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

Percentage Accurate: 99.9% → 99.9%

Time: 4.6s

Alternatives: 8

Speedup: 1.0×

• 21.5% 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: 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]

Derivation

1. Initial program 100.0%

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

2. Final simplification 100.0%

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

Alternative 2: 56.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + \frac{z \cdot -4}{y}\\ t_1 := 1 + x \cdot \frac{4}{y}\\ \mathbf{if}\;x \leq -0.48:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.5 \cdot 10^{-137}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -1.55 \cdot 10^{-303}:\\ \;\;\;\;2\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-56}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{+21}:\\ \;\;\;\;2\\ \mathbf{elif}\;x \leq 10^{+108}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ 1.0 (/ (* z -4.0) y))) (t_1 (+ 1.0 (* x (/ 4.0 y)))))
   (if (<= x -0.48)
     t_1
     (if (<= x -1.5e-137)
       t_0
       (if (<= x -1.55e-303)
         2.0
         (if (<= x 7e-56)
           t_0
           (if (<= x 1.2e+21) 2.0 (if (<= x 1e+108) t_0 t_1))))))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 + ((z * -4.0) / y);
	double t_1 = 1.0 + (x * (4.0 / y));
	double tmp;
	if (x <= -0.48) {
		tmp = t_1;
	} else if (x <= -1.5e-137) {
		tmp = t_0;
	} else if (x <= -1.55e-303) {
		tmp = 2.0;
	} else if (x <= 7e-56) {
		tmp = t_0;
	} else if (x <= 1.2e+21) {
		tmp = 2.0;
	} else if (x <= 1e+108) {
		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 + ((z * (-4.0d0)) / y)
    t_1 = 1.0d0 + (x * (4.0d0 / y))
    if (x <= (-0.48d0)) then
        tmp = t_1
    else if (x <= (-1.5d-137)) then
        tmp = t_0
    else if (x <= (-1.55d-303)) then
        tmp = 2.0d0
    else if (x <= 7d-56) then
        tmp = t_0
    else if (x <= 1.2d+21) then
        tmp = 2.0d0
    else if (x <= 1d+108) 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 + ((z * -4.0) / y);
	double t_1 = 1.0 + (x * (4.0 / y));
	double tmp;
	if (x <= -0.48) {
		tmp = t_1;
	} else if (x <= -1.5e-137) {
		tmp = t_0;
	} else if (x <= -1.55e-303) {
		tmp = 2.0;
	} else if (x <= 7e-56) {
		tmp = t_0;
	} else if (x <= 1.2e+21) {
		tmp = 2.0;
	} else if (x <= 1e+108) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 + ((z * -4.0) / y)
	t_1 = 1.0 + (x * (4.0 / y))
	tmp = 0
	if x <= -0.48:
		tmp = t_1
	elif x <= -1.5e-137:
		tmp = t_0
	elif x <= -1.55e-303:
		tmp = 2.0
	elif x <= 7e-56:
		tmp = t_0
	elif x <= 1.2e+21:
		tmp = 2.0
	elif x <= 1e+108:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 + Float64(Float64(z * -4.0) / y))
	t_1 = Float64(1.0 + Float64(x * Float64(4.0 / y)))
	tmp = 0.0
	if (x <= -0.48)
		tmp = t_1;
	elseif (x <= -1.5e-137)
		tmp = t_0;
	elseif (x <= -1.55e-303)
		tmp = 2.0;
	elseif (x <= 7e-56)
		tmp = t_0;
	elseif (x <= 1.2e+21)
		tmp = 2.0;
	elseif (x <= 1e+108)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 + ((z * -4.0) / y);
	t_1 = 1.0 + (x * (4.0 / y));
	tmp = 0.0;
	if (x <= -0.48)
		tmp = t_1;
	elseif (x <= -1.5e-137)
		tmp = t_0;
	elseif (x <= -1.55e-303)
		tmp = 2.0;
	elseif (x <= 7e-56)
		tmp = t_0;
	elseif (x <= 1.2e+21)
		tmp = 2.0;
	elseif (x <= 1e+108)
		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[(N[(z * -4.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(1.0 + N[(x * N[(4.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -0.48], t$95$1, If[LessEqual[x, -1.5e-137], t$95$0, If[LessEqual[x, -1.55e-303], 2.0, If[LessEqual[x, 7e-56], t$95$0, If[LessEqual[x, 1.2e+21], 2.0, If[LessEqual[x, 1e+108], t$95$0, t$95$1]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -0.47999999999999998 or 1e108 < 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 78.2%

