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

Percentage Accurate: 100.0% → 100.0%

Time: 10.1s

Alternatives: 16

Speedup: 1.0×

• 57.5% 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. Add Preprocessing

Alternative 2: 89.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \cdot \log y \leq 20000000000000:\\ \;\;\;\;e^{x - z}\\ \mathbf{else}:\\ \;\;\;\;{y}^{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (* y (log y)) 20000000000000.0) (exp (- x z)) (pow y y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y * log(y)) <= 20000000000000.0) {
		tmp = exp((x - z));
	} else {
		tmp = pow(y, y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y * log(y)) <= 20000000000000.0d0) then
        tmp = exp((x - z))
    else
        tmp = y ** y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y * Math.log(y)) <= 20000000000000.0) {
		tmp = Math.exp((x - z));
	} else {
		tmp = Math.pow(y, y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y * math.log(y)) <= 20000000000000.0:
		tmp = math.exp((x - z))
	else:
		tmp = math.pow(y, y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(y * log(y)) <= 20000000000000.0)
		tmp = exp(Float64(x - z));
	else
		tmp = y ^ y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y * log(y)) <= 20000000000000.0)
		tmp = exp((x - z));
	else
		tmp = y ^ y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(y * N[Log[y], $MachinePrecision]), $MachinePrecision], 20000000000000.0], N[Exp[N[(x - z), $MachinePrecision]], $MachinePrecision], N[Power[y, y], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y (log.f64 y)) < 2e13

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. sub-neg N/A

         \[\leadsto e^{x + \left(\mathsf{neg}\left(z\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto e^{\left(\mathsf{neg}\left(z\right)\right) + x} \]

      3. remove-double-neg N/A

         \[\leadsto e^{\left(\mathsf{neg}\left(z\right)\right) + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right)\right)\right)} \]

      4. distribute-neg-in N/A

         \[\leadsto e^{\mathsf{neg}\left(\left(z + \left(\mathsf{neg}\left(x\right)\right)\right)\right)} \]

      5. neg-mul-1 N/A

         \[\leadsto e^{\mathsf{neg}\left(\left(z + -1 \cdot x\right)\right)} \]

      6. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(\left(z + -1 \cdot x\right)\right)\right)\right) \]

      7. neg-mul-1 N/A

         \[\leadsto \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(\left(z + \left(\mathsf{neg}\left(x\right)\right)\right)\right)\right)\right) \]

      8. +-commutative N/A

         \[\leadsto \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(x\right)\right) + z\right)\right)\right)\right) \]

      9. distribute-neg-in N/A

         \[\leadsto \mathsf{exp.f64}\left(\left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right)\right)\right) + \left(\mathsf{neg}\left(z\right)\right)\right)\right) \]

      10. unsub-neg N/A

          \[\leadsto \mathsf{exp.f64}\left(\left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right)\right)\right) - z\right)\right) \]

      11. remove-double-neg N/A

          \[\leadsto \mathsf{exp.f64}\left(\left(x - z\right)\right) \]

      12. --lowering--.f64 98.0%

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

   5. Simplified 98.0%

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

   if 2e13 < (*.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 y around inf

      \[\leadsto \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot \left(y \cdot \log \left(\frac{1}{y}\right)\right)\right)}\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(y \cdot \log \left(\frac{1}{y}\right)\right)\right)\right) \]

      2. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{exp.f64}\left(\left(y \cdot \left(\mathsf{neg}\left(\log \left(\frac{1}{y}\right)\right)\right)\right)\right) \]

      3. log-rec N/A

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

      4. remove-double-neg N/A

         \[\leadsto \mathsf{exp.f64}\left(\left(y \cdot \log y\right)\right) \]

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

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

      6. log-lowering-log.f64 86.6%

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

   5. Simplified 86.6%

      \[\leadsto e^{\color{blue}{y \cdot \log y}} \]
   6. Step-by-step derivation

      1. *-commutative N/A

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

      2. exp-to-pow N/A

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

      3. pow-lowering-pow.f64 86.6%

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

   7. Applied egg-rr 86.6%

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

Alternative 3: 72.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := e^{0 - z}\\ \mathbf{if}\;z \leq -390000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{+119}:\\ \;\;\;\;e^{x}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (exp (- 0.0 z))))
   (if (<= z -390000.0) t_0 (if (<= z 8.8e+119) (exp x) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = exp((0.0 - z));
	double tmp;
	if (z <= -390000.0) {
		tmp = t_0;
	} else if (z <= 8.8e+119) {
		tmp = exp(x);
	} 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 = exp((0.0d0 - z))
    if (z <= (-390000.0d0)) then
        tmp = t_0
    else if (z <= 8.8d+119) then
        tmp = exp(x)
    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.exp((0.0 - z));
	double tmp;
	if (z <= -390000.0) {
		tmp = t_0;
	} else if (z <= 8.8e+119) {
		tmp = Math.exp(x);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.exp((0.0 - z))
	tmp = 0
	if z <= -390000.0:
		tmp = t_0
	elif z <= 8.8e+119:
		tmp = math.exp(x)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = exp(Float64(0.0 - z))
	tmp = 0.0
	if (z <= -390000.0)
		tmp = t_0;
	elseif (z <= 8.8e+119)
		tmp = exp(x);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = exp((0.0 - z));
	tmp = 0.0;
	if (z <= -390000.0)
		tmp = t_0;
	elseif (z <= 8.8e+119)
		tmp = exp(x);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[Exp[N[(0.0 - z), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[z, -390000.0], t$95$0, If[LessEqual[z, 8.8e+119], N[Exp[x], $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.9e5 or 8.8000000000000005e119 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot z\right)}\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

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

      3. --lowering--.f64 89.4%

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

   5. Simplified 89.4%

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

      1. sub0-neg N/A

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

      2. neg-lowering-neg.f64 89.4%

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

   7. Applied egg-rr 89.4%

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

   if -3.9e5 < z < 8.8000000000000005e119

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{exp.f64}\left(\color{blue}{x}\right) \]
   4. Step-by-step derivation

   5. Simplified 65.4%

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

4. Final simplification 74.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -390000:\\ \;\;\;\;e^{0 - z}\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{+119}:\\ \;\;\;\;e^{x}\\ \mathbf{else}:\\ \;\;\;\;e^{0 - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 61.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+129}:\\ \;\;\;\;z \cdot \left(z \cdot \left(z \cdot -0.16666666666666666\right)\right)\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+132}:\\ \;\;\;\;e^{x}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(0.16666666666666666 \cdot \left(x \cdot x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -3.3e+129)
   (* z (* z (* z -0.16666666666666666)))
   (if (<= z 1.15e+132) (exp x) (* x (* 0.16666666666666666 (* x x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -3.3e+129) {
		tmp = z * (z * (z * -0.16666666666666666));
	} else if (z <= 1.15e+132) {
		tmp = exp(x);
	} else {
		tmp = x * (0.16666666666666666 * (x * x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-3.3d+129)) then
        tmp = z * (z * (z * (-0.16666666666666666d0)))
    else if (z <= 1.15d+132) then
        tmp = exp(x)
    else
        tmp = x * (0.16666666666666666d0 * (x * x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -3.3e+129) {
		tmp = z * (z * (z * -0.16666666666666666));
	} else if (z <= 1.15e+132) {
		tmp = Math.exp(x);
	} else {
		tmp = x * (0.16666666666666666 * (x * x));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -3.3e+129:
		tmp = z * (z * (z * -0.16666666666666666))
	elif z <= 1.15e+132:
		tmp = math.exp(x)
	else:
		tmp = x * (0.16666666666666666 * (x * x))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -3.3e+129)
		tmp = Float64(z * Float64(z * Float64(z * -0.16666666666666666)));
	elseif (z <= 1.15e+132)
		tmp = exp(x);
	else
		tmp = Float64(x * Float64(0.16666666666666666 * Float64(x * x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -3.3e+129)
		tmp = z * (z * (z * -0.16666666666666666));
	elseif (z <= 1.15e+132)
		tmp = exp(x);
	else
		tmp = x * (0.16666666666666666 * (x * x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -3.3e+129], N[(z * N[(z * N[(z * -0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.15e+132], N[Exp[x], $MachinePrecision], N[(x * N[(0.16666666666666666 * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.2999999999999999e129

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot z\right)}\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

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

      3. --lowering--.f64 97.1%

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

   5. Simplified 97.1%

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

   6. Taylor expanded in z around 0

      \[\leadsto \color{blue}{1 + z \cdot \left(z \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot z\right) - 1\right)} \]
   7. Step-by-step derivation

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

         \[\leadsto \mathsf{+.f64}\left(1, \color{blue}{\left(z \cdot \left(z \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot z\right) - 1\right)\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \color{blue}{\left(z \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot z\right) - 1\right)}\right)\right) \]

      3. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \left(z \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot z\right) + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \left(z \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot z\right) + -1\right)\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \left(-1 + \color{blue}{z \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot z\right)}\right)\right)\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \color{blue}{\left(z \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot z\right)\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(z, \color{blue}{\left(\frac{1}{2} + \frac{-1}{6} \cdot z\right)}\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{1}{2}, \color{blue}{\left(\frac{-1}{6} \cdot z\right)}\right)\right)\right)\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{1}{2}, \left(z \cdot \color{blue}{\frac{-1}{6}}\right)\right)\right)\right)\right)\right) \]

      10. *-lowering-*.f64 97.1%

          \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(z, \color{blue}{\frac{-1}{6}}\right)\right)\right)\right)\right)\right) \]

   8. Simplified 97.1%

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

   9. Taylor expanded in z around inf

      \[\leadsto \color{blue}{\frac{-1}{6} \cdot {z}^{3}} \]
   10. Step-by-step derivation

       1. cube-mult N/A

          \[\leadsto \frac{-1}{6} \cdot \left(z \cdot \color{blue}{\left(z \cdot z\right)}\right) \]

       2. unpow2 N/A

          \[\leadsto \frac{-1}{6} \cdot \left(z \cdot {z}^{\color{blue}{2}}\right) \]

       3. associate-*r* N/A

          \[\leadsto \left(\frac{-1}{6} \cdot z\right) \cdot \color{blue}{{z}^{2}} \]

       4. *-commutative N/A

          \[\leadsto {z}^{2} \cdot \color{blue}{\left(\frac{-1}{6} \cdot z\right)} \]

       5. unpow2 N/A

          \[\leadsto \left(z \cdot z\right) \cdot \left(\color{blue}{\frac{-1}{6}} \cdot z\right) \]

       6. associate-*r* N/A

          \[\leadsto z \cdot \color{blue}{\left(z \cdot \left(\frac{-1}{6} \cdot z\right)\right)} \]

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

          \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(z \cdot \left(\frac{-1}{6} \cdot z\right)\right)}\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, \color{blue}{\left(\frac{-1}{6} \cdot z\right)}\right)\right) \]

       9. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, \left(z \cdot \color{blue}{\frac{-1}{6}}\right)\right)\right) \]

       10. *-lowering-*.f64 97.1%

           \[\leadsto \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, \color{blue}{\frac{-1}{6}}\right)\right)\right) \]

   11. Simplified 97.1%

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

   if -3.2999999999999999e129 < z < 1.1500000000000001e132

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{exp.f64}\left(\color{blue}{x}\right) \]
   4. Step-by-step derivation

   5. Simplified 62.9%

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

   if 1.1500000000000001e132 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{exp.f64}\left(\color{blue}{x}\right) \]
   4. Step-by-step derivation

   5. Simplified 27.2%

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

   6. Taylor expanded in x around 0

      \[\leadsto \color{blue}{1 + x \cdot \left(1 + x \cdot \left(\frac{1}{2} + \frac{1}{6} \cdot x\right)\right)} \]
   7. Step-by-step derivation

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

         \[\leadsto \mathsf{+.f64}\left(1, \color{blue}{\left(x \cdot \left(1 + x \cdot \left(\frac{1}{2} + \frac{1}{6} \cdot x\right)\right)\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \color{blue}{\left(1 + x \cdot \left(\frac{1}{2} + \frac{1}{6} \cdot x\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(x \cdot \left(\frac{1}{2} + \frac{1}{6} \cdot x\right)\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{1}{2} + \frac{1}{6} \cdot x\right)}\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{1}{2}, \color{blue}{\left(\frac{1}{6} \cdot x\right)}\right)\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{1}{2}, \left(x \cdot \color{blue}{\frac{1}{6}}\right)\right)\right)\right)\right)\right) \]

      7. *-lowering-*.f64 6.0%

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(x, \color{blue}{\frac{1}{6}}\right)\right)\right)\right)\right)\right) \]

   8. Simplified 6.0%

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

   9. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{1}{6} \cdot {x}^{3}} \]
   10. Step-by-step derivation

       1. cube-mult N/A

          \[\leadsto \frac{1}{6} \cdot \left(x \cdot \color{blue}{\left(x \cdot x\right)}\right) \]

       2. unpow2 N/A

          \[\leadsto \frac{1}{6} \cdot \left(x \cdot {x}^{\color{blue}{2}}\right) \]

       3. associate-*r* N/A

          \[\leadsto \left(\frac{1}{6} \cdot x\right) \cdot \color{blue}{{x}^{2}} \]

       4. *-commutative N/A

          \[\leadsto {x}^{2} \cdot \color{blue}{\left(\frac{1}{6} \cdot x\right)} \]

       5. unpow2 N/A

          \[\leadsto \left(x \cdot x\right) \cdot \left(\color{blue}{\frac{1}{6}} \cdot x\right) \]

       6. associate-*r* N/A

          \[\leadsto x \cdot \color{blue}{\left(x \cdot \left(\frac{1}{6} \cdot x\right)\right)} \]

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

          \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(x \cdot \left(\frac{1}{6} \cdot x\right)\right)}\right) \]

       8. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\left(\frac{1}{6} \cdot x\right) \cdot \color{blue}{x}\right)\right) \]

       9. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{1}{6} \cdot \color{blue}{\left(x \cdot x\right)}\right)\right) \]

       10. unpow2 N/A

           \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{1}{6} \cdot {x}^{\color{blue}{2}}\right)\right) \]

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

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{6}, \color{blue}{\left({x}^{2}\right)}\right)\right) \]

       12. unpow2 N/A

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{6}, \left(x \cdot \color{blue}{x}\right)\right)\right) \]

       13. *-lowering-*.f64 54.6%

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{6}, \mathsf{*.f64}\left(x, \color{blue}{x}\right)\right)\right) \]

   11. Simplified 54.6%

       \[\leadsto \color{blue}{x \cdot \left(0.16666666666666666 \cdot \left(x \cdot x\right)\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 5: 72.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 530000000000:\\ \;\;\;\;e^{x}\\ \mathbf{else}:\\ \;\;\;\;{y}^{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 530000000000.0) (exp x) (pow y y)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 530000000000.0) {
		tmp = exp(x);
	} else {
		tmp = pow(y, y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= 530000000000.0d0) then
        tmp = exp(x)
    else
        tmp = y ** y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 530000000000.0) {
		tmp = Math.exp(x);
	} else {
		tmp = Math.pow(y, y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 530000000000.0:
		tmp = math.exp(x)
	else:
		tmp = math.pow(y, y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 530000000000.0)
		tmp = exp(x);
	else
		tmp = y ^ y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 530000000000.0)
		tmp = exp(x);
	else
		tmp = y ^ y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 530000000000.0], N[Exp[x], $MachinePrecision], N[Power[y, y], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 5.3e11

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{exp.f64}\left(\color{blue}{x}\right) \]
   4. Step-by-step derivation

   5. Simplified 73.3%

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

   if 5.3e11 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

      \[\leadsto \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot \left(y \cdot \log \left(\frac{1}{y}\right)\right)\right)}\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{exp.f64}\left(\left(\mathsf{neg}\left(y \cdot \log \left(\frac{1}{y}\right)\right)\right)\right) \]

      2. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{exp.f64}\left(\left(y \cdot \left(\mathsf{neg}\left(\log \left(\frac{1}{y}\right)\right)\right)\right)\right) \]

      3. log-rec N/A

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

      4. remove-double-neg N/A

         \[\leadsto \mathsf{exp.f64}\left(\left(y \cdot \log y\right)\right) \]

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

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

      6. log-lowering-log.f64 86.6%

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

   5. Simplified 86.6%

      \[\leadsto e^{\color{blue}{y \cdot \log y}} \]
   6. Step-by-step derivation

      1. *-commutative N/A

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

      2. exp-to-pow N/A

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

      3. pow-lowering-pow.f64 86.6%

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

   7. Applied egg-rr 86.6%

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

Alternative 6: 51.2% accurate, 4.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(x \cdot \left(0.5 + x \cdot 0.16666666666666666\right)\right)\\ \mathbf{if}\;x \leq -820:\\ \;\;\;\;z \cdot \left(z \cdot \left(z \cdot -0.16666666666666666\right)\right)\\ \mathbf{elif}\;x \leq 4.3 \cdot 10^{+51}:\\ \;\;\;\;1 + \frac{z \cdot \left(1 - 0.25 \cdot \left(z \cdot z\right)\right)}{-1 + z \cdot -0.5}\\ \mathbf{elif}\;x \leq 10^{+103}:\\ \;\;\;\;1 + \frac{x \cdot x - t\_0 \cdot t\_0}{x - t\_0}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(0.16666666666666666 \cdot \left(x \cdot x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (* x (+ 0.5 (* x 0.16666666666666666))))))
   (if (<= x -820.0)
     (* z (* z (* z -0.16666666666666666)))
     (if (<= x 4.3e+51)
       (+ 1.0 (/ (* z (- 1.0 (* 0.25 (* z z)))) (+ -1.0 (* z -0.5))))
       (if (<= x 1e+103)
         (+ 1.0 (/ (- (* x x) (* t_0 t_0)) (- x t_0)))
         (* x (* 0.16666666666666666 (* x x))))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (x * (0.5 + (x * 0.16666666666666666)));
	double tmp;
	if (x <= -820.0) {
		tmp = z * (z * (z * -0.16666666666666666));
	} else if (x <= 4.3e+51) {
		tmp = 1.0 + ((z * (1.0 - (0.25 * (z * z)))) / (-1.0 + (z * -0.5)));
	} else if (x <= 1e+103) {
		tmp = 1.0 + (((x * x) - (t_0 * t_0)) / (x - t_0));
	} else {
		tmp = x * (0.16666666666666666 * (x * x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x * (x * (0.5d0 + (x * 0.16666666666666666d0)))
    if (x <= (-820.0d0)) then
        tmp = z * (z * (z * (-0.16666666666666666d0)))
    else if (x <= 4.3d+51) then
        tmp = 1.0d0 + ((z * (1.0d0 - (0.25d0 * (z * z)))) / ((-1.0d0) + (z * (-0.5d0))))
    else if (x <= 1d+103) then
        tmp = 1.0d0 + (((x * x) - (t_0 * t_0)) / (x - t_0))
    else
        tmp = x * (0.16666666666666666d0 * (x * x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (x * (0.5 + (x * 0.16666666666666666)));
	double tmp;
	if (x <= -820.0) {
		tmp = z * (z * (z * -0.16666666666666666));
	} else if (x <= 4.3e+51) {
		tmp = 1.0 + ((z * (1.0 - (0.25 * (z * z)))) / (-1.0 + (z * -0.5)));
	} else if (x <= 1e+103) {
		tmp = 1.0 + (((x * x) - (t_0 * t_0)) / (x - t_0));
	} else {
		tmp = x * (0.16666666666666666 * (x * x));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (x * (0.5 + (x * 0.16666666666666666)))
	tmp = 0
	if x <= -820.0:
		tmp = z * (z * (z * -0.16666666666666666))
	elif x <= 4.3e+51:
		tmp = 1.0 + ((z * (1.0 - (0.25 * (z * z)))) / (-1.0 + (z * -0.5)))
	elif x <= 1e+103:
		tmp = 1.0 + (((x * x) - (t_0 * t_0)) / (x - t_0))
	else:
		tmp = x * (0.16666666666666666 * (x * x))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(x * Float64(0.5 + Float64(x * 0.16666666666666666))))
	tmp = 0.0
	if (x <= -820.0)
		tmp = Float64(z * Float64(z * Float64(z * -0.16666666666666666)));
	elseif (x <= 4.3e+51)
		tmp = Float64(1.0 + Float64(Float64(z * Float64(1.0 - Float64(0.25 * Float64(z * z)))) / Float64(-1.0 + Float64(z * -0.5))));
	elseif (x <= 1e+103)
		tmp = Float64(1.0 + Float64(Float64(Float64(x * x) - Float64(t_0 * t_0)) / Float64(x - t_0)));
	else
		tmp = Float64(x * Float64(0.16666666666666666 * Float64(x * x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (x * (0.5 + (x * 0.16666666666666666)));
	tmp = 0.0;
	if (x <= -820.0)
		tmp = z * (z * (z * -0.16666666666666666));
	elseif (x <= 4.3e+51)
		tmp = 1.0 + ((z * (1.0 - (0.25 * (z * z)))) / (-1.0 + (z * -0.5)));
	elseif (x <= 1e+103)
		tmp = 1.0 + (((x * x) - (t_0 * t_0)) / (x - t_0));
	else
		tmp = x * (0.16666666666666666 * (x * x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(x * N[(0.5 + N[(x * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -820.0], N[(z * N[(z * N[(z * -0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.3e+51], N[(1.0 + N[(N[(z * N[(1.0 - N[(0.25 * N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(-1.0 + N[(z * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1e+103], N[(1.0 + N[(N[(N[(x * x), $MachinePrecision] - N[(t$95$0 * t$95$0), $MachinePrecision]), $MachinePrecision] / N[(x - t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(0.16666666666666666 * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -820

