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

Percentage Accurate: 99.9% → 99.9%

Time: 9.2s

Alternatives: 10

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

\[\begin{array}{l} \\ \mathsf{fma}\left(\log y, x, \left(0 - z\right) - y\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (fma (log y) x (- (- 0.0 z) y)))

C

double code(double x, double y, double z) {
	return fma(log(y), x, ((0.0 - z) - y));
}

Julia

function code(x, y, z)
	return fma(log(y), x, Float64(Float64(0.0 - z) - y))
end

Wolfram

code[x_, y_, z_] := N[(N[Log[y], $MachinePrecision] * x + N[(N[(0.0 - z), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]

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- N/A

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

   2. *-commutative N/A

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

   3. fmm-def N/A

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

   4. fma-lowering-fma.f64 N/A

      \[\leadsto \mathsf{fma.f64}\left(\log y, \color{blue}{x}, \left(\mathsf{neg}\left(\left(z + y\right)\right)\right)\right) \]

   5. log-lowering-log.f64 N/A

      \[\leadsto \mathsf{fma.f64}\left(\mathsf{log.f64}\left(y\right), x, \left(\mathsf{neg}\left(\left(z + y\right)\right)\right)\right) \]

   6. distribute-neg-in N/A

      \[\leadsto \mathsf{fma.f64}\left(\mathsf{log.f64}\left(y\right), x, \left(\left(\mathsf{neg}\left(z\right)\right) + \left(\mathsf{neg}\left(y\right)\right)\right)\right) \]

   7. sub-neg N/A

      \[\leadsto \mathsf{fma.f64}\left(\mathsf{log.f64}\left(y\right), x, \left(\left(\mathsf{neg}\left(z\right)\right) - y\right)\right) \]

   8. --lowering--.f64 N/A

      \[\leadsto \mathsf{fma.f64}\left(\mathsf{log.f64}\left(y\right), x, \mathsf{\_.f64}\left(\left(\mathsf{neg}\left(z\right)\right), y\right)\right) \]

   9. neg-sub0 N/A

      \[\leadsto \mathsf{fma.f64}\left(\mathsf{log.f64}\left(y\right), x, \mathsf{\_.f64}\left(\left(0 - z\right), y\right)\right) \]

   10. --lowering--.f64 99.8%

       \[\leadsto \mathsf{fma.f64}\left(\mathsf{log.f64}\left(y\right), x, \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(0, z\right), y\right)\right) \]

4. Applied egg-rr 99.8%

   \[\leadsto \color{blue}{\mathsf{fma}\left(\log y, x, \left(0 - z\right) - y\right)} \]
5. Add Preprocessing

Alternative 2: 84.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \log y \cdot x\\ t_1 := t\_0 - z\\ \mathbf{if}\;z \leq -1.12 \cdot 10^{+76}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+116}:\\ \;\;\;\;t\_0 - y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (log y) x)) (t_1 (- t_0 z)))
   (if (<= z -1.12e+76) t_1 (if (<= z 7e+116) (- t_0 y) t_1))))

C

double code(double x, double y, double z) {
	double t_0 = log(y) * x;
	double t_1 = t_0 - z;
	double tmp;
	if (z <= -1.12e+76) {
		tmp = t_1;
	} else if (z <= 7e+116) {
		tmp = t_0 - y;
	} else {
		tmp = t_1;
	}
	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 = log(y) * x
    t_1 = t_0 - z
    if (z <= (-1.12d+76)) then
        tmp = t_1
    else if (z <= 7d+116) then
        tmp = t_0 - y
    else
        tmp = t_1
    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 t_1 = t_0 - z;
	double tmp;
	if (z <= -1.12e+76) {
		tmp = t_1;
	} else if (z <= 7e+116) {
		tmp = t_0 - y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.log(y) * x
	t_1 = t_0 - z
	tmp = 0
	if z <= -1.12e+76:
		tmp = t_1
	elif z <= 7e+116:
		tmp = t_0 - y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(log(y) * x)
	t_1 = Float64(t_0 - z)
	tmp = 0.0
	if (z <= -1.12e+76)
		tmp = t_1;
	elseif (z <= 7e+116)
		tmp = Float64(t_0 - y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = log(y) * x;
	t_1 = t_0 - z;
	tmp = 0.0;
	if (z <= -1.12e+76)
		tmp = t_1;
	elseif (z <= 7e+116)
		tmp = t_0 - y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Log[y], $MachinePrecision] * x), $MachinePrecision]}, Block[{t$95$1 = N[(t$95$0 - z), $MachinePrecision]}, If[LessEqual[z, -1.12e+76], t$95$1, If[LessEqual[z, 7e+116], N[(t$95$0 - y), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.12000000000000005e76 or 6.99999999999999993e116 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(x \cdot \log y\right), \color{blue}{z}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \log y\right), z\right) \]

