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

Percentage Accurate: 99.7% → 100.0%

Time: 4.9s

Alternatives: 4

Speedup: 1.2×

• 21.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

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: 99.7% 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, 1.2× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]
2. Step-by-step derivation

   1. associate-/l* 100.0%

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

   2. div-sub 100.0%

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

   3. remove-double-neg 100.0%

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

   4. distribute-lft-neg-out 100.0%

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

   5. distribute-frac-neg 100.0%

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

   6. neg-sub0 100.0%

      \[\leadsto 4 \cdot \left(\frac{x - y}{z} - \color{blue}{\left(0 - \frac{\left(-z\right) \cdot 0.5}{z}\right)}\right) \]

   7. associate-+l- 100.0%

      \[\leadsto 4 \cdot \color{blue}{\left(\left(\frac{x - y}{z} - 0\right) + \frac{\left(-z\right) \cdot 0.5}{z}\right)} \]

   8. div-sub 97.7%

      \[\leadsto 4 \cdot \left(\left(\color{blue}{\left(\frac{x}{z} - \frac{y}{z}\right)} - 0\right) + \frac{\left(-z\right) \cdot 0.5}{z}\right) \]

   9. associate--r+ 97.7%

      \[\leadsto 4 \cdot \left(\color{blue}{\left(\frac{x}{z} - \left(\frac{y}{z} + 0\right)\right)} + \frac{\left(-z\right) \cdot 0.5}{z}\right) \]

   10. add0 97.7%

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

   11. div-sub 100.0%

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

   12. distribute-rgt-in 100.0%

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

3. Simplified 100.0%

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

5. Final simplification 100.0%

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

Alternative 2: 85.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.05 \cdot 10^{+132} \lor \neg \left(x \leq 3.5 \cdot 10^{+98}\right):\\ \;\;\;\;-2 + 4 \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;-2 - 4 \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -2.05e+132) (not (<= x 3.5e+98)))
   (+ -2.0 (* 4.0 (/ x z)))
   (- -2.0 (* 4.0 (/ y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.05e+132) || !(x <= 3.5e+98)) {
		tmp = -2.0 + (4.0 * (x / z));
	} else {
		tmp = -2.0 - (4.0 * (y / 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 ((x <= (-2.05d+132)) .or. (.not. (x <= 3.5d+98))) then
        tmp = (-2.0d0) + (4.0d0 * (x / z))
    else
        tmp = (-2.0d0) - (4.0d0 * (y / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.05e+132) || !(x <= 3.5e+98)) {
		tmp = -2.0 + (4.0 * (x / z));
	} else {
		tmp = -2.0 - (4.0 * (y / z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -2.05e+132) or not (x <= 3.5e+98):
		tmp = -2.0 + (4.0 * (x / z))
	else:
		tmp = -2.0 - (4.0 * (y / z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -2.05e+132) || !(x <= 3.5e+98))
		tmp = Float64(-2.0 + Float64(4.0 * Float64(x / z)));
	else
		tmp = Float64(-2.0 - Float64(4.0 * Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -2.05e+132) || ~((x <= 3.5e+98)))
		tmp = -2.0 + (4.0 * (x / z));
	else
		tmp = -2.0 - (4.0 * (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -2.05e+132], N[Not[LessEqual[x, 3.5e+98]], $MachinePrecision]], N[(-2.0 + N[(4.0 * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-2.0 - N[(4.0 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.04999999999999996e132 or 3.5e98 < x

   1. Initial program 100.0%

      \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]
   2. Step-by-step derivation

      1. associate-/l* 100.0%

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

      2. div-sub 100.0%

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

      3. remove-double-neg 100.0%

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

      4. distribute-lft-neg-out 100.0%

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

      5. distribute-frac-neg 100.0%

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

      6. neg-sub0 100.0%

         \[\leadsto 4 \cdot \left(\frac{x - y}{z} - \color{blue}{\left(0 - \frac{\left(-z\right) \cdot 0.5}{z}\right)}\right) \]

      7. associate-+l- 100.0%

         \[\leadsto 4 \cdot \color{blue}{\left(\left(\frac{x - y}{z} - 0\right) + \frac{\left(-z\right) \cdot 0.5}{z}\right)} \]

      8. div-sub 96.2%

         \[\leadsto 4 \cdot \left(\left(\color{blue}{\left(\frac{x}{z} - \frac{y}{z}\right)} - 0\right) + \frac{\left(-z\right) \cdot 0.5}{z}\right) \]

      9. associate--r+ 96.2%

         \[\leadsto 4 \cdot \left(\color{blue}{\left(\frac{x}{z} - \left(\frac{y}{z} + 0\right)\right)} + \frac{\left(-z\right) \cdot 0.5}{z}\right) \]

      10. add0 96.2%

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

      11. div-sub 100.0%

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

      12. distribute-rgt-in 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 88.6%

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

   if -2.04999999999999996e132 < x < 3.5e98

   1. Initial program 100.0%

      \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]
   2. Step-by-step derivation

      1. associate-/l* 100.0%

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

      2. div-sub 100.0%

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

      3. remove-double-neg 100.0%

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

      4. distribute-lft-neg-out 100.0%

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

      5. distribute-frac-neg 100.0%

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

      6. neg-sub0 100.0%

         \[\leadsto 4 \cdot \left(\frac{x - y}{z} - \color{blue}{\left(0 - \frac{\left(-z\right) \cdot 0.5}{z}\right)}\right) \]

