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

Percentage Accurate: 99.9% → 99.9%

Time: 7.3s

Alternatives: 10

Speedup: 1.2×

• 20.6% 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, 1.2× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return 1.0 + ((y + (4.0 * (x - 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 + ((y + (4.0d0 * (x - z))) / y)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

3. Taylor expanded in y around 0 100.0%

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

Alternative 2: 53.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{z}{y} \cdot -4\\ \mathbf{if}\;z \leq -8.5 \cdot 10^{+44}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-305}:\\ \;\;\;\;\frac{4 \cdot x}{y}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+64}:\\ \;\;\;\;2\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (/ z y) -4.0)))
   (if (<= z -8.5e+44)
     t_0
     (if (<= z 1.95e-305) (/ (* 4.0 x) y) (if (<= z 1.15e+64) 2.0 t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = (z / y) * -4.0;
	double tmp;
	if (z <= -8.5e+44) {
		tmp = t_0;
	} else if (z <= 1.95e-305) {
		tmp = (4.0 * x) / y;
	} else if (z <= 1.15e+64) {
		tmp = 2.0;
	} else {
		tmp = t_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) :: t_0
    real(8) :: tmp
    t_0 = (z / y) * (-4.0d0)
    if (z <= (-8.5d+44)) then
        tmp = t_0
    else if (z <= 1.95d-305) then
        tmp = (4.0d0 * x) / y
    else if (z <= 1.15d+64) then
        tmp = 2.0d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (z / y) * -4.0;
	double tmp;
	if (z <= -8.5e+44) {
		tmp = t_0;
	} else if (z <= 1.95e-305) {
		tmp = (4.0 * x) / y;
	} else if (z <= 1.15e+64) {
		tmp = 2.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (z / y) * -4.0
	tmp = 0
	if z <= -8.5e+44:
		tmp = t_0
	elif z <= 1.95e-305:
		tmp = (4.0 * x) / y
	elif z <= 1.15e+64:
		tmp = 2.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(z / y) * -4.0)
	tmp = 0.0
	if (z <= -8.5e+44)
		tmp = t_0;
	elseif (z <= 1.95e-305)
		tmp = Float64(Float64(4.0 * x) / y);
	elseif (z <= 1.15e+64)
		tmp = 2.0;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (z / y) * -4.0;
	tmp = 0.0;
	if (z <= -8.5e+44)
		tmp = t_0;
	elseif (z <= 1.95e-305)
		tmp = (4.0 * x) / y;
	elseif (z <= 1.15e+64)
		tmp = 2.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(z / y), $MachinePrecision] * -4.0), $MachinePrecision]}, If[LessEqual[z, -8.5e+44], t$95$0, If[LessEqual[z, 1.95e-305], N[(N[(4.0 * x), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[z, 1.15e+64], 2.0, t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.5e44 or 1.15e64 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 74.9%