      3. log-lowering-log.f64 87.2%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), z\right) \]

   5. Simplified 87.2%

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

   if -1.12000000000000005e76 < z < 6.99999999999999993e116

   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. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(x \cdot \log y\right), \color{blue}{y}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \log y\right), y\right) \]

      3. log-lowering-log.f64 91.6%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), y\right) \]

   5. Simplified 91.6%

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

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.12 \cdot 10^{+76}:\\ \;\;\;\;\log y \cdot x - z\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+116}:\\ \;\;\;\;\log y \cdot x - y\\ \mathbf{else}:\\ \;\;\;\;\log y \cdot x - z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 83.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(0 - z\right) - y\\ \mathbf{if}\;z \leq -3.3 \cdot 10^{+129}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+125}:\\ \;\;\;\;\log y \cdot x - y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (- 0.0 z) y)))
   (if (<= z -3.3e+129) t_0 (if (<= z 2.1e+125) (- (* (log y) x) y) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (0.0 - z) - y;
	double tmp;
	if (z <= -3.3e+129) {
		tmp = t_0;
	} else if (z <= 2.1e+125) {
		tmp = (log(y) * x) - 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 = (0.0d0 - z) - y
    if (z <= (-3.3d+129)) then
        tmp = t_0
    else if (z <= 2.1d+125) then
        tmp = (log(y) * x) - 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 = (0.0 - z) - y;
	double tmp;
	if (z <= -3.3e+129) {
		tmp = t_0;
	} else if (z <= 2.1e+125) {
		tmp = (Math.log(y) * x) - y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (0.0 - z) - y
	tmp = 0
	if z <= -3.3e+129:
		tmp = t_0
	elif z <= 2.1e+125:
		tmp = (math.log(y) * x) - y
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(0.0 - z) - y)
	tmp = 0.0
	if (z <= -3.3e+129)
		tmp = t_0;
	elseif (z <= 2.1e+125)
		tmp = Float64(Float64(log(y) * x) - y);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (0.0 - z) - y;
	tmp = 0.0;
	if (z <= -3.3e+129)
		tmp = t_0;
	elseif (z <= 2.1e+125)
		tmp = (log(y) * x) - y;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(0.0 - z), $MachinePrecision] - y), $MachinePrecision]}, If[LessEqual[z, -3.3e+129], t$95$0, If[LessEqual[z, 2.1e+125], N[(N[(N[Log[y], $MachinePrecision] * x), $MachinePrecision] - y), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.2999999999999999e129 or 2.1000000000000001e125 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(\left(y + z\right)\right) \]

      2. distribute-neg-in N/A

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

      3. +-commutative N/A

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

      4. sub-neg N/A

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

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\mathsf{neg}\left(z\right)\right), \color{blue}{y}\right) \]

      6. neg-sub0 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(0 - z\right), y\right) \]

      7. --lowering--.f64 89.9%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(0, z\right), y\right) \]

   5. Simplified 89.9%

      \[\leadsto \color{blue}{\left(0 - z\right) - y} \]
   6. Step-by-step derivation

      1. sub0-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\mathsf{neg}\left(z\right)\right), y\right) \]

      2. neg-lowering-neg.f64 89.9%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{neg.f64}\left(z\right), y\right) \]

   7. Applied egg-rr 89.9%

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

   if -3.2999999999999999e129 < z < 2.1000000000000001e125

   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. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(x \cdot \log y\right), \color{blue}{y}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \log y\right), y\right) \]

      3. log-lowering-log.f64 89.3%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), y\right) \]

