Diagrams.Trail:splitAtParam from diagrams-lib-1.3.0.3, D

Percentage Accurate: 66.4% → 99.9%

Time: 13.8s

Alternatives: 14

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return 1.0 - (((1.0 - x) * y) / (y + 1.0))

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 66.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return 1.0 - (((1.0 - x) * y) / (y + 1.0))

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x - \frac{\left(x + -1\right) + \frac{x + -1}{y} \cdot \left(\frac{1}{y} + -1\right)}{y}\\ \mathbf{if}\;y \leq -10500:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 6200:\\ \;\;\;\;1 - \frac{\left(1 - x\right) \cdot y}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0
         (- x (/ (+ (+ x -1.0) (* (/ (+ x -1.0) y) (+ (/ 1.0 y) -1.0))) y))))
   (if (<= y -10500.0)
     t_0
     (if (<= y 6200.0) (- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0))) t_0))))

C

double code(double x, double y) {
	double t_0 = x - (((x + -1.0) + (((x + -1.0) / y) * ((1.0 / y) + -1.0))) / y);
	double tmp;
	if (y <= -10500.0) {
		tmp = t_0;
	} else if (y <= 6200.0) {
		tmp = 1.0 - (((1.0 - x) * y) / (y + 1.0));
	} else {
		tmp = t_0;
	}
	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 = x - (((x + (-1.0d0)) + (((x + (-1.0d0)) / y) * ((1.0d0 / y) + (-1.0d0)))) / y)
    if (y <= (-10500.0d0)) then
        tmp = t_0
    else if (y <= 6200.0d0) then
        tmp = 1.0d0 - (((1.0d0 - x) * y) / (y + 1.0d0))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = x - (((x + -1.0) + (((x + -1.0) / y) * ((1.0 / y) + -1.0))) / y);
	double tmp;
	if (y <= -10500.0) {
		tmp = t_0;
	} else if (y <= 6200.0) {
		tmp = 1.0 - (((1.0 - x) * y) / (y + 1.0));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x - (((x + -1.0) + (((x + -1.0) / y) * ((1.0 / y) + -1.0))) / y)
	tmp = 0
	if y <= -10500.0:
		tmp = t_0
	elif y <= 6200.0:
		tmp = 1.0 - (((1.0 - x) * y) / (y + 1.0))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x - Float64(Float64(Float64(x + -1.0) + Float64(Float64(Float64(x + -1.0) / y) * Float64(Float64(1.0 / y) + -1.0))) / y))
	tmp = 0.0
	if (y <= -10500.0)
		tmp = t_0;
	elseif (y <= 6200.0)
		tmp = Float64(1.0 - Float64(Float64(Float64(1.0 - x) * y) / Float64(y + 1.0)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = x - (((x + -1.0) + (((x + -1.0) / y) * ((1.0 / y) + -1.0))) / y);
	tmp = 0.0;
	if (y <= -10500.0)
		tmp = t_0;
	elseif (y <= 6200.0)
		tmp = 1.0 - (((1.0 - x) * y) / (y + 1.0));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x - N[(N[(N[(x + -1.0), $MachinePrecision] + N[(N[(N[(x + -1.0), $MachinePrecision] / y), $MachinePrecision] * N[(N[(1.0 / y), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -10500.0], t$95$0, If[LessEqual[y, 6200.0], N[(1.0 - N[(N[(N[(1.0 - x), $MachinePrecision] * y), $MachinePrecision] / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -10500 or 6200 < y

   1. Initial program 33.9%

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

   3. Taylor expanded in y around -inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -10500 < y < 6200

   1. Initial program 99.9%

      \[1 - \frac{\left(1 - x\right) \cdot y}{y + 1} \]
   2. Add Preprocessing
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 2: 85.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x - \frac{x}{y}\\ \mathbf{if}\;y \leq -1.08 \cdot 10^{+70}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{+33}:\\ \;\;\;\;\frac{1}{y}\\ \mathbf{elif}\;y \leq -1:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 9.5:\\ \;\;\;\;x \cdot y + 1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (- x (/ x y))))
   (if (<= y -1.08e+70)
     x
     (if (<= y -2.1e+33)
       (/ 1.0 y)
       (if (<= y -1.0) t_0 (if (<= y 9.5) (+ (* x y) 1.0) t_0))))))

