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

Percentage Accurate: 99.9% → 100.0%

Time: 4.9s

Alternatives: 7

Speedup: 1.4×

• 21.1% 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: 99.9% 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

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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. associate-/l* 99.8%

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

3. Simplified 99.8%

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

4. Taylor expanded in y around 0 100.0%

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

   1. +-commutative 100.0%

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

6. Simplified 100.0%

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

7. Final simplification 100.0%

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

Alternative 2: 57.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + 4 \cdot \frac{x}{y}\\ t_1 := 1 + -4 \cdot \frac{z}{y}\\ \mathbf{if}\;z \leq -1.2 \cdot 10^{+49}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-142}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-286}:\\ \;\;\;\;2\\ \mathbf{elif}\;z \leq 30000000000000:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ 1.0 (* 4.0 (/ x y)))) (t_1 (+ 1.0 (* -4.0 (/ z y)))))
   (if (<= z -1.2e+49)
     t_1
     (if (<= z -6e-142)
       t_0
       (if (<= z 2.1e-286) 2.0 (if (<= z 30000000000000.0) t_0 t_1))))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 + (4.0 * (x / y));
	double t_1 = 1.0 + (-4.0 * (z / y));
	double tmp;
	if (z <= -1.2e+49) {
		tmp = t_1;
	} else if (z <= -6e-142) {
		tmp = t_0;
	} else if (z <= 2.1e-286) {
		tmp = 2.0;
	} else if (z <= 30000000000000.0) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	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) :: tmp
    t_0 = 1.0d0 + (4.0d0 * (x / y))
    t_1 = 1.0d0 + ((-4.0d0) * (z / y))
    if (z <= (-1.2d+49)) then
        tmp = t_1
    else if (z <= (-6d-142)) then
        tmp = t_0
    else if (z <= 2.1d-286) then
        tmp = 2.0d0
    else if (z <= 30000000000000.0d0) then
        tmp = t_0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 1.0 + (4.0 * (x / y));
	double t_1 = 1.0 + (-4.0 * (z / y));
	double tmp;
	if (z <= -1.2e+49) {
		tmp = t_1;
	} else if (z <= -6e-142) {
		tmp = t_0;
	} else if (z <= 2.1e-286) {
		tmp = 2.0;
	} else if (z <= 30000000000000.0) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 + (4.0 * (x / y))
	t_1 = 1.0 + (-4.0 * (z / y))
	tmp = 0
	if z <= -1.2e+49:
		tmp = t_1
	elif z <= -6e-142:
		tmp = t_0
	elif z <= 2.1e-286:
		tmp = 2.0
	elif z <= 30000000000000.0:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 + Float64(4.0 * Float64(x / y)))
	t_1 = Float64(1.0 + Float64(-4.0 * Float64(z / y)))
	tmp = 0.0
	if (z <= -1.2e+49)
		tmp = t_1;
	elseif (z <= -6e-142)
		tmp = t_0;
	elseif (z <= 2.1e-286)
		tmp = 2.0;
	elseif (z <= 30000000000000.0)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 + (4.0 * (x / y));
	t_1 = 1.0 + (-4.0 * (z / y));
	tmp = 0.0;
	if (z <= -1.2e+49)
		tmp = t_1;
	elseif (z <= -6e-142)
		tmp = t_0;
	elseif (z <= 2.1e-286)
		tmp = 2.0;
	elseif (z <= 30000000000000.0)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(1.0 + N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(1.0 + N[(-4.0 * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.2e+49], t$95$1, If[LessEqual[z, -6e-142], t$95$0, If[LessEqual[z, 2.1e-286], 2.0, If[LessEqual[z, 30000000000000.0], t$95$0, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.2e49 or 3e13 < z

   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. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in z around inf 69.7%

      \[\leadsto 1 + \color{blue}{-4 \cdot \frac{z}{y}} \]
   5. Step-by-step derivation

      1. *-commutative 69.7%

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

   6. Simplified 69.7%

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

   if -1.2e49 < z < -6.0000000000000002e-142 or 2.09999999999999988e-286 < z < 3e13

   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. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 63.1%

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

   if -6.0000000000000002e-142 < z < 2.09999999999999988e-286

   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. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 68.4%

      \[\leadsto \color{blue}{2} \]
3. Recombined 3 regimes into one program.