   5. Simplified 89.3%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+129}:\\ \;\;\;\;\left(0 - z\right) - y\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+125}:\\ \;\;\;\;\log y \cdot x - y\\ \mathbf{else}:\\ \;\;\;\;\left(0 - z\right) - y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 79.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \log y \cdot x\\ \mathbf{if}\;x \leq -3.8 \cdot 10^{+153}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 5.4 \cdot 10^{+71}:\\ \;\;\;\;\left(0 - z\right) - y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (log y) x)))
   (if (<= x -3.8e+153) t_0 (if (<= x 5.4e+71) (- (- 0.0 z) y) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = log(y) * x;
	double tmp;
	if (x <= -3.8e+153) {
		tmp = t_0;
	} else if (x <= 5.4e+71) {
		tmp = (0.0 - 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 <= (-3.8d+153)) then
        tmp = t_0
    else if (x <= 5.4d+71) then
        tmp = (0.0d0 - 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 <= -3.8e+153) {
		tmp = t_0;
	} else if (x <= 5.4e+71) {
		tmp = (0.0 - z) - y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.log(y) * x
	tmp = 0
	if x <= -3.8e+153:
		tmp = t_0
	elif x <= 5.4e+71:
		tmp = (0.0 - 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 <= -3.8e+153)
		tmp = t_0;
	elseif (x <= 5.4e+71)
		tmp = Float64(Float64(0.0 - 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 <= -3.8e+153)
		tmp = t_0;
	elseif (x <= 5.4e+71)
		tmp = (0.0 - 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, -3.8e+153], t$95$0, If[LessEqual[x, 5.4e+71], N[(N[(0.0 - z), $MachinePrecision] - y), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -3.79999999999999966e153 or 5.39999999999999993e71 < x

   1. Initial program 99.6%

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

   3. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\log y}\right) \]

      2. log-lowering-log.f64 77.3%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right) \]

   5. Simplified 77.3%

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

   if -3.79999999999999966e153 < x < 5.39999999999999993e71

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(\left(y + z\right)\right) \]

      2. distribute-neg-in N/A

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

      3. +-commutative N/A

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

      4. sub-neg N/A

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

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\mathsf{neg}\left(z\right)\right), \color{blue}{y}\right) \]

      6. neg-sub0 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(0 - z\right), y\right) \]

      7. --lowering--.f64 80.6%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(0, z\right), y\right) \]

   5. Simplified 80.6%

      \[\leadsto \color{blue}{\left(0 - z\right) - y} \]
   6. Step-by-step derivation

      1. sub0-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\mathsf{neg}\left(z\right)\right), y\right) \]

      2. neg-lowering-neg.f64 80.6%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{neg.f64}\left(z\right), y\right) \]

   7. Applied egg-rr 80.6%

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

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{+153}:\\ \;\;\;\;\log y \cdot x\\ \mathbf{elif}\;x \leq 5.4 \cdot 10^{+71}:\\ \;\;\;\;\left(0 - z\right) - y\\ \mathbf{else}:\\ \;\;\;\;\log y \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 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 99.8%

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

3. Final simplification 99.8%

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

Alternative 6: 52.1% accurate, 8.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+82}:\\ \;\;\;\;0 - z\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+120}:\\ \;\;\;\;z - y\\ \mathbf{else}:\\ \;\;\;\;0 - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.1e+82) (- 0.0 z) (if (<= z 1.1e+120) (- z y) (- 0.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.1e+82) {
		tmp = 0.0 - z;
	} else if (z <= 1.1e+120) {
		tmp = z - y;
	} else {
		tmp = 0.0 - 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) :: tmp
    if (z <= (-1.1d+82)) then
        tmp = 0.0d0 - z
    else if (z <= 1.1d+120) then
        tmp = z - y
    else
        tmp = 0.0d0 - z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.1e+82) {
		tmp = 0.0 - z;
	} else if (z <= 1.1e+120) {
		tmp = z - y;
	} else {
		tmp = 0.0 - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.1e+82:
		tmp = 0.0 - z
	elif z <= 1.1e+120:
		tmp = z - y
	else:
		tmp = 0.0 - z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.1e+82)
		tmp = Float64(0.0 - z);
	elseif (z <= 1.1e+120)
		tmp = Float64(z - y);
	else
		tmp = Float64(0.0 - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.1e+82)
		tmp = 0.0 - z;
	elseif (z <= 1.1e+120)
		tmp = z - y;
	else
		tmp = 0.0 - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.1e+82], N[(0.0 - z), $MachinePrecision], If[LessEqual[z, 1.1e+120], N[(z - y), $MachinePrecision], N[(0.0 - z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.1000000000000001e82 or 1.1000000000000001e120 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

         \[\leadsto 0 - \color{blue}{z} \]