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot z\right)}\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

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

      3. --lowering--.f64 32.7%

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

   5. Simplified 32.7%

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

   6. Taylor expanded in z around 0

      \[\leadsto \color{blue}{1 + z \cdot \left(z \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot z\right) - 1\right)} \]
   7. Step-by-step derivation

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

         \[\leadsto \mathsf{+.f64}\left(1, \color{blue}{\left(z \cdot \left(z \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot z\right) - 1\right)\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \color{blue}{\left(z \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot z\right) - 1\right)}\right)\right) \]

      3. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \left(z \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot z\right) + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \left(z \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot z\right) + -1\right)\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \left(-1 + \color{blue}{z \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot z\right)}\right)\right)\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \color{blue}{\left(z \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot z\right)\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(z, \color{blue}{\left(\frac{1}{2} + \frac{-1}{6} \cdot z\right)}\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{1}{2}, \color{blue}{\left(\frac{-1}{6} \cdot z\right)}\right)\right)\right)\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{1}{2}, \left(z \cdot \color{blue}{\frac{-1}{6}}\right)\right)\right)\right)\right)\right) \]

      10. *-lowering-*.f64 13.1%

          \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(z, \color{blue}{\frac{-1}{6}}\right)\right)\right)\right)\right)\right) \]

   8. Simplified 13.1%

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

   9. Taylor expanded in z around inf

      \[\leadsto \color{blue}{\frac{-1}{6} \cdot {z}^{3}} \]
   10. Step-by-step derivation

       1. cube-mult N/A

          \[\leadsto \frac{-1}{6} \cdot \left(z \cdot \color{blue}{\left(z \cdot z\right)}\right) \]

       2. unpow2 N/A

          \[\leadsto \frac{-1}{6} \cdot \left(z \cdot {z}^{\color{blue}{2}}\right) \]

       3. associate-*r* N/A

          \[\leadsto \left(\frac{-1}{6} \cdot z\right) \cdot \color{blue}{{z}^{2}} \]

       4. *-commutative N/A

          \[\leadsto {z}^{2} \cdot \color{blue}{\left(\frac{-1}{6} \cdot z\right)} \]

       5. unpow2 N/A

          \[\leadsto \left(z \cdot z\right) \cdot \left(\color{blue}{\frac{-1}{6}} \cdot z\right) \]

       6. associate-*r* N/A

          \[\leadsto z \cdot \color{blue}{\left(z \cdot \left(\frac{-1}{6} \cdot z\right)\right)} \]

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

          \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(z \cdot \left(\frac{-1}{6} \cdot z\right)\right)}\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, \color{blue}{\left(\frac{-1}{6} \cdot z\right)}\right)\right) \]

       9. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, \left(z \cdot \color{blue}{\frac{-1}{6}}\right)\right)\right) \]

       10. *-lowering-*.f64 29.4%

           \[\leadsto \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, \color{blue}{\frac{-1}{6}}\right)\right)\right) \]

   11. Simplified 29.4%

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

   if -820 < x < 4.2999999999999997e51

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot z\right)}\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

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

      3. --lowering--.f64 63.8%

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

   5. Simplified 63.8%

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

   6. Taylor expanded in z around 0

      \[\leadsto \color{blue}{1 + z \cdot \left(\frac{1}{2} \cdot z - 1\right)} \]
   7. Step-by-step derivation

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

         \[\leadsto \mathsf{+.f64}\left(1, \color{blue}{\left(z \cdot \left(\frac{1}{2} \cdot z - 1\right)\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \color{blue}{\left(\frac{1}{2} \cdot z - 1\right)}\right)\right) \]

      3. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \left(\frac{1}{2} \cdot z + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \left(\frac{1}{2} \cdot z + -1\right)\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \left(-1 + \color{blue}{\frac{1}{2} \cdot z}\right)\right)\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \color{blue}{\left(\frac{1}{2} \cdot z\right)}\right)\right)\right) \]

      7. *-lowering-*.f64 36.7%

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{z}\right)\right)\right)\right) \]

   8. Simplified 36.7%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(1, \left(\left(-1 + \frac{1}{2} \cdot z\right) \cdot \color{blue}{z}\right)\right) \]

      2. flip-+ N/A

         \[\leadsto \mathsf{+.f64}\left(1, \left(\frac{-1 \cdot -1 - \left(\frac{1}{2} \cdot z\right) \cdot \left(\frac{1}{2} \cdot z\right)}{-1 - \frac{1}{2} \cdot z} \cdot z\right)\right) \]

      3. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(1, \left(\frac{\left(-1 \cdot -1 - \left(\frac{1}{2} \cdot z\right) \cdot \left(\frac{1}{2} \cdot z\right)\right) \cdot z}{\color{blue}{-1 - \frac{1}{2} \cdot z}}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\left(\left(-1 \cdot -1 - \left(\frac{1}{2} \cdot z\right) \cdot \left(\frac{1}{2} \cdot z\right)\right) \cdot z\right), \color{blue}{\left(-1 - \frac{1}{2} \cdot z\right)}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(-1 \cdot -1 - \left(\frac{1}{2} \cdot z\right) \cdot \left(\frac{1}{2} \cdot z\right)\right), z\right), \left(\color{blue}{-1} - \frac{1}{2} \cdot z\right)\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(1 - \left(\frac{1}{2} \cdot z\right) \cdot \left(\frac{1}{2} \cdot z\right)\right), z\right), \left(-1 - \frac{1}{2} \cdot z\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(1, \left(\left(\frac{1}{2} \cdot z\right) \cdot \left(\frac{1}{2} \cdot z\right)\right)\right), z\right), \left(-1 - \frac{1}{2} \cdot z\right)\right)\right) \]

      8. swap-sqr N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(1, \left(\left(\frac{1}{2} \cdot \frac{1}{2}\right) \cdot \left(z \cdot z\right)\right)\right), z\right), \left(-1 - \frac{1}{2} \cdot z\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(1, \mathsf{*.f64}\left(\left(\frac{1}{2} \cdot \frac{1}{2}\right), \left(z \cdot z\right)\right)\right), z\right), \left(-1 - \frac{1}{2} \cdot z\right)\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(1, \mathsf{*.f64}\left(\frac{1}{4}, \left(z \cdot z\right)\right)\right), z\right), \left(-1 - \frac{1}{2} \cdot z\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(1, \mathsf{*.f64}\left(\frac{1}{4}, \mathsf{*.f64}\left(z, z\right)\right)\right), z\right), \left(-1 - \frac{1}{2} \cdot z\right)\right)\right) \]

      12. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(1, \mathsf{*.f64}\left(\frac{1}{4}, \mathsf{*.f64}\left(z, z\right)\right)\right), z\right), \left(-1 + \color{blue}{\left(\mathsf{neg}\left(\frac{1}{2} \cdot z\right)\right)}\right)\right)\right) \]

      13. mul-1-neg N/A

          \[\leadsto \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(1, \mathsf{*.f64}\left(\frac{1}{4}, \mathsf{*.f64}\left(z, z\right)\right)\right), z\right), \left(-1 + -1 \cdot \color{blue}{\left(\frac{1}{2} \cdot z\right)}\right)\right)\right) \]

      14. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(1, \mathsf{*.f64}\left(\frac{1}{4}, \mathsf{*.f64}\left(z, z\right)\right)\right), z\right), \mathsf{+.f64}\left(-1, \color{blue}{\left(-1 \cdot \left(\frac{1}{2} \cdot z\right)\right)}\right)\right)\right) \]

      15. associate-*r* N/A

          \[\leadsto \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(1, \mathsf{*.f64}\left(\frac{1}{4}, \mathsf{*.f64}\left(z, z\right)\right)\right), z\right), \mathsf{+.f64}\left(-1, \left(\left(-1 \cdot \frac{1}{2}\right) \cdot \color{blue}{z}\right)\right)\right)\right) \]

      16. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(1, \mathsf{*.f64}\left(\frac{1}{4}, \mathsf{*.f64}\left(z, z\right)\right)\right), z\right), \mathsf{+.f64}\left(-1, \left(\frac{-1}{2} \cdot z\right)\right)\right)\right) \]

      17. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(1, \mathsf{*.f64}\left(\frac{1}{4}, \mathsf{*.f64}\left(z, z\right)\right)\right), z\right), \mathsf{+.f64}\left(-1, \left(\left(\mathsf{neg}\left(\frac{1}{2}\right)\right) \cdot z\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(1, \mathsf{*.f64}\left(\frac{1}{4}, \mathsf{*.f64}\left(z, z\right)\right)\right), z\right), \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(\left(\mathsf{neg}\left(\frac{1}{2}\right)\right), \color{blue}{z}\right)\right)\right)\right) \]

      19. metadata-eval 40.2%

          \[\leadsto \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(1, \mathsf{*.f64}\left(\frac{1}{4}, \mathsf{*.f64}\left(z, z\right)\right)\right), z\right), \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(\frac{-1}{2}, z\right)\right)\right)\right) \]

   10. Applied egg-rr 40.2%

       \[\leadsto 1 + \color{blue}{\frac{\left(1 - 0.25 \cdot \left(z \cdot z\right)\right) \cdot z}{-1 + -0.5 \cdot z}} \]

   if 4.2999999999999997e51 < x < 1e103

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{exp.f64}\left(\color{blue}{x}\right) \]
   4. Step-by-step derivation

   5. Simplified 92.4%

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

   6. Taylor expanded in x around 0

      \[\leadsto \color{blue}{1 + x \cdot \left(1 + x \cdot \left(\frac{1}{2} + \frac{1}{6} \cdot x\right)\right)} \]
   7. Step-by-step derivation

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

         \[\leadsto \mathsf{+.f64}\left(1, \color{blue}{\left(x \cdot \left(1 + x \cdot \left(\frac{1}{2} + \frac{1}{6} \cdot x\right)\right)\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \color{blue}{\left(1 + x \cdot \left(\frac{1}{2} + \frac{1}{6} \cdot x\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(x \cdot \left(\frac{1}{2} + \frac{1}{6} \cdot x\right)\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{1}{2} + \frac{1}{6} \cdot x\right)}\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{1}{2}, \color{blue}{\left(\frac{1}{6} \cdot x\right)}\right)\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{1}{2}, \left(x \cdot \color{blue}{\frac{1}{6}}\right)\right)\right)\right)\right)\right) \]

      7. *-lowering-*.f64 5.7%

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(x, \color{blue}{\frac{1}{6}}\right)\right)\right)\right)\right)\right) \]

   8. Simplified 5.7%

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

      1. distribute-rgt-in N/A

         \[\leadsto \mathsf{+.f64}\left(1, \left(1 \cdot x + \color{blue}{\left(x \cdot \left(\frac{1}{2} + x \cdot \frac{1}{6}\right)\right) \cdot x}\right)\right) \]

      2. *-lft-identity N/A

         \[\leadsto \mathsf{+.f64}\left(1, \left(x + \color{blue}{\left(x \cdot \left(\frac{1}{2} + x \cdot \frac{1}{6}\right)\right)} \cdot x\right)\right) \]

      3. flip-+ N/A

         \[\leadsto \mathsf{+.f64}\left(1, \left(\frac{x \cdot x - \left(\left(x \cdot \left(\frac{1}{2} + x \cdot \frac{1}{6}\right)\right) \cdot x\right) \cdot \left(\left(x \cdot \left(\frac{1}{2} + x \cdot \frac{1}{6}\right)\right) \cdot x\right)}{\color{blue}{x - \left(x \cdot \left(\frac{1}{2} + x \cdot \frac{1}{6}\right)\right) \cdot x}}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\left(x \cdot x - \left(\left(x \cdot \left(\frac{1}{2} + x \cdot \frac{1}{6}\right)\right) \cdot x\right) \cdot \left(\left(x \cdot \left(\frac{1}{2} + x \cdot \frac{1}{6}\right)\right) \cdot x\right)\right), \color{blue}{\left(x - \left(x \cdot \left(\frac{1}{2} + x \cdot \frac{1}{6}\right)\right) \cdot x\right)}\right)\right) \]

   10. Applied egg-rr 92.4%

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

   if 1e103 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{exp.f64}\left(\color{blue}{x}\right) \]
   4. Step-by-step derivation

   5. Simplified 100.0%

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

   6. Taylor expanded in x around 0

      \[\leadsto \color{blue}{1 + x \cdot \left(1 + x \cdot \left(\frac{1}{2} + \frac{1}{6} \cdot x\right)\right)} \]
   7. Step-by-step derivation

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

         \[\leadsto \mathsf{+.f64}\left(1, \color{blue}{\left(x \cdot \left(1 + x \cdot \left(\frac{1}{2} + \frac{1}{6} \cdot x\right)\right)\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \color{blue}{\left(1 + x \cdot \left(\frac{1}{2} + \frac{1}{6} \cdot x\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(x \cdot \left(\frac{1}{2} + \frac{1}{6} \cdot x\right)\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{1}{2} + \frac{1}{6} \cdot x\right)}\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{1}{2}, \color{blue}{\left(\frac{1}{6} \cdot x\right)}\right)\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{1}{2}, \left(x \cdot \color{blue}{\frac{1}{6}}\right)\right)\right)\right)\right)\right) \]

      7. *-lowering-*.f64 100.0%

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(x, \color{blue}{\frac{1}{6}}\right)\right)\right)\right)\right)\right) \]

   8. Simplified 100.0%

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

   9. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{1}{6} \cdot {x}^{3}} \]
   10. Step-by-step derivation

       1. cube-mult N/A

          \[\leadsto \frac{1}{6} \cdot \left(x \cdot \color{blue}{\left(x \cdot x\right)}\right) \]

       2. unpow2 N/A

          \[\leadsto \frac{1}{6} \cdot \left(x \cdot {x}^{\color{blue}{2}}\right) \]

       3. associate-*r* N/A

          \[\leadsto \left(\frac{1}{6} \cdot x\right) \cdot \color{blue}{{x}^{2}} \]

       4. *-commutative N/A

          \[\leadsto {x}^{2} \cdot \color{blue}{\left(\frac{1}{6} \cdot x\right)} \]

       5. unpow2 N/A

          \[\leadsto \left(x \cdot x\right) \cdot \left(\color{blue}{\frac{1}{6}} \cdot x\right) \]

       6. associate-*r* N/A

          \[\leadsto x \cdot \color{blue}{\left(x \cdot \left(\frac{1}{6} \cdot x\right)\right)} \]

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

          \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(x \cdot \left(\frac{1}{6} \cdot x\right)\right)}\right) \]

       8. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\left(\frac{1}{6} \cdot x\right) \cdot \color{blue}{x}\right)\right) \]

       9. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{1}{6} \cdot \color{blue}{\left(x \cdot x\right)}\right)\right) \]

       10. unpow2 N/A

           \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{1}{6} \cdot {x}^{\color{blue}{2}}\right)\right) \]

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

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{6}, \color{blue}{\left({x}^{2}\right)}\right)\right) \]

       12. unpow2 N/A

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{6}, \left(x \cdot \color{blue}{x}\right)\right)\right) \]

       13. *-lowering-*.f64 100.0%

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{6}, \mathsf{*.f64}\left(x, \color{blue}{x}\right)\right)\right) \]

