Data.Colour.SRGB:transferFunction from colour-2.3.3

Percentage Accurate: 100.0% → 100.0%

Time: 4.5s

Alternatives: 7

Speedup: N/A×

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

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[\left(x + 1\right) \cdot y - x \]
2. Step-by-step derivation

   1. sub-neg N/A

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

   2. distribute-rgt1-in N/A

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

   3. *-commutative N/A

      \[\leadsto \left(y + y \cdot x\right) + \left(\mathsf{neg}\left(x\right)\right) \]

   4. associate-+l+ N/A

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

   5. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{\left(y \cdot x + \left(\mathsf{neg}\left(x\right)\right)\right)}\right) \]

   6. neg-mul-1 N/A

      \[\leadsto \mathsf{+.f64}\left(y, \left(y \cdot x + -1 \cdot \color{blue}{x}\right)\right) \]

   7. distribute-rgt-out N/A

      \[\leadsto \mathsf{+.f64}\left(y, \left(x \cdot \color{blue}{\left(y + -1\right)}\right)\right) \]

   8. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(x, \color{blue}{\left(y + -1\right)}\right)\right) \]

   9. +-lowering-+.f64 100.0%

      \[\leadsto \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(y, \color{blue}{-1}\right)\right)\right) \]

3. Simplified 100.0%

   \[\leadsto \color{blue}{y + x \cdot \left(y + -1\right)} \]
4. Add Preprocessing
5. Add Preprocessing

Alternative 2: 62.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{+136}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -8.2 \cdot 10^{-42}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-46}:\\ \;\;\;\;0 - x\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+91}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -5.2e+136)
   (* y x)
   (if (<= y -8.2e-42)
     y
     (if (<= y 4.2e-46) (- 0.0 x) (if (<= y 1.55e+91) y (* y x))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -5.2e+136) {
		tmp = y * x;
	} else if (y <= -8.2e-42) {
		tmp = y;
	} else if (y <= 4.2e-46) {
		tmp = 0.0 - x;
	} else if (y <= 1.55e+91) {
		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 <= (-5.2d+136)) then
        tmp = y * x
    else if (y <= (-8.2d-42)) then
        tmp = y
    else if (y <= 4.2d-46) then
        tmp = 0.0d0 - x
    else if (y <= 1.55d+91) 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 <= -5.2e+136) {
		tmp = y * x;
	} else if (y <= -8.2e-42) {
		tmp = y;
	} else if (y <= 4.2e-46) {
		tmp = 0.0 - x;
	} else if (y <= 1.55e+91) {
		tmp = y;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -5.2e+136:
		tmp = y * x
	elif y <= -8.2e-42:
		tmp = y
	elif y <= 4.2e-46:
		tmp = 0.0 - x
	elif y <= 1.55e+91:
		tmp = y
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -5.2e+136)
		tmp = Float64(y * x);
	elseif (y <= -8.2e-42)
		tmp = y;
	elseif (y <= 4.2e-46)
		tmp = Float64(0.0 - x);
	elseif (y <= 1.55e+91)
		tmp = y;
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -5.2e+136)
		tmp = y * x;
	elseif (y <= -8.2e-42)
		tmp = y;
	elseif (y <= 4.2e-46)
		tmp = 0.0 - x;
	elseif (y <= 1.55e+91)
		tmp = y;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -5.2e+136], N[(y * x), $MachinePrecision], If[LessEqual[y, -8.2e-42], y, If[LessEqual[y, 4.2e-46], N[(0.0 - x), $MachinePrecision], If[LessEqual[y, 1.55e+91], y, N[(y * x), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.2000000000000003e136 or 1.54999999999999999e91 < y

   1. Initial program 100.0%

      \[\left(x + 1\right) \cdot y - x \]
   2. Step-by-step derivation

      1. sub-neg N/A

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

      2. distribute-rgt1-in N/A

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

      3. *-commutative N/A

         \[\leadsto \left(y + y \cdot x\right) + \left(\mathsf{neg}\left(x\right)\right) \]

      4. associate-+l+ N/A

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

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{\left(y \cdot x + \left(\mathsf{neg}\left(x\right)\right)\right)}\right) \]

      6. neg-mul-1 N/A

         \[\leadsto \mathsf{+.f64}\left(y, \left(y \cdot x + -1 \cdot \color{blue}{x}\right)\right) \]

      7. distribute-rgt-out N/A

         \[\leadsto \mathsf{+.f64}\left(y, \left(x \cdot \color{blue}{\left(y + -1\right)}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(x, \color{blue}{\left(y + -1\right)}\right)\right) \]