C

double code(double x, double y) {
	double t_0 = x - (x / y);
	double tmp;
	if (y <= -1.08e+70) {
		tmp = x;
	} else if (y <= -2.1e+33) {
		tmp = 1.0 / y;
	} else if (y <= -1.0) {
		tmp = t_0;
	} else if (y <= 9.5) {
		tmp = (x * y) + 1.0;
	} else {
		tmp = t_0;
	}
	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 = x - (x / y)
    if (y <= (-1.08d+70)) then
        tmp = x
    else if (y <= (-2.1d+33)) then
        tmp = 1.0d0 / y
    else if (y <= (-1.0d0)) then
        tmp = t_0
    else if (y <= 9.5d0) then
        tmp = (x * y) + 1.0d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = x - (x / y);
	double tmp;
	if (y <= -1.08e+70) {
		tmp = x;
	} else if (y <= -2.1e+33) {
		tmp = 1.0 / y;
	} else if (y <= -1.0) {
		tmp = t_0;
	} else if (y <= 9.5) {
		tmp = (x * y) + 1.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x - (x / y)
	tmp = 0
	if y <= -1.08e+70:
		tmp = x
	elif y <= -2.1e+33:
		tmp = 1.0 / y
	elif y <= -1.0:
		tmp = t_0
	elif y <= 9.5:
		tmp = (x * y) + 1.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x - Float64(x / y))
	tmp = 0.0
	if (y <= -1.08e+70)
		tmp = x;
	elseif (y <= -2.1e+33)
		tmp = Float64(1.0 / y);
	elseif (y <= -1.0)
		tmp = t_0;
	elseif (y <= 9.5)
		tmp = Float64(Float64(x * y) + 1.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = x - (x / y);
	tmp = 0.0;
	if (y <= -1.08e+70)
		tmp = x;
	elseif (y <= -2.1e+33)
		tmp = 1.0 / y;
	elseif (y <= -1.0)
		tmp = t_0;
	elseif (y <= 9.5)
		tmp = (x * y) + 1.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x - N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.08e+70], x, If[LessEqual[y, -2.1e+33], N[(1.0 / y), $MachinePrecision], If[LessEqual[y, -1.0], t$95$0, If[LessEqual[y, 9.5], N[(N[(x * y), $MachinePrecision] + 1.0), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.0799999999999999e70

   1. Initial program 32.4%

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

   3. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -1.0799999999999999e70 < y < -2.1000000000000001e33

   1. Initial program 18.3%

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

   3. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   if -2.1000000000000001e33 < y < -1 or 9.5 < y

   1. Initial program 38.3%

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

   3. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   if -1 < y < 9.5

   1. Initial program 99.9%

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

   4. Applied egg-rr 0

      \[\leadsto expr\]

