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

Percentage Accurate: 99.9% → 99.9%

Time: 7.4s

Alternatives: 10

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: 94.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+55} \lor \neg \left(y \leq 1.22 \cdot 10^{+69}\right):\\ \;\;\;\;1 + y \cdot \sqrt{x}\\ \mathbf{else}:\\ \;\;\;\;1 - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -9.5e+55) (not (<= y 1.22e+69)))
   (+ 1.0 (* y (sqrt x)))
   (- 1.0 x)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -9.5e+55) || !(y <= 1.22e+69)) {
		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 <= (-9.5d+55)) .or. (.not. (y <= 1.22d+69))) 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 <= -9.5e+55) || !(y <= 1.22e+69)) {
		tmp = 1.0 + (y * Math.sqrt(x));
	} else {
		tmp = 1.0 - x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -9.5e+55) or not (y <= 1.22e+69):
		tmp = 1.0 + (y * math.sqrt(x))
	else:
		tmp = 1.0 - x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -9.5e+55) || !(y <= 1.22e+69))
		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 <= -9.5e+55) || ~((y <= 1.22e+69)))
		tmp = 1.0 + (y * sqrt(x));
	else
		tmp = 1.0 - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -9.5e+55], N[Not[LessEqual[y, 1.22e+69]], $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 < -9.49999999999999989e55 or 1.22e69 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 91.9%

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

   if -9.49999999999999989e55 < y < 1.22e69

   1. Initial program 100.0%

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

      1. add-cbrt-cube 95.9%

         \[\leadsto \left(1 - x\right) + \color{blue}{\sqrt[3]{\left(\left(y \cdot \sqrt{x}\right) \cdot \left(y \cdot \sqrt{x}\right)\right) \cdot \left(y \cdot \sqrt{x}\right)}} \]

      2. pow3 95.9%

         \[\leadsto \left(1 - x\right) + \sqrt[3]{\color{blue}{{\left(y \cdot \sqrt{x}\right)}^{3}}} \]

   4. Applied egg-rr 95.9%

      \[\leadsto \left(1 - x\right) + \color{blue}{\sqrt[3]{{\left(y \cdot \sqrt{x}\right)}^{3}}} \]

   5. Taylor expanded in y around 0 95.5%

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

4. Final simplification 93.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+55} \lor \neg \left(y \leq 1.22 \cdot 10^{+69}\right):\\ \;\;\;\;1 + y \cdot \sqrt{x}\\ \mathbf{else}:\\ \;\;\;\;1 - x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 91.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{+127} \lor \neg \left(y \leq 9.6 \cdot 10^{+96}\right):\\ \;\;\;\;y \cdot \sqrt{x}\\ \mathbf{else}:\\ \;\;\;\;1 - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -3.3e+127) (not (<= y 9.6e+96))) (* y (sqrt x)) (- 1.0 x)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -3.3e+127) || !(y <= 9.6e+96)) {
		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 <= (-3.3d+127)) .or. (.not. (y <= 9.6d+96))) 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 <= -3.3e+127) || !(y <= 9.6e+96)) {
		tmp = y * Math.sqrt(x);
	} else {
		tmp = 1.0 - x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -3.3e+127) or not (y <= 9.6e+96):
		tmp = y * math.sqrt(x)
	else:
		tmp = 1.0 - x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -3.3e+127) || !(y <= 9.6e+96))
		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 <= -3.3e+127) || ~((y <= 9.6e+96)))
		tmp = y * sqrt(x);
	else
		tmp = 1.0 - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -3.3e+127], N[Not[LessEqual[y, 9.6e+96]], $MachinePrecision]], N[(y * N[Sqrt[x], $MachinePrecision]), $MachinePrecision], N[(1.0 - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.29999999999999977e127 or 9.59999999999999972e96 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 97.8%

