Numeric.SpecFunctions:invIncompleteGamma from math-functions-0.1.5.2, C

Percentage Accurate: 100.0% → 100.0%

Time: 4.9s

Alternatives: 7

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \frac{2.30753 + x \cdot 0.27061}{1 + x \cdot \left(0.99229 + x \cdot 0.04481\right)} - x \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (- (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) x))

C

double code(double x) {
	return ((2.30753 + (x * 0.27061)) / (1.0 + (x * (0.99229 + (x * 0.04481))))) - x;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = ((2.30753d0 + (x * 0.27061d0)) / (1.0d0 + (x * (0.99229d0 + (x * 0.04481d0))))) - x
end function

Java

public static double code(double x) {
	return ((2.30753 + (x * 0.27061)) / (1.0 + (x * (0.99229 + (x * 0.04481))))) - x;
}

Python

def code(x):
	return ((2.30753 + (x * 0.27061)) / (1.0 + (x * (0.99229 + (x * 0.04481))))) - x

Julia

function code(x)
	return Float64(Float64(Float64(2.30753 + Float64(x * 0.27061)) / Float64(1.0 + Float64(x * Float64(0.99229 + Float64(x * 0.04481))))) - x)
end

MATLAB

function tmp = code(x)
	tmp = ((2.30753 + (x * 0.27061)) / (1.0 + (x * (0.99229 + (x * 0.04481))))) - x;
end

Wolfram

code[x_] := N[(N[(N[(2.30753 + N[(x * 0.27061), $MachinePrecision]), $MachinePrecision] / N[(1.0 + N[(x * N[(0.99229 + N[(x * 0.04481), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{2.30753 + x \cdot 0.27061}{1 + x \cdot \left(0.99229 + x \cdot 0.04481\right)} - x \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (- (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) x))

C

double code(double x) {
	return ((2.30753 + (x * 0.27061)) / (1.0 + (x * (0.99229 + (x * 0.04481))))) - x;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = ((2.30753d0 + (x * 0.27061d0)) / (1.0d0 + (x * (0.99229d0 + (x * 0.04481d0))))) - x
end function

Java

public static double code(double x) {
	return ((2.30753 + (x * 0.27061)) / (1.0 + (x * (0.99229 + (x * 0.04481))))) - x;
}

Python

def code(x):
	return ((2.30753 + (x * 0.27061)) / (1.0 + (x * (0.99229 + (x * 0.04481))))) - x

Julia

function code(x)
	return Float64(Float64(Float64(2.30753 + Float64(x * 0.27061)) / Float64(1.0 + Float64(x * Float64(0.99229 + Float64(x * 0.04481))))) - x)
end

MATLAB

function tmp = code(x)
	tmp = ((2.30753 + (x * 0.27061)) / (1.0 + (x * (0.99229 + (x * 0.04481))))) - x;
end

Wolfram

code[x_] := N[(N[(N[(2.30753 + N[(x * 0.27061), $MachinePrecision]), $MachinePrecision] / N[(1.0 + N[(x * N[(0.99229 + N[(x * 0.04481), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]

Alternative 1: 100.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \frac{2.30753 + x \cdot 0.27061}{1 + \left(\left(\left(1 + x \cdot \left(x \cdot 0.04481\right)\right) + -1\right) + x \cdot 0.99229\right)} - x \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (-
  (/
   (+ 2.30753 (* x 0.27061))
   (+ 1.0 (+ (+ (+ 1.0 (* x (* x 0.04481))) -1.0) (* x 0.99229))))
  x))

C

double code(double x) {
	return ((2.30753 + (x * 0.27061)) / (1.0 + (((1.0 + (x * (x * 0.04481))) + -1.0) + (x * 0.99229)))) - x;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = ((2.30753d0 + (x * 0.27061d0)) / (1.0d0 + (((1.0d0 + (x * (x * 0.04481d0))) + (-1.0d0)) + (x * 0.99229d0)))) - x
end function

Java

public static double code(double x) {
	return ((2.30753 + (x * 0.27061)) / (1.0 + (((1.0 + (x * (x * 0.04481))) + -1.0) + (x * 0.99229)))) - x;
}

Python

def code(x):
	return ((2.30753 + (x * 0.27061)) / (1.0 + (((1.0 + (x * (x * 0.04481))) + -1.0) + (x * 0.99229)))) - x

Julia

function code(x)
	return Float64(Float64(Float64(2.30753 + Float64(x * 0.27061)) / Float64(1.0 + Float64(Float64(Float64(1.0 + Float64(x * Float64(x * 0.04481))) + -1.0) + Float64(x * 0.99229)))) - x)
end

