Data.Colour.SRGB:transferFunction from colour-2.3.3

Percentage Accurate: 100.0% → 100.0%

Time: 6.3s

Alternatives: 8

Speedup: 1.2×

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, 1.2× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(y, x, y - x\right) \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (fma y x (- y x)))

C

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

Julia

function code(x, y)
	return fma(y, x, Float64(y - x))
end

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. lift-+.f64 N/A

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

   2. *-commutative N/A

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

   3. lift-+.f64 N/A

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

   4. distribute-lft-in N/A

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

   5. *-rgt-identity N/A

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

   6. associate--l+ N/A

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

   7. lower-fma.f64 N/A

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, x, y - x\right)} \]

   8. lower--.f64 100.0

      \[\leadsto \mathsf{fma}\left(y, x, \color{blue}{y - x}\right) \]

4. Applied rewrites 100.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(y, x, y - x\right)} \]
5. Add Preprocessing

Alternative 2: 86.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(x + 1\right) - x\\ \mathbf{if}\;t\_0 \leq -4 \cdot 10^{+301}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;t\_0 \leq 10^{+298}:\\ \;\;\;\;y - x\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (- (* y (+ x 1.0)) x)))
   (if (<= t_0 -4e+301) (* y x) (if (<= t_0 1e+298) (- y x) (* y x)))))

C

double code(double x, double y) {
	double t_0 = (y * (x + 1.0)) - x;
	double tmp;
	if (t_0 <= -4e+301) {
		tmp = y * x;
	} else if (t_0 <= 1e+298) {
		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) :: t_0
    real(8) :: tmp
    t_0 = (y * (x + 1.0d0)) - x
    if (t_0 <= (-4d+301)) then
        tmp = y * x
    else if (t_0 <= 1d+298) then
        tmp = y - x
    else
        tmp = y * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = (y * (x + 1.0)) - x;
	double tmp;
	if (t_0 <= -4e+301) {
		tmp = y * x;
	} else if (t_0 <= 1e+298) {
		tmp = y - x;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (y * (x + 1.0)) - x
	tmp = 0
	if t_0 <= -4e+301:
		tmp = y * x
	elif t_0 <= 1e+298:
		tmp = y - x
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(y * Float64(x + 1.0)) - x)
	tmp = 0.0
	if (t_0 <= -4e+301)
		tmp = Float64(y * x);
	elseif (t_0 <= 1e+298)
		tmp = Float64(y - x);
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = (y * (x + 1.0)) - x;
	tmp = 0.0;
	if (t_0 <= -4e+301)
		tmp = y * x;
	elseif (t_0 <= 1e+298)
		tmp = y - x;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(y * N[(x + 1.0), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]}, If[LessEqual[t$95$0, -4e+301], N[(y * x), $MachinePrecision], If[LessEqual[t$95$0, 1e+298], N[(y - x), $MachinePrecision], N[(y * x), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) y) x) < -4.00000000000000021e301 or 9.9999999999999996e297 < (-.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) y) x)

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

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

      1. +-commutative N/A

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

      2. distribute-lft-in N/A

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

      3. *-rgt-identity N/A

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

      4. lower-fma.f64 100.0

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in x around inf

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

      1. lower-*.f64 94.9

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

   8. Applied rewrites 94.9%

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

   if -4.00000000000000021e301 < (-.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) y) x) < 9.9999999999999996e297

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 81.0%

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

      1. *-lft-identity 81.0

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

   7. Applied rewrites 81.0%

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

4. Final simplification 83.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(x + 1\right) - x \leq -4 \cdot 10^{+301}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \cdot \left(x + 1\right) - x \leq 10^{+298}:\\ \;\;\;\;y - x\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.8% accurate, 0.6× speedup

Math

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

FPCore

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

C

double code(double x, double y) {
	double t_0 = fma(y, x, -x);
	double tmp;
	if (x <= -1.0) {
		tmp = t_0;
	} else if (x <= 1.0) {
		tmp = y - x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y)
	t_0 = fma(y, x, Float64(-x))
	tmp = 0.0
	if (x <= -1.0)
		tmp = t_0;
	elseif (x <= 1.0)
		tmp = Float64(y - x);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if x < -1 or 1 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 97.8

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

   5. Applied rewrites 97.8%

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

      1. lift-*.f64 N/A

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

      2. sub-neg N/A

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

      3. lift-*.f64 N/A

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

      4. lift-neg.f64 N/A

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

      5. lower-fma.f64 97.8

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, x, -x\right)} \]

