Data.Colour.SRGB:invTransferFunction from colour-2.3.3

Percentage Accurate: 100.0% → 100.0%

Time: 5.0s

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: 86.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + \frac{x + -1}{y}\\ t_1 := \frac{x}{y + 1}\\ \mathbf{if}\;y \leq -320000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-123}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-79}:\\ \;\;\;\;\frac{y}{y + 1}\\ \mathbf{elif}\;y \leq 59:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ 1.0 (/ (+ x -1.0) y))) (t_1 (/ x (+ y 1.0))))
   (if (<= y -320000.0)
     t_0
     (if (<= y 5.5e-123)
       t_1
       (if (<= y 2.1e-79) (/ y (+ y 1.0)) (if (<= y 59.0) t_1 t_0))))))

C

double code(double x, double y) {
	double t_0 = 1.0 + ((x + -1.0) / y);
	double t_1 = x / (y + 1.0);
	double tmp;
	if (y <= -320000.0) {
		tmp = t_0;
	} else if (y <= 5.5e-123) {
		tmp = t_1;
	} else if (y <= 2.1e-79) {
		tmp = y / (y + 1.0);
	} else if (y <= 59.0) {
		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 + ((x + (-1.0d0)) / y)
    t_1 = x / (y + 1.0d0)
    if (y <= (-320000.0d0)) then
        tmp = t_0
    else if (y <= 5.5d-123) then
        tmp = t_1
    else if (y <= 2.1d-79) then
        tmp = y / (y + 1.0d0)
    else if (y <= 59.0d0) 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 + ((x + -1.0) / y);
	double t_1 = x / (y + 1.0);
	double tmp;
	if (y <= -320000.0) {
		tmp = t_0;
	} else if (y <= 5.5e-123) {
		tmp = t_1;
	} else if (y <= 2.1e-79) {
		tmp = y / (y + 1.0);
	} else if (y <= 59.0) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 1.0 + ((x + -1.0) / y)
	t_1 = x / (y + 1.0)
	tmp = 0
	if y <= -320000.0:
		tmp = t_0
	elif y <= 5.5e-123:
		tmp = t_1
	elif y <= 2.1e-79:
		tmp = y / (y + 1.0)
	elif y <= 59.0:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(1.0 + Float64(Float64(x + -1.0) / y))
	t_1 = Float64(x / Float64(y + 1.0))
	tmp = 0.0
	if (y <= -320000.0)
		tmp = t_0;
	elseif (y <= 5.5e-123)
		tmp = t_1;
	elseif (y <= 2.1e-79)
		tmp = Float64(y / Float64(y + 1.0));
	elseif (y <= 59.0)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = 1.0 + ((x + -1.0) / y);
	t_1 = x / (y + 1.0);
	tmp = 0.0;
	if (y <= -320000.0)
		tmp = t_0;
	elseif (y <= 5.5e-123)
		tmp = t_1;
	elseif (y <= 2.1e-79)
		tmp = y / (y + 1.0);
	elseif (y <= 59.0)
		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[(x + -1.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -320000.0], t$95$0, If[LessEqual[y, 5.5e-123], t$95$1, If[LessEqual[y, 2.1e-79], N[(y / N[(y + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 59.0], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.2e5 or 59 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 99.3%

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

      1. associate--l+ 99.3%

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

      2. div-sub 99.3%

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

      3. sub-neg 99.3%

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

      4. metadata-eval 99.3%

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

   5. Simplified 99.3%

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

   if -3.2e5 < y < 5.5e-123 or 2.0999999999999999e-79 < y < 59

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 75.3%

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

      1. +-commutative 75.3%

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

   5. Simplified 75.3%

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

   if 5.5e-123 < y < 2.0999999999999999e-79

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 87.7%

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

      1. +-commutative 87.7%

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

   5. Simplified 87.7%

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

Alternative 3: 74.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{y + 1}\\ \mathbf{if}\;y \leq -3.5 \cdot 10^{+35}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-123}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-77}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+43}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ x (+ y 1.0))))
   (if (<= y -3.5e+35)
     1.0
     (if (<= y 4.8e-123)
       t_0
       (if (<= y 1.3e-77) y (if (<= y 1.7e+43) t_0 1.0))))))

