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

Percentage Accurate: 99.9% → 99.9%

Time: 8.2s

Alternatives: 12

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, 0.5× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(y, \sqrt{x}, 1 - x\right) \end{array} \]

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. +-commutative 99.9%

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

   2. fma-define 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \sqrt{x}, 1 - x\right)} \]

3. Simplified 99.9%

   \[\leadsto \color{blue}{\mathsf{fma}\left(y, \sqrt{x}, 1 - x\right)} \]
4. Add Preprocessing
5. Add Preprocessing

Alternative 2: 95.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+46} \lor \neg \left(y \leq 2.6 \cdot 10^{+30}\right):\\ \;\;\;\;1 + y \cdot \sqrt{x}\\ \mathbf{else}:\\ \;\;\;\;1 - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1.5e+46) (not (<= y 2.6e+30)))
   (+ 1.0 (* y (sqrt x)))
   (- 1.0 x)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1.5e+46) || !(y <= 2.6e+30)) {
		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 <= (-1.5d+46)) .or. (.not. (y <= 2.6d+30))) 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 <= -1.5e+46) || !(y <= 2.6e+30)) {
		tmp = 1.0 + (y * Math.sqrt(x));
	} else {
		tmp = 1.0 - x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -1.5e+46) or not (y <= 2.6e+30):
		tmp = 1.0 + (y * math.sqrt(x))
	else:
		tmp = 1.0 - x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -1.5e+46) || !(y <= 2.6e+30))
		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 <= -1.5e+46) || ~((y <= 2.6e+30)))
		tmp = 1.0 + (y * sqrt(x));
	else
		tmp = 1.0 - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -1.5e+46], N[Not[LessEqual[y, 2.6e+30]], $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 < -1.50000000000000012e46 or 2.59999999999999988e30 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 92.5%

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

   if -1.50000000000000012e46 < y < 2.59999999999999988e30

   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 100.0%

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

      2. pow2 100.0%

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

      3. pow1/2 100.0%

         \[\leadsto \left(1 - x\right) + y \cdot {\left(\sqrt{\color{blue}{{x}^{0.5}}}\right)}^{2} \]

      4. sqrt-pow1 100.0%

         \[\leadsto \left(1 - x\right) + y \cdot {\color{blue}{\left({x}^{\left(\frac{0.5}{2}\right)}\right)}}^{2} \]

      5. metadata-eval 100.0%

         \[\leadsto \left(1 - x\right) + y \cdot {\left({x}^{\color{blue}{0.25}}\right)}^{2} \]

   4. Applied egg-rr 100.0%

      \[\leadsto \left(1 - x\right) + y \cdot \color{blue}{{\left({x}^{0.25}\right)}^{2}} \]

   5. Taylor expanded in y around 0 99.4%

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

4. Final simplification 96.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+46} \lor \neg \left(y \leq 2.6 \cdot 10^{+30}\right):\\ \;\;\;\;1 + y \cdot \sqrt{x}\\ \mathbf{else}:\\ \;\;\;\;1 - x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 92.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+51} \lor \neg \left(y \leq 9.9 \cdot 10^{+76}\right):\\ \;\;\;\;y \cdot \sqrt{x}\\ \mathbf{else}:\\ \;\;\;\;1 - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -7.5e+51) (not (<= y 9.9e+76))) (* y (sqrt x)) (- 1.0 x)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -7.5e+51) || !(y <= 9.9e+76)) {
		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 <= (-7.5d+51)) .or. (.not. (y <= 9.9d+76))) 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 <= -7.5e+51) || !(y <= 9.9e+76)) {
		tmp = y * Math.sqrt(x);
	} else {
		tmp = 1.0 - x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -7.5e+51) or not (y <= 9.9e+76):
		tmp = y * math.sqrt(x)
	else:
		tmp = 1.0 - x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -7.5e+51) || !(y <= 9.9e+76))
		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 <= -7.5e+51) || ~((y <= 9.9e+76)))
		tmp = y * sqrt(x);
	else
		tmp = 1.0 - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -7.5e+51], N[Not[LessEqual[y, 9.9e+76]], $MachinePrecision]], N[(y * N[Sqrt[x], $MachinePrecision]), $MachinePrecision], N[(1.0 - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.4999999999999999e51 or 9.90000000000000018e76 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 80.4%