MATLAB

function tmp = code(x)
	tmp = ((2.30753 + (x * 0.27061)) / (1.0 + (((1.0 + (x * (x * 0.04481))) + -1.0) + (x * 0.99229)))) - x;
end

Wolfram

code[x_] := N[(N[(N[(2.30753 + N[(x * 0.27061), $MachinePrecision]), $MachinePrecision] / N[(1.0 + N[(N[(N[(1.0 + N[(x * N[(x * 0.04481), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision] + N[(x * 0.99229), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\frac{2.30753 + x \cdot 0.27061}{1 + x \cdot \left(0.99229 + x \cdot 0.04481\right)} - x \]
2. Step-by-step derivation

   1. +-commutative 100.0%

      \[\leadsto \frac{2.30753 + x \cdot 0.27061}{1 + x \cdot \color{blue}{\left(x \cdot 0.04481 + 0.99229\right)}} - x \]

   2. distribute-lft-in 100.0%

      \[\leadsto \frac{2.30753 + x \cdot 0.27061}{1 + \color{blue}{\left(x \cdot \left(x \cdot 0.04481\right) + x \cdot 0.99229\right)}} - x \]

3. Applied egg-rr 100.0%

   \[\leadsto \frac{2.30753 + x \cdot 0.27061}{1 + \color{blue}{\left(x \cdot \left(x \cdot 0.04481\right) + x \cdot 0.99229\right)}} - x \]
4. Step-by-step derivation

   1. expm1-log1p-u 100.0%

      \[\leadsto \frac{2.30753 + x \cdot 0.27061}{1 + \left(\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(x \cdot \left(x \cdot 0.04481\right)\right)\right)} + x \cdot 0.99229\right)} - x \]

   2. expm1-udef 100.0%

      \[\leadsto \frac{2.30753 + x \cdot 0.27061}{1 + \left(\color{blue}{\left(e^{\mathsf{log1p}\left(x \cdot \left(x \cdot 0.04481\right)\right)} - 1\right)} + x \cdot 0.99229\right)} - x \]

   3. log1p-udef 100.0%

      \[\leadsto \frac{2.30753 + x \cdot 0.27061}{1 + \left(\left(e^{\color{blue}{\log \left(1 + x \cdot \left(x \cdot 0.04481\right)\right)}} - 1\right) + x \cdot 0.99229\right)} - x \]

   4. add-exp-log 100.0%

      \[\leadsto \frac{2.30753 + x \cdot 0.27061}{1 + \left(\left(\color{blue}{\left(1 + x \cdot \left(x \cdot 0.04481\right)\right)} - 1\right) + x \cdot 0.99229\right)} - x \]

5. Applied egg-rr 100.0%

   \[\leadsto \frac{2.30753 + x \cdot 0.27061}{1 + \left(\color{blue}{\left(\left(1 + x \cdot \left(x \cdot 0.04481\right)\right) - 1\right)} + x \cdot 0.99229\right)} - x \]

6. Final simplification 100.0%

   \[\leadsto \frac{2.30753 + x \cdot 0.27061}{1 + \left(\left(\left(1 + x \cdot \left(x \cdot 0.04481\right)\right) + -1\right) + x \cdot 0.99229\right)} - x \]

Alternative 2: 100.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \frac{2.30753 + x \cdot 0.27061}{1 + \left(x \cdot \left(x \cdot 0.04481\right) + x \cdot 0.99229\right)} - x \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (-
  (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (+ (* x (* x 0.04481)) (* x 0.99229))))
  x))

C

double code(double x) {
	return ((2.30753 + (x * 0.27061)) / (1.0 + ((x * (x * 0.04481)) + (x * 0.99229)))) - x;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = ((2.30753d0 + (x * 0.27061d0)) / (1.0d0 + ((x * (x * 0.04481d0)) + (x * 0.99229d0)))) - x
end function

Java

public static double code(double x) {
	return ((2.30753 + (x * 0.27061)) / (1.0 + ((x * (x * 0.04481)) + (x * 0.99229)))) - x;
}

Python

def code(x):
	return ((2.30753 + (x * 0.27061)) / (1.0 + ((x * (x * 0.04481)) + (x * 0.99229)))) - x

Julia

function code(x)
	return Float64(Float64(Float64(2.30753 + Float64(x * 0.27061)) / Float64(1.0 + Float64(Float64(x * Float64(x * 0.04481)) + Float64(x * 0.99229)))) - x)
end

MATLAB

function tmp = code(x)
	tmp = ((2.30753 + (x * 0.27061)) / (1.0 + ((x * (x * 0.04481)) + (x * 0.99229)))) - x;
end