C

double code(double x, double y) {
	double t_0 = x / (y + 1.0);
	double tmp;
	if (y <= -3.5e+35) {
		tmp = 1.0;
	} else if (y <= 4.8e-123) {
		tmp = t_0;
	} else if (y <= 1.3e-77) {
		tmp = y;
	} else if (y <= 1.7e+43) {
		tmp = t_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) :: t_0
    real(8) :: tmp
    t_0 = x / (y + 1.0d0)
    if (y <= (-3.5d+35)) then
        tmp = 1.0d0
    else if (y <= 4.8d-123) then
        tmp = t_0
    else if (y <= 1.3d-77) then
        tmp = y
    else if (y <= 1.7d+43) then
        tmp = t_0
    else
        tmp = 1.0d0
    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 (y <= -3.5e+35) {
		tmp = 1.0;
	} else if (y <= 4.8e-123) {
		tmp = t_0;
	} else if (y <= 1.3e-77) {
		tmp = y;
	} else if (y <= 1.7e+43) {
		tmp = t_0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x / (y + 1.0)
	tmp = 0
	if y <= -3.5e+35:
		tmp = 1.0
	elif y <= 4.8e-123:
		tmp = t_0
	elif y <= 1.3e-77:
		tmp = y
	elif y <= 1.7e+43:
		tmp = t_0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x / Float64(y + 1.0))
	tmp = 0.0
	if (y <= -3.5e+35)
		tmp = 1.0;
	elseif (y <= 4.8e-123)
		tmp = t_0;
	elseif (y <= 1.3e-77)
		tmp = y;
	elseif (y <= 1.7e+43)
		tmp = t_0;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = x / (y + 1.0);
	tmp = 0.0;
	if (y <= -3.5e+35)
		tmp = 1.0;
	elseif (y <= 4.8e-123)
		tmp = t_0;
	elseif (y <= 1.3e-77)
		tmp = y;
	elseif (y <= 1.7e+43)
		tmp = t_0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.5e+35], 1.0, If[LessEqual[y, 4.8e-123], t$95$0, If[LessEqual[y, 1.3e-77], y, If[LessEqual[y, 1.7e+43], t$95$0, 1.0]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.5000000000000001e35 or 1.70000000000000006e43 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 81.1%

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

   if -3.5000000000000001e35 < y < 4.8e-123 or 1.3000000000000001e-77 < y < 1.70000000000000006e43

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 71.6%

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

      1. +-commutative 71.6%

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

   5. Simplified 71.6%

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

   if 4.8e-123 < y < 1.3000000000000001e-77

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 87.7%

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

      1. +-commutative 87.7%

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

   5. Simplified 87.7%

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

   6. Taylor expanded in y around 0 87.7%

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

Alternative 4: 73.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(1 - y\right)\\ \mathbf{if}\;y \leq -1:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-123}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1.18 \cdot 10^{-79}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 0.64:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* x (- 1.0 y))))
   (if (<= y -1.0)
     1.0
     (if (<= y 5.5e-123)
       t_0
       (if (<= y 1.18e-79) y (if (<= y 0.64) t_0 1.0))))))