   5. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 3: 85.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.08 \cdot 10^{+70}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -7 \cdot 10^{+33}:\\ \;\;\;\;\frac{1}{y}\\ \mathbf{elif}\;y \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 27:\\ \;\;\;\;x \cdot y + 1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.08e+70)
   x
   (if (<= y -7e+33)
     (/ 1.0 y)
     (if (<= y -1.0) x (if (<= y 27.0) (+ (* x y) 1.0) x)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.08e+70) {
		tmp = x;
	} else if (y <= -7e+33) {
		tmp = 1.0 / y;
	} else if (y <= -1.0) {
		tmp = x;
	} else if (y <= 27.0) {
		tmp = (x * y) + 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 (y <= (-1.08d+70)) then
        tmp = x
    else if (y <= (-7d+33)) then
        tmp = 1.0d0 / y
    else if (y <= (-1.0d0)) then
        tmp = x
    else if (y <= 27.0d0) then
        tmp = (x * y) + 1.0d0
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -1.08e+70) {
		tmp = x;
	} else if (y <= -7e+33) {
		tmp = 1.0 / y;
	} else if (y <= -1.0) {
		tmp = x;
	} else if (y <= 27.0) {
		tmp = (x * y) + 1.0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.08e+70:
		tmp = x
	elif y <= -7e+33:
		tmp = 1.0 / y
	elif y <= -1.0:
		tmp = x
	elif y <= 27.0:
		tmp = (x * y) + 1.0
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.08e+70)
		tmp = x;
	elseif (y <= -7e+33)
		tmp = Float64(1.0 / y);
	elseif (y <= -1.0)
		tmp = x;
	elseif (y <= 27.0)
		tmp = Float64(Float64(x * y) + 1.0);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.08e+70)
		tmp = x;
	elseif (y <= -7e+33)
		tmp = 1.0 / y;
	elseif (y <= -1.0)
		tmp = x;
	elseif (y <= 27.0)
		tmp = (x * y) + 1.0;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.08e+70], x, If[LessEqual[y, -7e+33], N[(1.0 / y), $MachinePrecision], If[LessEqual[y, -1.0], x, If[LessEqual[y, 27.0], N[(N[(x * y), $MachinePrecision] + 1.0), $MachinePrecision], x]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.0799999999999999e70 or -7.0000000000000002e33 < y < -1 or 27 < y

   1. Initial program 36.0%

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

   3. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -1.0799999999999999e70 < y < -7.0000000000000002e33

   1. Initial program 18.3%

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

   3. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   if -1 < y < 27

   1. Initial program 99.9%

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

   4. Applied egg-rr 0

      \[\leadsto expr\]

   5. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 4: 73.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.04 \cdot 10^{+70}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{+33}:\\ \;\;\;\;\frac{1}{y}\\ \mathbf{elif}\;y \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-17}:\\ \;\;\;\;1 - y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.04e+70)
   x
   (if (<= y -9.5e+33)
     (/ 1.0 y)
     (if (<= y -1.0) x (if (<= y 6.5e-17) (- 1.0 y) x)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.04e+70) {
		tmp = x;
	} else if (y <= -9.5e+33) {
		tmp = 1.0 / y;
	} else if (y <= -1.0) {
		tmp = x;
	} else if (y <= 6.5e-17) {
		tmp = 1.0 - y;
	} 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 (y <= (-1.04d+70)) then
        tmp = x
    else if (y <= (-9.5d+33)) then
        tmp = 1.0d0 / y
    else if (y <= (-1.0d0)) then
        tmp = x
    else if (y <= 6.5d-17) then
        tmp = 1.0d0 - y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -1.04e+70) {
		tmp = x;
	} else if (y <= -9.5e+33) {
		tmp = 1.0 / y;
	} else if (y <= -1.0) {
		tmp = x;
	} else if (y <= 6.5e-17) {
		tmp = 1.0 - y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.04e+70:
		tmp = x
	elif y <= -9.5e+33:
		tmp = 1.0 / y
	elif y <= -1.0:
		tmp = x
	elif y <= 6.5e-17:
		tmp = 1.0 - y
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.04e+70)
		tmp = x;
	elseif (y <= -9.5e+33)
		tmp = Float64(1.0 / y);
	elseif (y <= -1.0)
		tmp = x;
	elseif (y <= 6.5e-17)
		tmp = Float64(1.0 - y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.04e+70)
		tmp = x;
	elseif (y <= -9.5e+33)
		tmp = 1.0 / y;
	elseif (y <= -1.0)
		tmp = x;
	elseif (y <= 6.5e-17)
		tmp = 1.0 - y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.04e+70], x, If[LessEqual[y, -9.5e+33], N[(1.0 / y), $MachinePrecision], If[LessEqual[y, -1.0], x, If[LessEqual[y, 6.5e-17], N[(1.0 - y), $MachinePrecision], x]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.0400000000000001e70 or -9.5000000000000003e33 < y < -1 or 6.4999999999999996e-17 < y

