Data.Colour.SRGB:transferFunction from colour-2.3.3

Percentage Accurate: 100.0% → 100.0%

Time: 6.6s

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. *-commutative N/A

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

   2. +-commutative N/A

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

   3. distribute-rgt-in N/A

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

   4. *-lft-identity N/A

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

   5. *-commutative N/A

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

   6. +-commutative N/A

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

   7. associate--l+ N/A

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

   8. accelerator-lowering-fma.f64 N/A

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

   9. --lowering--.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: 86.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(x + 1\right) - x\\ \mathbf{if}\;t\_0 \leq -\infty:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;t\_0 \leq 10^{+292}:\\ \;\;\;\;y - x\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (- (* y (+ x 1.0)) x)))
   (if (<= t_0 (- INFINITY)) (* y x) (if (<= t_0 1e+292) (- y x) (* y x)))))

C

double code(double x, double y) {
	double t_0 = (y * (x + 1.0)) - x;
	double tmp;
	if (t_0 <= -((double) INFINITY)) {
		tmp = y * x;
	} else if (t_0 <= 1e+292) {
		tmp = y - x;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Java

public static double code(double x, double y) {
	double t_0 = (y * (x + 1.0)) - x;
	double tmp;
	if (t_0 <= -Double.POSITIVE_INFINITY) {
		tmp = y * x;
	} else if (t_0 <= 1e+292) {
		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 <= -math.inf:
		tmp = y * x
	elif t_0 <= 1e+292:
		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 <= Float64(-Inf))
		tmp = Float64(y * x);
	elseif (t_0 <= 1e+292)
		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 <= -Inf)
		tmp = y * x;
	elseif (t_0 <= 1e+292)
		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, (-Infinity)], N[(y * x), $MachinePrecision], If[LessEqual[t$95$0, 1e+292], 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) < -inf.0 or 1e292 < (-.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 x around inf

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

   5. Simplified 100.0%

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

      1. sub-neg N/A

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

      2. *-commutative N/A

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

      3. neg-mul-1 N/A

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

      4. distribute-rgt-out N/A

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 N/A

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

      7. +-lowering-+.f64 100.0

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

   7. Applied egg-rr 100.0%

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

   8. Taylor expanded in y around inf

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

   10. Simplified 94.1%

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

   if -inf.0 < (-.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) y) x) < 1e292

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

   5. Simplified 88.1%

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

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(x + 1\right) - x \leq -\infty:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \cdot \left(x + 1\right) - x \leq 10^{+292}:\\ \;\;\;\;y - x\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(y + -1\right)\\ \mathbf{if}\;x \leq -1.4 \cdot 10^{+29}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;y - x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* x (+ y -1.0))))
   (if (<= x -1.4e+29) t_0 (if (<= x 1.0) (- y x) t_0))))

C

double code(double x, double y) {
	double t_0 = x * (y + -1.0);
	double tmp;
	if (x <= -1.4e+29) {
		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 = x * (y + (-1.0d0))
    if (x <= (-1.4d+29)) 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 = x * (y + -1.0);
	double tmp;
	if (x <= -1.4e+29) {
		tmp = t_0;
	} else if (x <= 1.0) {
		tmp = y - x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x * (y + -1.0)
	tmp = 0
	if x <= -1.4e+29:
		tmp = t_0
	elif x <= 1.0:
		tmp = y - x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x * Float64(y + -1.0))
	tmp = 0.0
	if (x <= -1.4e+29)
		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 = x * (y + -1.0);
	tmp = 0.0;
	if (x <= -1.4e+29)
		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[(x * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.4e+29], 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 < -1.4e29 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

   5. Simplified 100.0%

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

      1. sub-neg N/A

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

      2. *-commutative N/A

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

      3. neg-mul-1 N/A

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

      4. distribute-rgt-out N/A

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 N/A

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

      7. +-lowering-+.f64 100.0

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

   7. Applied egg-rr 100.0%

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

   if -1.4e29 < x < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

   5. Simplified 98.1%

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

4. Final simplification 98.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{+29}:\\ \;\;\;\;x \cdot \left(y + -1\right)\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;y - x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 99.1% 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. accelerator-lowering-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 -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