      3. --lowering--.f64 72.1%

         \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{z}\right) \]

   5. Simplified 72.1%

      \[\leadsto \color{blue}{0 - z} \]

   if -1.1000000000000001e82 < z < 1.1000000000000001e120

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(\left(y + z\right)\right) \]

      2. distribute-neg-in N/A

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

      3. +-commutative N/A

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

      4. sub-neg N/A

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

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\mathsf{neg}\left(z\right)\right), \color{blue}{y}\right) \]

      6. neg-sub0 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(0 - z\right), y\right) \]

      7. --lowering--.f64 52.2%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(0, z\right), y\right) \]

   5. Simplified 52.2%

      \[\leadsto \color{blue}{\left(0 - z\right) - y} \]
   6. Step-by-step derivation

      1. flip3-- N/A

         \[\leadsto \frac{{0}^{3} - {z}^{3}}{0 \cdot 0 + \left(z \cdot z + 0 \cdot z\right)} - y \]

      2. metadata-eval N/A

         \[\leadsto \frac{0 - {z}^{3}}{0 \cdot 0 + \left(z \cdot z + 0 \cdot z\right)} - y \]

      3. sub-neg N/A

         \[\leadsto \frac{0 + \left(\mathsf{neg}\left({z}^{3}\right)\right)}{0 \cdot 0 + \left(z \cdot z + 0 \cdot z\right)} - y \]

      4. metadata-eval N/A

         \[\leadsto \frac{{0}^{3} + \left(\mathsf{neg}\left({z}^{3}\right)\right)}{0 \cdot 0 + \left(z \cdot z + 0 \cdot z\right)} - y \]

      5. cube-neg N/A

         \[\leadsto \frac{{0}^{3} + {\left(\mathsf{neg}\left(z\right)\right)}^{3}}{0 \cdot 0 + \left(z \cdot z + 0 \cdot z\right)} - y \]

      6. sub0-neg N/A

         \[\leadsto \frac{{0}^{3} + {\left(0 - z\right)}^{3}}{0 \cdot 0 + \left(z \cdot z + 0 \cdot z\right)} - y \]

      7. sqr-pow N/A

         \[\leadsto \frac{{0}^{3} + {\left(0 - z\right)}^{\left(\frac{3}{2}\right)} \cdot {\left(0 - z\right)}^{\left(\frac{3}{2}\right)}}{0 \cdot 0 + \left(z \cdot z + 0 \cdot z\right)} - y \]

      8. pow-prod-down N/A

         \[\leadsto \frac{{0}^{3} + {\left(\left(0 - z\right) \cdot \left(0 - z\right)\right)}^{\left(\frac{3}{2}\right)}}{0 \cdot 0 + \left(z \cdot z + 0 \cdot z\right)} - y \]

      9. sub0-neg N/A

         \[\leadsto \frac{{0}^{3} + {\left(\left(\mathsf{neg}\left(z\right)\right) \cdot \left(0 - z\right)\right)}^{\left(\frac{3}{2}\right)}}{0 \cdot 0 + \left(z \cdot z + 0 \cdot z\right)} - y \]

      10. sub0-neg N/A

          \[\leadsto \frac{{0}^{3} + {\left(\left(\mathsf{neg}\left(z\right)\right) \cdot \left(\mathsf{neg}\left(z\right)\right)\right)}^{\left(\frac{3}{2}\right)}}{0 \cdot 0 + \left(z \cdot z + 0 \cdot z\right)} - y \]

      11. sqr-neg N/A

          \[\leadsto \frac{{0}^{3} + {\left(z \cdot z\right)}^{\left(\frac{3}{2}\right)}}{0 \cdot 0 + \left(z \cdot z + 0 \cdot z\right)} - y \]

      12. pow-prod-down N/A

          \[\leadsto \frac{{0}^{3} + {z}^{\left(\frac{3}{2}\right)} \cdot {z}^{\left(\frac{3}{2}\right)}}{0 \cdot 0 + \left(z \cdot z + 0 \cdot z\right)} - y \]

      13. sqr-pow N/A

          \[\leadsto \frac{{0}^{3} + {z}^{3}}{0 \cdot 0 + \left(z \cdot z + 0 \cdot z\right)} - y \]