   1. Initial program 37.9%

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

   3. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -1.0400000000000001e70 < y < -9.5000000000000003e33

   1. Initial program 18.3%

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

   3. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   if -1 < y < 6.4999999999999996e-17

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 5: 99.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{1}{y} + -1\\ \mathbf{if}\;y \leq -8400000000:\\ \;\;\;\;x + \frac{\left(x + -1\right) \cdot t\_0}{y}\\ \mathbf{elif}\;y \leq 280000:\\ \;\;\;\;1 - \frac{\left(1 - x\right) \cdot y}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{x + -1}{y} \cdot t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ (/ 1.0 y) -1.0)))
   (if (<= y -8400000000.0)
     (+ x (/ (* (+ x -1.0) t_0) y))
     (if (<= y 280000.0)
       (- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
       (+ x (* (/ (+ x -1.0) y) t_0))))))

C

double code(double x, double y) {
	double t_0 = (1.0 / y) + -1.0;
	double tmp;
	if (y <= -8400000000.0) {
		tmp = x + (((x + -1.0) * t_0) / y);
	} else if (y <= 280000.0) {
		tmp = 1.0 - (((1.0 - x) * y) / (y + 1.0));
	} else {
		tmp = x + (((x + -1.0) / y) * t_0);
	}
	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 / y) + (-1.0d0)
    if (y <= (-8400000000.0d0)) then
        tmp = x + (((x + (-1.0d0)) * t_0) / y)
    else if (y <= 280000.0d0) then
        tmp = 1.0d0 - (((1.0d0 - x) * y) / (y + 1.0d0))
    else
        tmp = x + (((x + (-1.0d0)) / y) * t_0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = (1.0 / y) + -1.0;
	double tmp;
	if (y <= -8400000000.0) {
		tmp = x + (((x + -1.0) * t_0) / y);
	} else if (y <= 280000.0) {
		tmp = 1.0 - (((1.0 - x) * y) / (y + 1.0));
	} else {
		tmp = x + (((x + -1.0) / y) * t_0);
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (1.0 / y) + -1.0
	tmp = 0
	if y <= -8400000000.0:
		tmp = x + (((x + -1.0) * t_0) / y)
	elif y <= 280000.0:
		tmp = 1.0 - (((1.0 - x) * y) / (y + 1.0))
	else:
		tmp = x + (((x + -1.0) / y) * t_0)
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(1.0 / y) + -1.0)
	tmp = 0.0
	if (y <= -8400000000.0)
		tmp = Float64(x + Float64(Float64(Float64(x + -1.0) * t_0) / y));
	elseif (y <= 280000.0)
		tmp = Float64(1.0 - Float64(Float64(Float64(1.0 - x) * y) / Float64(y + 1.0)));
	else
		tmp = Float64(x + Float64(Float64(Float64(x + -1.0) / y) * t_0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = (1.0 / y) + -1.0;
	tmp = 0.0;
	if (y <= -8400000000.0)
		tmp = x + (((x + -1.0) * t_0) / y);
	elseif (y <= 280000.0)
		tmp = 1.0 - (((1.0 - x) * y) / (y + 1.0));
	else
		tmp = x + (((x + -1.0) / y) * t_0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(1.0 / y), $MachinePrecision] + -1.0), $MachinePrecision]}, If[LessEqual[y, -8400000000.0], N[(x + N[(N[(N[(x + -1.0), $MachinePrecision] * t$95$0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 280000.0], N[(1.0 - N[(N[(N[(1.0 - x), $MachinePrecision] * y), $MachinePrecision] / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(N[(x + -1.0), $MachinePrecision] / y), $MachinePrecision] * t$95$0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.4e9

