Numeric.SpecFunctions:invErfc from math-functions-0.1.5.2, A

Percentage Accurate: 95.7% → 99.9%

Time: 5.2s

Alternatives: 4

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ x (/ y (- (* 1.1283791670955126 (exp z)) (* x y)))))

C

double code(double x, double y, double z) {
	return x + (y / ((1.1283791670955126 * exp(z)) - (x * 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 + (y / ((1.1283791670955126d0 * exp(z)) - (x * y)))
end function

Java

public static double code(double x, double y, double z) {
	return x + (y / ((1.1283791670955126 * Math.exp(z)) - (x * y)));
}

Python

def code(x, y, z):
	return x + (y / ((1.1283791670955126 * math.exp(z)) - (x * y)))

Julia

function code(x, y, z)
	return Float64(x + Float64(y / Float64(Float64(1.1283791670955126 * exp(z)) - Float64(x * y))))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + (y / ((1.1283791670955126 * exp(z)) - (x * y)));
end

Wolfram

code[x_, y_, z_] := N[(x + N[(y / N[(N[(1.1283791670955126 * N[Exp[z], $MachinePrecision]), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 95.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ x (/ y (- (* 1.1283791670955126 (exp z)) (* x y)))))

C

double code(double x, double y, double z) {
	return x + (y / ((1.1283791670955126 * exp(z)) - (x * 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 + (y / ((1.1283791670955126d0 * exp(z)) - (x * y)))
end function

Java

public static double code(double x, double y, double z) {
	return x + (y / ((1.1283791670955126 * Math.exp(z)) - (x * y)));
}

Python

def code(x, y, z):
	return x + (y / ((1.1283791670955126 * math.exp(z)) - (x * y)))

Julia

function code(x, y, z)
	return Float64(x + Float64(y / Float64(Float64(1.1283791670955126 * exp(z)) - Float64(x * y))))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + (y / ((1.1283791670955126 * exp(z)) - (x * y)));
end

Wolfram

code[x_, y_, z_] := N[(x + N[(y / N[(N[(1.1283791670955126 * N[Exp[z], $MachinePrecision]), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \frac{1}{1.1283791670955126 \cdot \frac{e^{z}}{y} - x} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ x (/ 1.0 (- (* 1.1283791670955126 (/ (exp z) y)) x))))

C

double code(double x, double y, double z) {
	return x + (1.0 / ((1.1283791670955126 * (exp(z) / y)) - 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 + (1.0d0 / ((1.1283791670955126d0 * (exp(z) / y)) - x))
end function

Java

public static double code(double x, double y, double z) {
	return x + (1.0 / ((1.1283791670955126 * (Math.exp(z) / y)) - x));
}

Python

def code(x, y, z):
	return x + (1.0 / ((1.1283791670955126 * (math.exp(z) / y)) - x))

Julia

function code(x, y, z)
	return Float64(x + Float64(1.0 / Float64(Float64(1.1283791670955126 * Float64(exp(z) / y)) - x)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + (1.0 / ((1.1283791670955126 * (exp(z) / y)) - x));
end

Wolfram

code[x_, y_, z_] := N[(x + N[(1.0 / N[(N[(1.1283791670955126 * N[(N[Exp[z], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 93.3%

   \[x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y} \]
2. Step-by-step derivation

   1. *-lft-identity 93.3%

      \[\leadsto x + \frac{\color{blue}{1 \cdot y}}{1.1283791670955126 \cdot e^{z} - x \cdot y} \]

   2. associate-/l* 93.3%

      \[\leadsto x + \color{blue}{\frac{1}{\frac{1.1283791670955126 \cdot e^{z} - x \cdot y}{y}}} \]

   3. remove-double-neg 93.3%

      \[\leadsto x + \frac{1}{\frac{1.1283791670955126 \cdot e^{z} - x \cdot y}{\color{blue}{-\left(-y\right)}}} \]

   4. neg-mul-1 93.3%

      \[\leadsto x + \frac{1}{\frac{1.1283791670955126 \cdot e^{z} - x \cdot y}{\color{blue}{-1 \cdot \left(-y\right)}}} \]

   5. associate-/r* 93.3%

      \[\leadsto x + \frac{1}{\color{blue}{\frac{\frac{1.1283791670955126 \cdot e^{z} - x \cdot y}{-1}}{-y}}} \]

   6. div-sub 93.5%

      \[\leadsto x + \frac{1}{\frac{\color{blue}{\frac{1.1283791670955126 \cdot e^{z}}{-1} - \frac{x \cdot y}{-1}}}{-y}} \]

