Data.Colour.SRGB:invTransferFunction from colour-2.3.3

Percentage Accurate: 100.0% → 100.0%

Time: 4.1s

Alternatives: 9

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \frac{x + y}{y + 1} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x + y}{y + 1} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x + y}{y + 1} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[\frac{x + y}{y + 1} \]

2. Final simplification 100.0%

   \[\leadsto \frac{x + y}{y + 1} \]

Alternative 2: 71.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{y + 1}\\ \mathbf{if}\;y \leq -4.4 \cdot 10^{+14}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-75}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -4.4 \cdot 10^{-135}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-61}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-50}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+50}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+128}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 5.7 \cdot 10^{+177}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ x (+ y 1.0))))
   (if (<= y -4.4e+14)
     1.0
     (if (<= y -2.1e-75)
       t_0
       (if (<= y -4.4e-135)
         y
         (if (<= y 1.2e-61)
           t_0
           (if (<= y 6.5e-50)
             y
             (if (<= y 2.1e+50)
               t_0
               (if (<= y 2.6e+128)
                 1.0
                 (if (<= y 5.7e+177) (/ x y) 1.0))))))))))

C

double code(double x, double y) {
	double t_0 = x / (y + 1.0);
	double tmp;
	if (y <= -4.4e+14) {
		tmp = 1.0;
	} else if (y <= -2.1e-75) {
		tmp = t_0;
	} else if (y <= -4.4e-135) {
		tmp = y;
	} else if (y <= 1.2e-61) {
		tmp = t_0;
	} else if (y <= 6.5e-50) {
		tmp = y;
	} else if (y <= 2.1e+50) {
		tmp = t_0;
	} else if (y <= 2.6e+128) {
		tmp = 1.0;
	} else if (y <= 5.7e+177) {
		tmp = x / y;
	} else {
		tmp = 1.0;
	}
	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 / (y + 1.0d0)
    if (y <= (-4.4d+14)) then
        tmp = 1.0d0
    else if (y <= (-2.1d-75)) then
        tmp = t_0
    else if (y <= (-4.4d-135)) then
        tmp = y
    else if (y <= 1.2d-61) then
        tmp = t_0
    else if (y <= 6.5d-50) then
        tmp = y
    else if (y <= 2.1d+50) then
        tmp = t_0
    else if (y <= 2.6d+128) then
        tmp = 1.0d0
    else if (y <= 5.7d+177) then
        tmp = x / y
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = x / (y + 1.0);
	double tmp;
	if (y <= -4.4e+14) {
		tmp = 1.0;
	} else if (y <= -2.1e-75) {
		tmp = t_0;
	} else if (y <= -4.4e-135) {
		tmp = y;
	} else if (y <= 1.2e-61) {
		tmp = t_0;
	} else if (y <= 6.5e-50) {
		tmp = y;
	} else if (y <= 2.1e+50) {
		tmp = t_0;
	} else if (y <= 2.6e+128) {
		tmp = 1.0;
	} else if (y <= 5.7e+177) {
		tmp = x / y;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x / (y + 1.0)
	tmp = 0
	if y <= -4.4e+14:
		tmp = 1.0
	elif y <= -2.1e-75:
		tmp = t_0
	elif y <= -4.4e-135:
		tmp = y
	elif y <= 1.2e-61:
		tmp = t_0
	elif y <= 6.5e-50:
		tmp = y
	elif y <= 2.1e+50:
		tmp = t_0
	elif y <= 2.6e+128:
		tmp = 1.0
	elif y <= 5.7e+177:
		tmp = x / y
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x / Float64(y + 1.0))
	tmp = 0.0
	if (y <= -4.4e+14)
		tmp = 1.0;
	elseif (y <= -2.1e-75)
		tmp = t_0;
	elseif (y <= -4.4e-135)
		tmp = y;
	elseif (y <= 1.2e-61)
		tmp = t_0;
	elseif (y <= 6.5e-50)
		tmp = y;
	elseif (y <= 2.1e+50)
		tmp = t_0;
	elseif (y <= 2.6e+128)
		tmp = 1.0;
	elseif (y <= 5.7e+177)
		tmp = Float64(x / y);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = x / (y + 1.0);
	tmp = 0.0;
	if (y <= -4.4e+14)
		tmp = 1.0;
	elseif (y <= -2.1e-75)
		tmp = t_0;
	elseif (y <= -4.4e-135)
		tmp = y;
	elseif (y <= 1.2e-61)
		tmp = t_0;
	elseif (y <= 6.5e-50)
		tmp = y;
	elseif (y <= 2.1e+50)
		tmp = t_0;
	elseif (y <= 2.6e+128)
		tmp = 1.0;
	elseif (y <= 5.7e+177)
		tmp = x / y;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.4e+14], 1.0, If[LessEqual[y, -2.1e-75], t$95$0, If[LessEqual[y, -4.4e-135], y, If[LessEqual[y, 1.2e-61], t$95$0, If[LessEqual[y, 6.5e-50], y, If[LessEqual[y, 2.1e+50], t$95$0, If[LessEqual[y, 2.6e+128], 1.0, If[LessEqual[y, 5.7e+177], N[(x / y), $MachinePrecision], 1.0]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.4e14 or 2.1e50 < y < 2.6e128 or 5.70000000000000015e177 < y