   1. Initial program 32.6%

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

   4. Applied egg-rr 0

      \[\leadsto expr\]

   5. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if -8.4e9 < y < 2.8e5

   1. Initial program 99.9%

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

   if 2.8e5 < y

   1. Initial program 33.2%

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

   3. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 6: 99.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + \frac{x + -1}{y} \cdot \left(\frac{1}{y} + -1\right)\\ \mathbf{if}\;y \leq -8400000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 260000:\\ \;\;\;\;1 - \frac{\left(1 - x\right) \cdot y}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ x (* (/ (+ x -1.0) y) (+ (/ 1.0 y) -1.0)))))
   (if (<= y -8400000000.0)
     t_0
     (if (<= y 260000.0) (- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0))) t_0))))

C

double code(double x, double y) {
	double t_0 = x + (((x + -1.0) / y) * ((1.0 / y) + -1.0));
	double tmp;
	if (y <= -8400000000.0) {
		tmp = t_0;
	} else if (y <= 260000.0) {
		tmp = 1.0 - (((1.0 - x) * y) / (y + 1.0));
	} else {
		tmp = t_0;
	}
	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 = x + (((x + (-1.0d0)) / y) * ((1.0d0 / y) + (-1.0d0)))
    if (y <= (-8400000000.0d0)) then
        tmp = t_0
    else if (y <= 260000.0d0) then
        tmp = 1.0d0 - (((1.0d0 - x) * y) / (y + 1.0d0))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = x + (((x + -1.0) / y) * ((1.0 / y) + -1.0));
	double tmp;
	if (y <= -8400000000.0) {
		tmp = t_0;
	} else if (y <= 260000.0) {
		tmp = 1.0 - (((1.0 - x) * y) / (y + 1.0));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x + (((x + -1.0) / y) * ((1.0 / y) + -1.0))
	tmp = 0
	if y <= -8400000000.0:
		tmp = t_0
	elif y <= 260000.0:
		tmp = 1.0 - (((1.0 - x) * y) / (y + 1.0))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x + Float64(Float64(Float64(x + -1.0) / y) * Float64(Float64(1.0 / y) + -1.0)))
	tmp = 0.0
	if (y <= -8400000000.0)
		tmp = t_0;
	elseif (y <= 260000.0)
		tmp = Float64(1.0 - Float64(Float64(Float64(1.0 - x) * y) / Float64(y + 1.0)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = x + (((x + -1.0) / y) * ((1.0 / y) + -1.0));
	tmp = 0.0;
	if (y <= -8400000000.0)
		tmp = t_0;
	elseif (y <= 260000.0)
		tmp = 1.0 - (((1.0 - x) * y) / (y + 1.0));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x + N[(N[(N[(x + -1.0), $MachinePrecision] / y), $MachinePrecision] * N[(N[(1.0 / y), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -8400000000.0], t$95$0, If[LessEqual[y, 260000.0], N[(1.0 - N[(N[(N[(1.0 - x), $MachinePrecision] * y), $MachinePrecision] / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -8.4e9 or 2.6e5 < y

   1. Initial program 32.9%

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

   3. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -8.4e9 < y < 2.6e5

   1. Initial program 99.9%

      \[1 - \frac{\left(1 - x\right) \cdot y}{y + 1} \]
   2. Add Preprocessing
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 99.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + \frac{1 - x}{y}\\ \mathbf{if}\;y \leq -125000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 2700000000:\\ \;\;\;\;1 - \frac{y}{1 + y} \cdot \left(1 - x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ x (/ (- 1.0 x) y))))
   (if (<= y -125000000.0)
     t_0
     (if (<= y 2700000000.0) (- 1.0 (* (/ y (+ 1.0 y)) (- 1.0 x))) t_0))))

