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

Percentage Accurate: 99.8% → 100.0%

Time: 4.1s

Alternatives: 5

Speedup: 1.4×

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: 100.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \frac{x - z}{y \cdot 0.25} + 2 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ (/ (- x z) (* y 0.25)) 2.0))

C

double code(double x, double y, double z) {
	return ((x - z) / (y * 0.25)) + 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 = ((x - z) / (y * 0.25d0)) + 2.0d0
end function

Java

public static double code(double x, double y, double z) {
	return ((x - z) / (y * 0.25)) + 2.0;
}

Python

def code(x, y, z):
	return ((x - z) / (y * 0.25)) + 2.0

Julia

function code(x, y, z)
	return Float64(Float64(Float64(x - z) / Float64(y * 0.25)) + 2.0)
end

MATLAB

function tmp = code(x, y, z)
	tmp = ((x - z) / (y * 0.25)) + 2.0;
end

Wolfram

code[x_, y_, z_] := N[(N[(N[(x - z), $MachinePrecision] / N[(y * 0.25), $MachinePrecision]), $MachinePrecision] + 2.0), $MachinePrecision]

Derivation

1. Initial program 99.6%

   \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
2. Step-by-step derivation

   1. +-commutative 99.6%

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

   2. associate-*l/ 99.7%

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

   3. +-commutative 99.7%

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

   4. associate--l+ 99.7%

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

   5. +-commutative 99.7%

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

   6. distribute-lft-in 99.8%

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

   7. associate-+l+ 99.8%

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

   8. associate-*l/ 99.8%

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

   9. *-commutative 99.8%

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

   10. associate-*l* 99.8%

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

   11. metadata-eval 99.8%

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

   12. *-rgt-identity 99.8%

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

   13. *-inverses 99.8%

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

   14. metadata-eval 99.8%

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

3. Simplified 99.8%

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

   1. *-commutative 99.8%

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

   2. clear-num 99.8%

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

   3. div-inv 99.8%

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

   4. metadata-eval 99.8%

      \[\leadsto \left(x - z\right) \cdot \frac{1}{y \cdot \color{blue}{0.25}} + 2 \]

   5. un-div-inv 100.0%

      \[\leadsto \color{blue}{\frac{x - z}{y \cdot 0.25}} + 2 \]

6. Applied egg-rr 100.0%

   \[\leadsto \color{blue}{\frac{x - z}{y \cdot 0.25}} + 2 \]
7. Add Preprocessing

Alternative 2: 85.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{-67} \lor \neg \left(z \leq 8.2 \cdot 10^{+90}\right):\\ \;\;\;\;2 + -4 \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;2 + 4 \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.25e-67) (not (<= z 8.2e+90)))
   (+ 2.0 (* -4.0 (/ z y)))
   (+ 2.0 (* 4.0 (/ x y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.25e-67) || !(z <= 8.2e+90)) {
		tmp = 2.0 + (-4.0 * (z / y));
	} else {
		tmp = 2.0 + (4.0 * (x / 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 ((z <= (-1.25d-67)) .or. (.not. (z <= 8.2d+90))) then
        tmp = 2.0d0 + ((-4.0d0) * (z / y))
    else
        tmp = 2.0d0 + (4.0d0 * (x / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.25e-67) || !(z <= 8.2e+90)) {
		tmp = 2.0 + (-4.0 * (z / y));
	} else {
		tmp = 2.0 + (4.0 * (x / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.25e-67) or not (z <= 8.2e+90):
		tmp = 2.0 + (-4.0 * (z / y))
	else:
		tmp = 2.0 + (4.0 * (x / y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.25e-67) || !(z <= 8.2e+90))
		tmp = Float64(2.0 + Float64(-4.0 * Float64(z / y)));
	else
		tmp = Float64(2.0 + Float64(4.0 * Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.25e-67) || ~((z <= 8.2e+90)))
		tmp = 2.0 + (-4.0 * (z / y));
	else
		tmp = 2.0 + (4.0 * (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.25e-67], N[Not[LessEqual[z, 8.2e+90]], $MachinePrecision]], N[(2.0 + N[(-4.0 * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 + N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.25e-67 or 8.20000000000000083e90 < z