      14. fma-define N/A

          \[\leadsto \frac{{0}^{3} + {z}^{3}}{0 \cdot 0 + \mathsf{fma}\left(z, z, 0 \cdot z\right)} - y \]

      15. mul0-lft N/A

          \[\leadsto \frac{{0}^{3} + {z}^{3}}{0 \cdot 0 + \mathsf{fma}\left(z, z, 0\right)} - y \]

      16. metadata-eval N/A

          \[\leadsto \frac{{0}^{3} + {z}^{3}}{0 \cdot 0 + \mathsf{fma}\left(z, z, \mathsf{neg}\left(0\right)\right)} - y \]

      17. fmm-def N/A

          \[\leadsto \frac{{0}^{3} + {z}^{3}}{0 \cdot 0 + \left(z \cdot z - 0\right)} - y \]

      18. mul0-lft N/A

          \[\leadsto \frac{{0}^{3} + {z}^{3}}{0 \cdot 0 + \left(z \cdot z - 0 \cdot z\right)} - y \]

      19. flip3-+ N/A

          \[\leadsto \left(0 + z\right) - y \]

      20. +-lft-identity N/A

          \[\leadsto z - y \]

   7. Applied egg-rr 45.4%

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

Alternative 7: 52.3% accurate, 8.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+78}:\\ \;\;\;\;0 - z\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{+119}:\\ \;\;\;\;0 - y\\ \mathbf{else}:\\ \;\;\;\;0 - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -2.1e+78) (- 0.0 z) (if (<= z 8.8e+119) (- 0.0 y) (- 0.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.1e+78) {
		tmp = 0.0 - z;
	} else if (z <= 8.8e+119) {
		tmp = 0.0 - y;
	} else {
		tmp = 0.0 - 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) :: tmp
    if (z <= (-2.1d+78)) then
        tmp = 0.0d0 - z
    else if (z <= 8.8d+119) then
        tmp = 0.0d0 - y
    else
        tmp = 0.0d0 - z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.1e+78) {
		tmp = 0.0 - z;
	} else if (z <= 8.8e+119) {
		tmp = 0.0 - y;
	} else {
		tmp = 0.0 - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -2.1e+78:
		tmp = 0.0 - z
	elif z <= 8.8e+119:
		tmp = 0.0 - y
	else:
		tmp = 0.0 - z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -2.1e+78)
		tmp = Float64(0.0 - z);
	elseif (z <= 8.8e+119)
		tmp = Float64(0.0 - y);
	else
		tmp = Float64(0.0 - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -2.1e+78)
		tmp = 0.0 - z;
	elseif (z <= 8.8e+119)
		tmp = 0.0 - y;
	else
		tmp = 0.0 - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -2.1e+78], N[(0.0 - z), $MachinePrecision], If[LessEqual[z, 8.8e+119], N[(0.0 - y), $MachinePrecision], N[(0.0 - z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.1000000000000001e78 or 8.8000000000000005e119 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

         \[\leadsto 0 - \color{blue}{z} \]

      3. --lowering--.f64 72.1%

         \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{z}\right) \]

   5. Simplified 72.1%

      \[\leadsto \color{blue}{0 - z} \]

   if -2.1000000000000001e78 < z < 8.8000000000000005e119

   1. Initial program 99.8%

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

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

      2. neg-sub0 N/A

         \[\leadsto 0 - \color{blue}{y} \]

      3. --lowering--.f64 45.2%

         \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{y}\right) \]

   5. Simplified 45.2%

      \[\leadsto \color{blue}{0 - y} \]
   6. Step-by-step derivation

      1. sub0-neg N/A

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

      2. neg-lowering-neg.f64 45.2%

         \[\leadsto \mathsf{neg.f64}\left(y\right) \]

   7. Applied egg-rr 45.2%

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

4. Final simplification 53.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+78}:\\ \;\;\;\;0 - z\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{+119}:\\ \;\;\;\;0 - y\\ \mathbf{else}:\\ \;\;\;\;0 - z\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 67.0% accurate, 21.4× speedup

Math

\[\begin{array}{l} \\ \left(0 - z\right) - y \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (- (- 0.0 z) y))

C

double code(double x, double y, double z) {
	return (0.0 - 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 = (0.0d0 - z) - y
end function

Java

public static double code(double x, double y, double z) {
	return (0.0 - z) - y;
}