C

double code(double x, double y) {
	double t_0 = x + ((1.0 - x) / y);
	double tmp;
	if (y <= -125000000.0) {
		tmp = t_0;
	} else if (y <= 2700000000.0) {
		tmp = 1.0 - ((y / (1.0 + y)) * (1.0 - x));
	} else {
		tmp = t_0;
	}
	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 = x + ((1.0d0 - x) / y)
    if (y <= (-125000000.0d0)) then
        tmp = t_0
    else if (y <= 2700000000.0d0) then
        tmp = 1.0d0 - ((y / (1.0d0 + y)) * (1.0d0 - x))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = x + ((1.0 - x) / y);
	double tmp;
	if (y <= -125000000.0) {
		tmp = t_0;
	} else if (y <= 2700000000.0) {
		tmp = 1.0 - ((y / (1.0 + y)) * (1.0 - x));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x + ((1.0 - x) / y)
	tmp = 0
	if y <= -125000000.0:
		tmp = t_0
	elif y <= 2700000000.0:
		tmp = 1.0 - ((y / (1.0 + y)) * (1.0 - x))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x + Float64(Float64(1.0 - x) / y))
	tmp = 0.0
	if (y <= -125000000.0)
		tmp = t_0;
	elseif (y <= 2700000000.0)
		tmp = Float64(1.0 - Float64(Float64(y / Float64(1.0 + y)) * Float64(1.0 - x)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = x + ((1.0 - x) / y);
	tmp = 0.0;
	if (y <= -125000000.0)
		tmp = t_0;
	elseif (y <= 2700000000.0)
		tmp = 1.0 - ((y / (1.0 + y)) * (1.0 - x));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x + N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -125000000.0], t$95$0, If[LessEqual[y, 2700000000.0], N[(1.0 - N[(N[(y / N[(1.0 + y), $MachinePrecision]), $MachinePrecision] * N[(1.0 - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.25e8 or 2.7e9 < y

   1. Initial program 32.7%

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

   3. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -1.25e8 < y < 2.7e9

   1. Initial program 99.6%

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

   4. Applied egg-rr 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 8: 98.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + \frac{1 - x}{y}\\ \mathbf{if}\;y \leq -1:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;1 - y \cdot \left(\left(x + -1\right) \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if y < -1 or 1 < y

   1. Initial program 34.8%

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

   3. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -1 < y < 1

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 9: 98.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + \frac{1 - x}{y}\\ \mathbf{if}\;y \leq -700000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 27000000:\\ \;\;\;\;1 - x \cdot \frac{y}{-1 - y}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ x (/ (- 1.0 x) y))))
   (if (<= y -700000.0)
     t_0
     (if (<= y 27000000.0) (- 1.0 (* x (/ y (- -1.0 y)))) t_0))))

C

double code(double x, double y) {
	double t_0 = x + ((1.0 - x) / y);
	double tmp;
	if (y <= -700000.0) {
		tmp = t_0;
	} else if (y <= 27000000.0) {
		tmp = 1.0 - (x * (y / (-1.0 - y)));
	} else {
		tmp = t_0;
	}
	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 = x + ((1.0d0 - x) / y)
    if (y <= (-700000.0d0)) then
        tmp = t_0
    else if (y <= 27000000.0d0) then
        tmp = 1.0d0 - (x * (y / ((-1.0d0) - y)))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = x + ((1.0 - x) / y);
	double tmp;
	if (y <= -700000.0) {
		tmp = t_0;
	} else if (y <= 27000000.0) {
		tmp = 1.0 - (x * (y / (-1.0 - y)));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x + ((1.0 - x) / y)
	tmp = 0
	if y <= -700000.0:
		tmp = t_0
	elif y <= 27000000.0:
		tmp = 1.0 - (x * (y / (-1.0 - y)))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x + Float64(Float64(1.0 - x) / y))
	tmp = 0.0
	if (y <= -700000.0)
		tmp = t_0;
	elseif (y <= 27000000.0)
		tmp = Float64(1.0 - Float64(x * Float64(y / Float64(-1.0 - y))));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = x + ((1.0 - x) / y);
	tmp = 0.0;
	if (y <= -700000.0)
		tmp = t_0;
	elseif (y <= 27000000.0)
		tmp = 1.0 - (x * (y / (-1.0 - y)));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x + N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -700000.0], t$95$0, If[LessEqual[y, 27000000.0], N[(1.0 - N[(x * N[(y / N[(-1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -7e5 or 2.7e7 < y