      9. +-lowering-+.f64 100.0%

         \[\leadsto \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(y, \color{blue}{-1}\right)\right)\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{y + x \cdot \left(y + -1\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(y - 1\right)} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(y - 1\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(y + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right) \]

      3. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(y + -1\right)\right) \]

      4. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(-1 + \color{blue}{y}\right)\right) \]

      5. +-lowering-+.f64 65.8%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(-1, \color{blue}{y}\right)\right) \]

   7. Simplified 65.8%

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

   8. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 65.8%

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{y}\right) \]

   10. Simplified 65.8%

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

   if -5.2000000000000003e136 < y < -8.2000000000000003e-42 or 4.19999999999999975e-46 < y < 1.54999999999999999e91

   1. Initial program 100.0%

      \[\left(x + 1\right) \cdot y - x \]
   2. Step-by-step derivation

      1. sub-neg N/A

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

      2. distribute-rgt1-in N/A

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

      3. *-commutative N/A

         \[\leadsto \left(y + y \cdot x\right) + \left(\mathsf{neg}\left(x\right)\right) \]

      4. associate-+l+ N/A

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

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{\left(y \cdot x + \left(\mathsf{neg}\left(x\right)\right)\right)}\right) \]

      6. neg-mul-1 N/A

         \[\leadsto \mathsf{+.f64}\left(y, \left(y \cdot x + -1 \cdot \color{blue}{x}\right)\right) \]

      7. distribute-rgt-out N/A

         \[\leadsto \mathsf{+.f64}\left(y, \left(x \cdot \color{blue}{\left(y + -1\right)}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(x, \color{blue}{\left(y + -1\right)}\right)\right) \]

      9. +-lowering-+.f64 100.0%

         \[\leadsto \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(y, \color{blue}{-1}\right)\right)\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{y + x \cdot \left(y + -1\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0

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

   7. Simplified 63.9%

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

   if -8.2000000000000003e-42 < y < 4.19999999999999975e-46

   1. Initial program 100.0%

      \[\left(x + 1\right) \cdot y - x \]
   2. Step-by-step derivation

      1. sub-neg N/A

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

      2. distribute-rgt1-in N/A

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

      3. *-commutative N/A

         \[\leadsto \left(y + y \cdot x\right) + \left(\mathsf{neg}\left(x\right)\right) \]

      4. associate-+l+ N/A

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

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{\left(y \cdot x + \left(\mathsf{neg}\left(x\right)\right)\right)}\right) \]

      6. neg-mul-1 N/A

         \[\leadsto \mathsf{+.f64}\left(y, \left(y \cdot x + -1 \cdot \color{blue}{x}\right)\right) \]

      7. distribute-rgt-out N/A

         \[\leadsto \mathsf{+.f64}\left(y, \left(x \cdot \color{blue}{\left(y + -1\right)}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(x, \color{blue}{\left(y + -1\right)}\right)\right) \]

      9. +-lowering-+.f64 100.0%

         \[\leadsto \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(y, \color{blue}{-1}\right)\right)\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{y + x \cdot \left(y + -1\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(x\right) \]

      2. neg-sub0 N/A

         \[\leadsto 0 - \color{blue}{x} \]

      3. --lowering--.f64 84.7%

         \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{x}\right) \]

   7. Simplified 84.7%

      \[\leadsto \color{blue}{0 - x} \]
   8. Step-by-step derivation

      1. sub0-neg N/A

         \[\leadsto \mathsf{neg}\left(x\right) \]

      2. neg-lowering-neg.f64 84.7%

         \[\leadsto \mathsf{neg.f64}\left(x\right) \]

   9. Applied egg-rr 84.7%

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

4. Final simplification 73.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{+136}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -8.2 \cdot 10^{-42}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-46}:\\ \;\;\;\;0 - x\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+91}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y + y \cdot x\\ \mathbf{if}\;y \leq -1:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 5.1 \cdot 10^{-8}:\\ \;\;\;\;y - x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ y (* y x))))
   (if (<= y -1.0) t_0 (if (<= y 5.1e-8) (- y x) t_0))))

