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

Percentage Accurate: 99.9% → 99.9%

Time: 8.1s

Alternatives: 7

Speedup: 1.0×

Specification

Math

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

FPCore

(FPCore (x y) :precision binary64 (+ (- 1.0 x) (* y (sqrt x))))

C

double code(double x, double y) {
	return (1.0 - x) + (y * sqrt(x));
}

Fortran

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

Java

public static double code(double x, double y) {
	return (1.0 - x) + (y * Math.sqrt(x));
}

Python

def code(x, y):
	return (1.0 - x) + (y * math.sqrt(x))

Julia

function code(x, y)
	return Float64(Float64(1.0 - x) + Float64(y * sqrt(x)))
end

MATLAB

function tmp = code(x, y)
	tmp = (1.0 - x) + (y * sqrt(x));
end

Wolfram

code[x_, y_] := N[(N[(1.0 - x), $MachinePrecision] + N[(y * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y) :precision binary64 (+ (- 1.0 x) (* y (sqrt x))))

C

double code(double x, double y) {
	return (1.0 - x) + (y * sqrt(x));
}

Fortran

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

Java

public static double code(double x, double y) {
	return (1.0 - x) + (y * Math.sqrt(x));
}

Python

def code(x, y):
	return (1.0 - x) + (y * math.sqrt(x))

Julia

function code(x, y)
	return Float64(Float64(1.0 - x) + Float64(y * sqrt(x)))
end

MATLAB

function tmp = code(x, y)
	tmp = (1.0 - x) + (y * sqrt(x));
end

Wolfram

code[x_, y_] := N[(N[(1.0 - x), $MachinePrecision] + N[(y * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.9% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y) :precision binary64 (+ (- 1.0 x) (* y (sqrt x))))

C

double code(double x, double y) {
	return (1.0 - x) + (y * sqrt(x));
}

Fortran

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

Java

public static double code(double x, double y) {
	return (1.0 - x) + (y * Math.sqrt(x));
}

Python

def code(x, y):
	return (1.0 - x) + (y * math.sqrt(x))

Julia

function code(x, y)
	return Float64(Float64(1.0 - x) + Float64(y * sqrt(x)))
end

MATLAB

function tmp = code(x, y)
	tmp = (1.0 - x) + (y * sqrt(x));
end

Wolfram

code[x_, y_] := N[(N[(1.0 - x), $MachinePrecision] + N[(y * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[\left(1 - x\right) + y \cdot \sqrt{x} \]
2. Add Preprocessing
3. Add Preprocessing

Alternative 2: 95.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+67} \lor \neg \left(y \leq 1.9 \cdot 10^{+71}\right):\\ \;\;\;\;1 + y \cdot \sqrt{x}\\ \mathbf{else}:\\ \;\;\;\;1 - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1.25e+67) (not (<= y 1.9e+71)))
   (+ 1.0 (* y (sqrt x)))
   (- 1.0 x)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1.25e+67) || !(y <= 1.9e+71)) {
		tmp = 1.0 + (y * sqrt(x));
	} else {
		tmp = 1.0 - x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-1.25d+67)) .or. (.not. (y <= 1.9d+71))) then
        tmp = 1.0d0 + (y * sqrt(x))
    else
        tmp = 1.0d0 - x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -1.25e+67) || !(y <= 1.9e+71)) {
		tmp = 1.0 + (y * Math.sqrt(x));
	} else {
		tmp = 1.0 - x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -1.25e+67) or not (y <= 1.9e+71):
		tmp = 1.0 + (y * math.sqrt(x))
	else:
		tmp = 1.0 - x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -1.25e+67) || !(y <= 1.9e+71))
		tmp = Float64(1.0 + Float64(y * sqrt(x)));
	else
		tmp = Float64(1.0 - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -1.25e+67) || ~((y <= 1.9e+71)))
		tmp = 1.0 + (y * sqrt(x));
	else
		tmp = 1.0 - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -1.25e+67], N[Not[LessEqual[y, 1.9e+71]], $MachinePrecision]], N[(1.0 + N[(y * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.24999999999999994e67 or 1.9e71 < y

   1. Initial program 99.7%

      \[\left(1 - x\right) + y \cdot \sqrt{x} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 96.0%

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

   if -1.24999999999999994e67 < y < 1.9e71

   1. Initial program 100.0%

      \[\left(1 - x\right) + y \cdot \sqrt{x} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. add-sqr-sqrt 47.2%

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

      2. sqrt-unprod 92.3%

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

      3. *-commutative 92.3%

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

      4. *-commutative 92.3%

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

      5. swap-sqr 92.3%

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

      6. add-sqr-sqrt 92.3%

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

      7. pow2 92.3%

         \[\leadsto \left(1 - x\right) + \sqrt{x \cdot \color{blue}{{y}^{2}}} \]