   7. Applied rewrites 97.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, x, -x\right)} \]

   if -1 < x < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 98.8%

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

      1. *-lft-identity 98.8

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

   7. Applied rewrites 98.8%

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

Alternative 4: 98.8% accurate, 0.6× speedup

Math

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

FPCore

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

C

double code(double x, double y) {
	double t_0 = (y * x) - x;
	double tmp;
	if (x <= -1.0) {
		tmp = t_0;
	} else if (x <= 1.0) {
		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 * x) - x
    if (x <= (-1.0d0)) then
        tmp = t_0
    else if (x <= 1.0d0) 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 * x) - x;
	double tmp;
	if (x <= -1.0) {
		tmp = t_0;
	} else if (x <= 1.0) {
		tmp = y - x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if x < -1 or 1 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 97.8

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

   5. Applied rewrites 97.8%

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

   if -1 < x < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 98.8%

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

      1. *-lft-identity 98.8

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

   7. Applied rewrites 98.8%

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

Alternative 5: 98.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;\mathsf{fma}\left(y, x, y\right)\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;y - x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, x, y\right)\\ \end{array} \end{array} \]

FPCore

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

C

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

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.0)
		tmp = fma(y, x, y);
	elseif (y <= 1.0)
		tmp = Float64(y - x);
	else
		tmp = fma(y, x, y);
	end
	return tmp
end

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if y < -1 or 1 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

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

      1. +-commutative N/A

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

      2. distribute-lft-in N/A

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

      3. *-rgt-identity N/A

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

      4. lower-fma.f64 97.6

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

   5. Applied rewrites 97.6%

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

   if -1 < y < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 98.0%

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

      1. *-lft-identity 98.0

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

   7. Applied rewrites 98.0%

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

Alternative 6: 61.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{-10}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{-83}:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.2e-10) (+ y x) (if (<= y 4.4e-83) (- x) (+ y x))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.2e-10) {
		tmp = y + x;
	} else if (y <= 4.4e-83) {
		tmp = -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 <= (-1.2d-10)) then
        tmp = y + x
    else if (y <= 4.4d-83) then
        tmp = -x
    else
        tmp = y + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -1.2e-10) {
		tmp = y + x;
	} else if (y <= 4.4e-83) {
		tmp = -x;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.2e-10:
		tmp = y + x
	elif y <= 4.4e-83:
		tmp = -x
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.2e-10)
		tmp = Float64(y + x);
	elseif (y <= 4.4e-83)
		tmp = Float64(-x);
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.2e-10)
		tmp = y + x;
	elseif (y <= 4.4e-83)
		tmp = -x;
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.2e-10], N[(y + x), $MachinePrecision], If[LessEqual[y, 4.4e-83], (-x), N[(y + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.2e-10 or 4.40000000000000015e-83 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 47.8%

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

      1. *-lft-identity 47.8

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

   7. Applied rewrites 47.8%

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

      1. sub-neg N/A

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

      2. neg-sub0 N/A

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

      3. flip3-- N/A

         \[\leadsto y + \color{blue}{\frac{{0}^{3} - {x}^{3}}{0 \cdot 0 + \left(x \cdot x + 0 \cdot x\right)}} \]

      4. metadata-eval N/A

         \[\leadsto y + \frac{\color{blue}{0} - {x}^{3}}{0 \cdot 0 + \left(x \cdot x + 0 \cdot x\right)} \]

      5. neg-sub0 N/A

         \[\leadsto y + \frac{\color{blue}{\mathsf{neg}\left({x}^{3}\right)}}{0 \cdot 0 + \left(x \cdot x + 0 \cdot x\right)} \]

      6. cube-neg N/A

         \[\leadsto y + \frac{\color{blue}{{\left(\mathsf{neg}\left(x\right)\right)}^{3}}}{0 \cdot 0 + \left(x \cdot x + 0 \cdot x\right)} \]

      7. lift-neg.f64 N/A

         \[\leadsto y + \frac{{\color{blue}{\left(\mathsf{neg}\left(x\right)\right)}}^{3}}{0 \cdot 0 + \left(x \cdot x + 0 \cdot x\right)} \]

