Statistics.Distribution.Poisson.Internal:probability from math-functions-0.1.5.2

Percentage Accurate: 100.0% → 100.0%

Time: 8.3s

Alternatives: 15

Speedup: 1.0×

• 58.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[e^{\left(x + y \cdot \log y\right) - z} \]
2. Add Preprocessing

3. Final simplification 100.0%

   \[\leadsto e^{\left(x + y \cdot \log y\right) - z} \]
4. Add Preprocessing

Alternative 2: 89.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \log y\\ \mathbf{if}\;t\_0 \leq -5 \cdot 10^{-305} \lor \neg \left(t\_0 \leq 2 \cdot 10^{+27}\right) \land t\_0 \leq 2 \cdot 10^{+51}:\\ \;\;\;\;e^{x - z}\\ \mathbf{else}:\\ \;\;\;\;e^{t\_0}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (log y))))
   (if (or (<= t_0 -5e-305) (and (not (<= t_0 2e+27)) (<= t_0 2e+51)))
     (exp (- x z))
     (exp t_0))))

C

double code(double x, double y, double z) {
	double t_0 = y * log(y);
	double tmp;
	if ((t_0 <= -5e-305) || (!(t_0 <= 2e+27) && (t_0 <= 2e+51))) {
		tmp = exp((x - z));
	} else {
		tmp = exp(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 = y * log(y)
    if ((t_0 <= (-5d-305)) .or. (.not. (t_0 <= 2d+27)) .and. (t_0 <= 2d+51)) then
        tmp = exp((x - z))
    else
        tmp = exp(t_0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * Math.log(y);
	double tmp;
	if ((t_0 <= -5e-305) || (!(t_0 <= 2e+27) && (t_0 <= 2e+51))) {
		tmp = Math.exp((x - z));
	} else {
		tmp = Math.exp(t_0);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * math.log(y)
	tmp = 0
	if (t_0 <= -5e-305) or (not (t_0 <= 2e+27) and (t_0 <= 2e+51)):
		tmp = math.exp((x - z))
	else:
		tmp = math.exp(t_0)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * log(y))
	tmp = 0.0
	if ((t_0 <= -5e-305) || (!(t_0 <= 2e+27) && (t_0 <= 2e+51)))
		tmp = exp(Float64(x - z));
	else
		tmp = exp(t_0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * log(y);
	tmp = 0.0;
	if ((t_0 <= -5e-305) || (~((t_0 <= 2e+27)) && (t_0 <= 2e+51)))
		tmp = exp((x - z));
	else
		tmp = exp(t_0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[Log[y], $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$0, -5e-305], And[N[Not[LessEqual[t$95$0, 2e+27]], $MachinePrecision], LessEqual[t$95$0, 2e+51]]], N[Exp[N[(x - z), $MachinePrecision]], $MachinePrecision], N[Exp[t$95$0], $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y (log.f64 y)) < -4.99999999999999985e-305 or 2e27 < (*.f64 y (log.f64 y)) < 2e51

   1. Initial program 100.0%

      \[e^{\left(x + y \cdot \log y\right) - z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 99.9%

      \[\leadsto e^{\color{blue}{x} - z} \]

   if -4.99999999999999985e-305 < (*.f64 y (log.f64 y)) < 2e27 or 2e51 < (*.f64 y (log.f64 y))

   1. Initial program 100.0%

      \[e^{\left(x + y \cdot \log y\right) - z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 92.4%

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

   4. Taylor expanded in y around inf 85.6%

      \[\leadsto e^{\color{blue}{-1 \cdot \left(y \cdot \log \left(\frac{1}{y}\right)\right)}} \]
   5. Step-by-step derivation

      1. mul-1-neg 85.6%

         \[\leadsto e^{\color{blue}{-y \cdot \log \left(\frac{1}{y}\right)}} \]

      2. distribute-rgt-neg-in 85.6%

         \[\leadsto e^{\color{blue}{y \cdot \left(-\log \left(\frac{1}{y}\right)\right)}} \]

      3. log-rec 85.6%

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

      4. remove-double-neg 85.6%

         \[\leadsto e^{y \cdot \color{blue}{\log y}} \]

   6. Simplified 85.6%

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

4. Final simplification 93.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \log y \leq -5 \cdot 10^{-305} \lor \neg \left(y \cdot \log y \leq 2 \cdot 10^{+27}\right) \land y \cdot \log y \leq 2 \cdot 10^{+51}:\\ \;\;\;\;e^{x - z}\\ \mathbf{else}:\\ \;\;\;\;e^{y \cdot \log y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 94.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \log y\\ \mathbf{if}\;t\_0 \leq -5 \cdot 10^{-286}:\\ \;\;\;\;\frac{{y}^{y}}{e^{z - x}}\\ \mathbf{else}:\\ \;\;\;\;e^{t\_0 - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (log y))))
   (if (<= t_0 -5e-286) (/ (pow y y) (exp (- z x))) (exp (- t_0 z)))))

C

double code(double x, double y, double z) {
	double t_0 = y * log(y);
	double tmp;
	if (t_0 <= -5e-286) {
		tmp = pow(y, y) / exp((z - x));
	} else {
		tmp = exp((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 = y * log(y)
    if (t_0 <= (-5d-286)) then
        tmp = (y ** y) / exp((z - x))
    else
        tmp = exp((t_0 - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * Math.log(y);
	double tmp;
	if (t_0 <= -5e-286) {
		tmp = Math.pow(y, y) / Math.exp((z - x));
	} else {
		tmp = Math.exp((t_0 - z));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * math.log(y)
	tmp = 0
	if t_0 <= -5e-286:
		tmp = math.pow(y, y) / math.exp((z - x))
	else:
		tmp = math.exp((t_0 - z))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * log(y))
	tmp = 0.0
	if (t_0 <= -5e-286)
		tmp = Float64((y ^ y) / exp(Float64(z - x)));
	else
		tmp = exp(Float64(t_0 - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * log(y);
	tmp = 0.0;
	if (t_0 <= -5e-286)
		tmp = (y ^ y) / exp((z - x));
	else
		tmp = exp((t_0 - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[Log[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -5e-286], N[(N[Power[y, y], $MachinePrecision] / N[Exp[N[(z - x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[Exp[N[(t$95$0 - z), $MachinePrecision]], $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y (log.f64 y)) < -5.00000000000000037e-286

   1. Initial program 100.0%

      \[e^{\left(x + y \cdot \log y\right) - z} \]
   2. Step-by-step derivation

      1. associate--l+ 100.0%

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

      2. +-commutative 100.0%

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

      3. exp-sum 87.2%

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

      4. exp-diff 87.2%

         \[\leadsto \color{blue}{\frac{e^{y \cdot \log y}}{e^{z}}} \cdot e^{x} \]

      5. associate-/r/ 87.2%

         \[\leadsto \color{blue}{\frac{e^{y \cdot \log y}}{\frac{e^{z}}{e^{x}}}} \]

      6. *-commutative 87.2%

         \[\leadsto \frac{e^{\color{blue}{\log y \cdot y}}}{\frac{e^{z}}{e^{x}}} \]

      7. exp-to-pow 87.2%

         \[\leadsto \frac{\color{blue}{{y}^{y}}}{\frac{e^{z}}{e^{x}}} \]

      8. div-exp 100.0%

         \[\leadsto \frac{{y}^{y}}{\color{blue}{e^{z - x}}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{{y}^{y}}{e^{z - x}}} \]
   4. Add Preprocessing

   if -5.00000000000000037e-286 < (*.f64 y (log.f64 y))

   1. Initial program 100.0%

      \[e^{\left(x + y \cdot \log y\right) - z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 91.0%

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

4. Final simplification 95.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \log y \leq -5 \cdot 10^{-286}:\\ \;\;\;\;\frac{{y}^{y}}{e^{z - x}}\\ \mathbf{else}:\\ \;\;\;\;e^{y \cdot \log y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 93.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \log y\\ \mathbf{if}\;t\_0 \leq -5 \cdot 10^{-286}:\\ \;\;\;\;e^{x - z}\\ \mathbf{else}:\\ \;\;\;\;e^{t\_0 - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (log y))))
   (if (<= t_0 -5e-286) (exp (- x z)) (exp (- t_0 z)))))

C

double code(double x, double y, double z) {
	double t_0 = y * log(y);
	double tmp;
	if (t_0 <= -5e-286) {
		tmp = exp((x - z));
	} else {
		tmp = exp((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 = y * log(y)
    if (t_0 <= (-5d-286)) then
        tmp = exp((x - z))
    else
        tmp = exp((t_0 - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * Math.log(y);
	double tmp;
	if (t_0 <= -5e-286) {
		tmp = Math.exp((x - z));
	} else {
		tmp = Math.exp((t_0 - z));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * math.log(y)
	tmp = 0
	if t_0 <= -5e-286:
		tmp = math.exp((x - z))
	else:
		tmp = math.exp((t_0 - z))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * log(y))
	tmp = 0.0
	if (t_0 <= -5e-286)
		tmp = exp(Float64(x - z));
	else
		tmp = exp(Float64(t_0 - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * log(y);
	tmp = 0.0;
	if (t_0 <= -5e-286)
		tmp = exp((x - z));
	else
		tmp = exp((t_0 - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[Log[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -5e-286], N[Exp[N[(x - z), $MachinePrecision]], $MachinePrecision], N[Exp[N[(t$95$0 - z), $MachinePrecision]], $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y (log.f64 y)) < -5.00000000000000037e-286