   1. Initial program 100.0%

      \[\frac{x + y}{y + 1} \]

   2. Taylor expanded in y around inf 79.2%

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

   if -4.4e14 < y < -2.1000000000000001e-75 or -4.3999999999999999e-135 < y < 1.2e-61 or 6.49999999999999987e-50 < y < 2.1e50

   1. Initial program 100.0%

      \[\frac{x + y}{y + 1} \]

   2. Taylor expanded in x around inf 80.3%

      \[\leadsto \color{blue}{\frac{x}{1 + y}} \]
   3. Step-by-step derivation

      1. +-commutative 80.3%

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

   4. Simplified 80.3%

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

   if -2.1000000000000001e-75 < y < -4.3999999999999999e-135 or 1.2e-61 < y < 6.49999999999999987e-50

   1. Initial program 100.0%

      \[\frac{x + y}{y + 1} \]

   2. Taylor expanded in x around 0 77.0%

      \[\leadsto \color{blue}{\frac{y}{1 + y}} \]
   3. Step-by-step derivation

      1. +-commutative 77.0%

         \[\leadsto \frac{y}{\color{blue}{y + 1}} \]

   4. Simplified 77.0%

      \[\leadsto \color{blue}{\frac{y}{y + 1}} \]

   5. Taylor expanded in y around 0 77.0%

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

   if 2.6e128 < y < 5.70000000000000015e177

   1. Initial program 100.0%

      \[\frac{x + y}{y + 1} \]

