Data.Colour.SRGB:invTransferFunction from colour-2.3.3

Percentage Accurate: 100.0% → 100.0%

Time: 9.0s

Alternatives: 9

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[\frac{x + y}{y + 1} \]
2. Add Preprocessing
3. Add Preprocessing

Alternative 2: 86.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{+53}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;\left(x + y\right) \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -4.8e+53)
   1.0
   (if (<= y -1.0) (/ x y) (if (<= y 1.0) (* (+ x y) (- 1.0 y)) 1.0))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -4.8e+53) {
		tmp = 1.0;
	} else if (y <= -1.0) {
		tmp = x / y;
	} else if (y <= 1.0) {
		tmp = (x + y) * (1.0 - 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 <= (-4.8d+53)) then
        tmp = 1.0d0
    else if (y <= (-1.0d0)) then
        tmp = x / y
    else if (y <= 1.0d0) then
        tmp = (x + y) * (1.0d0 - y)
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -4.8e+53) {
		tmp = 1.0;
	} else if (y <= -1.0) {
		tmp = x / y;
	} else if (y <= 1.0) {
		tmp = (x + y) * (1.0 - y);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -4.8e+53:
		tmp = 1.0
	elif y <= -1.0:
		tmp = x / y
	elif y <= 1.0:
		tmp = (x + y) * (1.0 - y)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -4.8e+53)
		tmp = 1.0;
	elseif (y <= -1.0)
		tmp = Float64(x / y);
	elseif (y <= 1.0)
		tmp = Float64(Float64(x + y) * Float64(1.0 - y));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -4.8e+53)
		tmp = 1.0;
	elseif (y <= -1.0)
		tmp = x / y;
	elseif (y <= 1.0)
		tmp = (x + y) * (1.0 - y);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -4.8e+53], 1.0, If[LessEqual[y, -1.0], N[(x / y), $MachinePrecision], If[LessEqual[y, 1.0], N[(N[(x + y), $MachinePrecision] * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], 1.0]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.8e53 or 1 < y

   1. Initial program 100.0%

      \[\frac{x + y}{y + 1} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{1} \]
   4. Step-by-step derivation

   5. Applied rewrites 76.2%

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

   if -4.8e53 < y < -1

   1. Initial program 100.0%

      \[\frac{x + y}{y + 1} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 50.8

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

   5. Applied rewrites 50.8%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 44.9%

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

   if -1 < y < 1

   1. Initial program 100.0%

      \[\frac{x + y}{y + 1} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. div-inv N/A

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

      3. lift-+.f64 N/A

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

      4. flip3-+ N/A

         \[\leadsto \left(x + y\right) \cdot \frac{1}{\color{blue}{\frac{{y}^{3} + {1}^{3}}{y \cdot y + \left(1 \cdot 1 - y \cdot 1\right)}}} \]

      5. clear-num N/A

         \[\leadsto \left(x + y\right) \cdot \color{blue}{\frac{y \cdot y + \left(1 \cdot 1 - y \cdot 1\right)}{{y}^{3} + {1}^{3}}} \]

      6. *-commutative N/A

         \[\leadsto \color{blue}{\frac{y \cdot y + \left(1 \cdot 1 - y \cdot 1\right)}{{y}^{3} + {1}^{3}} \cdot \left(x + y\right)} \]

      7. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{y \cdot y + \left(1 \cdot 1 - y \cdot 1\right)}{{y}^{3} + {1}^{3}} \cdot \left(x + y\right)} \]

      8. clear-num N/A

         \[\leadsto \color{blue}{\frac{1}{\frac{{y}^{3} + {1}^{3}}{y \cdot y + \left(1 \cdot 1 - y \cdot 1\right)}}} \cdot \left(x + y\right) \]

      9. flip3-+ N/A

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

      10. lift-+.f64 N/A

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

      11. lower-/.f64 100.0

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

   4. Applied rewrites 100.0%

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

   5. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. lower--.f64 99.1

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

   7. Applied rewrites 99.1%

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

4. Final simplification 86.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{+53}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;\left(x + y\right) \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024228 
(FPCore (x y)
  :name "Data.Colour.SRGB:invTransferFunction from colour-2.3.3"
  :precision binary64
  (/ (+ x y) (+ y 1.0)))