   1. Initial program 100.0%

      \[e^{\left(x + y \cdot \log y\right) - z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 99.9%

      \[\leadsto e^{\color{blue}{x} - z} \]

   if -5.00000000000000037e-286 < (*.f64 y (log.f64 y))

   1. Initial program 100.0%

      \[e^{\left(x + y \cdot \log y\right) - z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 91.0%

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

4. Final simplification 95.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \log y \leq -5 \cdot 10^{-286}:\\ \;\;\;\;e^{x - z}\\ \mathbf{else}:\\ \;\;\;\;e^{y \cdot \log y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{-8} \lor \neg \left(x \leq 5.1 \cdot 10^{-14}\right):\\ \;\;\;\;e^{x}\\ \mathbf{else}:\\ \;\;\;\;e^{-z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.9e-8) (not (<= x 5.1e-14))) (exp x) (exp (- z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.9e-8) || !(x <= 5.1e-14)) {
		tmp = exp(x);
	} else {
		tmp = exp(-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 <= (-1.9d-8)) .or. (.not. (x <= 5.1d-14))) then
        tmp = exp(x)
    else
        tmp = exp(-z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.9e-8) || !(x <= 5.1e-14)) {
		tmp = Math.exp(x);
	} else {
		tmp = Math.exp(-z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.9e-8) or not (x <= 5.1e-14):
		tmp = math.exp(x)
	else:
		tmp = math.exp(-z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.9e-8) || !(x <= 5.1e-14))
		tmp = exp(x);
	else
		tmp = exp(Float64(-z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.9e-8) || ~((x <= 5.1e-14)))
		tmp = exp(x);
	else
		tmp = exp(-z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.9e-8], N[Not[LessEqual[x, 5.1e-14]], $MachinePrecision]], N[Exp[x], $MachinePrecision], N[Exp[(-z)], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.90000000000000014e-8 or 5.0999999999999997e-14 < x

   1. Initial program 100.0%

      \[e^{\left(x + y \cdot \log y\right) - z} \]
   2. Step-by-step derivation

      1. associate--l+ 100.0%

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

      2. +-commutative 100.0%

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

      3. exp-sum 64.6%

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

      4. exp-diff 58.5%

         \[\leadsto \color{blue}{\frac{e^{y \cdot \log y}}{e^{z}}} \cdot e^{x} \]

      5. associate-/r/ 58.5%

         \[\leadsto \color{blue}{\frac{e^{y \cdot \log y}}{\frac{e^{z}}{e^{x}}}} \]

      6. *-commutative 58.5%

         \[\leadsto \frac{e^{\color{blue}{\log y \cdot y}}}{\frac{e^{z}}{e^{x}}} \]

      7. exp-to-pow 58.5%

         \[\leadsto \frac{\color{blue}{{y}^{y}}}{\frac{e^{z}}{e^{x}}} \]

      8. div-exp 76.2%

         \[\leadsto \frac{{y}^{y}}{\color{blue}{e^{z - x}}} \]

   3. Simplified 76.2%

      \[\leadsto \color{blue}{\frac{{y}^{y}}{e^{z - x}}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 84.9%

      \[\leadsto \color{blue}{\frac{1}{e^{z - x}}} \]

   6. Taylor expanded in z around 0 76.6%

      \[\leadsto \color{blue}{\frac{1}{e^{-x}}} \]
   7. Step-by-step derivation

      1. exp-neg 76.6%

         \[\leadsto \frac{1}{\color{blue}{\frac{1}{e^{x}}}} \]

      2. remove-double-div 76.6%

         \[\leadsto \color{blue}{e^{x}} \]

   8. Simplified 76.6%

      \[\leadsto \color{blue}{e^{x}} \]

   if -1.90000000000000014e-8 < x < 5.0999999999999997e-14

   1. Initial program 100.0%

      \[e^{\left(x + y \cdot \log y\right) - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 61.4%

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

      1. neg-mul-1 61.4%

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

   5. Simplified 61.4%

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

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{-8} \lor \neg \left(x \leq 5.1 \cdot 10^{-14}\right):\\ \;\;\;\;e^{x}\\ \mathbf{else}:\\ \;\;\;\;e^{-z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 68.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+154}:\\ \;\;\;\;1 + z \cdot \left(z \cdot 0.5 + -1\right)\\ \mathbf{elif}\;z \leq 125000000:\\ \;\;\;\;e^{x}\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.9e+154)
   (+ 1.0 (* z (+ (* z 0.5) -1.0)))
   (if (<= z 125000000.0) (exp x) 0.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.9e+154) {
		tmp = 1.0 + (z * ((z * 0.5) + -1.0));
	} else if (z <= 125000000.0) {
		tmp = exp(x);
	} else {
		tmp = 0.0;
	}
	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) :: tmp
    if (z <= (-1.9d+154)) then
        tmp = 1.0d0 + (z * ((z * 0.5d0) + (-1.0d0)))
    else if (z <= 125000000.0d0) then
        tmp = exp(x)
    else
        tmp = 0.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.9e+154) {
		tmp = 1.0 + (z * ((z * 0.5) + -1.0));
	} else if (z <= 125000000.0) {
		tmp = Math.exp(x);
	} else {
		tmp = 0.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.9e+154:
		tmp = 1.0 + (z * ((z * 0.5) + -1.0))
	elif z <= 125000000.0:
		tmp = math.exp(x)
	else:
		tmp = 0.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.9e+154)
		tmp = Float64(1.0 + Float64(z * Float64(Float64(z * 0.5) + -1.0)));
	elseif (z <= 125000000.0)
		tmp = exp(x);
	else
		tmp = 0.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.9e+154)
		tmp = 1.0 + (z * ((z * 0.5) + -1.0));
	elseif (z <= 125000000.0)
		tmp = exp(x);
	else
		tmp = 0.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.9e+154], N[(1.0 + N[(z * N[(N[(z * 0.5), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 125000000.0], N[Exp[x], $MachinePrecision], 0.0]]

Derivation

1. Split input into 3 regimes

2. if z < -1.8999999999999999e154

   1. Initial program 100.0%

      \[e^{\left(x + y \cdot \log y\right) - z} \]
   2. Step-by-step derivation

      1. associate--l+ 100.0%

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

      2. +-commutative 100.0%

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

      3. exp-sum 79.3%

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

      4. exp-diff 79.3%

         \[\leadsto \color{blue}{\frac{e^{y \cdot \log y}}{e^{z}}} \cdot e^{x} \]

      5. associate-/r/ 79.3%

         \[\leadsto \color{blue}{\frac{e^{y \cdot \log y}}{\frac{e^{z}}{e^{x}}}} \]

      6. *-commutative 79.3%

         \[\leadsto \frac{e^{\color{blue}{\log y \cdot y}}}{\frac{e^{z}}{e^{x}}} \]

      7. exp-to-pow 79.3%

         \[\leadsto \frac{\color{blue}{{y}^{y}}}{\frac{e^{z}}{e^{x}}} \]

      8. div-exp 100.0%

         \[\leadsto \frac{{y}^{y}}{\color{blue}{e^{z - x}}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{{y}^{y}}{e^{z - x}}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 100.0%

      \[\leadsto \color{blue}{\frac{1}{e^{z - x}}} \]

   6. Taylor expanded in x around 0 100.0%

      \[\leadsto \color{blue}{\frac{1}{e^{z}}} \]

   7. Taylor expanded in z around 0 100.0%

      \[\leadsto \color{blue}{1 + z \cdot \left(0.5 \cdot z - 1\right)} \]

   if -1.8999999999999999e154 < z < 1.25e8

   1. Initial program 100.0%

      \[e^{\left(x + y \cdot \log y\right) - z} \]
   2. Step-by-step derivation

      1. associate--l+ 100.0%

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

      2. +-commutative 100.0%

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

      3. exp-sum 82.8%

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

      4. exp-diff 82.8%

         \[\leadsto \color{blue}{\frac{e^{y \cdot \log y}}{e^{z}}} \cdot e^{x} \]

      5. associate-/r/ 82.8%

         \[\leadsto \color{blue}{\frac{e^{y \cdot \log y}}{\frac{e^{z}}{e^{x}}}} \]

      6. *-commutative 82.8%

         \[\leadsto \frac{e^{\color{blue}{\log y \cdot y}}}{\frac{e^{z}}{e^{x}}} \]

      7. exp-to-pow 82.8%

         \[\leadsto \frac{\color{blue}{{y}^{y}}}{\frac{e^{z}}{e^{x}}} \]

      8. div-exp 88.7%

         \[\leadsto \frac{{y}^{y}}{\color{blue}{e^{z - x}}} \]

   3. Simplified 88.7%

      \[\leadsto \color{blue}{\frac{{y}^{y}}{e^{z - x}}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 67.8%

      \[\leadsto \color{blue}{\frac{1}{e^{z - x}}} \]

   6. Taylor expanded in z around 0 59.4%

      \[\leadsto \color{blue}{\frac{1}{e^{-x}}} \]
   7. Step-by-step derivation

      1. exp-neg 59.4%

         \[\leadsto \frac{1}{\color{blue}{\frac{1}{e^{x}}}} \]