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

      1. neg-mul-1 97.8%

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

   5. Simplified 97.8%

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

   6. Taylor expanded in x around 0 95.8%

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

   if -3.29999999999999977e127 < y < 9.59999999999999972e96

   1. Initial program 99.9%

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

      1. add-cbrt-cube 91.5%

         \[\leadsto \left(1 - x\right) + \color{blue}{\sqrt[3]{\left(\left(y \cdot \sqrt{x}\right) \cdot \left(y \cdot \sqrt{x}\right)\right) \cdot \left(y \cdot \sqrt{x}\right)}} \]

      2. pow3 91.5%

         \[\leadsto \left(1 - x\right) + \sqrt[3]{\color{blue}{{\left(y \cdot \sqrt{x}\right)}^{3}}} \]

   4. Applied egg-rr 91.5%

      \[\leadsto \left(1 - x\right) + \color{blue}{\sqrt[3]{{\left(y \cdot \sqrt{x}\right)}^{3}}} \]

   5. Taylor expanded in y around 0 89.5%

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

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{+127} \lor \neg \left(y \leq 9.6 \cdot 10^{+96}\right):\\ \;\;\;\;y \cdot \sqrt{x}\\ \mathbf{else}:\\ \;\;\;\;1 - x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 98.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \sqrt{x}\\ \mathbf{if}\;x \leq 0.0108:\\ \;\;\;\;1 + t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_0 - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* y (sqrt x)))) (if (<= x 0.0108) (+ 1.0 t_0) (- t_0 x))))

C

double code(double x, double y) {
	double t_0 = y * sqrt(x);
	double tmp;
	if (x <= 0.0108) {
		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 <= 0.0108d0) 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 <= 0.0108) {
		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 <= 0.0108:
		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 <= 0.0108)
		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 <= 0.0108)
		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, 0.0108], N[(1.0 + t$95$0), $MachinePrecision], N[(t$95$0 - x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < 0.010800000000000001

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 99.0%

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

   if 0.010800000000000001 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 98.5%

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

      1. neg-mul-1 98.5%

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

   5. Simplified 98.5%

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

   6. Taylor expanded in x around 0 98.5%

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

      1. mul-1-neg 98.5%

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

      2. +-commutative 98.5%

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

      3. sub-neg 98.5%

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

   8. Simplified 98.5%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 0.0108:\\ \;\;\;\;1 + y \cdot \sqrt{x}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \sqrt{x} - x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 67.7% accurate, 5.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - x \cdot x\\ \mathbf{if}\;y \leq -6.2 \cdot 10^{+168}:\\ \;\;\;\;\frac{t\_0}{1 + x}\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{+131}:\\ \;\;\;\;1 - x\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_0}{1 - x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (- 1.0 (* x x))))
   (if (<= y -6.2e+168)
     (/ t_0 (+ 1.0 x))
     (if (<= y 5.8e+131) (- 1.0 x) (/ t_0 (- 1.0 x))))))

C

double code(double x, double y) {
	double t_0 = 1.0 - (x * x);
	double tmp;
	if (y <= -6.2e+168) {
		tmp = t_0 / (1.0 + x);
	} else if (y <= 5.8e+131) {
		tmp = 1.0 - x;
	} else {
		tmp = t_0 / (1.0 - 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 = 1.0d0 - (x * x)
    if (y <= (-6.2d+168)) then
        tmp = t_0 / (1.0d0 + x)
    else if (y <= 5.8d+131) then
        tmp = 1.0d0 - x
    else
        tmp = t_0 / (1.0d0 - x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = 1.0 - (x * x);
	double tmp;
	if (y <= -6.2e+168) {
		tmp = t_0 / (1.0 + x);
	} else if (y <= 5.8e+131) {
		tmp = 1.0 - x;
	} else {
		tmp = t_0 / (1.0 - x);
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 1.0 - (x * x)
	tmp = 0
	if y <= -6.2e+168:
		tmp = t_0 / (1.0 + x)
	elif y <= 5.8e+131:
		tmp = 1.0 - x
	else:
		tmp = t_0 / (1.0 - x)
	return tmp

