Data.Colour.SRGB:invTransferFunction from colour-2.3.3

Percentage Accurate: 100.0% → 100.0%

Time: 5.1s

Alternatives: 7

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: 84.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{1 - x}{y}\\ t_1 := \frac{x}{y + 1}\\ \mathbf{if}\;y \leq -2.6 \cdot 10^{+40}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-123}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-67}:\\ \;\;\;\;\frac{y}{y + 1}\\ \mathbf{elif}\;y \leq 21000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ (- 1.0 x) y))) (t_1 (/ x (+ y 1.0))))
   (if (<= y -2.6e+40)
     t_0
     (if (<= y 1.25e-123)
       t_1
       (if (<= y 1.9e-67) (/ y (+ y 1.0)) (if (<= y 21000000.0) t_1 t_0))))))

C

double code(double x, double y) {
	double t_0 = 1.0 - ((1.0 - x) / y);
	double t_1 = x / (y + 1.0);
	double tmp;
	if (y <= -2.6e+40) {
		tmp = t_0;
	} else if (y <= 1.25e-123) {
		tmp = t_1;
	} else if (y <= 1.9e-67) {
		tmp = y / (y + 1.0);
	} else if (y <= 21000000.0) {
		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 - ((1.0d0 - x) / y)
    t_1 = x / (y + 1.0d0)
    if (y <= (-2.6d+40)) then
        tmp = t_0
    else if (y <= 1.25d-123) then
        tmp = t_1
    else if (y <= 1.9d-67) then
        tmp = y / (y + 1.0d0)
    else if (y <= 21000000.0d0) 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 - ((1.0 - x) / y);
	double t_1 = x / (y + 1.0);
	double tmp;
	if (y <= -2.6e+40) {
		tmp = t_0;
	} else if (y <= 1.25e-123) {
		tmp = t_1;
	} else if (y <= 1.9e-67) {
		tmp = y / (y + 1.0);
	} else if (y <= 21000000.0) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 1.0 - ((1.0 - x) / y)
	t_1 = x / (y + 1.0)
	tmp = 0
	if y <= -2.6e+40:
		tmp = t_0
	elif y <= 1.25e-123:
		tmp = t_1
	elif y <= 1.9e-67:
		tmp = y / (y + 1.0)
	elif y <= 21000000.0:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(1.0 - Float64(Float64(1.0 - x) / y))
	t_1 = Float64(x / Float64(y + 1.0))
	tmp = 0.0
	if (y <= -2.6e+40)
		tmp = t_0;
	elseif (y <= 1.25e-123)
		tmp = t_1;
	elseif (y <= 1.9e-67)
		tmp = Float64(y / Float64(y + 1.0));
	elseif (y <= 21000000.0)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = 1.0 - ((1.0 - x) / y);
	t_1 = x / (y + 1.0);
	tmp = 0.0;
	if (y <= -2.6e+40)
		tmp = t_0;
	elseif (y <= 1.25e-123)
		tmp = t_1;
	elseif (y <= 1.9e-67)
		tmp = y / (y + 1.0);
	elseif (y <= 21000000.0)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(1.0 - N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.6e+40], t$95$0, If[LessEqual[y, 1.25e-123], t$95$1, If[LessEqual[y, 1.9e-67], N[(y / N[(y + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 21000000.0], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.6000000000000001e40 or 2.1e7 < y

   1. Initial program 99.9%

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

   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%

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

   if -2.6000000000000001e40 < y < 1.25000000000000007e-123 or 1.89999999999999994e-67 < y < 2.1e7

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 80.9%

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

      1. +-commutative 80.9%

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

   4. Simplified 80.9%

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

   if 1.25000000000000007e-123 < y < 1.89999999999999994e-67

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 70.8%

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

      1. +-commutative 70.8%

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

   4. Simplified 70.8%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+40}:\\ \;\;\;\;1 - \frac{1 - x}{y}\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-123}:\\ \;\;\;\;\frac{x}{y + 1}\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-67}:\\ \;\;\;\;\frac{y}{y + 1}\\ \mathbf{elif}\;y \leq 21000000:\\ \;\;\;\;\frac{x}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{1 - x}{y}\\ \end{array} \]