   7. metadata-eval 93.5%

      \[\leadsto x + \frac{1}{\frac{\frac{1.1283791670955126 \cdot e^{z}}{-1} - \frac{x \cdot y}{\color{blue}{\frac{1}{-1}}}}{-y}} \]

   8. associate-/l* 93.5%

      \[\leadsto x + \frac{1}{\frac{\frac{1.1283791670955126 \cdot e^{z}}{-1} - \color{blue}{\frac{\left(x \cdot y\right) \cdot -1}{1}}}{-y}} \]

   9. *-commutative 93.5%

      \[\leadsto x + \frac{1}{\frac{\frac{1.1283791670955126 \cdot e^{z}}{-1} - \frac{\color{blue}{-1 \cdot \left(x \cdot y\right)}}{1}}{-y}} \]

   10. associate-*l* 93.5%

       \[\leadsto x + \frac{1}{\frac{\frac{1.1283791670955126 \cdot e^{z}}{-1} - \frac{\color{blue}{\left(-1 \cdot x\right) \cdot y}}{1}}{-y}} \]

   11. neg-mul-1 93.5%

       \[\leadsto x + \frac{1}{\frac{\frac{1.1283791670955126 \cdot e^{z}}{-1} - \frac{\color{blue}{\left(-x\right)} \cdot y}{1}}{-y}} \]

   12. /-rgt-identity 93.5%

       \[\leadsto x + \frac{1}{\frac{\frac{1.1283791670955126 \cdot e^{z}}{-1} - \color{blue}{\left(-x\right) \cdot y}}{-y}} \]

   13. div-sub 93.3%

       \[\leadsto x + \frac{1}{\color{blue}{\frac{\frac{1.1283791670955126 \cdot e^{z}}{-1}}{-y} - \frac{\left(-x\right) \cdot y}{-y}}} \]

   14. associate-/r* 93.3%

       \[\leadsto x + \frac{1}{\color{blue}{\frac{1.1283791670955126 \cdot e^{z}}{-1 \cdot \left(-y\right)}} - \frac{\left(-x\right) \cdot y}{-y}} \]

   15. neg-mul-1 93.3%

       \[\leadsto x + \frac{1}{\frac{1.1283791670955126 \cdot e^{z}}{\color{blue}{-\left(-y\right)}} - \frac{\left(-x\right) \cdot y}{-y}} \]

   16. remove-double-neg 93.3%

       \[\leadsto x + \frac{1}{\frac{1.1283791670955126 \cdot e^{z}}{\color{blue}{y}} - \frac{\left(-x\right) \cdot y}{-y}} \]

   17. associate-*r/ 93.3%

       \[\leadsto x + \frac{1}{\color{blue}{1.1283791670955126 \cdot \frac{e^{z}}{y}} - \frac{\left(-x\right) \cdot y}{-y}} \]

   18. distribute-lft-neg-out 93.3%

       \[\leadsto x + \frac{1}{1.1283791670955126 \cdot \frac{e^{z}}{y} - \frac{\color{blue}{-x \cdot y}}{-y}} \]

   19. neg-mul-1 93.3%

       \[\leadsto x + \frac{1}{1.1283791670955126 \cdot \frac{e^{z}}{y} - \frac{\color{blue}{-1 \cdot \left(x \cdot y\right)}}{-y}} \]

   20. *-commutative 93.3%

       \[\leadsto x + \frac{1}{1.1283791670955126 \cdot \frac{e^{z}}{y} - \frac{\color{blue}{\left(x \cdot y\right) \cdot -1}}{-y}} \]

3. Simplified 99.9%

   \[\leadsto \color{blue}{x + \frac{1}{1.1283791670955126 \cdot \frac{e^{z}}{y} - x}} \]
4. Add Preprocessing

5. Final simplification 99.9%

   \[\leadsto x + \frac{1}{1.1283791670955126 \cdot \frac{e^{z}}{y} - x} \]
6. Add Preprocessing

Alternative 2: 80.9% accurate, 12.3× speedup

Math

\[\begin{array}{l} \\ x + \frac{1}{\frac{1.1283791670955126}{y} - x} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ x (/ 1.0 (- (/ 1.1283791670955126 y) x))))

C

double code(double x, double y, double z) {
	return x + (1.0 / ((1.1283791670955126 / y) - 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 + (1.0d0 / ((1.1283791670955126d0 / y) - x))
end function