Julia

function code(x, y)
	t_0 = Float64(1.0 - Float64(x * x))
	tmp = 0.0
	if (y <= -6.2e+168)
		tmp = Float64(t_0 / Float64(1.0 + x));
	elseif (y <= 5.8e+131)
		tmp = Float64(1.0 - x);
	else
		tmp = Float64(t_0 / Float64(1.0 - x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = 1.0 - (x * x);
	tmp = 0.0;
	if (y <= -6.2e+168)
		tmp = t_0 / (1.0 + x);
	elseif (y <= 5.8e+131)
		tmp = 1.0 - x;
	else
		tmp = t_0 / (1.0 - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(1.0 - N[(x * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.2e+168], N[(t$95$0 / N[(1.0 + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.8e+131], N[(1.0 - x), $MachinePrecision], N[(t$95$0 / N[(1.0 - x), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.19999999999999993e168

   1. Initial program 99.8%

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

      1. add-cbrt-cube 38.5%

         \[\leadsto \left(1 - x\right) + \color{blue}{\sqrt[3]{\left(\left(y \cdot \sqrt{x}\right) \cdot \left(y \cdot \sqrt{x}\right)\right) \cdot \left(y \cdot \sqrt{x}\right)}} \]

      2. pow3 38.5%

         \[\leadsto \left(1 - x\right) + \sqrt[3]{\color{blue}{{\left(y \cdot \sqrt{x}\right)}^{3}}} \]

   4. Applied egg-rr 38.5%

      \[\leadsto \left(1 - x\right) + \color{blue}{\sqrt[3]{{\left(y \cdot \sqrt{x}\right)}^{3}}} \]

   5. Taylor expanded in y around 0 3.4%

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

      1. sub-neg 3.4%

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

      2. flip-+ 22.7%

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

      3. metadata-eval 22.7%

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

   7. Applied egg-rr 22.7%

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

   if -6.19999999999999993e168 < y < 5.8000000000000002e131

   1. Initial program 99.9%

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

      1. add-cbrt-cube 88.6%

         \[\leadsto \left(1 - x\right) + \color{blue}{\sqrt[3]{\left(\left(y \cdot \sqrt{x}\right) \cdot \left(y \cdot \sqrt{x}\right)\right) \cdot \left(y \cdot \sqrt{x}\right)}} \]

      2. pow3 88.6%

         \[\leadsto \left(1 - x\right) + \sqrt[3]{\color{blue}{{\left(y \cdot \sqrt{x}\right)}^{3}}} \]

   4. Applied egg-rr 88.6%

      \[\leadsto \left(1 - x\right) + \color{blue}{\sqrt[3]{{\left(y \cdot \sqrt{x}\right)}^{3}}} \]

   5. Taylor expanded in y around 0 83.2%

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

   if 5.8000000000000002e131 < y

   1. Initial program 99.8%

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

      1. add-cbrt-cube 40.9%

         \[\leadsto \left(1 - x\right) + \color{blue}{\sqrt[3]{\left(\left(y \cdot \sqrt{x}\right) \cdot \left(y \cdot \sqrt{x}\right)\right) \cdot \left(y \cdot \sqrt{x}\right)}} \]

      2. pow3 40.9%

         \[\leadsto \left(1 - x\right) + \sqrt[3]{\color{blue}{{\left(y \cdot \sqrt{x}\right)}^{3}}} \]

   4. Applied egg-rr 40.9%

      \[\leadsto \left(1 - x\right) + \color{blue}{\sqrt[3]{{\left(y \cdot \sqrt{x}\right)}^{3}}} \]