Alternative 3: 72.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.02 \cdot 10^{+49}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{-7}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+42}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+58}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.02e+49)
   1.0
   (if (<= y -1.0)
     (/ x y)
     (if (<= y 5.6e-7)
       x
       (if (<= y 6.2e+42) 1.0 (if (<= y 2e+58) (/ x y) 1.0))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.02e+49) {
		tmp = 1.0;
	} else if (y <= -1.0) {
		tmp = x / y;
	} else if (y <= 5.6e-7) {
		tmp = x;
	} else if (y <= 6.2e+42) {
		tmp = 1.0;
	} else if (y <= 2e+58) {
		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 <= (-1.02d+49)) then
        tmp = 1.0d0
    else if (y <= (-1.0d0)) then
        tmp = x / y
    else if (y <= 5.6d-7) then
        tmp = x
    else if (y <= 6.2d+42) then
        tmp = 1.0d0
    else if (y <= 2d+58) 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 <= -1.02e+49) {
		tmp = 1.0;
	} else if (y <= -1.0) {
		tmp = x / y;
	} else if (y <= 5.6e-7) {
		tmp = x;
	} else if (y <= 6.2e+42) {
		tmp = 1.0;
	} else if (y <= 2e+58) {
		tmp = x / y;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.02e+49:
		tmp = 1.0
	elif y <= -1.0:
		tmp = x / y
	elif y <= 5.6e-7:
		tmp = x
	elif y <= 6.2e+42:
		tmp = 1.0
	elif y <= 2e+58:
		tmp = x / y
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.02e+49)
		tmp = 1.0;
	elseif (y <= -1.0)
		tmp = Float64(x / y);
	elseif (y <= 5.6e-7)
		tmp = x;
	elseif (y <= 6.2e+42)
		tmp = 1.0;
	elseif (y <= 2e+58)
		tmp = Float64(x / y);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.02e+49)
		tmp = 1.0;
	elseif (y <= -1.0)
		tmp = x / y;
	elseif (y <= 5.6e-7)
		tmp = x;
	elseif (y <= 6.2e+42)
		tmp = 1.0;
	elseif (y <= 2e+58)
		tmp = x / y;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.02e+49], 1.0, If[LessEqual[y, -1.0], N[(x / y), $MachinePrecision], If[LessEqual[y, 5.6e-7], x, If[LessEqual[y, 6.2e+42], 1.0, If[LessEqual[y, 2e+58], N[(x / y), $MachinePrecision], 1.0]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.02e49 or 5.60000000000000038e-7 < y < 6.2000000000000003e42 or 1.99999999999999989e58 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 81.2%

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

   if -1.02e49 < y < -1 or 6.2000000000000003e42 < y < 1.99999999999999989e58

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 83.7%

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

      1. +-commutative 83.7%

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

   4. Simplified 83.7%

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

   5. Taylor expanded in y around inf 77.5%

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

   if -1 < y < 5.60000000000000038e-7

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 74.9%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.02 \cdot 10^{+49}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{-7}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+42}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+58}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 4: 73.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+50}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{-7} \lor \neg \left(y \leq 2.6 \cdot 10^{+43}\right) \land y \leq 1.35 \cdot 10^{+58}:\\ \;\;\;\;\frac{x}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.1e+50)
   1.0
   (if (or (<= y 5.6e-7) (and (not (<= y 2.6e+43)) (<= y 1.35e+58)))
     (/ x (+ y 1.0))
     1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.1e+50) {
		tmp = 1.0;
	} else if ((y <= 5.6e-7) || (!(y <= 2.6e+43) && (y <= 1.35e+58))) {
		tmp = x / (y + 1.0);
	} 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 <= (-1.1d+50)) then
        tmp = 1.0d0
    else if ((y <= 5.6d-7) .or. (.not. (y <= 2.6d+43)) .and. (y <= 1.35d+58)) then
        tmp = x / (y + 1.0d0)
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -1.1e+50) {
		tmp = 1.0;
	} else if ((y <= 5.6e-7) || (!(y <= 2.6e+43) && (y <= 1.35e+58))) {
		tmp = x / (y + 1.0);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.1e+50:
		tmp = 1.0
	elif (y <= 5.6e-7) or (not (y <= 2.6e+43) and (y <= 1.35e+58)):
		tmp = x / (y + 1.0)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.1e+50)
		tmp = 1.0;
	elseif ((y <= 5.6e-7) || (!(y <= 2.6e+43) && (y <= 1.35e+58)))
		tmp = Float64(x / Float64(y + 1.0));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.1e+50)
		tmp = 1.0;
	elseif ((y <= 5.6e-7) || (~((y <= 2.6e+43)) && (y <= 1.35e+58)))
		tmp = x / (y + 1.0);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.1e+50], 1.0, If[Or[LessEqual[y, 5.6e-7], And[N[Not[LessEqual[y, 2.6e+43]], $MachinePrecision], LessEqual[y, 1.35e+58]]], N[(x / N[(y + 1.0), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -1.10000000000000008e50 or 5.60000000000000038e-7 < y < 2.60000000000000021e43 or 1.3500000000000001e58 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 81.2%

