Data.Colour.SRGB:transferFunction from colour-2.3.3

Percentage Accurate: 100.0% → 100.0%

Time: 6.5s

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 egg-rr 100.0%

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

Alternative 2: 86.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(x + 1\right) - x\\ \mathbf{if}\;t\_0 \leq -5 \cdot 10^{+300}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;t\_0 \leq 10^{+308}:\\ \;\;\;\;y - x\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (- (* y (+ x 1.0)) x)))
   (if (<= t_0 -5e+300) (* y x) (if (<= t_0 1e+308) (- 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+300) {
		tmp = y * x;
	} else if (t_0 <= 1e+308) {
		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+300)) then
        tmp = y * x
    else if (t_0 <= 1d+308) 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+300) {
		tmp = y * x;
	} else if (t_0 <= 1e+308) {
		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+300:
		tmp = y * x
	elif t_0 <= 1e+308:
		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+300)
		tmp = Float64(y * x);
	elseif (t_0 <= 1e+308)
		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+300)
		tmp = y * x;
	elseif (t_0 <= 1e+308)
		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+300], N[(y * x), $MachinePrecision], If[LessEqual[t$95$0, 1e+308], 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) < -5.00000000000000026e300 or 1e308 < (-.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. Simplified 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 100.0

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

   8. Simplified 100.0%

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

   if -5.00000000000000026e300 < (-.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) y) x) < 1e308

   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. Simplified 84.2%

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

      1. *-lft-identity 84.2

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

   7. Applied egg-rr 84.2%

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

4. Final simplification 85.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(x + 1\right) - x \leq -5 \cdot 10^{+300}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \cdot \left(x + 1\right) - x \leq 10^{+308}:\\ \;\;\;\;y - x\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(y, x, -x\right)\\ \mathbf{if}\;x \leq -9500000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-14}:\\ \;\;\;\;y - x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (fma y x (- x))))
   (if (<= x -9500000.0) t_0 (if (<= x 7e-14) (- y x) t_0))))

C

double code(double x, double y) {
	double t_0 = fma(y, x, -x);
	double tmp;
	if (x <= -9500000.0) {
		tmp = t_0;
	} else if (x <= 7e-14) {
		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 <= -9500000.0)
		tmp = t_0;
	elseif (x <= 7e-14)
		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, -9500000.0], t$95$0, If[LessEqual[x, 7e-14], N[(y - x), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -9.5e6 or 7.0000000000000005e-14 < 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 99.4

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

   5. Simplified 99.4%

      \[\leadsto \color{blue}{y \cdot x} - x \]
   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 99.4

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

   7. Applied egg-rr 99.4%

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

   if -9.5e6 < x < 7.0000000000000005e-14

   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. Simplified 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 egg-rr 100.0%

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

Alternative 4: 98.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot x - x\\ \mathbf{if}\;x \leq -9500000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-14}:\\ \;\;\;\;y - x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (- (* y x) x)))
   (if (<= x -9500000.0) t_0 (if (<= x 7e-14) (- y x) t_0))))

C

double code(double x, double y) {
	double t_0 = (y * x) - x;
	double tmp;
	if (x <= -9500000.0) {
		tmp = t_0;
	} else if (x <= 7e-14) {
		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 <= (-9500000.0d0)) then
        tmp = t_0
    else if (x <= 7d-14) 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 <= -9500000.0) {
		tmp = t_0;
	} else if (x <= 7e-14) {
		tmp = y - x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (y * x) - x
	tmp = 0
	if x <= -9500000.0:
		tmp = t_0
	elif x <= 7e-14:
		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 <= -9500000.0)
		tmp = t_0;
	elseif (x <= 7e-14)
		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 <= -9500000.0)
		tmp = t_0;
	elseif (x <= 7e-14)
		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, -9500000.0], t$95$0, If[LessEqual[x, 7e-14], N[(y - x), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -9.5e6 or 7.0000000000000005e-14 < 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 99.4

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

   5. Simplified 99.4%

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

   if -9.5e6 < x < 7.0000000000000005e-14

   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. Simplified 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 egg-rr 100.0%

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

Alternative 5: 98.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -50000000:\\ \;\;\;\;\mathsf{fma}\left(y, x, y\right)\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-5}:\\ \;\;\;\;y - x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, x, y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -50000000.0) (fma y x y) (if (<= y 3.4e-5) (- y x) (fma y x y))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -50000000.0) {
		tmp = fma(y, x, y);
	} else if (y <= 3.4e-5) {
		tmp = y - x;
	} else {
		tmp = fma(y, x, y);
	}
	return tmp;
}

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -50000000.0)
		tmp = fma(y, x, y);
	elseif (y <= 3.4e-5)
		tmp = Float64(y - x);
	else
		tmp = fma(y, x, y);
	end
	return tmp
end

Wolfram

code[x_, y_] := If[LessEqual[y, -50000000.0], N[(y * x + y), $MachinePrecision], If[LessEqual[y, 3.4e-5], N[(y - x), $MachinePrecision], N[(y * x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -5e7 or 3.4e-5 < 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. Simplified 99.1%

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

   if -5e7 < y < 3.4e-5

   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. Simplified 99.7%

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

      1. *-lft-identity 99.7

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

   7. Applied egg-rr 99.7%

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

Alternative 6: 62.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.9 \cdot 10^{-23}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-13}:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -3.9e-23) (+ y x) (if (<= y 9.5e-13) (- x) (+ y x))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -3.9e-23) {
		tmp = y + x;
	} else if (y <= 9.5e-13) {
		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 <= (-3.9d-23)) then
        tmp = y + x
    else if (y <= 9.5d-13) 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 <= -3.9e-23) {
		tmp = y + x;
	} else if (y <= 9.5e-13) {
		tmp = -x;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -3.9e-23:
		tmp = y + x
	elif y <= 9.5e-13:
		tmp = -x
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -3.9e-23)
		tmp = Float64(y + x);
	elseif (y <= 9.5e-13)
		tmp = Float64(-x);
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -3.9e-23)
		tmp = y + x;
	elseif (y <= 9.5e-13)
		tmp = -x;
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -3.9e-23], N[(y + x), $MachinePrecision], If[LessEqual[y, 9.5e-13], (-x), N[(y + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.9e-23 or 9.49999999999999991e-13 < 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. Simplified 56.8%

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

      1. *-lft-identity 56.8

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

   7. Applied egg-rr 56.8%

      \[\leadsto \color{blue}{y} - x \]
   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 egg-rr 56.7%

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

   if -3.9e-23 < y < 9.49999999999999991e-13

   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 80.0

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

   5. Simplified 80.0%

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

Alternative 7: 74.9% 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. Simplified 78.8%

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

   1. *-lft-identity 78.8

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

7. Applied egg-rr 78.8%

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

Alternative 8: 39.3% 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 42.2

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

5. Simplified 42.2%

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

Reproduce

herbie shell --seed 2024207 
(FPCore (x y)
  :name "Data.Colour.SRGB:transferFunction from colour-2.3.3"
  :precision binary64
  (- (* (+ x 1.0) y) x))