C

double code(double x, double y) {
	double t_0 = y + (y * x);
	double tmp;
	if (y <= -1.0) {
		tmp = t_0;
	} else if (y <= 5.1e-8) {
		tmp = y - x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = y + (y * x)
    if (y <= (-1.0d0)) then
        tmp = t_0
    else if (y <= 5.1d-8) then
        tmp = y - x
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = y + (y * x);
	double tmp;
	if (y <= -1.0) {
		tmp = t_0;
	} else if (y <= 5.1e-8) {
		tmp = y - x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = y + (y * x)
	tmp = 0
	if y <= -1.0:
		tmp = t_0
	elif y <= 5.1e-8:
		tmp = y - x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(y + Float64(y * x))
	tmp = 0.0
	if (y <= -1.0)
		tmp = t_0;
	elseif (y <= 5.1e-8)
		tmp = Float64(y - x);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = y + (y * x);
	tmp = 0.0;
	if (y <= -1.0)
		tmp = t_0;
	elseif (y <= 5.1e-8)
		tmp = y - x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(y + N[(y * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.0], t$95$0, If[LessEqual[y, 5.1e-8], N[(y - x), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 5.10000000000000001e-8 < y

   1. Initial program 100.0%

      \[\left(x + 1\right) \cdot y - x \]
   2. Step-by-step derivation

      1. sub-neg N/A

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

      2. distribute-rgt1-in N/A

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

      3. *-commutative N/A

         \[\leadsto \left(y + y \cdot x\right) + \left(\mathsf{neg}\left(x\right)\right) \]

      4. associate-+l+ N/A

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

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{\left(y \cdot x + \left(\mathsf{neg}\left(x\right)\right)\right)}\right) \]

      6. neg-mul-1 N/A

         \[\leadsto \mathsf{+.f64}\left(y, \left(y \cdot x + -1 \cdot \color{blue}{x}\right)\right) \]

      7. distribute-rgt-out N/A

         \[\leadsto \mathsf{+.f64}\left(y, \left(x \cdot \color{blue}{\left(y + -1\right)}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(x, \color{blue}{\left(y + -1\right)}\right)\right) \]

      9. +-lowering-+.f64 100.0%

         \[\leadsto \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(y, \color{blue}{-1}\right)\right)\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{y + x \cdot \left(y + -1\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf

      \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{\left(x \cdot y\right)}\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 99.2%

         \[\leadsto \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(x, \color{blue}{y}\right)\right) \]

   7. Simplified 99.2%

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

   if -1 < y < 5.10000000000000001e-8

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{y}, x\right) \]
   4. Step-by-step derivation

   5. Simplified 99.8%

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

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;y + y \cdot x\\ \mathbf{elif}\;y \leq 5.1 \cdot 10^{-8}:\\ \;\;\;\;y - x\\ \mathbf{else}:\\ \;\;\;\;y + y \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 98.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(y + -1\right)\\ \mathbf{if}\;x \leq -4.5:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 0.0126:\\ \;\;\;\;y - x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* x (+ y -1.0))))
   (if (<= x -4.5) t_0 (if (<= x 0.0126) (- y x) t_0))))

C

double code(double x, double y) {
	double t_0 = x * (y + -1.0);
	double tmp;
	if (x <= -4.5) {
		tmp = t_0;
	} else if (x <= 0.0126) {
		tmp = y - x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x * (y + (-1.0d0))
    if (x <= (-4.5d0)) then
        tmp = t_0
    else if (x <= 0.0126d0) then
        tmp = y - x
    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 <= -4.5) {
		tmp = t_0;
	} else if (x <= 0.0126) {
		tmp = y - x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x * (y + -1.0)
	tmp = 0
	if x <= -4.5:
		tmp = t_0
	elif x <= 0.0126:
		tmp = y - x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x * Float64(y + -1.0))
	tmp = 0.0
	if (x <= -4.5)
		tmp = t_0;
	elseif (x <= 0.0126)
		tmp = Float64(y - x);
	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 <= -4.5)
		tmp = t_0;
	elseif (x <= 0.0126)
		tmp = y - x;
	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, -4.5], t$95$0, If[LessEqual[x, 0.0126], N[(y - x), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -4.5 or 0.0126 < x

   1. Initial program 100.0%

      \[\left(x + 1\right) \cdot y - x \]
   2. Step-by-step derivation

      1. sub-neg N/A

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

      2. distribute-rgt1-in N/A

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

      3. *-commutative N/A

         \[\leadsto \left(y + y \cdot x\right) + \left(\mathsf{neg}\left(x\right)\right) \]

      4. associate-+l+ N/A

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

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{\left(y \cdot x + \left(\mathsf{neg}\left(x\right)\right)\right)}\right) \]

      6. neg-mul-1 N/A

         \[\leadsto \mathsf{+.f64}\left(y, \left(y \cdot x + -1 \cdot \color{blue}{x}\right)\right) \]

      7. distribute-rgt-out N/A

         \[\leadsto \mathsf{+.f64}\left(y, \left(x \cdot \color{blue}{\left(y + -1\right)}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(x, \color{blue}{\left(y + -1\right)}\right)\right) \]

