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

Percentage Accurate: 99.8% → 100.0%

Time: 1.3s

Alternatives: 5

Speedup: 1.0×

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

Specification

\[\mathsf{TRUE}\left(\right)\]

Math

\[\begin{array}{l} \\ \frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (/ (* 4.0 (- (- x y) (* z 0.5))) z))

C

double code(double x, double y, double z) {
	return (4.0 * ((x - y) - (z * 0.5))) / 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 = (4.0d0 * ((x - y) - (z * 0.5d0))) / z
end function

Java

public static double code(double x, double y, double z) {
	return (4.0 * ((x - y) - (z * 0.5))) / z;
}

Python

def code(x, y, z):
	return (4.0 * ((x - y) - (z * 0.5))) / z

Julia

function code(x, y, z)
	return Float64(Float64(4.0 * Float64(Float64(x - y) - Float64(z * 0.5))) / z)
end

MATLAB

function tmp = code(x, y, z)
	tmp = (4.0 * ((x - y) - (z * 0.5))) / z;
end

Wolfram

code[x_, y_, z_] := N[(N[(4.0 * N[(N[(x - y), $MachinePrecision] - N[(z * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]

Initial Program: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (/ (* 4.0 (- (- x y) (* z 0.5))) z))

C

double code(double x, double y, double z) {
	return (4.0 * ((x - y) - (z * 0.5))) / 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 = (4.0d0 * ((x - y) - (z * 0.5d0))) / z
end function

Java

public static double code(double x, double y, double z) {
	return (4.0 * ((x - y) - (z * 0.5))) / z;
}

Python

def code(x, y, z):
	return (4.0 * ((x - y) - (z * 0.5))) / z

Julia

function code(x, y, z)
	return Float64(Float64(4.0 * Float64(Float64(x - y) - Float64(z * 0.5))) / z)
end

MATLAB

function tmp = code(x, y, z)
	tmp = (4.0 * ((x - y) - (z * 0.5))) / z;
end

Wolfram

code[x_, y_, z_] := N[(N[(4.0 * N[(N[(x - y), $MachinePrecision] - N[(z * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]

Alternative 1: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ 4 \cdot \frac{\left(x - y\right) - z \cdot 0.5}{z} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* 4.0 (/ (- (- x y) (* z 0.5)) z)))

C

double code(double x, double y, double z) {
	return 4.0 * (((x - y) - (z * 0.5)) / 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 = 4.0d0 * (((x - y) - (z * 0.5d0)) / z)
end function

Java

public static double code(double x, double y, double z) {
	return 4.0 * (((x - y) - (z * 0.5)) / z);
}

Python

def code(x, y, z):
	return 4.0 * (((x - y) - (z * 0.5)) / z)

Julia

function code(x, y, z)
	return Float64(4.0 * Float64(Float64(Float64(x - y) - Float64(z * 0.5)) / z))
end

MATLAB

function tmp = code(x, y, z)
	tmp = 4.0 * (((x - y) - (z * 0.5)) / z);
end

Wolfram

code[x_, y_, z_] := N[(4.0 * N[(N[(N[(x - y), $MachinePrecision] - N[(z * 0.5), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.6%

   \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{-4 \cdot \frac{y + \frac{1}{2} \cdot z}{z} + 4 \cdot \frac{x}{z}} \]

5. Applied rewrites 3.1%

   \[\leadsto \color{blue}{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)} \]

6. Taylor expanded in x around 0

   \[\leadsto 4 \cdot \left(-1 \cdot \color{blue}{\left(y + \frac{1}{2} \cdot z\right)}\right) \]

8. Applied rewrites 62.9%

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

9. Taylor expanded in x around inf

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

11. Applied rewrites 100.0%

    \[\leadsto 4 \cdot \frac{\left(x - y\right) - z \cdot 0.5}{z} \]
12. Add Preprocessing