   11. Simplified 100.0%

       \[\leadsto \color{blue}{x \cdot \left(0.16666666666666666 \cdot \left(x \cdot x\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 50.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -820:\\ \;\;\;\;z \cdot \left(z \cdot \left(z \cdot -0.16666666666666666\right)\right)\\ \mathbf{elif}\;x \leq 4.3 \cdot 10^{+51}:\\ \;\;\;\;1 + \frac{z \cdot \left(1 - 0.25 \cdot \left(z \cdot z\right)\right)}{-1 + z \cdot -0.5}\\ \mathbf{elif}\;x \leq 10^{+103}:\\ \;\;\;\;1 + \frac{x \cdot x - \left(x \cdot \left(x \cdot \left(0.5 + x \cdot 0.16666666666666666\right)\right)\right) \cdot \left(x \cdot \left(x \cdot \left(0.5 + x \cdot 0.16666666666666666\right)\right)\right)}{x - x \cdot \left(x \cdot \left(0.5 + x \cdot 0.16666666666666666\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(0.16666666666666666 \cdot \left(x \cdot x\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 48.5% accurate, 6.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.32 \cdot 10^{+62}:\\ \;\;\;\;z \cdot \left(z \cdot \left(z \cdot -0.16666666666666666\right)\right)\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-163}:\\ \;\;\;\;1 + x \cdot \left(1 + x \cdot \left(0.5 + x \cdot 0.16666666666666666\right)\right)\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-308}:\\ \;\;\;\;1 + z \cdot \left(z \cdot \left(z \cdot \left(-0.16666666666666666 + \frac{\frac{-1}{z} - -0.5}{z}\right)\right)\right)\\ \mathbf{elif}\;z \leq 0.0004:\\ \;\;\;\;1 + x \cdot \left(1 + x \cdot 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(0.16666666666666666 \cdot \left(x \cdot x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.32e+62)
   (* z (* z (* z -0.16666666666666666)))
   (if (<= z -8e-163)
     (+ 1.0 (* x (+ 1.0 (* x (+ 0.5 (* x 0.16666666666666666))))))
     (if (<= z -1.1e-308)
       (+
        1.0
        (* z (* z (* z (+ -0.16666666666666666 (/ (- (/ -1.0 z) -0.5) z))))))
       (if (<= z 0.0004)
         (+ 1.0 (* x (+ 1.0 (* x 0.5))))
         (* x (* 0.16666666666666666 (* x x))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.32e+62) {
		tmp = z * (z * (z * -0.16666666666666666));
	} else if (z <= -8e-163) {
		tmp = 1.0 + (x * (1.0 + (x * (0.5 + (x * 0.16666666666666666)))));
	} else if (z <= -1.1e-308) {
		tmp = 1.0 + (z * (z * (z * (-0.16666666666666666 + (((-1.0 / z) - -0.5) / z)))));
	} else if (z <= 0.0004) {
		tmp = 1.0 + (x * (1.0 + (x * 0.5)));
	} else {
		tmp = x * (0.16666666666666666 * (x * x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-1.32d+62)) then
        tmp = z * (z * (z * (-0.16666666666666666d0)))
    else if (z <= (-8d-163)) then
        tmp = 1.0d0 + (x * (1.0d0 + (x * (0.5d0 + (x * 0.16666666666666666d0)))))
    else if (z <= (-1.1d-308)) then
        tmp = 1.0d0 + (z * (z * (z * ((-0.16666666666666666d0) + ((((-1.0d0) / z) - (-0.5d0)) / z)))))
    else if (z <= 0.0004d0) then
        tmp = 1.0d0 + (x * (1.0d0 + (x * 0.5d0)))
    else
        tmp = x * (0.16666666666666666d0 * (x * x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.32e+62) {
		tmp = z * (z * (z * -0.16666666666666666));
	} else if (z <= -8e-163) {
		tmp = 1.0 + (x * (1.0 + (x * (0.5 + (x * 0.16666666666666666)))));
	} else if (z <= -1.1e-308) {
		tmp = 1.0 + (z * (z * (z * (-0.16666666666666666 + (((-1.0 / z) - -0.5) / z)))));
	} else if (z <= 0.0004) {
		tmp = 1.0 + (x * (1.0 + (x * 0.5)));
	} else {
		tmp = x * (0.16666666666666666 * (x * x));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.32e+62:
		tmp = z * (z * (z * -0.16666666666666666))
	elif z <= -8e-163:
		tmp = 1.0 + (x * (1.0 + (x * (0.5 + (x * 0.16666666666666666)))))
	elif z <= -1.1e-308:
		tmp = 1.0 + (z * (z * (z * (-0.16666666666666666 + (((-1.0 / z) - -0.5) / z)))))
	elif z <= 0.0004:
		tmp = 1.0 + (x * (1.0 + (x * 0.5)))
	else:
		tmp = x * (0.16666666666666666 * (x * x))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.32e+62)
		tmp = Float64(z * Float64(z * Float64(z * -0.16666666666666666)));
	elseif (z <= -8e-163)
		tmp = Float64(1.0 + Float64(x * Float64(1.0 + Float64(x * Float64(0.5 + Float64(x * 0.16666666666666666))))));
	elseif (z <= -1.1e-308)
		tmp = Float64(1.0 + Float64(z * Float64(z * Float64(z * Float64(-0.16666666666666666 + Float64(Float64(Float64(-1.0 / z) - -0.5) / z))))));
	elseif (z <= 0.0004)
		tmp = Float64(1.0 + Float64(x * Float64(1.0 + Float64(x * 0.5))));
	else
		tmp = Float64(x * Float64(0.16666666666666666 * Float64(x * x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.32e+62)
		tmp = z * (z * (z * -0.16666666666666666));
	elseif (z <= -8e-163)
		tmp = 1.0 + (x * (1.0 + (x * (0.5 + (x * 0.16666666666666666)))));
	elseif (z <= -1.1e-308)
		tmp = 1.0 + (z * (z * (z * (-0.16666666666666666 + (((-1.0 / z) - -0.5) / z)))));
	elseif (z <= 0.0004)
		tmp = 1.0 + (x * (1.0 + (x * 0.5)));
	else
		tmp = x * (0.16666666666666666 * (x * x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.32e+62], N[(z * N[(z * N[(z * -0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -8e-163], N[(1.0 + N[(x * N[(1.0 + N[(x * N[(0.5 + N[(x * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.1e-308], N[(1.0 + N[(z * N[(z * N[(z * N[(-0.16666666666666666 + N[(N[(N[(-1.0 / z), $MachinePrecision] - -0.5), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.0004], N[(1.0 + N[(x * N[(1.0 + N[(x * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(0.16666666666666666 * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.3199999999999999e62

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot z\right)}\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

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

      3. --lowering--.f64 89.1%

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

   5. Simplified 89.1%

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

   6. Taylor expanded in z around 0

      \[\leadsto \color{blue}{1 + z \cdot \left(z \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot z\right) - 1\right)} \]
   7. Step-by-step derivation

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

         \[\leadsto \mathsf{+.f64}\left(1, \color{blue}{\left(z \cdot \left(z \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot z\right) - 1\right)\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \color{blue}{\left(z \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot z\right) - 1\right)}\right)\right) \]

      3. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \left(z \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot z\right) + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \left(z \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot z\right) + -1\right)\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \left(-1 + \color{blue}{z \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot z\right)}\right)\right)\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \color{blue}{\left(z \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot z\right)\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(z, \color{blue}{\left(\frac{1}{2} + \frac{-1}{6} \cdot z\right)}\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{1}{2}, \color{blue}{\left(\frac{-1}{6} \cdot z\right)}\right)\right)\right)\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{1}{2}, \left(z \cdot \color{blue}{\frac{-1}{6}}\right)\right)\right)\right)\right)\right) \]

      10. *-lowering-*.f64 80.9%

          \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(z, \color{blue}{\frac{-1}{6}}\right)\right)\right)\right)\right)\right) \]

   8. Simplified 80.9%

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

   9. Taylor expanded in z around inf

      \[\leadsto \color{blue}{\frac{-1}{6} \cdot {z}^{3}} \]
   10. Step-by-step derivation

       1. cube-mult N/A

          \[\leadsto \frac{-1}{6} \cdot \left(z \cdot \color{blue}{\left(z \cdot z\right)}\right) \]

       2. unpow2 N/A

          \[\leadsto \frac{-1}{6} \cdot \left(z \cdot {z}^{\color{blue}{2}}\right) \]

       3. associate-*r* N/A

          \[\leadsto \left(\frac{-1}{6} \cdot z\right) \cdot \color{blue}{{z}^{2}} \]

       4. *-commutative N/A

          \[\leadsto {z}^{2} \cdot \color{blue}{\left(\frac{-1}{6} \cdot z\right)} \]

       5. unpow2 N/A

          \[\leadsto \left(z \cdot z\right) \cdot \left(\color{blue}{\frac{-1}{6}} \cdot z\right) \]

       6. associate-*r* N/A

          \[\leadsto z \cdot \color{blue}{\left(z \cdot \left(\frac{-1}{6} \cdot z\right)\right)} \]

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

          \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(z \cdot \left(\frac{-1}{6} \cdot z\right)\right)}\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, \color{blue}{\left(\frac{-1}{6} \cdot z\right)}\right)\right) \]

       9. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, \left(z \cdot \color{blue}{\frac{-1}{6}}\right)\right)\right) \]

       10. *-lowering-*.f64 80.9%

           \[\leadsto \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, \color{blue}{\frac{-1}{6}}\right)\right)\right) \]

   11. Simplified 80.9%

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

   if -1.3199999999999999e62 < z < -7.99999999999999939e-163

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{exp.f64}\left(\color{blue}{x}\right) \]
   4. Step-by-step derivation

   5. Simplified 66.0%

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

   6. Taylor expanded in x around 0

      \[\leadsto \color{blue}{1 + x \cdot \left(1 + x \cdot \left(\frac{1}{2} + \frac{1}{6} \cdot x\right)\right)} \]
   7. Step-by-step derivation

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

         \[\leadsto \mathsf{+.f64}\left(1, \color{blue}{\left(x \cdot \left(1 + x \cdot \left(\frac{1}{2} + \frac{1}{6} \cdot x\right)\right)\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \color{blue}{\left(1 + x \cdot \left(\frac{1}{2} + \frac{1}{6} \cdot x\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(x \cdot \left(\frac{1}{2} + \frac{1}{6} \cdot x\right)\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{1}{2} + \frac{1}{6} \cdot x\right)}\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{1}{2}, \color{blue}{\left(\frac{1}{6} \cdot x\right)}\right)\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{1}{2}, \left(x \cdot \color{blue}{\frac{1}{6}}\right)\right)\right)\right)\right)\right) \]

      7. *-lowering-*.f64 36.8%

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(x, \color{blue}{\frac{1}{6}}\right)\right)\right)\right)\right)\right) \]

   8. Simplified 36.8%

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

   if -7.99999999999999939e-163 < z < -1.1000000000000001e-308

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot z\right)}\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

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

      3. --lowering--.f64 21.5%

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

   5. Simplified 21.5%

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

   6. Taylor expanded in z around 0

      \[\leadsto \color{blue}{1 + z \cdot \left(z \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot z\right) - 1\right)} \]
   7. Step-by-step derivation

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

         \[\leadsto \mathsf{+.f64}\left(1, \color{blue}{\left(z \cdot \left(z \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot z\right) - 1\right)\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \color{blue}{\left(z \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot z\right) - 1\right)}\right)\right) \]

      3. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \left(z \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot z\right) + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \left(z \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot z\right) + -1\right)\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \left(-1 + \color{blue}{z \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot z\right)}\right)\right)\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \color{blue}{\left(z \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot z\right)\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(z, \color{blue}{\left(\frac{1}{2} + \frac{-1}{6} \cdot z\right)}\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{1}{2}, \color{blue}{\left(\frac{-1}{6} \cdot z\right)}\right)\right)\right)\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{1}{2}, \left(z \cdot \color{blue}{\frac{-1}{6}}\right)\right)\right)\right)\right)\right) \]

      10. *-lowering-*.f64 21.5%

          \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(z, \color{blue}{\frac{-1}{6}}\right)\right)\right)\right)\right)\right) \]

   8. Simplified 21.5%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \left(\left(\frac{1}{2} + z \cdot \frac{-1}{6}\right) \cdot \color{blue}{z}\right)\right)\right)\right) \]

      2. flip-+ N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \left(\frac{\frac{1}{2} \cdot \frac{1}{2} - \left(z \cdot \frac{-1}{6}\right) \cdot \left(z \cdot \frac{-1}{6}\right)}{\frac{1}{2} - z \cdot \frac{-1}{6}} \cdot z\right)\right)\right)\right) \]

      3. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \left(\frac{\left(\frac{1}{2} \cdot \frac{1}{2} - \left(z \cdot \frac{-1}{6}\right) \cdot \left(z \cdot \frac{-1}{6}\right)\right) \cdot z}{\color{blue}{\frac{1}{2} - z \cdot \frac{-1}{6}}}\right)\right)\right)\right) \]

      4. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \left(\frac{1}{\color{blue}{\frac{\frac{1}{2} - z \cdot \frac{-1}{6}}{\left(\frac{1}{2} \cdot \frac{1}{2} - \left(z \cdot \frac{-1}{6}\right) \cdot \left(z \cdot \frac{-1}{6}\right)\right) \cdot z}}}\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \mathsf{/.f64}\left(1, \color{blue}{\left(\frac{\frac{1}{2} - z \cdot \frac{-1}{6}}{\left(\frac{1}{2} \cdot \frac{1}{2} - \left(z \cdot \frac{-1}{6}\right) \cdot \left(z \cdot \frac{-1}{6}\right)\right) \cdot z}\right)}\right)\right)\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\left(\frac{1}{2} - z \cdot \frac{-1}{6}\right), \color{blue}{\left(\left(\frac{1}{2} \cdot \frac{1}{2} - \left(z \cdot \frac{-1}{6}\right) \cdot \left(z \cdot \frac{-1}{6}\right)\right) \cdot z\right)}\right)\right)\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\left(\frac{1}{2} - \frac{-1}{6} \cdot z\right), \left(\left(\frac{1}{2} \cdot \frac{1}{2} - \color{blue}{\left(z \cdot \frac{-1}{6}\right) \cdot \left(z \cdot \frac{-1}{6}\right)}\right) \cdot z\right)\right)\right)\right)\right)\right) \]

      8. cancel-sign-sub-inv N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\left(\frac{1}{2} + \left(\mathsf{neg}\left(\frac{-1}{6}\right)\right) \cdot z\right), \left(\color{blue}{\left(\frac{1}{2} \cdot \frac{1}{2} - \left(z \cdot \frac{-1}{6}\right) \cdot \left(z \cdot \frac{-1}{6}\right)\right)} \cdot z\right)\right)\right)\right)\right)\right) \]

      9. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{1}{2}, \left(\left(\mathsf{neg}\left(\frac{-1}{6}\right)\right) \cdot z\right)\right), \left(\color{blue}{\left(\frac{1}{2} \cdot \frac{1}{2} - \left(z \cdot \frac{-1}{6}\right) \cdot \left(z \cdot \frac{-1}{6}\right)\right)} \cdot z\right)\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\left(\mathsf{neg}\left(\frac{-1}{6}\right)\right), z\right)\right), \left(\left(\frac{1}{2} \cdot \frac{1}{2} - \color{blue}{\left(z \cdot \frac{-1}{6}\right) \cdot \left(z \cdot \frac{-1}{6}\right)}\right) \cdot z\right)\right)\right)\right)\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\frac{1}{6}, z\right)\right), \left(\left(\frac{1}{2} \cdot \frac{1}{2} - \color{blue}{\left(z \cdot \frac{-1}{6}\right)} \cdot \left(z \cdot \frac{-1}{6}\right)\right) \cdot z\right)\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\frac{1}{6}, z\right)\right), \mathsf{*.f64}\left(\left(\frac{1}{2} \cdot \frac{1}{2} - \left(z \cdot \frac{-1}{6}\right) \cdot \left(z \cdot \frac{-1}{6}\right)\right), \color{blue}{z}\right)\right)\right)\right)\right)\right) \]

      13. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\frac{1}{6}, z\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\left(\frac{1}{2} \cdot \frac{1}{2}\right), \left(\left(z \cdot \frac{-1}{6}\right) \cdot \left(z \cdot \frac{-1}{6}\right)\right)\right), z\right)\right)\right)\right)\right)\right) \]

      14. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\frac{1}{6}, z\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\frac{1}{4}, \left(\left(z \cdot \frac{-1}{6}\right) \cdot \left(z \cdot \frac{-1}{6}\right)\right)\right), z\right)\right)\right)\right)\right)\right) \]

      15. swap-sqr N/A

          \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\frac{1}{6}, z\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\frac{1}{4}, \left(\left(z \cdot z\right) \cdot \left(\frac{-1}{6} \cdot \frac{-1}{6}\right)\right)\right), z\right)\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\frac{1}{6}, z\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\frac{1}{4}, \mathsf{*.f64}\left(\left(z \cdot z\right), \left(\frac{-1}{6} \cdot \frac{-1}{6}\right)\right)\right), z\right)\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\frac{1}{6}, z\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\frac{1}{4}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(z, z\right), \left(\frac{-1}{6} \cdot \frac{-1}{6}\right)\right)\right), z\right)\right)\right)\right)\right)\right) \]

      18. metadata-eval 21.5%

          \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\frac{1}{6}, z\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\frac{1}{4}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(z, z\right), \frac{1}{36}\right)\right), z\right)\right)\right)\right)\right)\right) \]

   10. Applied egg-rr 21.5%

       \[\leadsto 1 + z \cdot \left(-1 + \color{blue}{\frac{1}{\frac{0.5 + 0.16666666666666666 \cdot z}{\left(0.25 - \left(z \cdot z\right) \cdot 0.027777777777777776\right) \cdot z}}}\right) \]

   11. Taylor expanded in z around inf

       \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \color{blue}{\left({z}^{2} \cdot \left(\frac{1}{2} \cdot \frac{1}{z} - \left(\frac{1}{6} + \frac{1}{{z}^{2}}\right)\right)\right)}\right)\right) \]
   12. Step-by-step derivation

       1. unpow2 N/A

          \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \left(\left(z \cdot z\right) \cdot \left(\color{blue}{\frac{1}{2} \cdot \frac{1}{z}} - \left(\frac{1}{6} + \frac{1}{{z}^{2}}\right)\right)\right)\right)\right) \]

       2. associate-*l* N/A

          \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \left(z \cdot \color{blue}{\left(z \cdot \left(\frac{1}{2} \cdot \frac{1}{z} - \left(\frac{1}{6} + \frac{1}{{z}^{2}}\right)\right)\right)}\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, \color{blue}{\left(z \cdot \left(\frac{1}{2} \cdot \frac{1}{z} - \left(\frac{1}{6} + \frac{1}{{z}^{2}}\right)\right)\right)}\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, \color{blue}{\left(\frac{1}{2} \cdot \frac{1}{z} - \left(\frac{1}{6} + \frac{1}{{z}^{2}}\right)\right)}\right)\right)\right)\right) \]

       5. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, \left(\frac{1}{2} \cdot \frac{1}{z} + \color{blue}{\left(\mathsf{neg}\left(\left(\frac{1}{6} + \frac{1}{{z}^{2}}\right)\right)\right)}\right)\right)\right)\right)\right) \]

       6. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, \left(\left(\mathsf{neg}\left(\left(\frac{1}{6} + \frac{1}{{z}^{2}}\right)\right)\right) + \color{blue}{\frac{1}{2} \cdot \frac{1}{z}}\right)\right)\right)\right)\right) \]

       7. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, \left(\left(\left(\mathsf{neg}\left(\frac{1}{6}\right)\right) + \left(\mathsf{neg}\left(\frac{1}{{z}^{2}}\right)\right)\right) + \color{blue}{\frac{1}{2}} \cdot \frac{1}{z}\right)\right)\right)\right)\right) \]

       8. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, \left(\left(\frac{-1}{6} + \left(\mathsf{neg}\left(\frac{1}{{z}^{2}}\right)\right)\right) + \frac{1}{2} \cdot \frac{1}{z}\right)\right)\right)\right)\right) \]

