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

Percentage Accurate: 99.9% → 100.0%

Time: 5.4s

Alternatives: 10

Speedup: 1.4×

• 21.3% 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* 99.7%

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

3. Simplified 99.7%

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

4. Taylor expanded in 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: 58.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -4 \cdot \frac{z}{y} + 1\\ t_1 := 1 + \frac{4}{\frac{y}{x}}\\ \mathbf{if}\;x \leq -6.6 \cdot 10^{-5}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{-275}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-181}:\\ \;\;\;\;2\\ \mathbf{elif}\;x \leq 1200:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ (* -4.0 (/ z y)) 1.0)) (t_1 (+ 1.0 (/ 4.0 (/ y x)))))
   (if (<= x -6.6e-5)
     t_1
     (if (<= x 5.8e-275)
       t_0
       (if (<= x 5.5e-181) 2.0 (if (<= x 1200.0) t_0 t_1))))))

C

double code(double x, double y, double z) {
	double t_0 = (-4.0 * (z / y)) + 1.0;
	double t_1 = 1.0 + (4.0 / (y / x));
	double tmp;
	if (x <= -6.6e-5) {
		tmp = t_1;
	} else if (x <= 5.8e-275) {
		tmp = t_0;
	} else if (x <= 5.5e-181) {
		tmp = 2.0;
	} else if (x <= 1200.0) {
		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 = ((-4.0d0) * (z / y)) + 1.0d0
    t_1 = 1.0d0 + (4.0d0 / (y / x))
    if (x <= (-6.6d-5)) then
        tmp = t_1
    else if (x <= 5.8d-275) then
        tmp = t_0
    else if (x <= 5.5d-181) then
        tmp = 2.0d0
    else if (x <= 1200.0d0) 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 = (-4.0 * (z / y)) + 1.0;
	double t_1 = 1.0 + (4.0 / (y / x));
	double tmp;
	if (x <= -6.6e-5) {
		tmp = t_1;
	} else if (x <= 5.8e-275) {
		tmp = t_0;
	} else if (x <= 5.5e-181) {
		tmp = 2.0;
	} else if (x <= 1200.0) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (-4.0 * (z / y)) + 1.0
	t_1 = 1.0 + (4.0 / (y / x))
	tmp = 0
	if x <= -6.6e-5:
		tmp = t_1
	elif x <= 5.8e-275:
		tmp = t_0
	elif x <= 5.5e-181:
		tmp = 2.0
	elif x <= 1200.0:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(-4.0 * Float64(z / y)) + 1.0)
	t_1 = Float64(1.0 + Float64(4.0 / Float64(y / x)))
	tmp = 0.0
	if (x <= -6.6e-5)
		tmp = t_1;
	elseif (x <= 5.8e-275)
		tmp = t_0;
	elseif (x <= 5.5e-181)
		tmp = 2.0;
	elseif (x <= 1200.0)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (-4.0 * (z / y)) + 1.0;
	t_1 = 1.0 + (4.0 / (y / x));
	tmp = 0.0;
	if (x <= -6.6e-5)
		tmp = t_1;
	elseif (x <= 5.8e-275)
		tmp = t_0;
	elseif (x <= 5.5e-181)
		tmp = 2.0;
	elseif (x <= 1200.0)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(-4.0 * N[(z / y), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$1 = N[(1.0 + N[(4.0 / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -6.6e-5], t$95$1, If[LessEqual[x, 5.8e-275], t$95$0, If[LessEqual[x, 5.5e-181], 2.0, If[LessEqual[x, 1200.0], t$95$0, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.6000000000000005e-5 or 1200 < 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* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around inf 65.8%

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

      1. associate-*r/ 65.8%

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

      2. associate-/l* 65.7%

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

   6. Simplified 65.7%

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

   if -6.6000000000000005e-5 < x < 5.800000000000001e-275 or 5.50000000000000033e-181 < x < 1200

   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 63.3%

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

      1. *-commutative 63.3%

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

   6. Simplified 63.3%

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

   if 5.800000000000001e-275 < x < 5.50000000000000033e-181

   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* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 78.6%

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

4. Final simplification 65.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.6 \cdot 10^{-5}:\\ \;\;\;\;1 + \frac{4}{\frac{y}{x}}\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{-275}:\\ \;\;\;\;-4 \cdot \frac{z}{y} + 1\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-181}:\\ \;\;\;\;2\\ \mathbf{elif}\;x \leq 1200:\\ \;\;\;\;-4 \cdot \frac{z}{y} + 1\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{4}{\frac{y}{x}}\\ \end{array} \]