      2. remove-double-div 59.4%

         \[\leadsto \color{blue}{e^{x}} \]

   8. Simplified 59.4%

      \[\leadsto \color{blue}{e^{x}} \]

   if 1.25e8 < z

   1. Initial program 100.0%

      \[e^{\left(x + y \cdot \log y\right) - z} \]
   2. Step-by-step derivation

      1. associate--l+ 100.0%

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

      2. +-commutative 100.0%

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

      3. exp-sum 81.0%

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

      4. exp-diff 37.9%

         \[\leadsto \color{blue}{\frac{e^{y \cdot \log y}}{e^{z}}} \cdot e^{x} \]

      5. associate-/r/ 37.9%

         \[\leadsto \color{blue}{\frac{e^{y \cdot \log y}}{\frac{e^{z}}{e^{x}}}} \]

      6. *-commutative 37.9%

         \[\leadsto \frac{e^{\color{blue}{\log y \cdot y}}}{\frac{e^{z}}{e^{x}}} \]

      7. exp-to-pow 37.9%

         \[\leadsto \frac{\color{blue}{{y}^{y}}}{\frac{e^{z}}{e^{x}}} \]

      8. div-exp 50.0%

         \[\leadsto \frac{{y}^{y}}{\color{blue}{e^{z - x}}} \]

   3. Simplified 50.0%

      \[\leadsto \color{blue}{\frac{{y}^{y}}{e^{z - x}}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 76.2%

      \[\leadsto \color{blue}{\frac{1}{e^{z - x}}} \]

   6. Taylor expanded in z around 0 36.4%

      \[\leadsto \color{blue}{\frac{1}{e^{-x}}} \]

   8. Applied egg-rr 67.8%

      \[\leadsto \color{blue}{0} \]
3. Recombined 3 regimes into one program.

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+154}:\\ \;\;\;\;1 + z \cdot \left(z \cdot 0.5 + -1\right)\\ \mathbf{elif}\;z \leq 125000000:\\ \;\;\;\;e^{x}\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 77.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 8.8 \cdot 10^{+64}:\\ \;\;\;\;e^{x - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{{z}^{6}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 8.8e+64) (exp (- x z)) (/ 1.0 (pow z 6.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 8.8e+64) {
		tmp = exp((x - z));
	} else {
		tmp = 1.0 / pow(z, 6.0);
	}
	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) :: tmp
    if (y <= 8.8d+64) then
        tmp = exp((x - z))
    else
        tmp = 1.0d0 / (z ** 6.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 8.8e+64) {
		tmp = Math.exp((x - z));
	} else {
		tmp = 1.0 / Math.pow(z, 6.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 8.8e+64:
		tmp = math.exp((x - z))
	else:
		tmp = 1.0 / math.pow(z, 6.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 8.8e+64)
		tmp = exp(Float64(x - z));
	else
		tmp = Float64(1.0 / (z ^ 6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 8.8e+64)
		tmp = exp((x - z));
	else
		tmp = 1.0 / (z ^ 6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 8.8e+64], N[Exp[N[(x - z), $MachinePrecision]], $MachinePrecision], N[(1.0 / N[Power[z, 6.0], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 8.80000000000000007e64

   1. Initial program 100.0%

      \[e^{\left(x + y \cdot \log y\right) - z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 93.7%

      \[\leadsto e^{\color{blue}{x} - z} \]

   if 8.80000000000000007e64 < y

   1. Initial program 100.0%

      \[e^{\left(x + y \cdot \log y\right) - z} \]
   2. Step-by-step derivation

      1. associate--l+ 100.0%

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

      2. +-commutative 100.0%

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

      3. exp-sum 77.0%

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

      4. exp-diff 56.0%

         \[\leadsto \color{blue}{\frac{e^{y \cdot \log y}}{e^{z}}} \cdot e^{x} \]

      5. associate-/r/ 56.0%

         \[\leadsto \color{blue}{\frac{e^{y \cdot \log y}}{\frac{e^{z}}{e^{x}}}} \]

      6. *-commutative 56.0%

         \[\leadsto \frac{e^{\color{blue}{\log y \cdot y}}}{\frac{e^{z}}{e^{x}}} \]

      7. exp-to-pow 56.0%

         \[\leadsto \frac{\color{blue}{{y}^{y}}}{\frac{e^{z}}{e^{x}}} \]

      8. div-exp 62.0%

         \[\leadsto \frac{{y}^{y}}{\color{blue}{e^{z - x}}} \]

   3. Simplified 62.0%

      \[\leadsto \color{blue}{\frac{{y}^{y}}{e^{z - x}}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 41.6%

      \[\leadsto \color{blue}{\frac{1}{e^{z - x}}} \]

   6. Taylor expanded in x around 0 29.0%

      \[\leadsto \color{blue}{\frac{1}{e^{z}}} \]

   8. Applied egg-rr 50.5%

      \[\leadsto \color{blue}{{\left(\mathsf{expm1}\left(z\right)\right)}^{-6}} \]

   9. Taylor expanded in z around 0 51.2%

      \[\leadsto \color{blue}{\frac{1}{{z}^{6}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 8.8 \cdot 10^{+64}:\\ \;\;\;\;e^{x - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{{z}^{6}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 79.4% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ e^{x - z} \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[e^{\left(x + y \cdot \log y\right) - z} \]
2. Add Preprocessing

3. Taylor expanded in x around inf 73.4%

   \[\leadsto e^{\color{blue}{x} - z} \]

4. Final simplification 73.4%

   \[\leadsto e^{x - z} \]
5. Add Preprocessing

Alternative 9: 41.5% accurate, 8.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{-30}:\\ \;\;\;\;0\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{-269}:\\ \;\;\;\;1 - z\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-148}:\\ \;\;\;\;0\\ \mathbf{else}:\\ \;\;\;\;1 + x \cdot \left(1 + x \cdot 0.5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -4e-30)
   0.0
   (if (<= x 9.5e-269)
     (- 1.0 z)
     (if (<= x 3.5e-148) 0.0 (+ 1.0 (* x (+ 1.0 (* x 0.5))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -4e-30) {
		tmp = 0.0;
	} else if (x <= 9.5e-269) {
		tmp = 1.0 - z;
	} else if (x <= 3.5e-148) {
		tmp = 0.0;
	} else {
		tmp = 1.0 + (x * (1.0 + (x * 0.5)));
	}
	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 <= (-4d-30)) then
        tmp = 0.0d0
    else if (x <= 9.5d-269) then
        tmp = 1.0d0 - z
    else if (x <= 3.5d-148) then
        tmp = 0.0d0
    else
        tmp = 1.0d0 + (x * (1.0d0 + (x * 0.5d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -4e-30) {
		tmp = 0.0;
	} else if (x <= 9.5e-269) {
		tmp = 1.0 - z;
	} else if (x <= 3.5e-148) {
		tmp = 0.0;
	} else {
		tmp = 1.0 + (x * (1.0 + (x * 0.5)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -4e-30:
		tmp = 0.0
	elif x <= 9.5e-269:
		tmp = 1.0 - z
	elif x <= 3.5e-148:
		tmp = 0.0
	else:
		tmp = 1.0 + (x * (1.0 + (x * 0.5)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -4e-30)
		tmp = 0.0;
	elseif (x <= 9.5e-269)
		tmp = Float64(1.0 - z);
	elseif (x <= 3.5e-148)
		tmp = 0.0;
	else
		tmp = Float64(1.0 + Float64(x * Float64(1.0 + Float64(x * 0.5))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -4e-30)
		tmp = 0.0;
	elseif (x <= 9.5e-269)
		tmp = 1.0 - z;
	elseif (x <= 3.5e-148)
		tmp = 0.0;
	else
		tmp = 1.0 + (x * (1.0 + (x * 0.5)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -4e-30], 0.0, If[LessEqual[x, 9.5e-269], N[(1.0 - z), $MachinePrecision], If[LessEqual[x, 3.5e-148], 0.0, N[(1.0 + N[(x * N[(1.0 + N[(x * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -4e-30 or 9.5000000000000006e-269 < x < 3.5e-148

   1. Initial program 100.0%

      \[e^{\left(x + y \cdot \log y\right) - z} \]
   2. Step-by-step derivation

      1. associate--l+ 100.0%

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

      2. +-commutative 100.0%

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

      3. exp-sum 64.8%

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

      4. exp-diff 52.8%

         \[\leadsto \color{blue}{\frac{e^{y \cdot \log y}}{e^{z}}} \cdot e^{x} \]

      5. associate-/r/ 52.8%

         \[\leadsto \color{blue}{\frac{e^{y \cdot \log y}}{\frac{e^{z}}{e^{x}}}} \]

      6. *-commutative 52.8%

         \[\leadsto \frac{e^{\color{blue}{\log y \cdot y}}}{\frac{e^{z}}{e^{x}}} \]

      7. exp-to-pow 52.8%

         \[\leadsto \frac{\color{blue}{{y}^{y}}}{\frac{e^{z}}{e^{x}}} \]

      8. div-exp 66.7%

         \[\leadsto \frac{{y}^{y}}{\color{blue}{e^{z - x}}} \]

   3. Simplified 66.7%

      \[\leadsto \color{blue}{\frac{{y}^{y}}{e^{z - x}}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 71.9%

      \[\leadsto \color{blue}{\frac{1}{e^{z - x}}} \]

