Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, G

Percentage Accurate: 84.3% → 99.9%

Time: 11.4s

Alternatives: 8

Speedup: 15.1×

• Could not converge on a ground truth

  1. x = -1.1762618348574264e-73
  2. y = 1.4358576855543654e+205
  3. z = 3.276749795772517e-85

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 84.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+43} \lor \neg \left(y \leq 10\right):\\ \;\;\;\;x + \frac{e^{-z}}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{{\left(e^{y}\right)}^{\log \left(\frac{y}{y + z}\right)}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -4e+43) (not (<= y 10.0)))
   (+ x (/ (exp (- z)) y))
   (+ x (/ (pow (exp y) (log (/ y (+ y z)))) y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4e+43) || !(y <= 10.0)) {
		tmp = x + (exp(-z) / y);
	} else {
		tmp = x + (pow(exp(y), log((y / (y + z)))) / 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 <= (-4d+43)) .or. (.not. (y <= 10.0d0))) then
        tmp = x + (exp(-z) / y)
    else
        tmp = x + ((exp(y) ** log((y / (y + z)))) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4e+43) || !(y <= 10.0)) {
		tmp = x + (Math.exp(-z) / y);
	} else {
		tmp = x + (Math.pow(Math.exp(y), Math.log((y / (y + z)))) / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -4e+43) or not (y <= 10.0):
		tmp = x + (math.exp(-z) / y)
	else:
		tmp = x + (math.pow(math.exp(y), math.log((y / (y + z)))) / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -4e+43) || !(y <= 10.0))
		tmp = Float64(x + Float64(exp(Float64(-z)) / y));
	else
		tmp = Float64(x + Float64((exp(y) ^ log(Float64(y / Float64(y + z)))) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -4e+43) || ~((y <= 10.0)))
		tmp = x + (exp(-z) / y);
	else
		tmp = x + ((exp(y) ^ log((y / (y + z)))) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -4e+43], N[Not[LessEqual[y, 10.0]], $MachinePrecision]], N[(x + N[(N[Exp[(-z)], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[Power[N[Exp[y], $MachinePrecision], N[Log[N[(y / N[(y + z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.00000000000000006e43 or 10 < y

   1. Initial program 83.6%

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

      1. *-commutative 83.6%

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

      2. exp-to-pow 83.6%

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

      3. +-commutative 83.6%

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

   3. Simplified 83.6%

      \[\leadsto \color{blue}{x + \frac{{\left(\frac{y}{y + z}\right)}^{y}}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 100.0%

      \[\leadsto \color{blue}{x + \frac{e^{-1 \cdot z}}{y}} \]
   6. Step-by-step derivation

      1. mul-1-neg 100.0%

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

   7. Simplified 100.0%

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

   if -4.00000000000000006e43 < y < 10

   1. Initial program 84.2%

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

      1. exp-prod 99.7%

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

      2. +-commutative 99.7%

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

   3. Simplified 99.7%

      \[\leadsto \color{blue}{x + \frac{{\left(e^{y}\right)}^{\log \left(\frac{y}{y + z}\right)}}{y}} \]
   4. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+43} \lor \neg \left(y \leq 10\right):\\ \;\;\;\;x + \frac{e^{-z}}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{{\left(e^{y}\right)}^{\log \left(\frac{y}{y + z}\right)}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 98.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+21} \lor \neg \left(y \leq 0.65\right):\\ \;\;\;\;x + \frac{e^{-z}}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.4e+21) (not (<= y 0.65)))
   (+ x (/ (exp (- z)) y))
   (+ x (/ 1.0 y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.4e+21) || !(y <= 0.65)) {
		tmp = x + (exp(-z) / y);
	} else {
		tmp = x + (1.0 / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-2.4d+21)) .or. (.not. (y <= 0.65d0))) then
        tmp = x + (exp(-z) / y)
    else
        tmp = x + (1.0d0 / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.4e+21) || !(y <= 0.65)) {
		tmp = x + (Math.exp(-z) / y);
	} else {
		tmp = x + (1.0 / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.4e+21) or not (y <= 0.65):
		tmp = x + (math.exp(-z) / y)
	else:
		tmp = x + (1.0 / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.4e+21) || !(y <= 0.65))
		tmp = Float64(x + Float64(exp(Float64(-z)) / y));
	else
		tmp = Float64(x + Float64(1.0 / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -2.4e+21) || ~((y <= 0.65)))
		tmp = x + (exp(-z) / y);
	else
		tmp = x + (1.0 / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.4e+21], N[Not[LessEqual[y, 0.65]], $MachinePrecision]], N[(x + N[(N[Exp[(-z)], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x + N[(1.0 / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.4e21 or 0.650000000000000022 < y

