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

Percentage Accurate: 99.8% → 100.0%

Time: 5.6s

Alternatives: 9

Speedup: 1.4×

• 20.5% 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: 99.8% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z)
 :precision binary64
 (+ 1.0 (/ (* 4.0 (- (+ x (* y 0.25)) z)) y)))

C

double code(double x, double y, double z) {
	return 1.0 + ((4.0 * ((x + (y * 0.25)) - z)) / y);
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = 1.0d0 + ((4.0d0 * ((x + (y * 0.25d0)) - z)) / y)
end function

Java

public static double code(double x, double y, double z) {
	return 1.0 + ((4.0 * ((x + (y * 0.25)) - z)) / y);
}

Python

def code(x, y, z):
	return 1.0 + ((4.0 * ((x + (y * 0.25)) - z)) / y)

Julia

function code(x, y, z)
	return Float64(1.0 + Float64(Float64(4.0 * Float64(Float64(x + Float64(y * 0.25)) - z)) / y))
end

MATLAB

function tmp = code(x, y, z)
	tmp = 1.0 + ((4.0 * ((x + (y * 0.25)) - z)) / y);
end

Wolfram

code[x_, y_, z_] := N[(1.0 + N[(N[(4.0 * N[(N[(x + N[(y * 0.25), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]

Alternative 1: 100.0% accurate, 1.4× speedup

Math

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

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%

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

   2. associate--l+ 99.7%

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

3. Simplified 99.7%

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

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: 57.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + \frac{4}{\frac{y}{x}}\\ t_1 := 1 + -4 \cdot \frac{z}{y}\\ \mathbf{if}\;z \leq -640:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{-249}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-278}:\\ \;\;\;\;2\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-179}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 950000:\\ \;\;\;\;2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ 1.0 (/ 4.0 (/ y x)))) (t_1 (+ 1.0 (* -4.0 (/ z y)))))
   (if (<= z -640.0)
     t_1
     (if (<= z -4.6e-249)
       t_0
       (if (<= z 6.2e-278)
         2.0
         (if (<= z 7.2e-179) t_0 (if (<= z 950000.0) 2.0 t_1)))))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 + (4.0 / (y / x));
	double t_1 = 1.0 + (-4.0 * (z / y));
	double tmp;
	if (z <= -640.0) {
		tmp = t_1;
	} else if (z <= -4.6e-249) {
		tmp = t_0;
	} else if (z <= 6.2e-278) {
		tmp = 2.0;
	} else if (z <= 7.2e-179) {
		tmp = t_0;
	} else if (z <= 950000.0) {
		tmp = 2.0;
	} 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 / (y / x))
    t_1 = 1.0d0 + ((-4.0d0) * (z / y))
    if (z <= (-640.0d0)) then
        tmp = t_1
    else if (z <= (-4.6d-249)) then
        tmp = t_0
    else if (z <= 6.2d-278) then
        tmp = 2.0d0
    else if (z <= 7.2d-179) then
        tmp = t_0
    else if (z <= 950000.0d0) then
        tmp = 2.0d0
    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 / (y / x));
	double t_1 = 1.0 + (-4.0 * (z / y));
	double tmp;
	if (z <= -640.0) {
		tmp = t_1;
	} else if (z <= -4.6e-249) {
		tmp = t_0;
	} else if (z <= 6.2e-278) {
		tmp = 2.0;
	} else if (z <= 7.2e-179) {
		tmp = t_0;
	} else if (z <= 950000.0) {
		tmp = 2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 + (4.0 / (y / x))
	t_1 = 1.0 + (-4.0 * (z / y))
	tmp = 0
	if z <= -640.0:
		tmp = t_1
	elif z <= -4.6e-249:
		tmp = t_0
	elif z <= 6.2e-278:
		tmp = 2.0
	elif z <= 7.2e-179:
		tmp = t_0
	elif z <= 950000.0:
		tmp = 2.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 + Float64(4.0 / Float64(y / x)))
	t_1 = Float64(1.0 + Float64(-4.0 * Float64(z / y)))
	tmp = 0.0
	if (z <= -640.0)
		tmp = t_1;
	elseif (z <= -4.6e-249)
		tmp = t_0;
	elseif (z <= 6.2e-278)
		tmp = 2.0;
	elseif (z <= 7.2e-179)
		tmp = t_0;
	elseif (z <= 950000.0)
		tmp = 2.0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 + (4.0 / (y / x));
	t_1 = 1.0 + (-4.0 * (z / y));
	tmp = 0.0;
	if (z <= -640.0)
		tmp = t_1;
	elseif (z <= -4.6e-249)
		tmp = t_0;
	elseif (z <= 6.2e-278)
		tmp = 2.0;
	elseif (z <= 7.2e-179)
		tmp = t_0;
	elseif (z <= 950000.0)
		tmp = 2.0;
	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[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(1.0 + N[(-4.0 * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -640.0], t$95$1, If[LessEqual[z, -4.6e-249], t$95$0, If[LessEqual[z, 6.2e-278], 2.0, If[LessEqual[z, 7.2e-179], t$95$0, If[LessEqual[z, 950000.0], 2.0, t$95$1]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -640 or 9.5e5 < 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%

