Data.Array.Repa.Algorithms.ColorRamp:rampColorHotToCold from repa-algorithms-3.4.0.1, C

Percentage Accurate: 99.9% → 99.9%

Time: 1.7s

Alternatives: 11

Speedup: 1.0×

• 20.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ 1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ 1.0 (/ (* 4.0 (- (+ x (* y 0.25)) z)) y)))

C

double code(double x, double y, double z) {
	return 1.0 + ((4.0 * ((x + (y * 0.25)) - z)) / y);
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = 1.0d0 + ((4.0d0 * ((x + (y * 0.25d0)) - z)) / y)
end function

Java

public static double code(double x, double y, double z) {
	return 1.0 + ((4.0 * ((x + (y * 0.25)) - z)) / y);
}

Python

def code(x, y, z):
	return 1.0 + ((4.0 * ((x + (y * 0.25)) - z)) / y)

Julia

function code(x, y, z)
	return Float64(1.0 + Float64(Float64(4.0 * Float64(Float64(x + Float64(y * 0.25)) - z)) / y))
end

MATLAB

function tmp = code(x, y, z)
	tmp = 1.0 + ((4.0 * ((x + (y * 0.25)) - z)) / y);
end

Wolfram

code[x_, y_, z_] := N[(1.0 + N[(N[(4.0 * N[(N[(x + N[(y * 0.25), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ 1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ 1.0 (/ (* 4.0 (- (+ x (* y 0.25)) z)) y)))

C

double code(double x, double y, double z) {
	return 1.0 + ((4.0 * ((x + (y * 0.25)) - z)) / y);
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = 1.0d0 + ((4.0d0 * ((x + (y * 0.25d0)) - z)) / y)
end function

Java

public static double code(double x, double y, double z) {
	return 1.0 + ((4.0 * ((x + (y * 0.25)) - z)) / y);
}

Python

def code(x, y, z):
	return 1.0 + ((4.0 * ((x + (y * 0.25)) - z)) / y)

Julia

function code(x, y, z)
	return Float64(1.0 + Float64(Float64(4.0 * Float64(Float64(x + Float64(y * 0.25)) - z)) / y))
end

MATLAB

function tmp = code(x, y, z)
	tmp = 1.0 + ((4.0 * ((x + (y * 0.25)) - z)) / y);
end

Wolfram

code[x_, y_, z_] := N[(1.0 + N[(N[(4.0 * N[(N[(x + N[(y * 0.25), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ 1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ 1.0 (/ (* 4.0 (- (+ x (* y 0.25)) z)) y)))

C

double code(double x, double y, double z) {
	return 1.0 + ((4.0 * ((x + (y * 0.25)) - z)) / y);
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = 1.0d0 + ((4.0d0 * ((x + (y * 0.25d0)) - z)) / y)
end function

Java

public static double code(double x, double y, double z) {
	return 1.0 + ((4.0 * ((x + (y * 0.25)) - z)) / y);
}

Python

def code(x, y, z):
	return 1.0 + ((4.0 * ((x + (y * 0.25)) - z)) / y)

Julia

function code(x, y, z)
	return Float64(1.0 + Float64(Float64(4.0 * Float64(Float64(x + Float64(y * 0.25)) - z)) / y))
end

MATLAB

function tmp = code(x, y, z)
	tmp = 1.0 + ((4.0 * ((x + (y * 0.25)) - z)) / y);
end

Wolfram

code[x_, y_, z_] := N[(1.0 + N[(N[(4.0 * N[(N[(x + N[(y * 0.25), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
2. Add Preprocessing
3. Add Preprocessing