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

      1. *-commutative 74.9%

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

   5. Simplified 74.9%

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

   if -8.5e44 < z < 1.95000000000000013e-305

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 55.5%

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

      1. associate-*r/ 55.5%

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

   5. Simplified 55.5%

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

   if 1.95000000000000013e-305 < z < 1.15e64

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 52.6%

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

Alternative 3: 53.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{z}{y} \cdot -4\\ \mathbf{if}\;z \leq -7.8 \cdot 10^{+46}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-305}:\\ \;\;\;\;x \cdot \frac{4}{y}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+62}:\\ \;\;\;\;2\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (/ z y) -4.0)))
   (if (<= z -7.8e+46)
     t_0
     (if (<= z 7e-305) (* x (/ 4.0 y)) (if (<= z 1.15e+62) 2.0 t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = (z / y) * -4.0;
	double tmp;
	if (z <= -7.8e+46) {
		tmp = t_0;
	} else if (z <= 7e-305) {
		tmp = x * (4.0 / y);
	} else if (z <= 1.15e+62) {
		tmp = 2.0;
	} else {
		tmp = t_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) :: t_0
    real(8) :: tmp
    t_0 = (z / y) * (-4.0d0)
    if (z <= (-7.8d+46)) then
        tmp = t_0
    else if (z <= 7d-305) then
        tmp = x * (4.0d0 / y)
    else if (z <= 1.15d+62) then
        tmp = 2.0d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (z / y) * -4.0;
	double tmp;
	if (z <= -7.8e+46) {
		tmp = t_0;
	} else if (z <= 7e-305) {
		tmp = x * (4.0 / y);
	} else if (z <= 1.15e+62) {
		tmp = 2.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (z / y) * -4.0
	tmp = 0
	if z <= -7.8e+46:
		tmp = t_0
	elif z <= 7e-305:
		tmp = x * (4.0 / y)
	elif z <= 1.15e+62:
		tmp = 2.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(z / y) * -4.0)
	tmp = 0.0
	if (z <= -7.8e+46)
		tmp = t_0;
	elseif (z <= 7e-305)
		tmp = Float64(x * Float64(4.0 / y));
	elseif (z <= 1.15e+62)
		tmp = 2.0;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (z / y) * -4.0;
	tmp = 0.0;
	if (z <= -7.8e+46)
		tmp = t_0;
	elseif (z <= 7e-305)
		tmp = x * (4.0 / y);
	elseif (z <= 1.15e+62)
		tmp = 2.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(z / y), $MachinePrecision] * -4.0), $MachinePrecision]}, If[LessEqual[z, -7.8e+46], t$95$0, If[LessEqual[z, 7e-305], N[(x * N[(4.0 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.15e+62], 2.0, t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.7999999999999999e46 or 1.14999999999999992e62 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 74.9%

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

      1. *-commutative 74.9%

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

   5. Simplified 74.9%

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

   if -7.7999999999999999e46 < z < 6.9999999999999996e-305

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 55.5%

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

      1. associate-*r/ 55.5%

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

      2. associate-*l/ 55.4%

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

      3. *-commutative 55.4%

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

   5. Simplified 55.4%

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

   if 6.9999999999999996e-305 < z < 1.14999999999999992e62

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 52.6%

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

Alternative 4: 53.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \frac{-4}{y}\\ \mathbf{if}\;z \leq -2.6 \cdot 10^{+44}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-306}:\\ \;\;\;\;x \cdot \frac{4}{y}\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{+61}:\\ \;\;\;\;2\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (/ -4.0 y))))
   (if (<= z -2.6e+44)
     t_0
     (if (<= z 3.5e-306) (* x (/ 4.0 y)) (if (<= z 8.8e+61) 2.0 t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = z * (-4.0 / y);
	double tmp;
	if (z <= -2.6e+44) {
		tmp = t_0;
	} else if (z <= 3.5e-306) {
		tmp = x * (4.0 / y);
	} else if (z <= 8.8e+61) {
		tmp = 2.0;
	} else {
		tmp = t_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) :: t_0
    real(8) :: tmp
    t_0 = z * ((-4.0d0) / y)
    if (z <= (-2.6d+44)) then
        tmp = t_0
    else if (z <= 3.5d-306) then
        tmp = x * (4.0d0 / y)
    else if (z <= 8.8d+61) then
        tmp = 2.0d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * (-4.0 / y);
	double tmp;
	if (z <= -2.6e+44) {
		tmp = t_0;
	} else if (z <= 3.5e-306) {
		tmp = x * (4.0 / y);
	} else if (z <= 8.8e+61) {
		tmp = 2.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * (-4.0 / y)
	tmp = 0
	if z <= -2.6e+44:
		tmp = t_0
	elif z <= 3.5e-306:
		tmp = x * (4.0 / y)
	elif z <= 8.8e+61:
		tmp = 2.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(-4.0 / y))
	tmp = 0.0
	if (z <= -2.6e+44)
		tmp = t_0;
	elseif (z <= 3.5e-306)
		tmp = Float64(x * Float64(4.0 / y));
	elseif (z <= 8.8e+61)
		tmp = 2.0;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * (-4.0 / y);
	tmp = 0.0;
	if (z <= -2.6e+44)
		tmp = t_0;
	elseif (z <= 3.5e-306)
		tmp = x * (4.0 / y);
	elseif (z <= 8.8e+61)
		tmp = 2.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(-4.0 / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.6e+44], t$95$0, If[LessEqual[z, 3.5e-306], N[(x * N[(4.0 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.8e+61], 2.0, t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.5999999999999999e44 or 8.8000000000000001e61 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 74.9%