   1. Initial program 84.5%

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

      1. *-commutative 84.5%

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

      2. exp-to-pow 84.5%

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

      3. +-commutative 84.5%

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

   3. Simplified 84.5%

      \[\leadsto \color{blue}{x + \frac{{\left(\frac{y}{y + z}\right)}^{y}}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 100.0%

      \[\leadsto \color{blue}{x + \frac{e^{-1 \cdot z}}{y}} \]
   6. Step-by-step derivation

      1. mul-1-neg 100.0%

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

   7. Simplified 100.0%

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

   if -2.4e21 < y < 0.650000000000000022

   1. Initial program 83.2%

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

      1. exp-prod 99.7%

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

      2. +-commutative 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around inf 98.3%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+21} \lor \neg \left(y \leq 0.65\right):\\ \;\;\;\;x + \frac{e^{-z}}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 88.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+255} \lor \neg \left(z \leq -14500000\right):\\ \;\;\;\;x + \frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{e^{-z}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -4e+255) (not (<= z -14500000.0)))
   (+ x (/ 1.0 y))
   (/ (exp (- z)) y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4e+255) || !(z <= -14500000.0)) {
		tmp = x + (1.0 / y);
	} else {
		tmp = exp(-z) / 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 ((z <= (-4d+255)) .or. (.not. (z <= (-14500000.0d0)))) then
        tmp = x + (1.0d0 / y)
    else
        tmp = exp(-z) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4e+255) || !(z <= -14500000.0)) {
		tmp = x + (1.0 / y);
	} else {
		tmp = Math.exp(-z) / y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -4e+255) or not (z <= -14500000.0):
		tmp = x + (1.0 / y)
	else:
		tmp = math.exp(-z) / y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -4e+255) || !(z <= -14500000.0))
		tmp = Float64(x + Float64(1.0 / y));
	else
		tmp = Float64(exp(Float64(-z)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -4e+255) || ~((z <= -14500000.0)))
		tmp = x + (1.0 / y);
	else
		tmp = exp(-z) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -4e+255], N[Not[LessEqual[z, -14500000.0]], $MachinePrecision]], N[(x + N[(1.0 / y), $MachinePrecision]), $MachinePrecision], N[(N[Exp[(-z)], $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.99999999999999995e255 or -1.45e7 < z

   1. Initial program 88.9%

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

      1. exp-prod 97.4%

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

      2. +-commutative 97.4%

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

   3. Simplified 97.4%

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

   5. Taylor expanded in y around inf 94.6%

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

   if -3.99999999999999995e255 < z < -1.45e7

   1. Initial program 52.6%

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

      1. *-commutative 52.6%

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

      2. exp-to-pow 52.6%

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

      3. +-commutative 52.6%

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

   3. Simplified 52.6%

      \[\leadsto \color{blue}{x + \frac{{\left(\frac{y}{y + z}\right)}^{y}}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 75.8%

      \[\leadsto \color{blue}{x + \frac{e^{-1 \cdot z}}{y}} \]
   6. Step-by-step derivation