Alternative 2: 12.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + \frac{y \cdot 0.25}{y}\\ \mathbf{if}\;y \leq -0.032:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1.16 \cdot 10^{+30}:\\ \;\;\;\;1 + \left(1 + \left(\left(x + y \cdot 0.25\right) - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ 1.0 (/ (* y 0.25) y))))
   (if (<= y -0.032)
     t_0
     (if (<= y 1.16e+30) (+ 1.0 (+ 1.0 (- (+ x (* y 0.25)) z))) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 + ((y * 0.25) / y);
	double tmp;
	if (y <= -0.032) {
		tmp = t_0;
	} else if (y <= 1.16e+30) {
		tmp = 1.0 + (1.0 + ((x + (y * 0.25)) - z));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 1.0d0 + ((y * 0.25d0) / y)
    if (y <= (-0.032d0)) then
        tmp = t_0
    else if (y <= 1.16d+30) then
        tmp = 1.0d0 + (1.0d0 + ((x + (y * 0.25d0)) - z))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 1.0 + ((y * 0.25) / y);
	double tmp;
	if (y <= -0.032) {
		tmp = t_0;
	} else if (y <= 1.16e+30) {
		tmp = 1.0 + (1.0 + ((x + (y * 0.25)) - z));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 + ((y * 0.25) / y)
	tmp = 0
	if y <= -0.032:
		tmp = t_0
	elif y <= 1.16e+30:
		tmp = 1.0 + (1.0 + ((x + (y * 0.25)) - z))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 + Float64(Float64(y * 0.25) / y))
	tmp = 0.0
	if (y <= -0.032)
		tmp = t_0;
	elseif (y <= 1.16e+30)
		tmp = Float64(1.0 + Float64(1.0 + Float64(Float64(x + Float64(y * 0.25)) - z)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 + ((y * 0.25) / y);
	tmp = 0.0;
	if (y <= -0.032)
		tmp = t_0;
	elseif (y <= 1.16e+30)
		tmp = 1.0 + (1.0 + ((x + (y * 0.25)) - z));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(1.0 + N[(N[(y * 0.25), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -0.032], t$95$0, If[LessEqual[y, 1.16e+30], N[(1.0 + N[(1.0 + N[(N[(x + N[(y * 0.25), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -0.032000000000000001 or 1.16e30 < y

   1. Initial program 100.0%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto 1 + \frac{\color{blue}{4 \cdot \left(\frac{1}{4} \cdot y - z\right)}}{y} \]

   5. Applied rewrites 13.8%

      \[\leadsto 1 + \frac{\color{blue}{y \cdot 0.25}}{y} \]

   if -0.032000000000000001 < y < 1.16e30

   1. Initial program 100.0%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto 1 + \color{blue}{\left(4 \cdot \frac{x}{y} + 4 \cdot \frac{\frac{1}{4} \cdot y - z}{y}\right)} \]

   5. Applied rewrites 6.5%

      \[\leadsto 1 + \color{blue}{\left(\left(x + y \cdot 0.25\right) - z\right)} \]

   6. Taylor expanded in x around 0

      \[\leadsto 1 + \left(\frac{1}{4} \cdot y - \color{blue}{z}\right) \]

   8. Applied rewrites 17.3%

      \[\leadsto 1 + \left(1 + \color{blue}{\left(\left(x + y \cdot 0.25\right) - z\right)}\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 72.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (/ (* 4.0 (- (+ x (* y 0.25)) z)) y))

C

double code(double x, double y, double z) {
	return (4.0 * ((x + (y * 0.25)) - z)) / y;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (4.0d0 * ((x + (y * 0.25d0)) - z)) / y
end function

Java

public static double code(double x, double y, double z) {
	return (4.0 * ((x + (y * 0.25)) - z)) / y;
}

Python

def code(x, y, z):
	return (4.0 * ((x + (y * 0.25)) - z)) / y

Julia

function code(x, y, z)
	return Float64(Float64(4.0 * Float64(Float64(x + Float64(y * 0.25)) - z)) / y)
end

MATLAB

function tmp = code(x, y, z)
	tmp = (4.0 * ((x + (y * 0.25)) - z)) / y;
end

Wolfram

code[x_, y_, z_] := N[(N[(4.0 * N[(N[(x + N[(y * 0.25), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{1 + \left(4 \cdot \frac{x}{y} + 4 \cdot \frac{\frac{1}{4} \cdot y - z}{y}\right)} \]