   5. Taylor expanded in y around 0 1.7%

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

      1. sub-neg 1.7%

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

      2. flip-+ 1.7%

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

      3. metadata-eval 1.7%

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

   7. Applied egg-rr 1.7%

      \[\leadsto \color{blue}{\frac{1 - \left(-x\right) \cdot \left(-x\right)}{1 - \left(-x\right)}} \]
   8. Step-by-step derivation

      1. neg-sub0 1.7%

         \[\leadsto \frac{1 - \left(-x\right) \cdot \left(-x\right)}{1 - \color{blue}{\left(0 - x\right)}} \]

      2. sub-neg 1.7%

         \[\leadsto \frac{1 - \left(-x\right) \cdot \left(-x\right)}{1 - \color{blue}{\left(0 + \left(-x\right)\right)}} \]

      3. add-sqr-sqrt 0.0%

         \[\leadsto \frac{1 - \left(-x\right) \cdot \left(-x\right)}{1 - \left(0 + \color{blue}{\sqrt{-x} \cdot \sqrt{-x}}\right)} \]

      4. sqrt-unprod 3.1%

         \[\leadsto \frac{1 - \left(-x\right) \cdot \left(-x\right)}{1 - \left(0 + \color{blue}{\sqrt{\left(-x\right) \cdot \left(-x\right)}}\right)} \]

      5. sqr-neg 3.1%

         \[\leadsto \frac{1 - \left(-x\right) \cdot \left(-x\right)}{1 - \left(0 + \sqrt{\color{blue}{x \cdot x}}\right)} \]

      6. sqrt-unprod 26.5%

         \[\leadsto \frac{1 - \left(-x\right) \cdot \left(-x\right)}{1 - \left(0 + \color{blue}{\sqrt{x} \cdot \sqrt{x}}\right)} \]

      7. add-sqr-sqrt 26.5%

         \[\leadsto \frac{1 - \left(-x\right) \cdot \left(-x\right)}{1 - \left(0 + \color{blue}{x}\right)} \]

   9. Applied egg-rr 26.5%

      \[\leadsto \frac{1 - \left(-x\right) \cdot \left(-x\right)}{1 - \color{blue}{\left(0 + x\right)}} \]
   10. Step-by-step derivation

       1. +-lft-identity 26.5%

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

   11. Simplified 26.5%

       \[\leadsto \frac{1 - \left(-x\right) \cdot \left(-x\right)}{1 - \color{blue}{x}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 66.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+168}:\\ \;\;\;\;\frac{1 - x \cdot x}{1 + x}\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{+131}:\\ \;\;\;\;1 - x\\ \mathbf{else}:\\ \;\;\;\;\frac{1 - x \cdot x}{1 - x}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 67.7% accurate, 5.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - x \cdot x\\ \mathbf{if}\;y \leq -7 \cdot 10^{+168}:\\ \;\;\;\;\frac{t\_0}{x}\\ \mathbf{elif}\;y \leq 8.6 \cdot 10^{+131}:\\ \;\;\;\;1 - x\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_0}{1 - x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (- 1.0 (* x x))))
   (if (<= y -7e+168)
     (/ t_0 x)
     (if (<= y 8.6e+131) (- 1.0 x) (/ t_0 (- 1.0 x))))))

C

double code(double x, double y) {
	double t_0 = 1.0 - (x * x);
	double tmp;
	if (y <= -7e+168) {
		tmp = t_0 / x;
	} else if (y <= 8.6e+131) {
		tmp = 1.0 - x;
	} else {
		tmp = t_0 / (1.0 - 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 = 1.0d0 - (x * x)
    if (y <= (-7d+168)) then
        tmp = t_0 / x
    else if (y <= 8.6d+131) then
        tmp = 1.0d0 - x
    else
        tmp = t_0 / (1.0d0 - x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = 1.0 - (x * x);
	double tmp;
	if (y <= -7e+168) {
		tmp = t_0 / x;
	} else if (y <= 8.6e+131) {
		tmp = 1.0 - x;
	} else {
		tmp = t_0 / (1.0 - x);
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 1.0 - (x * x)
	tmp = 0
	if y <= -7e+168:
		tmp = t_0 / x
	elif y <= 8.6e+131:
		tmp = 1.0 - x
	else:
		tmp = t_0 / (1.0 - x)
	return tmp