Wolfram

code[x_] := N[(N[(N[(2.30753 + N[(x * 0.27061), $MachinePrecision]), $MachinePrecision] / N[(1.0 + N[(N[(x * N[(x * 0.04481), $MachinePrecision]), $MachinePrecision] + N[(x * 0.99229), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\frac{2.30753 + x \cdot 0.27061}{1 + x \cdot \left(0.99229 + x \cdot 0.04481\right)} - x \]
2. Step-by-step derivation

   1. +-commutative 100.0%

      \[\leadsto \frac{2.30753 + x \cdot 0.27061}{1 + x \cdot \color{blue}{\left(x \cdot 0.04481 + 0.99229\right)}} - x \]

   2. distribute-lft-in 100.0%

      \[\leadsto \frac{2.30753 + x \cdot 0.27061}{1 + \color{blue}{\left(x \cdot \left(x \cdot 0.04481\right) + x \cdot 0.99229\right)}} - x \]

3. Applied egg-rr 100.0%

   \[\leadsto \frac{2.30753 + x \cdot 0.27061}{1 + \color{blue}{\left(x \cdot \left(x \cdot 0.04481\right) + x \cdot 0.99229\right)}} - x \]

4. Final simplification 100.0%

   \[\leadsto \frac{2.30753 + x \cdot 0.27061}{1 + \left(x \cdot \left(x \cdot 0.04481\right) + x \cdot 0.99229\right)} - x \]

Alternative 3: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{2.30753 + x \cdot 0.27061}{1 + x \cdot \left(x \cdot 0.04481 + 0.99229\right)} - x \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (- (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ (* x 0.04481) 0.99229)))) x))

C

double code(double x) {
	return ((2.30753 + (x * 0.27061)) / (1.0 + (x * ((x * 0.04481) + 0.99229)))) - x;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = ((2.30753d0 + (x * 0.27061d0)) / (1.0d0 + (x * ((x * 0.04481d0) + 0.99229d0)))) - x
end function

Java

public static double code(double x) {
	return ((2.30753 + (x * 0.27061)) / (1.0 + (x * ((x * 0.04481) + 0.99229)))) - x;
}

Python

def code(x):
	return ((2.30753 + (x * 0.27061)) / (1.0 + (x * ((x * 0.04481) + 0.99229)))) - x

Julia

function code(x)
	return Float64(Float64(Float64(2.30753 + Float64(x * 0.27061)) / Float64(1.0 + Float64(x * Float64(Float64(x * 0.04481) + 0.99229)))) - x)
end

MATLAB

function tmp = code(x)
	tmp = ((2.30753 + (x * 0.27061)) / (1.0 + (x * ((x * 0.04481) + 0.99229)))) - x;
end

Wolfram

code[x_] := N[(N[(N[(2.30753 + N[(x * 0.27061), $MachinePrecision]), $MachinePrecision] / N[(1.0 + N[(x * N[(N[(x * 0.04481), $MachinePrecision] + 0.99229), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\frac{2.30753 + x \cdot 0.27061}{1 + x \cdot \left(0.99229 + x \cdot 0.04481\right)} - x \]

2. Final simplification 100.0%

   \[\leadsto \frac{2.30753 + x \cdot 0.27061}{1 + x \cdot \left(x \cdot 0.04481 + 0.99229\right)} - x \]

Alternative 4: 98.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \frac{2.30753 + x \cdot 0.27061}{1 + x \cdot 0.99229} - x \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (- (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x 0.99229))) x))

C

double code(double x) {
	return ((2.30753 + (x * 0.27061)) / (1.0 + (x * 0.99229))) - x;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = ((2.30753d0 + (x * 0.27061d0)) / (1.0d0 + (x * 0.99229d0))) - x
end function

Java

public static double code(double x) {
	return ((2.30753 + (x * 0.27061)) / (1.0 + (x * 0.99229))) - x;
}

Python

def code(x):
	return ((2.30753 + (x * 0.27061)) / (1.0 + (x * 0.99229))) - x

Julia

function code(x)
	return Float64(Float64(Float64(2.30753 + Float64(x * 0.27061)) / Float64(1.0 + Float64(x * 0.99229))) - x)
end

MATLAB

function tmp = code(x)
	tmp = ((2.30753 + (x * 0.27061)) / (1.0 + (x * 0.99229))) - x;
end

Wolfram

code[x_] := N[(N[(N[(2.30753 + N[(x * 0.27061), $MachinePrecision]), $MachinePrecision] / N[(1.0 + N[(x * 0.99229), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\frac{2.30753 + x \cdot 0.27061}{1 + x \cdot \left(0.99229 + x \cdot 0.04481\right)} - x \]