5. Applied rewrites 68.3%

   \[\leadsto \color{blue}{\frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}} \]
6. Add Preprocessing

Alternative 4: 9.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.032:\\ \;\;\;\;\frac{y \cdot 0.25}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + \left(1 + \left(\left(x + y \cdot 0.25\right) - z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -0.032) (/ (* y 0.25) y) (+ 1.0 (+ 1.0 (- (+ x (* y 0.25)) z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -0.032) {
		tmp = (y * 0.25) / y;
	} else {
		tmp = 1.0 + (1.0 + ((x + (y * 0.25)) - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-0.032d0)) then
        tmp = (y * 0.25d0) / y
    else
        tmp = 1.0d0 + (1.0d0 + ((x + (y * 0.25d0)) - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -0.032) {
		tmp = (y * 0.25) / y;
	} else {
		tmp = 1.0 + (1.0 + ((x + (y * 0.25)) - z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -0.032:
		tmp = (y * 0.25) / y
	else:
		tmp = 1.0 + (1.0 + ((x + (y * 0.25)) - z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -0.032)
		tmp = Float64(Float64(y * 0.25) / y);
	else
		tmp = Float64(1.0 + Float64(1.0 + Float64(Float64(x + Float64(y * 0.25)) - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -0.032)
		tmp = (y * 0.25) / y;
	else
		tmp = 1.0 + (1.0 + ((x + (y * 0.25)) - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -0.032], N[(N[(y * 0.25), $MachinePrecision] / y), $MachinePrecision], N[(1.0 + N[(1.0 + N[(N[(x + N[(y * 0.25), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -0.032000000000000001

   1. Initial program 100.0%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{1 + \left(4 \cdot \frac{x}{y} + 4 \cdot \frac{\frac{1}{4} \cdot y - z}{y}\right)} \]

   5. Applied rewrites 44.2%

      \[\leadsto \color{blue}{\frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}} \]

   6. Taylor expanded in x around inf

      \[\leadsto \color{blue}{4 \cdot \frac{x}{y}} \]

   8. Applied rewrites 12.0%

      \[\leadsto \color{blue}{\frac{y \cdot 0.25}{y}} \]

   if -0.032000000000000001 < y

   1. Initial program 100.0%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto 1 + \color{blue}{\left(4 \cdot \frac{x}{y} + 4 \cdot \frac{\frac{1}{4} \cdot y - z}{y}\right)} \]

   5. Applied rewrites 6.0%

      \[\leadsto 1 + \color{blue}{\left(\left(x + y \cdot 0.25\right) - z\right)} \]

   6. Taylor expanded in x around 0

      \[\leadsto 1 + \left(\frac{1}{4} \cdot y - \color{blue}{z}\right) \]

   8. Applied rewrites 13.8%

      \[\leadsto 1 + \left(1 + \color{blue}{\left(\left(x + y \cdot 0.25\right) - z\right)}\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 9.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -16000000:\\ \;\;\;\;\frac{y \cdot 0.25}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + \left(1 + \left(y \cdot 0.25 - z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -16000000.0) (/ (* y 0.25) y) (+ 1.0 (+ 1.0 (- (* y 0.25) z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -16000000.0) {
		tmp = (y * 0.25) / y;
	} else {
		tmp = 1.0 + (1.0 + ((y * 0.25) - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-16000000.0d0)) then
        tmp = (y * 0.25d0) / y
    else
        tmp = 1.0d0 + (1.0d0 + ((y * 0.25d0) - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -16000000.0) {
		tmp = (y * 0.25) / y;
	} else {
		tmp = 1.0 + (1.0 + ((y * 0.25) - z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -16000000.0:
		tmp = (y * 0.25) / y
	else:
		tmp = 1.0 + (1.0 + ((y * 0.25) - z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -16000000.0)
		tmp = Float64(Float64(y * 0.25) / y);
	else
		tmp = Float64(1.0 + Float64(1.0 + Float64(Float64(y * 0.25) - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -16000000.0)
		tmp = (y * 0.25) / y;
	else
		tmp = 1.0 + (1.0 + ((y * 0.25) - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -16000000.0], N[(N[(y * 0.25), $MachinePrecision] / y), $MachinePrecision], N[(1.0 + N[(1.0 + N[(N[(y * 0.25), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.6e7