C

double code(double x, double y) {
	double t_0 = x * (1.0 - y);
	double tmp;
	if (y <= -1.0) {
		tmp = 1.0;
	} else if (y <= 5.5e-123) {
		tmp = t_0;
	} else if (y <= 1.18e-79) {
		tmp = y;
	} else if (y <= 0.64) {
		tmp = t_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) :: t_0
    real(8) :: tmp
    t_0 = x * (1.0d0 - y)
    if (y <= (-1.0d0)) then
        tmp = 1.0d0
    else if (y <= 5.5d-123) then
        tmp = t_0
    else if (y <= 1.18d-79) then
        tmp = y
    else if (y <= 0.64d0) then
        tmp = t_0
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = x * (1.0 - y);
	double tmp;
	if (y <= -1.0) {
		tmp = 1.0;
	} else if (y <= 5.5e-123) {
		tmp = t_0;
	} else if (y <= 1.18e-79) {
		tmp = y;
	} else if (y <= 0.64) {
		tmp = t_0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x * (1.0 - y)
	tmp = 0
	if y <= -1.0:
		tmp = 1.0
	elif y <= 5.5e-123:
		tmp = t_0
	elif y <= 1.18e-79:
		tmp = y
	elif y <= 0.64:
		tmp = t_0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x * Float64(1.0 - y))
	tmp = 0.0
	if (y <= -1.0)
		tmp = 1.0;
	elseif (y <= 5.5e-123)
		tmp = t_0;
	elseif (y <= 1.18e-79)
		tmp = y;
	elseif (y <= 0.64)
		tmp = t_0;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = x * (1.0 - y);
	tmp = 0.0;
	if (y <= -1.0)
		tmp = 1.0;
	elseif (y <= 5.5e-123)
		tmp = t_0;
	elseif (y <= 1.18e-79)
		tmp = y;
	elseif (y <= 0.64)
		tmp = t_0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.0], 1.0, If[LessEqual[y, 5.5e-123], t$95$0, If[LessEqual[y, 1.18e-79], y, If[LessEqual[y, 0.64], t$95$0, 1.0]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1 or 0.640000000000000013 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 74.0%

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

   if -1 < y < 5.5e-123 or 1.18e-79 < y < 0.640000000000000013

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 75.1%

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

      1. +-commutative 75.1%

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

   5. Simplified 75.1%

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

   6. Taylor expanded in y around 0 74.0%

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

      1. +-commutative 74.0%

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

      2. remove-double-neg 74.0%

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

      3. mul-1-neg 74.0%

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

      4. distribute-neg-out 74.0%

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

      5. neg-mul-1 74.0%

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

      6. *-commutative 74.0%

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

      7. distribute-lft-in 74.0%

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

      8. metadata-eval 74.0%

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

      9. sub-neg 74.0%

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

      10. distribute-rgt-neg-in 74.0%

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

      11. sub0-neg 74.0%

          \[\leadsto x \cdot \color{blue}{\left(0 - \left(y - 1\right)\right)} \]

      12. associate-+l- 74.0%

          \[\leadsto x \cdot \color{blue}{\left(\left(0 - y\right) + 1\right)} \]

      13. neg-sub0 74.0%

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

      14. +-commutative 74.0%

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

      15. sub-neg 74.0%

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

   8. Simplified 74.0%

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

   if 5.5e-123 < y < 1.18e-79

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 87.7%

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

      1. +-commutative 87.7%

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

   5. Simplified 87.7%

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

   6. Taylor expanded in y around 0 87.7%

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

Alternative 5: 73.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-128}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-79}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 0.39:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.0)
   1.0
   (if (<= y 4.6e-128) x (if (<= y 8e-79) y (if (<= y 0.39) x 1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = 1.0;
	} else if (y <= 4.6e-128) {
		tmp = x;
	} else if (y <= 8e-79) {
		tmp = y;
	} else if (y <= 0.39) {
		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 <= 4.6d-128) then
        tmp = x
    else if (y <= 8d-79) then
        tmp = y
    else if (y <= 0.39d0) 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 <= 4.6e-128) {
		tmp = x;
	} else if (y <= 8e-79) {
		tmp = y;
	} else if (y <= 0.39) {
		tmp = x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = 1.0
	elif y <= 4.6e-128:
		tmp = x
	elif y <= 8e-79:
		tmp = y
	elif y <= 0.39:
		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 <= 4.6e-128)
		tmp = x;
	elseif (y <= 8e-79)
		tmp = y;
	elseif (y <= 0.39)
		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 <= 4.6e-128)
		tmp = x;
	elseif (y <= 8e-79)
		tmp = y;
	elseif (y <= 0.39)
		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, 4.6e-128], x, If[LessEqual[y, 8e-79], y, If[LessEqual[y, 0.39], x, 1.0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1 or 0.39000000000000001 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 74.0%