   1. Initial program 32.9%

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

   3. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -7e5 < y < 2.7e7

   1. Initial program 99.9%

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

   4. Applied egg-rr 0

      \[\leadsto expr\]

   5. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 10: 98.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + \frac{1 - x}{y}\\ \mathbf{if}\;y \leq -1:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;1 - y \cdot \left(1 - x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if y < -1 or 1 < y

   1. Initial program 34.8%

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

   3. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -1 < y < 1

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 11: 98.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + \frac{1 - x}{y}\\ \mathbf{if}\;y \leq -1:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1.22:\\ \;\;\;\;x \cdot y + 1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ x (/ (- 1.0 x) y))))
   (if (<= y -1.0) t_0 (if (<= y 1.22) (+ (* x y) 1.0) t_0))))

C

double code(double x, double y) {
	double t_0 = x + ((1.0 - x) / y);
	double tmp;
	if (y <= -1.0) {
		tmp = t_0;
	} else if (y <= 1.22) {
		tmp = (x * y) + 1.0;
	} else {
		tmp = t_0;
	}
	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 = x + ((1.0d0 - x) / y)
    if (y <= (-1.0d0)) then
        tmp = t_0
    else if (y <= 1.22d0) then
        tmp = (x * y) + 1.0d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = x + ((1.0 - x) / y);
	double tmp;
	if (y <= -1.0) {
		tmp = t_0;
	} else if (y <= 1.22) {
		tmp = (x * y) + 1.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x + ((1.0 - x) / y)
	tmp = 0
	if y <= -1.0:
		tmp = t_0
	elif y <= 1.22:
		tmp = (x * y) + 1.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x + Float64(Float64(1.0 - x) / y))
	tmp = 0.0
	if (y <= -1.0)
		tmp = t_0;
	elseif (y <= 1.22)
		tmp = Float64(Float64(x * y) + 1.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = x + ((1.0 - x) / y);
	tmp = 0.0;
	if (y <= -1.0)
		tmp = t_0;
	elseif (y <= 1.22)
		tmp = (x * y) + 1.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x + N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.0], t$95$0, If[LessEqual[y, 1.22], N[(N[(x * y), $MachinePrecision] + 1.0), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 1.21999999999999997 < y

   1. Initial program 34.8%

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

   3. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -1 < y < 1.21999999999999997

   1. Initial program 99.9%

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

   4. Applied egg-rr 0

      \[\leadsto expr\]

   5. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 12: 73.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-17}:\\ \;\;\;\;1 - y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.0) x (if (<= y 6.5e-17) (- 1.0 y) x)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = x;
	} else if (y <= 6.5e-17) {
		tmp = 1.0 - y;
	} 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 (y <= (-1.0d0)) then
        tmp = x
    else if (y <= 6.5d-17) then
        tmp = 1.0d0 - y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = x;
	} else if (y <= 6.5e-17) {
		tmp = 1.0 - y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = x
	elif y <= 6.5e-17:
		tmp = 1.0 - y
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.0)
		tmp = x;
	elseif (y <= 6.5e-17)
		tmp = Float64(1.0 - y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.0)
		tmp = x;
	elseif (y <= 6.5e-17)
		tmp = 1.0 - y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.0], x, If[LessEqual[y, 6.5e-17], N[(1.0 - y), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 6.4999999999999996e-17 < y

   1. Initial program 36.6%

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

   3. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -1 < y < 6.4999999999999996e-17