   6. Taylor expanded in z around 0 48.6%

      \[\leadsto \color{blue}{\frac{1}{e^{-x}}} \]

   8. Applied egg-rr 53.6%

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

   if -4e-30 < x < 9.5000000000000006e-269

   1. Initial program 100.0%

      \[e^{\left(x + y \cdot \log y\right) - z} \]
   2. Step-by-step derivation

      1. associate--l+ 100.0%

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

      2. +-commutative 100.0%

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

      3. exp-sum 100.0%

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

      4. exp-diff 90.5%

         \[\leadsto \color{blue}{\frac{e^{y \cdot \log y}}{e^{z}}} \cdot e^{x} \]

      5. associate-/r/ 90.5%

         \[\leadsto \color{blue}{\frac{e^{y \cdot \log y}}{\frac{e^{z}}{e^{x}}}} \]

      6. *-commutative 90.5%

         \[\leadsto \frac{e^{\color{blue}{\log y \cdot y}}}{\frac{e^{z}}{e^{x}}} \]

      7. exp-to-pow 90.5%

         \[\leadsto \frac{\color{blue}{{y}^{y}}}{\frac{e^{z}}{e^{x}}} \]

      8. div-exp 90.5%

         \[\leadsto \frac{{y}^{y}}{\color{blue}{e^{z - x}}} \]

   3. Simplified 90.5%

      \[\leadsto \color{blue}{\frac{{y}^{y}}{e^{z - x}}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 66.0%

      \[\leadsto \color{blue}{\frac{1}{e^{z - x}}} \]

   6. Taylor expanded in x around 0 66.0%

      \[\leadsto \color{blue}{\frac{1}{e^{z}}} \]

   7. Taylor expanded in z around 0 29.0%

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

      1. mul-1-neg 29.0%

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

      2. unsub-neg 29.0%

         \[\leadsto \color{blue}{1 - z} \]

   9. Simplified 29.0%

      \[\leadsto \color{blue}{1 - z} \]

   if 3.5e-148 < x

   1. Initial program 100.0%

      \[e^{\left(x + y \cdot \log y\right) - z} \]
   2. Step-by-step derivation

      1. associate--l+ 100.0%

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

      2. +-commutative 100.0%

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

      3. exp-sum 90.6%

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

      4. exp-diff 83.5%

         \[\leadsto \color{blue}{\frac{e^{y \cdot \log y}}{e^{z}}} \cdot e^{x} \]

      5. associate-/r/ 83.5%

         \[\leadsto \color{blue}{\frac{e^{y \cdot \log y}}{\frac{e^{z}}{e^{x}}}} \]

      6. *-commutative 83.5%

         \[\leadsto \frac{e^{\color{blue}{\log y \cdot y}}}{\frac{e^{z}}{e^{x}}} \]

      7. exp-to-pow 83.5%

         \[\leadsto \frac{\color{blue}{{y}^{y}}}{\frac{e^{z}}{e^{x}}} \]

      8. div-exp 92.9%

         \[\leadsto \frac{{y}^{y}}{\color{blue}{e^{z - x}}} \]

   3. Simplified 92.9%

      \[\leadsto \color{blue}{\frac{{y}^{y}}{e^{z - x}}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 80.6%

      \[\leadsto \color{blue}{\frac{1}{e^{z - x}}} \]

   6. Taylor expanded in z around 0 73.1%

      \[\leadsto \color{blue}{\frac{1}{e^{-x}}} \]

   7. Taylor expanded in x around 0 50.8%

      \[\leadsto \color{blue}{1 + x \cdot \left(1 + 0.5 \cdot x\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 46.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{-30}:\\ \;\;\;\;0\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{-269}:\\ \;\;\;\;1 - z\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-148}:\\ \;\;\;\;0\\ \mathbf{else}:\\ \;\;\;\;1 + x \cdot \left(1 + x \cdot 0.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 32.4% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.05 \cdot 10^{-29}:\\ \;\;\;\;0\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-269} \lor \neg \left(x \leq 3.06 \cdot 10^{-148}\right) \land x \leq 4.35 \cdot 10^{-48}:\\ \;\;\;\;1 - z\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -2.05e-29)
   0.0
   (if (or (<= x 3.5e-269) (and (not (<= x 3.06e-148)) (<= x 4.35e-48)))
     (- 1.0 z)
     0.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.05e-29) {
		tmp = 0.0;
	} else if ((x <= 3.5e-269) || (!(x <= 3.06e-148) && (x <= 4.35e-48))) {
		tmp = 1.0 - z;
	} else {
		tmp = 0.0;
	}
	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) :: tmp
    if (x <= (-2.05d-29)) then
        tmp = 0.0d0
    else if ((x <= 3.5d-269) .or. (.not. (x <= 3.06d-148)) .and. (x <= 4.35d-48)) then
        tmp = 1.0d0 - z
    else
        tmp = 0.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.05e-29) {
		tmp = 0.0;
	} else if ((x <= 3.5e-269) || (!(x <= 3.06e-148) && (x <= 4.35e-48))) {
		tmp = 1.0 - z;
	} else {
		tmp = 0.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -2.05e-29:
		tmp = 0.0
	elif (x <= 3.5e-269) or (not (x <= 3.06e-148) and (x <= 4.35e-48)):
		tmp = 1.0 - z
	else:
		tmp = 0.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2.05e-29)
		tmp = 0.0;
	elseif ((x <= 3.5e-269) || (!(x <= 3.06e-148) && (x <= 4.35e-48)))
		tmp = Float64(1.0 - z);
	else
		tmp = 0.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -2.05e-29)
		tmp = 0.0;
	elseif ((x <= 3.5e-269) || (~((x <= 3.06e-148)) && (x <= 4.35e-48)))
		tmp = 1.0 - z;
	else
		tmp = 0.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2.05e-29], 0.0, If[Or[LessEqual[x, 3.5e-269], And[N[Not[LessEqual[x, 3.06e-148]], $MachinePrecision], LessEqual[x, 4.35e-48]]], N[(1.0 - z), $MachinePrecision], 0.0]]

Derivation

1. Split input into 2 regimes

2. if x < -2.0499999999999999e-29 or 3.50000000000000019e-269 < x < 3.0600000000000001e-148 or 4.3499999999999998e-48 < x

   1. Initial program 100.0%

      \[e^{\left(x + y \cdot \log y\right) - z} \]
   2. Step-by-step derivation

      1. associate--l+ 100.0%

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

      2. +-commutative 100.0%

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

      3. exp-sum 73.3%

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

      4. exp-diff 62.8%

         \[\leadsto \color{blue}{\frac{e^{y \cdot \log y}}{e^{z}}} \cdot e^{x} \]

      5. associate-/r/ 62.8%

         \[\leadsto \color{blue}{\frac{e^{y \cdot \log y}}{\frac{e^{z}}{e^{x}}}} \]

      6. *-commutative 62.8%

         \[\leadsto \frac{e^{\color{blue}{\log y \cdot y}}}{\frac{e^{z}}{e^{x}}} \]

      7. exp-to-pow 62.8%

         \[\leadsto \frac{\color{blue}{{y}^{y}}}{\frac{e^{z}}{e^{x}}} \]

      8. div-exp 76.2%

         \[\leadsto \frac{{y}^{y}}{\color{blue}{e^{z - x}}} \]

   3. Simplified 76.2%

      \[\leadsto \color{blue}{\frac{{y}^{y}}{e^{z - x}}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 78.4%

      \[\leadsto \color{blue}{\frac{1}{e^{z - x}}} \]

   6. Taylor expanded in z around 0 60.9%

      \[\leadsto \color{blue}{\frac{1}{e^{-x}}} \]

   8. Applied egg-rr 38.3%

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

   if -2.0499999999999999e-29 < x < 3.50000000000000019e-269 or 3.0600000000000001e-148 < x < 4.3499999999999998e-48

   1. Initial program 100.0%

      \[e^{\left(x + y \cdot \log y\right) - z} \]
   2. Step-by-step derivation

      1. associate--l+ 100.0%

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

      2. +-commutative 100.0%

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

      3. exp-sum 100.0%

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

      4. exp-diff 91.6%

         \[\leadsto \color{blue}{\frac{e^{y \cdot \log y}}{e^{z}}} \cdot e^{x} \]

      5. associate-/r/ 91.6%

         \[\leadsto \color{blue}{\frac{e^{y \cdot \log y}}{\frac{e^{z}}{e^{x}}}} \]

      6. *-commutative 91.6%

         \[\leadsto \frac{e^{\color{blue}{\log y \cdot y}}}{\frac{e^{z}}{e^{x}}} \]

      7. exp-to-pow 91.6%

         \[\leadsto \frac{\color{blue}{{y}^{y}}}{\frac{e^{z}}{e^{x}}} \]

      8. div-exp 91.6%

         \[\leadsto \frac{{y}^{y}}{\color{blue}{e^{z - x}}} \]

   3. Simplified 91.6%

      \[\leadsto \color{blue}{\frac{{y}^{y}}{e^{z - x}}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 63.0%

      \[\leadsto \color{blue}{\frac{1}{e^{z - x}}} \]

   6. Taylor expanded in x around 0 63.0%

      \[\leadsto \color{blue}{\frac{1}{e^{z}}} \]

   7. Taylor expanded in z around 0 33.4%

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

      1. mul-1-neg 33.4%

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

      2. unsub-neg 33.4%

         \[\leadsto \color{blue}{1 - z} \]

   9. Simplified 33.4%

      \[\leadsto \color{blue}{1 - z} \]
3. Recombined 2 regimes into one program.

