Data.Colour.SRGB:transferFunction from colour-2.3.3

Percentage Accurate: 100.0% → 100.0%

Time: 3.5s

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 99.9%

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

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: 75.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{+215}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -7 \cdot 10^{+169}:\\ \;\;\;\;y - x\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{+36}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 68000000000000:\\ \;\;\;\;y - x\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+30}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+74}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+170}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+283}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -2.9e+215)
   (* y x)
   (if (<= y -7e+169)
     (- y x)
     (if (<= y -2.4e+36)
       (* y x)
       (if (<= y 68000000000000.0)
         (- y x)
         (if (<= y 6.2e+30)
           (* y x)
           (if (<= y 2.2e+74)
             y
             (if (<= y 8e+170) (* y x) (if (<= y 7.2e+283) y (* y x))))))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -2.9e+215) {
		tmp = y * x;
	} else if (y <= -7e+169) {
		tmp = y - x;
	} else if (y <= -2.4e+36) {
		tmp = y * x;
	} else if (y <= 68000000000000.0) {
		tmp = y - x;
	} else if (y <= 6.2e+30) {
		tmp = y * x;
	} else if (y <= 2.2e+74) {
		tmp = y;
	} else if (y <= 8e+170) {
		tmp = y * x;
	} else if (y <= 7.2e+283) {
		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 <= (-2.9d+215)) then
        tmp = y * x
    else if (y <= (-7d+169)) then
        tmp = y - x
    else if (y <= (-2.4d+36)) then
        tmp = y * x
    else if (y <= 68000000000000.0d0) then
        tmp = y - x
    else if (y <= 6.2d+30) then
        tmp = y * x
    else if (y <= 2.2d+74) then
        tmp = y
    else if (y <= 8d+170) then
        tmp = y * x
    else if (y <= 7.2d+283) 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 <= -2.9e+215) {
		tmp = y * x;
	} else if (y <= -7e+169) {
		tmp = y - x;
	} else if (y <= -2.4e+36) {
		tmp = y * x;
	} else if (y <= 68000000000000.0) {
		tmp = y - x;
	} else if (y <= 6.2e+30) {
		tmp = y * x;
	} else if (y <= 2.2e+74) {
		tmp = y;
	} else if (y <= 8e+170) {
		tmp = y * x;
	} else if (y <= 7.2e+283) {
		tmp = y;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -2.9e+215:
		tmp = y * x
	elif y <= -7e+169:
		tmp = y - x
	elif y <= -2.4e+36:
		tmp = y * x
	elif y <= 68000000000000.0:
		tmp = y - x
	elif y <= 6.2e+30:
		tmp = y * x
	elif y <= 2.2e+74:
		tmp = y
	elif y <= 8e+170:
		tmp = y * x
	elif y <= 7.2e+283:
		tmp = y
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -2.9e+215)
		tmp = Float64(y * x);
	elseif (y <= -7e+169)
		tmp = Float64(y - x);
	elseif (y <= -2.4e+36)
		tmp = Float64(y * x);
	elseif (y <= 68000000000000.0)
		tmp = Float64(y - x);
	elseif (y <= 6.2e+30)
		tmp = Float64(y * x);
	elseif (y <= 2.2e+74)
		tmp = y;
	elseif (y <= 8e+170)
		tmp = Float64(y * x);
	elseif (y <= 7.2e+283)
		tmp = y;
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -2.9e+215)
		tmp = y * x;
	elseif (y <= -7e+169)
		tmp = y - x;
	elseif (y <= -2.4e+36)
		tmp = y * x;
	elseif (y <= 68000000000000.0)
		tmp = y - x;
	elseif (y <= 6.2e+30)
		tmp = y * x;
	elseif (y <= 2.2e+74)
		tmp = y;
	elseif (y <= 8e+170)
		tmp = y * x;
	elseif (y <= 7.2e+283)
		tmp = y;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -2.9e+215], N[(y * x), $MachinePrecision], If[LessEqual[y, -7e+169], N[(y - x), $MachinePrecision], If[LessEqual[y, -2.4e+36], N[(y * x), $MachinePrecision], If[LessEqual[y, 68000000000000.0], N[(y - x), $MachinePrecision], If[LessEqual[y, 6.2e+30], N[(y * x), $MachinePrecision], If[LessEqual[y, 2.2e+74], y, If[LessEqual[y, 8e+170], N[(y * x), $MachinePrecision], If[LessEqual[y, 7.2e+283], y, N[(y * x), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.8999999999999999e215 or -7.00000000000000038e169 < y < -2.39999999999999992e36 or 6.8e13 < y < 6.1999999999999995e30 or 2.2000000000000001e74 < y < 8.00000000000000028e170 or 7.20000000000000034e283 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 72.8%

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

   3. Taylor expanded in y around inf 72.8%

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

   if -2.8999999999999999e215 < y < -7.00000000000000038e169 or -2.39999999999999992e36 < y < 6.8e13