2. Taylor expanded in x around 0 97.9%

   \[\leadsto \frac{2.30753 + x \cdot 0.27061}{1 + \color{blue}{0.99229 \cdot x}} - x \]
3. Step-by-step derivation

   1. *-commutative 97.9%

      \[\leadsto \frac{2.30753 + x \cdot 0.27061}{1 + \color{blue}{x \cdot 0.99229}} - x \]

4. Simplified 97.9%

   \[\leadsto \frac{2.30753 + x \cdot 0.27061}{1 + \color{blue}{x \cdot 0.99229}} - x \]

5. Final simplification 97.9%

   \[\leadsto \frac{2.30753 + x \cdot 0.27061}{1 + x \cdot 0.99229} - x \]

Alternative 5: 57.2% accurate, 5.7× speedup

Math

\[\begin{array}{l} \\ 0.2727126142559131 - x \end{array} \]

FPCore

(FPCore (x) :precision binary64 (- 0.2727126142559131 x))

C

double code(double x) {
	return 0.2727126142559131 - x;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = 0.2727126142559131d0 - x
end function

Java

public static double code(double x) {
	return 0.2727126142559131 - x;
}

Python

def code(x):
	return 0.2727126142559131 - x

Julia

function code(x)
	return Float64(0.2727126142559131 - x)
end

MATLAB

function tmp = code(x)
	tmp = 0.2727126142559131 - x;
end

Wolfram

code[x_] := N[(0.2727126142559131 - x), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\frac{2.30753 + x \cdot 0.27061}{1 + x \cdot \left(0.99229 + x \cdot 0.04481\right)} - x \]

2. Taylor expanded in x around 0 97.9%

   \[\leadsto \frac{2.30753 + x \cdot 0.27061}{1 + \color{blue}{0.99229 \cdot x}} - x \]
3. Step-by-step derivation

   1. *-commutative 97.9%

      \[\leadsto \frac{2.30753 + x \cdot 0.27061}{1 + \color{blue}{x \cdot 0.99229}} - x \]

4. Simplified 97.9%

   \[\leadsto \frac{2.30753 + x \cdot 0.27061}{1 + \color{blue}{x \cdot 0.99229}} - x \]

5. Taylor expanded in x around inf 55.5%

   \[\leadsto \color{blue}{0.2727126142559131} - x \]

6. Final simplification 55.5%

   \[\leadsto 0.2727126142559131 - x \]

Alternative 6: 97.9% accurate, 5.7× speedup

Math

\[\begin{array}{l} \\ 2.30753 - x \end{array} \]

FPCore

(FPCore (x) :precision binary64 (- 2.30753 x))

C

double code(double x) {
	return 2.30753 - x;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = 2.30753d0 - x
end function

Java

public static double code(double x) {
	return 2.30753 - x;
}

Python

def code(x):
	return 2.30753 - x

Julia

function code(x)
	return Float64(2.30753 - x)
end

MATLAB

function tmp = code(x)
	tmp = 2.30753 - x;
end

Wolfram

code[x_] := N[(2.30753 - x), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\frac{2.30753 + x \cdot 0.27061}{1 + x \cdot \left(0.99229 + x \cdot 0.04481\right)} - x \]

2. Taylor expanded in x around 0 97.5%

   \[\leadsto \color{blue}{2.30753} - x \]

3. Final simplification 97.5%

   \[\leadsto 2.30753 - x \]

Alternative 7: 51.5% accurate, 8.5× speedup

Math

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

FPCore

(FPCore (x) :precision binary64 (- x))

C

double code(double x) {
	return -x;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = -x
end function

Java

public static double code(double x) {
	return -x;
}

Python

def code(x):
	return -x

Julia

function code(x)
	return Float64(-x)
end

MATLAB

function tmp = code(x)
	tmp = -x;
end

Wolfram

code[x_] := (-x)

Derivation

1. Initial program 100.0%

   \[\frac{2.30753 + x \cdot 0.27061}{1 + x \cdot \left(0.99229 + x \cdot 0.04481\right)} - x \]

2. Taylor expanded in x around 0 97.5%

   \[\leadsto \color{blue}{2.30753} - x \]

3. Taylor expanded in x around inf 50.0%

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

   1. neg-mul-1 50.0%

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

5. Simplified 50.0%

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

6. Final simplification 50.0%

   \[\leadsto -x \]

Reproduce

herbie shell --seed 2023224 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteGamma from math-functions-0.1.5.2, C"
  :precision binary64
  (- (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) x))