       9. associate-+l+ N/A

          \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, \left(\frac{-1}{6} + \color{blue}{\left(\left(\mathsf{neg}\left(\frac{1}{{z}^{2}}\right)\right) + \frac{1}{2} \cdot \frac{1}{z}\right)}\right)\right)\right)\right)\right) \]

       10. neg-sub0 N/A

           \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, \left(\frac{-1}{6} + \left(\left(0 - \frac{1}{{z}^{2}}\right) + \color{blue}{\frac{1}{2}} \cdot \frac{1}{z}\right)\right)\right)\right)\right)\right) \]

       11. associate--r- N/A

           \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, \left(\frac{-1}{6} + \left(0 - \color{blue}{\left(\frac{1}{{z}^{2}} - \frac{1}{2} \cdot \frac{1}{z}\right)}\right)\right)\right)\right)\right)\right) \]

       12. sub-neg N/A

           \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, \left(\frac{-1}{6} + \left(0 - \left(\frac{1}{{z}^{2}} + \color{blue}{\left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{z}\right)\right)}\right)\right)\right)\right)\right)\right)\right) \]

       13. +-commutative N/A

           \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, \left(\frac{-1}{6} + \left(0 - \left(\left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{z}\right)\right) + \color{blue}{\frac{1}{{z}^{2}}}\right)\right)\right)\right)\right)\right)\right) \]

       14. neg-sub0 N/A

           \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, \left(\frac{-1}{6} + \left(0 - \left(\left(0 - \frac{1}{2} \cdot \frac{1}{z}\right) + \frac{\color{blue}{1}}{{z}^{2}}\right)\right)\right)\right)\right)\right)\right) \]

       15. associate--r- N/A

           \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, \left(\frac{-1}{6} + \left(0 - \left(0 - \color{blue}{\left(\frac{1}{2} \cdot \frac{1}{z} - \frac{1}{{z}^{2}}\right)}\right)\right)\right)\right)\right)\right)\right) \]

       16. associate-*r/ N/A

           \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, \left(\frac{-1}{6} + \left(0 - \left(0 - \left(\frac{\frac{1}{2} \cdot 1}{z} - \frac{\color{blue}{1}}{{z}^{2}}\right)\right)\right)\right)\right)\right)\right)\right) \]

       17. metadata-eval N/A

           \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, \left(\frac{-1}{6} + \left(0 - \left(0 - \left(\frac{\frac{1}{2}}{z} - \frac{1}{{z}^{2}}\right)\right)\right)\right)\right)\right)\right)\right) \]

       18. unpow2 N/A

           \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, \left(\frac{-1}{6} + \left(0 - \left(0 - \left(\frac{\frac{1}{2}}{z} - \frac{1}{z \cdot \color{blue}{z}}\right)\right)\right)\right)\right)\right)\right)\right) \]

   13. Simplified 65.2%

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

   if -1.1000000000000001e-308 < z < 4.00000000000000019e-4

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{exp.f64}\left(\color{blue}{x}\right) \]
   4. Step-by-step derivation

   5. Simplified 61.1%

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

   6. Taylor expanded in x around 0

      \[\leadsto \color{blue}{1 + x \cdot \left(1 + \frac{1}{2} \cdot x\right)} \]
   7. Step-by-step derivation

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

         \[\leadsto \mathsf{+.f64}\left(1, \color{blue}{\left(x \cdot \left(1 + \frac{1}{2} \cdot x\right)\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \color{blue}{\left(1 + \frac{1}{2} \cdot x\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(\frac{1}{2} \cdot x\right)}\right)\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \left(x \cdot \color{blue}{\frac{1}{2}}\right)\right)\right)\right) \]

      5. *-lowering-*.f64 43.5%

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \color{blue}{\frac{1}{2}}\right)\right)\right)\right) \]

   8. Simplified 43.5%

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

   if 4.00000000000000019e-4 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{exp.f64}\left(\color{blue}{x}\right) \]
   4. Step-by-step derivation

   5. Simplified 42.1%

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

   6. Taylor expanded in x around 0

      \[\leadsto \color{blue}{1 + x \cdot \left(1 + x \cdot \left(\frac{1}{2} + \frac{1}{6} \cdot x\right)\right)} \]
   7. Step-by-step derivation

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

         \[\leadsto \mathsf{+.f64}\left(1, \color{blue}{\left(x \cdot \left(1 + x \cdot \left(\frac{1}{2} + \frac{1}{6} \cdot x\right)\right)\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \color{blue}{\left(1 + x \cdot \left(\frac{1}{2} + \frac{1}{6} \cdot x\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(x \cdot \left(\frac{1}{2} + \frac{1}{6} \cdot x\right)\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{1}{2} + \frac{1}{6} \cdot x\right)}\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{1}{2}, \color{blue}{\left(\frac{1}{6} \cdot x\right)}\right)\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{1}{2}, \left(x \cdot \color{blue}{\frac{1}{6}}\right)\right)\right)\right)\right)\right) \]

      7. *-lowering-*.f64 17.6%

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(x, \color{blue}{\frac{1}{6}}\right)\right)\right)\right)\right)\right) \]

   8. Simplified 17.6%

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

   9. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{1}{6} \cdot {x}^{3}} \]
   10. Step-by-step derivation

       1. cube-mult N/A

          \[\leadsto \frac{1}{6} \cdot \left(x \cdot \color{blue}{\left(x \cdot x\right)}\right) \]

       2. unpow2 N/A

          \[\leadsto \frac{1}{6} \cdot \left(x \cdot {x}^{\color{blue}{2}}\right) \]

       3. associate-*r* N/A

          \[\leadsto \left(\frac{1}{6} \cdot x\right) \cdot \color{blue}{{x}^{2}} \]

       4. *-commutative N/A

          \[\leadsto {x}^{2} \cdot \color{blue}{\left(\frac{1}{6} \cdot x\right)} \]

       5. unpow2 N/A

          \[\leadsto \left(x \cdot x\right) \cdot \left(\color{blue}{\frac{1}{6}} \cdot x\right) \]

       6. associate-*r* N/A

          \[\leadsto x \cdot \color{blue}{\left(x \cdot \left(\frac{1}{6} \cdot x\right)\right)} \]

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

          \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(x \cdot \left(\frac{1}{6} \cdot x\right)\right)}\right) \]

       8. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\left(\frac{1}{6} \cdot x\right) \cdot \color{blue}{x}\right)\right) \]

       9. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{1}{6} \cdot \color{blue}{\left(x \cdot x\right)}\right)\right) \]

       10. unpow2 N/A

           \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{1}{6} \cdot {x}^{\color{blue}{2}}\right)\right) \]

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

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{6}, \color{blue}{\left({x}^{2}\right)}\right)\right) \]

       12. unpow2 N/A

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{6}, \left(x \cdot \color{blue}{x}\right)\right)\right) \]

       13. *-lowering-*.f64 45.5%

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{6}, \mathsf{*.f64}\left(x, \color{blue}{x}\right)\right)\right) \]

   11. Simplified 45.5%

       \[\leadsto \color{blue}{x \cdot \left(0.16666666666666666 \cdot \left(x \cdot x\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 51.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.32 \cdot 10^{+62}:\\ \;\;\;\;z \cdot \left(z \cdot \left(z \cdot -0.16666666666666666\right)\right)\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-163}:\\ \;\;\;\;1 + x \cdot \left(1 + x \cdot \left(0.5 + x \cdot 0.16666666666666666\right)\right)\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-308}:\\ \;\;\;\;1 + z \cdot \left(z \cdot \left(z \cdot \left(-0.16666666666666666 + \frac{\frac{-1}{z} - -0.5}{z}\right)\right)\right)\\ \mathbf{elif}\;z \leq 0.0004:\\ \;\;\;\;1 + x \cdot \left(1 + x \cdot 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(0.16666666666666666 \cdot \left(x \cdot x\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 47.1% accurate, 7.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{-146}:\\ \;\;\;\;z \cdot \left(\left(z \cdot z\right) \cdot \left(\frac{0.5 + \frac{-1 + \frac{1}{z}}{z}}{z} - 0.16666666666666666\right)\right)\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-307}:\\ \;\;\;\;1 + z \cdot \left(z \cdot \left(z \cdot \left(-0.16666666666666666 + \frac{\frac{-1}{z} - -0.5}{z}\right)\right)\right)\\ \mathbf{elif}\;z \leq 0.00012:\\ \;\;\;\;1 + x \cdot \left(1 + x \cdot 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(0.16666666666666666 \cdot \left(x \cdot x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -3.2e-146)
   (*
    z
    (* (* z z) (- (/ (+ 0.5 (/ (+ -1.0 (/ 1.0 z)) z)) z) 0.16666666666666666)))
   (if (<= z -2e-307)
     (+
      1.0
      (* z (* z (* z (+ -0.16666666666666666 (/ (- (/ -1.0 z) -0.5) z))))))
     (if (<= z 0.00012)
       (+ 1.0 (* x (+ 1.0 (* x 0.5))))
       (* x (* 0.16666666666666666 (* x x)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -3.2e-146) {
		tmp = z * ((z * z) * (((0.5 + ((-1.0 + (1.0 / z)) / z)) / z) - 0.16666666666666666));
	} else if (z <= -2e-307) {
		tmp = 1.0 + (z * (z * (z * (-0.16666666666666666 + (((-1.0 / z) - -0.5) / z)))));
	} else if (z <= 0.00012) {
		tmp = 1.0 + (x * (1.0 + (x * 0.5)));
	} else {
		tmp = x * (0.16666666666666666 * (x * x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-3.2d-146)) then
        tmp = z * ((z * z) * (((0.5d0 + (((-1.0d0) + (1.0d0 / z)) / z)) / z) - 0.16666666666666666d0))
    else if (z <= (-2d-307)) then
        tmp = 1.0d0 + (z * (z * (z * ((-0.16666666666666666d0) + ((((-1.0d0) / z) - (-0.5d0)) / z)))))
    else if (z <= 0.00012d0) then
        tmp = 1.0d0 + (x * (1.0d0 + (x * 0.5d0)))
    else
        tmp = x * (0.16666666666666666d0 * (x * x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -3.2e-146) {
		tmp = z * ((z * z) * (((0.5 + ((-1.0 + (1.0 / z)) / z)) / z) - 0.16666666666666666));
	} else if (z <= -2e-307) {
		tmp = 1.0 + (z * (z * (z * (-0.16666666666666666 + (((-1.0 / z) - -0.5) / z)))));
	} else if (z <= 0.00012) {
		tmp = 1.0 + (x * (1.0 + (x * 0.5)));
	} else {
		tmp = x * (0.16666666666666666 * (x * x));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -3.2e-146:
		tmp = z * ((z * z) * (((0.5 + ((-1.0 + (1.0 / z)) / z)) / z) - 0.16666666666666666))
	elif z <= -2e-307:
		tmp = 1.0 + (z * (z * (z * (-0.16666666666666666 + (((-1.0 / z) - -0.5) / z)))))
	elif z <= 0.00012:
		tmp = 1.0 + (x * (1.0 + (x * 0.5)))
	else:
		tmp = x * (0.16666666666666666 * (x * x))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -3.2e-146)
		tmp = Float64(z * Float64(Float64(z * z) * Float64(Float64(Float64(0.5 + Float64(Float64(-1.0 + Float64(1.0 / z)) / z)) / z) - 0.16666666666666666)));
	elseif (z <= -2e-307)
		tmp = Float64(1.0 + Float64(z * Float64(z * Float64(z * Float64(-0.16666666666666666 + Float64(Float64(Float64(-1.0 / z) - -0.5) / z))))));
	elseif (z <= 0.00012)
		tmp = Float64(1.0 + Float64(x * Float64(1.0 + Float64(x * 0.5))));
	else
		tmp = Float64(x * Float64(0.16666666666666666 * Float64(x * x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -3.2e-146)
		tmp = z * ((z * z) * (((0.5 + ((-1.0 + (1.0 / z)) / z)) / z) - 0.16666666666666666));
	elseif (z <= -2e-307)
		tmp = 1.0 + (z * (z * (z * (-0.16666666666666666 + (((-1.0 / z) - -0.5) / z)))));
	elseif (z <= 0.00012)
		tmp = 1.0 + (x * (1.0 + (x * 0.5)));
	else
		tmp = x * (0.16666666666666666 * (x * x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -3.2e-146], N[(z * N[(N[(z * z), $MachinePrecision] * N[(N[(N[(0.5 + N[(N[(-1.0 + N[(1.0 / z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] - 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2e-307], N[(1.0 + N[(z * N[(z * N[(z * N[(-0.16666666666666666 + N[(N[(N[(-1.0 / z), $MachinePrecision] - -0.5), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.00012], N[(1.0 + N[(x * N[(1.0 + N[(x * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(0.16666666666666666 * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.1999999999999999e-146

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot z\right)}\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

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

      3. --lowering--.f64 64.1%

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

   5. Simplified 64.1%

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

   6. Taylor expanded in z around 0

      \[\leadsto \color{blue}{1 + z \cdot \left(z \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot z\right) - 1\right)} \]
   7. Step-by-step derivation

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

         \[\leadsto \mathsf{+.f64}\left(1, \color{blue}{\left(z \cdot \left(z \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot z\right) - 1\right)\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \color{blue}{\left(z \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot z\right) - 1\right)}\right)\right) \]

      3. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \left(z \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot z\right) + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \left(z \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot z\right) + -1\right)\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \left(-1 + \color{blue}{z \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot z\right)}\right)\right)\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \color{blue}{\left(z \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot z\right)\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(z, \color{blue}{\left(\frac{1}{2} + \frac{-1}{6} \cdot z\right)}\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{1}{2}, \color{blue}{\left(\frac{-1}{6} \cdot z\right)}\right)\right)\right)\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{1}{2}, \left(z \cdot \color{blue}{\frac{-1}{6}}\right)\right)\right)\right)\right)\right) \]

      10. *-lowering-*.f64 43.7%

          \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(z, \color{blue}{\frac{-1}{6}}\right)\right)\right)\right)\right)\right) \]

   8. Simplified 43.7%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \left(\left(\frac{1}{2} + z \cdot \frac{-1}{6}\right) \cdot \color{blue}{z}\right)\right)\right)\right) \]

      2. flip-+ N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \left(\frac{\frac{1}{2} \cdot \frac{1}{2} - \left(z \cdot \frac{-1}{6}\right) \cdot \left(z \cdot \frac{-1}{6}\right)}{\frac{1}{2} - z \cdot \frac{-1}{6}} \cdot z\right)\right)\right)\right) \]

      3. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \left(\frac{\left(\frac{1}{2} \cdot \frac{1}{2} - \left(z \cdot \frac{-1}{6}\right) \cdot \left(z \cdot \frac{-1}{6}\right)\right) \cdot z}{\color{blue}{\frac{1}{2} - z \cdot \frac{-1}{6}}}\right)\right)\right)\right) \]

      4. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \left(\frac{1}{\color{blue}{\frac{\frac{1}{2} - z \cdot \frac{-1}{6}}{\left(\frac{1}{2} \cdot \frac{1}{2} - \left(z \cdot \frac{-1}{6}\right) \cdot \left(z \cdot \frac{-1}{6}\right)\right) \cdot z}}}\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \mathsf{/.f64}\left(1, \color{blue}{\left(\frac{\frac{1}{2} - z \cdot \frac{-1}{6}}{\left(\frac{1}{2} \cdot \frac{1}{2} - \left(z \cdot \frac{-1}{6}\right) \cdot \left(z \cdot \frac{-1}{6}\right)\right) \cdot z}\right)}\right)\right)\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\left(\frac{1}{2} - z \cdot \frac{-1}{6}\right), \color{blue}{\left(\left(\frac{1}{2} \cdot \frac{1}{2} - \left(z \cdot \frac{-1}{6}\right) \cdot \left(z \cdot \frac{-1}{6}\right)\right) \cdot z\right)}\right)\right)\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\left(\frac{1}{2} - \frac{-1}{6} \cdot z\right), \left(\left(\frac{1}{2} \cdot \frac{1}{2} - \color{blue}{\left(z \cdot \frac{-1}{6}\right) \cdot \left(z \cdot \frac{-1}{6}\right)}\right) \cdot z\right)\right)\right)\right)\right)\right) \]

      8. cancel-sign-sub-inv N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\left(\frac{1}{2} + \left(\mathsf{neg}\left(\frac{-1}{6}\right)\right) \cdot z\right), \left(\color{blue}{\left(\frac{1}{2} \cdot \frac{1}{2} - \left(z \cdot \frac{-1}{6}\right) \cdot \left(z \cdot \frac{-1}{6}\right)\right)} \cdot z\right)\right)\right)\right)\right)\right) \]

      9. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{1}{2}, \left(\left(\mathsf{neg}\left(\frac{-1}{6}\right)\right) \cdot z\right)\right), \left(\color{blue}{\left(\frac{1}{2} \cdot \frac{1}{2} - \left(z \cdot \frac{-1}{6}\right) \cdot \left(z \cdot \frac{-1}{6}\right)\right)} \cdot z\right)\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\left(\mathsf{neg}\left(\frac{-1}{6}\right)\right), z\right)\right), \left(\left(\frac{1}{2} \cdot \frac{1}{2} - \color{blue}{\left(z \cdot \frac{-1}{6}\right) \cdot \left(z \cdot \frac{-1}{6}\right)}\right) \cdot z\right)\right)\right)\right)\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\frac{1}{6}, z\right)\right), \left(\left(\frac{1}{2} \cdot \frac{1}{2} - \color{blue}{\left(z \cdot \frac{-1}{6}\right)} \cdot \left(z \cdot \frac{-1}{6}\right)\right) \cdot z\right)\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\frac{1}{6}, z\right)\right), \mathsf{*.f64}\left(\left(\frac{1}{2} \cdot \frac{1}{2} - \left(z \cdot \frac{-1}{6}\right) \cdot \left(z \cdot \frac{-1}{6}\right)\right), \color{blue}{z}\right)\right)\right)\right)\right)\right) \]

      13. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\frac{1}{6}, z\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\left(\frac{1}{2} \cdot \frac{1}{2}\right), \left(\left(z \cdot \frac{-1}{6}\right) \cdot \left(z \cdot \frac{-1}{6}\right)\right)\right), z\right)\right)\right)\right)\right)\right) \]

      14. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\frac{1}{6}, z\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\frac{1}{4}, \left(\left(z \cdot \frac{-1}{6}\right) \cdot \left(z \cdot \frac{-1}{6}\right)\right)\right), z\right)\right)\right)\right)\right)\right) \]

      15. swap-sqr N/A

          \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\frac{1}{6}, z\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\frac{1}{4}, \left(\left(z \cdot z\right) \cdot \left(\frac{-1}{6} \cdot \frac{-1}{6}\right)\right)\right), z\right)\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\frac{1}{6}, z\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\frac{1}{4}, \mathsf{*.f64}\left(\left(z \cdot z\right), \left(\frac{-1}{6} \cdot \frac{-1}{6}\right)\right)\right), z\right)\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\frac{1}{6}, z\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\frac{1}{4}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(z, z\right), \left(\frac{-1}{6} \cdot \frac{-1}{6}\right)\right)\right), z\right)\right)\right)\right)\right)\right) \]