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

      1. associate-*r/ 74.9%

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

      2. *-commutative 74.9%

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

      3. associate-/l* 74.7%

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

   5. Simplified 74.7%

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

   if -2.5999999999999999e44 < z < 3.50000000000000018e-306

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 55.5%

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

      1. associate-*r/ 55.5%

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

      2. associate-*l/ 55.4%

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

      3. *-commutative 55.4%

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

   5. Simplified 55.4%

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

   if 3.50000000000000018e-306 < z < 8.8000000000000001e61

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 52.6%

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

Alternative 5: 86.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+44} \lor \neg \left(z \leq 1.3 \cdot 10^{+57}\right):\\ \;\;\;\;2 + \frac{z}{y} \cdot -4\\ \mathbf{else}:\\ \;\;\;\;2 + x \cdot \frac{4}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.25e+44) (not (<= z 1.3e+57)))
   (+ 2.0 (* (/ z y) -4.0))
   (+ 2.0 (* x (/ 4.0 y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.25e+44) || !(z <= 1.3e+57)) {
		tmp = 2.0 + ((z / y) * -4.0);
	} else {
		tmp = 2.0 + (x * (4.0 / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-1.25d+44)) .or. (.not. (z <= 1.3d+57))) then
        tmp = 2.0d0 + ((z / y) * (-4.0d0))
    else
        tmp = 2.0d0 + (x * (4.0d0 / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.25e+44) || !(z <= 1.3e+57)) {
		tmp = 2.0 + ((z / y) * -4.0);
	} else {
		tmp = 2.0 + (x * (4.0 / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.25e+44) or not (z <= 1.3e+57):
		tmp = 2.0 + ((z / y) * -4.0)
	else:
		tmp = 2.0 + (x * (4.0 / y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.25e+44) || !(z <= 1.3e+57))
		tmp = Float64(2.0 + Float64(Float64(z / y) * -4.0));
	else
		tmp = Float64(2.0 + Float64(x * Float64(4.0 / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.25e+44) || ~((z <= 1.3e+57)))
		tmp = 2.0 + ((z / y) * -4.0);
	else
		tmp = 2.0 + (x * (4.0 / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.25e+44], N[Not[LessEqual[z, 1.3e+57]], $MachinePrecision]], N[(2.0 + N[(N[(z / y), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision], N[(2.0 + N[(x * N[(4.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.2499999999999999e44 or 1.3e57 < 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. +-commutative 100.0%