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

   4. Taylor expanded in y around inf 95.8%

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

      1. mul-1-neg 95.8%

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

      2. unsub-neg 95.8%

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

   6. Simplified 95.8%

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

   7. Taylor expanded in x around 0 89.5%

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

   if -7.4999999999999999e51 < y < 9.90000000000000018e76

   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 100.0%

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

      2. pow2 100.0%

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

      3. pow1/2 100.0%

         \[\leadsto \left(1 - x\right) + y \cdot {\left(\sqrt{\color{blue}{{x}^{0.5}}}\right)}^{2} \]

      4. sqrt-pow1 100.0%

         \[\leadsto \left(1 - x\right) + y \cdot {\color{blue}{\left({x}^{\left(\frac{0.5}{2}\right)}\right)}}^{2} \]

      5. metadata-eval 100.0%

         \[\leadsto \left(1 - x\right) + y \cdot {\left({x}^{\color{blue}{0.25}}\right)}^{2} \]

   4. Applied egg-rr 100.0%

      \[\leadsto \left(1 - x\right) + y \cdot \color{blue}{{\left({x}^{0.25}\right)}^{2}} \]

   5. Taylor expanded in y around 0 97.2%

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

4. Final simplification 94.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+51} \lor \neg \left(y \leq 9.9 \cdot 10^{+76}\right):\\ \;\;\;\;y \cdot \sqrt{x}\\ \mathbf{else}:\\ \;\;\;\;1 - x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 98.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \sqrt{x}\\ \mathbf{if}\;x \leq 1.35 \cdot 10^{-7}:\\ \;\;\;\;1 + t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_0 - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* y (sqrt x)))) (if (<= x 1.35e-7) (+ 1.0 t_0) (- t_0 x))))

C

double code(double x, double y) {
	double t_0 = y * sqrt(x);
	double tmp;
	if (x <= 1.35e-7) {
		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 <= 1.35d-7) 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 <= 1.35e-7) {
		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 <= 1.35e-7:
		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 <= 1.35e-7)
		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 <= 1.35e-7)
		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, 1.35e-7], N[(1.0 + t$95$0), $MachinePrecision], N[(t$95$0 - x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < 1.35000000000000004e-7

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 99.5%

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

   if 1.35000000000000004e-7 < x

   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 99.8%

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

      2. pow2 99.8%

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

      3. pow1/2 99.8%

         \[\leadsto \left(1 - x\right) + y \cdot {\left(\sqrt{\color{blue}{{x}^{0.5}}}\right)}^{2} \]

      4. sqrt-pow1 99.8%

         \[\leadsto \left(1 - x\right) + y \cdot {\color{blue}{\left({x}^{\left(\frac{0.5}{2}\right)}\right)}}^{2} \]

      5. metadata-eval 99.8%

         \[\leadsto \left(1 - x\right) + y \cdot {\left({x}^{\color{blue}{0.25}}\right)}^{2} \]

   4. Applied egg-rr 99.8%

      \[\leadsto \left(1 - x\right) + y \cdot \color{blue}{{\left({x}^{0.25}\right)}^{2}} \]