Python

def code(x, y, z):
	return (0.0 - z) - y

Julia

function code(x, y, z)
	return Float64(Float64(0.0 - z) - y)
end

MATLAB

function tmp = code(x, y, z)
	tmp = (0.0 - z) - y;
end

Wolfram

code[x_, y_, z_] := N[(N[(0.0 - z), $MachinePrecision] - y), $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

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

   1. mul-1-neg N/A

      \[\leadsto \mathsf{neg}\left(\left(y + z\right)\right) \]

   2. distribute-neg-in N/A

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

   3. +-commutative N/A

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

   4. sub-neg N/A

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

   5. --lowering--.f64 N/A

      \[\leadsto \mathsf{\_.f64}\left(\left(\mathsf{neg}\left(z\right)\right), \color{blue}{y}\right) \]

   6. neg-sub0 N/A

      \[\leadsto \mathsf{\_.f64}\left(\left(0 - z\right), y\right) \]

   7. --lowering--.f64 61.4%

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(0, z\right), y\right) \]

5. Simplified 61.4%

   \[\leadsto \color{blue}{\left(0 - z\right) - y} \]
6. Step-by-step derivation

   1. sub0-neg N/A

      \[\leadsto \mathsf{\_.f64}\left(\left(\mathsf{neg}\left(z\right)\right), y\right) \]

   2. neg-lowering-neg.f64 61.4%

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{neg.f64}\left(z\right), y\right) \]

7. Applied egg-rr 61.4%

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

8. Final simplification 61.4%

   \[\leadsto \left(0 - z\right) - y \]
9. Add Preprocessing

Alternative 9: 33.9% accurate, 35.7× speedup

Math

\[\begin{array}{l} \\ 0 - y \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (- 0.0 y))

C

double code(double x, double y, double z) {
	return 0.0 - 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 = 0.0d0 - y
end function

Java

public static double code(double x, double y, double z) {
	return 0.0 - y;
}

Python

def code(x, y, z):
	return 0.0 - y

Julia

function code(x, y, z)
	return Float64(0.0 - y)
end

MATLAB

function tmp = code(x, y, z)
	tmp = 0.0 - y;
end

Wolfram

code[x_, y_, z_] := N[(0.0 - y), $MachinePrecision]

Derivation

1. Initial program 99.8%

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

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

   2. neg-sub0 N/A

      \[\leadsto 0 - \color{blue}{y} \]

   3. --lowering--.f64 35.8%

      \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{y}\right) \]

5. Simplified 35.8%

   \[\leadsto \color{blue}{0 - y} \]
6. Step-by-step derivation

   1. sub0-neg N/A

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

   2. neg-lowering-neg.f64 35.8%

      \[\leadsto \mathsf{neg.f64}\left(y\right) \]

7. Applied egg-rr 35.8%

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

8. Final simplification 35.8%

   \[\leadsto 0 - y \]
9. Add Preprocessing

Alternative 10: 2.2% accurate, 107.0× speedup

Math

\[\begin{array}{l} \\ z \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := z

Derivation

1. Initial program 99.8%

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

3. Taylor expanded in x around 0

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

   1. mul-1-neg N/A

      \[\leadsto \mathsf{neg}\left(\left(y + z\right)\right) \]

   2. distribute-neg-in N/A

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

   3. +-commutative N/A

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

   4. sub-neg N/A

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

   5. --lowering--.f64 N/A

      \[\leadsto \mathsf{\_.f64}\left(\left(\mathsf{neg}\left(z\right)\right), \color{blue}{y}\right) \]

   6. neg-sub0 N/A

      \[\leadsto \mathsf{\_.f64}\left(\left(0 - z\right), y\right) \]

   7. --lowering--.f64 61.4%

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(0, z\right), y\right) \]

5. Simplified 61.4%

   \[\leadsto \color{blue}{\left(0 - z\right) - y} \]
6. Step-by-step derivation

   1. flip3-- N/A

      \[\leadsto \mathsf{\_.f64}\left(\left(\frac{{0}^{3} - {z}^{3}}{0 \cdot 0 + \left(z \cdot z + 0 \cdot z\right)}\right), y\right) \]

   2. metadata-eval N/A

      \[\leadsto \mathsf{\_.f64}\left(\left(\frac{{0}^{3} - {z}^{3}}{0 + \left(z \cdot z + 0 \cdot z\right)}\right), y\right) \]