4. Final simplification 66.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+49}:\\ \;\;\;\;1 + -4 \cdot \frac{z}{y}\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-142}:\\ \;\;\;\;1 + 4 \cdot \frac{x}{y}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-286}:\\ \;\;\;\;2\\ \mathbf{elif}\;z \leq 30000000000000:\\ \;\;\;\;1 + 4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + -4 \cdot \frac{z}{y}\\ \end{array} \]

Alternative 3: 52.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{+127} \lor \neg \left(x \leq 3.4 \cdot 10^{-94}\right):\\ \;\;\;\;1 + 4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -2.1e+127) (not (<= x 3.4e-94))) (+ 1.0 (* 4.0 (/ x y))) 2.0))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.1e+127) || !(x <= 3.4e-94)) {
		tmp = 1.0 + (4.0 * (x / y));
	} else {
		tmp = 2.0;
	}
	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) :: tmp
    if ((x <= (-2.1d+127)) .or. (.not. (x <= 3.4d-94))) then
        tmp = 1.0d0 + (4.0d0 * (x / y))
    else
        tmp = 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.1e+127) || !(x <= 3.4e-94)) {
		tmp = 1.0 + (4.0 * (x / y));
	} else {
		tmp = 2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -2.1e+127) or not (x <= 3.4e-94):
		tmp = 1.0 + (4.0 * (x / y))
	else:
		tmp = 2.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -2.1e+127) || !(x <= 3.4e-94))
		tmp = Float64(1.0 + Float64(4.0 * Float64(x / y)));
	else
		tmp = 2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -2.1e+127) || ~((x <= 3.4e-94)))
		tmp = 1.0 + (4.0 * (x / y));
	else
		tmp = 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -2.1e+127], N[Not[LessEqual[x, 3.4e-94]], $MachinePrecision]], N[(1.0 + N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 2.0]

Derivation

1. Split input into 2 regimes

2. if x < -2.09999999999999992e127 or 3.3999999999999998e-94 < x

   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. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 75.2%

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

   if -2.09999999999999992e127 < x < 3.3999999999999998e-94

   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. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 51.4%

      \[\leadsto \color{blue}{2} \]
3. Recombined 2 regimes into one program.

4. Final simplification 61.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{+127} \lor \neg \left(x \leq 3.4 \cdot 10^{-94}\right):\\ \;\;\;\;1 + 4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;2\\ \end{array} \]

Alternative 4: 80.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+124} \lor \neg \left(z \leq 5.8 \cdot 10^{+106}\right):\\ \;\;\;\;1 + -4 \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;2 + 4 \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -3.3e+124) (not (<= z 5.8e+106)))
   (+ 1.0 (* -4.0 (/ z y)))
   (+ 2.0 (* 4.0 (/ x y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3.3e+124) || !(z <= 5.8e+106)) {
		tmp = 1.0 + (-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 <= (-3.3d+124)) .or. (.not. (z <= 5.8d+106))) then
        tmp = 1.0d0 + ((-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 <= -3.3e+124) || !(z <= 5.8e+106)) {
		tmp = 1.0 + (-4.0 * (z / y));
	} else {
		tmp = 2.0 + (4.0 * (x / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -3.3e+124) or not (z <= 5.8e+106):
		tmp = 1.0 + (-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 <= -3.3e+124) || !(z <= 5.8e+106))
		tmp = Float64(1.0 + 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 <= -3.3e+124) || ~((z <= 5.8e+106)))
		tmp = 1.0 + (-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, -3.3e+124], N[Not[LessEqual[z, 5.8e+106]], $MachinePrecision]], N[(1.0 + 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 < -3.30000000000000015e124 or 5.8000000000000004e106 < z