      18. metadata-eval 43.7%

          \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\frac{1}{6}, z\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\frac{1}{4}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(z, z\right), \frac{1}{36}\right)\right), z\right)\right)\right)\right)\right)\right) \]

   10. Applied egg-rr 43.7%

       \[\leadsto 1 + z \cdot \left(-1 + \color{blue}{\frac{1}{\frac{0.5 + 0.16666666666666666 \cdot z}{\left(0.25 - \left(z \cdot z\right) \cdot 0.027777777777777776\right) \cdot z}}}\right) \]

   11. Taylor expanded in z around -inf

       \[\leadsto \color{blue}{-1 \cdot \left({z}^{3} \cdot \left(\frac{1}{6} + -1 \cdot \frac{\frac{1}{2} + -1 \cdot \frac{1 - \frac{1}{z}}{z}}{z}\right)\right)} \]
   12. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto \mathsf{neg}\left({z}^{3} \cdot \left(\frac{1}{6} + -1 \cdot \frac{\frac{1}{2} + -1 \cdot \frac{1 - \frac{1}{z}}{z}}{z}\right)\right) \]

       2. neg-sub0 N/A

          \[\leadsto 0 - \color{blue}{{z}^{3} \cdot \left(\frac{1}{6} + -1 \cdot \frac{\frac{1}{2} + -1 \cdot \frac{1 - \frac{1}{z}}{z}}{z}\right)} \]

       3. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{\left({z}^{3} \cdot \left(\frac{1}{6} + -1 \cdot \frac{\frac{1}{2} + -1 \cdot \frac{1 - \frac{1}{z}}{z}}{z}\right)\right)}\right) \]

       4. cube-mult N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \left(\left(z \cdot \left(z \cdot z\right)\right) \cdot \left(\color{blue}{\frac{1}{6}} + -1 \cdot \frac{\frac{1}{2} + -1 \cdot \frac{1 - \frac{1}{z}}{z}}{z}\right)\right)\right) \]

       5. unpow2 N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \left(\left(z \cdot {z}^{2}\right) \cdot \left(\frac{1}{6} + -1 \cdot \frac{\frac{1}{2} + -1 \cdot \frac{1 - \frac{1}{z}}{z}}{z}\right)\right)\right) \]

       6. associate-*l* N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \left(z \cdot \color{blue}{\left({z}^{2} \cdot \left(\frac{1}{6} + -1 \cdot \frac{\frac{1}{2} + -1 \cdot \frac{1 - \frac{1}{z}}{z}}{z}\right)\right)}\right)\right) \]

       7. *-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \left(z \cdot \left(\left(\frac{1}{6} + -1 \cdot \frac{\frac{1}{2} + -1 \cdot \frac{1 - \frac{1}{z}}{z}}{z}\right) \cdot \color{blue}{{z}^{2}}\right)\right)\right) \]

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

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \color{blue}{\left(\left(\frac{1}{6} + -1 \cdot \frac{\frac{1}{2} + -1 \cdot \frac{1 - \frac{1}{z}}{z}}{z}\right) \cdot {z}^{2}\right)}\right)\right) \]

       9. *-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \left({z}^{2} \cdot \color{blue}{\left(\frac{1}{6} + -1 \cdot \frac{\frac{1}{2} + -1 \cdot \frac{1 - \frac{1}{z}}{z}}{z}\right)}\right)\right)\right) \]

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

           \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(\left({z}^{2}\right), \color{blue}{\left(\frac{1}{6} + -1 \cdot \frac{\frac{1}{2} + -1 \cdot \frac{1 - \frac{1}{z}}{z}}{z}\right)}\right)\right)\right) \]

       11. unpow2 N/A

           \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(\left(z \cdot z\right), \left(\color{blue}{\frac{1}{6}} + -1 \cdot \frac{\frac{1}{2} + -1 \cdot \frac{1 - \frac{1}{z}}{z}}{z}\right)\right)\right)\right) \]

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

           \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(\mathsf{*.f64}\left(z, z\right), \left(\color{blue}{\frac{1}{6}} + -1 \cdot \frac{\frac{1}{2} + -1 \cdot \frac{1 - \frac{1}{z}}{z}}{z}\right)\right)\right)\right) \]

       13. mul-1-neg N/A

           \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(\mathsf{*.f64}\left(z, z\right), \left(\frac{1}{6} + \left(\mathsf{neg}\left(\frac{\frac{1}{2} + -1 \cdot \frac{1 - \frac{1}{z}}{z}}{z}\right)\right)\right)\right)\right)\right) \]

   13. Simplified 53.0%

       \[\leadsto \color{blue}{0 - z \cdot \left(\left(z \cdot z\right) \cdot \left(0.16666666666666666 - \frac{0.5 + \frac{-1 + \frac{1}{z}}{z}}{z}\right)\right)} \]

   if -3.1999999999999999e-146 < z < -1.99999999999999982e-307

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot z\right)}\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

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

      3. --lowering--.f64 26.8%

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

   5. Simplified 26.8%

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

   6. Taylor expanded in z around 0

      \[\leadsto \color{blue}{1 + z \cdot \left(z \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot z\right) - 1\right)} \]
   7. Step-by-step derivation

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

         \[\leadsto \mathsf{+.f64}\left(1, \color{blue}{\left(z \cdot \left(z \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot z\right) - 1\right)\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \color{blue}{\left(z \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot z\right) - 1\right)}\right)\right) \]

      3. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \left(z \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot z\right) + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \left(z \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot z\right) + -1\right)\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \left(-1 + \color{blue}{z \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot z\right)}\right)\right)\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \color{blue}{\left(z \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot z\right)\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(z, \color{blue}{\left(\frac{1}{2} + \frac{-1}{6} \cdot z\right)}\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{1}{2}, \color{blue}{\left(\frac{-1}{6} \cdot z\right)}\right)\right)\right)\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{1}{2}, \left(z \cdot \color{blue}{\frac{-1}{6}}\right)\right)\right)\right)\right)\right) \]

      10. *-lowering-*.f64 26.8%

          \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(z, \color{blue}{\frac{-1}{6}}\right)\right)\right)\right)\right)\right) \]

   8. Simplified 26.8%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \left(\left(\frac{1}{2} + z \cdot \frac{-1}{6}\right) \cdot \color{blue}{z}\right)\right)\right)\right) \]

      2. flip-+ N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \left(\frac{\frac{1}{2} \cdot \frac{1}{2} - \left(z \cdot \frac{-1}{6}\right) \cdot \left(z \cdot \frac{-1}{6}\right)}{\frac{1}{2} - z \cdot \frac{-1}{6}} \cdot z\right)\right)\right)\right) \]

      3. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \left(\frac{\left(\frac{1}{2} \cdot \frac{1}{2} - \left(z \cdot \frac{-1}{6}\right) \cdot \left(z \cdot \frac{-1}{6}\right)\right) \cdot z}{\color{blue}{\frac{1}{2} - z \cdot \frac{-1}{6}}}\right)\right)\right)\right) \]

      4. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \left(\frac{1}{\color{blue}{\frac{\frac{1}{2} - z \cdot \frac{-1}{6}}{\left(\frac{1}{2} \cdot \frac{1}{2} - \left(z \cdot \frac{-1}{6}\right) \cdot \left(z \cdot \frac{-1}{6}\right)\right) \cdot z}}}\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \mathsf{/.f64}\left(1, \color{blue}{\left(\frac{\frac{1}{2} - z \cdot \frac{-1}{6}}{\left(\frac{1}{2} \cdot \frac{1}{2} - \left(z \cdot \frac{-1}{6}\right) \cdot \left(z \cdot \frac{-1}{6}\right)\right) \cdot z}\right)}\right)\right)\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\left(\frac{1}{2} - z \cdot \frac{-1}{6}\right), \color{blue}{\left(\left(\frac{1}{2} \cdot \frac{1}{2} - \left(z \cdot \frac{-1}{6}\right) \cdot \left(z \cdot \frac{-1}{6}\right)\right) \cdot z\right)}\right)\right)\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\left(\frac{1}{2} - \frac{-1}{6} \cdot z\right), \left(\left(\frac{1}{2} \cdot \frac{1}{2} - \color{blue}{\left(z \cdot \frac{-1}{6}\right) \cdot \left(z \cdot \frac{-1}{6}\right)}\right) \cdot z\right)\right)\right)\right)\right)\right) \]

      8. cancel-sign-sub-inv N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\left(\frac{1}{2} + \left(\mathsf{neg}\left(\frac{-1}{6}\right)\right) \cdot z\right), \left(\color{blue}{\left(\frac{1}{2} \cdot \frac{1}{2} - \left(z \cdot \frac{-1}{6}\right) \cdot \left(z \cdot \frac{-1}{6}\right)\right)} \cdot z\right)\right)\right)\right)\right)\right) \]

      9. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{1}{2}, \left(\left(\mathsf{neg}\left(\frac{-1}{6}\right)\right) \cdot z\right)\right), \left(\color{blue}{\left(\frac{1}{2} \cdot \frac{1}{2} - \left(z \cdot \frac{-1}{6}\right) \cdot \left(z \cdot \frac{-1}{6}\right)\right)} \cdot z\right)\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\left(\mathsf{neg}\left(\frac{-1}{6}\right)\right), z\right)\right), \left(\left(\frac{1}{2} \cdot \frac{1}{2} - \color{blue}{\left(z \cdot \frac{-1}{6}\right) \cdot \left(z \cdot \frac{-1}{6}\right)}\right) \cdot z\right)\right)\right)\right)\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\frac{1}{6}, z\right)\right), \left(\left(\frac{1}{2} \cdot \frac{1}{2} - \color{blue}{\left(z \cdot \frac{-1}{6}\right)} \cdot \left(z \cdot \frac{-1}{6}\right)\right) \cdot z\right)\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\frac{1}{6}, z\right)\right), \mathsf{*.f64}\left(\left(\frac{1}{2} \cdot \frac{1}{2} - \left(z \cdot \frac{-1}{6}\right) \cdot \left(z \cdot \frac{-1}{6}\right)\right), \color{blue}{z}\right)\right)\right)\right)\right)\right) \]

      13. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\frac{1}{6}, z\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\left(\frac{1}{2} \cdot \frac{1}{2}\right), \left(\left(z \cdot \frac{-1}{6}\right) \cdot \left(z \cdot \frac{-1}{6}\right)\right)\right), z\right)\right)\right)\right)\right)\right) \]

      14. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\frac{1}{6}, z\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\frac{1}{4}, \left(\left(z \cdot \frac{-1}{6}\right) \cdot \left(z \cdot \frac{-1}{6}\right)\right)\right), z\right)\right)\right)\right)\right)\right) \]

      15. swap-sqr N/A

          \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\frac{1}{6}, z\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\frac{1}{4}, \left(\left(z \cdot z\right) \cdot \left(\frac{-1}{6} \cdot \frac{-1}{6}\right)\right)\right), z\right)\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\frac{1}{6}, z\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\frac{1}{4}, \mathsf{*.f64}\left(\left(z \cdot z\right), \left(\frac{-1}{6} \cdot \frac{-1}{6}\right)\right)\right), z\right)\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\frac{1}{6}, z\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\frac{1}{4}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(z, z\right), \left(\frac{-1}{6} \cdot \frac{-1}{6}\right)\right)\right), z\right)\right)\right)\right)\right)\right) \]

      18. metadata-eval 26.8%

          \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(\frac{1}{6}, z\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\frac{1}{4}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(z, z\right), \frac{1}{36}\right)\right), z\right)\right)\right)\right)\right)\right) \]

   10. Applied egg-rr 26.8%

       \[\leadsto 1 + z \cdot \left(-1 + \color{blue}{\frac{1}{\frac{0.5 + 0.16666666666666666 \cdot z}{\left(0.25 - \left(z \cdot z\right) \cdot 0.027777777777777776\right) \cdot z}}}\right) \]

   11. Taylor expanded in z around inf

       \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \color{blue}{\left({z}^{2} \cdot \left(\frac{1}{2} \cdot \frac{1}{z} - \left(\frac{1}{6} + \frac{1}{{z}^{2}}\right)\right)\right)}\right)\right) \]
   12. Step-by-step derivation

       1. unpow2 N/A

          \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \left(\left(z \cdot z\right) \cdot \left(\color{blue}{\frac{1}{2} \cdot \frac{1}{z}} - \left(\frac{1}{6} + \frac{1}{{z}^{2}}\right)\right)\right)\right)\right) \]

       2. associate-*l* N/A

          \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \left(z \cdot \color{blue}{\left(z \cdot \left(\frac{1}{2} \cdot \frac{1}{z} - \left(\frac{1}{6} + \frac{1}{{z}^{2}}\right)\right)\right)}\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, \color{blue}{\left(z \cdot \left(\frac{1}{2} \cdot \frac{1}{z} - \left(\frac{1}{6} + \frac{1}{{z}^{2}}\right)\right)\right)}\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, \color{blue}{\left(\frac{1}{2} \cdot \frac{1}{z} - \left(\frac{1}{6} + \frac{1}{{z}^{2}}\right)\right)}\right)\right)\right)\right) \]

       5. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, \left(\frac{1}{2} \cdot \frac{1}{z} + \color{blue}{\left(\mathsf{neg}\left(\left(\frac{1}{6} + \frac{1}{{z}^{2}}\right)\right)\right)}\right)\right)\right)\right)\right) \]

       6. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, \left(\left(\mathsf{neg}\left(\left(\frac{1}{6} + \frac{1}{{z}^{2}}\right)\right)\right) + \color{blue}{\frac{1}{2} \cdot \frac{1}{z}}\right)\right)\right)\right)\right) \]

       7. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, \left(\left(\left(\mathsf{neg}\left(\frac{1}{6}\right)\right) + \left(\mathsf{neg}\left(\frac{1}{{z}^{2}}\right)\right)\right) + \color{blue}{\frac{1}{2}} \cdot \frac{1}{z}\right)\right)\right)\right)\right) \]

       8. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, \left(\left(\frac{-1}{6} + \left(\mathsf{neg}\left(\frac{1}{{z}^{2}}\right)\right)\right) + \frac{1}{2} \cdot \frac{1}{z}\right)\right)\right)\right)\right) \]

       9. associate-+l+ N/A

          \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, \left(\frac{-1}{6} + \color{blue}{\left(\left(\mathsf{neg}\left(\frac{1}{{z}^{2}}\right)\right) + \frac{1}{2} \cdot \frac{1}{z}\right)}\right)\right)\right)\right)\right) \]

       10. neg-sub0 N/A

           \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, \left(\frac{-1}{6} + \left(\left(0 - \frac{1}{{z}^{2}}\right) + \color{blue}{\frac{1}{2}} \cdot \frac{1}{z}\right)\right)\right)\right)\right)\right) \]

       11. associate--r- N/A

           \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, \left(\frac{-1}{6} + \left(0 - \color{blue}{\left(\frac{1}{{z}^{2}} - \frac{1}{2} \cdot \frac{1}{z}\right)}\right)\right)\right)\right)\right)\right) \]

       12. sub-neg N/A

           \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, \left(\frac{-1}{6} + \left(0 - \left(\frac{1}{{z}^{2}} + \color{blue}{\left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{z}\right)\right)}\right)\right)\right)\right)\right)\right)\right) \]

       13. +-commutative N/A

           \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, \left(\frac{-1}{6} + \left(0 - \left(\left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{z}\right)\right) + \color{blue}{\frac{1}{{z}^{2}}}\right)\right)\right)\right)\right)\right)\right) \]

       14. neg-sub0 N/A

           \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, \left(\frac{-1}{6} + \left(0 - \left(\left(0 - \frac{1}{2} \cdot \frac{1}{z}\right) + \frac{\color{blue}{1}}{{z}^{2}}\right)\right)\right)\right)\right)\right)\right) \]

       15. associate--r- N/A

           \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, \left(\frac{-1}{6} + \left(0 - \left(0 - \color{blue}{\left(\frac{1}{2} \cdot \frac{1}{z} - \frac{1}{{z}^{2}}\right)}\right)\right)\right)\right)\right)\right)\right) \]

       16. associate-*r/ N/A

           \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, \left(\frac{-1}{6} + \left(0 - \left(0 - \left(\frac{\frac{1}{2} \cdot 1}{z} - \frac{\color{blue}{1}}{{z}^{2}}\right)\right)\right)\right)\right)\right)\right)\right) \]

       17. metadata-eval N/A

           \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, \left(\frac{-1}{6} + \left(0 - \left(0 - \left(\frac{\frac{1}{2}}{z} - \frac{1}{{z}^{2}}\right)\right)\right)\right)\right)\right)\right)\right) \]

       18. unpow2 N/A

           \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, \left(\frac{-1}{6} + \left(0 - \left(0 - \left(\frac{\frac{1}{2}}{z} - \frac{1}{z \cdot \color{blue}{z}}\right)\right)\right)\right)\right)\right)\right)\right) \]

   13. Simplified 64.3%

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

   if -1.99999999999999982e-307 < z < 1.20000000000000003e-4

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{exp.f64}\left(\color{blue}{x}\right) \]
   4. Step-by-step derivation

   5. Simplified 61.1%

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

   6. Taylor expanded in x around 0

      \[\leadsto \color{blue}{1 + x \cdot \left(1 + \frac{1}{2} \cdot x\right)} \]
   7. Step-by-step derivation

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

         \[\leadsto \mathsf{+.f64}\left(1, \color{blue}{\left(x \cdot \left(1 + \frac{1}{2} \cdot x\right)\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \color{blue}{\left(1 + \frac{1}{2} \cdot x\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(\frac{1}{2} \cdot x\right)}\right)\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \left(x \cdot \color{blue}{\frac{1}{2}}\right)\right)\right)\right) \]

      5. *-lowering-*.f64 43.5%

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \color{blue}{\frac{1}{2}}\right)\right)\right)\right) \]

   8. Simplified 43.5%

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

   if 1.20000000000000003e-4 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{exp.f64}\left(\color{blue}{x}\right) \]
   4. Step-by-step derivation

   5. Simplified 42.1%

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

   6. Taylor expanded in x around 0

      \[\leadsto \color{blue}{1 + x \cdot \left(1 + x \cdot \left(\frac{1}{2} + \frac{1}{6} \cdot x\right)\right)} \]
   7. Step-by-step derivation

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

         \[\leadsto \mathsf{+.f64}\left(1, \color{blue}{\left(x \cdot \left(1 + x \cdot \left(\frac{1}{2} + \frac{1}{6} \cdot x\right)\right)\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \color{blue}{\left(1 + x \cdot \left(\frac{1}{2} + \frac{1}{6} \cdot x\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(x \cdot \left(\frac{1}{2} + \frac{1}{6} \cdot x\right)\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{1}{2} + \frac{1}{6} \cdot x\right)}\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{1}{2}, \color{blue}{\left(\frac{1}{6} \cdot x\right)}\right)\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{1}{2}, \left(x \cdot \color{blue}{\frac{1}{6}}\right)\right)\right)\right)\right)\right) \]