   2. Taylor expanded in x around inf 70.4%

      \[\leadsto \color{blue}{\frac{x}{1 + y}} \]
   3. Step-by-step derivation

      1. +-commutative 70.4%

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

   4. Simplified 70.4%

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

   5. Taylor expanded in y around inf 70.4%

      \[\leadsto \color{blue}{\frac{x}{y}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+14}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-75}:\\ \;\;\;\;\frac{x}{y + 1}\\ \mathbf{elif}\;y \leq -4.4 \cdot 10^{-135}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-61}:\\ \;\;\;\;\frac{x}{y + 1}\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-50}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+50}:\\ \;\;\;\;\frac{x}{y + 1}\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+128}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 5.7 \cdot 10^{+177}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 3: 72.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-63}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 9.6 \cdot 10^{-50}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-8}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+49}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{+128}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 5.7 \cdot 10^{+177}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.0)
   1.0
   (if (<= y 3.6e-63)
     x
     (if (<= y 9.6e-50)
       y
       (if (<= y 7e-8)
         x
         (if (<= y 1.6e+49)
           (/ x y)
           (if (<= y 5.4e+128) 1.0 (if (<= y 5.7e+177) (/ x y) 1.0))))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = 1.0;
	} else if (y <= 3.6e-63) {
		tmp = x;
	} else if (y <= 9.6e-50) {
		tmp = y;
	} else if (y <= 7e-8) {
		tmp = x;
	} else if (y <= 1.6e+49) {
		tmp = x / y;
	} else if (y <= 5.4e+128) {
		tmp = 1.0;
	} else if (y <= 5.7e+177) {
		tmp = x / y;
	} else {
		tmp = 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 <= (-1.0d0)) then
        tmp = 1.0d0
    else if (y <= 3.6d-63) then
        tmp = x
    else if (y <= 9.6d-50) then
        tmp = y
    else if (y <= 7d-8) then
        tmp = x
    else if (y <= 1.6d+49) then
        tmp = x / y
    else if (y <= 5.4d+128) then
        tmp = 1.0d0
    else if (y <= 5.7d+177) then
        tmp = x / y
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = 1.0;
	} else if (y <= 3.6e-63) {
		tmp = x;
	} else if (y <= 9.6e-50) {
		tmp = y;
	} else if (y <= 7e-8) {
		tmp = x;
	} else if (y <= 1.6e+49) {
		tmp = x / y;
	} else if (y <= 5.4e+128) {
		tmp = 1.0;
	} else if (y <= 5.7e+177) {
		tmp = x / y;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = 1.0
	elif y <= 3.6e-63:
		tmp = x
	elif y <= 9.6e-50:
		tmp = y
	elif y <= 7e-8:
		tmp = x
	elif y <= 1.6e+49:
		tmp = x / y
	elif y <= 5.4e+128:
		tmp = 1.0
	elif y <= 5.7e+177:
		tmp = x / y
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.0)
		tmp = 1.0;
	elseif (y <= 3.6e-63)
		tmp = x;
	elseif (y <= 9.6e-50)
		tmp = y;
	elseif (y <= 7e-8)
		tmp = x;
	elseif (y <= 1.6e+49)
		tmp = Float64(x / y);
	elseif (y <= 5.4e+128)
		tmp = 1.0;
	elseif (y <= 5.7e+177)
		tmp = Float64(x / y);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.0)
		tmp = 1.0;
	elseif (y <= 3.6e-63)
		tmp = x;
	elseif (y <= 9.6e-50)
		tmp = y;
	elseif (y <= 7e-8)
		tmp = x;
	elseif (y <= 1.6e+49)
		tmp = x / y;
	elseif (y <= 5.4e+128)
		tmp = 1.0;
	elseif (y <= 5.7e+177)
		tmp = x / y;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.0], 1.0, If[LessEqual[y, 3.6e-63], x, If[LessEqual[y, 9.6e-50], y, If[LessEqual[y, 7e-8], x, If[LessEqual[y, 1.6e+49], N[(x / y), $MachinePrecision], If[LessEqual[y, 5.4e+128], 1.0, If[LessEqual[y, 5.7e+177], N[(x / y), $MachinePrecision], 1.0]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1 or 1.60000000000000007e49 < y < 5.40000000000000002e128 or 5.70000000000000015e177 < y

   1. Initial program 100.0%

      \[\frac{x + y}{y + 1} \]

   2. Taylor expanded in y around inf 75.7%

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

   if -1 < y < 3.60000000000000008e-63 or 9.60000000000000007e-50 < y < 7.00000000000000048e-8

   1. Initial program 100.0%

      \[\frac{x + y}{y + 1} \]

   2. Taylor expanded in y around 0 74.4%

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

   if 3.60000000000000008e-63 < y < 9.60000000000000007e-50

   1. Initial program 100.0%

      \[\frac{x + y}{y + 1} \]

   2. Taylor expanded in x around 0 90.4%

      \[\leadsto \color{blue}{\frac{y}{1 + y}} \]
   3. Step-by-step derivation

      1. +-commutative 90.4%

         \[\leadsto \frac{y}{\color{blue}{y + 1}} \]