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 94.5%

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

   if 6.1999999999999995e30 < y < 2.2000000000000001e74 or 8.00000000000000028e170 < y < 7.20000000000000034e283

   1. Initial program 99.9%

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

   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 73.2%

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

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{+215}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -7 \cdot 10^{+169}:\\ \;\;\;\;y - x\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{+36}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 68000000000000:\\ \;\;\;\;y - x\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+30}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+74}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+170}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+283}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

Alternative 3: 62.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+215}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{+169}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{+22}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -9 \cdot 10^{-51}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-15}:\\ \;\;\;\;-x\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+170}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+282}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -3.4e+215)
   (* y x)
   (if (<= y -6.5e+169)
     y
     (if (<= y -1.2e+22)
       (* y x)
       (if (<= y -9e-51)
         y
         (if (<= y 1.35e-15)
           (- x)
           (if (<= y 2.9e+170) (* y x) (if (<= y 9.5e+282) y (* y x)))))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -3.4e+215) {
		tmp = y * x;
	} else if (y <= -6.5e+169) {
		tmp = y;
	} else if (y <= -1.2e+22) {
		tmp = y * x;
	} else if (y <= -9e-51) {
		tmp = y;
	} else if (y <= 1.35e-15) {
		tmp = -x;
	} else if (y <= 2.9e+170) {
		tmp = y * x;
	} else if (y <= 9.5e+282) {
		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 <= (-3.4d+215)) then
        tmp = y * x
    else if (y <= (-6.5d+169)) then
        tmp = y
    else if (y <= (-1.2d+22)) then
        tmp = y * x
    else if (y <= (-9d-51)) then
        tmp = y
    else if (y <= 1.35d-15) then
        tmp = -x
    else if (y <= 2.9d+170) then
        tmp = y * x
    else if (y <= 9.5d+282) 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 <= -3.4e+215) {
		tmp = y * x;
	} else if (y <= -6.5e+169) {
		tmp = y;
	} else if (y <= -1.2e+22) {
		tmp = y * x;
	} else if (y <= -9e-51) {
		tmp = y;
	} else if (y <= 1.35e-15) {
		tmp = -x;
	} else if (y <= 2.9e+170) {
		tmp = y * x;
	} else if (y <= 9.5e+282) {
		tmp = y;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -3.4e+215:
		tmp = y * x
	elif y <= -6.5e+169:
		tmp = y
	elif y <= -1.2e+22:
		tmp = y * x
	elif y <= -9e-51:
		tmp = y
	elif y <= 1.35e-15:
		tmp = -x
	elif y <= 2.9e+170:
		tmp = y * x
	elif y <= 9.5e+282:
		tmp = y
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -3.4e+215)
		tmp = Float64(y * x);
	elseif (y <= -6.5e+169)
		tmp = y;
	elseif (y <= -1.2e+22)
		tmp = Float64(y * x);
	elseif (y <= -9e-51)
		tmp = y;
	elseif (y <= 1.35e-15)
		tmp = Float64(-x);
	elseif (y <= 2.9e+170)
		tmp = Float64(y * x);
	elseif (y <= 9.5e+282)
		tmp = y;
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -3.4e+215)
		tmp = y * x;
	elseif (y <= -6.5e+169)
		tmp = y;
	elseif (y <= -1.2e+22)
		tmp = y * x;
	elseif (y <= -9e-51)
		tmp = y;
	elseif (y <= 1.35e-15)
		tmp = -x;
	elseif (y <= 2.9e+170)
		tmp = y * x;
	elseif (y <= 9.5e+282)
		tmp = y;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -3.4e+215], N[(y * x), $MachinePrecision], If[LessEqual[y, -6.5e+169], y, If[LessEqual[y, -1.2e+22], N[(y * x), $MachinePrecision], If[LessEqual[y, -9e-51], y, If[LessEqual[y, 1.35e-15], (-x), If[LessEqual[y, 2.9e+170], N[(y * x), $MachinePrecision], If[LessEqual[y, 9.5e+282], y, N[(y * x), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.40000000000000018e215 or -6.4999999999999995e169 < y < -1.2e22 or 1.35000000000000005e-15 < y < 2.9000000000000001e170 or 9.5000000000000005e282 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 64.9%

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

   3. Taylor expanded in y around inf 61.5%

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

   if -3.40000000000000018e215 < y < -6.4999999999999995e169 or -1.2e22 < y < -8.99999999999999948e-51 or 2.9000000000000001e170 < y < 9.5000000000000005e282

   1. Initial program 99.9%

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

   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 72.8%

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

   if -8.99999999999999948e-51 < y < 1.35000000000000005e-15

   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 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+215}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{+169}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{+22}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -9 \cdot 10^{-51}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-15}:\\ \;\;\;\;-x\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+170}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+282}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