   5. Taylor expanded in x around inf 98.2%

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

      1. sub-neg 98.2%

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

      2. metadata-eval 98.2%

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

      3. distribute-rgt-in 98.2%

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

      4. *-commutative 98.2%

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

      5. neg-mul-1 98.2%

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

      6. unsub-neg 98.2%

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

   7. Simplified 98.4%

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

4. Final simplification 98.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1.35 \cdot 10^{-7}:\\ \;\;\;\;1 + y \cdot \sqrt{x}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \sqrt{x} - x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 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 6: 68.0% accurate, 4.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{+154}:\\ \;\;\;\;\frac{1 - x \cdot x}{x + 1}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+117}:\\ \;\;\;\;1 - x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x - \frac{x}{y} \cdot \frac{x}{y}}{\frac{x}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.35e+154)
   (/ (- 1.0 (* x x)) (+ x 1.0))
   (if (<= y 1.6e+117) (- 1.0 x) (* y (/ (- x (* (/ x y) (/ x y))) (/ x y))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.35e+154) {
		tmp = (1.0 - (x * x)) / (x + 1.0);
	} else if (y <= 1.6e+117) {
		tmp = 1.0 - x;
	} else {
		tmp = y * ((x - ((x / y) * (x / y))) / (x / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-1.35d+154)) then
        tmp = (1.0d0 - (x * x)) / (x + 1.0d0)
    else if (y <= 1.6d+117) then
        tmp = 1.0d0 - x
    else
        tmp = y * ((x - ((x / y) * (x / y))) / (x / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -1.35e+154) {
		tmp = (1.0 - (x * x)) / (x + 1.0);
	} else if (y <= 1.6e+117) {
		tmp = 1.0 - x;
	} else {
		tmp = y * ((x - ((x / y) * (x / y))) / (x / y));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.35e+154:
		tmp = (1.0 - (x * x)) / (x + 1.0)
	elif y <= 1.6e+117:
		tmp = 1.0 - x
	else:
		tmp = y * ((x - ((x / y) * (x / y))) / (x / y))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.35e+154)
		tmp = Float64(Float64(1.0 - Float64(x * x)) / Float64(x + 1.0));
	elseif (y <= 1.6e+117)
		tmp = Float64(1.0 - x);
	else
		tmp = Float64(y * Float64(Float64(x - Float64(Float64(x / y) * Float64(x / y))) / Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.35e+154)
		tmp = (1.0 - (x * x)) / (x + 1.0);
	elseif (y <= 1.6e+117)
		tmp = 1.0 - x;
	else
		tmp = y * ((x - ((x / y) * (x / y))) / (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.35e+154], N[(N[(1.0 - N[(x * x), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.6e+117], N[(1.0 - x), $MachinePrecision], N[(y * N[(N[(x - N[(N[(x / y), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.35000000000000003e154

   1. Initial program 99.8%

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

      1. add-sqr-sqrt 99.4%

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

      2. pow2 99.4%

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

      3. pow1/2 99.4%

         \[\leadsto \left(1 - x\right) + y \cdot {\left(\sqrt{\color{blue}{{x}^{0.5}}}\right)}^{2} \]

      4. sqrt-pow1 99.5%

         \[\leadsto \left(1 - x\right) + y \cdot {\color{blue}{\left({x}^{\left(\frac{0.5}{2}\right)}\right)}}^{2} \]

      5. metadata-eval 99.5%

         \[\leadsto \left(1 - x\right) + y \cdot {\left({x}^{\color{blue}{0.25}}\right)}^{2} \]

   4. Applied egg-rr 99.5%

      \[\leadsto \left(1 - x\right) + y \cdot \color{blue}{{\left({x}^{0.25}\right)}^{2}} \]

   5. Taylor expanded in y around 0 3.0%

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

      1. sub-neg 3.0%

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

      2. flip-+ 17.7%

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

      3. metadata-eval 17.7%

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

   7. Applied egg-rr 17.7%

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

   if -1.35000000000000003e154 < y < 1.60000000000000002e117

   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 99.9%

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

      2. pow2 99.9%

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

      3. pow1/2 99.9%

         \[\leadsto \left(1 - x\right) + y \cdot {\left(\sqrt{\color{blue}{{x}^{0.5}}}\right)}^{2} \]

      4. sqrt-pow1 99.9%

         \[\leadsto \left(1 - x\right) + y \cdot {\color{blue}{\left({x}^{\left(\frac{0.5}{2}\right)}\right)}}^{2} \]

