Data.Colour.SRGB:transferFunction from colour-2.3.3

Percentage Accurate: 100.0% → 100.0%

Time: 6.1s

Alternatives: 9

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[\left(x + 1\right) \cdot y - x \]

2. Taylor expanded in x around 0 100.0%

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

3. Final simplification 100.0%

   \[\leadsto \left(y + y \cdot x\right) - x \]

Alternative 2: 62.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{+215}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{+151}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{-16}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-53}:\\ \;\;\;\;-x\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{+61}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.75e+215)
   y
   (if (<= y -2.5e+151)
     (* y x)
     (if (<= y -2.9e-16)
       y
       (if (<= y 3.8e-53) (- x) (if (<= y 4.7e+61) y (* y x)))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.75e+215) {
		tmp = y;
	} else if (y <= -2.5e+151) {
		tmp = y * x;
	} else if (y <= -2.9e-16) {
		tmp = y;
	} else if (y <= 3.8e-53) {
		tmp = -x;
	} else if (y <= 4.7e+61) {
		tmp = y;
	} else {
		tmp = y * 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 <= (-1.75d+215)) then
        tmp = y
    else if (y <= (-2.5d+151)) then
        tmp = y * x
    else if (y <= (-2.9d-16)) then
        tmp = y
    else if (y <= 3.8d-53) then
        tmp = -x
    else if (y <= 4.7d+61) then
        tmp = y
    else
        tmp = y * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -1.75e+215) {
		tmp = y;
	} else if (y <= -2.5e+151) {
		tmp = y * x;
	} else if (y <= -2.9e-16) {
		tmp = y;
	} else if (y <= 3.8e-53) {
		tmp = -x;
	} else if (y <= 4.7e+61) {
		tmp = y;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.75e+215:
		tmp = y
	elif y <= -2.5e+151:
		tmp = y * x
	elif y <= -2.9e-16:
		tmp = y
	elif y <= 3.8e-53:
		tmp = -x
	elif y <= 4.7e+61:
		tmp = y
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.75e+215)
		tmp = y;
	elseif (y <= -2.5e+151)
		tmp = Float64(y * x);
	elseif (y <= -2.9e-16)
		tmp = y;
	elseif (y <= 3.8e-53)
		tmp = Float64(-x);
	elseif (y <= 4.7e+61)
		tmp = y;
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.75e+215)
		tmp = y;
	elseif (y <= -2.5e+151)
		tmp = y * x;
	elseif (y <= -2.9e-16)
		tmp = y;
	elseif (y <= 3.8e-53)
		tmp = -x;
	elseif (y <= 4.7e+61)
		tmp = y;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.75e+215], y, If[LessEqual[y, -2.5e+151], N[(y * x), $MachinePrecision], If[LessEqual[y, -2.9e-16], y, If[LessEqual[y, 3.8e-53], (-x), If[LessEqual[y, 4.7e+61], y, N[(y * x), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.74999999999999988e215 or -2.5000000000000001e151 < y < -2.8999999999999998e-16 or 3.7999999999999998e-53 < y < 4.6999999999999998e61

   1. Initial program 100.0%

      \[\left(x + 1\right) \cdot y - x \]

   2. Taylor expanded in x around 0 100.0%

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

   3. Taylor expanded in x around 0 64.1%

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

   if -1.74999999999999988e215 < y < -2.5000000000000001e151 or 4.6999999999999998e61 < y

   1. Initial program 100.0%

      \[\left(x + 1\right) \cdot y - x \]

   2. Taylor expanded in x around inf 66.2%

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

   3. Taylor expanded in y around inf 66.2%

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

   if -2.8999999999999998e-16 < y < 3.7999999999999998e-53

   1. Initial program 100.0%

      \[\left(x + 1\right) \cdot y - x \]

   2. Taylor expanded in y around 0 80.8%

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

      1. neg-mul-1 80.8%

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

   4. Simplified 80.8%

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

4. Final simplification 71.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{+215}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{+151}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{-16}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-53}:\\ \;\;\;\;-x\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{+61}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