Alternative 3: 58.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -4 \cdot \frac{z}{y} + 1\\ t_1 := 1 + \frac{4 \cdot x}{y}\\ \mathbf{if}\;x \leq -1.55 \cdot 10^{-6}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{-270}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{-181}:\\ \;\;\;\;2\\ \mathbf{elif}\;x \leq 220:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ (* -4.0 (/ z y)) 1.0)) (t_1 (+ 1.0 (/ (* 4.0 x) y))))
   (if (<= x -1.55e-6)
     t_1
     (if (<= x 2.3e-270)
       t_0
       (if (<= x 7.2e-181) 2.0 (if (<= x 220.0) t_0 t_1))))))

C

double code(double x, double y, double z) {
	double t_0 = (-4.0 * (z / y)) + 1.0;
	double t_1 = 1.0 + ((4.0 * x) / y);
	double tmp;
	if (x <= -1.55e-6) {
		tmp = t_1;
	} else if (x <= 2.3e-270) {
		tmp = t_0;
	} else if (x <= 7.2e-181) {
		tmp = 2.0;
	} else if (x <= 220.0) {
		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 = ((-4.0d0) * (z / y)) + 1.0d0
    t_1 = 1.0d0 + ((4.0d0 * x) / y)
    if (x <= (-1.55d-6)) then
        tmp = t_1
    else if (x <= 2.3d-270) then
        tmp = t_0
    else if (x <= 7.2d-181) then
        tmp = 2.0d0
    else if (x <= 220.0d0) 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 = (-4.0 * (z / y)) + 1.0;
	double t_1 = 1.0 + ((4.0 * x) / y);
	double tmp;
	if (x <= -1.55e-6) {
		tmp = t_1;
	} else if (x <= 2.3e-270) {
		tmp = t_0;
	} else if (x <= 7.2e-181) {
		tmp = 2.0;
	} else if (x <= 220.0) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (-4.0 * (z / y)) + 1.0
	t_1 = 1.0 + ((4.0 * x) / y)
	tmp = 0
	if x <= -1.55e-6:
		tmp = t_1
	elif x <= 2.3e-270:
		tmp = t_0
	elif x <= 7.2e-181:
		tmp = 2.0
	elif x <= 220.0:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(-4.0 * Float64(z / y)) + 1.0)
	t_1 = Float64(1.0 + Float64(Float64(4.0 * x) / y))
	tmp = 0.0
	if (x <= -1.55e-6)
		tmp = t_1;
	elseif (x <= 2.3e-270)
		tmp = t_0;
	elseif (x <= 7.2e-181)
		tmp = 2.0;
	elseif (x <= 220.0)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (-4.0 * (z / y)) + 1.0;
	t_1 = 1.0 + ((4.0 * x) / y);
	tmp = 0.0;
	if (x <= -1.55e-6)
		tmp = t_1;
	elseif (x <= 2.3e-270)
		tmp = t_0;
	elseif (x <= 7.2e-181)
		tmp = 2.0;
	elseif (x <= 220.0)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(-4.0 * N[(z / y), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$1 = N[(1.0 + N[(N[(4.0 * x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.55e-6], t$95$1, If[LessEqual[x, 2.3e-270], t$95$0, If[LessEqual[x, 7.2e-181], 2.0, If[LessEqual[x, 220.0], t$95$0, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.55e-6 or 220 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 65.8%

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

   if -1.55e-6 < x < 2.3000000000000001e-270 or 7.1999999999999998e-181 < x < 220

   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 63.3%

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

      1. *-commutative 63.3%

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

   6. Simplified 63.3%

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

   if 2.3000000000000001e-270 < x < 7.1999999999999998e-181

   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* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 78.6%

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

4. Final simplification 65.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{-6}:\\ \;\;\;\;1 + \frac{4 \cdot x}{y}\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{-270}:\\ \;\;\;\;-4 \cdot \frac{z}{y} + 1\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{-181}:\\ \;\;\;\;2\\ \mathbf{elif}\;x \leq 220:\\ \;\;\;\;-4 \cdot \frac{z}{y} + 1\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{4 \cdot x}{y}\\ \end{array} \]

Alternative 4: 54.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{-14} \lor \neg \left(z \leq 260000000\right):\\ \;\;\;\;-4 \cdot \frac{z}{y} + 1\\ \mathbf{else}:\\ \;\;\;\;2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -3.9e-14) (not (<= z 260000000.0)))
   (+ (* -4.0 (/ z y)) 1.0)
   2.0))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3.9e-14) || !(z <= 260000000.0)) {
		tmp = (-4.0 * (z / y)) + 1.0;
	} 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 ((z <= (-3.9d-14)) .or. (.not. (z <= 260000000.0d0))) then
        tmp = ((-4.0d0) * (z / y)) + 1.0d0
    else
        tmp = 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3.9e-14) || !(z <= 260000000.0)) {
		tmp = (-4.0 * (z / y)) + 1.0;
	} else {
		tmp = 2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -3.9e-14) or not (z <= 260000000.0):
		tmp = (-4.0 * (z / y)) + 1.0
	else:
		tmp = 2.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -3.9e-14) || !(z <= 260000000.0))
		tmp = Float64(Float64(-4.0 * Float64(z / y)) + 1.0);
	else
		tmp = 2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -3.9e-14) || ~((z <= 260000000.0)))
		tmp = (-4.0 * (z / y)) + 1.0;
	else
		tmp = 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -3.9e-14], N[Not[LessEqual[z, 260000000.0]], $MachinePrecision]], N[(N[(-4.0 * N[(z / y), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision], 2.0]