4. Final simplification 36.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.05 \cdot 10^{-29}:\\ \;\;\;\;0\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-269} \lor \neg \left(x \leq 3.06 \cdot 10^{-148}\right) \land x \leq 4.35 \cdot 10^{-48}:\\ \;\;\;\;1 - z\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 52.8% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.8 \cdot 10^{-19}:\\ \;\;\;\;0\\ \mathbf{elif}\;x \leq 9 \cdot 10^{+42}:\\ \;\;\;\;1 + z \cdot \left(z \cdot 0.5 + -1\right)\\ \mathbf{else}:\\ \;\;\;\;1 + x \cdot \left(1 + x \cdot \left(0.5 + x \cdot 0.16666666666666666\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -9.8e-19)
   0.0
   (if (<= x 9e+42)
     (+ 1.0 (* z (+ (* z 0.5) -1.0)))
     (+ 1.0 (* x (+ 1.0 (* x (+ 0.5 (* x 0.16666666666666666)))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -9.8e-19) {
		tmp = 0.0;
	} else if (x <= 9e+42) {
		tmp = 1.0 + (z * ((z * 0.5) + -1.0));
	} else {
		tmp = 1.0 + (x * (1.0 + (x * (0.5 + (x * 0.16666666666666666)))));
	}
	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 <= (-9.8d-19)) then
        tmp = 0.0d0
    else if (x <= 9d+42) then
        tmp = 1.0d0 + (z * ((z * 0.5d0) + (-1.0d0)))
    else
        tmp = 1.0d0 + (x * (1.0d0 + (x * (0.5d0 + (x * 0.16666666666666666d0)))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -9.8e-19) {
		tmp = 0.0;
	} else if (x <= 9e+42) {
		tmp = 1.0 + (z * ((z * 0.5) + -1.0));
	} else {
		tmp = 1.0 + (x * (1.0 + (x * (0.5 + (x * 0.16666666666666666)))));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -9.8e-19:
		tmp = 0.0
	elif x <= 9e+42:
		tmp = 1.0 + (z * ((z * 0.5) + -1.0))
	else:
		tmp = 1.0 + (x * (1.0 + (x * (0.5 + (x * 0.16666666666666666)))))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -9.8e-19)
		tmp = 0.0;
	elseif (x <= 9e+42)
		tmp = Float64(1.0 + Float64(z * Float64(Float64(z * 0.5) + -1.0)));
	else
		tmp = Float64(1.0 + Float64(x * Float64(1.0 + Float64(x * Float64(0.5 + Float64(x * 0.16666666666666666))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -9.8e-19)
		tmp = 0.0;
	elseif (x <= 9e+42)
		tmp = 1.0 + (z * ((z * 0.5) + -1.0));
	else
		tmp = 1.0 + (x * (1.0 + (x * (0.5 + (x * 0.16666666666666666)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -9.8e-19], 0.0, If[LessEqual[x, 9e+42], N[(1.0 + N[(z * N[(N[(z * 0.5), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(x * N[(1.0 + N[(x * N[(0.5 + N[(x * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -9.79999999999999985e-19

   1. Initial program 100.0%

      \[e^{\left(x + y \cdot \log y\right) - z} \]
   2. Step-by-step derivation

      1. associate--l+ 100.0%

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

      2. +-commutative 100.0%

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

      3. exp-sum 48.6%

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

      4. exp-diff 41.9%

         \[\leadsto \color{blue}{\frac{e^{y \cdot \log y}}{e^{z}}} \cdot e^{x} \]

      5. associate-/r/ 41.9%

         \[\leadsto \color{blue}{\frac{e^{y \cdot \log y}}{\frac{e^{z}}{e^{x}}}} \]

      6. *-commutative 41.9%

         \[\leadsto \frac{e^{\color{blue}{\log y \cdot y}}}{\frac{e^{z}}{e^{x}}} \]

      7. exp-to-pow 41.9%

         \[\leadsto \frac{\color{blue}{{y}^{y}}}{\frac{e^{z}}{e^{x}}} \]

      8. div-exp 62.2%

         \[\leadsto \frac{{y}^{y}}{\color{blue}{e^{z - x}}} \]

   3. Simplified 62.2%

      \[\leadsto \color{blue}{\frac{{y}^{y}}{e^{z - x}}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 80.0%

      \[\leadsto \color{blue}{\frac{1}{e^{z - x}}} \]

   6. Taylor expanded in z around 0 65.4%

      \[\leadsto \color{blue}{\frac{1}{e^{-x}}} \]

   8. Applied egg-rr 66.8%

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

   if -9.79999999999999985e-19 < x < 9.00000000000000025e42

   1. Initial program 100.0%

      \[e^{\left(x + y \cdot \log y\right) - z} \]
   2. Step-by-step derivation

      1. associate--l+ 100.0%

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

      2. +-commutative 100.0%

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

      3. exp-sum 99.2%

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

      4. exp-diff 86.4%

         \[\leadsto \color{blue}{\frac{e^{y \cdot \log y}}{e^{z}}} \cdot e^{x} \]

      5. associate-/r/ 86.4%

         \[\leadsto \color{blue}{\frac{e^{y \cdot \log y}}{\frac{e^{z}}{e^{x}}}} \]

      6. *-commutative 86.4%

         \[\leadsto \frac{e^{\color{blue}{\log y \cdot y}}}{\frac{e^{z}}{e^{x}}} \]

      7. exp-to-pow 86.4%

         \[\leadsto \frac{\color{blue}{{y}^{y}}}{\frac{e^{z}}{e^{x}}} \]

      8. div-exp 86.4%

         \[\leadsto \frac{{y}^{y}}{\color{blue}{e^{z - x}}} \]

   3. Simplified 86.4%

      \[\leadsto \color{blue}{\frac{{y}^{y}}{e^{z - x}}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 60.3%

      \[\leadsto \color{blue}{\frac{1}{e^{z - x}}} \]

   6. Taylor expanded in x around 0 58.8%

      \[\leadsto \color{blue}{\frac{1}{e^{z}}} \]

   7. Taylor expanded in z around 0 35.9%

      \[\leadsto \color{blue}{1 + z \cdot \left(0.5 \cdot z - 1\right)} \]

   if 9.00000000000000025e42 < x

   1. Initial program 100.0%

      \[e^{\left(x + y \cdot \log y\right) - z} \]
   2. Step-by-step derivation

      1. associate--l+ 100.0%

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

      2. +-commutative 100.0%

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

      3. exp-sum 86.0%

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

      4. exp-diff 80.0%

         \[\leadsto \color{blue}{\frac{e^{y \cdot \log y}}{e^{z}}} \cdot e^{x} \]

      5. associate-/r/ 80.0%

         \[\leadsto \color{blue}{\frac{e^{y \cdot \log y}}{\frac{e^{z}}{e^{x}}}} \]

      6. *-commutative 80.0%

         \[\leadsto \frac{e^{\color{blue}{\log y \cdot y}}}{\frac{e^{z}}{e^{x}}} \]

      7. exp-to-pow 80.0%

         \[\leadsto \frac{\color{blue}{{y}^{y}}}{\frac{e^{z}}{e^{x}}} \]

      8. div-exp 96.0%

         \[\leadsto \frac{{y}^{y}}{\color{blue}{e^{z - x}}} \]

   3. Simplified 96.0%

      \[\leadsto \color{blue}{\frac{{y}^{y}}{e^{z - x}}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 98.0%

      \[\leadsto \color{blue}{\frac{1}{e^{z - x}}} \]

   6. Taylor expanded in z around 0 94.1%

      \[\leadsto \color{blue}{\frac{1}{e^{-x}}} \]

   7. Taylor expanded in x around 0 80.9%

      \[\leadsto \color{blue}{1 + x \cdot \left(1 + x \cdot \left(0.5 + 0.16666666666666666 \cdot x\right)\right)} \]
   8. Step-by-step derivation

      1. +-commutative 80.9%

         \[\leadsto 1 + x \cdot \color{blue}{\left(x \cdot \left(0.5 + 0.16666666666666666 \cdot x\right) + 1\right)} \]

      2. distribute-lft-in 80.9%

         \[\leadsto 1 + \color{blue}{\left(x \cdot \left(x \cdot \left(0.5 + 0.16666666666666666 \cdot x\right)\right) + x \cdot 1\right)} \]

      3. *-rgt-identity 80.9%

         \[\leadsto 1 + \left(x \cdot \left(x \cdot \left(0.5 + 0.16666666666666666 \cdot x\right)\right) + \color{blue}{x}\right) \]

      4. remove-double-neg 80.9%

         \[\leadsto 1 + \left(x \cdot \left(x \cdot \left(0.5 + 0.16666666666666666 \cdot x\right)\right) + \color{blue}{\left(-\left(-x\right)\right)}\right) \]