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

      2. associate--l+ 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in z around inf 68.3%

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

      1. *-commutative 68.3%

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

   6. Simplified 68.3%

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

   if -640 < z < -4.5999999999999996e-249 or 6.19999999999999983e-278 < z < 7.20000000000000015e-179

   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%

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

      2. associate--l+ 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around inf 65.4%

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

      1. associate-*r/ 65.4%

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

      2. associate-/l* 65.2%

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

   6. Simplified 65.2%

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

   if -4.5999999999999996e-249 < z < 6.19999999999999983e-278 or 7.20000000000000015e-179 < z < 9.5e5

   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%

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

      2. associate--l+ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 67.1%

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

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -640:\\ \;\;\;\;1 + -4 \cdot \frac{z}{y}\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{-249}:\\ \;\;\;\;1 + \frac{4}{\frac{y}{x}}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-278}:\\ \;\;\;\;2\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-179}:\\ \;\;\;\;1 + \frac{4}{\frac{y}{x}}\\ \mathbf{elif}\;z \leq 950000:\\ \;\;\;\;2\\ \mathbf{else}:\\ \;\;\;\;1 + -4 \cdot \frac{z}{y}\\ \end{array} \]

Alternative 3: 57.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + \frac{4 \cdot x}{y}\\ t_1 := 1 + -4 \cdot \frac{z}{y}\\ \mathbf{if}\;z \leq -1600:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -8.8 \cdot 10^{-250}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-276}:\\ \;\;\;\;2\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{-181}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 245000:\\ \;\;\;\;2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

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 -1600.0)
     t_1
     (if (<= z -8.8e-250)
       t_0
       (if (<= z 1.45e-276)
         2.0
         (if (<= z 7.6e-181) t_0 (if (<= z 245000.0) 2.0 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 <= -1600.0) {
		tmp = t_1;
	} else if (z <= -8.8e-250) {
		tmp = t_0;
	} else if (z <= 1.45e-276) {
		tmp = 2.0;
	} else if (z <= 7.6e-181) {
		tmp = t_0;
	} else if (z <= 245000.0) {
		tmp = 2.0;
	} 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 <= (-1600.0d0)) then
        tmp = t_1
    else if (z <= (-8.8d-250)) then
        tmp = t_0
    else if (z <= 1.45d-276) then
        tmp = 2.0d0
    else if (z <= 7.6d-181) then
        tmp = t_0
    else if (z <= 245000.0d0) then
        tmp = 2.0d0
    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 <= -1600.0) {
		tmp = t_1;
	} else if (z <= -8.8e-250) {
		tmp = t_0;
	} else if (z <= 1.45e-276) {
		tmp = 2.0;
	} else if (z <= 7.6e-181) {
		tmp = t_0;
	} else if (z <= 245000.0) {
		tmp = 2.0;
	} 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 <= -1600.0:
		tmp = t_1
	elif z <= -8.8e-250:
		tmp = t_0
	elif z <= 1.45e-276:
		tmp = 2.0
	elif z <= 7.6e-181:
		tmp = t_0
	elif z <= 245000.0:
		tmp = 2.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 + Float64(Float64(4.0 * x) / y))
	t_1 = Float64(1.0 + Float64(-4.0 * Float64(z / y)))
	tmp = 0.0
	if (z <= -1600.0)
		tmp = t_1;
	elseif (z <= -8.8e-250)
		tmp = t_0;
	elseif (z <= 1.45e-276)
		tmp = 2.0;
	elseif (z <= 7.6e-181)
		tmp = t_0;
	elseif (z <= 245000.0)
		tmp = 2.0;
	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 <= -1600.0)
		tmp = t_1;
	elseif (z <= -8.8e-250)
		tmp = t_0;
	elseif (z <= 1.45e-276)
		tmp = 2.0;
	elseif (z <= 7.6e-181)
		tmp = t_0;
	elseif (z <= 245000.0)
		tmp = 2.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(1.0 + N[(N[(4.0 * x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(1.0 + N[(-4.0 * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1600.0], t$95$1, If[LessEqual[z, -8.8e-250], t$95$0, If[LessEqual[z, 1.45e-276], 2.0, If[LessEqual[z, 7.6e-181], t$95$0, If[LessEqual[z, 245000.0], 2.0, t$95$1]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1600 or 245000 < 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%

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

      2. associate--l+ 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in z around inf 68.3%