      1. mul-1-neg 75.8%

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

   7. Simplified 75.8%

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

   8. Taylor expanded in x around 0 75.8%

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

4. Final simplification 92.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+255} \lor \neg \left(z \leq -14500000\right):\\ \;\;\;\;x + \frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{e^{-z}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 88.7% accurate, 9.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+21}:\\ \;\;\;\;x + \frac{1 + z \cdot \left(z \cdot \left(0.5 + z \cdot -0.16666666666666666\right) + -1\right)}{y}\\ \mathbf{elif}\;y \leq 0.4:\\ \;\;\;\;x + \frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{y + y \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.4e+21)
   (+ x (/ (+ 1.0 (* z (+ (* z (+ 0.5 (* z -0.16666666666666666))) -1.0))) y))
   (if (<= y 0.4) (+ x (/ 1.0 y)) (+ x (/ 1.0 (+ y (* y z)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.4e+21) {
		tmp = x + ((1.0 + (z * ((z * (0.5 + (z * -0.16666666666666666))) + -1.0))) / y);
	} else if (y <= 0.4) {
		tmp = x + (1.0 / y);
	} else {
		tmp = x + (1.0 / (y + (y * z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-2.4d+21)) then
        tmp = x + ((1.0d0 + (z * ((z * (0.5d0 + (z * (-0.16666666666666666d0)))) + (-1.0d0)))) / y)
    else if (y <= 0.4d0) then
        tmp = x + (1.0d0 / y)
    else
        tmp = x + (1.0d0 / (y + (y * z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.4e+21) {
		tmp = x + ((1.0 + (z * ((z * (0.5 + (z * -0.16666666666666666))) + -1.0))) / y);
	} else if (y <= 0.4) {
		tmp = x + (1.0 / y);
	} else {
		tmp = x + (1.0 / (y + (y * z)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.4e+21:
		tmp = x + ((1.0 + (z * ((z * (0.5 + (z * -0.16666666666666666))) + -1.0))) / y)
	elif y <= 0.4:
		tmp = x + (1.0 / y)
	else:
		tmp = x + (1.0 / (y + (y * z)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.4e+21)
		tmp = Float64(x + Float64(Float64(1.0 + Float64(z * Float64(Float64(z * Float64(0.5 + Float64(z * -0.16666666666666666))) + -1.0))) / y));
	elseif (y <= 0.4)
		tmp = Float64(x + Float64(1.0 / y));
	else
		tmp = Float64(x + Float64(1.0 / Float64(y + Float64(y * z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2.4e+21)
		tmp = x + ((1.0 + (z * ((z * (0.5 + (z * -0.16666666666666666))) + -1.0))) / y);
	elseif (y <= 0.4)
		tmp = x + (1.0 / y);
	else
		tmp = x + (1.0 / (y + (y * z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.4e+21], N[(x + N[(N[(1.0 + N[(z * N[(N[(z * N[(0.5 + N[(z * -0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 0.4], N[(x + N[(1.0 / y), $MachinePrecision]), $MachinePrecision], N[(x + N[(1.0 / N[(y + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.4e21

   1. Initial program 82.8%

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

      1. *-commutative 82.8%

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

      2. exp-to-pow 82.8%

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

      3. +-commutative 82.8%

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

   3. Simplified 82.8%

      \[\leadsto \color{blue}{x + \frac{{\left(\frac{y}{y + z}\right)}^{y}}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 100.0%

      \[\leadsto \color{blue}{x + \frac{e^{-1 \cdot z}}{y}} \]
   6. Step-by-step derivation

      1. mul-1-neg 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in z around 0 77.3%

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

   if -2.4e21 < y < 0.40000000000000002

   1. Initial program 83.2%

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

      1. exp-prod 99.7%

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

      2. +-commutative 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around inf 98.3%

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

   if 0.40000000000000002 < y

   1. Initial program 86.2%

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

      1. exp-prod 86.2%

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

      2. +-commutative 86.2%

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

   3. Simplified 86.2%

      \[\leadsto \color{blue}{x + \frac{{\left(e^{y}\right)}^{\log \left(\frac{y}{y + z}\right)}}{y}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num 86.2%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{y}{{\left(e^{y}\right)}^{\log \left(\frac{y}{y + z}\right)}}}} \]

      2. add-exp-log 85.5%

         \[\leadsto x + \frac{1}{\frac{\color{blue}{e^{\log y}}}{{\left(e^{y}\right)}^{\log \left(\frac{y}{y + z}\right)}}} \]

      3. add-exp-log 85.5%

         \[\leadsto x + \frac{1}{\frac{e^{\log y}}{\color{blue}{e^{\log \left({\left(e^{y}\right)}^{\log \left(\frac{y}{y + z}\right)}\right)}}}} \]

      4. div-exp 85.5%

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

      5. pow-exp 85.5%

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

      6. add-log-exp 85.5%

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

      7. log-pow 85.5%

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

      8. div-exp 85.5%

         \[\leadsto x + \frac{1}{\color{blue}{\frac{e^{\log y}}{e^{\log \left({\left(\frac{y}{y + z}\right)}^{y}\right)}}}} \]

      9. add-exp-log 86.2%

         \[\leadsto x + \frac{1}{\frac{\color{blue}{y}}{e^{\log \left({\left(\frac{y}{y + z}\right)}^{y}\right)}}} \]