Julia

function code(x, y)
	t_0 = Float64(1.0 - Float64(x * x))
	tmp = 0.0
	if (y <= -7e+168)
		tmp = Float64(t_0 / x);
	elseif (y <= 8.6e+131)
		tmp = Float64(1.0 - x);
	else
		tmp = Float64(t_0 / Float64(1.0 - x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = 1.0 - (x * x);
	tmp = 0.0;
	if (y <= -7e+168)
		tmp = t_0 / x;
	elseif (y <= 8.6e+131)
		tmp = 1.0 - x;
	else
		tmp = t_0 / (1.0 - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(1.0 - N[(x * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7e+168], N[(t$95$0 / x), $MachinePrecision], If[LessEqual[y, 8.6e+131], N[(1.0 - x), $MachinePrecision], N[(t$95$0 / N[(1.0 - x), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.0000000000000004e168

   1. Initial program 99.8%

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

      1. add-cbrt-cube 38.5%

         \[\leadsto \left(1 - x\right) + \color{blue}{\sqrt[3]{\left(\left(y \cdot \sqrt{x}\right) \cdot \left(y \cdot \sqrt{x}\right)\right) \cdot \left(y \cdot \sqrt{x}\right)}} \]

      2. pow3 38.5%

         \[\leadsto \left(1 - x\right) + \sqrt[3]{\color{blue}{{\left(y \cdot \sqrt{x}\right)}^{3}}} \]

   4. Applied egg-rr 38.5%

      \[\leadsto \left(1 - x\right) + \color{blue}{\sqrt[3]{{\left(y \cdot \sqrt{x}\right)}^{3}}} \]

   5. Taylor expanded in y around 0 3.4%

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

      1. sub-neg 3.4%

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

      2. flip-+ 22.7%

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

      3. metadata-eval 22.7%

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

   7. Applied egg-rr 22.7%

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

   8. Taylor expanded in x around inf 22.5%

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

   if -7.0000000000000004e168 < y < 8.6000000000000003e131

   1. Initial program 99.9%

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

      1. add-cbrt-cube 88.6%

         \[\leadsto \left(1 - x\right) + \color{blue}{\sqrt[3]{\left(\left(y \cdot \sqrt{x}\right) \cdot \left(y \cdot \sqrt{x}\right)\right) \cdot \left(y \cdot \sqrt{x}\right)}} \]

      2. pow3 88.6%

         \[\leadsto \left(1 - x\right) + \sqrt[3]{\color{blue}{{\left(y \cdot \sqrt{x}\right)}^{3}}} \]

   4. Applied egg-rr 88.6%

      \[\leadsto \left(1 - x\right) + \color{blue}{\sqrt[3]{{\left(y \cdot \sqrt{x}\right)}^{3}}} \]

   5. Taylor expanded in y around 0 83.2%

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

   if 8.6000000000000003e131 < y

   1. Initial program 99.8%

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

      1. add-cbrt-cube 40.9%

         \[\leadsto \left(1 - x\right) + \color{blue}{\sqrt[3]{\left(\left(y \cdot \sqrt{x}\right) \cdot \left(y \cdot \sqrt{x}\right)\right) \cdot \left(y \cdot \sqrt{x}\right)}} \]

      2. pow3 40.9%

         \[\leadsto \left(1 - x\right) + \sqrt[3]{\color{blue}{{\left(y \cdot \sqrt{x}\right)}^{3}}} \]

   4. Applied egg-rr 40.9%

      \[\leadsto \left(1 - x\right) + \color{blue}{\sqrt[3]{{\left(y \cdot \sqrt{x}\right)}^{3}}} \]