      5. metadata-eval 99.9%

         \[\leadsto \left(1 - x\right) + y \cdot {\left({x}^{\color{blue}{0.25}}\right)}^{2} \]

   4. Applied egg-rr 99.9%

      \[\leadsto \left(1 - x\right) + y \cdot \color{blue}{{\left({x}^{0.25}\right)}^{2}} \]

   5. Taylor expanded in y around 0 85.7%

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

   if 1.60000000000000002e117 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 76.0%

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

   4. Taylor expanded in y around inf 99.8%

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

      1. mul-1-neg 99.8%

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

      2. unsub-neg 99.8%

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

   6. Simplified 99.8%

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

      1. sub-neg 99.8%

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

      2. flip-+ 99.7%

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

      3. add-sqr-sqrt 99.3%

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

      4. distribute-neg-frac2 99.3%

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

      5. distribute-neg-frac2 99.3%

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

      6. distribute-neg-frac2 99.3%

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

   8. Applied egg-rr 99.3%

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

   9. Taylor expanded in y around 0 26.2%

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

4. Final simplification 66.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{+154}:\\ \;\;\;\;\frac{1 - x \cdot x}{x + 1}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+117}:\\ \;\;\;\;1 - x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x - \frac{x}{y} \cdot \frac{x}{y}}{\frac{x}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 67.3% accurate, 5.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+151}:\\ \;\;\;\;\frac{1 - x \cdot x}{x + 1}\\ \mathbf{elif}\;y \leq 5.3 \cdot 10^{+128}:\\ \;\;\;\;1 - x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot x + -1}{x + -1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -9e+151)
   (/ (- 1.0 (* x x)) (+ x 1.0))
   (if (<= y 5.3e+128) (- 1.0 x) (/ (+ (* x x) -1.0) (+ x -1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -9e+151) {
		tmp = (1.0 - (x * x)) / (x + 1.0);
	} else if (y <= 5.3e+128) {
		tmp = 1.0 - x;
	} else {
		tmp = ((x * x) + -1.0) / (x + -1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-9d+151)) then
        tmp = (1.0d0 - (x * x)) / (x + 1.0d0)
    else if (y <= 5.3d+128) then
        tmp = 1.0d0 - x
    else
        tmp = ((x * x) + (-1.0d0)) / (x + (-1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -9e+151) {
		tmp = (1.0 - (x * x)) / (x + 1.0);
	} else if (y <= 5.3e+128) {
		tmp = 1.0 - x;
	} else {
		tmp = ((x * x) + -1.0) / (x + -1.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -9e+151:
		tmp = (1.0 - (x * x)) / (x + 1.0)
	elif y <= 5.3e+128:
		tmp = 1.0 - x
	else:
		tmp = ((x * x) + -1.0) / (x + -1.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -9e+151)
		tmp = Float64(Float64(1.0 - Float64(x * x)) / Float64(x + 1.0));
	elseif (y <= 5.3e+128)
		tmp = Float64(1.0 - x);
	else
		tmp = Float64(Float64(Float64(x * x) + -1.0) / Float64(x + -1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -9e+151)
		tmp = (1.0 - (x * x)) / (x + 1.0);
	elseif (y <= 5.3e+128)
		tmp = 1.0 - x;
	else
		tmp = ((x * x) + -1.0) / (x + -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -9e+151], N[(N[(1.0 - N[(x * x), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.3e+128], N[(1.0 - x), $MachinePrecision], N[(N[(N[(x * x), $MachinePrecision] + -1.0), $MachinePrecision] / N[(x + -1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.9999999999999997e151

   1. Initial program 99.8%

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

      1. add-sqr-sqrt 99.4%

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

      2. pow2 99.4%

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

      3. pow1/2 99.4%

         \[\leadsto \left(1 - x\right) + y \cdot {\left(\sqrt{\color{blue}{{x}^{0.5}}}\right)}^{2} \]

      4. sqrt-pow1 99.5%

         \[\leadsto \left(1 - x\right) + y \cdot {\color{blue}{\left({x}^{\left(\frac{0.5}{2}\right)}\right)}}^{2} \]