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

   if -1 < y < 4.6000000000000002e-128 or 8e-79 < y < 0.39000000000000001

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 71.5%

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

   if 4.6000000000000002e-128 < y < 8e-79

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 87.7%

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

      1. +-commutative 87.7%

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

   5. Simplified 87.7%

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

   6. Taylor expanded in y around 0 87.7%

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

Alternative 6: 98.3% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if y < -1 or 1 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 98.9%

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

      1. associate--l+ 98.9%

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

      2. div-sub 98.9%

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

      3. sub-neg 98.9%

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

      4. metadata-eval 98.9%

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

   5. Simplified 98.9%

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

   if -1 < y < 1

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 97.4%

      \[\leadsto \color{blue}{x + y \cdot \left(1 - x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.1%

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

Alternative 7: 75.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.6 \cdot 10^{-46} \lor \neg \left(x \leq 1.75 \cdot 10^{-44}\right):\\ \;\;\;\;\frac{x}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -4.6e-46) (not (<= x 1.75e-44)))
   (/ x (+ y 1.0))
   (/ y (+ y 1.0))))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -4.6e-46) || !(x <= 1.75e-44)) {
		tmp = x / (y + 1.0);
	} else {
		tmp = y / (y + 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 ((x <= (-4.6d-46)) .or. (.not. (x <= 1.75d-44))) then
        tmp = x / (y + 1.0d0)
    else
        tmp = y / (y + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -4.6e-46) || !(x <= 1.75e-44)) {
		tmp = x / (y + 1.0);
	} else {
		tmp = y / (y + 1.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -4.6e-46) or not (x <= 1.75e-44):
		tmp = x / (y + 1.0)
	else:
		tmp = y / (y + 1.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -4.6e-46) || !(x <= 1.75e-44))
		tmp = Float64(x / Float64(y + 1.0));
	else
		tmp = Float64(y / Float64(y + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -4.6e-46) || ~((x <= 1.75e-44)))
		tmp = x / (y + 1.0);
	else
		tmp = y / (y + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -4.6e-46], N[Not[LessEqual[x, 1.75e-44]], $MachinePrecision]], N[(x / N[(y + 1.0), $MachinePrecision]), $MachinePrecision], N[(y / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.5999999999999998e-46 or 1.7499999999999999e-44 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 74.2%

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

      1. +-commutative 74.2%

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

   5. Simplified 74.2%

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

   if -4.5999999999999998e-46 < x < 1.7499999999999999e-44

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 87.4%

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

      1. +-commutative 87.4%

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

   5. Simplified 87.4%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.6 \cdot 10^{-46} \lor \neg \left(x \leq 1.75 \cdot 10^{-44}\right):\\ \;\;\;\;\frac{x}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 74.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 2.4:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= y -1.0) 1.0 (if (<= y 2.4) x 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = 1.0;
	} else if (y <= 2.4) {
		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 <= 2.4d0) 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 <= 2.4) {
		tmp = x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = 1.0
	elif y <= 2.4:
		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 <= 2.4)
		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 <= 2.4)
		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, 2.4], x, 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 2.39999999999999991 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 74.0%

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

   if -1 < y < 2.39999999999999991

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 68.0%

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

Alternative 9: 38.6% 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. Add Preprocessing

3. Taylor expanded in y around inf 40.8%

   \[\leadsto \color{blue}{1} \]
4. Add Preprocessing

Reproduce

herbie shell --seed 2024108 
(FPCore (x y)
  :name "Data.Colour.SRGB:invTransferFunction from colour-2.3.3"
  :precision binary64
  (/ (+ x y) (+ y 1.0)))