Java

public static double code(double x, double y, double z) {
	return x + (1.0 / ((1.1283791670955126 / y) - x));
}

Python

def code(x, y, z):
	return x + (1.0 / ((1.1283791670955126 / y) - x))

Julia

function code(x, y, z)
	return Float64(x + Float64(1.0 / Float64(Float64(1.1283791670955126 / y) - x)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + (1.0 / ((1.1283791670955126 / y) - x));
end

Wolfram

code[x_, y_, z_] := N[(x + N[(1.0 / N[(N[(1.1283791670955126 / y), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 93.3%

   \[x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y} \]
2. Step-by-step derivation

   1. *-lft-identity 93.3%

      \[\leadsto x + \frac{\color{blue}{1 \cdot y}}{1.1283791670955126 \cdot e^{z} - x \cdot y} \]

   2. associate-/l* 93.3%

      \[\leadsto x + \color{blue}{\frac{1}{\frac{1.1283791670955126 \cdot e^{z} - x \cdot y}{y}}} \]

   3. remove-double-neg 93.3%

      \[\leadsto x + \frac{1}{\frac{1.1283791670955126 \cdot e^{z} - x \cdot y}{\color{blue}{-\left(-y\right)}}} \]

   4. neg-mul-1 93.3%

      \[\leadsto x + \frac{1}{\frac{1.1283791670955126 \cdot e^{z} - x \cdot y}{\color{blue}{-1 \cdot \left(-y\right)}}} \]

   5. associate-/r* 93.3%

      \[\leadsto x + \frac{1}{\color{blue}{\frac{\frac{1.1283791670955126 \cdot e^{z} - x \cdot y}{-1}}{-y}}} \]

   6. div-sub 93.5%

      \[\leadsto x + \frac{1}{\frac{\color{blue}{\frac{1.1283791670955126 \cdot e^{z}}{-1} - \frac{x \cdot y}{-1}}}{-y}} \]

   7. metadata-eval 93.5%

      \[\leadsto x + \frac{1}{\frac{\frac{1.1283791670955126 \cdot e^{z}}{-1} - \frac{x \cdot y}{\color{blue}{\frac{1}{-1}}}}{-y}} \]

   8. associate-/l* 93.5%

      \[\leadsto x + \frac{1}{\frac{\frac{1.1283791670955126 \cdot e^{z}}{-1} - \color{blue}{\frac{\left(x \cdot y\right) \cdot -1}{1}}}{-y}} \]

   9. *-commutative 93.5%

      \[\leadsto x + \frac{1}{\frac{\frac{1.1283791670955126 \cdot e^{z}}{-1} - \frac{\color{blue}{-1 \cdot \left(x \cdot y\right)}}{1}}{-y}} \]

   10. associate-*l* 93.5%

       \[\leadsto x + \frac{1}{\frac{\frac{1.1283791670955126 \cdot e^{z}}{-1} - \frac{\color{blue}{\left(-1 \cdot x\right) \cdot y}}{1}}{-y}} \]

   11. neg-mul-1 93.5%

       \[\leadsto x + \frac{1}{\frac{\frac{1.1283791670955126 \cdot e^{z}}{-1} - \frac{\color{blue}{\left(-x\right)} \cdot y}{1}}{-y}} \]

   12. /-rgt-identity 93.5%

       \[\leadsto x + \frac{1}{\frac{\frac{1.1283791670955126 \cdot e^{z}}{-1} - \color{blue}{\left(-x\right) \cdot y}}{-y}} \]

   13. div-sub 93.3%

       \[\leadsto x + \frac{1}{\color{blue}{\frac{\frac{1.1283791670955126 \cdot e^{z}}{-1}}{-y} - \frac{\left(-x\right) \cdot y}{-y}}} \]

   14. associate-/r* 93.3%

       \[\leadsto x + \frac{1}{\color{blue}{\frac{1.1283791670955126 \cdot e^{z}}{-1 \cdot \left(-y\right)}} - \frac{\left(-x\right) \cdot y}{-y}} \]

   15. neg-mul-1 93.3%

       \[\leadsto x + \frac{1}{\frac{1.1283791670955126 \cdot e^{z}}{\color{blue}{-\left(-y\right)}} - \frac{\left(-x\right) \cdot y}{-y}} \]

   16. remove-double-neg 93.3%

       \[\leadsto x + \frac{1}{\frac{1.1283791670955126 \cdot e^{z}}{\color{blue}{y}} - \frac{\left(-x\right) \cdot y}{-y}} \]