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

      1. associate-*r/ 78.2%

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

      2. associate-*l/ 78.1%

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

      3. *-commutative 78.1%

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

   4. Simplified 78.1%

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

   if -0.47999999999999998 < x < -1.4999999999999999e-137 or -1.55e-303 < x < 6.9999999999999996e-56 or 1.2e21 < x < 1e108

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 58.6%

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

      1. associate-*r/ 58.6%

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

   4. Simplified 58.6%

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

   if -1.4999999999999999e-137 < x < -1.55e-303 or 6.9999999999999996e-56 < x < 1.2e21

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 62.3%

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

4. Final simplification 66.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.48:\\ \;\;\;\;1 + x \cdot \frac{4}{y}\\ \mathbf{elif}\;x \leq -1.5 \cdot 10^{-137}:\\ \;\;\;\;1 + \frac{z \cdot -4}{y}\\ \mathbf{elif}\;x \leq -1.55 \cdot 10^{-303}:\\ \;\;\;\;2\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-56}:\\ \;\;\;\;1 + \frac{z \cdot -4}{y}\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{+21}:\\ \;\;\;\;2\\ \mathbf{elif}\;x \leq 10^{+108}:\\ \;\;\;\;1 + \frac{z \cdot -4}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + x \cdot \frac{4}{y}\\ \end{array} \]

Alternative 3: 57.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + \frac{z \cdot -4}{y}\\ t_1 := 1 + \frac{4 \cdot x}{y}\\ \mathbf{if}\;x \leq -118000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.25 \cdot 10^{-135}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -1.65 \cdot 10^{-303}:\\ \;\;\;\;2\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{-56}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 2.35 \cdot 10^{+22}:\\ \;\;\;\;2\\ \mathbf{elif}\;x \leq 9 \cdot 10^{+107}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ 1.0 (/ (* z -4.0) y))) (t_1 (+ 1.0 (/ (* 4.0 x) y))))
   (if (<= x -118000000.0)
     t_1
     (if (<= x -1.25e-135)
       t_0
       (if (<= x -1.65e-303)
         2.0
         (if (<= x 3.3e-56)
           t_0
           (if (<= x 2.35e+22) 2.0 (if (<= x 9e+107) t_0 t_1))))))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 + ((z * -4.0) / y);
	double t_1 = 1.0 + ((4.0 * x) / y);
	double tmp;
	if (x <= -118000000.0) {
		tmp = t_1;
	} else if (x <= -1.25e-135) {
		tmp = t_0;
	} else if (x <= -1.65e-303) {
		tmp = 2.0;
	} else if (x <= 3.3e-56) {
		tmp = t_0;
	} else if (x <= 2.35e+22) {
		tmp = 2.0;
	} else if (x <= 9e+107) {
		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 + ((z * (-4.0d0)) / y)
    t_1 = 1.0d0 + ((4.0d0 * x) / y)
    if (x <= (-118000000.0d0)) then
        tmp = t_1
    else if (x <= (-1.25d-135)) then
        tmp = t_0
    else if (x <= (-1.65d-303)) then
        tmp = 2.0d0
    else if (x <= 3.3d-56) then
        tmp = t_0
    else if (x <= 2.35d+22) then
        tmp = 2.0d0
    else if (x <= 9d+107) 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 + ((z * -4.0) / y);
	double t_1 = 1.0 + ((4.0 * x) / y);
	double tmp;
	if (x <= -118000000.0) {
		tmp = t_1;
	} else if (x <= -1.25e-135) {
		tmp = t_0;
	} else if (x <= -1.65e-303) {
		tmp = 2.0;
	} else if (x <= 3.3e-56) {
		tmp = t_0;
	} else if (x <= 2.35e+22) {
		tmp = 2.0;
	} else if (x <= 9e+107) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 + ((z * -4.0) / y)
	t_1 = 1.0 + ((4.0 * x) / y)
	tmp = 0
	if x <= -118000000.0:
		tmp = t_1
	elif x <= -1.25e-135:
		tmp = t_0
	elif x <= -1.65e-303:
		tmp = 2.0
	elif x <= 3.3e-56:
		tmp = t_0
	elif x <= 2.35e+22:
		tmp = 2.0
	elif x <= 9e+107:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 + Float64(Float64(z * -4.0) / y))
	t_1 = Float64(1.0 + Float64(Float64(4.0 * x) / y))
	tmp = 0.0
	if (x <= -118000000.0)
		tmp = t_1;
	elseif (x <= -1.25e-135)
		tmp = t_0;
	elseif (x <= -1.65e-303)
		tmp = 2.0;
	elseif (x <= 3.3e-56)
		tmp = t_0;
	elseif (x <= 2.35e+22)
		tmp = 2.0;
	elseif (x <= 9e+107)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 + ((z * -4.0) / y);
	t_1 = 1.0 + ((4.0 * x) / y);
	tmp = 0.0;
	if (x <= -118000000.0)
		tmp = t_1;
	elseif (x <= -1.25e-135)
		tmp = t_0;
	elseif (x <= -1.65e-303)
		tmp = 2.0;
	elseif (x <= 3.3e-56)
		tmp = t_0;
	elseif (x <= 2.35e+22)
		tmp = 2.0;
	elseif (x <= 9e+107)
		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[(N[(z * -4.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(1.0 + N[(N[(4.0 * x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -118000000.0], t$95$1, If[LessEqual[x, -1.25e-135], t$95$0, If[LessEqual[x, -1.65e-303], 2.0, If[LessEqual[x, 3.3e-56], t$95$0, If[LessEqual[x, 2.35e+22], 2.0, If[LessEqual[x, 9e+107], t$95$0, t$95$1]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.18e8 or 9e107 < 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 78.2%