      10. add-exp-log 86.2%

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

      11. inv-pow 86.2%

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

   6. Applied egg-rr 86.2%

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

      1. unpow-1 86.2%

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

   8. Simplified 86.2%

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

   9. Taylor expanded in z around 0 86.7%

      \[\leadsto x + \frac{1}{\color{blue}{y + y \cdot z}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+21}:\\ \;\;\;\;x + \frac{1 + z \cdot \left(z \cdot \left(0.5 + z \cdot -0.16666666666666666\right) + -1\right)}{y}\\ \mathbf{elif}\;y \leq 0.4:\\ \;\;\;\;x + \frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{y + y \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 85.7% accurate, 15.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 0.022:\\ \;\;\;\;x + \frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{y + y \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 0.022) (+ x (/ 1.0 y)) (+ x (/ 1.0 (+ y (* y z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 0.022) {
		tmp = x + (1.0 / y);
	} else {
		tmp = x + (1.0 / (y + (y * z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= 0.022d0) then
        tmp = x + (1.0d0 / y)
    else
        tmp = x + (1.0d0 / (y + (y * z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 0.022) {
		tmp = x + (1.0 / y);
	} else {
		tmp = x + (1.0 / (y + (y * z)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 0.022:
		tmp = x + (1.0 / y)
	else:
		tmp = x + (1.0 / (y + (y * z)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 0.022)
		tmp = Float64(x + Float64(1.0 / y));
	else
		tmp = Float64(x + Float64(1.0 / Float64(y + Float64(y * z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 0.022)
		tmp = x + (1.0 / y);
	else
		tmp = x + (1.0 / (y + (y * z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 0.022], N[(x + N[(1.0 / y), $MachinePrecision]), $MachinePrecision], N[(x + N[(1.0 / N[(y + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 0.021999999999999999

   1. Initial program 83.1%

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

      1. exp-prod 93.6%

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

      2. +-commutative 93.6%

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

   3. Simplified 93.6%

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

   5. Taylor expanded in y around inf 87.1%

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

   if 0.021999999999999999 < y

   1. Initial program 86.2%

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

      1. exp-prod 86.2%

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

      2. +-commutative 86.2%

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

   3. Simplified 86.2%

      \[\leadsto \color{blue}{x + \frac{{\left(e^{y}\right)}^{\log \left(\frac{y}{y + z}\right)}}{y}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num 86.2%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{y}{{\left(e^{y}\right)}^{\log \left(\frac{y}{y + z}\right)}}}} \]

      2. add-exp-log 85.5%

         \[\leadsto x + \frac{1}{\frac{\color{blue}{e^{\log y}}}{{\left(e^{y}\right)}^{\log \left(\frac{y}{y + z}\right)}}} \]

      3. add-exp-log 85.5%

         \[\leadsto x + \frac{1}{\frac{e^{\log y}}{\color{blue}{e^{\log \left({\left(e^{y}\right)}^{\log \left(\frac{y}{y + z}\right)}\right)}}}} \]

      4. div-exp 85.5%

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

      5. pow-exp 85.5%

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

      6. add-log-exp 85.5%

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

      7. log-pow 85.5%

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

      8. div-exp 85.5%

         \[\leadsto x + \frac{1}{\color{blue}{\frac{e^{\log y}}{e^{\log \left({\left(\frac{y}{y + z}\right)}^{y}\right)}}}} \]

      9. add-exp-log 86.2%

         \[\leadsto x + \frac{1}{\frac{\color{blue}{y}}{e^{\log \left({\left(\frac{y}{y + z}\right)}^{y}\right)}}} \]

      10. add-exp-log 86.2%

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

      11. inv-pow 86.2%

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

   6. Applied egg-rr 86.2%

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

      1. unpow-1 86.2%

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

   8. Simplified 86.2%

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

   9. Taylor expanded in z around 0 86.7%

      \[\leadsto x + \frac{1}{\color{blue}{y + y \cdot z}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 65.0% accurate, 16.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.55 \cdot 10^{+109}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-94}:\\ \;\;\;\;\frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3.55e+109) x (if (<= y 6e-94) (/ 1.0 y) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.55e+109) {
		tmp = x;
	} else if (y <= 6e-94) {
		tmp = 1.0 / y;
	} else {
		tmp = 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 (y <= (-3.55d+109)) then
        tmp = x
    else if (y <= 6d-94) then
        tmp = 1.0d0 / y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.55e+109) {
		tmp = x;
	} else if (y <= 6e-94) {
		tmp = 1.0 / y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -3.55e+109:
		tmp = x
	elif y <= 6e-94:
		tmp = 1.0 / y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3.55e+109)
		tmp = x;
	elseif (y <= 6e-94)
		tmp = Float64(1.0 / y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -3.55e+109)
		tmp = x;
	elseif (y <= 6e-94)
		tmp = 1.0 / y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3.55e+109], x, If[LessEqual[y, 6e-94], N[(1.0 / y), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -3.5500000000000001e109 or 6.0000000000000003e-94 < y