   17. associate-*r/ 93.3%

       \[\leadsto x + \frac{1}{\color{blue}{1.1283791670955126 \cdot \frac{e^{z}}{y}} - \frac{\left(-x\right) \cdot y}{-y}} \]

   18. distribute-lft-neg-out 93.3%

       \[\leadsto x + \frac{1}{1.1283791670955126 \cdot \frac{e^{z}}{y} - \frac{\color{blue}{-x \cdot y}}{-y}} \]

   19. neg-mul-1 93.3%

       \[\leadsto x + \frac{1}{1.1283791670955126 \cdot \frac{e^{z}}{y} - \frac{\color{blue}{-1 \cdot \left(x \cdot y\right)}}{-y}} \]

   20. *-commutative 93.3%

       \[\leadsto x + \frac{1}{1.1283791670955126 \cdot \frac{e^{z}}{y} - \frac{\color{blue}{\left(x \cdot y\right) \cdot -1}}{-y}} \]

3. Simplified 99.9%

   \[\leadsto \color{blue}{x + \frac{1}{1.1283791670955126 \cdot \frac{e^{z}}{y} - x}} \]
4. Add Preprocessing

5. Taylor expanded in z around 0 78.7%

   \[\leadsto x + \frac{1}{\color{blue}{\frac{1.1283791670955126}{y}} - x} \]

6. Final simplification 78.7%

   \[\leadsto x + \frac{1}{\frac{1.1283791670955126}{y} - x} \]
7. Add Preprocessing

Alternative 3: 69.2% accurate, 22.2× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return x + (-1.0 / 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 + ((-1.0d0) / x)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.3%

   \[x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y} \]
2. Step-by-step derivation

   1. *-lft-identity 93.3%

      \[\leadsto x + \frac{\color{blue}{1 \cdot y}}{1.1283791670955126 \cdot e^{z} - x \cdot y} \]

   2. associate-/l* 93.3%

      \[\leadsto x + \color{blue}{\frac{1}{\frac{1.1283791670955126 \cdot e^{z} - x \cdot y}{y}}} \]

   3. remove-double-neg 93.3%

      \[\leadsto x + \frac{1}{\frac{1.1283791670955126 \cdot e^{z} - x \cdot y}{\color{blue}{-\left(-y\right)}}} \]

   4. neg-mul-1 93.3%

      \[\leadsto x + \frac{1}{\frac{1.1283791670955126 \cdot e^{z} - x \cdot y}{\color{blue}{-1 \cdot \left(-y\right)}}} \]

   5. associate-/r* 93.3%

      \[\leadsto x + \frac{1}{\color{blue}{\frac{\frac{1.1283791670955126 \cdot e^{z} - x \cdot y}{-1}}{-y}}} \]

   6. div-sub 93.5%

      \[\leadsto x + \frac{1}{\frac{\color{blue}{\frac{1.1283791670955126 \cdot e^{z}}{-1} - \frac{x \cdot y}{-1}}}{-y}} \]

   7. metadata-eval 93.5%

      \[\leadsto x + \frac{1}{\frac{\frac{1.1283791670955126 \cdot e^{z}}{-1} - \frac{x \cdot y}{\color{blue}{\frac{1}{-1}}}}{-y}} \]

   8. associate-/l* 93.5%

      \[\leadsto x + \frac{1}{\frac{\frac{1.1283791670955126 \cdot e^{z}}{-1} - \color{blue}{\frac{\left(x \cdot y\right) \cdot -1}{1}}}{-y}} \]

   9. *-commutative 93.5%

      \[\leadsto x + \frac{1}{\frac{\frac{1.1283791670955126 \cdot e^{z}}{-1} - \frac{\color{blue}{-1 \cdot \left(x \cdot y\right)}}{1}}{-y}} \]

   10. associate-*l* 93.5%

       \[\leadsto x + \frac{1}{\frac{\frac{1.1283791670955126 \cdot e^{z}}{-1} - \frac{\color{blue}{\left(-1 \cdot x\right) \cdot y}}{1}}{-y}} \]

   11. neg-mul-1 93.5%

       \[\leadsto x + \frac{1}{\frac{\frac{1.1283791670955126 \cdot e^{z}}{-1} - \frac{\color{blue}{\left(-x\right)} \cdot y}{1}}{-y}} \]

   12. /-rgt-identity 93.5%

       \[\leadsto x + \frac{1}{\frac{\frac{1.1283791670955126 \cdot e^{z}}{-1} - \color{blue}{\left(-x\right) \cdot y}}{-y}} \]