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

      1. associate-*r/ 78.2%

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

      2. *-commutative 78.2%

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

   4. Simplified 78.2%

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

   if -1.18e8 < x < -1.25000000000000005e-135 or -1.6499999999999999e-303 < x < 3.29999999999999984e-56 or 2.3500000000000001e22 < x < 9e107

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 58.6%

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

      1. associate-*r/ 58.6%

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

   4. Simplified 58.6%

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

   if -1.25000000000000005e-135 < x < -1.6499999999999999e-303 or 3.29999999999999984e-56 < x < 2.3500000000000001e22

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 62.3%

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

4. Final simplification 66.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -118000000:\\ \;\;\;\;1 + \frac{4 \cdot x}{y}\\ \mathbf{elif}\;x \leq -1.25 \cdot 10^{-135}:\\ \;\;\;\;1 + \frac{z \cdot -4}{y}\\ \mathbf{elif}\;x \leq -1.65 \cdot 10^{-303}:\\ \;\;\;\;2\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{-56}:\\ \;\;\;\;1 + \frac{z \cdot -4}{y}\\ \mathbf{elif}\;x \leq 2.35 \cdot 10^{+22}:\\ \;\;\;\;2\\ \mathbf{elif}\;x \leq 9 \cdot 10^{+107}:\\ \;\;\;\;1 + \frac{z \cdot -4}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{4 \cdot x}{y}\\ \end{array} \]

Alternative 4: 55.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{-23} \lor \neg \left(x \leq 1.35 \cdot 10^{+58}\right):\\ \;\;\;\;1 + x \cdot \frac{4}{y}\\ \mathbf{else}:\\ \;\;\;\;2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -9.5e-23) (not (<= x 1.35e+58))) (+ 1.0 (* x (/ 4.0 y))) 2.0))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -9.5e-23) || !(x <= 1.35e+58)) {
		tmp = 1.0 + (x * (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 ((x <= (-9.5d-23)) .or. (.not. (x <= 1.35d+58))) then
        tmp = 1.0d0 + (x * (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 ((x <= -9.5e-23) || !(x <= 1.35e+58)) {
		tmp = 1.0 + (x * (4.0 / y));
	} else {
		tmp = 2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -9.5e-23) or not (x <= 1.35e+58):
		tmp = 1.0 + (x * (4.0 / y))
	else:
		tmp = 2.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -9.5e-23) || !(x <= 1.35e+58))
		tmp = Float64(1.0 + Float64(x * Float64(4.0 / y)));
	else
		tmp = 2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -9.5e-23) || ~((x <= 1.35e+58)))
		tmp = 1.0 + (x * (4.0 / y));
	else
		tmp = 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -9.5e-23], N[Not[LessEqual[x, 1.35e+58]], $MachinePrecision]], N[(1.0 + N[(x * N[(4.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 2.0]

Derivation

1. Split input into 2 regimes

2. if x < -9.50000000000000058e-23 or 1.3500000000000001e58 < 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 71.1%