   1. Initial program 85.8%

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

      1. exp-prod 85.6%

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

      2. +-commutative 85.6%

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

   3. Simplified 85.6%

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

   5. Taylor expanded in x around inf 71.8%

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

   if -3.5500000000000001e109 < y < 6.0000000000000003e-94

   1. Initial program 81.5%

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

      1. exp-prod 99.1%

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

      2. +-commutative 99.1%

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

   3. Simplified 99.1%

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

   5. Taylor expanded in y around 0 75.6%

      \[\leadsto \color{blue}{\frac{1}{y}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 84.3% accurate, 42.2× speedup

Math

\[\begin{array}{l} \\ x + \frac{1}{y} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ x (/ 1.0 y)))

C

double code(double x, double y, double z) {
	return x + (1.0 / y);
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + (1.0d0 / y)
end function

Java

public static double code(double x, double y, double z) {
	return x + (1.0 / y);
}

Python

def code(x, y, z):
	return x + (1.0 / y)

Julia

function code(x, y, z)
	return Float64(x + Float64(1.0 / y))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + (1.0 / y);
end

Wolfram

code[x_, y_, z_] := N[(x + N[(1.0 / y), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 83.9%

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

   1. exp-prod 91.7%

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

   2. +-commutative 91.7%

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

3. Simplified 91.7%

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

5. Taylor expanded in y around inf 85.3%

   \[\leadsto \color{blue}{x + \frac{1}{y}} \]
6. Add Preprocessing

Alternative 8: 49.4% accurate, 211.0× speedup

Math

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

FPCore

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

C

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

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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 83.9%

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

   1. exp-prod 91.7%

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

   2. +-commutative 91.7%

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

3. Simplified 91.7%

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

5. Taylor expanded in x around inf 48.6%

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

Developer Target 1: 90.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{y}{z + y} < 7.11541576 \cdot 10^{-315}:\\ \;\;\;\;x + \frac{e^{\frac{-1}{z}}}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{e^{\log \left({\left(\frac{y}{y + z}\right)}^{y}\right)}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (< (/ y (+ z y)) 7.11541576e-315)
   (+ x (/ (exp (/ -1.0 z)) y))
   (+ x (/ (exp (log (pow (/ y (+ y z)) y))) y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y / (z + y)) < 7.11541576e-315) {
		tmp = x + (exp((-1.0 / z)) / y);
	} else {
		tmp = x + (exp(log(pow((y / (y + z)), 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 / (z + y)) < 7.11541576d-315) then
        tmp = x + (exp(((-1.0d0) / z)) / y)
    else
        tmp = x + (exp(log(((y / (y + z)) ** y))) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y / (z + y)) < 7.11541576e-315) {
		tmp = x + (Math.exp((-1.0 / z)) / y);
	} else {
		tmp = x + (Math.exp(Math.log(Math.pow((y / (y + z)), y))) / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y / (z + y)) < 7.11541576e-315:
		tmp = x + (math.exp((-1.0 / z)) / y)
	else:
		tmp = x + (math.exp(math.log(math.pow((y / (y + z)), y))) / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(y / Float64(z + y)) < 7.11541576e-315)
		tmp = Float64(x + Float64(exp(Float64(-1.0 / z)) / y));
	else
		tmp = Float64(x + Float64(exp(log((Float64(y / Float64(y + z)) ^ y))) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y / (z + y)) < 7.11541576e-315)
		tmp = x + (exp((-1.0 / z)) / y);
	else
		tmp = x + (exp(log(((y / (y + z)) ^ y))) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Less[N[(y / N[(z + y), $MachinePrecision]), $MachinePrecision], 7.11541576e-315], N[(x + N[(N[Exp[N[(-1.0 / z), $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[Exp[N[Log[N[Power[N[(y / N[(y + z), $MachinePrecision]), $MachinePrecision], y], $MachinePrecision]], $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Reproduce

herbie shell --seed 2024172 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, G"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< (/ y (+ z y)) 17788539399477/2500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ x (/ (exp (/ -1 z)) y)) (+ x (/ (exp (log (pow (/ y (+ y z)) y))) y))))

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