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

Percentage Accurate: 99.8% → 99.9%

Time: 6.1s

Alternatives: 4

Speedup: 1.4×

• 20.1% 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: 99.8% 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, 1.4× speedup

Math

\[\begin{array}{l} \\ 2 + \frac{4 \cdot \left(x - z\right)}{y} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ 2.0 (/ (* 4.0 (- x z)) y)))

C

double code(double x, double y, double z) {
	return 2.0 + ((4.0 * (x - 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 = 2.0d0 + ((4.0d0 * (x - z)) / y)
end function

Java

public static double code(double x, double y, double z) {
	return 2.0 + ((4.0 * (x - z)) / y);
}

Python

def code(x, y, z):
	return 2.0 + ((4.0 * (x - z)) / y)

Julia

function code(x, y, z)
	return Float64(2.0 + Float64(Float64(4.0 * Float64(x - z)) / y))
end

MATLAB

function tmp = code(x, y, z)
	tmp = 2.0 + ((4.0 * (x - z)) / y);
end

Wolfram

code[x_, y_, z_] := N[(2.0 + N[(N[(4.0 * N[(x - 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. Taylor expanded in y around 0 100.0%

   \[\leadsto \color{blue}{2 + 4 \cdot \frac{x - z}{y}} \]
4. Step-by-step derivation

   1. associate-*r/ 100.0%

      \[\leadsto 2 + \color{blue}{\frac{4 \cdot \left(x - z\right)}{y}} \]

5. Simplified 100.0%

   \[\leadsto \color{blue}{2 + \frac{4 \cdot \left(x - z\right)}{y}} \]

6. Final simplification 100.0%

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

Alternative 2: 85.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{-55} \lor \neg \left(x \leq 3.1 \cdot 10^{+77}\right):\\ \;\;\;\;2 + \frac{4 \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;2 + -4 \cdot \frac{z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.4e-55) (not (<= x 3.1e+77)))
   (+ 2.0 (/ (* 4.0 x) y))
   (+ 2.0 (* -4.0 (/ z y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.4e-55) || !(x <= 3.1e+77)) {
		tmp = 2.0 + ((4.0 * x) / y);
	} else {
		tmp = 2.0 + (-4.0 * (z / y));
	}
	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 ((x <= (-1.4d-55)) .or. (.not. (x <= 3.1d+77))) then
        tmp = 2.0d0 + ((4.0d0 * x) / y)
    else
        tmp = 2.0d0 + ((-4.0d0) * (z / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.4e-55) || !(x <= 3.1e+77)) {
		tmp = 2.0 + ((4.0 * x) / y);
	} else {
		tmp = 2.0 + (-4.0 * (z / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.4e-55) or not (x <= 3.1e+77):
		tmp = 2.0 + ((4.0 * x) / y)
	else:
		tmp = 2.0 + (-4.0 * (z / y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.4e-55) || !(x <= 3.1e+77))
		tmp = Float64(2.0 + Float64(Float64(4.0 * x) / y));
	else
		tmp = Float64(2.0 + Float64(-4.0 * Float64(z / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.4e-55) || ~((x <= 3.1e+77)))
		tmp = 2.0 + ((4.0 * x) / y);
	else
		tmp = 2.0 + (-4.0 * (z / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.4e-55], N[Not[LessEqual[x, 3.1e+77]], $MachinePrecision]], N[(2.0 + N[(N[(4.0 * x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(2.0 + N[(-4.0 * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.39999999999999992e-55 or 3.09999999999999999e77 < x

   1. Initial program 100.0%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0 83.8%

      \[\leadsto \color{blue}{2 + 4 \cdot \frac{x}{y}} \]
   6. Step-by-step derivation

      1. +-commutative 83.8%

         \[\leadsto \color{blue}{4 \cdot \frac{x}{y} + 2} \]

      2. associate-*r/ 83.8%

         \[\leadsto \color{blue}{\frac{4 \cdot x}{y}} + 2 \]

   7. Simplified 83.8%

      \[\leadsto \color{blue}{\frac{4 \cdot x}{y} + 2} \]

   if -1.39999999999999992e-55 < x < 3.09999999999999999e77

   1. Initial program 100.0%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around 0 93.3%

      \[\leadsto \color{blue}{2 + -4 \cdot \frac{z}{y}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{-55} \lor \neg \left(x \leq 3.1 \cdot 10^{+77}\right):\\ \;\;\;\;2 + \frac{4 \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;2 + -4 \cdot \frac{z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 68.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ 2 + -4 \cdot \frac{z}{y} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ 2.0 (* -4.0 (/ z y))))

C

double code(double x, double y, double z) {
	return 2.0 + (-4.0 * (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 = 2.0d0 + ((-4.0d0) * (z / y))
end function

Java

public static double code(double x, double y, double z) {
	return 2.0 + (-4.0 * (z / y));
}

Python

def code(x, y, z):
	return 2.0 + (-4.0 * (z / y))

Julia

function code(x, y, z)
	return Float64(2.0 + Float64(-4.0 * Float64(z / y)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = 2.0 + (-4.0 * (z / y));
end

Wolfram

code[x_, y_, z_] := N[(2.0 + N[(-4.0 * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

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

3. Simplified 99.8%

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

5. Taylor expanded in x around 0 71.6%

   \[\leadsto \color{blue}{2 + -4 \cdot \frac{z}{y}} \]

6. Final simplification 71.6%

   \[\leadsto 2 + -4 \cdot \frac{z}{y} \]
7. Add Preprocessing

Alternative 4: 34.4% accurate, 13.0× speedup

Math

\[\begin{array}{l} \\ 2 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 2.0)

C

double code(double x, double y, double z) {
	return 2.0;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = 2.0d0
end function

Java

public static double code(double x, double y, double z) {
	return 2.0;
}

Python

def code(x, y, z):
	return 2.0

Julia

function code(x, y, z)
	return 2.0
end

MATLAB

function tmp = code(x, y, z)
	tmp = 2.0;
end

Wolfram

code[x_, y_, z_] := 2.0

Derivation

1. Initial program 100.0%

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

3. Simplified 99.8%

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

5. Taylor expanded in y around inf 38.7%

   \[\leadsto \color{blue}{2} \]

6. Final simplification 38.7%

   \[\leadsto 2 \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024034 
(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)))