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

      2. associate-*l/ 99.8%

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

      3. +-commutative 99.8%

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

      4. associate--l+ 99.8%

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

      5. +-commutative 99.8%

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

      6. distribute-lft-in 99.8%

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

      7. associate-+l+ 99.8%

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

      8. associate-*l/ 99.8%

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

      9. *-commutative 99.8%

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

      10. associate-*l* 99.8%

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

      11. metadata-eval 99.8%

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

      12. *-rgt-identity 99.8%

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

      13. *-inverses 99.8%

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

      14. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around 0 91.7%

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

      1. *-commutative 91.7%

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

   7. Simplified 91.7%

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

   if -1.2499999999999999e44 < z < 1.3e57

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. associate-*l/ 99.8%

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

      3. +-commutative 99.8%

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

      4. associate--l+ 99.8%

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

      5. +-commutative 99.8%

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

      6. distribute-lft-in 99.8%

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

      7. associate-+l+ 99.8%

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

      8. associate-*l/ 99.8%

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

      9. *-commutative 99.8%

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

      10. associate-*l* 99.8%

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

      11. metadata-eval 99.8%

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

      12. *-rgt-identity 99.8%

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

      13. *-inverses 99.8%

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

      14. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 90.1%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+44} \lor \neg \left(z \leq 1.3 \cdot 10^{+57}\right):\\ \;\;\;\;2 + \frac{z}{y} \cdot -4\\ \mathbf{else}:\\ \;\;\;\;2 + x \cdot \frac{4}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 83.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{-71} \lor \neg \left(y \leq 7 \cdot 10^{+138}\right):\\ \;\;\;\;2 + \frac{z}{y} \cdot -4\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \frac{x - z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.5e-71) (not (<= y 7e+138)))
   (+ 2.0 (* (/ z y) -4.0))
   (* 4.0 (/ (- x z) y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.5e-71) || !(y <= 7e+138)) {
		tmp = 2.0 + ((z / y) * -4.0);
	} else {
		tmp = 4.0 * ((x - 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 ((y <= (-2.5d-71)) .or. (.not. (y <= 7d+138))) then
        tmp = 2.0d0 + ((z / y) * (-4.0d0))
    else
        tmp = 4.0d0 * ((x - z) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.5e-71) || !(y <= 7e+138)) {
		tmp = 2.0 + ((z / y) * -4.0);
	} else {
		tmp = 4.0 * ((x - z) / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.5e-71) or not (y <= 7e+138):
		tmp = 2.0 + ((z / y) * -4.0)
	else:
		tmp = 4.0 * ((x - z) / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.5e-71) || !(y <= 7e+138))
		tmp = Float64(2.0 + Float64(Float64(z / y) * -4.0));
	else
		tmp = Float64(4.0 * Float64(Float64(x - z) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -2.5e-71) || ~((y <= 7e+138)))
		tmp = 2.0 + ((z / y) * -4.0);
	else
		tmp = 4.0 * ((x - z) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.5e-71], N[Not[LessEqual[y, 7e+138]], $MachinePrecision]], N[(2.0 + N[(N[(z / y), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision], N[(4.0 * N[(N[(x - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.49999999999999999e-71 or 6.9999999999999996e138 < y