   5. Taylor expanded in y around 0 1.7%

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

      1. sub-neg 1.7%

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

      2. flip-+ 1.7%

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

      3. metadata-eval 1.7%

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

   7. Applied egg-rr 1.7%

      \[\leadsto \color{blue}{\frac{1 - \left(-x\right) \cdot \left(-x\right)}{1 - \left(-x\right)}} \]
   8. Step-by-step derivation

      1. neg-sub0 1.7%

         \[\leadsto \frac{1 - \left(-x\right) \cdot \left(-x\right)}{1 - \color{blue}{\left(0 - x\right)}} \]

      2. sub-neg 1.7%

         \[\leadsto \frac{1 - \left(-x\right) \cdot \left(-x\right)}{1 - \color{blue}{\left(0 + \left(-x\right)\right)}} \]

      3. add-sqr-sqrt 0.0%

         \[\leadsto \frac{1 - \left(-x\right) \cdot \left(-x\right)}{1 - \left(0 + \color{blue}{\sqrt{-x} \cdot \sqrt{-x}}\right)} \]

      4. sqrt-unprod 3.1%

         \[\leadsto \frac{1 - \left(-x\right) \cdot \left(-x\right)}{1 - \left(0 + \color{blue}{\sqrt{\left(-x\right) \cdot \left(-x\right)}}\right)} \]

      5. sqr-neg 3.1%

         \[\leadsto \frac{1 - \left(-x\right) \cdot \left(-x\right)}{1 - \left(0 + \sqrt{\color{blue}{x \cdot x}}\right)} \]

      6. sqrt-unprod 26.5%

         \[\leadsto \frac{1 - \left(-x\right) \cdot \left(-x\right)}{1 - \left(0 + \color{blue}{\sqrt{x} \cdot \sqrt{x}}\right)} \]

      7. add-sqr-sqrt 26.5%

         \[\leadsto \frac{1 - \left(-x\right) \cdot \left(-x\right)}{1 - \left(0 + \color{blue}{x}\right)} \]

   9. Applied egg-rr 26.5%

      \[\leadsto \frac{1 - \left(-x\right) \cdot \left(-x\right)}{1 - \color{blue}{\left(0 + x\right)}} \]
   10. Step-by-step derivation

       1. +-lft-identity 26.5%

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

   11. Simplified 26.5%

       \[\leadsto \frac{1 - \left(-x\right) \cdot \left(-x\right)}{1 - \color{blue}{x}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 66.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+168}:\\ \;\;\;\;\frac{1 - x \cdot x}{x}\\ \mathbf{elif}\;y \leq 8.6 \cdot 10^{+131}:\\ \;\;\;\;1 - x\\ \mathbf{else}:\\ \;\;\;\;\frac{1 - x \cdot x}{1 - x}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 65.5% accurate, 8.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{+168}:\\ \;\;\;\;\frac{1 - x \cdot x}{x}\\ \mathbf{else}:\\ \;\;\;\;1 - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -6.8e+168) (/ (- 1.0 (* x x)) x) (- 1.0 x)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -6.8e+168) {
		tmp = (1.0 - (x * x)) / 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+168)) then
        tmp = (1.0d0 - (x * x)) / 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+168) {
		tmp = (1.0 - (x * x)) / x;
	} else {
		tmp = 1.0 - x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -6.8e+168:
		tmp = (1.0 - (x * x)) / x
	else:
		tmp = 1.0 - x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -6.8e+168)
		tmp = Float64(Float64(1.0 - Float64(x * x)) / 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+168)
		tmp = (1.0 - (x * x)) / x;
	else
		tmp = 1.0 - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -6.8e+168], N[(N[(1.0 - N[(x * x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision], N[(1.0 - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.80000000000000005e168

   1. Initial program 99.8%

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

      1. add-cbrt-cube 38.5%

         \[\leadsto \left(1 - x\right) + \color{blue}{\sqrt[3]{\left(\left(y \cdot \sqrt{x}\right) \cdot \left(y \cdot \sqrt{x}\right)\right) \cdot \left(y \cdot \sqrt{x}\right)}} \]