Derivation

1. Split input into 2 regimes

2. if z < -3.8999999999999998e-14 or 2.6e8 < 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 64.2%

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

      1. *-commutative 64.2%

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

   6. Simplified 64.2%

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

   if -3.8999999999999998e-14 < z < 2.6e8

   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 46.0%

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

4. Final simplification 55.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{-14} \lor \neg \left(z \leq 260000000\right):\\ \;\;\;\;-4 \cdot \frac{z}{y} + 1\\ \mathbf{else}:\\ \;\;\;\;2\\ \end{array} \]

Alternative 5: 81.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.18 \cdot 10^{+107} \lor \neg \left(x \leq 3.8 \cdot 10^{+93}\right):\\ \;\;\;\;1 + \frac{4 \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;2 + -4 \cdot \frac{z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.18e+107) (not (<= x 3.8e+93)))
   (+ 1.0 (/ (* 4.0 x) y))
   (+ 2.0 (* -4.0 (/ z y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.18e+107) || !(x <= 3.8e+93)) {
		tmp = 1.0 + ((4.0 * x) / y);
	} else {
		tmp = 2.0 + (-4.0 * (z / 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 ((x <= (-1.18d+107)) .or. (.not. (x <= 3.8d+93))) then
        tmp = 1.0d0 + ((4.0d0 * x) / y)
    else
        tmp = 2.0d0 + ((-4.0d0) * (z / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.18e+107) || !(x <= 3.8e+93)) {
		tmp = 1.0 + ((4.0 * x) / y);
	} else {
		tmp = 2.0 + (-4.0 * (z / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.18e+107) or not (x <= 3.8e+93):
		tmp = 1.0 + ((4.0 * x) / y)
	else:
		tmp = 2.0 + (-4.0 * (z / y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.18e+107) || !(x <= 3.8e+93))
		tmp = Float64(1.0 + Float64(Float64(4.0 * x) / y));
	else
		tmp = Float64(2.0 + Float64(-4.0 * Float64(z / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.18e+107) || ~((x <= 3.8e+93)))
		tmp = 1.0 + ((4.0 * x) / y);
	else
		tmp = 2.0 + (-4.0 * (z / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.18e+107], N[Not[LessEqual[x, 3.8e+93]], $MachinePrecision]], N[(1.0 + N[(N[(4.0 * x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(2.0 + N[(-4.0 * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.18000000000000005e107 or 3.7999999999999998e93 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 75.8%

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

   if -1.18000000000000005e107 < x < 3.7999999999999998e93

   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 86.9%

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

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.18 \cdot 10^{+107} \lor \neg \left(x \leq 3.8 \cdot 10^{+93}\right):\\ \;\;\;\;1 + \frac{4 \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;2 + -4 \cdot \frac{z}{y}\\ \end{array} \]

Alternative 6: 85.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.2 \cdot 10^{-13} \lor \neg \left(x \leq 240\right):\\ \;\;\;\;2 + 4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;2 + -4 \cdot \frac{z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -8.2e-13) (not (<= x 240.0)))
   (+ 2.0 (* 4.0 (/ x y)))
   (+ 2.0 (* -4.0 (/ z y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -8.2e-13) || !(x <= 240.0)) {
		tmp = 2.0 + (4.0 * (x / y));
	} else {
		tmp = 2.0 + (-4.0 * (z / 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 ((x <= (-8.2d-13)) .or. (.not. (x <= 240.0d0))) then
        tmp = 2.0d0 + (4.0d0 * (x / y))
    else
        tmp = 2.0d0 + ((-4.0d0) * (z / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -8.2e-13) || !(x <= 240.0)) {
		tmp = 2.0 + (4.0 * (x / y));
	} else {
		tmp = 2.0 + (-4.0 * (z / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -8.2e-13) or not (x <= 240.0):
		tmp = 2.0 + (4.0 * (x / y))
	else:
		tmp = 2.0 + (-4.0 * (z / y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -8.2e-13) || !(x <= 240.0))
		tmp = Float64(2.0 + Float64(4.0 * Float64(x / y)));
	else
		tmp = Float64(2.0 + Float64(-4.0 * Float64(z / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -8.2e-13) || ~((x <= 240.0)))
		tmp = 2.0 + (4.0 * (x / y));
	else
		tmp = 2.0 + (-4.0 * (z / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -8.2e-13], N[Not[LessEqual[x, 240.0]], $MachinePrecision]], N[(2.0 + N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 + N[(-4.0 * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -8.2000000000000004e-13 or 240 < 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* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in 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 81.9%