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

   5. Simplified 98.5%

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

Alternative 5: 62.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.6 \cdot 10^{-13}:\\ \;\;\;\;0 - x\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-6}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;0 - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -3.6e-13) (- 0.0 x) (if (<= x 1.8e-6) y (- 0.0 x))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -3.6e-13) {
		tmp = 0.0 - x;
	} else if (x <= 1.8e-6) {
		tmp = y;
	} else {
		tmp = 0.0 - x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-3.6d-13)) then
        tmp = 0.0d0 - x
    else if (x <= 1.8d-6) then
        tmp = y
    else
        tmp = 0.0d0 - x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -3.6e-13) {
		tmp = 0.0 - x;
	} else if (x <= 1.8e-6) {
		tmp = y;
	} else {
		tmp = 0.0 - x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -3.6e-13:
		tmp = 0.0 - x
	elif x <= 1.8e-6:
		tmp = y
	else:
		tmp = 0.0 - x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -3.6e-13)
		tmp = Float64(0.0 - x);
	elseif (x <= 1.8e-6)
		tmp = y;
	else
		tmp = Float64(0.0 - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -3.6e-13)
		tmp = 0.0 - x;
	elseif (x <= 1.8e-6)
		tmp = y;
	else
		tmp = 0.0 - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -3.6e-13], N[(0.0 - x), $MachinePrecision], If[LessEqual[x, 1.8e-6], y, N[(0.0 - x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -3.5999999999999998e-13 or 1.79999999999999992e-6 < 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. neg-sub0 N/A

         \[\leadsto \color{blue}{0 - x} \]

      3. --lowering--.f64 50.7

         \[\leadsto \color{blue}{0 - x} \]

   5. Simplified 50.7%

      \[\leadsto \color{blue}{0 - x} \]
   6. Step-by-step derivation

      1. sub0-neg N/A

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

      2. neg-lowering-neg.f64 50.7

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

   7. Applied egg-rr 50.7%

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

   if -3.5999999999999998e-13 < x < 1.79999999999999992e-6

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

   5. Simplified 74.5%

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

4. Final simplification 64.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.6 \cdot 10^{-13}:\\ \;\;\;\;0 - x\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-6}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;0 - x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 75.3% 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

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

5. Simplified 77.9%

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

Alternative 7: 38.4% accurate, 12.0× speedup

Math

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

FPCore

(FPCore (x y) :precision binary64 y)

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return y

Julia

function code(x, y)
	return y
end

MATLAB

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

Wolfram

code[x_, y_] := y

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in x around 0

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

5. Simplified 43.2%

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

Alternative 8: 2.6% accurate, 12.0× 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 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. neg-sub0 N/A

      \[\leadsto \color{blue}{0 - x} \]

   3. --lowering--.f64 36.0

      \[\leadsto \color{blue}{0 - x} \]

5. Simplified 36.0%

   \[\leadsto \color{blue}{0 - x} \]
6. Step-by-step derivation

   1. sub0-neg N/A

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

   2. neg-lowering-neg.f64 36.0

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

7. Applied egg-rr 36.0%

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

   1. neg-sub0 N/A

      \[\leadsto \color{blue}{0 - x} \]

   2. flip3-- N/A

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

   3. metadata-eval N/A

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

   4. neg-sub0 N/A

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

   5. cube-neg N/A

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

   6. sqr-pow N/A

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

   7. unpow-prod-down N/A

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

   8. sqr-neg N/A

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

   9. pow-prod-down N/A

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

   10. sqr-pow N/A

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

   11. metadata-eval N/A

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

   12. +-lft-identity N/A

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

   13. distribute-rgt-out N/A

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

   14. +-commutative N/A

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

   15. +-lft-identity N/A

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

   16. pow2 N/A

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

   17. pow-div N/A

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

   18. metadata-eval N/A

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

   19. unpow1 3.0

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

9. Applied egg-rr 3.0%

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

Reproduce

herbie shell --seed 2024196 
(FPCore (x y)
  :name "Data.Colour.SRGB:transferFunction from colour-2.3.3"
  :precision binary64
  (- (* (+ x 1.0) y) x))