      5. metadata-eval 99.5%

         \[\leadsto \left(1 - x\right) + y \cdot {\left({x}^{\color{blue}{0.25}}\right)}^{2} \]

   4. Applied egg-rr 99.5%

      \[\leadsto \left(1 - x\right) + y \cdot \color{blue}{{\left({x}^{0.25}\right)}^{2}} \]

   5. Taylor expanded in y around 0 2.9%

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

      1. sub-neg 2.9%

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

      2. flip-+ 17.2%

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

      3. metadata-eval 17.2%

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

   7. Applied egg-rr 17.2%

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

   if -8.9999999999999997e151 < y < 5.3000000000000002e128

   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 99.9%

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

      2. pow2 99.9%

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

      3. pow1/2 99.9%

         \[\leadsto \left(1 - x\right) + y \cdot {\left(\sqrt{\color{blue}{{x}^{0.5}}}\right)}^{2} \]

      4. sqrt-pow1 99.9%

         \[\leadsto \left(1 - x\right) + y \cdot {\color{blue}{\left({x}^{\left(\frac{0.5}{2}\right)}\right)}}^{2} \]

      5. metadata-eval 99.9%

         \[\leadsto \left(1 - x\right) + y \cdot {\left({x}^{\color{blue}{0.25}}\right)}^{2} \]

   4. Applied egg-rr 99.9%

      \[\leadsto \left(1 - x\right) + y \cdot \color{blue}{{\left({x}^{0.25}\right)}^{2}} \]

   5. Taylor expanded in y around 0 84.6%

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

   if 5.3000000000000002e128 < y

   1. Initial program 99.8%

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

      1. add-sqr-sqrt 99.4%

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

      2. pow2 99.4%

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

      3. pow1/2 99.4%

         \[\leadsto \left(1 - x\right) + y \cdot {\left(\sqrt{\color{blue}{{x}^{0.5}}}\right)}^{2} \]

      4. sqrt-pow1 99.4%

         \[\leadsto \left(1 - x\right) + y \cdot {\color{blue}{\left({x}^{\left(\frac{0.5}{2}\right)}\right)}}^{2} \]

      5. metadata-eval 99.4%

         \[\leadsto \left(1 - x\right) + y \cdot {\left({x}^{\color{blue}{0.25}}\right)}^{2} \]

   4. Applied egg-rr 99.4%

      \[\leadsto \left(1 - x\right) + y \cdot \color{blue}{{\left({x}^{0.25}\right)}^{2}} \]