      8. sqr-pow N/A

         \[\leadsto y + \frac{\color{blue}{{\left(\mathsf{neg}\left(x\right)\right)}^{\left(\frac{3}{2}\right)} \cdot {\left(\mathsf{neg}\left(x\right)\right)}^{\left(\frac{3}{2}\right)}}}{0 \cdot 0 + \left(x \cdot x + 0 \cdot x\right)} \]

      9. pow-prod-down N/A

         \[\leadsto y + \frac{\color{blue}{{\left(\left(\mathsf{neg}\left(x\right)\right) \cdot \left(\mathsf{neg}\left(x\right)\right)\right)}^{\left(\frac{3}{2}\right)}}}{0 \cdot 0 + \left(x \cdot x + 0 \cdot x\right)} \]

      10. lift-neg.f64 N/A

          \[\leadsto y + \frac{{\left(\color{blue}{\left(\mathsf{neg}\left(x\right)\right)} \cdot \left(\mathsf{neg}\left(x\right)\right)\right)}^{\left(\frac{3}{2}\right)}}{0 \cdot 0 + \left(x \cdot x + 0 \cdot x\right)} \]

      11. lift-neg.f64 N/A

          \[\leadsto y + \frac{{\left(\left(\mathsf{neg}\left(x\right)\right) \cdot \color{blue}{\left(\mathsf{neg}\left(x\right)\right)}\right)}^{\left(\frac{3}{2}\right)}}{0 \cdot 0 + \left(x \cdot x + 0 \cdot x\right)} \]

      12. sqr-neg N/A

          \[\leadsto y + \frac{{\color{blue}{\left(x \cdot x\right)}}^{\left(\frac{3}{2}\right)}}{0 \cdot 0 + \left(x \cdot x + 0 \cdot x\right)} \]

      13. pow-prod-down N/A

          \[\leadsto y + \frac{\color{blue}{{x}^{\left(\frac{3}{2}\right)} \cdot {x}^{\left(\frac{3}{2}\right)}}}{0 \cdot 0 + \left(x \cdot x + 0 \cdot x\right)} \]

      14. sqr-pow N/A

          \[\leadsto y + \frac{\color{blue}{{x}^{3}}}{0 \cdot 0 + \left(x \cdot x + 0 \cdot x\right)} \]

      15. metadata-eval N/A

          \[\leadsto y + \frac{{x}^{3}}{\color{blue}{0} + \left(x \cdot x + 0 \cdot x\right)} \]

      16. +-lft-identity N/A

          \[\leadsto y + \frac{{x}^{3}}{\color{blue}{x \cdot x + 0 \cdot x}} \]

      17. distribute-rgt-out N/A

          \[\leadsto y + \frac{{x}^{3}}{\color{blue}{x \cdot \left(x + 0\right)}} \]

      18. +-commutative N/A

          \[\leadsto y + \frac{{x}^{3}}{x \cdot \color{blue}{\left(0 + x\right)}} \]

      19. +-lft-identity N/A

          \[\leadsto y + \frac{{x}^{3}}{x \cdot \color{blue}{x}} \]

      20. pow2 N/A

          \[\leadsto y + \frac{{x}^{3}}{\color{blue}{{x}^{2}}} \]

      21. pow-div N/A

          \[\leadsto y + \color{blue}{{x}^{\left(3 - 2\right)}} \]

      22. metadata-eval N/A

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

      23. unpow1 N/A

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

      24. remove-double-neg N/A

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

      25. neg-mul-1 N/A

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

      26. *-commutative N/A

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

      27. distribute-lft-neg-in N/A

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

   9. Applied rewrites 45.4%

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

   if -1.2e-10 < y < 4.40000000000000015e-83

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 82.8

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

   5. Applied rewrites 82.8%

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

Alternative 7: 74.7% accurate, 3.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in x around 0

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

5. Applied rewrites 70.1%

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

   1. *-lft-identity 70.1

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

7. Applied rewrites 70.1%

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

Alternative 8: 38.1% accurate, 4.0× speedup

Math

\[\begin{array}{l} \\ -x \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return -x

Julia

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

MATLAB

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

Wolfram

code[x_, y_] := (-x)

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in y around 0

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

   1. mul-1-neg N/A

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

   2. lower-neg.f64 39.0

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

5. Applied rewrites 39.0%

   \[\leadsto \color{blue}{-x} \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024216 
(FPCore (x y)
  :name "Data.Colour.SRGB:transferFunction from colour-2.3.3"
  :precision binary64
  (- (* (+ x 1.0) y) x))