

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

5. Simplified 63.0%

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

6. Final simplification 63.0%

   \[\leadsto \left(-y\right) - z \]
7. Add Preprocessing

Alternative 8: 34.6% accurate, 53.5× 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 99.8%

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

3. Taylor expanded in y around inf 31.2%

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

   1. mul-1-neg 31.2%

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

5. Simplified 31.2%

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

Alternative 9: 2.2% accurate, 107.0× 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 y
end

MATLAB

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

Wolfram

code[x_, y_, z_] := y

Derivation

1. Initial program 99.8%

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

   1. associate--l- 99.8%

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

   2. fma-neg 99.8%

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

   3. +-commutative 99.8%

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

   4. distribute-neg-out 99.8%

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

   5. sub-neg 99.8%

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

   6. add-cube-cbrt 97.9%

      \[\leadsto \color{blue}{\left(\sqrt[3]{\mathsf{fma}\left(x, \log y, \left(-y\right) - z\right)} \cdot \sqrt[3]{\mathsf{fma}\left(x, \log y, \left(-y\right) - z\right)}\right) \cdot \sqrt[3]{\mathsf{fma}\left(x, \log y, \left(-y\right) - z\right)}} \]

   7. pow3 97.9%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(x, \log y, \left(-y\right) - z\right)}\right)}^{3}} \]

4. Applied egg-rr 67.8%

   \[\leadsto \color{blue}{{\left(\sqrt[3]{y + \left(x \cdot \log y - z\right)}\right)}^{3}} \]

5. Taylor expanded in y around inf 2.4%

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

Reproduce

herbie shell --seed 2024097 
(FPCore (x y z)
  :name "Statistics.Distribution.Poisson:$clogProbability from math-functions-0.1.5.2"
  :precision binary64
  (- (- (* x (log y)) z) y))