   5. Taylor expanded in y around 0 2.8%

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

      1. sub-neg 2.8%

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

      2. flip-+ 2.8%

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

      3. metadata-eval 2.8%

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

   7. Applied egg-rr 2.8%

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

      1. pow1 2.8%

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

      2. metadata-eval 2.8%

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

      3. sqrt-pow1 3.6%

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

      4. pow2 3.6%

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

      5. sqr-neg 3.6%

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

      6. sqrt-prod 19.9%

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

      7. add-sqr-sqrt 19.9%

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

      8. flip-- 3.6%

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

      9. metadata-eval 3.6%

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

      10. sqr-neg 3.6%

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

      11. remove-double-neg 3.6%

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

      12. sub-neg 3.6%

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

      13. frac-2neg 3.6%

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

      14. distribute-frac-neg 3.6%

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

      15. distribute-neg-frac2 3.6%

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

      16. metadata-eval 3.6%

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

      17. sqr-neg 3.6%

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

      18. sub-neg 3.6%

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

      19. remove-double-neg 3.6%

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

      20. flip-- 19.9%

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

      21. sub-neg 19.9%

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

      22. pow1 19.9%

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

      23. metadata-eval 19.9%

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

   9. Applied egg-rr 19.9%

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

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+151}:\\ \;\;\;\;\frac{1 - x \cdot x}{x + 1}\\ \mathbf{elif}\;y \leq 5.3 \cdot 10^{+128}:\\ \;\;\;\;1 - x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot x + -1}{x + -1}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 67.2% accurate, 5.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.8 \cdot 10^{+178}:\\ \;\;\;\;\frac{1 - x \cdot x}{x}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+133}:\\ \;\;\;\;1 - x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot x + -1}{x + -1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -7.8e+178)
   (/ (- 1.0 (* x x)) x)
   (if (<= y 4e+133) (- 1.0 x) (/ (+ (* x x) -1.0) (+ x -1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -7.8e+178) {
		tmp = (1.0 - (x * x)) / x;
	} else if (y <= 4e+133) {
		tmp = 1.0 - x;
	} else {
		tmp = ((x * x) + -1.0) / (x + -1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-7.8d+178)) then
        tmp = (1.0d0 - (x * x)) / x
    else if (y <= 4d+133) then
        tmp = 1.0d0 - x
    else
        tmp = ((x * x) + (-1.0d0)) / (x + (-1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -7.8e+178) {
		tmp = (1.0 - (x * x)) / x;
	} else if (y <= 4e+133) {
		tmp = 1.0 - x;
	} else {
		tmp = ((x * x) + -1.0) / (x + -1.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -7.8e+178:
		tmp = (1.0 - (x * x)) / x
	elif y <= 4e+133:
		tmp = 1.0 - x
	else:
		tmp = ((x * x) + -1.0) / (x + -1.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -7.8e+178)
		tmp = Float64(Float64(1.0 - Float64(x * x)) / x);
	elseif (y <= 4e+133)
		tmp = Float64(1.0 - x);
	else
		tmp = Float64(Float64(Float64(x * x) + -1.0) / Float64(x + -1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -7.8e+178)
		tmp = (1.0 - (x * x)) / x;
	elseif (y <= 4e+133)
		tmp = 1.0 - x;
	else
		tmp = ((x * x) + -1.0) / (x + -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -7.8e+178], N[(N[(1.0 - N[(x * x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision], If[LessEqual[y, 4e+133], N[(1.0 - x), $MachinePrecision], N[(N[(N[(x * x), $MachinePrecision] + -1.0), $MachinePrecision] / N[(x + -1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.7999999999999995e178

   1. Initial program 99.8%

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

      1. add-sqr-sqrt 99.4%

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

      2. pow2 99.4%

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

      3. pow1/2 99.4%

         \[\leadsto \left(1 - x\right) + y \cdot {\left(\sqrt{\color{blue}{{x}^{0.5}}}\right)}^{2} \]

      4. sqrt-pow1 99.6%

         \[\leadsto \left(1 - x\right) + y \cdot {\color{blue}{\left({x}^{\left(\frac{0.5}{2}\right)}\right)}}^{2} \]

      5. metadata-eval 99.6%

         \[\leadsto \left(1 - x\right) + y \cdot {\left({x}^{\color{blue}{0.25}}\right)}^{2} \]

   4. Applied egg-rr 99.6%

      \[\leadsto \left(1 - x\right) + y \cdot \color{blue}{{\left({x}^{0.25}\right)}^{2}} \]

   5. Taylor expanded in y around 0 3.3%

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

      1. sub-neg 3.3%

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

      2. flip-+ 22.1%

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

      3. metadata-eval 22.1%

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

   7. Applied egg-rr 22.1%

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

   8. Taylor expanded in x around inf 21.9%

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

   if -7.7999999999999995e178 < y < 4.0000000000000001e133

   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 99.9%

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

      2. pow2 99.9%

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

      3. pow1/2 99.9%

         \[\leadsto \left(1 - x\right) + y \cdot {\left(\sqrt{\color{blue}{{x}^{0.5}}}\right)}^{2} \]

      4. sqrt-pow1 99.9%

         \[\leadsto \left(1 - x\right) + y \cdot {\color{blue}{\left({x}^{\left(\frac{0.5}{2}\right)}\right)}}^{2} \]

      5. metadata-eval 99.9%

         \[\leadsto \left(1 - x\right) + y \cdot {\left({x}^{\color{blue}{0.25}}\right)}^{2} \]