   4. Simplified 90.4%

      \[\leadsto \color{blue}{\frac{y}{y + 1}} \]

   5. Taylor expanded in y around 0 90.4%

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

   if 7.00000000000000048e-8 < y < 1.60000000000000007e49 or 5.40000000000000002e128 < y < 5.70000000000000015e177

   1. Initial program 99.9%

      \[\frac{x + y}{y + 1} \]

   2. Taylor expanded in x around inf 73.7%

      \[\leadsto \color{blue}{\frac{x}{1 + y}} \]
   3. Step-by-step derivation

      1. +-commutative 73.7%

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

   4. Simplified 73.7%

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

   5. Taylor expanded in y around inf 72.2%

      \[\leadsto \color{blue}{\frac{x}{y}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-63}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 9.6 \cdot 10^{-50}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-8}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+49}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{+128}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 5.7 \cdot 10^{+177}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 4: 74.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{y + 1}\\ \mathbf{if}\;x \leq -5.1 \cdot 10^{-9}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 1.32 \cdot 10^{-27}:\\ \;\;\;\;\frac{y}{y + 1}\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{+14}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{+68}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ x (+ y 1.0))))
   (if (<= x -5.1e-9)
     t_0
     (if (<= x 1.32e-27)
       (/ y (+ y 1.0))
       (if (<= x 1.2e+14) x (if (<= x 2.4e+68) 1.0 t_0))))))

C

double code(double x, double y) {
	double t_0 = x / (y + 1.0);
	double tmp;
	if (x <= -5.1e-9) {
		tmp = t_0;
	} else if (x <= 1.32e-27) {
		tmp = y / (y + 1.0);
	} else if (x <= 1.2e+14) {
		tmp = x;
	} else if (x <= 2.4e+68) {
		tmp = 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 / (y + 1.0d0)
    if (x <= (-5.1d-9)) then
        tmp = t_0
    else if (x <= 1.32d-27) then
        tmp = y / (y + 1.0d0)
    else if (x <= 1.2d+14) then
        tmp = x
    else if (x <= 2.4d+68) then
        tmp = 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 / (y + 1.0);
	double tmp;
	if (x <= -5.1e-9) {
		tmp = t_0;
	} else if (x <= 1.32e-27) {
		tmp = y / (y + 1.0);
	} else if (x <= 1.2e+14) {
		tmp = x;
	} else if (x <= 2.4e+68) {
		tmp = 1.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x / (y + 1.0)
	tmp = 0
	if x <= -5.1e-9:
		tmp = t_0
	elif x <= 1.32e-27:
		tmp = y / (y + 1.0)
	elif x <= 1.2e+14:
		tmp = x
	elif x <= 2.4e+68:
		tmp = 1.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x / Float64(y + 1.0))
	tmp = 0.0
	if (x <= -5.1e-9)
		tmp = t_0;
	elseif (x <= 1.32e-27)
		tmp = Float64(y / Float64(y + 1.0));
	elseif (x <= 1.2e+14)
		tmp = x;
	elseif (x <= 2.4e+68)
		tmp = 1.0;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = x / (y + 1.0);
	tmp = 0.0;
	if (x <= -5.1e-9)
		tmp = t_0;
	elseif (x <= 1.32e-27)
		tmp = y / (y + 1.0);
	elseif (x <= 1.2e+14)
		tmp = x;
	elseif (x <= 2.4e+68)
		tmp = 1.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -5.1e-9], t$95$0, If[LessEqual[x, 1.32e-27], N[(y / N[(y + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.2e+14], x, If[LessEqual[x, 2.4e+68], 1.0, t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -5.10000000000000017e-9 or 2.40000000000000008e68 < x

   1. Initial program 100.0%

      \[\frac{x + y}{y + 1} \]