   4. Applied egg-rr 92.3%

      \[\leadsto \left(1 - x\right) + \color{blue}{\sqrt{x \cdot {y}^{2}}} \]

   5. Taylor expanded in y around 0 94.2%

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

4. Final simplification 94.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+67} \lor \neg \left(y \leq 1.9 \cdot 10^{+71}\right):\\ \;\;\;\;1 + y \cdot \sqrt{x}\\ \mathbf{else}:\\ \;\;\;\;1 - x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 92.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{+73} \lor \neg \left(y \leq 1.52 \cdot 10^{+74}\right):\\ \;\;\;\;y \cdot \sqrt{x}\\ \mathbf{else}:\\ \;\;\;\;1 - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -6.8e+73) (not (<= y 1.52e+74))) (* y (sqrt x)) (- 1.0 x)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -6.8e+73) || !(y <= 1.52e+74)) {
		tmp = y * sqrt(x);
	} else {
		tmp = 1.0 - x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-6.8d+73)) .or. (.not. (y <= 1.52d+74))) then
        tmp = y * sqrt(x)
    else
        tmp = 1.0d0 - x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -6.8e+73) || !(y <= 1.52e+74)) {
		tmp = y * Math.sqrt(x);
	} else {
		tmp = 1.0 - x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -6.8e+73) or not (y <= 1.52e+74):
		tmp = y * math.sqrt(x)
	else:
		tmp = 1.0 - x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -6.8e+73) || !(y <= 1.52e+74))
		tmp = Float64(y * sqrt(x));
	else
		tmp = Float64(1.0 - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -6.8e+73) || ~((y <= 1.52e+74)))
		tmp = y * sqrt(x);
	else
		tmp = 1.0 - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -6.8e+73], N[Not[LessEqual[y, 1.52e+74]], $MachinePrecision]], N[(y * N[Sqrt[x], $MachinePrecision]), $MachinePrecision], N[(1.0 - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.8000000000000003e73 or 1.52000000000000009e74 < y

   1. Initial program 99.7%

      \[\left(1 - x\right) + y \cdot \sqrt{x} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 96.0%

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

   4. Taylor expanded in y around inf 96.1%

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

   5. Taylor expanded in x around inf 92.9%

      \[\leadsto y \cdot \color{blue}{\sqrt{x}} \]

   if -6.8000000000000003e73 < y < 1.52000000000000009e74

   1. Initial program 100.0%

      \[\left(1 - x\right) + y \cdot \sqrt{x} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. add-sqr-sqrt 47.2%

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

      2. sqrt-unprod 92.3%

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

      3. *-commutative 92.3%

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

      4. *-commutative 92.3%

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

      5. swap-sqr 92.3%

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

      6. add-sqr-sqrt 92.3%

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

      7. pow2 92.3%

         \[\leadsto \left(1 - x\right) + \sqrt{x \cdot \color{blue}{{y}^{2}}} \]

   4. Applied egg-rr 92.3%

      \[\leadsto \left(1 - x\right) + \color{blue}{\sqrt{x \cdot {y}^{2}}} \]

   5. Taylor expanded in y around 0 94.2%

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

4. Final simplification 93.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{+73} \lor \neg \left(y \leq 1.52 \cdot 10^{+74}\right):\\ \;\;\;\;y \cdot \sqrt{x}\\ \mathbf{else}:\\ \;\;\;\;1 - x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 98.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \sqrt{x}\\ \mathbf{if}\;x \leq 0.0042:\\ \;\;\;\;1 + t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_0 - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* y (sqrt x)))) (if (<= x 0.0042) (+ 1.0 t_0) (- t_0 x))))

C

double code(double x, double y) {
	double t_0 = y * sqrt(x);
	double tmp;
	if (x <= 0.0042) {
		tmp = 1.0 + t_0;
	} else {
		tmp = t_0 - x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = y * sqrt(x)
    if (x <= 0.0042d0) then
        tmp = 1.0d0 + t_0
    else
        tmp = t_0 - x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = y * Math.sqrt(x);
	double tmp;
	if (x <= 0.0042) {
		tmp = 1.0 + t_0;
	} else {
		tmp = t_0 - x;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = y * math.sqrt(x)
	tmp = 0
	if x <= 0.0042:
		tmp = 1.0 + t_0
	else:
		tmp = t_0 - x
	return tmp