   4. Applied egg-rr 99.9%

      \[\leadsto \left(1 - x\right) + y \cdot \color{blue}{{\left({x}^{0.25}\right)}^{2}} \]

   5. Taylor expanded in y around 0 80.8%

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

   if 4.0000000000000001e133 < y

   1. Initial program 99.8%

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

      1. add-sqr-sqrt 99.5%

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

      2. pow2 99.5%

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

      3. pow1/2 99.5%

         \[\leadsto \left(1 - x\right) + y \cdot {\left(\sqrt{\color{blue}{{x}^{0.5}}}\right)}^{2} \]

      4. sqrt-pow1 99.5%

         \[\leadsto \left(1 - x\right) + y \cdot {\color{blue}{\left({x}^{\left(\frac{0.5}{2}\right)}\right)}}^{2} \]

      5. metadata-eval 99.5%

         \[\leadsto \left(1 - x\right) + y \cdot {\left({x}^{\color{blue}{0.25}}\right)}^{2} \]

   4. Applied egg-rr 99.5%

      \[\leadsto \left(1 - x\right) + y \cdot \color{blue}{{\left({x}^{0.25}\right)}^{2}} \]

   5. Taylor expanded in y around 0 2.7%

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

      1. sub-neg 2.7%

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

      2. flip-+ 2.7%

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

      3. metadata-eval 2.7%

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

   7. Applied egg-rr 2.7%

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

      1. pow1 2.7%

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

      2. metadata-eval 2.7%

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

      3. sqrt-pow1 3.5%

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

      4. pow2 3.5%

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

      5. sqr-neg 3.5%

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

      6. sqrt-prod 20.3%

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

      7. add-sqr-sqrt 20.3%

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

      8. flip-- 3.5%

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

      9. metadata-eval 3.5%

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

      10. sqr-neg 3.5%

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

      11. remove-double-neg 3.5%

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

      12. sub-neg 3.5%

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

      13. frac-2neg 3.5%

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

      14. distribute-frac-neg 3.5%

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

      15. distribute-neg-frac2 3.5%

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

      16. metadata-eval 3.5%

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

      17. sqr-neg 3.5%

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

      18. sub-neg 3.5%

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

      19. remove-double-neg 3.5%

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

      20. flip-- 20.3%

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

      21. sub-neg 20.3%

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

      22. pow1 20.3%

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

      23. metadata-eval 20.3%

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

   9. Applied egg-rr 20.3%

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

4. Final simplification 66.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.8 \cdot 10^{+178}:\\ \;\;\;\;\frac{1 - x \cdot x}{x}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+133}:\\ \;\;\;\;1 - x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot x + -1}{x + -1}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 64.7% accurate, 8.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.8 \cdot 10^{+178}:\\ \;\;\;\;\frac{1 - x \cdot x}{x}\\ \mathbf{else}:\\ \;\;\;\;1 - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -7.8e+178) (/ (- 1.0 (* x x)) x) (- 1.0 x)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -7.8e+178) {
		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 <= (-7.8d+178)) 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 <= -7.8e+178) {
		tmp = (1.0 - (x * x)) / x;
	} else {
		tmp = 1.0 - x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -7.8e+178:
		tmp = (1.0 - (x * x)) / x
	else:
		tmp = 1.0 - x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -7.8e+178)
		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 <= -7.8e+178)
		tmp = (1.0 - (x * x)) / x;
	else
		tmp = 1.0 - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -7.8e+178], 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 < -7.7999999999999995e178

   1. Initial program 99.8%

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

      1. add-sqr-sqrt 99.4%

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

      2. pow2 99.4%

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

      3. pow1/2 99.4%

         \[\leadsto \left(1 - x\right) + y \cdot {\left(\sqrt{\color{blue}{{x}^{0.5}}}\right)}^{2} \]

      4. sqrt-pow1 99.6%

         \[\leadsto \left(1 - x\right) + y \cdot {\color{blue}{\left({x}^{\left(\frac{0.5}{2}\right)}\right)}}^{2} \]