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 13: 73.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-17}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= y -1.0) x (if (<= y 6.5e-17) 1.0 x)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = x;
	} else if (y <= 6.5e-17) {
		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 (y <= (-1.0d0)) then
        tmp = x
    else if (y <= 6.5d-17) 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 (y <= -1.0) {
		tmp = x;
	} else if (y <= 6.5e-17) {
		tmp = 1.0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = x
	elif y <= 6.5e-17:
		tmp = 1.0
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.0)
		tmp = x;
	elseif (y <= 6.5e-17)
		tmp = 1.0;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.0)
		tmp = x;
	elseif (y <= 6.5e-17)
		tmp = 1.0;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.0], x, If[LessEqual[y, 6.5e-17], 1.0, x]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 6.4999999999999996e-17 < y

   1. Initial program 36.6%

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

   3. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -1 < y < 6.4999999999999996e-17

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 14: 39.5% accurate, 11.0× 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 64.8%

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

3. Taylor expanded in y around 0 0

   \[\leadsto expr\]

5. Simplified 0

   \[\leadsto expr\]
6. Add Preprocessing

Developer target: 99.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{1}{y} - \left(\frac{x}{y} - x\right)\\ \mathbf{if}\;y < -3693.8482788297247:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y < 6799310503.41891:\\ \;\;\;\;1 - \frac{\left(1 - x\right) \cdot y}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (- (/ 1.0 y) (- (/ x y) x))))
   (if (< y -3693.8482788297247)
     t_0
     (if (< y 6799310503.41891) (- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0))) t_0))))

C

double code(double x, double y) {
	double t_0 = (1.0 / y) - ((x / y) - x);
	double tmp;
	if (y < -3693.8482788297247) {
		tmp = t_0;
	} else if (y < 6799310503.41891) {
		tmp = 1.0 - (((1.0 - x) * y) / (y + 1.0));
	} else {
		tmp = t_0;
	}
	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 / y) - ((x / y) - x)
    if (y < (-3693.8482788297247d0)) then
        tmp = t_0
    else if (y < 6799310503.41891d0) then
        tmp = 1.0d0 - (((1.0d0 - x) * y) / (y + 1.0d0))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = (1.0 / y) - ((x / y) - x);
	double tmp;
	if (y < -3693.8482788297247) {
		tmp = t_0;
	} else if (y < 6799310503.41891) {
		tmp = 1.0 - (((1.0 - x) * y) / (y + 1.0));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (1.0 / y) - ((x / y) - x)
	tmp = 0
	if y < -3693.8482788297247:
		tmp = t_0
	elif y < 6799310503.41891:
		tmp = 1.0 - (((1.0 - x) * y) / (y + 1.0))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(1.0 / y) - Float64(Float64(x / y) - x))
	tmp = 0.0
	if (y < -3693.8482788297247)
		tmp = t_0;
	elseif (y < 6799310503.41891)
		tmp = Float64(1.0 - Float64(Float64(Float64(1.0 - x) * y) / Float64(y + 1.0)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = (1.0 / y) - ((x / y) - x);
	tmp = 0.0;
	if (y < -3693.8482788297247)
		tmp = t_0;
	elseif (y < 6799310503.41891)
		tmp = 1.0 - (((1.0 - x) * y) / (y + 1.0));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(1.0 / y), $MachinePrecision] - N[(N[(x / y), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]}, If[Less[y, -3693.8482788297247], t$95$0, If[Less[y, 6799310503.41891], N[(1.0 - N[(N[(N[(1.0 - x), $MachinePrecision] * y), $MachinePrecision] / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Reproduce

herbie shell --seed 2024110 
(FPCore (x y)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, D"
  :precision binary64

  :alt
  (if (< y -3693.8482788297247) (- (/ 1.0 y) (- (/ x y) x)) (if (< y 6799310503.41891) (- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0))) (- (/ 1.0 y) (- (/ x y) x))))

  (- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0))))