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

Percentage Accurate: 99.7% → 99.7%

Time: 1.6s

Alternatives: 10

Speedup: 1.0×

• 20.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

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

Math

\[\begin{array}{l} \\ 1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ 1.0 (/ (* 4.0 (- (+ x (* y 0.75)) z)) y)))

C

double code(double x, double y, double z) {
	return 1.0 + ((4.0 * ((x + (y * 0.75)) - 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 * 0.75d0)) - z)) / y)
end function

Java

public static double code(double x, double y, double z) {
	return 1.0 + ((4.0 * ((x + (y * 0.75)) - z)) / y);
}

Python

def code(x, y, z):
	return 1.0 + ((4.0 * ((x + (y * 0.75)) - z)) / y)

Julia

function code(x, y, z)
	return Float64(1.0 + Float64(Float64(4.0 * Float64(Float64(x + Float64(y * 0.75)) - z)) / y))
end

MATLAB

function tmp = code(x, y, z)
	tmp = 1.0 + ((4.0 * ((x + (y * 0.75)) - z)) / y);
end

Wolfram

code[x_, y_, z_] := N[(1.0 + N[(N[(4.0 * N[(N[(x + N[(y * 0.75), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ 1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ 1.0 (/ (* 4.0 (- (+ x (* y 0.75)) z)) y)))

C

double code(double x, double y, double z) {
	return 1.0 + ((4.0 * ((x + (y * 0.75)) - 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 * 0.75d0)) - z)) / y)
end function

Java

public static double code(double x, double y, double z) {
	return 1.0 + ((4.0 * ((x + (y * 0.75)) - z)) / y);
}

Python

def code(x, y, z):
	return 1.0 + ((4.0 * ((x + (y * 0.75)) - z)) / y)

Julia

function code(x, y, z)
	return Float64(1.0 + Float64(Float64(4.0 * Float64(Float64(x + Float64(y * 0.75)) - z)) / y))
end

MATLAB

function tmp = code(x, y, z)
	tmp = 1.0 + ((4.0 * ((x + (y * 0.75)) - z)) / y);
end

Wolfram

code[x_, y_, z_] := N[(1.0 + N[(N[(4.0 * N[(N[(x + N[(y * 0.75), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ 1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ 1.0 (/ (* 4.0 (- (+ x (* y 0.75)) z)) y)))

C

double code(double x, double y, double z) {
	return 1.0 + ((4.0 * ((x + (y * 0.75)) - 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 * 0.75d0)) - z)) / y)
end function

Java

public static double code(double x, double y, double z) {
	return 1.0 + ((4.0 * ((x + (y * 0.75)) - z)) / y);
}

Python

def code(x, y, z):
	return 1.0 + ((4.0 * ((x + (y * 0.75)) - z)) / y)

Julia

function code(x, y, z)
	return Float64(1.0 + Float64(Float64(4.0 * Float64(Float64(x + Float64(y * 0.75)) - z)) / y))
end

MATLAB

function tmp = code(x, y, z)
	tmp = 1.0 + ((4.0 * ((x + (y * 0.75)) - z)) / y);
end

Wolfram

code[x_, y_, z_] := N[(1.0 + N[(N[(4.0 * N[(N[(x + N[(y * 0.75), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
2. Add Preprocessing
3. Add Preprocessing

Alternative 2: 71.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (/ (* 4.0 (- (+ x (* y 0.75)) z)) y))

C

double code(double x, double y, double z) {
	return (4.0 * ((x + (y * 0.75)) - 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 * 0.75d0)) - z)) / y
end function

Java

public static double code(double x, double y, double z) {
	return (4.0 * ((x + (y * 0.75)) - z)) / y;
}

Python

def code(x, y, z):
	return (4.0 * ((x + (y * 0.75)) - z)) / y

Julia

function code(x, y, z)
	return Float64(Float64(4.0 * Float64(Float64(x + Float64(y * 0.75)) - z)) / y)
end