Alternative 3: 75.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.4 \cdot 10^{+211} \lor \neg \left(y \leq -5.05 \cdot 10^{+151}\right) \land y \leq 2.4 \cdot 10^{+62}:\\ \;\;\;\;y - x\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -6.4e+211) (and (not (<= y -5.05e+151)) (<= y 2.4e+62)))
   (- y x)
   (* y x)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -6.4e+211) || (!(y <= -5.05e+151) && (y <= 2.4e+62))) {
		tmp = y - x;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-6.4d+211)) .or. (.not. (y <= (-5.05d+151))) .and. (y <= 2.4d+62)) then
        tmp = y - x
    else
        tmp = y * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -6.4e+211) || (!(y <= -5.05e+151) && (y <= 2.4e+62))) {
		tmp = y - x;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -6.4e+211) or (not (y <= -5.05e+151) and (y <= 2.4e+62)):
		tmp = y - x
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -6.4e+211) || (!(y <= -5.05e+151) && (y <= 2.4e+62)))
		tmp = Float64(y - x);
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -6.4e+211) || (~((y <= -5.05e+151)) && (y <= 2.4e+62)))
		tmp = y - x;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -6.4e+211], And[N[Not[LessEqual[y, -5.05e+151]], $MachinePrecision], LessEqual[y, 2.4e+62]]], N[(y - x), $MachinePrecision], N[(y * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.39999999999999953e211 or -5.0499999999999998e151 < y < 2.4e62

   1. Initial program 100.0%

      \[\left(x + 1\right) \cdot y - x \]

   2. Taylor expanded in x around 0 87.6%

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

   if -6.39999999999999953e211 < y < -5.0499999999999998e151 or 2.4e62 < y

   1. Initial program 100.0%

      \[\left(x + 1\right) \cdot y - x \]

   2. Taylor expanded in x around inf 66.2%

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

   3. Taylor expanded in y around inf 66.2%

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

4. Final simplification 81.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.4 \cdot 10^{+211} \lor \neg \left(y \leq -5.05 \cdot 10^{+151}\right) \land y \leq 2.4 \cdot 10^{+62}:\\ \;\;\;\;y - x\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

Alternative 4: 98.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8500000 \lor \neg \left(y \leq 1\right):\\ \;\;\;\;y \cdot \left(x + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -8500000.0) (not (<= y 1.0))) (* y (+ x 1.0)) (- y x)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -8500000.0) || !(y <= 1.0)) {
		tmp = y * (x + 1.0);
	} else {
		tmp = y - 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 <= (-8500000.0d0)) .or. (.not. (y <= 1.0d0))) then
        tmp = y * (x + 1.0d0)
    else
        tmp = y - x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -8500000.0) || !(y <= 1.0)) {
		tmp = y * (x + 1.0);
	} else {
		tmp = y - x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -8500000.0) or not (y <= 1.0):
		tmp = y * (x + 1.0)
	else:
		tmp = y - x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -8500000.0) || !(y <= 1.0))
		tmp = Float64(y * Float64(x + 1.0));
	else
		tmp = Float64(y - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -8500000.0) || ~((y <= 1.0)))
		tmp = y * (x + 1.0);
	else
		tmp = y - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -8500000.0], N[Not[LessEqual[y, 1.0]], $MachinePrecision]], N[(y * N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(y - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.5e6 or 1 < y

   1. Initial program 100.0%

      \[\left(x + 1\right) \cdot y - x \]

   2. Taylor expanded in x around 0 100.0%

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

   3. Taylor expanded in y around inf 99.3%

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

   if -8.5e6 < y < 1

   1. Initial program 100.0%

      \[\left(x + 1\right) \cdot y - x \]

   2. Taylor expanded in x around 0 97.7%

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

4. Final simplification 98.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8500000 \lor \neg \left(y \leq 1\right):\\ \;\;\;\;y \cdot \left(x + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y - x\\ \end{array} \]

Alternative 5: 98.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -19000 \lor \neg \left(x \leq 1\right):\\ \;\;\;\;x \cdot \left(y - 1\right)\\ \mathbf{else}:\\ \;\;\;\;y - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -19000.0) (not (<= x 1.0))) (* x (- y 1.0)) (- y x)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -19000.0) || !(x <= 1.0)) {
		tmp = x * (y - 1.0);
	} else {
		tmp = y - x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((x <= (-19000.0d0)) .or. (.not. (x <= 1.0d0))) then
        tmp = x * (y - 1.0d0)
    else
        tmp = y - x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -19000.0) || !(x <= 1.0)) {
		tmp = x * (y - 1.0);
	} else {
		tmp = y - x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -19000.0) or not (x <= 1.0):
		tmp = x * (y - 1.0)
	else:
		tmp = y - x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -19000.0) || !(x <= 1.0))
		tmp = Float64(x * Float64(y - 1.0));
	else
		tmp = Float64(y - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -19000.0) || ~((x <= 1.0)))
		tmp = x * (y - 1.0);
	else
		tmp = y - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -19000.0], N[Not[LessEqual[x, 1.0]], $MachinePrecision]], N[(x * N[(y - 1.0), $MachinePrecision]), $MachinePrecision], N[(y - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -19000 or 1 < x

   1. Initial program 100.0%

      \[\left(x + 1\right) \cdot y - x \]