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. associate-*l/ 99.9%

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

      3. +-commutative 99.9%

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

      4. associate--l+ 99.9%

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

      5. +-commutative 99.9%

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

      6. distribute-lft-in 99.9%

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

      7. associate-+l+ 99.9%

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

      8. associate-*l/ 99.9%

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

      9. *-commutative 99.9%

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

      10. associate-*l* 99.9%

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

      11. metadata-eval 99.9%

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

      12. *-rgt-identity 99.9%

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

      13. *-inverses 99.9%

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

      14. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 83.0%

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

      1. *-commutative 83.0%

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

   7. Simplified 83.0%

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

   if -2.49999999999999999e-71 < y < 6.9999999999999996e138

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 87.8%

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

4. Final simplification 85.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{-71} \lor \neg \left(y \leq 7 \cdot 10^{+138}\right):\\ \;\;\;\;2 + \frac{z}{y} \cdot -4\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \frac{x - z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 80.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.1 \cdot 10^{+141}:\\ \;\;\;\;2\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{+139}:\\ \;\;\;\;4 \cdot \frac{x - z}{y}\\ \mathbf{else}:\\ \;\;\;\;2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -5.1e+141) 2.0 (if (<= y 2.05e+139) (* 4.0 (/ (- x z) y)) 2.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -5.1e+141) {
		tmp = 2.0;
	} else if (y <= 2.05e+139) {
		tmp = 4.0 * ((x - 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 (y <= (-5.1d+141)) then
        tmp = 2.0d0
    else if (y <= 2.05d+139) then
        tmp = 4.0d0 * ((x - 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 (y <= -5.1e+141) {
		tmp = 2.0;
	} else if (y <= 2.05e+139) {
		tmp = 4.0 * ((x - z) / y);
	} else {
		tmp = 2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -5.1e+141:
		tmp = 2.0
	elif y <= 2.05e+139:
		tmp = 4.0 * ((x - z) / y)
	else:
		tmp = 2.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -5.1e+141)
		tmp = 2.0;
	elseif (y <= 2.05e+139)
		tmp = Float64(4.0 * Float64(Float64(x - z) / y));
	else
		tmp = 2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -5.1e+141)
		tmp = 2.0;
	elseif (y <= 2.05e+139)
		tmp = 4.0 * ((x - z) / y);
	else
		tmp = 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -5.1e+141], 2.0, If[LessEqual[y, 2.05e+139], N[(4.0 * N[(N[(x - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], 2.0]]

Derivation

1. Split input into 2 regimes

2. if y < -5.0999999999999997e141 or 2.0500000000000001e139 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 82.0%

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

   if -5.0999999999999997e141 < y < 2.0500000000000001e139

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 80.5%

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

Alternative 8: 51.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{-73}:\\ \;\;\;\;2\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+138}:\\ \;\;\;\;x \cdot \frac{4}{y}\\ \mathbf{else}:\\ \;\;\;\;2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.3e-73) 2.0 (if (<= y 7e+138) (* x (/ 4.0 y)) 2.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.3e-73) {
		tmp = 2.0;
	} else if (y <= 7e+138) {
		tmp = 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 (y <= (-1.3d-73)) then
        tmp = 2.0d0
    else if (y <= 7d+138) then
        tmp = 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 (y <= -1.3e-73) {
		tmp = 2.0;
	} else if (y <= 7e+138) {
		tmp = x * (4.0 / y);
	} else {
		tmp = 2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.3e-73:
		tmp = 2.0
	elif y <= 7e+138:
		tmp = x * (4.0 / y)
	else:
		tmp = 2.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.3e-73)
		tmp = 2.0;
	elseif (y <= 7e+138)
		tmp = 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 (y <= -1.3e-73)
		tmp = 2.0;
	elseif (y <= 7e+138)
		tmp = x * (4.0 / y);
	else
		tmp = 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.3e-73], 2.0, If[LessEqual[y, 7e+138], N[(x * N[(4.0 / y), $MachinePrecision]), $MachinePrecision], 2.0]]

Derivation

1. Split input into 2 regimes

2. if y < -1.3e-73 or 6.9999999999999996e138 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 61.3%

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

   if -1.3e-73 < y < 6.9999999999999996e138

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 48.9%

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

      1. associate-*r/ 48.9%

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

      2. associate-*l/ 48.8%

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

      3. *-commutative 48.8%

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

   5. Simplified 48.8%

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

Alternative 9: 99.8% accurate, 1.4× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(N[(N[(x - z), $MachinePrecision] * N[(4.0 / 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. +-commutative 100.0%

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

   2. associate-*l/ 99.8%

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

   3. +-commutative 99.8%

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

   4. associate--l+ 99.8%

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

   5. +-commutative 99.8%

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

   6. distribute-lft-in 99.8%

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

   7. associate-+l+ 99.8%

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

   8. associate-*l/ 99.8%

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

   9. *-commutative 99.8%

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

   10. associate-*l* 99.8%

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

   11. metadata-eval 99.8%

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

   12. *-rgt-identity 99.8%

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

   13. *-inverses 99.8%

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

   14. metadata-eval 99.8%

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

3. Simplified 99.8%

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

5. Final simplification 99.8%

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

Alternative 10: 34.4% 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. Add Preprocessing

3. Taylor expanded in y around inf 35.1%

   \[\leadsto \color{blue}{2} \]
4. Add Preprocessing

Reproduce

herbie shell --seed 2024139 
(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)))