Alternative 2: 70.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 4 \cdot \frac{x - y}{z}\\ t_1 := \left(x - y\right) - z \cdot 0.5\\ t_2 := \frac{4 \cdot t\_1}{z}\\ \mathbf{if}\;t\_2 \leq -10:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;t\_2 \leq -1:\\ \;\;\;\;\frac{t\_1}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 4.0 (/ (- x y) z)))
        (t_1 (- (- x y) (* z 0.5)))
        (t_2 (/ (* 4.0 t_1) z)))
   (if (<= t_2 -10.0) t_0 (if (<= t_2 -1.0) (/ t_1 z) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = 4.0 * ((x - y) / z);
	double t_1 = (x - y) - (z * 0.5);
	double t_2 = (4.0 * t_1) / z;
	double tmp;
	if (t_2 <= -10.0) {
		tmp = t_0;
	} else if (t_2 <= -1.0) {
		tmp = t_1 / 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = 4.0d0 * ((x - y) / z)
    t_1 = (x - y) - (z * 0.5d0)
    t_2 = (4.0d0 * t_1) / z
    if (t_2 <= (-10.0d0)) then
        tmp = t_0
    else if (t_2 <= (-1.0d0)) then
        tmp = t_1 / 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 = 4.0 * ((x - y) / z);
	double t_1 = (x - y) - (z * 0.5);
	double t_2 = (4.0 * t_1) / z;
	double tmp;
	if (t_2 <= -10.0) {
		tmp = t_0;
	} else if (t_2 <= -1.0) {
		tmp = t_1 / z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 4.0 * ((x - y) / z)
	t_1 = (x - y) - (z * 0.5)
	t_2 = (4.0 * t_1) / z
	tmp = 0
	if t_2 <= -10.0:
		tmp = t_0
	elif t_2 <= -1.0:
		tmp = t_1 / z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(4.0 * Float64(Float64(x - y) / z))
	t_1 = Float64(Float64(x - y) - Float64(z * 0.5))
	t_2 = Float64(Float64(4.0 * t_1) / z)
	tmp = 0.0
	if (t_2 <= -10.0)
		tmp = t_0;
	elseif (t_2 <= -1.0)
		tmp = Float64(t_1 / z);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 4.0 * ((x - y) / z);
	t_1 = (x - y) - (z * 0.5);
	t_2 = (4.0 * t_1) / z;
	tmp = 0.0;
	if (t_2 <= -10.0)
		tmp = t_0;
	elseif (t_2 <= -1.0)
		tmp = t_1 / z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(4.0 * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] - N[(z * 0.5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(4.0 * t$95$1), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[t$95$2, -10.0], t$95$0, If[LessEqual[t$95$2, -1.0], N[(t$95$1 / z), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (*.f64 z #s(literal 1/2 binary64)))) z) < -10 or -1 < (/.f64 (*.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (*.f64 z #s(literal 1/2 binary64)))) z)

   1. Initial program 99.4%

      \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{-4 \cdot \frac{y + \frac{1}{2} \cdot z}{z} + 4 \cdot \frac{x}{z}} \]

   5. Applied rewrites 3.1%

      \[\leadsto \color{blue}{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)} \]

   6. Taylor expanded in x around 0

      \[\leadsto 4 \cdot \left(-1 \cdot \color{blue}{\left(y + \frac{1}{2} \cdot z\right)}\right) \]

   8. Applied rewrites 96.7%

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

   if -10 < (/.f64 (*.f64 #s(literal 4 binary64) (-.f64 (-.f64 x y) (*.f64 z #s(literal 1/2 binary64)))) z) < -1

   1. Initial program 100.0%

      \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \frac{\color{blue}{-4 \cdot \left(y + \frac{1}{2} \cdot z\right)}}{z} \]

   5. Applied rewrites 17.2%

      \[\leadsto \frac{\color{blue}{\left(x - y\right) - z \cdot 0.5}}{z} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 66.2% accurate, 1.4× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.6%

   \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{-4 \cdot \frac{y + \frac{1}{2} \cdot z}{z} + 4 \cdot \frac{x}{z}} \]

5. Applied rewrites 3.1%

   \[\leadsto \color{blue}{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)} \]

6. Taylor expanded in x around 0

   \[\leadsto 4 \cdot \left(-1 \cdot \color{blue}{\left(y + \frac{1}{2} \cdot z\right)}\right) \]

8. Applied rewrites 62.9%

   \[\leadsto 4 \cdot \frac{x - y}{\color{blue}{z}} \]
9. Add Preprocessing

Alternative 4: 29.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \frac{x - y}{z} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (/ (- x y) z))

C

double code(double x, double y, double z) {
	return (x - y) / 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 = (x - y) / z
end function

Java

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

Python

def code(x, y, z):
	return (x - y) / z

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.6%

   \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto \frac{\color{blue}{-4 \cdot \left(y + \frac{1}{2} \cdot z\right) + 4 \cdot x}}{z} \]

5. Applied rewrites 25.1%

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

Alternative 5: 3.6% accurate, 7.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return x - 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 = x - y
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.6%

   \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{-4 \cdot \frac{y + \frac{1}{2} \cdot z}{z} + 4 \cdot \frac{x}{z}} \]

5. Applied rewrites 3.1%

   \[\leadsto \color{blue}{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)} \]

6. Taylor expanded in x around 0

   \[\leadsto -4 \cdot \left(y + \frac{1}{2} \cdot z\right) + \color{blue}{4 \cdot x} \]

8. Applied rewrites 3.4%

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

Developer Target 1: 97.9% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024321 
(FPCore (x y z)
  :name "Data.Array.Repa.Algorithms.ColorRamp:rampColorHotToCold from repa-algorithms-3.4.0.1, B"
  :precision binary64
  :pre (TRUE)

  :alt
  (! :herbie-platform default (- (* 4 (/ x z)) (+ 2 (* 4 (/ y z)))))

  (/ (* 4.0 (- (- x y) (* z 0.5))) z))