   1. Initial program 100.0%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{1 + \left(4 \cdot \frac{x}{y} + 4 \cdot \frac{\frac{1}{4} \cdot y - z}{y}\right)} \]

   5. Applied rewrites 41.6%

      \[\leadsto \color{blue}{\frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}} \]

   6. Taylor expanded in x around inf

      \[\leadsto \color{blue}{4 \cdot \frac{x}{y}} \]

   8. Applied rewrites 12.5%

      \[\leadsto \color{blue}{\frac{y \cdot 0.25}{y}} \]

   if -1.6e7 < y

   1. Initial program 100.0%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto 1 + \color{blue}{\left(4 \cdot \frac{x}{y} + 4 \cdot \frac{\frac{1}{4} \cdot y - z}{y}\right)} \]

   5. Applied rewrites 5.9%

      \[\leadsto 1 + \color{blue}{\left(\left(x + y \cdot 0.25\right) - z\right)} \]

   6. Taylor expanded in x around 0

      \[\leadsto 1 + \left(\frac{1}{4} \cdot y - \color{blue}{z}\right) \]

   8. Applied rewrites 13.6%

      \[\leadsto 1 + \left(1 + \color{blue}{\left(\left(x + y \cdot 0.25\right) - z\right)}\right) \]

   9. Taylor expanded in x around 0

      \[\leadsto 1 + \left(1 + \left(\frac{1}{4} \cdot y - z\right)\right) \]

   11. Applied rewrites 12.8%

       \[\leadsto 1 + \left(1 + \left(y \cdot 0.25 - z\right)\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 6.9% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ 1 + \left(1 + \left(y \cdot 0.25 - z\right)\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ 1.0 (+ 1.0 (- (* y 0.25) z))))

C

double code(double x, double y, double z) {
	return 1.0 + (1.0 + ((y * 0.25) - z));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = 1.0d0 + (1.0d0 + ((y * 0.25d0) - z))
end function

Java

public static double code(double x, double y, double z) {
	return 1.0 + (1.0 + ((y * 0.25) - z));
}

Python

def code(x, y, z):
	return 1.0 + (1.0 + ((y * 0.25) - z))

Julia

function code(x, y, z)
	return Float64(1.0 + Float64(1.0 + Float64(Float64(y * 0.25) - z)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = 1.0 + (1.0 + ((y * 0.25) - z));
end

Wolfram

code[x_, y_, z_] := N[(1.0 + N[(1.0 + N[(N[(y * 0.25), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto 1 + \color{blue}{\left(4 \cdot \frac{x}{y} + 4 \cdot \frac{\frac{1}{4} \cdot y - z}{y}\right)} \]

5. Applied rewrites 4.7%

   \[\leadsto 1 + \color{blue}{\left(\left(x + y \cdot 0.25\right) - z\right)} \]

6. Taylor expanded in x around 0

   \[\leadsto 1 + \left(\frac{1}{4} \cdot y - \color{blue}{z}\right) \]

8. Applied rewrites 10.4%

   \[\leadsto 1 + \left(1 + \color{blue}{\left(\left(x + y \cdot 0.25\right) - z\right)}\right) \]

9. Taylor expanded in x around 0

   \[\leadsto 1 + \left(1 + \left(\frac{1}{4} \cdot y - z\right)\right) \]

11. Applied rewrites 9.9%

    \[\leadsto 1 + \left(1 + \left(y \cdot 0.25 - z\right)\right) \]
12. Add Preprocessing

Alternative 7: 6.6% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ 1 + \left(1 + y \cdot 0.25\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ 1.0 (+ 1.0 (* y 0.25))))