   2. Taylor expanded in x around inf 80.6%

      \[\leadsto \color{blue}{\frac{x}{1 + y}} \]
   3. Step-by-step derivation

      1. +-commutative 80.6%

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

   4. Simplified 80.6%

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

   if -5.10000000000000017e-9 < x < 1.3200000000000001e-27

   1. Initial program 100.0%

      \[\frac{x + y}{y + 1} \]

   2. Taylor expanded in x around 0 82.9%

      \[\leadsto \color{blue}{\frac{y}{1 + y}} \]
   3. Step-by-step derivation

      1. +-commutative 82.9%

         \[\leadsto \frac{y}{\color{blue}{y + 1}} \]

   4. Simplified 82.9%

      \[\leadsto \color{blue}{\frac{y}{y + 1}} \]

   if 1.3200000000000001e-27 < x < 1.2e14

   1. Initial program 100.0%

      \[\frac{x + y}{y + 1} \]

   2. Taylor expanded in y around 0 85.0%

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

   if 1.2e14 < x < 2.40000000000000008e68

   1. Initial program 100.0%

      \[\frac{x + y}{y + 1} \]

   2. Taylor expanded in y around inf 69.2%

      \[\leadsto \color{blue}{1} \]
3. Recombined 4 regimes into one program.

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.1 \cdot 10^{-9}:\\ \;\;\;\;\frac{x}{y + 1}\\ \mathbf{elif}\;x \leq 1.32 \cdot 10^{-27}:\\ \;\;\;\;\frac{y}{y + 1}\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{+14}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{+68}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y + 1}\\ \end{array} \]

Alternative 5: 86.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + \frac{x}{y}\\ t_1 := \frac{x}{y + 1}\\ \mathbf{if}\;y \leq -950000000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-61}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-50}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 62000000000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ 1.0 (/ x y))) (t_1 (/ x (+ y 1.0))))
   (if (<= y -950000000.0)
     t_0
     (if (<= y 1.2e-61)
       t_1
       (if (<= y 6.8e-50) y (if (<= y 62000000000000.0) t_1 t_0))))))

C

double code(double x, double y) {
	double t_0 = 1.0 + (x / y);
	double t_1 = x / (y + 1.0);
	double tmp;
	if (y <= -950000000.0) {
		tmp = t_0;
	} else if (y <= 1.2e-61) {
		tmp = t_1;
	} else if (y <= 6.8e-50) {
		tmp = y;
	} else if (y <= 62000000000000.0) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_0 = 1.0d0 + (x / y)
    t_1 = x / (y + 1.0d0)
    if (y <= (-950000000.0d0)) then
        tmp = t_0
    else if (y <= 1.2d-61) then
        tmp = t_1
    else if (y <= 6.8d-50) then
        tmp = y
    else if (y <= 62000000000000.0d0) then
        tmp = t_1
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = 1.0 + (x / y);
	double t_1 = x / (y + 1.0);
	double tmp;
	if (y <= -950000000.0) {
		tmp = t_0;
	} else if (y <= 1.2e-61) {
		tmp = t_1;
	} else if (y <= 6.8e-50) {
		tmp = y;
	} else if (y <= 62000000000000.0) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 1.0 + (x / y)
	t_1 = x / (y + 1.0)
	tmp = 0
	if y <= -950000000.0:
		tmp = t_0
	elif y <= 1.2e-61:
		tmp = t_1
	elif y <= 6.8e-50:
		tmp = y
	elif y <= 62000000000000.0:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(1.0 + Float64(x / y))
	t_1 = Float64(x / Float64(y + 1.0))
	tmp = 0.0
	if (y <= -950000000.0)
		tmp = t_0;
	elseif (y <= 1.2e-61)
		tmp = t_1;
	elseif (y <= 6.8e-50)
		tmp = y;
	elseif (y <= 62000000000000.0)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = 1.0 + (x / y);
	t_1 = x / (y + 1.0);
	tmp = 0.0;
	if (y <= -950000000.0)
		tmp = t_0;
	elseif (y <= 1.2e-61)
		tmp = t_1;
	elseif (y <= 6.8e-50)
		tmp = y;
	elseif (y <= 62000000000000.0)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(1.0 + N[(x / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -950000000.0], t$95$0, If[LessEqual[y, 1.2e-61], t$95$1, If[LessEqual[y, 6.8e-50], y, If[LessEqual[y, 62000000000000.0], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.5e8 or 6.2e13 < y