   1. Initial program 99.3%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
   2. Step-by-step derivation

      1. +-commutative 99.3%

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

      2. associate-*l/ 99.7%

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

      3. +-commutative 99.7%

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

      4. associate--l+ 99.7%

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

      5. +-commutative 99.7%

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

      6. distribute-lft-in 99.7%

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

      7. associate-+l+ 99.7%

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

      8. associate-*l/ 99.7%

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

      9. *-commutative 99.7%

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

      10. associate-*l* 99.7%

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

      11. metadata-eval 99.7%

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

      12. *-rgt-identity 99.7%

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

      13. *-inverses 99.7%

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

      14. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around 0 85.5%

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

   if -1.25e-67 < z < 8.20000000000000083e90

   1. Initial program 100.0%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
   2. Step-by-step derivation

      1. +-commutative 100.0%

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

      2. associate-*l/ 99.8%

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

      3. +-commutative 99.8%

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

      4. associate--l+ 99.8%

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

      5. +-commutative 99.8%

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

      6. distribute-lft-in 99.8%

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

      7. associate-+l+ 99.8%

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

      8. associate-*l/ 99.8%

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

      9. *-commutative 99.8%

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

      10. associate-*l* 99.8%

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

      11. metadata-eval 99.8%

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

      12. *-rgt-identity 99.8%

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

      13. *-inverses 99.8%

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

      14. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 90.1%

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

      1. *-commutative 90.1%

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

   7. Simplified 90.1%

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

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{-67} \lor \neg \left(z \leq 8.2 \cdot 10^{+90}\right):\\ \;\;\;\;2 + -4 \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;2 + 4 \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 99.8% accurate, 1.4× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.6%

   \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
2. Step-by-step derivation

   1. +-commutative 99.6%

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

   2. associate-*l/ 99.7%

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

   3. +-commutative 99.7%

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

   4. associate--l+ 99.7%

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

   5. +-commutative 99.7%

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

   6. distribute-lft-in 99.8%

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

   7. associate-+l+ 99.8%

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

   8. associate-*l/ 99.8%

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

   9. *-commutative 99.8%

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

   10. associate-*l* 99.8%

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

   11. metadata-eval 99.8%

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

   12. *-rgt-identity 99.8%

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

   13. *-inverses 99.8%

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

   14. metadata-eval 99.8%

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

3. Simplified 99.8%

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

5. Final simplification 99.8%

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

Alternative 4: 67.8% 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 99.6%

   \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
2. Step-by-step derivation

   1. +-commutative 99.6%

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

   2. associate-*l/ 99.7%

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

   3. +-commutative 99.7%

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

   4. associate--l+ 99.7%

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

   5. +-commutative 99.7%

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

   6. distribute-lft-in 99.8%

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

   7. associate-+l+ 99.8%

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

   8. associate-*l/ 99.8%

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

   9. *-commutative 99.8%

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

   10. associate-*l* 99.8%

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

   11. metadata-eval 99.8%

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

   12. *-rgt-identity 99.8%

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

   13. *-inverses 99.8%

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

   14. metadata-eval 99.8%

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

3. Simplified 99.8%

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

5. Taylor expanded in x around 0 69.1%

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

6. Final simplification 69.1%

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

Alternative 5: 33.7% 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 99.6%

   \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
2. Step-by-step derivation

   1. associate-/l* 100.0%

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

   2. associate--l+ 100.0%

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

3. Simplified 100.0%

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

5. Taylor expanded in y around inf 31.5%

   \[\leadsto 1 + 4 \cdot \color{blue}{0.25} \]

6. Final simplification 31.5%

   \[\leadsto 2 \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024108 
(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)))