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

   if -1.10000000000000008e50 < y < 5.60000000000000038e-7 or 2.60000000000000021e43 < y < 1.3500000000000001e58

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 76.7%

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

      1. +-commutative 76.7%

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

   4. Simplified 76.7%

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

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+50}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{-7} \lor \neg \left(y \leq 2.6 \cdot 10^{+43}\right) \land y \leq 1.35 \cdot 10^{+58}:\\ \;\;\;\;\frac{x}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 5: 73.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{y + 1}\\ \mathbf{if}\;x \leq -4.4 \cdot 10^{-35}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{-23}:\\ \;\;\;\;\frac{y}{y + 1}\\ \mathbf{elif}\;x \leq 2 \cdot 10^{+20}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{+87}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ x (+ y 1.0))))
   (if (<= x -4.4e-35)
     t_0
     (if (<= x 4.5e-23)
       (/ y (+ y 1.0))
       (if (<= x 2e+20) x (if (<= x 7.5e+87) 1.0 t_0))))))

C

double code(double x, double y) {
	double t_0 = x / (y + 1.0);
	double tmp;
	if (x <= -4.4e-35) {
		tmp = t_0;
	} else if (x <= 4.5e-23) {
		tmp = y / (y + 1.0);
	} else if (x <= 2e+20) {
		tmp = x;
	} else if (x <= 7.5e+87) {
		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 <= (-4.4d-35)) then
        tmp = t_0
    else if (x <= 4.5d-23) then
        tmp = y / (y + 1.0d0)
    else if (x <= 2d+20) then
        tmp = x
    else if (x <= 7.5d+87) 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 <= -4.4e-35) {
		tmp = t_0;
	} else if (x <= 4.5e-23) {
		tmp = y / (y + 1.0);
	} else if (x <= 2e+20) {
		tmp = x;
	} else if (x <= 7.5e+87) {
		tmp = 1.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x / (y + 1.0)
	tmp = 0
	if x <= -4.4e-35:
		tmp = t_0
	elif x <= 4.5e-23:
		tmp = y / (y + 1.0)
	elif x <= 2e+20:
		tmp = x
	elif x <= 7.5e+87:
		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 <= -4.4e-35)
		tmp = t_0;
	elseif (x <= 4.5e-23)
		tmp = Float64(y / Float64(y + 1.0));
	elseif (x <= 2e+20)
		tmp = x;
	elseif (x <= 7.5e+87)
		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 <= -4.4e-35)
		tmp = t_0;
	elseif (x <= 4.5e-23)
		tmp = y / (y + 1.0);
	elseif (x <= 2e+20)
		tmp = x;
	elseif (x <= 7.5e+87)
		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, -4.4e-35], t$95$0, If[LessEqual[x, 4.5e-23], N[(y / N[(y + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2e+20], x, If[LessEqual[x, 7.5e+87], 1.0, t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -4.39999999999999987e-35 or 7.50000000000000014e87 < x

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 80.5%

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

      1. +-commutative 80.5%

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

   4. Simplified 80.5%

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

   if -4.39999999999999987e-35 < x < 4.49999999999999975e-23

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 83.3%

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

      1. +-commutative 83.3%

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

   4. Simplified 83.3%

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

   if 4.49999999999999975e-23 < x < 2e20

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 88.7%

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

   if 2e20 < x < 7.50000000000000014e87

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 66.5%

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

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.4 \cdot 10^{-35}:\\ \;\;\;\;\frac{x}{y + 1}\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{-23}:\\ \;\;\;\;\frac{y}{y + 1}\\ \mathbf{elif}\;x \leq 2 \cdot 10^{+20}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{+87}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y + 1}\\ \end{array} \]

Alternative 6: 72.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{-7}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.0) 1.0 (if (<= y 5.6e-7) x 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = 1.0;
	} else if (y <= 5.6e-7) {
		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 <= 5.6d-7) 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 <= 5.6e-7) {
		tmp = x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = 1.0
	elif y <= 5.6e-7:
		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 <= 5.6e-7)
		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 <= 5.6e-7)
		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, 5.6e-7], x, 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 5.60000000000000038e-7 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 72.8%

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

   if -1 < y < 5.60000000000000038e-7

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 74.9%

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

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{-7}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 7: 38.4% 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 41.9%

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

3. Final simplification 41.9%

   \[\leadsto 1 \]

Reproduce

herbie shell --seed 2023274 
(FPCore (x y)
  :name "Data.Colour.SRGB:invTransferFunction from colour-2.3.3"
  :precision binary64
  (/ (+ x y) (+ y 1.0)))