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

   if -8.2000000000000004e-13 < x < 240

   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 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 93.0%

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

4. Final simplification 87.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.2 \cdot 10^{-13} \lor \neg \left(x \leq 240\right):\\ \;\;\;\;2 + 4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;2 + -4 \cdot \frac{z}{y}\\ \end{array} \]

Alternative 7: 53.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{+95} \lor \neg \left(z \leq 250000000\right):\\ \;\;\;\;z \cdot \frac{-4}{y}\\ \mathbf{else}:\\ \;\;\;\;2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.15e+95) (not (<= z 250000000.0))) (* z (/ -4.0 y)) 2.0))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.15e+95) || !(z <= 250000000.0)) {
		tmp = z * (-4.0 / 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 ((z <= (-2.15d+95)) .or. (.not. (z <= 250000000.0d0))) then
        tmp = z * ((-4.0d0) / 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 ((z <= -2.15e+95) || !(z <= 250000000.0)) {
		tmp = z * (-4.0 / y);
	} else {
		tmp = 2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2.15e+95) or not (z <= 250000000.0):
		tmp = z * (-4.0 / y)
	else:
		tmp = 2.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -2.15e+95) || !(z <= 250000000.0))
		tmp = Float64(z * Float64(-4.0 / y));
	else
		tmp = 2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -2.15e+95) || ~((z <= 250000000.0)))
		tmp = z * (-4.0 / y);
	else
		tmp = 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2.15e+95], N[Not[LessEqual[z, 250000000.0]], $MachinePrecision]], N[(z * N[(-4.0 / y), $MachinePrecision]), $MachinePrecision], 2.0]

Derivation

1. Split input into 2 regimes

2. if z < -2.15e95 or 2.5e8 < 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 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 80.7%

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

   8. Taylor expanded in z around inf 68.1%

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

      1. associate-*r/ 68.1%

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

      2. *-commutative 68.1%

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

      3. associate-*r/ 67.9%

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

   10. Simplified 67.9%

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

   if -2.15e95 < z < 2.5e8

   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 43.4%

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

4. Final simplification 54.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{+95} \lor \neg \left(z \leq 250000000\right):\\ \;\;\;\;z \cdot \frac{-4}{y}\\ \mathbf{else}:\\ \;\;\;\;2\\ \end{array} \]

Alternative 8: 53.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+95} \lor \neg \left(z \leq 70000000\right):\\ \;\;\;\;\frac{z}{\frac{y}{-4}}\\ \mathbf{else}:\\ \;\;\;\;2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1e+95) (not (<= z 70000000.0))) (/ z (/ y -4.0)) 2.0))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1e+95) || !(z <= 70000000.0)) {
		tmp = z / (y / -4.0);
	} 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 ((z <= (-1d+95)) .or. (.not. (z <= 70000000.0d0))) then
        tmp = z / (y / (-4.0d0))
    else
        tmp = 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1e+95) || !(z <= 70000000.0)) {
		tmp = z / (y / -4.0);
	} else {
		tmp = 2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1e+95) or not (z <= 70000000.0):
		tmp = z / (y / -4.0)
	else:
		tmp = 2.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1e+95) || !(z <= 70000000.0))
		tmp = Float64(z / Float64(y / -4.0));
	else
		tmp = 2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1e+95) || ~((z <= 70000000.0)))
		tmp = z / (y / -4.0);
	else
		tmp = 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1e+95], N[Not[LessEqual[z, 70000000.0]], $MachinePrecision]], N[(z / N[(y / -4.0), $MachinePrecision]), $MachinePrecision], 2.0]

Derivation

1. Split input into 2 regimes

2. if z < -1.00000000000000002e95 or 7e7 < 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 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 80.7%

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

   8. Taylor expanded in z around inf 68.1%

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

      1. *-commutative 68.1%

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

      2. associate-/r/ 68.1%

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

   10. Simplified 68.1%

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

   if -1.00000000000000002e95 < z < 7e7

   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 43.4%

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

4. Final simplification 54.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+95} \lor \neg \left(z \leq 70000000\right):\\ \;\;\;\;\frac{z}{\frac{y}{-4}}\\ \mathbf{else}:\\ \;\;\;\;2\\ \end{array} \]

Alternative 9: 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 99.4%

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

   5. associate-+r+ 99.4%

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

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 10: 33.0% 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* 99.7%

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

3. Simplified 99.7%

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

4. Taylor expanded in y around inf 30.3%

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

5. Final simplification 30.3%

   \[\leadsto 2 \]

Reproduce

herbie shell --seed 2023297 
(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)))