      7. *-lowering-*.f64 17.6%

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(x, \color{blue}{\frac{1}{6}}\right)\right)\right)\right)\right)\right) \]

   8. Simplified 17.6%

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

   9. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{1}{6} \cdot {x}^{3}} \]
   10. Step-by-step derivation

       1. cube-mult N/A

          \[\leadsto \frac{1}{6} \cdot \left(x \cdot \color{blue}{\left(x \cdot x\right)}\right) \]

       2. unpow2 N/A

          \[\leadsto \frac{1}{6} \cdot \left(x \cdot {x}^{\color{blue}{2}}\right) \]

       3. associate-*r* N/A

          \[\leadsto \left(\frac{1}{6} \cdot x\right) \cdot \color{blue}{{x}^{2}} \]

       4. *-commutative N/A

          \[\leadsto {x}^{2} \cdot \color{blue}{\left(\frac{1}{6} \cdot x\right)} \]

       5. unpow2 N/A

          \[\leadsto \left(x \cdot x\right) \cdot \left(\color{blue}{\frac{1}{6}} \cdot x\right) \]

       6. associate-*r* N/A

          \[\leadsto x \cdot \color{blue}{\left(x \cdot \left(\frac{1}{6} \cdot x\right)\right)} \]

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

          \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(x \cdot \left(\frac{1}{6} \cdot x\right)\right)}\right) \]

       8. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\left(\frac{1}{6} \cdot x\right) \cdot \color{blue}{x}\right)\right) \]

       9. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{1}{6} \cdot \color{blue}{\left(x \cdot x\right)}\right)\right) \]

       10. unpow2 N/A

           \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{1}{6} \cdot {x}^{\color{blue}{2}}\right)\right) \]

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

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{6}, \color{blue}{\left({x}^{2}\right)}\right)\right) \]

       12. unpow2 N/A

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{6}, \left(x \cdot \color{blue}{x}\right)\right)\right) \]

       13. *-lowering-*.f64 45.5%

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{6}, \mathsf{*.f64}\left(x, \color{blue}{x}\right)\right)\right) \]

   11. Simplified 45.5%

       \[\leadsto \color{blue}{x \cdot \left(0.16666666666666666 \cdot \left(x \cdot x\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 50.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{-146}:\\ \;\;\;\;z \cdot \left(\left(z \cdot z\right) \cdot \left(\frac{0.5 + \frac{-1 + \frac{1}{z}}{z}}{z} - 0.16666666666666666\right)\right)\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-307}:\\ \;\;\;\;1 + z \cdot \left(z \cdot \left(z \cdot \left(-0.16666666666666666 + \frac{\frac{-1}{z} - -0.5}{z}\right)\right)\right)\\ \mathbf{elif}\;z \leq 0.00012:\\ \;\;\;\;1 + x \cdot \left(1 + x \cdot 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(0.16666666666666666 \cdot \left(x \cdot x\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 46.6% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{+63}:\\ \;\;\;\;z \cdot \left(z \cdot \left(z \cdot -0.16666666666666666\right)\right)\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{+32}:\\ \;\;\;\;1 + x \cdot \left(1 + x \cdot \left(0.5 + x \cdot 0.16666666666666666\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(0.16666666666666666 \cdot \left(x \cdot x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -5.6e+63)
   (* z (* z (* z -0.16666666666666666)))
   (if (<= z 6.6e+32)
     (+ 1.0 (* x (+ 1.0 (* x (+ 0.5 (* x 0.16666666666666666))))))
     (* x (* 0.16666666666666666 (* x x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -5.6e+63) {
		tmp = z * (z * (z * -0.16666666666666666));
	} else if (z <= 6.6e+32) {
		tmp = 1.0 + (x * (1.0 + (x * (0.5 + (x * 0.16666666666666666)))));
	} else {
		tmp = x * (0.16666666666666666 * (x * x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-5.6d+63)) then
        tmp = z * (z * (z * (-0.16666666666666666d0)))
    else if (z <= 6.6d+32) then
        tmp = 1.0d0 + (x * (1.0d0 + (x * (0.5d0 + (x * 0.16666666666666666d0)))))
    else
        tmp = x * (0.16666666666666666d0 * (x * x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -5.6e+63) {
		tmp = z * (z * (z * -0.16666666666666666));
	} else if (z <= 6.6e+32) {
		tmp = 1.0 + (x * (1.0 + (x * (0.5 + (x * 0.16666666666666666)))));
	} else {
		tmp = x * (0.16666666666666666 * (x * x));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -5.6e+63:
		tmp = z * (z * (z * -0.16666666666666666))
	elif z <= 6.6e+32:
		tmp = 1.0 + (x * (1.0 + (x * (0.5 + (x * 0.16666666666666666)))))
	else:
		tmp = x * (0.16666666666666666 * (x * x))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -5.6e+63)
		tmp = Float64(z * Float64(z * Float64(z * -0.16666666666666666)));
	elseif (z <= 6.6e+32)
		tmp = Float64(1.0 + Float64(x * Float64(1.0 + Float64(x * Float64(0.5 + Float64(x * 0.16666666666666666))))));
	else
		tmp = Float64(x * Float64(0.16666666666666666 * Float64(x * x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -5.6e+63)
		tmp = z * (z * (z * -0.16666666666666666));
	elseif (z <= 6.6e+32)
		tmp = 1.0 + (x * (1.0 + (x * (0.5 + (x * 0.16666666666666666)))));
	else
		tmp = x * (0.16666666666666666 * (x * x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -5.6e+63], N[(z * N[(z * N[(z * -0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.6e+32], N[(1.0 + N[(x * N[(1.0 + N[(x * N[(0.5 + N[(x * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(0.16666666666666666 * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.59999999999999974e63

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot z\right)}\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

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

      3. --lowering--.f64 89.1%

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

   5. Simplified 89.1%

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

   6. Taylor expanded in z around 0

      \[\leadsto \color{blue}{1 + z \cdot \left(z \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot z\right) - 1\right)} \]
   7. Step-by-step derivation

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

         \[\leadsto \mathsf{+.f64}\left(1, \color{blue}{\left(z \cdot \left(z \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot z\right) - 1\right)\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \color{blue}{\left(z \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot z\right) - 1\right)}\right)\right) \]

      3. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \left(z \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot z\right) + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \left(z \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot z\right) + -1\right)\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \left(-1 + \color{blue}{z \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot z\right)}\right)\right)\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \color{blue}{\left(z \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot z\right)\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(z, \color{blue}{\left(\frac{1}{2} + \frac{-1}{6} \cdot z\right)}\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{1}{2}, \color{blue}{\left(\frac{-1}{6} \cdot z\right)}\right)\right)\right)\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{1}{2}, \left(z \cdot \color{blue}{\frac{-1}{6}}\right)\right)\right)\right)\right)\right) \]

      10. *-lowering-*.f64 80.9%

          \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(z, \color{blue}{\frac{-1}{6}}\right)\right)\right)\right)\right)\right) \]

   8. Simplified 80.9%

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

   9. Taylor expanded in z around inf

      \[\leadsto \color{blue}{\frac{-1}{6} \cdot {z}^{3}} \]
   10. Step-by-step derivation

       1. cube-mult N/A

          \[\leadsto \frac{-1}{6} \cdot \left(z \cdot \color{blue}{\left(z \cdot z\right)}\right) \]

       2. unpow2 N/A

          \[\leadsto \frac{-1}{6} \cdot \left(z \cdot {z}^{\color{blue}{2}}\right) \]

       3. associate-*r* N/A

          \[\leadsto \left(\frac{-1}{6} \cdot z\right) \cdot \color{blue}{{z}^{2}} \]

       4. *-commutative N/A

          \[\leadsto {z}^{2} \cdot \color{blue}{\left(\frac{-1}{6} \cdot z\right)} \]

       5. unpow2 N/A

          \[\leadsto \left(z \cdot z\right) \cdot \left(\color{blue}{\frac{-1}{6}} \cdot z\right) \]

       6. associate-*r* N/A

          \[\leadsto z \cdot \color{blue}{\left(z \cdot \left(\frac{-1}{6} \cdot z\right)\right)} \]

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

          \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(z \cdot \left(\frac{-1}{6} \cdot z\right)\right)}\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, \color{blue}{\left(\frac{-1}{6} \cdot z\right)}\right)\right) \]

       9. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, \left(z \cdot \color{blue}{\frac{-1}{6}}\right)\right)\right) \]

       10. *-lowering-*.f64 80.9%

           \[\leadsto \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, \color{blue}{\frac{-1}{6}}\right)\right)\right) \]

   11. Simplified 80.9%

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

   if -5.59999999999999974e63 < z < 6.60000000000000039e32

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{exp.f64}\left(\color{blue}{x}\right) \]
   4. Step-by-step derivation

   5. Simplified 64.1%

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

   6. Taylor expanded in x around 0

      \[\leadsto \color{blue}{1 + x \cdot \left(1 + x \cdot \left(\frac{1}{2} + \frac{1}{6} \cdot x\right)\right)} \]
   7. Step-by-step derivation

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

         \[\leadsto \mathsf{+.f64}\left(1, \color{blue}{\left(x \cdot \left(1 + x \cdot \left(\frac{1}{2} + \frac{1}{6} \cdot x\right)\right)\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \color{blue}{\left(1 + x \cdot \left(\frac{1}{2} + \frac{1}{6} \cdot x\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(x \cdot \left(\frac{1}{2} + \frac{1}{6} \cdot x\right)\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{1}{2} + \frac{1}{6} \cdot x\right)}\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{1}{2}, \color{blue}{\left(\frac{1}{6} \cdot x\right)}\right)\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{1}{2}, \left(x \cdot \color{blue}{\frac{1}{6}}\right)\right)\right)\right)\right)\right) \]

      7. *-lowering-*.f64 38.6%

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(x, \color{blue}{\frac{1}{6}}\right)\right)\right)\right)\right)\right) \]

   8. Simplified 38.6%

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

   if 6.60000000000000039e32 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{exp.f64}\left(\color{blue}{x}\right) \]
   4. Step-by-step derivation

   5. Simplified 36.7%

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

   6. Taylor expanded in x around 0

      \[\leadsto \color{blue}{1 + x \cdot \left(1 + x \cdot \left(\frac{1}{2} + \frac{1}{6} \cdot x\right)\right)} \]
   7. Step-by-step derivation

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

         \[\leadsto \mathsf{+.f64}\left(1, \color{blue}{\left(x \cdot \left(1 + x \cdot \left(\frac{1}{2} + \frac{1}{6} \cdot x\right)\right)\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \color{blue}{\left(1 + x \cdot \left(\frac{1}{2} + \frac{1}{6} \cdot x\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(x \cdot \left(\frac{1}{2} + \frac{1}{6} \cdot x\right)\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{1}{2} + \frac{1}{6} \cdot x\right)}\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{1}{2}, \color{blue}{\left(\frac{1}{6} \cdot x\right)}\right)\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{1}{2}, \left(x \cdot \color{blue}{\frac{1}{6}}\right)\right)\right)\right)\right)\right) \]

      7. *-lowering-*.f64 14.0%

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(x, \color{blue}{\frac{1}{6}}\right)\right)\right)\right)\right)\right) \]

   8. Simplified 14.0%

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

   9. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{1}{6} \cdot {x}^{3}} \]
   10. Step-by-step derivation

       1. cube-mult N/A

          \[\leadsto \frac{1}{6} \cdot \left(x \cdot \color{blue}{\left(x \cdot x\right)}\right) \]

       2. unpow2 N/A

          \[\leadsto \frac{1}{6} \cdot \left(x \cdot {x}^{\color{blue}{2}}\right) \]

       3. associate-*r* N/A

          \[\leadsto \left(\frac{1}{6} \cdot x\right) \cdot \color{blue}{{x}^{2}} \]

       4. *-commutative N/A

          \[\leadsto {x}^{2} \cdot \color{blue}{\left(\frac{1}{6} \cdot x\right)} \]

       5. unpow2 N/A

          \[\leadsto \left(x \cdot x\right) \cdot \left(\color{blue}{\frac{1}{6}} \cdot x\right) \]

       6. associate-*r* N/A

          \[\leadsto x \cdot \color{blue}{\left(x \cdot \left(\frac{1}{6} \cdot x\right)\right)} \]

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

          \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(x \cdot \left(\frac{1}{6} \cdot x\right)\right)}\right) \]

       8. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\left(\frac{1}{6} \cdot x\right) \cdot \color{blue}{x}\right)\right) \]

       9. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{1}{6} \cdot \color{blue}{\left(x \cdot x\right)}\right)\right) \]

       10. unpow2 N/A

           \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{1}{6} \cdot {x}^{\color{blue}{2}}\right)\right) \]

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

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{6}, \color{blue}{\left({x}^{2}\right)}\right)\right) \]

       12. unpow2 N/A

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{6}, \left(x \cdot \color{blue}{x}\right)\right)\right) \]

       13. *-lowering-*.f64 47.9%

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{6}, \mathsf{*.f64}\left(x, \color{blue}{x}\right)\right)\right) \]

   11. Simplified 47.9%

       \[\leadsto \color{blue}{x \cdot \left(0.16666666666666666 \cdot \left(x \cdot x\right)\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 10: 46.3% accurate, 9.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{+63}:\\ \;\;\;\;z \cdot \left(z \cdot \left(z \cdot -0.16666666666666666\right)\right)\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+32}:\\ \;\;\;\;1 + x \cdot \left(x \cdot \left(0.5 + x \cdot 0.16666666666666666\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(0.16666666666666666 \cdot \left(x \cdot x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -5.6e+63)
   (* z (* z (* z -0.16666666666666666)))
   (if (<= z 3.8e+32)
     (+ 1.0 (* x (* x (+ 0.5 (* x 0.16666666666666666)))))
     (* x (* 0.16666666666666666 (* x x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -5.6e+63) {
		tmp = z * (z * (z * -0.16666666666666666));
	} else if (z <= 3.8e+32) {
		tmp = 1.0 + (x * (x * (0.5 + (x * 0.16666666666666666))));
	} else {
		tmp = x * (0.16666666666666666 * (x * x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-5.6d+63)) then
        tmp = z * (z * (z * (-0.16666666666666666d0)))
    else if (z <= 3.8d+32) then
        tmp = 1.0d0 + (x * (x * (0.5d0 + (x * 0.16666666666666666d0))))
    else
        tmp = x * (0.16666666666666666d0 * (x * x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -5.6e+63) {
		tmp = z * (z * (z * -0.16666666666666666));
	} else if (z <= 3.8e+32) {
		tmp = 1.0 + (x * (x * (0.5 + (x * 0.16666666666666666))));
	} else {
		tmp = x * (0.16666666666666666 * (x * x));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -5.6e+63:
		tmp = z * (z * (z * -0.16666666666666666))
	elif z <= 3.8e+32:
		tmp = 1.0 + (x * (x * (0.5 + (x * 0.16666666666666666))))
	else:
		tmp = x * (0.16666666666666666 * (x * x))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -5.6e+63)
		tmp = Float64(z * Float64(z * Float64(z * -0.16666666666666666)));
	elseif (z <= 3.8e+32)
		tmp = Float64(1.0 + Float64(x * Float64(x * Float64(0.5 + Float64(x * 0.16666666666666666)))));
	else
		tmp = Float64(x * Float64(0.16666666666666666 * Float64(x * x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -5.6e+63)
		tmp = z * (z * (z * -0.16666666666666666));
	elseif (z <= 3.8e+32)
		tmp = 1.0 + (x * (x * (0.5 + (x * 0.16666666666666666))));
	else
		tmp = x * (0.16666666666666666 * (x * x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -5.6e+63], N[(z * N[(z * N[(z * -0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.8e+32], N[(1.0 + N[(x * N[(x * N[(0.5 + N[(x * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(0.16666666666666666 * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.59999999999999974e63

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot z\right)}\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

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

      3. --lowering--.f64 89.1%

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

   5. Simplified 89.1%

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

   6. Taylor expanded in z around 0

      \[\leadsto \color{blue}{1 + z \cdot \left(z \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot z\right) - 1\right)} \]
   7. Step-by-step derivation

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

         \[\leadsto \mathsf{+.f64}\left(1, \color{blue}{\left(z \cdot \left(z \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot z\right) - 1\right)\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \color{blue}{\left(z \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot z\right) - 1\right)}\right)\right) \]

      3. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \left(z \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot z\right) + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \left(z \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot z\right) + -1\right)\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \left(-1 + \color{blue}{z \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot z\right)}\right)\right)\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \color{blue}{\left(z \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot z\right)\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(z, \color{blue}{\left(\frac{1}{2} + \frac{-1}{6} \cdot z\right)}\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{1}{2}, \color{blue}{\left(\frac{-1}{6} \cdot z\right)}\right)\right)\right)\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{1}{2}, \left(z \cdot \color{blue}{\frac{-1}{6}}\right)\right)\right)\right)\right)\right) \]

      10. *-lowering-*.f64 80.9%

          \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(z, \color{blue}{\frac{-1}{6}}\right)\right)\right)\right)\right)\right) \]

   8. Simplified 80.9%

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

   9. Taylor expanded in z around inf

      \[\leadsto \color{blue}{\frac{-1}{6} \cdot {z}^{3}} \]
   10. Step-by-step derivation

       1. cube-mult N/A

          \[\leadsto \frac{-1}{6} \cdot \left(z \cdot \color{blue}{\left(z \cdot z\right)}\right) \]

       2. unpow2 N/A

          \[\leadsto \frac{-1}{6} \cdot \left(z \cdot {z}^{\color{blue}{2}}\right) \]

       3. associate-*r* N/A

          \[\leadsto \left(\frac{-1}{6} \cdot z\right) \cdot \color{blue}{{z}^{2}} \]

       4. *-commutative N/A

          \[\leadsto {z}^{2} \cdot \color{blue}{\left(\frac{-1}{6} \cdot z\right)} \]

       5. unpow2 N/A

          \[\leadsto \left(z \cdot z\right) \cdot \left(\color{blue}{\frac{-1}{6}} \cdot z\right) \]

       6. associate-*r* N/A

          \[\leadsto z \cdot \color{blue}{\left(z \cdot \left(\frac{-1}{6} \cdot z\right)\right)} \]

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

          \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(z \cdot \left(\frac{-1}{6} \cdot z\right)\right)}\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, \color{blue}{\left(\frac{-1}{6} \cdot z\right)}\right)\right) \]

       9. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, \left(z \cdot \color{blue}{\frac{-1}{6}}\right)\right)\right) \]

       10. *-lowering-*.f64 80.9%

           \[\leadsto \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, \color{blue}{\frac{-1}{6}}\right)\right)\right) \]