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

      1. associate-*r/ 71.1%

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

      2. associate-*l/ 71.0%

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

      3. *-commutative 71.0%

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

   4. Simplified 71.0%

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

   if -9.50000000000000058e-23 < x < 1.3500000000000001e58

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 49.0%

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

4. Final simplification 59.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{-23} \lor \neg \left(x \leq 1.35 \cdot 10^{+58}\right):\\ \;\;\;\;1 + x \cdot \frac{4}{y}\\ \mathbf{else}:\\ \;\;\;\;2\\ \end{array} \]

Alternative 5: 81.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+135} \lor \neg \left(z \leq 5.8 \cdot 10^{+130}\right):\\ \;\;\;\;1 + \frac{z \cdot -4}{y}\\ \mathbf{else}:\\ \;\;\;\;2 + 4 \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -5.8e+135) (not (<= z 5.8e+130)))
   (+ 1.0 (/ (* z -4.0) y))
   (+ 2.0 (* 4.0 (/ x y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5.8e+135) || !(z <= 5.8e+130)) {
		tmp = 1.0 + ((z * -4.0) / 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 <= (-5.8d+135)) .or. (.not. (z <= 5.8d+130))) then
        tmp = 1.0d0 + ((z * (-4.0d0)) / 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 <= -5.8e+135) || !(z <= 5.8e+130)) {
		tmp = 1.0 + ((z * -4.0) / y);
	} else {
		tmp = 2.0 + (4.0 * (x / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -5.8e+135) or not (z <= 5.8e+130):
		tmp = 1.0 + ((z * -4.0) / y)
	else:
		tmp = 2.0 + (4.0 * (x / y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -5.8e+135) || !(z <= 5.8e+130))
		tmp = Float64(1.0 + Float64(Float64(z * -4.0) / 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 <= -5.8e+135) || ~((z <= 5.8e+130)))
		tmp = 1.0 + ((z * -4.0) / y);
	else
		tmp = 2.0 + (4.0 * (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -5.8e+135], N[Not[LessEqual[z, 5.8e+130]], $MachinePrecision]], N[(1.0 + N[(N[(z * -4.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(2.0 + N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.7999999999999997e135 or 5.7999999999999998e130 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 81.8%

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

      1. associate-*r/ 81.8%

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

   4. Simplified 81.8%

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

   if -5.7999999999999997e135 < z < 5.7999999999999998e130

   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+ 99.9%

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

      6. associate-*l/ 99.9%

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

      7. *-commutative 99.9%

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

      8. associate-/l* 99.9%

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

      9. metadata-eval 99.9%

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

      10. metadata-eval 99.9%

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

      11. associate-/l* 99.9%

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

      12. distribute-rgt-neg-in 99.9%

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

      13. distribute-lft-neg-out 99.9%

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

      14. associate-/l* 99.9%

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

      15. *-commutative 99.9%

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

      16. neg-mul-1 99.9%

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

      17. distribute-lft-neg-out 99.9%

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

      18. *-inverses 99.9%

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

      19. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

      1. associate-*l/ 100.0%

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

      2. associate-/l* 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in x around inf 87.0%

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

4. Final simplification 85.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+135} \lor \neg \left(z \leq 5.8 \cdot 10^{+130}\right):\\ \;\;\;\;1 + \frac{z \cdot -4}{y}\\ \mathbf{else}:\\ \;\;\;\;2 + 4 \cdot \frac{x}{y}\\ \end{array} \]

Alternative 6: 85.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+28} \lor \neg \left(z \leq 1.02 \cdot 10^{+121}\right):\\ \;\;\;\;2 + \frac{z}{y \cdot -0.25}\\ \mathbf{else}:\\ \;\;\;\;2 + 4 \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -3.1e+28) (not (<= z 1.02e+121)))
   (+ 2.0 (/ z (* y -0.25)))
   (+ 2.0 (* 4.0 (/ x y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3.1e+28) || !(z <= 1.02e+121)) {
		tmp = 2.0 + (z / (y * -0.25));
	} 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 <= (-3.1d+28)) .or. (.not. (z <= 1.02d+121))) then
        tmp = 2.0d0 + (z / (y * (-0.25d0)))
    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 <= -3.1e+28) || !(z <= 1.02e+121)) {
		tmp = 2.0 + (z / (y * -0.25));
	} else {
		tmp = 2.0 + (4.0 * (x / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -3.1e+28) or not (z <= 1.02e+121):
		tmp = 2.0 + (z / (y * -0.25))
	else:
		tmp = 2.0 + (4.0 * (x / y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -3.1e+28) || !(z <= 1.02e+121))
		tmp = Float64(2.0 + Float64(z / Float64(y * -0.25)));
	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 <= -3.1e+28) || ~((z <= 1.02e+121)))
		tmp = 2.0 + (z / (y * -0.25));
	else
		tmp = 2.0 + (4.0 * (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -3.1e+28], N[Not[LessEqual[z, 1.02e+121]], $MachinePrecision]], N[(2.0 + N[(z / N[(y * -0.25), $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 < -3.1000000000000001e28 or 1.02000000000000005e121 < 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/ 99.9%