C

double code(double x, double y, double z) {
	return 1.0 + (1.0 + (y * 0.25));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = 1.0d0 + (1.0d0 + (y * 0.25d0))
end function

Java

public static double code(double x, double y, double z) {
	return 1.0 + (1.0 + (y * 0.25));
}

Python

def code(x, y, z):
	return 1.0 + (1.0 + (y * 0.25))

Julia

function code(x, y, z)
	return Float64(1.0 + Float64(1.0 + Float64(y * 0.25)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = 1.0 + (1.0 + (y * 0.25));
end

Wolfram

code[x_, y_, z_] := N[(1.0 + N[(1.0 + N[(y * 0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto 1 + \color{blue}{4 \cdot \frac{\frac{1}{4} \cdot y - z}{y}} \]

5. Applied rewrites 5.0%

   \[\leadsto 1 + \color{blue}{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)} \]

6. Taylor expanded in x around 0

   \[\leadsto 1 + 4 \cdot \left(\frac{1}{4} \cdot y - \color{blue}{z}\right) \]

8. Applied rewrites 5.0%

   \[\leadsto 1 + 4 \cdot \left(1 + \color{blue}{\left(\left(x + y \cdot 0.25\right) - z\right)}\right) \]

9. Taylor expanded in x around 0

   \[\leadsto 1 + 4 \cdot \color{blue}{\left(\frac{1}{4} \cdot y - z\right)} \]

11. Applied rewrites 9.6%

    \[\leadsto 1 + \left(1 + \color{blue}{y \cdot 0.25}\right) \]
12. Add Preprocessing

Alternative 8: 3.5% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ 1 + y \cdot 0.25 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ 1.0 (* y 0.25)))

C

double code(double x, double y, double z) {
	return 1.0 + (y * 0.25);
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = 1.0d0 + (y * 0.25d0)
end function

Java

public static double code(double x, double y, double z) {
	return 1.0 + (y * 0.25);
}

Python

def code(x, y, z):
	return 1.0 + (y * 0.25)

Julia

function code(x, y, z)
	return Float64(1.0 + Float64(y * 0.25))
end

MATLAB

function tmp = code(x, y, z)
	tmp = 1.0 + (y * 0.25);
end

Wolfram

code[x_, y_, z_] := N[(1.0 + N[(y * 0.25), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto 1 + \color{blue}{\left(4 \cdot \frac{x}{y} + 4 \cdot \frac{\frac{1}{4} \cdot y - z}{y}\right)} \]

5. Applied rewrites 4.7%

   \[\leadsto 1 + \color{blue}{\left(\left(x + y \cdot 0.25\right) - z\right)} \]

6. Taylor expanded in x around 0

   \[\leadsto 1 + \left(\frac{1}{4} \cdot y - \color{blue}{z}\right) \]

8. Applied rewrites 10.4%

   \[\leadsto 1 + \left(1 + \color{blue}{\left(\left(x + y \cdot 0.25\right) - z\right)}\right) \]

9. Taylor expanded in x around 0

   \[\leadsto 1 + \left(\left(x + \frac{1}{4} \cdot y\right) - \color{blue}{z}\right) \]

11. Applied rewrites 3.8%

    \[\leadsto 1 + y \cdot \color{blue}{0.25} \]
12. Add Preprocessing

Alternative 9: 3.1% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ x + y \cdot 0.25 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ x (* y 0.25)))

C

double code(double x, double y, double z) {
	return x + (y * 0.25);
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + (y * 0.25d0)
end function

Java

public static double code(double x, double y, double z) {
	return x + (y * 0.25);
}

Python

def code(x, y, z):
	return x + (y * 0.25)

Julia

function code(x, y, z)
	return Float64(x + Float64(y * 0.25))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + (y * 0.25);
end

Wolfram

code[x_, y_, z_] := N[(x + N[(y * 0.25), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto 1 + \color{blue}{\left(4 \cdot \frac{x}{y} + 4 \cdot \frac{\frac{1}{4} \cdot y - z}{y}\right)} \]