      7. associate-+l- 100.0%

         \[\leadsto 4 \cdot \color{blue}{\left(\left(\frac{x - y}{z} - 0\right) + \frac{\left(-z\right) \cdot 0.5}{z}\right)} \]

      8. div-sub 98.3%

         \[\leadsto 4 \cdot \left(\left(\color{blue}{\left(\frac{x}{z} - \frac{y}{z}\right)} - 0\right) + \frac{\left(-z\right) \cdot 0.5}{z}\right) \]

      9. associate--r+ 98.3%

         \[\leadsto 4 \cdot \left(\color{blue}{\left(\frac{x}{z} - \left(\frac{y}{z} + 0\right)\right)} + \frac{\left(-z\right) \cdot 0.5}{z}\right) \]

      10. add0 98.3%

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

      11. div-sub 100.0%

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

      12. distribute-rgt-in 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 91.2%

      \[\leadsto \color{blue}{\left(-1 \cdot \frac{y}{z}\right)} \cdot 4 + -2 \]
   6. Step-by-step derivation

      1. neg-mul-1 91.2%

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

      2. distribute-neg-frac2 91.2%

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

   7. Simplified 91.2%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.05 \cdot 10^{+132} \lor \neg \left(x \leq 3.5 \cdot 10^{+98}\right):\\ \;\;\;\;-2 + 4 \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;-2 - 4 \cdot \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 67.4% accurate, 1.6× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]
2. Step-by-step derivation

   1. associate-/l* 100.0%

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

   2. div-sub 100.0%

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

   3. remove-double-neg 100.0%

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

   4. distribute-lft-neg-out 100.0%

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

   5. distribute-frac-neg 100.0%

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

   6. neg-sub0 100.0%

      \[\leadsto 4 \cdot \left(\frac{x - y}{z} - \color{blue}{\left(0 - \frac{\left(-z\right) \cdot 0.5}{z}\right)}\right) \]

   7. associate-+l- 100.0%

      \[\leadsto 4 \cdot \color{blue}{\left(\left(\frac{x - y}{z} - 0\right) + \frac{\left(-z\right) \cdot 0.5}{z}\right)} \]

   8. div-sub 97.7%

      \[\leadsto 4 \cdot \left(\left(\color{blue}{\left(\frac{x}{z} - \frac{y}{z}\right)} - 0\right) + \frac{\left(-z\right) \cdot 0.5}{z}\right) \]

   9. associate--r+ 97.7%

      \[\leadsto 4 \cdot \left(\color{blue}{\left(\frac{x}{z} - \left(\frac{y}{z} + 0\right)\right)} + \frac{\left(-z\right) \cdot 0.5}{z}\right) \]

   10. add0 97.7%

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

   11. div-sub 100.0%

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

   12. distribute-rgt-in 100.0%

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

3. Simplified 100.0%

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

5. Taylor expanded in x around inf 59.1%

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

6. Taylor expanded in x around 0 59.1%

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

   1. associate-*r/ 59.1%

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

   2. *-commutative 59.1%

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

   3. associate-*r/ 59.1%

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

8. Simplified 59.1%

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

9. Final simplification 59.1%

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

Alternative 4: 67.5% accurate, 1.6× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]
2. Step-by-step derivation

   1. associate-/l* 100.0%

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

   2. div-sub 100.0%

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

   3. remove-double-neg 100.0%

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

   4. distribute-lft-neg-out 100.0%

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

   5. distribute-frac-neg 100.0%

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

   6. neg-sub0 100.0%

      \[\leadsto 4 \cdot \left(\frac{x - y}{z} - \color{blue}{\left(0 - \frac{\left(-z\right) \cdot 0.5}{z}\right)}\right) \]

   7. associate-+l- 100.0%

      \[\leadsto 4 \cdot \color{blue}{\left(\left(\frac{x - y}{z} - 0\right) + \frac{\left(-z\right) \cdot 0.5}{z}\right)} \]

   8. div-sub 97.7%

      \[\leadsto 4 \cdot \left(\left(\color{blue}{\left(\frac{x}{z} - \frac{y}{z}\right)} - 0\right) + \frac{\left(-z\right) \cdot 0.5}{z}\right) \]

   9. associate--r+ 97.7%

      \[\leadsto 4 \cdot \left(\color{blue}{\left(\frac{x}{z} - \left(\frac{y}{z} + 0\right)\right)} + \frac{\left(-z\right) \cdot 0.5}{z}\right) \]

   10. add0 97.7%

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

   11. div-sub 100.0%

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

   12. distribute-rgt-in 100.0%

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

3. Simplified 100.0%

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

5. Taylor expanded in x around inf 59.1%

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

6. Final simplification 59.1%

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

Developer target: 97.9% accurate, 0.8× 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 2024046 
(FPCore (x y z)
  :name "Data.Array.Repa.Algorithms.ColorRamp:rampColorHotToCold from repa-algorithms-3.4.0.1, B"
  :precision binary64

  :alt
  (- (* 4.0 (/ x z)) (+ 2.0 (* 4.0 (/ y z))))

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