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

      2. +-commutative 99.9%

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

      3. associate--l+ 99.9%

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

      4. distribute-lft-in 99.9%

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

      5. associate-+r+ 99.9%

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

      6. associate-*l/ 99.9%

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

      7. *-commutative 99.9%

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

      8. associate-/l* 99.9%

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

      9. metadata-eval 99.9%

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

      10. metadata-eval 99.9%

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

      11. associate-/l* 99.9%

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

      12. distribute-rgt-neg-in 99.9%

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

      13. distribute-lft-neg-out 99.9%

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

      14. associate-/l* 99.9%

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

      15. *-commutative 99.9%

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

      16. neg-mul-1 99.9%

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

      17. distribute-lft-neg-out 99.9%

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

      18. *-inverses 99.9%

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

      19. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

      1. associate-*l/ 100.0%

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

      2. associate-/l* 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in x around 0 88.0%

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

      1. associate-*r/ 88.0%

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

      2. *-commutative 88.0%

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

      3. /-rgt-identity 88.0%

         \[\leadsto 2 + \frac{\color{blue}{\frac{z \cdot -4}{1}}}{y} \]

      4. associate-/l* 88.0%

         \[\leadsto 2 + \frac{\color{blue}{\frac{z}{\frac{1}{-4}}}}{y} \]

      5. associate-/l/ 88.0%

         \[\leadsto 2 + \color{blue}{\frac{z}{y \cdot \frac{1}{-4}}} \]

      6. metadata-eval 88.0%

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

   8. Simplified 88.0%

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

   if -3.1000000000000001e28 < z < 1.02000000000000005e121

   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%

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

      6. associate-*l/ 99.8%

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

      7. *-commutative 99.8%

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

      8. associate-/l* 99.8%

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

      9. metadata-eval 99.8%

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

      10. metadata-eval 99.8%

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

      11. associate-/l* 99.8%

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

      12. distribute-rgt-neg-in 99.8%

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

      13. distribute-lft-neg-out 99.8%

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

      14. associate-/l* 99.8%

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

      15. *-commutative 99.8%

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

      16. neg-mul-1 99.8%

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

      17. distribute-lft-neg-out 99.8%

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

      18. *-inverses 99.8%

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

      19. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

      1. associate-*l/ 100.0%

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

      2. associate-/l* 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in x around inf 90.2%

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

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+28} \lor \neg \left(z \leq 1.02 \cdot 10^{+121}\right):\\ \;\;\;\;2 + \frac{z}{y \cdot -0.25}\\ \mathbf{else}:\\ \;\;\;\;2 + 4 \cdot \frac{x}{y}\\ \end{array} \]

Alternative 7: 99.8% accurate, 1.4× speedup

Math

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

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(Float64(4.0 / y) * Float64(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[(N[(4.0 / y), $MachinePrecision] * N[(x - z), $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+ 99.9%

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

   6. associate-*l/ 99.9%

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

   7. *-commutative 99.9%

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

   8. associate-/l* 99.9%

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

   9. metadata-eval 99.9%

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

   10. metadata-eval 99.9%

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

   11. associate-/l* 99.9%

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

   12. distribute-rgt-neg-in 99.9%

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

   13. distribute-lft-neg-out 99.9%

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

   14. associate-/l* 99.9%

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

   15. *-commutative 99.9%

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

   16. neg-mul-1 99.9%

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

   17. distribute-lft-neg-out 99.9%

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

   18. *-inverses 99.9%

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

   19. metadata-eval 99.9%

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

3. Simplified 99.9%

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

4. Final simplification 99.9%

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

Alternative 8: 34.1% 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. Taylor expanded in y around inf 33.1%

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

3. Final simplification 33.1%

   \[\leadsto 2 \]

Reproduce

herbie shell --seed 2023318 
(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)))