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

Percentage Accurate: 99.9% → 99.9%

Time: 1.2s

Alternatives: 4

Speedup: 1.0×

• 25.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

\[\mathsf{TRUE}\left(\right)\]

Math

\[\begin{array}{l} \\ 1 - x \cdot \left(0.253 + x \cdot 0.12\right) \end{array} \]

FPCore

(FPCore (x) :precision binary64 (- 1.0 (* x (+ 0.253 (* x 0.12)))))

C

double code(double x) {
	return 1.0 - (x * (0.253 + (x * 0.12)));
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = 1.0d0 - (x * (0.253d0 + (x * 0.12d0)))
end function

Java

public static double code(double x) {
	return 1.0 - (x * (0.253 + (x * 0.12)));
}

Python

def code(x):
	return 1.0 - (x * (0.253 + (x * 0.12)))

Julia

function code(x)
	return Float64(1.0 - Float64(x * Float64(0.253 + Float64(x * 0.12))))
end

MATLAB

function tmp = code(x)
	tmp = 1.0 - (x * (0.253 + (x * 0.12)));
end

Wolfram

code[x_] := N[(1.0 - N[(x * N[(0.253 + N[(x * 0.12), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ 1 - x \cdot \left(0.253 + x \cdot 0.12\right) \end{array} \]

FPCore

(FPCore (x) :precision binary64 (- 1.0 (* x (+ 0.253 (* x 0.12)))))

C

double code(double x) {
	return 1.0 - (x * (0.253 + (x * 0.12)));
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = 1.0d0 - (x * (0.253d0 + (x * 0.12d0)))
end function

Java

public static double code(double x) {
	return 1.0 - (x * (0.253 + (x * 0.12)));
}

Python

def code(x):
	return 1.0 - (x * (0.253 + (x * 0.12)))

Julia

function code(x)
	return Float64(1.0 - Float64(x * Float64(0.253 + Float64(x * 0.12))))
end

MATLAB

function tmp = code(x)
	tmp = 1.0 - (x * (0.253 + (x * 0.12)));
end

Wolfram

code[x_] := N[(1.0 - N[(x * N[(0.253 + N[(x * 0.12), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ 1 - x \cdot \left(0.253 + x \cdot 0.12\right) \end{array} \]

FPCore

(FPCore (x) :precision binary64 (- 1.0 (* x (+ 0.253 (* x 0.12)))))

C

double code(double x) {
	return 1.0 - (x * (0.253 + (x * 0.12)));
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = 1.0d0 - (x * (0.253d0 + (x * 0.12d0)))
end function

Java

public static double code(double x) {
	return 1.0 - (x * (0.253 + (x * 0.12)));
}

Python

def code(x):
	return 1.0 - (x * (0.253 + (x * 0.12)))

Julia

function code(x)
	return Float64(1.0 - Float64(x * Float64(0.253 + Float64(x * 0.12))))
end

MATLAB

function tmp = code(x)
	tmp = 1.0 - (x * (0.253 + (x * 0.12)));
end

Wolfram

code[x_] := N[(1.0 - N[(x * N[(0.253 + N[(x * 0.12), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.8%

   \[1 - x \cdot \left(0.253 + x \cdot 0.12\right) \]
2. Add Preprocessing
3. Add Preprocessing

Alternative 2: 52.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.1:\\ \;\;\;\;x \cdot 0.12\\ \mathbf{else}:\\ \;\;\;\;1 - x \cdot 0.12\\ \end{array} \end{array} \]

FPCore

(FPCore (x) :precision binary64 (if (<= x -4.1) (* x 0.12) (- 1.0 (* x 0.12))))