MATLAB

function tmp = code(x, y, z)
	tmp = (4.0 * ((x + (y * 0.75)) - z)) / y;
end

Wolfram

code[x_, y_, z_] := N[(N[(4.0 * N[(N[(x + N[(y * 0.75), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{1 + \left(4 \cdot \frac{x}{y} + 4 \cdot \frac{\frac{3}{4} \cdot y - z}{y}\right)} \]

5. Applied rewrites 74.0%

   \[\leadsto \color{blue}{\frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}} \]
6. Add Preprocessing

Alternative 3: 33.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \frac{\left(x + y \cdot 0.75\right) - z}{y} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (/ (- (+ x (* y 0.75)) z) y))

C

double code(double x, double y, double z) {
	return ((x + (y * 0.75)) - 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 = ((x + (y * 0.75d0)) - z) / y
end function

Java

public static double code(double x, double y, double z) {
	return ((x + (y * 0.75)) - z) / y;
}

Python

def code(x, y, z):
	return ((x + (y * 0.75)) - z) / y

Julia

function code(x, y, z)
	return Float64(Float64(Float64(x + Float64(y * 0.75)) - z) / y)
end

MATLAB

function tmp = code(x, y, z)
	tmp = ((x + (y * 0.75)) - z) / y;
end

Wolfram

code[x_, y_, z_] := N[(N[(N[(x + N[(y * 0.75), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision] / y), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{1 + \left(4 \cdot \frac{x}{y} + 4 \cdot \frac{\frac{3}{4} \cdot y - z}{y}\right)} \]

5. Applied rewrites 74.0%

   \[\leadsto \color{blue}{\frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}} \]

6. Taylor expanded in x around inf

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

8. Applied rewrites 22.9%

   \[\leadsto \color{blue}{\frac{x + y \cdot 0.75}{y}} \]

9. Taylor expanded in x around 0

   \[\leadsto \frac{x + \frac{3}{4} \cdot y}{y} \]

11. Applied rewrites 32.9%

    \[\leadsto \frac{\left(x + y \cdot 0.75\right) - z}{y} \]
12. Add Preprocessing

Alternative 4: 21.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \frac{x + y \cdot 0.75}{y} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (/ (+ x (* y 0.75)) y))

C

double code(double x, double y, double z) {
	return (x + (y * 0.75)) / 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 * 0.75d0)) / y
end function

Java

public static double code(double x, double y, double z) {
	return (x + (y * 0.75)) / y;
}

Python

def code(x, y, z):
	return (x + (y * 0.75)) / y

Julia

function code(x, y, z)
	return Float64(Float64(x + Float64(y * 0.75)) / y)
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x + (y * 0.75)) / y;
end

Wolfram

code[x_, y_, z_] := N[(N[(x + N[(y * 0.75), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{1 + \left(4 \cdot \frac{x}{y} + 4 \cdot \frac{\frac{3}{4} \cdot y - z}{y}\right)} \]

5. Applied rewrites 74.0%

   \[\leadsto \color{blue}{\frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}} \]

6. Taylor expanded in x around inf

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

8. Applied rewrites 22.9%

   \[\leadsto \color{blue}{\frac{x + y \cdot 0.75}{y}} \]
9. Add Preprocessing

Alternative 5: 7.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \frac{y \cdot 0.75}{y} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (/ (* y 0.75) y))

C

double code(double x, double y, double z) {
	return (y * 0.75) / 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 = (y * 0.75d0) / y
end function

Java

public static double code(double x, double y, double z) {
	return (y * 0.75) / y;
}

Python

def code(x, y, z):
	return (y * 0.75) / y

Julia

function code(x, y, z)
	return Float64(Float64(y * 0.75) / y)
end

MATLAB

function tmp = code(x, y, z)
	tmp = (y * 0.75) / y;
end

Wolfram

code[x_, y_, z_] := N[(N[(y * 0.75), $MachinePrecision] / y), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{1 + \left(4 \cdot \frac{x}{y} + 4 \cdot \frac{\frac{3}{4} \cdot y - z}{y}\right)} \]