   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. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in z around inf 78.4%

      \[\leadsto 1 + \color{blue}{-4 \cdot \frac{z}{y}} \]
   5. Step-by-step derivation

      1. *-commutative 78.4%

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

   6. Simplified 78.4%

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

   if -3.30000000000000015e124 < z < 5.8000000000000004e106

   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. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around 0 100.0%

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

      1. +-commutative 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in x around inf 89.4%

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

      1. *-commutative 89.4%

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

   9. Simplified 89.4%

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

4. Final simplification 86.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+124} \lor \neg \left(z \leq 5.8 \cdot 10^{+106}\right):\\ \;\;\;\;1 + -4 \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;2 + 4 \cdot \frac{x}{y}\\ \end{array} \]

Alternative 5: 83.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{+127} \lor \neg \left(x \leq 2.8 \cdot 10^{-95}\right):\\ \;\;\;\;2 + 4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;2 + \frac{z}{\frac{y}{-4}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -2.2e+127) (not (<= x 2.8e-95)))
   (+ 2.0 (* 4.0 (/ x y)))
   (+ 2.0 (/ z (/ y -4.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.2e+127) || !(x <= 2.8e-95)) {
		tmp = 2.0 + (4.0 * (x / y));
	} else {
		tmp = 2.0 + (z / (y / -4.0));
	}
	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) :: tmp
    if ((x <= (-2.2d+127)) .or. (.not. (x <= 2.8d-95))) then
        tmp = 2.0d0 + (4.0d0 * (x / y))
    else
        tmp = 2.0d0 + (z / (y / (-4.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.2e+127) || !(x <= 2.8e-95)) {
		tmp = 2.0 + (4.0 * (x / y));
	} else {
		tmp = 2.0 + (z / (y / -4.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -2.2e+127) or not (x <= 2.8e-95):
		tmp = 2.0 + (4.0 * (x / y))
	else:
		tmp = 2.0 + (z / (y / -4.0))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -2.2e+127) || !(x <= 2.8e-95))
		tmp = Float64(2.0 + Float64(4.0 * Float64(x / y)));
	else
		tmp = Float64(2.0 + Float64(z / Float64(y / -4.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -2.2e+127) || ~((x <= 2.8e-95)))
		tmp = 2.0 + (4.0 * (x / y));
	else
		tmp = 2.0 + (z / (y / -4.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -2.2e+127], N[Not[LessEqual[x, 2.8e-95]], $MachinePrecision]], N[(2.0 + N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 + N[(z / N[(y / -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.2000000000000002e127 or 2.7999999999999999e-95 < x

   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. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around 0 100.0%

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

      1. +-commutative 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in x around inf 87.0%

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

      1. *-commutative 87.0%

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

   9. Simplified 87.0%

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

   if -2.2000000000000002e127 < x < 2.7999999999999999e-95

   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. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around 0 100.0%

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

      1. +-commutative 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in x around 0 93.3%

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

      1. *-commutative 93.3%

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

      2. associate-/r/ 93.3%

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

   9. Simplified 93.3%

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

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{+127} \lor \neg \left(x \leq 2.8 \cdot 10^{-95}\right):\\ \;\;\;\;2 + 4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;2 + \frac{z}{\frac{y}{-4}}\\ \end{array} \]

Alternative 6: 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 100.0%

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

   1. associate-*l/ 99.8%

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

   2. +-commutative 99.8%

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

   3. associate--l+ 99.8%

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

   4. distribute-lft-in 99.8%

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

   5. associate-+r+ 99.8%

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

3. Simplified 99.8%

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

4. Final simplification 99.8%

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

Alternative 7: 34.0% 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%

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

   1. associate-/l* 99.8%

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

3. Simplified 99.8%

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

4. Taylor expanded in y around inf 35.8%

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

5. Final simplification 35.8%

   \[\leadsto 2 \]

Reproduce

herbie shell --seed 2023271 
(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)))