Julia

function code(x, y)
	t_0 = Float64(y * sqrt(x))
	tmp = 0.0
	if (x <= 0.0042)
		tmp = Float64(1.0 + t_0);
	else
		tmp = Float64(t_0 - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = y * sqrt(x);
	tmp = 0.0;
	if (x <= 0.0042)
		tmp = 1.0 + t_0;
	else
		tmp = t_0 - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(y * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, 0.0042], N[(1.0 + t$95$0), $MachinePrecision], N[(t$95$0 - x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < 0.00419999999999999974

   1. Initial program 99.8%

      \[\left(1 - x\right) + y \cdot \sqrt{x} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 98.2%

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

   if 0.00419999999999999974 < x

   1. Initial program 99.9%

      \[\left(1 - x\right) + y \cdot \sqrt{x} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 99.4%

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

   4. Taylor expanded in x around 0 99.5%

      \[\leadsto \color{blue}{-1 \cdot x + \sqrt{x} \cdot y} \]
   5. Step-by-step derivation

      1. neg-mul-1 99.5%

         \[\leadsto \color{blue}{\left(-x\right)} + \sqrt{x} \cdot y \]

      2. +-commutative 99.5%

         \[\leadsto \color{blue}{\sqrt{x} \cdot y + \left(-x\right)} \]

      3. fma-define 99.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\sqrt{x}, y, -x\right)} \]

      4. fma-neg 99.5%

         \[\leadsto \color{blue}{\sqrt{x} \cdot y - x} \]

   6. Simplified 99.5%

      \[\leadsto \color{blue}{\sqrt{x} \cdot y - x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 0.0042:\\ \;\;\;\;1 + y \cdot \sqrt{x}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \sqrt{x} - x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 61.8% accurate, 15.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 0.0042:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= x 0.0042) 1.0 (- x)))

C

double code(double x, double y) {
	double tmp;
	if (x <= 0.0042) {
		tmp = 1.0;
	} else {
		tmp = -x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= 0.0042d0) then
        tmp = 1.0d0
    else
        tmp = -x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= 0.0042) {
		tmp = 1.0;
	} else {
		tmp = -x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 0.0042:
		tmp = 1.0
	else:
		tmp = -x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 0.0042)
		tmp = 1.0;
	else
		tmp = Float64(-x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= 0.0042)
		tmp = 1.0;
	else
		tmp = -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 0.0042], 1.0, (-x)]

Derivation

1. Split input into 2 regimes

2. if x < 0.00419999999999999974

   1. Initial program 99.8%

      \[\left(1 - x\right) + y \cdot \sqrt{x} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 98.2%

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

   4. Taylor expanded in y around 0 54.9%

      \[\leadsto \color{blue}{1} \]

   if 0.00419999999999999974 < x

   1. Initial program 99.9%

      \[\left(1 - x\right) + y \cdot \sqrt{x} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 99.4%

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

   4. Taylor expanded in y around 0 68.3%

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

      1. neg-mul-1 68.3%

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

   6. Simplified 68.3%

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

Alternative 6: 62.9% accurate, 35.7× speedup

Math

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

FPCore

(FPCore (x y) :precision binary64 (- 1.0 x))

C

double code(double x, double y) {
	return 1.0 - x;
}

Fortran

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

Java

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

Python

def code(x, y):
	return 1.0 - x

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

   \[\left(1 - x\right) + y \cdot \sqrt{x} \]
2. Add Preprocessing
3. Step-by-step derivation

   1. add-sqr-sqrt 49.5%

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

   2. sqrt-unprod 72.0%

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

   3. *-commutative 72.0%

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

   4. *-commutative 72.0%

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

   5. swap-sqr 68.2%

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

   6. add-sqr-sqrt 68.3%

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

   7. pow2 68.3%

      \[\leadsto \left(1 - x\right) + \sqrt{x \cdot \color{blue}{{y}^{2}}} \]

4. Applied egg-rr 68.3%

   \[\leadsto \left(1 - x\right) + \color{blue}{\sqrt{x \cdot {y}^{2}}} \]

5. Taylor expanded in y around 0 62.4%

   \[\leadsto \color{blue}{1 - x} \]
6. Add Preprocessing

Alternative 7: 31.9% accurate, 107.0× speedup

Math

\[\begin{array}{l} \\ 1 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 1.0)

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return 1.0

Julia

function code(x, y)
	return 1.0
end

MATLAB

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

Wolfram

code[x_, y_] := 1.0

Derivation

1. Initial program 99.9%

   \[\left(1 - x\right) + y \cdot \sqrt{x} \]
2. Add Preprocessing

3. Taylor expanded in x around 0 63.9%

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

4. Taylor expanded in y around 0 27.4%

   \[\leadsto \color{blue}{1} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024141 
(FPCore (x y)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, E"
  :precision binary64
  (+ (- 1.0 x) (* y (sqrt x))))