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

      1. *-commutative 68.3%

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

   6. Simplified 68.3%

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

   if -1600 < z < -8.8e-250 or 1.44999999999999994e-276 < z < 7.5999999999999996e-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* 99.7%

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

      2. associate--l+ 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around inf 65.4%

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

      1. associate-*r/ 65.4%

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

      2. *-commutative 65.4%

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

   6. Simplified 65.4%

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

   if -8.8e-250 < z < 1.44999999999999994e-276 or 7.5999999999999996e-181 < z < 245000

   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%

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

      2. associate--l+ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 67.1%

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

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1600:\\ \;\;\;\;1 + -4 \cdot \frac{z}{y}\\ \mathbf{elif}\;z \leq -8.8 \cdot 10^{-250}:\\ \;\;\;\;1 + \frac{4 \cdot x}{y}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-276}:\\ \;\;\;\;2\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{-181}:\\ \;\;\;\;1 + \frac{4 \cdot x}{y}\\ \mathbf{elif}\;z \leq 245000:\\ \;\;\;\;2\\ \mathbf{else}:\\ \;\;\;\;1 + -4 \cdot \frac{z}{y}\\ \end{array} \]

Alternative 4: 85.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{-31} \lor \neg \left(y \leq 1.75 \cdot 10^{+136}\right):\\ \;\;\;\;2 + -4 \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{4}{\frac{y}{x - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -7.2e-31) (not (<= y 1.75e+136)))
   (+ 2.0 (* -4.0 (/ z y)))
   (+ 1.0 (/ 4.0 (/ y (- x z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -7.2e-31) || !(y <= 1.75e+136)) {
		tmp = 2.0 + (-4.0 * (z / y));
	} else {
		tmp = 1.0 + (4.0 / (y / (x - z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-7.2d-31)) .or. (.not. (y <= 1.75d+136))) then
        tmp = 2.0d0 + ((-4.0d0) * (z / y))
    else
        tmp = 1.0d0 + (4.0d0 / (y / (x - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -7.2e-31) || !(y <= 1.75e+136)) {
		tmp = 2.0 + (-4.0 * (z / y));
	} else {
		tmp = 1.0 + (4.0 / (y / (x - z)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -7.2e-31) or not (y <= 1.75e+136):
		tmp = 2.0 + (-4.0 * (z / y))
	else:
		tmp = 1.0 + (4.0 / (y / (x - z)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -7.2e-31) || !(y <= 1.75e+136))
		tmp = Float64(2.0 + Float64(-4.0 * Float64(z / y)));
	else
		tmp = Float64(1.0 + Float64(4.0 / Float64(y / Float64(x - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -7.2e-31) || ~((y <= 1.75e+136)))
		tmp = 2.0 + (-4.0 * (z / y));
	else
		tmp = 1.0 + (4.0 / (y / (x - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -7.2e-31], N[Not[LessEqual[y, 1.75e+136]], $MachinePrecision]], N[(2.0 + N[(-4.0 * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(4.0 / N[(y / N[(x - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.20000000000000007e-31 or 1.75000000000000001e136 < y

   1. Initial program 99.9%

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

      1. associate-/l* 99.7%

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

      2. associate--l+ 99.7%

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

   3. Simplified 99.7%

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

   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 89.4%

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

   if -7.20000000000000007e-31 < y < 1.75000000000000001e136

   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%

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

      2. associate--l+ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around 0 90.0%

      \[\leadsto 1 + \frac{4}{\color{blue}{\frac{y}{x - z}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{-31} \lor \neg \left(y \leq 1.75 \cdot 10^{+136}\right):\\ \;\;\;\;2 + -4 \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{4}{\frac{y}{x - z}}\\ \end{array} \]

Alternative 5: 55.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+31} \lor \neg \left(z \leq 450000\right):\\ \;\;\;\;1 + -4 \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.95e+31) (not (<= z 450000.0))) (+ 1.0 (* -4.0 (/ z y))) 2.0))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.95e+31) || !(z <= 450000.0)) {
		tmp = 1.0 + (-4.0 * (z / 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 <= (-1.95d+31)) .or. (.not. (z <= 450000.0d0))) then
        tmp = 1.0d0 + ((-4.0d0) * (z / 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 <= -1.95e+31) || !(z <= 450000.0)) {
		tmp = 1.0 + (-4.0 * (z / y));
	} else {
		tmp = 2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.95e+31) or not (z <= 450000.0):
		tmp = 1.0 + (-4.0 * (z / y))
	else:
		tmp = 2.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.95e+31) || !(z <= 450000.0))
		tmp = Float64(1.0 + Float64(-4.0 * Float64(z / y)));
	else
		tmp = 2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.95e+31) || ~((z <= 450000.0)))
		tmp = 1.0 + (-4.0 * (z / y));
	else
		tmp = 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.95e+31], N[Not[LessEqual[z, 450000.0]], $MachinePrecision]], N[(1.0 + N[(-4.0 * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 2.0]