      5. mul-1-neg 80.9%

         \[\leadsto 1 + \left(x \cdot \left(x \cdot \left(0.5 + 0.16666666666666666 \cdot x\right)\right) + \left(-\color{blue}{-1 \cdot x}\right)\right) \]

      6. unsub-neg 80.9%

         \[\leadsto 1 + \color{blue}{\left(x \cdot \left(x \cdot \left(0.5 + 0.16666666666666666 \cdot x\right)\right) - -1 \cdot x\right)} \]

      7. unsub-neg 80.9%

         \[\leadsto 1 + \color{blue}{\left(x \cdot \left(x \cdot \left(0.5 + 0.16666666666666666 \cdot x\right)\right) + \left(--1 \cdot x\right)\right)} \]

      8. mul-1-neg 80.9%

         \[\leadsto 1 + \left(x \cdot \left(x \cdot \left(0.5 + 0.16666666666666666 \cdot x\right)\right) + \left(-\color{blue}{\left(-x\right)}\right)\right) \]

      9. remove-double-neg 80.9%

         \[\leadsto 1 + \left(x \cdot \left(x \cdot \left(0.5 + 0.16666666666666666 \cdot x\right)\right) + \color{blue}{x}\right) \]

      10. *-rgt-identity 80.9%

          \[\leadsto 1 + \left(x \cdot \left(x \cdot \left(0.5 + 0.16666666666666666 \cdot x\right)\right) + \color{blue}{x \cdot 1}\right) \]

      11. distribute-lft-in 80.9%

          \[\leadsto 1 + \color{blue}{x \cdot \left(x \cdot \left(0.5 + 0.16666666666666666 \cdot x\right) + 1\right)} \]

      12. +-commutative 80.9%

          \[\leadsto 1 + x \cdot \color{blue}{\left(1 + x \cdot \left(0.5 + 0.16666666666666666 \cdot x\right)\right)} \]

      13. *-commutative 80.9%

          \[\leadsto 1 + x \cdot \left(1 + x \cdot \left(0.5 + \color{blue}{x \cdot 0.16666666666666666}\right)\right) \]

   9. Simplified 80.9%

      \[\leadsto \color{blue}{1 + x \cdot \left(1 + x \cdot \left(0.5 + x \cdot 0.16666666666666666\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 53.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.8 \cdot 10^{-19}:\\ \;\;\;\;0\\ \mathbf{elif}\;x \leq 9 \cdot 10^{+42}:\\ \;\;\;\;1 + z \cdot \left(z \cdot 0.5 + -1\right)\\ \mathbf{else}:\\ \;\;\;\;1 + x \cdot \left(1 + x \cdot \left(0.5 + x \cdot 0.16666666666666666\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 54.1% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.25 \cdot 10^{-18}:\\ \;\;\;\;0\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{+77}:\\ \;\;\;\;1 + z \cdot \left(z \cdot \left(0.5 + z \cdot -0.16666666666666666\right) + -1\right)\\ \mathbf{else}:\\ \;\;\;\;1 + x \cdot \left(1 + x \cdot \left(0.5 + x \cdot 0.16666666666666666\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -2.25e-18)
   0.0
   (if (<= x 1.4e+77)
     (+ 1.0 (* z (+ (* z (+ 0.5 (* z -0.16666666666666666))) -1.0)))
     (+ 1.0 (* x (+ 1.0 (* x (+ 0.5 (* x 0.16666666666666666)))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.25e-18) {
		tmp = 0.0;
	} else if (x <= 1.4e+77) {
		tmp = 1.0 + (z * ((z * (0.5 + (z * -0.16666666666666666))) + -1.0));
	} else {
		tmp = 1.0 + (x * (1.0 + (x * (0.5 + (x * 0.16666666666666666)))));
	}
	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 <= (-2.25d-18)) then
        tmp = 0.0d0
    else if (x <= 1.4d+77) then
        tmp = 1.0d0 + (z * ((z * (0.5d0 + (z * (-0.16666666666666666d0)))) + (-1.0d0)))
    else
        tmp = 1.0d0 + (x * (1.0d0 + (x * (0.5d0 + (x * 0.16666666666666666d0)))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.25e-18) {
		tmp = 0.0;
	} else if (x <= 1.4e+77) {
		tmp = 1.0 + (z * ((z * (0.5 + (z * -0.16666666666666666))) + -1.0));
	} else {
		tmp = 1.0 + (x * (1.0 + (x * (0.5 + (x * 0.16666666666666666)))));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -2.25e-18:
		tmp = 0.0
	elif x <= 1.4e+77:
		tmp = 1.0 + (z * ((z * (0.5 + (z * -0.16666666666666666))) + -1.0))
	else:
		tmp = 1.0 + (x * (1.0 + (x * (0.5 + (x * 0.16666666666666666)))))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2.25e-18)
		tmp = 0.0;
	elseif (x <= 1.4e+77)
		tmp = Float64(1.0 + Float64(z * Float64(Float64(z * Float64(0.5 + Float64(z * -0.16666666666666666))) + -1.0)));
	else
		tmp = Float64(1.0 + Float64(x * Float64(1.0 + Float64(x * Float64(0.5 + Float64(x * 0.16666666666666666))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -2.25e-18)
		tmp = 0.0;
	elseif (x <= 1.4e+77)
		tmp = 1.0 + (z * ((z * (0.5 + (z * -0.16666666666666666))) + -1.0));
	else
		tmp = 1.0 + (x * (1.0 + (x * (0.5 + (x * 0.16666666666666666)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2.25e-18], 0.0, If[LessEqual[x, 1.4e+77], N[(1.0 + N[(z * N[(N[(z * N[(0.5 + N[(z * -0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(x * N[(1.0 + N[(x * N[(0.5 + N[(x * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.24999999999999997e-18

   1. Initial program 100.0%

      \[e^{\left(x + y \cdot \log y\right) - z} \]
   2. Step-by-step derivation

      1. associate--l+ 100.0%

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

      2. +-commutative 100.0%

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

      3. exp-sum 48.6%

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

      4. exp-diff 41.9%

         \[\leadsto \color{blue}{\frac{e^{y \cdot \log y}}{e^{z}}} \cdot e^{x} \]

      5. associate-/r/ 41.9%

         \[\leadsto \color{blue}{\frac{e^{y \cdot \log y}}{\frac{e^{z}}{e^{x}}}} \]

      6. *-commutative 41.9%

         \[\leadsto \frac{e^{\color{blue}{\log y \cdot y}}}{\frac{e^{z}}{e^{x}}} \]

      7. exp-to-pow 41.9%

         \[\leadsto \frac{\color{blue}{{y}^{y}}}{\frac{e^{z}}{e^{x}}} \]

      8. div-exp 62.2%

         \[\leadsto \frac{{y}^{y}}{\color{blue}{e^{z - x}}} \]

   3. Simplified 62.2%

      \[\leadsto \color{blue}{\frac{{y}^{y}}{e^{z - x}}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 80.0%

      \[\leadsto \color{blue}{\frac{1}{e^{z - x}}} \]

   6. Taylor expanded in z around 0 65.4%

      \[\leadsto \color{blue}{\frac{1}{e^{-x}}} \]

   8. Applied egg-rr 66.8%

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

   if -2.24999999999999997e-18 < x < 1.4e77

   1. Initial program 100.0%

      \[e^{\left(x + y \cdot \log y\right) - z} \]
   2. Step-by-step derivation

      1. associate--l+ 100.0%

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

      2. +-commutative 100.0%

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

      3. exp-sum 99.3%

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

      4. exp-diff 86.8%

         \[\leadsto \color{blue}{\frac{e^{y \cdot \log y}}{e^{z}}} \cdot e^{x} \]

      5. associate-/r/ 86.8%

         \[\leadsto \color{blue}{\frac{e^{y \cdot \log y}}{\frac{e^{z}}{e^{x}}}} \]

      6. *-commutative 86.8%

         \[\leadsto \frac{e^{\color{blue}{\log y \cdot y}}}{\frac{e^{z}}{e^{x}}} \]

      7. exp-to-pow 86.8%

         \[\leadsto \frac{\color{blue}{{y}^{y}}}{\frac{e^{z}}{e^{x}}} \]

      8. div-exp 86.8%

         \[\leadsto \frac{{y}^{y}}{\color{blue}{e^{z - x}}} \]

   3. Simplified 86.8%

      \[\leadsto \color{blue}{\frac{{y}^{y}}{e^{z - x}}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 61.7%

      \[\leadsto \color{blue}{\frac{1}{e^{z - x}}} \]

   6. Taylor expanded in x around 0 57.5%

      \[\leadsto \color{blue}{\frac{1}{e^{z}}} \]

   7. Taylor expanded in z around 0 35.2%

      \[\leadsto \color{blue}{1 + z \cdot \left(z \cdot \left(0.5 + -0.16666666666666666 \cdot z\right) - 1\right)} \]

   if 1.4e77 < x

   1. Initial program 100.0%

      \[e^{\left(x + y \cdot \log y\right) - z} \]
   2. Step-by-step derivation

      1. associate--l+ 100.0%

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

      2. +-commutative 100.0%

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

      3. exp-sum 84.4%

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

      4. exp-diff 77.8%

         \[\leadsto \color{blue}{\frac{e^{y \cdot \log y}}{e^{z}}} \cdot e^{x} \]