   11. Simplified 80.9%

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

   if -5.59999999999999974e63 < z < 3.8000000000000003e32

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{exp.f64}\left(\color{blue}{x}\right) \]
   4. Step-by-step derivation

   5. Simplified 64.1%

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

   6. Taylor expanded in x around 0

      \[\leadsto \color{blue}{1 + x \cdot \left(1 + x \cdot \left(\frac{1}{2} + \frac{1}{6} \cdot x\right)\right)} \]
   7. Step-by-step derivation

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

         \[\leadsto \mathsf{+.f64}\left(1, \color{blue}{\left(x \cdot \left(1 + x \cdot \left(\frac{1}{2} + \frac{1}{6} \cdot x\right)\right)\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \color{blue}{\left(1 + x \cdot \left(\frac{1}{2} + \frac{1}{6} \cdot x\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(x \cdot \left(\frac{1}{2} + \frac{1}{6} \cdot x\right)\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{1}{2} + \frac{1}{6} \cdot x\right)}\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{1}{2}, \color{blue}{\left(\frac{1}{6} \cdot x\right)}\right)\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{1}{2}, \left(x \cdot \color{blue}{\frac{1}{6}}\right)\right)\right)\right)\right)\right) \]

      7. *-lowering-*.f64 38.6%

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(x, \color{blue}{\frac{1}{6}}\right)\right)\right)\right)\right)\right) \]

   8. Simplified 38.6%

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

   9. Taylor expanded in x around inf

      \[\leadsto \mathsf{+.f64}\left(1, \color{blue}{\left({x}^{3} \cdot \left(\frac{1}{6} + \frac{1}{2} \cdot \frac{1}{x}\right)\right)}\right) \]
   10. Step-by-step derivation

       1. cube-mult N/A

          \[\leadsto \mathsf{+.f64}\left(1, \left(\left(x \cdot \left(x \cdot x\right)\right) \cdot \left(\color{blue}{\frac{1}{6}} + \frac{1}{2} \cdot \frac{1}{x}\right)\right)\right) \]

       2. unpow2 N/A

          \[\leadsto \mathsf{+.f64}\left(1, \left(\left(x \cdot {x}^{2}\right) \cdot \left(\frac{1}{6} + \frac{1}{2} \cdot \frac{1}{x}\right)\right)\right) \]

       3. associate-*l* N/A

          \[\leadsto \mathsf{+.f64}\left(1, \left(x \cdot \color{blue}{\left({x}^{2} \cdot \left(\frac{1}{6} + \frac{1}{2} \cdot \frac{1}{x}\right)\right)}\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \color{blue}{\left({x}^{2} \cdot \left(\frac{1}{6} + \frac{1}{2} \cdot \frac{1}{x}\right)\right)}\right)\right) \]

       5. unpow2 N/A

          \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \left(\left(x \cdot x\right) \cdot \left(\color{blue}{\frac{1}{6}} + \frac{1}{2} \cdot \frac{1}{x}\right)\right)\right)\right) \]

       6. associate-*l* N/A

          \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \left(x \cdot \color{blue}{\left(x \cdot \left(\frac{1}{6} + \frac{1}{2} \cdot \frac{1}{x}\right)\right)}\right)\right)\right) \]

       7. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \left(x \cdot \left(\left(\frac{1}{6} + \frac{1}{2} \cdot \frac{1}{x}\right) \cdot \color{blue}{x}\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \color{blue}{\left(\left(\frac{1}{6} + \frac{1}{2} \cdot \frac{1}{x}\right) \cdot x\right)}\right)\right)\right) \]

       9. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \left(x \cdot \color{blue}{\left(\frac{1}{6} + \frac{1}{2} \cdot \frac{1}{x}\right)}\right)\right)\right)\right) \]

       10. +-commutative N/A

           \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \left(x \cdot \left(\frac{1}{2} \cdot \frac{1}{x} + \color{blue}{\frac{1}{6}}\right)\right)\right)\right)\right) \]

       11. distribute-rgt-in N/A

           \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \left(\left(\frac{1}{2} \cdot \frac{1}{x}\right) \cdot x + \color{blue}{\frac{1}{6} \cdot x}\right)\right)\right)\right) \]

       12. associate-*l* N/A

           \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \left(\frac{1}{2} \cdot \left(\frac{1}{x} \cdot x\right) + \color{blue}{\frac{1}{6}} \cdot x\right)\right)\right)\right) \]

       13. lft-mult-inverse N/A

           \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \left(\frac{1}{2} \cdot 1 + \frac{1}{6} \cdot x\right)\right)\right)\right) \]

       14. metadata-eval N/A

           \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \left(\frac{1}{2} + \color{blue}{\frac{1}{6}} \cdot x\right)\right)\right)\right) \]

       15. +-lowering-+.f64 N/A

           \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{1}{2}, \color{blue}{\left(\frac{1}{6} \cdot x\right)}\right)\right)\right)\right) \]

       16. *-commutative N/A

           \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{1}{2}, \left(x \cdot \color{blue}{\frac{1}{6}}\right)\right)\right)\right)\right) \]

       17. *-lowering-*.f64 38.5%

           \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(x, \color{blue}{\frac{1}{6}}\right)\right)\right)\right)\right) \]

   11. Simplified 38.5%

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

   if 3.8000000000000003e32 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{exp.f64}\left(\color{blue}{x}\right) \]
   4. Step-by-step derivation

   5. Simplified 36.7%

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

   6. Taylor expanded in x around 0

      \[\leadsto \color{blue}{1 + x \cdot \left(1 + x \cdot \left(\frac{1}{2} + \frac{1}{6} \cdot x\right)\right)} \]
   7. Step-by-step derivation

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

         \[\leadsto \mathsf{+.f64}\left(1, \color{blue}{\left(x \cdot \left(1 + x \cdot \left(\frac{1}{2} + \frac{1}{6} \cdot x\right)\right)\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \color{blue}{\left(1 + x \cdot \left(\frac{1}{2} + \frac{1}{6} \cdot x\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(x \cdot \left(\frac{1}{2} + \frac{1}{6} \cdot x\right)\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{1}{2} + \frac{1}{6} \cdot x\right)}\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{1}{2}, \color{blue}{\left(\frac{1}{6} \cdot x\right)}\right)\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{1}{2}, \left(x \cdot \color{blue}{\frac{1}{6}}\right)\right)\right)\right)\right)\right) \]

      7. *-lowering-*.f64 14.0%

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(x, \color{blue}{\frac{1}{6}}\right)\right)\right)\right)\right)\right) \]

   8. Simplified 14.0%

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

   9. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{1}{6} \cdot {x}^{3}} \]
   10. Step-by-step derivation

       1. cube-mult N/A

          \[\leadsto \frac{1}{6} \cdot \left(x \cdot \color{blue}{\left(x \cdot x\right)}\right) \]

       2. unpow2 N/A

          \[\leadsto \frac{1}{6} \cdot \left(x \cdot {x}^{\color{blue}{2}}\right) \]

       3. associate-*r* N/A

          \[\leadsto \left(\frac{1}{6} \cdot x\right) \cdot \color{blue}{{x}^{2}} \]

       4. *-commutative N/A

          \[\leadsto {x}^{2} \cdot \color{blue}{\left(\frac{1}{6} \cdot x\right)} \]

       5. unpow2 N/A

          \[\leadsto \left(x \cdot x\right) \cdot \left(\color{blue}{\frac{1}{6}} \cdot x\right) \]

       6. associate-*r* N/A

          \[\leadsto x \cdot \color{blue}{\left(x \cdot \left(\frac{1}{6} \cdot x\right)\right)} \]

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

          \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(x \cdot \left(\frac{1}{6} \cdot x\right)\right)}\right) \]

       8. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\left(\frac{1}{6} \cdot x\right) \cdot \color{blue}{x}\right)\right) \]

       9. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{1}{6} \cdot \color{blue}{\left(x \cdot x\right)}\right)\right) \]

       10. unpow2 N/A

           \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{1}{6} \cdot {x}^{\color{blue}{2}}\right)\right) \]

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

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{6}, \color{blue}{\left({x}^{2}\right)}\right)\right) \]

       12. unpow2 N/A

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{6}, \left(x \cdot \color{blue}{x}\right)\right)\right) \]

       13. *-lowering-*.f64 47.9%

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{6}, \mathsf{*.f64}\left(x, \color{blue}{x}\right)\right)\right) \]

   11. Simplified 47.9%

       \[\leadsto \color{blue}{x \cdot \left(0.16666666666666666 \cdot \left(x \cdot x\right)\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 11: 46.1% accurate, 10.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.1 \cdot 10^{+63}:\\ \;\;\;\;z \cdot \left(z \cdot \left(z \cdot -0.16666666666666666\right)\right)\\ \mathbf{elif}\;z \leq 0.000365:\\ \;\;\;\;1 + x \cdot \left(1 + x \cdot 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(0.16666666666666666 \cdot \left(x \cdot x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -5.1e+63)
   (* z (* z (* z -0.16666666666666666)))
   (if (<= z 0.000365)
     (+ 1.0 (* x (+ 1.0 (* x 0.5))))
     (* x (* 0.16666666666666666 (* x x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -5.1e+63) {
		tmp = z * (z * (z * -0.16666666666666666));
	} else if (z <= 0.000365) {
		tmp = 1.0 + (x * (1.0 + (x * 0.5)));
	} else {
		tmp = x * (0.16666666666666666 * (x * x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-5.1d+63)) then
        tmp = z * (z * (z * (-0.16666666666666666d0)))
    else if (z <= 0.000365d0) then
        tmp = 1.0d0 + (x * (1.0d0 + (x * 0.5d0)))
    else
        tmp = x * (0.16666666666666666d0 * (x * x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -5.1e+63) {
		tmp = z * (z * (z * -0.16666666666666666));
	} else if (z <= 0.000365) {
		tmp = 1.0 + (x * (1.0 + (x * 0.5)));
	} else {
		tmp = x * (0.16666666666666666 * (x * x));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -5.1e+63:
		tmp = z * (z * (z * -0.16666666666666666))
	elif z <= 0.000365:
		tmp = 1.0 + (x * (1.0 + (x * 0.5)))
	else:
		tmp = x * (0.16666666666666666 * (x * x))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -5.1e+63)
		tmp = Float64(z * Float64(z * Float64(z * -0.16666666666666666)));
	elseif (z <= 0.000365)
		tmp = Float64(1.0 + Float64(x * Float64(1.0 + Float64(x * 0.5))));
	else
		tmp = Float64(x * Float64(0.16666666666666666 * Float64(x * x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -5.1e+63)
		tmp = z * (z * (z * -0.16666666666666666));
	elseif (z <= 0.000365)
		tmp = 1.0 + (x * (1.0 + (x * 0.5)));
	else
		tmp = x * (0.16666666666666666 * (x * x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -5.1e+63], N[(z * N[(z * N[(z * -0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.000365], N[(1.0 + N[(x * N[(1.0 + N[(x * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(0.16666666666666666 * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.0999999999999998e63

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot z\right)}\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

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

      3. --lowering--.f64 89.1%

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

   5. Simplified 89.1%

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

   6. Taylor expanded in z around 0

      \[\leadsto \color{blue}{1 + z \cdot \left(z \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot z\right) - 1\right)} \]
   7. Step-by-step derivation

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

         \[\leadsto \mathsf{+.f64}\left(1, \color{blue}{\left(z \cdot \left(z \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot z\right) - 1\right)\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \color{blue}{\left(z \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot z\right) - 1\right)}\right)\right) \]

      3. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \left(z \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot z\right) + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \left(z \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot z\right) + -1\right)\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \left(-1 + \color{blue}{z \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot z\right)}\right)\right)\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \color{blue}{\left(z \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot z\right)\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(z, \color{blue}{\left(\frac{1}{2} + \frac{-1}{6} \cdot z\right)}\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{1}{2}, \color{blue}{\left(\frac{-1}{6} \cdot z\right)}\right)\right)\right)\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{1}{2}, \left(z \cdot \color{blue}{\frac{-1}{6}}\right)\right)\right)\right)\right)\right) \]

      10. *-lowering-*.f64 80.9%

          \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(z, \color{blue}{\frac{-1}{6}}\right)\right)\right)\right)\right)\right) \]

   8. Simplified 80.9%

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

   9. Taylor expanded in z around inf

      \[\leadsto \color{blue}{\frac{-1}{6} \cdot {z}^{3}} \]
   10. Step-by-step derivation

       1. cube-mult N/A

          \[\leadsto \frac{-1}{6} \cdot \left(z \cdot \color{blue}{\left(z \cdot z\right)}\right) \]

       2. unpow2 N/A

          \[\leadsto \frac{-1}{6} \cdot \left(z \cdot {z}^{\color{blue}{2}}\right) \]

       3. associate-*r* N/A

          \[\leadsto \left(\frac{-1}{6} \cdot z\right) \cdot \color{blue}{{z}^{2}} \]

       4. *-commutative N/A

          \[\leadsto {z}^{2} \cdot \color{blue}{\left(\frac{-1}{6} \cdot z\right)} \]

       5. unpow2 N/A

          \[\leadsto \left(z \cdot z\right) \cdot \left(\color{blue}{\frac{-1}{6}} \cdot z\right) \]

       6. associate-*r* N/A

          \[\leadsto z \cdot \color{blue}{\left(z \cdot \left(\frac{-1}{6} \cdot z\right)\right)} \]

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

          \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(z \cdot \left(\frac{-1}{6} \cdot z\right)\right)}\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, \color{blue}{\left(\frac{-1}{6} \cdot z\right)}\right)\right) \]

       9. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, \left(z \cdot \color{blue}{\frac{-1}{6}}\right)\right)\right) \]

       10. *-lowering-*.f64 80.9%

           \[\leadsto \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, \color{blue}{\frac{-1}{6}}\right)\right)\right) \]

   11. Simplified 80.9%

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

   if -5.0999999999999998e63 < z < 3.6499999999999998e-4

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{exp.f64}\left(\color{blue}{x}\right) \]
   4. Step-by-step derivation

   5. Simplified 63.9%

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

   6. Taylor expanded in x around 0

      \[\leadsto \color{blue}{1 + x \cdot \left(1 + \frac{1}{2} \cdot x\right)} \]
   7. Step-by-step derivation

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

         \[\leadsto \mathsf{+.f64}\left(1, \color{blue}{\left(x \cdot \left(1 + \frac{1}{2} \cdot x\right)\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \color{blue}{\left(1 + \frac{1}{2} \cdot x\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(\frac{1}{2} \cdot x\right)}\right)\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \left(x \cdot \color{blue}{\frac{1}{2}}\right)\right)\right)\right) \]

      5. *-lowering-*.f64 36.2%

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \color{blue}{\frac{1}{2}}\right)\right)\right)\right) \]

   8. Simplified 36.2%

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

   if 3.6499999999999998e-4 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{exp.f64}\left(\color{blue}{x}\right) \]
   4. Step-by-step derivation

   5. Simplified 42.1%

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

   6. Taylor expanded in x around 0

      \[\leadsto \color{blue}{1 + x \cdot \left(1 + x \cdot \left(\frac{1}{2} + \frac{1}{6} \cdot x\right)\right)} \]
   7. Step-by-step derivation

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

         \[\leadsto \mathsf{+.f64}\left(1, \color{blue}{\left(x \cdot \left(1 + x \cdot \left(\frac{1}{2} + \frac{1}{6} \cdot x\right)\right)\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \color{blue}{\left(1 + x \cdot \left(\frac{1}{2} + \frac{1}{6} \cdot x\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(x \cdot \left(\frac{1}{2} + \frac{1}{6} \cdot x\right)\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{1}{2} + \frac{1}{6} \cdot x\right)}\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{1}{2}, \color{blue}{\left(\frac{1}{6} \cdot x\right)}\right)\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{1}{2}, \left(x \cdot \color{blue}{\frac{1}{6}}\right)\right)\right)\right)\right)\right) \]

      7. *-lowering-*.f64 17.6%

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(x, \color{blue}{\frac{1}{6}}\right)\right)\right)\right)\right)\right) \]

   8. Simplified 17.6%

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

   9. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{1}{6} \cdot {x}^{3}} \]
   10. Step-by-step derivation

       1. cube-mult N/A

          \[\leadsto \frac{1}{6} \cdot \left(x \cdot \color{blue}{\left(x \cdot x\right)}\right) \]

       2. unpow2 N/A

          \[\leadsto \frac{1}{6} \cdot \left(x \cdot {x}^{\color{blue}{2}}\right) \]

       3. associate-*r* N/A

          \[\leadsto \left(\frac{1}{6} \cdot x\right) \cdot \color{blue}{{x}^{2}} \]

       4. *-commutative N/A

          \[\leadsto {x}^{2} \cdot \color{blue}{\left(\frac{1}{6} \cdot x\right)} \]

       5. unpow2 N/A

          \[\leadsto \left(x \cdot x\right) \cdot \left(\color{blue}{\frac{1}{6}} \cdot x\right) \]

       6. associate-*r* N/A

          \[\leadsto x \cdot \color{blue}{\left(x \cdot \left(\frac{1}{6} \cdot x\right)\right)} \]

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

          \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(x \cdot \left(\frac{1}{6} \cdot x\right)\right)}\right) \]

       8. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\left(\frac{1}{6} \cdot x\right) \cdot \color{blue}{x}\right)\right) \]

       9. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{1}{6} \cdot \color{blue}{\left(x \cdot x\right)}\right)\right) \]

       10. unpow2 N/A

           \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{1}{6} \cdot {x}^{\color{blue}{2}}\right)\right) \]

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

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{6}, \color{blue}{\left({x}^{2}\right)}\right)\right) \]

       12. unpow2 N/A

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{6}, \left(x \cdot \color{blue}{x}\right)\right)\right) \]

       13. *-lowering-*.f64 45.5%

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{6}, \mathsf{*.f64}\left(x, \color{blue}{x}\right)\right)\right) \]