Alternative 4: 98.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.2 \lor \neg \left(y \leq 1.35 \cdot 10^{-15}\right):\\ \;\;\;\;y \cdot \left(x + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -4.2) (not (<= y 1.35e-15))) (* y (+ x 1.0)) (- y x)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -4.2) || !(y <= 1.35e-15)) {
		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 <= (-4.2d0)) .or. (.not. (y <= 1.35d-15))) 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 <= -4.2) || !(y <= 1.35e-15)) {
		tmp = y * (x + 1.0);
	} else {
		tmp = y - x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -4.2) or not (y <= 1.35e-15):
		tmp = y * (x + 1.0)
	else:
		tmp = y - x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -4.2) || !(y <= 1.35e-15))
		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 <= -4.2) || ~((y <= 1.35e-15)))
		tmp = y * (x + 1.0);
	else
		tmp = y - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -4.2], N[Not[LessEqual[y, 1.35e-15]], $MachinePrecision]], N[(y * N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(y - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.20000000000000018 or 1.35000000000000005e-15 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 99.9%

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

   3. Taylor expanded in y around inf 96.7%

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

   if -4.20000000000000018 < y < 1.35000000000000005e-15

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 99.8%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \lor \neg \left(y \leq 1.35 \cdot 10^{-15}\right):\\ \;\;\;\;y \cdot \left(x + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y - x\\ \end{array} \]

Alternative 5: 98.9% accurate, 0.8× speedup

Math

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

FPCore

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

C

double code(double x, double y) {
	double tmp;
	if ((x <= -1.0) || !(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 <= (-1.0d0)) .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 <= -1.0) || !(x <= 1.0)) {
		tmp = x * (y + -1.0);
	} else {
		tmp = y - x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -1.0) 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 <= -1.0) || !(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 <= -1.0) || ~((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, -1.0], 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 < -1 or 1 < x

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 98.6%

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

   if -1 < x < 1

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 98.1%

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

4. Final simplification 98.4%

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

Alternative 6: 98.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.2 \lor \neg \left(y \leq 1.35 \cdot 10^{-15}\right):\\ \;\;\;\;y + y \cdot x\\ \mathbf{else}:\\ \;\;\;\;y - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -4.2) (not (<= y 1.35e-15))) (+ y (* y x)) (- y x)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -4.2) || !(y <= 1.35e-15)) {
		tmp = y + (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 <= (-4.2d0)) .or. (.not. (y <= 1.35d-15))) then
        tmp = y + (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 <= -4.2) || !(y <= 1.35e-15)) {
		tmp = y + (y * x);
	} else {
		tmp = y - x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -4.2) or not (y <= 1.35e-15):
		tmp = y + (y * x)
	else:
		tmp = y - x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -4.2) || !(y <= 1.35e-15))
		tmp = Float64(y + Float64(y * x));
	else
		tmp = Float64(y - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -4.2) || ~((y <= 1.35e-15)))
		tmp = y + (y * x);
	else
		tmp = y - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -4.2], N[Not[LessEqual[y, 1.35e-15]], $MachinePrecision]], N[(y + N[(y * x), $MachinePrecision]), $MachinePrecision], N[(y - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.20000000000000018 or 1.35000000000000005e-15 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 99.9%

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

   3. Taylor expanded in y around inf 96.7%

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

   4. Taylor expanded in x around 0 96.7%

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

   if -4.20000000000000018 < y < 1.35000000000000005e-15

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 99.8%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \lor \neg \left(y \leq 1.35 \cdot 10^{-15}\right):\\ \;\;\;\;y + y \cdot x\\ \mathbf{else}:\\ \;\;\;\;y - x\\ \end{array} \]

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 99.9%

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

2. Final simplification 99.9%

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

Alternative 8: 62.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{-51}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-17}:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -4.4e-51) y (if (<= y 3.8e-17) (- x) y)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -4.4e-51) {
		tmp = y;
	} else if (y <= 3.8e-17) {
		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 <= (-4.4d-51)) then
        tmp = y
    else if (y <= 3.8d-17) 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 <= -4.4e-51) {
		tmp = y;
	} else if (y <= 3.8e-17) {
		tmp = -x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -4.4e-51:
		tmp = y
	elif y <= 3.8e-17:
		tmp = -x
	else:
		tmp = y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -4.4e-51)
		tmp = y;
	elseif (y <= 3.8e-17)
		tmp = Float64(-x);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -4.4e-51)
		tmp = y;
	elseif (y <= 3.8e-17)
		tmp = -x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -4.4e-51], y, If[LessEqual[y, 3.8e-17], (-x), y]]

Derivation

1. Split input into 2 regimes

2. if y < -4.4e-51 or 3.8000000000000001e-17 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 99.9%

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

   3. Taylor expanded in x around 0 48.1%

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

   if -4.4e-51 < y < 3.8000000000000001e-17

   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 64.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{-51}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-17}:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 9: 38.2% 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 99.9%

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

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 34.5%

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

4. Final simplification 34.5%

   \[\leadsto y \]

Reproduce

herbie shell --seed 2023252 
(FPCore (x y)
  :name "Data.Colour.SRGB:transferFunction from colour-2.3.3"
  :precision binary64
  (- (* (+ x 1.0) y) x))