5. Applied rewrites 74.0%

   \[\leadsto \color{blue}{\frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}} \]

6. Taylor expanded in x around inf

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

8. Applied rewrites 22.9%

   \[\leadsto \color{blue}{\frac{x + y \cdot 0.75}{y}} \]

9. Taylor expanded in x around 0

   \[\leadsto \frac{4 \cdot x + 4 \cdot \left(\frac{3}{4} \cdot y - z\right)}{y} \]

11. Applied rewrites 7.3%

    \[\leadsto \frac{y \cdot 0.75}{y} \]
12. Add Preprocessing

Alternative 6: 3.9% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ 1 + \left(\left(x + y \cdot 0.75\right) - z\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ 1.0 (- (+ x (* y 0.75)) z)))

C

double code(double x, double y, double z) {
	return 1.0 + ((x + (y * 0.75)) - 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 + ((x + (y * 0.75d0)) - z)
end function

Java

public static double code(double x, double y, double z) {
	return 1.0 + ((x + (y * 0.75)) - z);
}

Python

def code(x, y, z):
	return 1.0 + ((x + (y * 0.75)) - z)

Julia

function code(x, y, z)
	return Float64(1.0 + Float64(Float64(x + Float64(y * 0.75)) - z))
end

MATLAB

function tmp = code(x, y, z)
	tmp = 1.0 + ((x + (y * 0.75)) - z);
end

Wolfram

code[x_, y_, z_] := N[(1.0 + N[(N[(x + N[(y * 0.75), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto 1 + \color{blue}{\left(4 \cdot \frac{x}{y} + 4 \cdot \frac{\frac{3}{4} \cdot y - z}{y}\right)} \]

5. Applied rewrites 3.8%

   \[\leadsto 1 + \color{blue}{\left(\left(x + y \cdot 0.75\right) - z\right)} \]
6. Add Preprocessing

Alternative 7: 3.3% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \left(\left(x + y \cdot 0.75\right) - z\right) - z \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (- (- (+ x (* y 0.75)) z) z))

C

double code(double x, double y, double z) {
	return ((x + (y * 0.75)) - z) - 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 * 0.75d0)) - z) - z
end function

Java

public static double code(double x, double y, double z) {
	return ((x + (y * 0.75)) - z) - z;
}

Python

def code(x, y, z):
	return ((x + (y * 0.75)) - z) - z

Julia

function code(x, y, z)
	return Float64(Float64(Float64(x + Float64(y * 0.75)) - z) - z)
end

MATLAB

function tmp = code(x, y, z)
	tmp = ((x + (y * 0.75)) - z) - z;
end

Wolfram

code[x_, y_, z_] := N[(N[(N[(x + N[(y * 0.75), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision] - z), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{1 + \left(4 \cdot \frac{x}{y} + 4 \cdot \frac{\frac{3}{4} \cdot y - z}{y}\right)} \]

5. Applied rewrites 74.0%

   \[\leadsto \color{blue}{\frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}} \]

6. Taylor expanded in x around 0

   \[\leadsto 4 \cdot \frac{x}{y} + \color{blue}{4 \cdot \frac{\frac{3}{4} \cdot y - z}{y}} \]

8. Applied rewrites 3.3%

   \[\leadsto \left(x + y \cdot 0.75\right) - \color{blue}{z} \]

9. Taylor expanded in x around 0

   \[\leadsto \left(x + \frac{3}{4} \cdot y\right) - z \]

11. Applied rewrites 3.3%

    \[\leadsto \left(\left(x + y \cdot 0.75\right) - z\right) - z \]
12. Add Preprocessing

Alternative 8: 3.3% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \left(x + y \cdot 0.75\right) - z \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (- (+ x (* y 0.75)) z))

C

double code(double x, double y, double z) {
	return (x + (y * 0.75)) - 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 * 0.75d0)) - z
end function

Java

public static double code(double x, double y, double z) {
	return (x + (y * 0.75)) - z;
}

