Data.Colour.SRGB:transferFunction from colour-2.3.3

Percentage Accurate: 100.0% → 100.0%

Time: 6.0s

Alternatives: 7

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: 85.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(x + 1\right) - x\\ \mathbf{if}\;t\_0 \leq -5 \cdot 10^{+307}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;t\_0 \leq 10^{+273}:\\ \;\;\;\;y - x\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (- (* y (+ x 1.0)) x)))
   (if (<= t_0 -5e+307) (* y x) (if (<= t_0 1e+273) (- y x) (* y x)))))

C

double code(double x, double y) {
	double t_0 = (y * (x + 1.0)) - x;
	double tmp;
	if (t_0 <= -5e+307) {
		tmp = y * x;
	} else if (t_0 <= 1e+273) {
		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 <= (-5d+307)) then
        tmp = y * x
    else if (t_0 <= 1d+273) 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 <= -5e+307) {
		tmp = y * x;
	} else if (t_0 <= 1e+273) {
		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 <= -5e+307:
		tmp = y * x
	elif t_0 <= 1e+273:
		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 <= -5e+307)
		tmp = Float64(y * x);
	elseif (t_0 <= 1e+273)
		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 <= -5e+307)
		tmp = y * x;
	elseif (t_0 <= 1e+273)
		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, -5e+307], N[(y * x), $MachinePrecision], If[LessEqual[t$95$0, 1e+273], 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) < -5e307 or 9.99999999999999945e272 < (-.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 97.5

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

   5. Applied rewrites 97.5%

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

   6. Taylor expanded in x around inf

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

      1. lower-*.f64 95.1

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

   8. Applied rewrites 95.1%

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

   if -5e307 < (-.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) y) x) < 9.99999999999999945e272

   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 87.6%

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

      1. *-lft-identity 87.6

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

   7. Applied rewrites 87.6%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(x + 1\right) - x \leq -5 \cdot 10^{+307}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \cdot \left(x + 1\right) - x \leq 10^{+273}:\\ \;\;\;\;y - x\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 99.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot x - x\\ \mathbf{if}\;x \leq -59:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 0.00028:\\ \;\;\;\;y - x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (- (* y x) x)))
   (if (<= x -59.0) t_0 (if (<= x 0.00028) (- y x) t_0))))

C

double code(double x, double y) {
	double t_0 = (y * x) - x;
	double tmp;
	if (x <= -59.0) {
		tmp = t_0;
	} else if (x <= 0.00028) {
		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 <= (-59.0d0)) then
        tmp = t_0
    else if (x <= 0.00028d0) 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 <= -59.0) {
		tmp = t_0;
	} else if (x <= 0.00028) {
		tmp = y - x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (y * x) - x
	tmp = 0
	if x <= -59.0:
		tmp = t_0
	elif x <= 0.00028:
		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 <= -59.0)
		tmp = t_0;
	elseif (x <= 0.00028)
		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 <= -59.0)
		tmp = t_0;
	elseif (x <= 0.00028)
		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, -59.0], t$95$0, If[LessEqual[x, 0.00028], N[(y - x), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -59 or 2.7999999999999998e-4 < 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 99.6

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

   5. Applied rewrites 99.6%

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

   if -59 < x < 2.7999999999999998e-4

   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 98.2%

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

      1. *-lft-identity 98.2

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

   7. Applied rewrites 98.2%

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

Alternative 4: 99.0% 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 99.1

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

   5. Applied rewrites 99.1%

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

   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 98.7%

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

      1. *-lft-identity 98.7

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

   7. Applied rewrites 98.7%

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

Alternative 5: 62.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{-33}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{-64}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -9e-33) (- x) (if (<= x 2.8e-64) (+ y x) (- x))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -9e-33) {
		tmp = -x;
	} else if (x <= 2.8e-64) {
		tmp = y + x;
	} else {
		tmp = -x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-9d-33)) then
        tmp = -x
    else if (x <= 2.8d-64) then
        tmp = y + x
    else
        tmp = -x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -9e-33) {
		tmp = -x;
	} else if (x <= 2.8e-64) {
		tmp = y + x;
	} else {
		tmp = -x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -9e-33:
		tmp = -x
	elif x <= 2.8e-64:
		tmp = y + x
	else:
		tmp = -x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -9e-33)
		tmp = Float64(-x);
	elseif (x <= 2.8e-64)
		tmp = Float64(y + x);
	else
		tmp = Float64(-x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -9e-33)
		tmp = -x;
	elseif (x <= 2.8e-64)
		tmp = y + x;
	else
		tmp = -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -9e-33], (-x), If[LessEqual[x, 2.8e-64], N[(y + x), $MachinePrecision], (-x)]]

Derivation

1. Split input into 2 regimes

2. if x < -8.99999999999999982e-33 or 2.80000000000000004e-64 < x

   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 53.3

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

   5. Applied rewrites 53.3%

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

   if -8.99999999999999982e-33 < x < 2.80000000000000004e-64

   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 100.0%

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

      1. *-lft-identity 100.0

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

   7. Applied rewrites 100.0%

      \[\leadsto \color{blue}{y} - x \]
   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. distribute-frac-neg N/A

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

      7. sqr-pow N/A

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

      8. pow-prod-down N/A

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

      9. sqr-neg N/A

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

      10. unpow-prod-down N/A

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

      11. sqr-pow N/A

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

      12. cube-neg N/A

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

      13. neg-sub0 N/A

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

      14. metadata-eval N/A

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

      15. flip3-- N/A

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

      16. neg-sub0 N/A

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

      17. remove-double-neg N/A

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

      18. lower-+.f64 81.6

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

   9. Applied rewrites 81.6%

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

Alternative 6: 75.4% 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 76.0%

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

   1. *-lft-identity 76.0

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

7. Applied rewrites 76.0%

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

Alternative 7: 38.6% 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 39.7

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

5. Applied rewrites 39.7%

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

Reproduce

herbie shell --seed 2024219 
(FPCore (x y)
  :name "Data.Colour.SRGB:transferFunction from colour-2.3.3"
  :precision binary64
  (- (* (+ x 1.0) y) x))