   2. Taylor expanded in x around inf 99.4%

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

   if -19000 < x < 1

   1. Initial program 100.0%

      \[\left(x + 1\right) \cdot y - x \]

   2. Taylor expanded in x around 0 98.5%

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

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -19000 \lor \neg \left(x \leq 1\right):\\ \;\;\;\;x \cdot \left(y - 1\right)\\ \mathbf{else}:\\ \;\;\;\;y - x\\ \end{array} \]

Alternative 6: 98.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -19000 \lor \neg \left(x \leq 1\right):\\ \;\;\;\;y \cdot x - x\\ \mathbf{else}:\\ \;\;\;\;y - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -19000.0) (not (<= x 1.0))) (- (* y x) x) (- y x)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -19000.0) || !(x <= 1.0)) {
		tmp = (y * x) - x;
	} else {
		tmp = y - x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((x <= (-19000.0d0)) .or. (.not. (x <= 1.0d0))) then
        tmp = (y * x) - x
    else
        tmp = y - x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -19000.0) || !(x <= 1.0)) {
		tmp = (y * x) - x;
	} else {
		tmp = y - x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -19000.0) or not (x <= 1.0):
		tmp = (y * x) - x
	else:
		tmp = y - x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -19000.0) || !(x <= 1.0))
		tmp = Float64(Float64(y * x) - x);
	else
		tmp = Float64(y - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -19000.0) || ~((x <= 1.0)))
		tmp = (y * x) - x;
	else
		tmp = y - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -19000.0], N[Not[LessEqual[x, 1.0]], $MachinePrecision]], N[(N[(y * x), $MachinePrecision] - x), $MachinePrecision], N[(y - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -19000 or 1 < x

   1. Initial program 100.0%

      \[\left(x + 1\right) \cdot y - x \]

   2. Taylor expanded in x around inf 99.5%

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

   if -19000 < x < 1

   1. Initial program 100.0%

      \[\left(x + 1\right) \cdot y - x \]

   2. Taylor expanded in x around 0 98.5%

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

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -19000 \lor \neg \left(x \leq 1\right):\\ \;\;\;\;y \cdot x - x\\ \mathbf{else}:\\ \;\;\;\;y - x\\ \end{array} \]

Alternative 7: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[\left(x + 1\right) \cdot y - x \]

2. Final simplification 100.0%

   \[\leadsto y \cdot \left(x + 1\right) - x \]

Alternative 8: 62.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{-15}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{-52}:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.6e-15) y (if (<= y 5.4e-52) (- x) y)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.6e-15) {
		tmp = y;
	} else if (y <= 5.4e-52) {
		tmp = -x;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-1.6d-15)) then
        tmp = y
    else if (y <= 5.4d-52) then
        tmp = -x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -1.6e-15) {
		tmp = y;
	} else if (y <= 5.4e-52) {
		tmp = -x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.6e-15:
		tmp = y
	elif y <= 5.4e-52:
		tmp = -x
	else:
		tmp = y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.6e-15)
		tmp = y;
	elseif (y <= 5.4e-52)
		tmp = Float64(-x);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.6e-15)
		tmp = y;
	elseif (y <= 5.4e-52)
		tmp = -x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.6e-15], y, If[LessEqual[y, 5.4e-52], (-x), y]]

Derivation

1. Split input into 2 regimes

2. if y < -1.6e-15 or 5.40000000000000019e-52 < y

   1. Initial program 100.0%

      \[\left(x + 1\right) \cdot y - x \]

   2. Taylor expanded in x around 0 100.0%

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

   3. Taylor expanded in x around 0 50.2%

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

   if -1.6e-15 < y < 5.40000000000000019e-52

   1. Initial program 100.0%

      \[\left(x + 1\right) \cdot y - x \]

   2. Taylor expanded in y around 0 80.8%

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

      1. neg-mul-1 80.8%

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

   4. Simplified 80.8%

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

4. Final simplification 63.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{-15}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{-52}:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 9: 39.1% accurate, 7.0× speedup

Math

\[\begin{array}{l} \\ y \end{array} \]

FPCore

(FPCore (x y) :precision binary64 y)

C

double code(double x, double y) {
	return y;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = y
end function

Java

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

Python

def code(x, y):
	return y

Julia

function code(x, y)
	return y
end

MATLAB

function tmp = code(x, y)
	tmp = y;
end

Wolfram

code[x_, y_] := y

Derivation

1. Initial program 100.0%

   \[\left(x + 1\right) \cdot y - x \]

2. Taylor expanded in x around 0 100.0%

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

3. Taylor expanded in x around 0 37.6%

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

4. Final simplification 37.6%

   \[\leadsto y \]

Reproduce

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