      9. +-lowering-+.f64 100.0%

         \[\leadsto \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(y, \color{blue}{-1}\right)\right)\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{y + x \cdot \left(y + -1\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(y - 1\right)} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(y - 1\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(y + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right) \]

      3. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(y + -1\right)\right) \]

      4. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(-1 + \color{blue}{y}\right)\right) \]

      5. +-lowering-+.f64 99.2%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(-1, \color{blue}{y}\right)\right) \]

   7. Simplified 99.2%

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

   if -4.5 < x < 0.0126

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{y}, x\right) \]
   4. Step-by-step derivation

   5. Simplified 98.6%

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

4. Final simplification 98.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.5:\\ \;\;\;\;x \cdot \left(y + -1\right)\\ \mathbf{elif}\;x \leq 0.0126:\\ \;\;\;\;y - x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+136}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+90}:\\ \;\;\;\;y - x\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -7e+136) (* y x) (if (<= y 3.4e+90) (- y x) (* y x))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -7e+136) {
		tmp = y * x;
	} else if (y <= 3.4e+90) {
		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 <= (-7d+136)) then
        tmp = y * x
    else if (y <= 3.4d+90) 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 <= -7e+136) {
		tmp = y * x;
	} else if (y <= 3.4e+90) {
		tmp = y - x;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -7e+136:
		tmp = y * x
	elif y <= 3.4e+90:
		tmp = y - x
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -7e+136)
		tmp = Float64(y * x);
	elseif (y <= 3.4e+90)
		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 <= -7e+136)
		tmp = y * x;
	elseif (y <= 3.4e+90)
		tmp = y - x;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -7e+136], N[(y * x), $MachinePrecision], If[LessEqual[y, 3.4e+90], N[(y - x), $MachinePrecision], N[(y * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -7.00000000000000002e136 or 3.40000000000000018e90 < y

   1. Initial program 100.0%

      \[\left(x + 1\right) \cdot y - x \]
   2. Step-by-step derivation

      1. sub-neg N/A

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

      2. distribute-rgt1-in N/A

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

      3. *-commutative N/A

         \[\leadsto \left(y + y \cdot x\right) + \left(\mathsf{neg}\left(x\right)\right) \]

      4. associate-+l+ N/A

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

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{\left(y \cdot x + \left(\mathsf{neg}\left(x\right)\right)\right)}\right) \]

      6. neg-mul-1 N/A

         \[\leadsto \mathsf{+.f64}\left(y, \left(y \cdot x + -1 \cdot \color{blue}{x}\right)\right) \]

      7. distribute-rgt-out N/A

         \[\leadsto \mathsf{+.f64}\left(y, \left(x \cdot \color{blue}{\left(y + -1\right)}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(x, \color{blue}{\left(y + -1\right)}\right)\right) \]

      9. +-lowering-+.f64 100.0%

         \[\leadsto \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(y, \color{blue}{-1}\right)\right)\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{y + x \cdot \left(y + -1\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(y - 1\right)} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(y - 1\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(y + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right) \]

      3. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(y + -1\right)\right) \]

      4. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(-1 + \color{blue}{y}\right)\right) \]

      5. +-lowering-+.f64 65.8%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(-1, \color{blue}{y}\right)\right) \]

   7. Simplified 65.8%

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

   8. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 65.8%

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{y}\right) \]

   10. Simplified 65.8%

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

   if -7.00000000000000002e136 < y < 3.40000000000000018e90

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{y}, x\right) \]
   4. Step-by-step derivation

   5. Simplified 87.1%

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

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+136}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+90}:\\ \;\;\;\;y - x\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 62.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{-42}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-46}:\\ \;\;\;\;0 - x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -8.2e-42) y (if (<= y 4.2e-46) (- 0.0 x) y)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -8.2e-42) {
		tmp = y;
	} else if (y <= 4.2e-46) {
		tmp = 0.0 - 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 <= (-8.2d-42)) then
        tmp = y
    else if (y <= 4.2d-46) then
        tmp = 0.0d0 - x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -8.2e-42) {
		tmp = y;
	} else if (y <= 4.2e-46) {
		tmp = 0.0 - x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -8.2e-42:
		tmp = y
	elif y <= 4.2e-46:
		tmp = 0.0 - x
	else:
		tmp = y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -8.2e-42)
		tmp = y;
	elseif (y <= 4.2e-46)
		tmp = Float64(0.0 - x);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -8.2e-42)
		tmp = y;
	elseif (y <= 4.2e-46)
		tmp = 0.0 - x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -8.2e-42], y, If[LessEqual[y, 4.2e-46], N[(0.0 - x), $MachinePrecision], y]]