   11. Simplified 45.5%

       \[\leadsto \color{blue}{x \cdot \left(0.16666666666666666 \cdot \left(x \cdot x\right)\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 12: 38.3% accurate, 12.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.4 \cdot 10^{-6}:\\ \;\;\;\;z \cdot \left(z \cdot \left(z \cdot -0.16666666666666666\right)\right)\\ \mathbf{elif}\;x \leq 5.4 \cdot 10^{+51}:\\ \;\;\;\;1 - z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(0.16666666666666666 \cdot \left(x \cdot x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -5.4e-6)
   (* z (* z (* z -0.16666666666666666)))
   (if (<= x 5.4e+51) (- 1.0 z) (* x (* 0.16666666666666666 (* x x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -5.4e-6) {
		tmp = z * (z * (z * -0.16666666666666666));
	} else if (x <= 5.4e+51) {
		tmp = 1.0 - z;
	} else {
		tmp = x * (0.16666666666666666 * (x * x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-5.4d-6)) then
        tmp = z * (z * (z * (-0.16666666666666666d0)))
    else if (x <= 5.4d+51) then
        tmp = 1.0d0 - z
    else
        tmp = x * (0.16666666666666666d0 * (x * x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -5.4e-6) {
		tmp = z * (z * (z * -0.16666666666666666));
	} else if (x <= 5.4e+51) {
		tmp = 1.0 - z;
	} else {
		tmp = x * (0.16666666666666666 * (x * x));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -5.4e-6:
		tmp = z * (z * (z * -0.16666666666666666))
	elif x <= 5.4e+51:
		tmp = 1.0 - z
	else:
		tmp = x * (0.16666666666666666 * (x * x))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -5.4e-6)
		tmp = Float64(z * Float64(z * Float64(z * -0.16666666666666666)));
	elseif (x <= 5.4e+51)
		tmp = Float64(1.0 - z);
	else
		tmp = Float64(x * Float64(0.16666666666666666 * Float64(x * x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -5.4e-6)
		tmp = z * (z * (z * -0.16666666666666666));
	elseif (x <= 5.4e+51)
		tmp = 1.0 - z;
	else
		tmp = x * (0.16666666666666666 * (x * x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -5.4e-6], N[(z * N[(z * N[(z * -0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.4e+51], N[(1.0 - z), $MachinePrecision], N[(x * N[(0.16666666666666666 * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.39999999999999997e-6

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot z\right)}\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

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

      3. --lowering--.f64 32.8%

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

   5. Simplified 32.8%

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

   6. Taylor expanded in z around 0

      \[\leadsto \color{blue}{1 + z \cdot \left(z \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot z\right) - 1\right)} \]
   7. Step-by-step derivation

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

         \[\leadsto \mathsf{+.f64}\left(1, \color{blue}{\left(z \cdot \left(z \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot z\right) - 1\right)\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \color{blue}{\left(z \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot z\right) - 1\right)}\right)\right) \]

      3. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \left(z \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot z\right) + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \left(z \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot z\right) + -1\right)\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \left(-1 + \color{blue}{z \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot z\right)}\right)\right)\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \color{blue}{\left(z \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot z\right)\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(z, \color{blue}{\left(\frac{1}{2} + \frac{-1}{6} \cdot z\right)}\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{1}{2}, \color{blue}{\left(\frac{-1}{6} \cdot z\right)}\right)\right)\right)\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{1}{2}, \left(z \cdot \color{blue}{\frac{-1}{6}}\right)\right)\right)\right)\right)\right) \]

      10. *-lowering-*.f64 14.0%

          \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(z, \color{blue}{\frac{-1}{6}}\right)\right)\right)\right)\right)\right) \]

   8. Simplified 14.0%

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

   9. Taylor expanded in z around inf

      \[\leadsto \color{blue}{\frac{-1}{6} \cdot {z}^{3}} \]
   10. Step-by-step derivation

       1. cube-mult N/A

          \[\leadsto \frac{-1}{6} \cdot \left(z \cdot \color{blue}{\left(z \cdot z\right)}\right) \]

       2. unpow2 N/A

          \[\leadsto \frac{-1}{6} \cdot \left(z \cdot {z}^{\color{blue}{2}}\right) \]

       3. associate-*r* N/A

          \[\leadsto \left(\frac{-1}{6} \cdot z\right) \cdot \color{blue}{{z}^{2}} \]

       4. *-commutative N/A

          \[\leadsto {z}^{2} \cdot \color{blue}{\left(\frac{-1}{6} \cdot z\right)} \]

       5. unpow2 N/A

          \[\leadsto \left(z \cdot z\right) \cdot \left(\color{blue}{\frac{-1}{6}} \cdot z\right) \]

       6. associate-*r* N/A

          \[\leadsto z \cdot \color{blue}{\left(z \cdot \left(\frac{-1}{6} \cdot z\right)\right)} \]

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

          \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(z \cdot \left(\frac{-1}{6} \cdot z\right)\right)}\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, \color{blue}{\left(\frac{-1}{6} \cdot z\right)}\right)\right) \]

       9. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, \left(z \cdot \color{blue}{\frac{-1}{6}}\right)\right)\right) \]

       10. *-lowering-*.f64 29.6%

           \[\leadsto \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, \color{blue}{\frac{-1}{6}}\right)\right)\right) \]

   11. Simplified 29.6%

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

   if -5.39999999999999997e-6 < x < 5.39999999999999983e51

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot z\right)}\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

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

      3. --lowering--.f64 64.4%

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

   5. Simplified 64.4%

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

   6. Taylor expanded in z around 0

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

      1. neg-mul-1 N/A

         \[\leadsto 1 + \left(\mathsf{neg}\left(z\right)\right) \]

      2. unsub-neg N/A

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

      3. --lowering--.f64 24.2%

         \[\leadsto \mathsf{\_.f64}\left(1, \color{blue}{z}\right) \]

   8. Simplified 24.2%

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

   if 5.39999999999999983e51 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{exp.f64}\left(\color{blue}{x}\right) \]
   4. Step-by-step derivation

   5. Simplified 98.3%

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

   6. Taylor expanded in x around 0

      \[\leadsto \color{blue}{1 + x \cdot \left(1 + x \cdot \left(\frac{1}{2} + \frac{1}{6} \cdot x\right)\right)} \]
   7. Step-by-step derivation

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

         \[\leadsto \mathsf{+.f64}\left(1, \color{blue}{\left(x \cdot \left(1 + x \cdot \left(\frac{1}{2} + \frac{1}{6} \cdot x\right)\right)\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \color{blue}{\left(1 + x \cdot \left(\frac{1}{2} + \frac{1}{6} \cdot x\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(x \cdot \left(\frac{1}{2} + \frac{1}{6} \cdot x\right)\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{1}{2} + \frac{1}{6} \cdot x\right)}\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{1}{2}, \color{blue}{\left(\frac{1}{6} \cdot x\right)}\right)\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{1}{2}, \left(x \cdot \color{blue}{\frac{1}{6}}\right)\right)\right)\right)\right)\right) \]

      7. *-lowering-*.f64 79.2%

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(x, \color{blue}{\frac{1}{6}}\right)\right)\right)\right)\right)\right) \]

   8. Simplified 79.2%

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

   9. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{1}{6} \cdot {x}^{3}} \]
   10. Step-by-step derivation

       1. cube-mult N/A

          \[\leadsto \frac{1}{6} \cdot \left(x \cdot \color{blue}{\left(x \cdot x\right)}\right) \]

       2. unpow2 N/A

          \[\leadsto \frac{1}{6} \cdot \left(x \cdot {x}^{\color{blue}{2}}\right) \]

       3. associate-*r* N/A

          \[\leadsto \left(\frac{1}{6} \cdot x\right) \cdot \color{blue}{{x}^{2}} \]

       4. *-commutative N/A

          \[\leadsto {x}^{2} \cdot \color{blue}{\left(\frac{1}{6} \cdot x\right)} \]

       5. unpow2 N/A

          \[\leadsto \left(x \cdot x\right) \cdot \left(\color{blue}{\frac{1}{6}} \cdot x\right) \]

       6. associate-*r* N/A

          \[\leadsto x \cdot \color{blue}{\left(x \cdot \left(\frac{1}{6} \cdot x\right)\right)} \]

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

          \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(x \cdot \left(\frac{1}{6} \cdot x\right)\right)}\right) \]

       8. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\left(\frac{1}{6} \cdot x\right) \cdot \color{blue}{x}\right)\right) \]

       9. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{1}{6} \cdot \color{blue}{\left(x \cdot x\right)}\right)\right) \]

       10. unpow2 N/A

           \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{1}{6} \cdot {x}^{\color{blue}{2}}\right)\right) \]

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

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{6}, \color{blue}{\left({x}^{2}\right)}\right)\right) \]

       12. unpow2 N/A

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{6}, \left(x \cdot \color{blue}{x}\right)\right)\right) \]

       13. *-lowering-*.f64 79.2%

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{6}, \mathsf{*.f64}\left(x, \color{blue}{x}\right)\right)\right) \]

   11. Simplified 79.2%

       \[\leadsto \color{blue}{x \cdot \left(0.16666666666666666 \cdot \left(x \cdot x\right)\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 13: 32.1% accurate, 17.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+130}:\\ \;\;\;\;\left(z \cdot z\right) \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(0.16666666666666666 \cdot \left(x \cdot x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -2.8e+130) (* (* z z) 0.5) (* x (* 0.16666666666666666 (* x x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.8e+130) {
		tmp = (z * z) * 0.5;
	} else {
		tmp = x * (0.16666666666666666 * (x * x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-2.8d+130)) then
        tmp = (z * z) * 0.5d0
    else
        tmp = x * (0.16666666666666666d0 * (x * x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.8e+130) {
		tmp = (z * z) * 0.5;
	} else {
		tmp = x * (0.16666666666666666 * (x * x));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -2.8e+130:
		tmp = (z * z) * 0.5
	else:
		tmp = x * (0.16666666666666666 * (x * x))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -2.8e+130)
		tmp = Float64(Float64(z * z) * 0.5);
	else
		tmp = Float64(x * Float64(0.16666666666666666 * Float64(x * x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -2.8e+130)
		tmp = (z * z) * 0.5;
	else
		tmp = x * (0.16666666666666666 * (x * x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -2.8e+130], N[(N[(z * z), $MachinePrecision] * 0.5), $MachinePrecision], N[(x * N[(0.16666666666666666 * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.7999999999999999e130

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot z\right)}\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

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

      3. --lowering--.f64 97.1%

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

   5. Simplified 97.1%

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

   6. Taylor expanded in z around 0

      \[\leadsto \color{blue}{1 + z \cdot \left(\frac{1}{2} \cdot z - 1\right)} \]
   7. Step-by-step derivation

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

         \[\leadsto \mathsf{+.f64}\left(1, \color{blue}{\left(z \cdot \left(\frac{1}{2} \cdot z - 1\right)\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \color{blue}{\left(\frac{1}{2} \cdot z - 1\right)}\right)\right) \]

      3. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \left(\frac{1}{2} \cdot z + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \left(\frac{1}{2} \cdot z + -1\right)\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \left(-1 + \color{blue}{\frac{1}{2} \cdot z}\right)\right)\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \color{blue}{\left(\frac{1}{2} \cdot z\right)}\right)\right)\right) \]

      7. *-lowering-*.f64 88.9%

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{z}\right)\right)\right)\right) \]

   8. Simplified 88.9%

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

   9. Taylor expanded in z around inf

      \[\leadsto \color{blue}{\frac{1}{2} \cdot {z}^{2}} \]
   10. Step-by-step derivation

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

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{\left({z}^{2}\right)}\right) \]

       2. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \left(z \cdot \color{blue}{z}\right)\right) \]

       3. *-lowering-*.f64 88.9%

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(z, \color{blue}{z}\right)\right) \]

   11. Simplified 88.9%

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

   if -2.7999999999999999e130 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{exp.f64}\left(\color{blue}{x}\right) \]
   4. Step-by-step derivation

   5. Simplified 58.4%

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

   6. Taylor expanded in x around 0

      \[\leadsto \color{blue}{1 + x \cdot \left(1 + x \cdot \left(\frac{1}{2} + \frac{1}{6} \cdot x\right)\right)} \]
   7. Step-by-step derivation

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

         \[\leadsto \mathsf{+.f64}\left(1, \color{blue}{\left(x \cdot \left(1 + x \cdot \left(\frac{1}{2} + \frac{1}{6} \cdot x\right)\right)\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \color{blue}{\left(1 + x \cdot \left(\frac{1}{2} + \frac{1}{6} \cdot x\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(x \cdot \left(\frac{1}{2} + \frac{1}{6} \cdot x\right)\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{1}{2} + \frac{1}{6} \cdot x\right)}\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{1}{2}, \color{blue}{\left(\frac{1}{6} \cdot x\right)}\right)\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{1}{2}, \left(x \cdot \color{blue}{\frac{1}{6}}\right)\right)\right)\right)\right)\right) \]

      7. *-lowering-*.f64 32.9%

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(x, \color{blue}{\frac{1}{6}}\right)\right)\right)\right)\right)\right) \]

   8. Simplified 32.9%

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

   9. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{1}{6} \cdot {x}^{3}} \]
   10. Step-by-step derivation

       1. cube-mult N/A

          \[\leadsto \frac{1}{6} \cdot \left(x \cdot \color{blue}{\left(x \cdot x\right)}\right) \]

       2. unpow2 N/A

          \[\leadsto \frac{1}{6} \cdot \left(x \cdot {x}^{\color{blue}{2}}\right) \]

       3. associate-*r* N/A

          \[\leadsto \left(\frac{1}{6} \cdot x\right) \cdot \color{blue}{{x}^{2}} \]

       4. *-commutative N/A

          \[\leadsto {x}^{2} \cdot \color{blue}{\left(\frac{1}{6} \cdot x\right)} \]

       5. unpow2 N/A

          \[\leadsto \left(x \cdot x\right) \cdot \left(\color{blue}{\frac{1}{6}} \cdot x\right) \]

       6. associate-*r* N/A

          \[\leadsto x \cdot \color{blue}{\left(x \cdot \left(\frac{1}{6} \cdot x\right)\right)} \]

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

          \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(x \cdot \left(\frac{1}{6} \cdot x\right)\right)}\right) \]

       8. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\left(\frac{1}{6} \cdot x\right) \cdot \color{blue}{x}\right)\right) \]

       9. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{1}{6} \cdot \color{blue}{\left(x \cdot x\right)}\right)\right) \]

       10. unpow2 N/A

           \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{1}{6} \cdot {x}^{\color{blue}{2}}\right)\right) \]

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

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{6}, \color{blue}{\left({x}^{2}\right)}\right)\right) \]

       12. unpow2 N/A

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{6}, \left(x \cdot \color{blue}{x}\right)\right)\right) \]

       13. *-lowering-*.f64 26.9%

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{6}, \mathsf{*.f64}\left(x, \color{blue}{x}\right)\right)\right) \]

   11. Simplified 26.9%

       \[\leadsto \color{blue}{x \cdot \left(0.16666666666666666 \cdot \left(x \cdot x\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 35.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+130}:\\ \;\;\;\;\left(z \cdot z\right) \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(0.16666666666666666 \cdot \left(x \cdot x\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 26.6% accurate, 20.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.245:\\ \;\;\;\;\left(z \cdot z\right) \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.245) (* (* z z) 0.5) (+ x 1.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.245) {
		tmp = (z * z) * 0.5;
	} else {
		tmp = x + 1.0;
	}
	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 <= (-0.245d0)) then
        tmp = (z * z) * 0.5d0
    else
        tmp = x + 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.245) {
		tmp = (z * z) * 0.5;
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.245:
		tmp = (z * z) * 0.5
	else:
		tmp = x + 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.245)
		tmp = Float64(Float64(z * z) * 0.5);
	else
		tmp = Float64(x + 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.245)
		tmp = (z * z) * 0.5;
	else
		tmp = x + 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.245], N[(N[(z * z), $MachinePrecision] * 0.5), $MachinePrecision], N[(x + 1.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.245

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{exp.f64}\left(\color{blue}{\left(-1 \cdot z\right)}\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

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

      3. --lowering--.f64 88.1%

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

   5. Simplified 88.1%

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

   6. Taylor expanded in z around 0

      \[\leadsto \color{blue}{1 + z \cdot \left(\frac{1}{2} \cdot z - 1\right)} \]
   7. Step-by-step derivation

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

         \[\leadsto \mathsf{+.f64}\left(1, \color{blue}{\left(z \cdot \left(\frac{1}{2} \cdot z - 1\right)\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \color{blue}{\left(\frac{1}{2} \cdot z - 1\right)}\right)\right) \]

      3. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \left(\frac{1}{2} \cdot z + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \left(\frac{1}{2} \cdot z + -1\right)\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \left(-1 + \color{blue}{\frac{1}{2} \cdot z}\right)\right)\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \color{blue}{\left(\frac{1}{2} \cdot z\right)}\right)\right)\right) \]

      7. *-lowering-*.f64 47.6%

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(-1, \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{z}\right)\right)\right)\right) \]

   8. Simplified 47.6%

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

   9. Taylor expanded in z around inf

      \[\leadsto \color{blue}{\frac{1}{2} \cdot {z}^{2}} \]
   10. Step-by-step derivation

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

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{\left({z}^{2}\right)}\right) \]

       2. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \left(z \cdot \color{blue}{z}\right)\right) \]

       3. *-lowering-*.f64 47.6%

          \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(z, \color{blue}{z}\right)\right) \]

   11. Simplified 47.6%

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

   if -0.245 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{exp.f64}\left(\color{blue}{x}\right) \]
   4. Step-by-step derivation

   5. Simplified 59.0%

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

   6. Taylor expanded in x around 0

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

      1. +-lowering-+.f64 17.7%

         \[\leadsto \mathsf{+.f64}\left(1, \color{blue}{x}\right) \]

   8. Simplified 17.7%

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

4. Final simplification 25.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.245:\\ \;\;\;\;\left(z \cdot z\right) \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 15.1% accurate, 69.0× speedup

Math

\[\begin{array}{l} \\ x + 1 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ x 1.0))

C

double code(double x, double y, double z) {
	return x + 1.0;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + 1.0d0
end function

Java

public static double code(double x, double y, double z) {
	return x + 1.0;
}

Python

def code(x, y, z):
	return x + 1.0

Julia

function code(x, y, z)
	return Float64(x + 1.0)
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + 1.0;
end

Wolfram

code[x_, y_, z_] := N[(x + 1.0), $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

   \[\leadsto \mathsf{exp.f64}\left(\color{blue}{x}\right) \]
4. Step-by-step derivation

5. Simplified 54.0%

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

6. Taylor expanded in x around 0

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

   1. +-lowering-+.f64 14.0%

      \[\leadsto \mathsf{+.f64}\left(1, \color{blue}{x}\right) \]

8. Simplified 14.0%

   \[\leadsto \color{blue}{1 + x} \]

9. Final simplification 14.0%

   \[\leadsto x + 1 \]
10. Add Preprocessing

Alternative 16: 14.9% accurate, 207.0× speedup

Math

\[\begin{array}{l} \\ 1 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 1.0)

C

double code(double x, double y, double z) {
	return 1.0;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = 1.0d0
end function

Java

public static double code(double x, double y, double z) {
	return 1.0;
}

Python

def code(x, y, z):
	return 1.0

Julia

function code(x, y, z)
	return 1.0
end

MATLAB

function tmp = code(x, y, z)
	tmp = 1.0;
end

Wolfram

code[x_, y_, z_] := 1.0

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

   \[\leadsto \mathsf{exp.f64}\left(\color{blue}{x}\right) \]
4. Step-by-step derivation

5. Simplified 54.0%

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

6. Taylor expanded in x around 0

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

8. Simplified 13.6%

   \[\leadsto \color{blue}{1} \]
9. Add Preprocessing

Developer Target 1: 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 2024152 
(FPCore (x y z)
  :name "Statistics.Distribution.Poisson.Internal:probability from math-functions-0.1.5.2"
  :precision binary64

  :alt
  (! :herbie-platform default (exp (+ (- x z) (* (log y) y))))

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