   3. +-lft-identity N/A

      \[\leadsto \mathsf{\_.f64}\left(\left(\frac{{0}^{3} - {z}^{3}}{z \cdot z + 0 \cdot z}\right), y\right) \]

   4. distribute-rgt-out N/A

      \[\leadsto \mathsf{\_.f64}\left(\left(\frac{{0}^{3} - {z}^{3}}{z \cdot \left(z + 0\right)}\right), y\right) \]

   5. +-commutative N/A

      \[\leadsto \mathsf{\_.f64}\left(\left(\frac{{0}^{3} - {z}^{3}}{z \cdot \left(0 + z\right)}\right), y\right) \]

   6. +-lft-identity N/A

      \[\leadsto \mathsf{\_.f64}\left(\left(\frac{{0}^{3} - {z}^{3}}{z \cdot z}\right), y\right) \]

   7. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\left({0}^{3} - {z}^{3}\right), \left(z \cdot z\right)\right), y\right) \]

   8. metadata-eval N/A

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\left(0 - {z}^{3}\right), \left(z \cdot z\right)\right), y\right) \]

   9. sub0-neg N/A

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\left(\mathsf{neg}\left({z}^{3}\right)\right), \left(z \cdot z\right)\right), y\right) \]

   10. cube-neg N/A

       \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\left({\left(\mathsf{neg}\left(z\right)\right)}^{3}\right), \left(z \cdot z\right)\right), y\right) \]

   11. sub0-neg N/A

       \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\left({\left(0 - z\right)}^{3}\right), \left(z \cdot z\right)\right), y\right) \]

   12. sqr-pow N/A

       \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\left({\left(0 - z\right)}^{\left(\frac{3}{2}\right)} \cdot {\left(0 - z\right)}^{\left(\frac{3}{2}\right)}\right), \left(z \cdot z\right)\right), y\right) \]

   13. pow-prod-down N/A

       \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\left({\left(\left(0 - z\right) \cdot \left(0 - z\right)\right)}^{\left(\frac{3}{2}\right)}\right), \left(z \cdot z\right)\right), y\right) \]

   14. sub0-neg N/A

       \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\left({\left(\left(\mathsf{neg}\left(z\right)\right) \cdot \left(0 - z\right)\right)}^{\left(\frac{3}{2}\right)}\right), \left(z \cdot z\right)\right), y\right) \]

   15. sub0-neg N/A

       \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\left({\left(\left(\mathsf{neg}\left(z\right)\right) \cdot \left(\mathsf{neg}\left(z\right)\right)\right)}^{\left(\frac{3}{2}\right)}\right), \left(z \cdot z\right)\right), y\right) \]

   16. sqr-neg N/A

       \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\left({\left(z \cdot z\right)}^{\left(\frac{3}{2}\right)}\right), \left(z \cdot z\right)\right), y\right) \]

   17. pow-prod-down N/A

       \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\left({z}^{\left(\frac{3}{2}\right)} \cdot {z}^{\left(\frac{3}{2}\right)}\right), \left(z \cdot z\right)\right), y\right) \]

   18. sqr-pow N/A

       \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\left({z}^{3}\right), \left(z \cdot z\right)\right), y\right) \]

   19. cube-mult N/A

       \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\left(z \cdot \left(z \cdot z\right)\right), \left(z \cdot z\right)\right), y\right) \]

   20. *-lowering-*.f64 N/A

       \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \left(z \cdot z\right)\right), \left(z \cdot z\right)\right), y\right) \]

   21. *-lowering-*.f64 N/A

       \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, z\right)\right), \left(z \cdot z\right)\right), y\right) \]

   22. *-lowering-*.f64 17.9%

       \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, z\right)\right), \mathsf{*.f64}\left(z, z\right)\right), y\right) \]

7. Applied egg-rr 17.9%

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

8. Taylor expanded in z around inf

   \[\leadsto \color{blue}{z} \]
9. Step-by-step derivation

10. Simplified 2.5%

    \[\leadsto \color{blue}{z} \]
11. Add Preprocessing

Reproduce

herbie shell --seed 2024152 
(FPCore (x y z)
  :name "Statistics.Distribution.Poisson:$clogProbability from math-functions-0.1.5.2"
  :precision binary64
  (- (- (* x (log y)) z) y))