   1. Initial program 100.0%

      \[\frac{x + y}{y + 1} \]

   2. Taylor expanded in y around -inf 99.7%

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

      1. mul-1-neg 99.7%

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

      2. unsub-neg 99.7%

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

      3. mul-1-neg 99.7%

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

      4. sub-neg 99.7%

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

   4. Simplified 99.7%

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

   5. Taylor expanded in x around inf 99.4%

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

      1. neg-mul-1 99.4%

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

   7. Simplified 99.4%

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

   if -9.5e8 < y < 1.2e-61 or 6.80000000000000029e-50 < y < 6.2e13

   1. Initial program 100.0%

      \[\frac{x + y}{y + 1} \]

   2. Taylor expanded in x around inf 75.8%

      \[\leadsto \color{blue}{\frac{x}{1 + y}} \]
   3. Step-by-step derivation

      1. +-commutative 75.8%

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

   4. Simplified 75.8%

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

   if 1.2e-61 < y < 6.80000000000000029e-50

   1. Initial program 100.0%

      \[\frac{x + y}{y + 1} \]

   2. Taylor expanded in x around 0 90.4%

      \[\leadsto \color{blue}{\frac{y}{1 + y}} \]
   3. Step-by-step derivation

      1. +-commutative 90.4%

         \[\leadsto \frac{y}{\color{blue}{y + 1}} \]

   4. Simplified 90.4%

      \[\leadsto \color{blue}{\frac{y}{y + 1}} \]

   5. Taylor expanded in y around 0 90.4%

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

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -950000000:\\ \;\;\;\;1 + \frac{x}{y}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-61}:\\ \;\;\;\;\frac{x}{y + 1}\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-50}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 62000000000000:\\ \;\;\;\;\frac{x}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x}{y}\\ \end{array} \]

Alternative 6: 86.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{y + 1}\\ \mathbf{if}\;y \leq -470000000:\\ \;\;\;\;1 + \frac{x + -1}{y}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-61}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-50}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 62000000000000:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ x (+ y 1.0))))
   (if (<= y -470000000.0)
     (+ 1.0 (/ (+ x -1.0) y))
     (if (<= y 1.2e-61)
       t_0
       (if (<= y 6.5e-50)
         y
         (if (<= y 62000000000000.0) t_0 (+ 1.0 (/ x y))))))))