   13. div-sub 93.3%

       \[\leadsto x + \frac{1}{\color{blue}{\frac{\frac{1.1283791670955126 \cdot e^{z}}{-1}}{-y} - \frac{\left(-x\right) \cdot y}{-y}}} \]

   14. associate-/r* 93.3%

       \[\leadsto x + \frac{1}{\color{blue}{\frac{1.1283791670955126 \cdot e^{z}}{-1 \cdot \left(-y\right)}} - \frac{\left(-x\right) \cdot y}{-y}} \]

   15. neg-mul-1 93.3%

       \[\leadsto x + \frac{1}{\frac{1.1283791670955126 \cdot e^{z}}{\color{blue}{-\left(-y\right)}} - \frac{\left(-x\right) \cdot y}{-y}} \]

   16. remove-double-neg 93.3%

       \[\leadsto x + \frac{1}{\frac{1.1283791670955126 \cdot e^{z}}{\color{blue}{y}} - \frac{\left(-x\right) \cdot y}{-y}} \]

   17. associate-*r/ 93.3%

       \[\leadsto x + \frac{1}{\color{blue}{1.1283791670955126 \cdot \frac{e^{z}}{y}} - \frac{\left(-x\right) \cdot y}{-y}} \]

   18. distribute-lft-neg-out 93.3%

       \[\leadsto x + \frac{1}{1.1283791670955126 \cdot \frac{e^{z}}{y} - \frac{\color{blue}{-x \cdot y}}{-y}} \]

   19. neg-mul-1 93.3%

       \[\leadsto x + \frac{1}{1.1283791670955126 \cdot \frac{e^{z}}{y} - \frac{\color{blue}{-1 \cdot \left(x \cdot y\right)}}{-y}} \]

   20. *-commutative 93.3%

       \[\leadsto x + \frac{1}{1.1283791670955126 \cdot \frac{e^{z}}{y} - \frac{\color{blue}{\left(x \cdot y\right) \cdot -1}}{-y}} \]

3. Simplified 99.9%

   \[\leadsto \color{blue}{x + \frac{1}{1.1283791670955126 \cdot \frac{e^{z}}{y} - x}} \]
4. Add Preprocessing

5. Taylor expanded in x around inf 69.7%

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

6. Final simplification 69.7%

   \[\leadsto x + \frac{-1}{x} \]
7. Add Preprocessing

Alternative 4: 68.8% accurate, 111.0× 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 93.3%

   \[x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y} \]
2. Step-by-step derivation

   1. *-lft-identity 93.3%

      \[\leadsto x + \frac{\color{blue}{1 \cdot y}}{1.1283791670955126 \cdot e^{z} - x \cdot y} \]

   2. associate-/l* 93.3%

      \[\leadsto x + \color{blue}{\frac{1}{\frac{1.1283791670955126 \cdot e^{z} - x \cdot y}{y}}} \]

   3. remove-double-neg 93.3%

      \[\leadsto x + \frac{1}{\frac{1.1283791670955126 \cdot e^{z} - x \cdot y}{\color{blue}{-\left(-y\right)}}} \]

   4. neg-mul-1 93.3%

      \[\leadsto x + \frac{1}{\frac{1.1283791670955126 \cdot e^{z} - x \cdot y}{\color{blue}{-1 \cdot \left(-y\right)}}} \]

   5. associate-/r* 93.3%

      \[\leadsto x + \frac{1}{\color{blue}{\frac{\frac{1.1283791670955126 \cdot e^{z} - x \cdot y}{-1}}{-y}}} \]

   6. div-sub 93.5%

      \[\leadsto x + \frac{1}{\frac{\color{blue}{\frac{1.1283791670955126 \cdot e^{z}}{-1} - \frac{x \cdot y}{-1}}}{-y}} \]

   7. metadata-eval 93.5%

      \[\leadsto x + \frac{1}{\frac{\frac{1.1283791670955126 \cdot e^{z}}{-1} - \frac{x \cdot y}{\color{blue}{\frac{1}{-1}}}}{-y}} \]

   8. associate-/l* 93.5%

      \[\leadsto x + \frac{1}{\frac{\frac{1.1283791670955126 \cdot e^{z}}{-1} - \color{blue}{\frac{\left(x \cdot y\right) \cdot -1}{1}}}{-y}} \]

   9. *-commutative 93.5%

      \[\leadsto x + \frac{1}{\frac{\frac{1.1283791670955126 \cdot e^{z}}{-1} - \frac{\color{blue}{-1 \cdot \left(x \cdot y\right)}}{1}}{-y}} \]