Python

def code(x, y, z):
	return (x + (y * 0.75)) - z

Julia

function code(x, y, z)
	return Float64(Float64(x + Float64(y * 0.75)) - z)
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x + (y * 0.75)) - z;
end

Wolfram

code[x_, y_, z_] := N[(N[(x + N[(y * 0.75), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{1 + \left(4 \cdot \frac{x}{y} + 4 \cdot \frac{\frac{3}{4} \cdot y - z}{y}\right)} \]

5. Applied rewrites 74.0%

   \[\leadsto \color{blue}{\frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}} \]

6. Taylor expanded in x around 0

   \[\leadsto 4 \cdot \frac{x}{y} + \color{blue}{4 \cdot \frac{\frac{3}{4} \cdot y - z}{y}} \]

8. Applied rewrites 3.3%

   \[\leadsto \left(x + y \cdot 0.75\right) - \color{blue}{z} \]
9. Add Preprocessing

Alternative 9: 3.1% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ x + y \cdot 0.75 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ x (* y 0.75)))

C

double code(double x, double y, double z) {
	return x + (y * 0.75);
}

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 * 0.75d0)
end function

Java

public static double code(double x, double y, double z) {
	return x + (y * 0.75);
}

Python

def code(x, y, z):
	return x + (y * 0.75)

Julia

function code(x, y, z)
	return Float64(x + Float64(y * 0.75))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + (y * 0.75);
end

Wolfram

code[x_, y_, z_] := N[(x + N[(y * 0.75), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{1 + \left(4 \cdot \frac{x}{y} + 4 \cdot \frac{\frac{3}{4} \cdot y - z}{y}\right)} \]

5. Applied rewrites 74.0%

   \[\leadsto \color{blue}{\frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}} \]

6. Taylor expanded in x around inf

   \[\leadsto \color{blue}{x \cdot \left(4 \cdot \frac{\frac{3}{4} - \frac{z}{y}}{x} + \left(\frac{1}{x} + 4 \cdot \frac{1}{y}\right)\right)} \]

8. Applied rewrites 3.1%

   \[\leadsto \color{blue}{x + y \cdot 0.75} \]
9. Add Preprocessing

Alternative 10: 2.7% accurate, 5.2× speedup

Math

\[\begin{array}{l} \\ y \cdot 0.75 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* y 0.75))

C

double code(double x, double y, double z) {
	return y * 0.75;
}

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 * 0.75d0
end function

Java

public static double code(double x, double y, double z) {
	return y * 0.75;
}

Python

def code(x, y, z):
	return y * 0.75

Julia

function code(x, y, z)
	return Float64(y * 0.75)
end

MATLAB

function tmp = code(x, y, z)
	tmp = y * 0.75;
end

Wolfram

code[x_, y_, z_] := N[(y * 0.75), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{1 + \left(4 \cdot \frac{x}{y} + 4 \cdot \frac{\frac{3}{4} \cdot y - z}{y}\right)} \]

5. Applied rewrites 74.0%

   \[\leadsto \color{blue}{\frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}} \]

6. Taylor expanded in x around inf

   \[\leadsto \color{blue}{x \cdot \left(4 \cdot \frac{\frac{3}{4} - \frac{z}{y}}{x} + \left(\frac{1}{x} + 4 \cdot \frac{1}{y}\right)\right)} \]

8. Applied rewrites 3.1%

   \[\leadsto \color{blue}{x + y \cdot 0.75} \]

9. Taylor expanded in x around 0

   \[\leadsto 4 \cdot x + \color{blue}{4 \cdot \left(\frac{3}{4} \cdot y - z\right)} \]

11. Applied rewrites 2.6%

    \[\leadsto y \cdot \color{blue}{0.75} \]
12. Add Preprocessing

Reproduce

herbie shell --seed 2024321 
(FPCore (x y z)
  :name "Data.Array.Repa.Algorithms.ColorRamp:rampColorHotToCold from repa-algorithms-3.4.0.1, A"
  :precision binary64
  :pre (TRUE)
  (+ 1.0 (/ (* 4.0 (- (+ x (* y 0.75)) z)) y)))