C

double code(double x, double y) {
	double t_0 = x / (y + 1.0);
	double tmp;
	if (y <= -470000000.0) {
		tmp = 1.0 + ((x + -1.0) / y);
	} else if (y <= 1.2e-61) {
		tmp = t_0;
	} else if (y <= 6.5e-50) {
		tmp = y;
	} else if (y <= 62000000000000.0) {
		tmp = t_0;
	} else {
		tmp = 1.0 + (x / y);
	}
	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 / (y + 1.0d0)
    if (y <= (-470000000.0d0)) then
        tmp = 1.0d0 + ((x + (-1.0d0)) / y)
    else if (y <= 1.2d-61) then
        tmp = t_0
    else if (y <= 6.5d-50) then
        tmp = y
    else if (y <= 62000000000000.0d0) then
        tmp = t_0
    else
        tmp = 1.0d0 + (x / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = x / (y + 1.0);
	double tmp;
	if (y <= -470000000.0) {
		tmp = 1.0 + ((x + -1.0) / y);
	} else if (y <= 1.2e-61) {
		tmp = t_0;
	} else if (y <= 6.5e-50) {
		tmp = y;
	} else if (y <= 62000000000000.0) {
		tmp = t_0;
	} else {
		tmp = 1.0 + (x / y);
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x / (y + 1.0)
	tmp = 0
	if y <= -470000000.0:
		tmp = 1.0 + ((x + -1.0) / y)
	elif y <= 1.2e-61:
		tmp = t_0
	elif y <= 6.5e-50:
		tmp = y
	elif y <= 62000000000000.0:
		tmp = t_0
	else:
		tmp = 1.0 + (x / y)
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x / Float64(y + 1.0))
	tmp = 0.0
	if (y <= -470000000.0)
		tmp = Float64(1.0 + Float64(Float64(x + -1.0) / y));
	elseif (y <= 1.2e-61)
		tmp = t_0;
	elseif (y <= 6.5e-50)
		tmp = y;
	elseif (y <= 62000000000000.0)
		tmp = t_0;
	else
		tmp = Float64(1.0 + Float64(x / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = x / (y + 1.0);
	tmp = 0.0;
	if (y <= -470000000.0)
		tmp = 1.0 + ((x + -1.0) / y);
	elseif (y <= 1.2e-61)
		tmp = t_0;
	elseif (y <= 6.5e-50)
		tmp = y;
	elseif (y <= 62000000000000.0)
		tmp = t_0;
	else
		tmp = 1.0 + (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -470000000.0], N[(1.0 + N[(N[(x + -1.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.2e-61], t$95$0, If[LessEqual[y, 6.5e-50], y, If[LessEqual[y, 62000000000000.0], t$95$0, N[(1.0 + N[(x / y), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.7e8

   1. Initial program 100.0%

      \[\frac{x + y}{y + 1} \]

   2. Taylor expanded in y around -inf 99.5%

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

      1. mul-1-neg 99.5%

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

      2. unsub-neg 99.5%

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

      3. mul-1-neg 99.5%

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

      4. sub-neg 99.5%

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

   4. Simplified 99.5%

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

   if -4.7e8 < y < 1.2e-61 or 6.49999999999999987e-50 < y < 6.2e13

   1. Initial program 100.0%

      \[\frac{x + y}{y + 1} \]

   2. Taylor expanded in x around inf 75.8%

      \[\leadsto \color{blue}{\frac{x}{1 + y}} \]
   3. Step-by-step derivation

      1. +-commutative 75.8%

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

   4. Simplified 75.8%

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

   if 1.2e-61 < y < 6.49999999999999987e-50

   1. Initial program 100.0%

      \[\frac{x + y}{y + 1} \]

   2. Taylor expanded in x around 0 90.4%

      \[\leadsto \color{blue}{\frac{y}{1 + y}} \]
   3. Step-by-step derivation

      1. +-commutative 90.4%

         \[\leadsto \frac{y}{\color{blue}{y + 1}} \]

   4. Simplified 90.4%

      \[\leadsto \color{blue}{\frac{y}{y + 1}} \]

   5. Taylor expanded in y around 0 90.4%

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

   if 6.2e13 < y

   1. Initial program 100.0%

      \[\frac{x + y}{y + 1} \]

   2. Taylor expanded in y around -inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. unsub-neg 100.0%

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

      3. mul-1-neg 100.0%

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

      4. sub-neg 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in x around inf 100.0%

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

      1. neg-mul-1 100.0%

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

   7. Simplified 100.0%

      \[\leadsto 1 - \color{blue}{\left(-\frac{x}{y}\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -470000000:\\ \;\;\;\;1 + \frac{x + -1}{y}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-61}:\\ \;\;\;\;\frac{x}{y + 1}\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-50}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 62000000000000:\\ \;\;\;\;\frac{x}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x}{y}\\ \end{array} \]