      5. associate-/r/ 77.8%

         \[\leadsto \color{blue}{\frac{e^{y \cdot \log y}}{\frac{e^{z}}{e^{x}}}} \]

      6. *-commutative 77.8%

         \[\leadsto \frac{e^{\color{blue}{\log y \cdot y}}}{\frac{e^{z}}{e^{x}}} \]

      7. exp-to-pow 77.8%

         \[\leadsto \frac{\color{blue}{{y}^{y}}}{\frac{e^{z}}{e^{x}}} \]

      8. div-exp 95.6%

         \[\leadsto \frac{{y}^{y}}{\color{blue}{e^{z - x}}} \]

   3. Simplified 95.6%

      \[\leadsto \color{blue}{\frac{{y}^{y}}{e^{z - x}}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 97.8%

      \[\leadsto \color{blue}{\frac{1}{e^{z - x}}} \]

   6. Taylor expanded in z around 0 93.4%

      \[\leadsto \color{blue}{\frac{1}{e^{-x}}} \]

   7. Taylor expanded in x around 0 89.3%

      \[\leadsto \color{blue}{1 + x \cdot \left(1 + x \cdot \left(0.5 + 0.16666666666666666 \cdot x\right)\right)} \]
   8. Step-by-step derivation

      1. +-commutative 89.3%

         \[\leadsto 1 + x \cdot \color{blue}{\left(x \cdot \left(0.5 + 0.16666666666666666 \cdot x\right) + 1\right)} \]

      2. distribute-lft-in 89.3%

         \[\leadsto 1 + \color{blue}{\left(x \cdot \left(x \cdot \left(0.5 + 0.16666666666666666 \cdot x\right)\right) + x \cdot 1\right)} \]

      3. *-rgt-identity 89.3%

         \[\leadsto 1 + \left(x \cdot \left(x \cdot \left(0.5 + 0.16666666666666666 \cdot x\right)\right) + \color{blue}{x}\right) \]

      4. remove-double-neg 89.3%

         \[\leadsto 1 + \left(x \cdot \left(x \cdot \left(0.5 + 0.16666666666666666 \cdot x\right)\right) + \color{blue}{\left(-\left(-x\right)\right)}\right) \]

      5. mul-1-neg 89.3%

         \[\leadsto 1 + \left(x \cdot \left(x \cdot \left(0.5 + 0.16666666666666666 \cdot x\right)\right) + \left(-\color{blue}{-1 \cdot x}\right)\right) \]

      6. unsub-neg 89.3%

         \[\leadsto 1 + \color{blue}{\left(x \cdot \left(x \cdot \left(0.5 + 0.16666666666666666 \cdot x\right)\right) - -1 \cdot x\right)} \]

      7. unsub-neg 89.3%

         \[\leadsto 1 + \color{blue}{\left(x \cdot \left(x \cdot \left(0.5 + 0.16666666666666666 \cdot x\right)\right) + \left(--1 \cdot x\right)\right)} \]

      8. mul-1-neg 89.3%

         \[\leadsto 1 + \left(x \cdot \left(x \cdot \left(0.5 + 0.16666666666666666 \cdot x\right)\right) + \left(-\color{blue}{\left(-x\right)}\right)\right) \]

      9. remove-double-neg 89.3%

         \[\leadsto 1 + \left(x \cdot \left(x \cdot \left(0.5 + 0.16666666666666666 \cdot x\right)\right) + \color{blue}{x}\right) \]

      10. *-rgt-identity 89.3%

          \[\leadsto 1 + \left(x \cdot \left(x \cdot \left(0.5 + 0.16666666666666666 \cdot x\right)\right) + \color{blue}{x \cdot 1}\right) \]

      11. distribute-lft-in 89.3%

          \[\leadsto 1 + \color{blue}{x \cdot \left(x \cdot \left(0.5 + 0.16666666666666666 \cdot x\right) + 1\right)} \]

      12. +-commutative 89.3%

          \[\leadsto 1 + x \cdot \color{blue}{\left(1 + x \cdot \left(0.5 + 0.16666666666666666 \cdot x\right)\right)} \]

      13. *-commutative 89.3%

          \[\leadsto 1 + x \cdot \left(1 + x \cdot \left(0.5 + \color{blue}{x \cdot 0.16666666666666666}\right)\right) \]

   9. Simplified 89.3%

      \[\leadsto \color{blue}{1 + x \cdot \left(1 + x \cdot \left(0.5 + x \cdot 0.16666666666666666\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 53.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.25 \cdot 10^{-18}:\\ \;\;\;\;0\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{+77}:\\ \;\;\;\;1 + z \cdot \left(z \cdot \left(0.5 + z \cdot -0.16666666666666666\right) + -1\right)\\ \mathbf{else}:\\ \;\;\;\;1 + x \cdot \left(1 + x \cdot \left(0.5 + x \cdot 0.16666666666666666\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 50.6% accurate, 10.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.25 \cdot 10^{-18}:\\ \;\;\;\;0\\ \mathbf{elif}\;x \leq 9 \cdot 10^{+145}:\\ \;\;\;\;1 + z \cdot \left(z \cdot 0.5 + -1\right)\\ \mathbf{else}:\\ \;\;\;\;1 + x \cdot \left(1 + x \cdot 0.5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -2.25e-18)
   0.0
   (if (<= x 9e+145)
     (+ 1.0 (* z (+ (* z 0.5) -1.0)))
     (+ 1.0 (* x (+ 1.0 (* x 0.5)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.25e-18) {
		tmp = 0.0;
	} else if (x <= 9e+145) {
		tmp = 1.0 + (z * ((z * 0.5) + -1.0));
	} else {
		tmp = 1.0 + (x * (1.0 + (x * 0.5)));
	}
	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 <= (-2.25d-18)) then
        tmp = 0.0d0
    else if (x <= 9d+145) then
        tmp = 1.0d0 + (z * ((z * 0.5d0) + (-1.0d0)))
    else
        tmp = 1.0d0 + (x * (1.0d0 + (x * 0.5d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.25e-18) {
		tmp = 0.0;
	} else if (x <= 9e+145) {
		tmp = 1.0 + (z * ((z * 0.5) + -1.0));
	} else {
		tmp = 1.0 + (x * (1.0 + (x * 0.5)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -2.25e-18:
		tmp = 0.0
	elif x <= 9e+145:
		tmp = 1.0 + (z * ((z * 0.5) + -1.0))
	else:
		tmp = 1.0 + (x * (1.0 + (x * 0.5)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2.25e-18)
		tmp = 0.0;
	elseif (x <= 9e+145)
		tmp = Float64(1.0 + Float64(z * Float64(Float64(z * 0.5) + -1.0)));
	else
		tmp = Float64(1.0 + Float64(x * Float64(1.0 + Float64(x * 0.5))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -2.25e-18)
		tmp = 0.0;
	elseif (x <= 9e+145)
		tmp = 1.0 + (z * ((z * 0.5) + -1.0));
	else
		tmp = 1.0 + (x * (1.0 + (x * 0.5)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2.25e-18], 0.0, If[LessEqual[x, 9e+145], N[(1.0 + N[(z * N[(N[(z * 0.5), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(x * N[(1.0 + N[(x * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.24999999999999997e-18

   1. Initial program 100.0%

      \[e^{\left(x + y \cdot \log y\right) - z} \]
   2. Step-by-step derivation

      1. associate--l+ 100.0%

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

      2. +-commutative 100.0%

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

      3. exp-sum 48.6%

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

      4. exp-diff 41.9%

         \[\leadsto \color{blue}{\frac{e^{y \cdot \log y}}{e^{z}}} \cdot e^{x} \]

      5. associate-/r/ 41.9%

         \[\leadsto \color{blue}{\frac{e^{y \cdot \log y}}{\frac{e^{z}}{e^{x}}}} \]

      6. *-commutative 41.9%

         \[\leadsto \frac{e^{\color{blue}{\log y \cdot y}}}{\frac{e^{z}}{e^{x}}} \]

      7. exp-to-pow 41.9%

         \[\leadsto \frac{\color{blue}{{y}^{y}}}{\frac{e^{z}}{e^{x}}} \]

      8. div-exp 62.2%

         \[\leadsto \frac{{y}^{y}}{\color{blue}{e^{z - x}}} \]

   3. Simplified 62.2%

      \[\leadsto \color{blue}{\frac{{y}^{y}}{e^{z - x}}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 80.0%

      \[\leadsto \color{blue}{\frac{1}{e^{z - x}}} \]

   6. Taylor expanded in z around 0 65.4%

      \[\leadsto \color{blue}{\frac{1}{e^{-x}}} \]

   8. Applied egg-rr 66.8%

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

   if -2.24999999999999997e-18 < x < 8.9999999999999996e145

   1. Initial program 100.0%

      \[e^{\left(x + y \cdot \log y\right) - z} \]
   2. Step-by-step derivation

      1. associate--l+ 100.0%

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

      2. +-commutative 100.0%

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

      3. exp-sum 97.3%

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

      4. exp-diff 85.2%

         \[\leadsto \color{blue}{\frac{e^{y \cdot \log y}}{e^{z}}} \cdot e^{x} \]

      5. associate-/r/ 85.2%

         \[\leadsto \color{blue}{\frac{e^{y \cdot \log y}}{\frac{e^{z}}{e^{x}}}} \]