Derivation

1. Split input into 2 regimes

2. if y < -8.2000000000000003e-42 or 4.19999999999999975e-46 < y

   1. Initial program 100.0%

      \[\left(x + 1\right) \cdot y - x \]
   2. Step-by-step derivation

      1. sub-neg N/A

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

      2. distribute-rgt1-in N/A

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

      3. *-commutative N/A

         \[\leadsto \left(y + y \cdot x\right) + \left(\mathsf{neg}\left(x\right)\right) \]

      4. associate-+l+ N/A

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

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{\left(y \cdot x + \left(\mathsf{neg}\left(x\right)\right)\right)}\right) \]

      6. neg-mul-1 N/A

         \[\leadsto \mathsf{+.f64}\left(y, \left(y \cdot x + -1 \cdot \color{blue}{x}\right)\right) \]

      7. distribute-rgt-out N/A

         \[\leadsto \mathsf{+.f64}\left(y, \left(x \cdot \color{blue}{\left(y + -1\right)}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(x, \color{blue}{\left(y + -1\right)}\right)\right) \]

      9. +-lowering-+.f64 100.0%

         \[\leadsto \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(y, \color{blue}{-1}\right)\right)\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{y + x \cdot \left(y + -1\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0

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

   7. Simplified 50.2%

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

   if -8.2000000000000003e-42 < y < 4.19999999999999975e-46

   1. Initial program 100.0%

      \[\left(x + 1\right) \cdot y - x \]
   2. Step-by-step derivation

      1. sub-neg N/A

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

      2. distribute-rgt1-in N/A

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

      3. *-commutative N/A

         \[\leadsto \left(y + y \cdot x\right) + \left(\mathsf{neg}\left(x\right)\right) \]

      4. associate-+l+ N/A

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

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{\left(y \cdot x + \left(\mathsf{neg}\left(x\right)\right)\right)}\right) \]

      6. neg-mul-1 N/A

         \[\leadsto \mathsf{+.f64}\left(y, \left(y \cdot x + -1 \cdot \color{blue}{x}\right)\right) \]

      7. distribute-rgt-out N/A

         \[\leadsto \mathsf{+.f64}\left(y, \left(x \cdot \color{blue}{\left(y + -1\right)}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(x, \color{blue}{\left(y + -1\right)}\right)\right) \]

      9. +-lowering-+.f64 100.0%

         \[\leadsto \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(y, \color{blue}{-1}\right)\right)\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{y + x \cdot \left(y + -1\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(x\right) \]

      2. neg-sub0 N/A

         \[\leadsto 0 - \color{blue}{x} \]

      3. --lowering--.f64 84.7%

         \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{x}\right) \]

   7. Simplified 84.7%

      \[\leadsto \color{blue}{0 - x} \]
   8. Step-by-step derivation

      1. sub0-neg N/A

         \[\leadsto \mathsf{neg}\left(x\right) \]

      2. neg-lowering-neg.f64 84.7%

         \[\leadsto \mathsf{neg.f64}\left(x\right) \]

   9. Applied egg-rr 84.7%

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

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{-42}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-46}:\\ \;\;\;\;0 - x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 38.0% 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. Step-by-step derivation

   1. sub-neg N/A

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

   2. distribute-rgt1-in N/A

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

   3. *-commutative N/A

      \[\leadsto \left(y + y \cdot x\right) + \left(\mathsf{neg}\left(x\right)\right) \]

   4. associate-+l+ N/A

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

   5. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{\left(y \cdot x + \left(\mathsf{neg}\left(x\right)\right)\right)}\right) \]

   6. neg-mul-1 N/A

      \[\leadsto \mathsf{+.f64}\left(y, \left(y \cdot x + -1 \cdot \color{blue}{x}\right)\right) \]

   7. distribute-rgt-out N/A

      \[\leadsto \mathsf{+.f64}\left(y, \left(x \cdot \color{blue}{\left(y + -1\right)}\right)\right) \]

   8. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(x, \color{blue}{\left(y + -1\right)}\right)\right) \]

   9. +-lowering-+.f64 100.0%

      \[\leadsto \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(y, \color{blue}{-1}\right)\right)\right) \]

3. Simplified 100.0%

   \[\leadsto \color{blue}{y + x \cdot \left(y + -1\right)} \]
4. Add Preprocessing

5. Taylor expanded in x around 0

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

7. Simplified 35.5%

   \[\leadsto \color{blue}{y} \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2024150 
(FPCore (x y)
  :name "Data.Colour.SRGB:transferFunction from colour-2.3.3"
  :precision binary64
  (- (* (+ x 1.0) y) x))