5. Applied rewrites 4.7%

   \[\leadsto 1 + \color{blue}{\left(\left(x + y \cdot 0.25\right) - z\right)} \]

6. Taylor expanded in x around 0

   \[\leadsto 1 + \left(\frac{1}{4} \cdot y - \color{blue}{z}\right) \]

8. Applied rewrites 10.4%

   \[\leadsto 1 + \left(1 + \color{blue}{\left(\left(x + y \cdot 0.25\right) - z\right)}\right) \]

9. Taylor expanded in x around inf

   \[\leadsto \color{blue}{4 \cdot \frac{x}{y}} \]

11. Applied rewrites 3.4%

    \[\leadsto \color{blue}{x + y \cdot 0.25} \]
12. Add Preprocessing

Alternative 10: 3.1% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ y \cdot 0.25 - z \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (- (* y 0.25) z))

C

double code(double x, double y, double z) {
	return (y * 0.25) - z;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (y * 0.25d0) - z
end function

Java

public static double code(double x, double y, double z) {
	return (y * 0.25) - z;
}

Python

def code(x, y, z):
	return (y * 0.25) - z

Julia

function code(x, y, z)
	return Float64(Float64(y * 0.25) - z)
end

MATLAB

function tmp = code(x, y, z)
	tmp = (y * 0.25) - z;
end

Wolfram

code[x_, y_, z_] := N[(N[(y * 0.25), $MachinePrecision] - z), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{1 + \left(4 \cdot \frac{x}{y} + 4 \cdot \frac{\frac{1}{4} \cdot y - z}{y}\right)} \]

5. Applied rewrites 68.3%

   \[\leadsto \color{blue}{\frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}} \]

6. Taylor expanded in x around 0

   \[\leadsto 4 \cdot \frac{x}{y} + \color{blue}{4 \cdot \frac{\frac{1}{4} \cdot y - z}{y}} \]

8. Applied rewrites 3.7%

   \[\leadsto \left(x + y \cdot 0.25\right) - \color{blue}{z} \]

9. Taylor expanded in x around 0

   \[\leadsto \frac{1}{4} \cdot y - z \]

11. Applied rewrites 3.2%

    \[\leadsto y \cdot 0.25 - z \]
12. Add Preprocessing

Alternative 11: 2.7% accurate, 5.2× speedup

Math

\[\begin{array}{l} \\ y \cdot 0.25 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* y 0.25))

C

double code(double x, double y, double z) {
	return y * 0.25;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = y * 0.25d0
end function

Java

public static double code(double x, double y, double z) {
	return y * 0.25;
}

Python

def code(x, y, z):
	return y * 0.25

Julia

function code(x, y, z)
	return Float64(y * 0.25)
end

MATLAB

function tmp = code(x, y, z)
	tmp = y * 0.25;
end

Wolfram

code[x_, y_, z_] := N[(y * 0.25), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{1 + \left(4 \cdot \frac{x}{y} + 4 \cdot \frac{\frac{1}{4} \cdot y - z}{y}\right)} \]

5. Applied rewrites 68.3%

   \[\leadsto \color{blue}{\frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}} \]

6. Taylor expanded in x around inf

   \[\leadsto x \cdot \color{blue}{\left(4 \cdot \frac{\frac{1}{4} - \frac{z}{y}}{x} + 4 \cdot \frac{1}{y}\right)} \]

8. Applied rewrites 2.7%

   \[\leadsto y \cdot \color{blue}{0.25} \]
9. Add Preprocessing

Reproduce

herbie shell --seed 2024313 
(FPCore (x y z)
  :name "Data.Array.Repa.Algorithms.ColorRamp:rampColorHotToCold from repa-algorithms-3.4.0.1, C"
  :precision binary64
  (+ 1.0 (/ (* 4.0 (- (+ x (* y 0.25)) z)) y)))