      2. pow3 38.5%

         \[\leadsto \left(1 - x\right) + \sqrt[3]{\color{blue}{{\left(y \cdot \sqrt{x}\right)}^{3}}} \]

   4. Applied egg-rr 38.5%

      \[\leadsto \left(1 - x\right) + \color{blue}{\sqrt[3]{{\left(y \cdot \sqrt{x}\right)}^{3}}} \]

   5. Taylor expanded in y around 0 3.4%

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

      1. sub-neg 3.4%

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

      2. flip-+ 22.7%

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

      3. metadata-eval 22.7%

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

   7. Applied egg-rr 22.7%

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

   8. Taylor expanded in x around inf 22.5%

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

   if -6.80000000000000005e168 < y

   1. Initial program 99.9%

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

      1. add-cbrt-cube 79.4%

         \[\leadsto \left(1 - x\right) + \color{blue}{\sqrt[3]{\left(\left(y \cdot \sqrt{x}\right) \cdot \left(y \cdot \sqrt{x}\right)\right) \cdot \left(y \cdot \sqrt{x}\right)}} \]

      2. pow3 79.4%

         \[\leadsto \left(1 - x\right) + \sqrt[3]{\color{blue}{{\left(y \cdot \sqrt{x}\right)}^{3}}} \]

   4. Applied egg-rr 79.4%

      \[\leadsto \left(1 - x\right) + \color{blue}{\sqrt[3]{{\left(y \cdot \sqrt{x}\right)}^{3}}} \]

   5. Taylor expanded in y around 0 67.4%

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

4. Final simplification 62.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{+168}:\\ \;\;\;\;\frac{1 - x \cdot x}{x}\\ \mathbf{else}:\\ \;\;\;\;1 - x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 62.4% accurate, 15.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 3.2:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= x 3.2) 1.0 (- x)))

C

double code(double x, double y) {
	double tmp;
	if (x <= 3.2) {
		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 <= 3.2d0) 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 <= 3.2) {
		tmp = 1.0;
	} else {
		tmp = -x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 3.2:
		tmp = 1.0
	else:
		tmp = -x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 3.2)
		tmp = 1.0;
	else
		tmp = Float64(-x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= 3.2)
		tmp = 1.0;
	else
		tmp = -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 3.2], 1.0, (-x)]

Derivation

1. Split input into 2 regimes

2. if x < 3.2000000000000002

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 99.0%

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

   4. Taylor expanded in y around 0 59.1%

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

   if 3.2000000000000002 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 98.4%

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

   4. Taylor expanded in y around 0 58.9%

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

      1. neg-mul-1 58.9%

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

   6. Simplified 58.9%

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

Alternative 9: 63.4% 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-cbrt-cube 74.7%

      \[\leadsto \left(1 - x\right) + \color{blue}{\sqrt[3]{\left(\left(y \cdot \sqrt{x}\right) \cdot \left(y \cdot \sqrt{x}\right)\right) \cdot \left(y \cdot \sqrt{x}\right)}} \]

   2. pow3 74.7%

      \[\leadsto \left(1 - x\right) + \sqrt[3]{\color{blue}{{\left(y \cdot \sqrt{x}\right)}^{3}}} \]

4. Applied egg-rr 74.7%

   \[\leadsto \left(1 - x\right) + \color{blue}{\sqrt[3]{{\left(y \cdot \sqrt{x}\right)}^{3}}} \]

5. Taylor expanded in y around 0 60.1%

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

Alternative 10: 31.8% 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 67.6%

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

4. Taylor expanded in y around 0 29.0%

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

Reproduce

herbie shell --seed 2024170 
(FPCore (x y)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, E"
  :precision binary64
  (+ (- 1.0 x) (* y (sqrt x))))