   10. associate-*l* 93.5%

       \[\leadsto x + \frac{1}{\frac{\frac{1.1283791670955126 \cdot e^{z}}{-1} - \frac{\color{blue}{\left(-1 \cdot x\right) \cdot y}}{1}}{-y}} \]

   11. neg-mul-1 93.5%

       \[\leadsto x + \frac{1}{\frac{\frac{1.1283791670955126 \cdot e^{z}}{-1} - \frac{\color{blue}{\left(-x\right)} \cdot y}{1}}{-y}} \]

   12. /-rgt-identity 93.5%

       \[\leadsto x + \frac{1}{\frac{\frac{1.1283791670955126 \cdot e^{z}}{-1} - \color{blue}{\left(-x\right) \cdot y}}{-y}} \]

   13. div-sub 93.3%

       \[\leadsto x + \frac{1}{\color{blue}{\frac{\frac{1.1283791670955126 \cdot e^{z}}{-1}}{-y} - \frac{\left(-x\right) \cdot y}{-y}}} \]

   14. associate-/r* 93.3%

       \[\leadsto x + \frac{1}{\color{blue}{\frac{1.1283791670955126 \cdot e^{z}}{-1 \cdot \left(-y\right)}} - \frac{\left(-x\right) \cdot y}{-y}} \]

   15. neg-mul-1 93.3%

       \[\leadsto x + \frac{1}{\frac{1.1283791670955126 \cdot e^{z}}{\color{blue}{-\left(-y\right)}} - \frac{\left(-x\right) \cdot y}{-y}} \]

   16. remove-double-neg 93.3%

       \[\leadsto x + \frac{1}{\frac{1.1283791670955126 \cdot e^{z}}{\color{blue}{y}} - \frac{\left(-x\right) \cdot y}{-y}} \]

   17. associate-*r/ 93.3%

       \[\leadsto x + \frac{1}{\color{blue}{1.1283791670955126 \cdot \frac{e^{z}}{y}} - \frac{\left(-x\right) \cdot y}{-y}} \]

   18. distribute-lft-neg-out 93.3%

       \[\leadsto x + \frac{1}{1.1283791670955126 \cdot \frac{e^{z}}{y} - \frac{\color{blue}{-x \cdot y}}{-y}} \]

   19. neg-mul-1 93.3%

       \[\leadsto x + \frac{1}{1.1283791670955126 \cdot \frac{e^{z}}{y} - \frac{\color{blue}{-1 \cdot \left(x \cdot y\right)}}{-y}} \]

   20. *-commutative 93.3%

       \[\leadsto x + \frac{1}{1.1283791670955126 \cdot \frac{e^{z}}{y} - \frac{\color{blue}{\left(x \cdot y\right) \cdot -1}}{-y}} \]

3. Simplified 99.9%

   \[\leadsto \color{blue}{x + \frac{1}{1.1283791670955126 \cdot \frac{e^{z}}{y} - x}} \]
4. Add Preprocessing

5. Taylor expanded in x around inf 67.2%

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

6. Final simplification 67.2%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \frac{1}{\frac{1.1283791670955126}{y} \cdot e^{z} - x} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ x (/ 1.0 (- (* (/ 1.1283791670955126 y) (exp z)) x))))

C

double code(double x, double y, double z) {
	return x + (1.0 / (((1.1283791670955126 / y) * exp(z)) - 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 + (1.0d0 / (((1.1283791670955126d0 / y) * exp(z)) - x))
end function

Java

public static double code(double x, double y, double z) {
	return x + (1.0 / (((1.1283791670955126 / y) * Math.exp(z)) - x));
}

Python

def code(x, y, z):
	return x + (1.0 / (((1.1283791670955126 / y) * math.exp(z)) - x))

Julia

function code(x, y, z)
	return Float64(x + Float64(1.0 / Float64(Float64(Float64(1.1283791670955126 / y) * exp(z)) - x)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + (1.0 / (((1.1283791670955126 / y) * exp(z)) - x));
end

Wolfram

code[x_, y_, z_] := N[(x + N[(1.0 / N[(N[(N[(1.1283791670955126 / y), $MachinePrecision] * N[Exp[z], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2024033 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:invErfc from math-functions-0.1.5.2, A"
  :precision binary64

  :herbie-target
  (+ x (/ 1.0 (- (* (/ 1.1283791670955126 y) (exp z)) x)))

  (+ x (/ y (- (* 1.1283791670955126 (exp z)) (* x y)))))