C

double code(double x) {
	double tmp;
	if (x <= -4.1) {
		tmp = x * 0.12;
	} else {
		tmp = 1.0 - (x * 0.12);
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: tmp
    if (x <= (-4.1d0)) then
        tmp = x * 0.12d0
    else
        tmp = 1.0d0 - (x * 0.12d0)
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (x <= -4.1) {
		tmp = x * 0.12;
	} else {
		tmp = 1.0 - (x * 0.12);
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if x <= -4.1:
		tmp = x * 0.12
	else:
		tmp = 1.0 - (x * 0.12)
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (x <= -4.1)
		tmp = Float64(x * 0.12);
	else
		tmp = Float64(1.0 - Float64(x * 0.12));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (x <= -4.1)
		tmp = x * 0.12;
	else
		tmp = 1.0 - (x * 0.12);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[x, -4.1], N[(x * 0.12), $MachinePrecision], N[(1.0 - N[(x * 0.12), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.0999999999999996

   1. Initial program 99.6%

      \[1 - x \cdot \left(0.253 + x \cdot 0.12\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{1 + x \cdot \left(\frac{-3}{25} \cdot x - \frac{253}{1000}\right)} \]

   5. Applied rewrites 6.6%

      \[\leadsto \color{blue}{0.253 + x \cdot 0.12} \]

   6. Taylor expanded in x around 0

      \[\leadsto \color{blue}{1 + x \cdot \left(\frac{-3}{25} \cdot x - \frac{253}{1000}\right)} \]

   8. Applied rewrites 6.6%

      \[\leadsto \color{blue}{x \cdot 0.12} \]

   if -4.0999999999999996 < x

   1. Initial program 99.9%

      \[1 - x \cdot \left(0.253 + x \cdot 0.12\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto 1 - \color{blue}{\frac{253}{1000} \cdot x} \]

   5. Applied rewrites 65.3%

      \[\leadsto 1 - \color{blue}{x \cdot 0.12} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 10.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ 0.253 + x \cdot 0.12 \end{array} \]

FPCore

(FPCore (x) :precision binary64 (+ 0.253 (* x 0.12)))

C

double code(double x) {
	return 0.253 + (x * 0.12);
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = 0.253d0 + (x * 0.12d0)
end function

Java

public static double code(double x) {
	return 0.253 + (x * 0.12);
}

Python

def code(x):
	return 0.253 + (x * 0.12)

Julia

function code(x)
	return Float64(0.253 + Float64(x * 0.12))
end

MATLAB

function tmp = code(x)
	tmp = 0.253 + (x * 0.12);
end

Wolfram

code[x_] := N[(0.253 + N[(x * 0.12), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.8%

   \[1 - x \cdot \left(0.253 + x \cdot 0.12\right) \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{1 + x \cdot \left(\frac{-3}{25} \cdot x - \frac{253}{1000}\right)} \]

5. Applied rewrites 10.0%

   \[\leadsto \color{blue}{0.253 + x \cdot 0.12} \]
6. Add Preprocessing

Alternative 4: 3.8% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ x \cdot 0.12 \end{array} \]

FPCore

(FPCore (x) :precision binary64 (* x 0.12))

C

double code(double x) {
	return x * 0.12;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = x * 0.12d0
end function

Java

public static double code(double x) {
	return x * 0.12;
}

Python

def code(x):
	return x * 0.12

Julia

function code(x)
	return Float64(x * 0.12)
end

MATLAB

function tmp = code(x)
	tmp = x * 0.12;
end

Wolfram

code[x_] := N[(x * 0.12), $MachinePrecision]

Derivation

1. Initial program 99.8%

   \[1 - x \cdot \left(0.253 + x \cdot 0.12\right) \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{1 + x \cdot \left(\frac{-3}{25} \cdot x - \frac{253}{1000}\right)} \]

5. Applied rewrites 10.0%

   \[\leadsto \color{blue}{0.253 + x \cdot 0.12} \]

6. Taylor expanded in x around 0

   \[\leadsto \color{blue}{1 + x \cdot \left(\frac{-3}{25} \cdot x - \frac{253}{1000}\right)} \]

8. Applied rewrites 3.6%

   \[\leadsto \color{blue}{x \cdot 0.12} \]
9. Add Preprocessing

Reproduce

herbie shell --seed 2024321 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteGamma from math-functions-0.1.5.2, A"
  :precision binary64
  :pre (TRUE)
  (- 1.0 (* x (+ 0.253 (* x 0.12)))))