      5. metadata-eval 99.6%

         \[\leadsto \left(1 - x\right) + y \cdot {\left({x}^{\color{blue}{0.25}}\right)}^{2} \]

   4. Applied egg-rr 99.6%

      \[\leadsto \left(1 - x\right) + y \cdot \color{blue}{{\left({x}^{0.25}\right)}^{2}} \]

   5. Taylor expanded in y around 0 3.3%

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

      1. sub-neg 3.3%

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

      2. flip-+ 22.1%

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

      3. metadata-eval 22.1%

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

   7. Applied egg-rr 22.1%

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

   8. Taylor expanded in x around inf 21.9%

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

   if -7.7999999999999995e178 < y

   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 99.8%

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

      2. pow2 99.8%

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

      3. pow1/2 99.8%

         \[\leadsto \left(1 - x\right) + y \cdot {\left(\sqrt{\color{blue}{{x}^{0.5}}}\right)}^{2} \]

      4. sqrt-pow1 99.8%

         \[\leadsto \left(1 - x\right) + y \cdot {\color{blue}{\left({x}^{\left(\frac{0.5}{2}\right)}\right)}}^{2} \]

      5. metadata-eval 99.8%

         \[\leadsto \left(1 - x\right) + y \cdot {\left({x}^{\color{blue}{0.25}}\right)}^{2} \]

   4. Applied egg-rr 99.8%

      \[\leadsto \left(1 - x\right) + y \cdot \color{blue}{{\left({x}^{0.25}\right)}^{2}} \]

   5. Taylor expanded in y around 0 67.9%

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

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.8 \cdot 10^{+178}:\\ \;\;\;\;\frac{1 - x \cdot x}{x}\\ \mathbf{else}:\\ \;\;\;\;1 - x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 61.4% accurate, 15.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 0.0175:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= x 0.0175) 1.0 (- x)))

C

double code(double x, double y) {
	double tmp;
	if (x <= 0.0175) {
		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 <= 0.0175d0) 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 <= 0.0175) {
		tmp = 1.0;
	} else {
		tmp = -x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 0.0175:
		tmp = 1.0
	else:
		tmp = -x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 0.0175)
		tmp = 1.0;
	else
		tmp = Float64(-x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= 0.0175)
		tmp = 1.0;
	else
		tmp = -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 0.0175], 1.0, (-x)]

Derivation

1. Split input into 2 regimes

2. if x < 0.017500000000000002

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 99.5%

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

   4. Taylor expanded in y around 0 59.3%

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

   if 0.017500000000000002 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 98.2%

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

   4. Taylor expanded in y around 0 61.9%

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

      1. neg-mul-1 61.9%

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

   6. Simplified 61.9%

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

Alternative 11: 62.6% 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 99.8%

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

   2. pow2 99.8%

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

   3. pow1/2 99.8%

      \[\leadsto \left(1 - x\right) + y \cdot {\left(\sqrt{\color{blue}{{x}^{0.5}}}\right)}^{2} \]

   4. sqrt-pow1 99.8%

      \[\leadsto \left(1 - x\right) + y \cdot {\color{blue}{\left({x}^{\left(\frac{0.5}{2}\right)}\right)}}^{2} \]

   5. metadata-eval 99.8%

      \[\leadsto \left(1 - x\right) + y \cdot {\left({x}^{\color{blue}{0.25}}\right)}^{2} \]

4. Applied egg-rr 99.8%

   \[\leadsto \left(1 - x\right) + y \cdot \color{blue}{{\left({x}^{0.25}\right)}^{2}} \]

5. Taylor expanded in y around 0 61.6%

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

Alternative 12: 30.6% 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 68.1%

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

4. Taylor expanded in y around 0 29.9%

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

Reproduce

herbie shell --seed 2024129 
(FPCore (x y)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, E"
  :precision binary64
  (+ (- 1.0 x) (* y (sqrt x))))