      6. *-commutative 85.2%

         \[\leadsto \frac{e^{\color{blue}{\log y \cdot y}}}{\frac{e^{z}}{e^{x}}} \]

      7. exp-to-pow 85.2%

         \[\leadsto \frac{\color{blue}{{y}^{y}}}{\frac{e^{z}}{e^{x}}} \]

      8. div-exp 86.6%

         \[\leadsto \frac{{y}^{y}}{\color{blue}{e^{z - x}}} \]

   3. Simplified 86.6%

      \[\leadsto \color{blue}{\frac{{y}^{y}}{e^{z - x}}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 64.2%

      \[\leadsto \color{blue}{\frac{1}{e^{z - x}}} \]

   6. Taylor expanded in x around 0 56.3%

      \[\leadsto \color{blue}{\frac{1}{e^{z}}} \]

   7. Taylor expanded in z around 0 34.2%

      \[\leadsto \color{blue}{1 + z \cdot \left(0.5 \cdot z - 1\right)} \]

   if 8.9999999999999996e145 < x

   1. Initial program 100.0%

      \[e^{\left(x + y \cdot \log y\right) - z} \]
   2. Step-by-step derivation

      1. associate--l+ 100.0%

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

      2. +-commutative 100.0%

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

      3. exp-sum 87.9%

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

      4. exp-diff 81.8%

         \[\leadsto \color{blue}{\frac{e^{y \cdot \log y}}{e^{z}}} \cdot e^{x} \]

      5. associate-/r/ 81.8%

         \[\leadsto \color{blue}{\frac{e^{y \cdot \log y}}{\frac{e^{z}}{e^{x}}}} \]

      6. *-commutative 81.8%

         \[\leadsto \frac{e^{\color{blue}{\log y \cdot y}}}{\frac{e^{z}}{e^{x}}} \]

      7. exp-to-pow 81.8%

         \[\leadsto \frac{\color{blue}{{y}^{y}}}{\frac{e^{z}}{e^{x}}} \]

      8. div-exp 100.0%

         \[\leadsto \frac{{y}^{y}}{\color{blue}{e^{z - x}}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{{y}^{y}}{e^{z - x}}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 100.0%

      \[\leadsto \color{blue}{\frac{1}{e^{z - x}}} \]

   6. Taylor expanded in z around 0 97.0%

      \[\leadsto \color{blue}{\frac{1}{e^{-x}}} \]

   7. Taylor expanded in x around 0 94.3%

      \[\leadsto \color{blue}{1 + x \cdot \left(1 + 0.5 \cdot x\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 51.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.25 \cdot 10^{-18}:\\ \;\;\;\;0\\ \mathbf{elif}\;x \leq 9 \cdot 10^{+145}:\\ \;\;\;\;1 + z \cdot \left(z \cdot 0.5 + -1\right)\\ \mathbf{else}:\\ \;\;\;\;1 + x \cdot \left(1 + x \cdot 0.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 32.1% accurate, 18.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -22:\\ \;\;\;\;0\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-236}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -22.0) 0.0 (if (<= z 2.9e-236) 1.0 0.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -22.0) {
		tmp = 0.0;
	} else if (z <= 2.9e-236) {
		tmp = 1.0;
	} else {
		tmp = 0.0;
	}
	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) :: tmp
    if (z <= (-22.0d0)) then
        tmp = 0.0d0
    else if (z <= 2.9d-236) then
        tmp = 1.0d0
    else
        tmp = 0.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -22.0) {
		tmp = 0.0;
	} else if (z <= 2.9e-236) {
		tmp = 1.0;
	} else {
		tmp = 0.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -22.0:
		tmp = 0.0
	elif z <= 2.9e-236:
		tmp = 1.0
	else:
		tmp = 0.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -22.0)
		tmp = 0.0;
	elseif (z <= 2.9e-236)
		tmp = 1.0;
	else
		tmp = 0.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -22.0)
		tmp = 0.0;
	elseif (z <= 2.9e-236)
		tmp = 1.0;
	else
		tmp = 0.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -22.0], 0.0, If[LessEqual[z, 2.9e-236], 1.0, 0.0]]

Derivation

1. Split input into 2 regimes

2. if z < -22 or 2.9e-236 < z

   1. Initial program 100.0%

      \[e^{\left(x + y \cdot \log y\right) - z} \]
   2. Step-by-step derivation

      1. associate--l+ 100.0%

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

      2. +-commutative 100.0%

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

      3. exp-sum 78.6%

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

      4. exp-diff 63.7%

         \[\leadsto \color{blue}{\frac{e^{y \cdot \log y}}{e^{z}}} \cdot e^{x} \]

      5. associate-/r/ 63.7%

         \[\leadsto \color{blue}{\frac{e^{y \cdot \log y}}{\frac{e^{z}}{e^{x}}}} \]

      6. *-commutative 63.7%

         \[\leadsto \frac{e^{\color{blue}{\log y \cdot y}}}{\frac{e^{z}}{e^{x}}} \]

      7. exp-to-pow 63.7%

         \[\leadsto \frac{\color{blue}{{y}^{y}}}{\frac{e^{z}}{e^{x}}} \]

      8. div-exp 77.4%

         \[\leadsto \frac{{y}^{y}}{\color{blue}{e^{z - x}}} \]

   3. Simplified 77.4%

      \[\leadsto \color{blue}{\frac{{y}^{y}}{e^{z - x}}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 77.9%

      \[\leadsto \color{blue}{\frac{1}{e^{z - x}}} \]

   6. Taylor expanded in z around 0 46.7%

      \[\leadsto \color{blue}{\frac{1}{e^{-x}}} \]

   8. Applied egg-rr 35.1%

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

   if -22 < z < 2.9e-236

   1. Initial program 100.0%

      \[e^{\left(x + y \cdot \log y\right) - z} \]
   2. Step-by-step derivation

      1. associate--l+ 100.0%

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

      2. +-commutative 100.0%

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

      3. exp-sum 88.6%

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

      4. exp-diff 88.6%

         \[\leadsto \color{blue}{\frac{e^{y \cdot \log y}}{e^{z}}} \cdot e^{x} \]

      5. associate-/r/ 88.6%

         \[\leadsto \color{blue}{\frac{e^{y \cdot \log y}}{\frac{e^{z}}{e^{x}}}} \]

      6. *-commutative 88.6%

         \[\leadsto \frac{e^{\color{blue}{\log y \cdot y}}}{\frac{e^{z}}{e^{x}}} \]

      7. exp-to-pow 88.6%

         \[\leadsto \frac{\color{blue}{{y}^{y}}}{\frac{e^{z}}{e^{x}}} \]

      8. div-exp 88.6%

         \[\leadsto \frac{{y}^{y}}{\color{blue}{e^{z - x}}} \]

   3. Simplified 88.6%

      \[\leadsto \color{blue}{\frac{{y}^{y}}{e^{z - x}}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 64.7%

      \[\leadsto \color{blue}{\frac{1}{e^{z - x}}} \]

   6. Taylor expanded in x around 0 31.7%

      \[\leadsto \color{blue}{\frac{1}{e^{z}}} \]

   7. Taylor expanded in z around 0 27.8%

      \[\leadsto \color{blue}{1} \]
3. Recombined 2 regimes into one program.

4. Final simplification 32.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -22:\\ \;\;\;\;0\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-236}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 30.2% accurate, 207.0× speedup

Math

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

FPCore

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

C

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

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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := 0.0

Derivation

1. Initial program 100.0%

   \[e^{\left(x + y \cdot \log y\right) - z} \]
2. Step-by-step derivation

   1. associate--l+ 100.0%

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

   2. +-commutative 100.0%

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

   3. exp-sum 82.0%

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

   4. exp-diff 72.3%

      \[\leadsto \color{blue}{\frac{e^{y \cdot \log y}}{e^{z}}} \cdot e^{x} \]

   5. associate-/r/ 72.3%

      \[\leadsto \color{blue}{\frac{e^{y \cdot \log y}}{\frac{e^{z}}{e^{x}}}} \]

   6. *-commutative 72.3%

      \[\leadsto \frac{e^{\color{blue}{\log y \cdot y}}}{\frac{e^{z}}{e^{x}}} \]

   7. exp-to-pow 72.3%

      \[\leadsto \frac{\color{blue}{{y}^{y}}}{\frac{e^{z}}{e^{x}}} \]

   8. div-exp 81.2%

      \[\leadsto \frac{{y}^{y}}{\color{blue}{e^{z - x}}} \]

3. Simplified 81.2%

   \[\leadsto \color{blue}{\frac{{y}^{y}}{e^{z - x}}} \]
4. Add Preprocessing

5. Taylor expanded in y around 0 73.4%

   \[\leadsto \color{blue}{\frac{1}{e^{z - x}}} \]

6. Taylor expanded in z around 0 51.6%

   \[\leadsto \color{blue}{\frac{1}{e^{-x}}} \]

8. Applied egg-rr 29.9%

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

9. Final simplification 29.9%

   \[\leadsto 0 \]
10. Add Preprocessing

Developer target: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024082 
(FPCore (x y z)
  :name "Statistics.Distribution.Poisson.Internal:probability from math-functions-0.1.5.2"
  :precision binary64

  :alt
  (exp (+ (- x z) (* (log y) y)))

  (exp (- (+ x (* y (log y))) z)))