Derivation

1. Split input into 2 regimes

2. if z < -1.95e31 or 4.5e5 < 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%

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

      2. associate--l+ 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in z around inf 70.7%

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

      1. *-commutative 70.7%

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

   6. Simplified 70.7%

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

   if -1.95e31 < z < 4.5e5

   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%

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

      2. associate--l+ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 50.4%

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

4. Final simplification 60.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+31} \lor \neg \left(z \leq 450000\right):\\ \;\;\;\;1 + -4 \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;2\\ \end{array} \]

Alternative 6: 81.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.62 \cdot 10^{+112} \lor \neg \left(x \leq 5 \cdot 10^{+140}\right):\\ \;\;\;\;1 + \frac{4 \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;2 + -4 \cdot \frac{z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.62e+112) (not (<= x 5e+140)))
   (+ 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 <= -1.62e+112) || !(x <= 5e+140)) {
		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 <= (-1.62d+112)) .or. (.not. (x <= 5d+140))) 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 <= -1.62e+112) || !(x <= 5e+140)) {
		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 <= -1.62e+112) or not (x <= 5e+140):
		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 <= -1.62e+112) || !(x <= 5e+140))
		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 <= -1.62e+112) || ~((x <= 5e+140)))
		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, -1.62e+112], N[Not[LessEqual[x, 5e+140]], $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 < -1.61999999999999994e112 or 5.00000000000000008e140 < 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%

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

      2. associate--l+ 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around inf 77.8%

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

      1. associate-*r/ 77.8%

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

      2. *-commutative 77.8%

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

   6. Simplified 77.8%

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

   if -1.61999999999999994e112 < x < 5.00000000000000008e140

   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%

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

      2. associate--l+ 99.8%

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

   3. Simplified 99.8%

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

   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 85.5%

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

4. Final simplification 83.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.62 \cdot 10^{+112} \lor \neg \left(x \leq 5 \cdot 10^{+140}\right):\\ \;\;\;\;1 + \frac{4 \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;2 + -4 \cdot \frac{z}{y}\\ \end{array} \]

Alternative 7: 85.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.1 \cdot 10^{+107} \lor \neg \left(x \leq 1.25 \cdot 10^{+107}\right):\\ \;\;\;\;2 + 4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;2 + -4 \cdot \frac{z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -4.1e+107) (not (<= x 1.25e+107)))
   (+ 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 <= -4.1e+107) || !(x <= 1.25e+107)) {
		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 <= (-4.1d+107)) .or. (.not. (x <= 1.25d+107))) 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 <= -4.1e+107) || !(x <= 1.25e+107)) {
		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 <= -4.1e+107) or not (x <= 1.25e+107):
		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 <= -4.1e+107) || !(x <= 1.25e+107))
		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 <= -4.1e+107) || ~((x <= 1.25e+107)))
		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, -4.1e+107], N[Not[LessEqual[x, 1.25e+107]], $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 < -4.0999999999999999e107 or 1.25e107 < 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%

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

      2. associate--l+ 99.7%

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

   3. Simplified 99.7%

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

   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 86.7%

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

   if -4.0999999999999999e107 < x < 1.25e107

   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%

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

      2. associate--l+ 99.7%

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

   3. Simplified 99.7%

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

   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 87.2%

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

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.1 \cdot 10^{+107} \lor \neg \left(x \leq 1.25 \cdot 10^{+107}\right):\\ \;\;\;\;2 + 4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;2 + -4 \cdot \frac{z}{y}\\ \end{array} \]

Alternative 8: 8.1% accurate, 13.0× speedup

Math

\[\begin{array}{l} \\ 1 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 1.0)

C

double code(double x, double y, double z) {
	return 1.0;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = 1.0d0
end function

Java

public static double code(double x, double y, double z) {
	return 1.0;
}

Python

def code(x, y, z):
	return 1.0

Julia

function code(x, y, z)
	return 1.0
end

MATLAB

function tmp = code(x, y, z)
	tmp = 1.0;
end

Wolfram

code[x_, y_, z_] := 1.0

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%

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

   2. associate--l+ 99.7%

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

3. Simplified 99.7%

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

4. Taylor expanded in z around inf 45.9%

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

   1. *-commutative 45.9%

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

6. Simplified 45.9%

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

7. Taylor expanded in z around 0 8.3%

   \[\leadsto \color{blue}{1} \]

8. Final simplification 8.3%

   \[\leadsto 1 \]

Alternative 9: 33.9% 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%

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

   2. associate--l+ 99.7%

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

3. Simplified 99.7%

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

4. Taylor expanded in y around inf 34.5%

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

5. Final simplification 34.5%

   \[\leadsto 2 \]

Reproduce

herbie shell --seed 2023178 
(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)))