Alternative 7: 73.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-61}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-50}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+32}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.0)
   1.0
   (if (<= y 1.2e-61) x (if (<= y 6.5e-50) y (if (<= y 3.8e+32) x 1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = 1.0;
	} else if (y <= 1.2e-61) {
		tmp = x;
	} else if (y <= 6.5e-50) {
		tmp = y;
	} else if (y <= 3.8e+32) {
		tmp = x;
	} else {
		tmp = 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 <= (-1.0d0)) then
        tmp = 1.0d0
    else if (y <= 1.2d-61) then
        tmp = x
    else if (y <= 6.5d-50) then
        tmp = y
    else if (y <= 3.8d+32) then
        tmp = x
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = 1.0;
	} else if (y <= 1.2e-61) {
		tmp = x;
	} else if (y <= 6.5e-50) {
		tmp = y;
	} else if (y <= 3.8e+32) {
		tmp = x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = 1.0
	elif y <= 1.2e-61:
		tmp = x
	elif y <= 6.5e-50:
		tmp = y
	elif y <= 3.8e+32:
		tmp = x
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.0)
		tmp = 1.0;
	elseif (y <= 1.2e-61)
		tmp = x;
	elseif (y <= 6.5e-50)
		tmp = y;
	elseif (y <= 3.8e+32)
		tmp = x;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.0)
		tmp = 1.0;
	elseif (y <= 1.2e-61)
		tmp = x;
	elseif (y <= 6.5e-50)
		tmp = y;
	elseif (y <= 3.8e+32)
		tmp = x;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.0], 1.0, If[LessEqual[y, 1.2e-61], x, If[LessEqual[y, 6.5e-50], y, If[LessEqual[y, 3.8e+32], x, 1.0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1 or 3.8000000000000003e32 < y

   1. Initial program 100.0%

      \[\frac{x + y}{y + 1} \]

   2. Taylor expanded in y around inf 70.4%

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

   if -1 < y < 1.2e-61 or 6.49999999999999987e-50 < y < 3.8000000000000003e32

   1. Initial program 100.0%

      \[\frac{x + y}{y + 1} \]

   2. Taylor expanded in y around 0 71.2%

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

   if 1.2e-61 < y < 6.49999999999999987e-50

   1. Initial program 100.0%

      \[\frac{x + y}{y + 1} \]

   2. Taylor expanded in x around 0 90.4%

      \[\leadsto \color{blue}{\frac{y}{1 + y}} \]
   3. Step-by-step derivation

      1. +-commutative 90.4%

         \[\leadsto \frac{y}{\color{blue}{y + 1}} \]

   4. Simplified 90.4%

      \[\leadsto \color{blue}{\frac{y}{y + 1}} \]

   5. Taylor expanded in y around 0 90.4%

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

4. Final simplification 71.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-61}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-50}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+32}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 8: 73.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+32}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.0) 1.0 (if (<= y 3.8e+32) x 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = 1.0;
	} else if (y <= 3.8e+32) {
		tmp = x;
	} else {
		tmp = 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 <= (-1.0d0)) then
        tmp = 1.0d0
    else if (y <= 3.8d+32) then
        tmp = x
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = 1.0;
	} else if (y <= 3.8e+32) {
		tmp = x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = 1.0
	elif y <= 3.8e+32:
		tmp = x
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.0)
		tmp = 1.0;
	elseif (y <= 3.8e+32)
		tmp = x;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.0)
		tmp = 1.0;
	elseif (y <= 3.8e+32)
		tmp = x;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.0], 1.0, If[LessEqual[y, 3.8e+32], x, 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 3.8000000000000003e32 < y

   1. Initial program 100.0%

      \[\frac{x + y}{y + 1} \]

   2. Taylor expanded in y around inf 70.4%

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

   if -1 < y < 3.8000000000000003e32

   1. Initial program 100.0%

      \[\frac{x + y}{y + 1} \]

   2. Taylor expanded in y around 0 68.6%

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

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+32}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 9: 39.1% accurate, 7.0× 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 100.0%

   \[\frac{x + y}{y + 1} \]

2. Taylor expanded in y around inf 37.0%

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

3. Final simplification 37.0%

   \[\leadsto 1 \]

Reproduce

herbie shell --seed 2023195 
(FPCore (x y)
  :name "Data.Colour.SRGB:invTransferFunction from colour-2.3.3"
  :precision binary64
  (/ (+ x y) (+ y 1.0)))