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

Percentage Accurate: 99.9% → 100.0%

Time: 7.2s

Alternatives: 8

Speedup: 1.4×

• 20.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ 2 + \frac{x - z}{y \cdot 0.25} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ 2.0 (/ (- x z) (* y 0.25))))

C

double code(double x, double y, double z) {
	return 2.0 + ((x - z) / (y * 0.25));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = 2.0d0 + ((x - z) / (y * 0.25d0))
end function

Java

public static double code(double x, double y, double z) {
	return 2.0 + ((x - z) / (y * 0.25));
}

Python

def code(x, y, z):
	return 2.0 + ((x - z) / (y * 0.25))

Julia

function code(x, y, z)
	return Float64(2.0 + Float64(Float64(x - z) / Float64(y * 0.25)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = 2.0 + ((x - z) / (y * 0.25));
end

Wolfram

code[x_, y_, z_] := N[(2.0 + N[(N[(x - z), $MachinePrecision] / N[(y * 0.25), $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%

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

3. Simplified 99.9%

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

   1. clear-num 99.9%

      \[\leadsto 2 + \color{blue}{\frac{1}{\frac{y}{4}}} \cdot \left(x - z\right) \]

   2. div-inv 99.9%

      \[\leadsto 2 + \frac{1}{\color{blue}{y \cdot \frac{1}{4}}} \cdot \left(x - z\right) \]

   3. metadata-eval 99.9%

      \[\leadsto 2 + \frac{1}{y \cdot \color{blue}{0.25}} \cdot \left(x - z\right) \]

   4. associate-*l/ 100.0%

      \[\leadsto 2 + \color{blue}{\frac{1 \cdot \left(x - z\right)}{y \cdot 0.25}} \]

   5. *-un-lft-identity 100.0%

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

6. Applied egg-rr 100.0%

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

7. Final simplification 100.0%

   \[\leadsto 2 + \frac{x - z}{y \cdot 0.25} \]
8. Add Preprocessing

Alternative 2: 57.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + \frac{x \cdot 4}{y}\\ t_1 := 1 + z \cdot \frac{-4}{y}\\ \mathbf{if}\;z \leq -64000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.05 \cdot 10^{-56}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-165}:\\ \;\;\;\;2\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{-259}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 5.7 \cdot 10^{-84}:\\ \;\;\;\;2\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+88}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ 1.0 (/ (* x 4.0) y))) (t_1 (+ 1.0 (* z (/ -4.0 y)))))
   (if (<= z -64000.0)
     t_1
     (if (<= z -2.05e-56)
       t_0
       (if (<= z -2.9e-165)
         2.0
         (if (<= z -3.7e-259)
           t_0
           (if (<= z 5.7e-84) 2.0 (if (<= z 5e+88) t_0 t_1))))))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 + ((x * 4.0) / y);
	double t_1 = 1.0 + (z * (-4.0 / y));
	double tmp;
	if (z <= -64000.0) {
		tmp = t_1;
	} else if (z <= -2.05e-56) {
		tmp = t_0;
	} else if (z <= -2.9e-165) {
		tmp = 2.0;
	} else if (z <= -3.7e-259) {
		tmp = t_0;
	} else if (z <= 5.7e-84) {
		tmp = 2.0;
	} else if (z <= 5e+88) {
		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 + ((x * 4.0d0) / y)
    t_1 = 1.0d0 + (z * ((-4.0d0) / y))
    if (z <= (-64000.0d0)) then
        tmp = t_1
    else if (z <= (-2.05d-56)) then
        tmp = t_0
    else if (z <= (-2.9d-165)) then
        tmp = 2.0d0
    else if (z <= (-3.7d-259)) then
        tmp = t_0
    else if (z <= 5.7d-84) then
        tmp = 2.0d0
    else if (z <= 5d+88) 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 + ((x * 4.0) / y);
	double t_1 = 1.0 + (z * (-4.0 / y));
	double tmp;
	if (z <= -64000.0) {
		tmp = t_1;
	} else if (z <= -2.05e-56) {
		tmp = t_0;
	} else if (z <= -2.9e-165) {
		tmp = 2.0;
	} else if (z <= -3.7e-259) {
		tmp = t_0;
	} else if (z <= 5.7e-84) {
		tmp = 2.0;
	} else if (z <= 5e+88) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 + ((x * 4.0) / y)
	t_1 = 1.0 + (z * (-4.0 / y))
	tmp = 0
	if z <= -64000.0:
		tmp = t_1
	elif z <= -2.05e-56:
		tmp = t_0
	elif z <= -2.9e-165:
		tmp = 2.0
	elif z <= -3.7e-259:
		tmp = t_0
	elif z <= 5.7e-84:
		tmp = 2.0
	elif z <= 5e+88:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 + Float64(Float64(x * 4.0) / y))
	t_1 = Float64(1.0 + Float64(z * Float64(-4.0 / y)))
	tmp = 0.0
	if (z <= -64000.0)
		tmp = t_1;
	elseif (z <= -2.05e-56)
		tmp = t_0;
	elseif (z <= -2.9e-165)
		tmp = 2.0;
	elseif (z <= -3.7e-259)
		tmp = t_0;
	elseif (z <= 5.7e-84)
		tmp = 2.0;
	elseif (z <= 5e+88)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 + ((x * 4.0) / y);
	t_1 = 1.0 + (z * (-4.0 / y));
	tmp = 0.0;
	if (z <= -64000.0)
		tmp = t_1;
	elseif (z <= -2.05e-56)
		tmp = t_0;
	elseif (z <= -2.9e-165)
		tmp = 2.0;
	elseif (z <= -3.7e-259)
		tmp = t_0;
	elseif (z <= 5.7e-84)
		tmp = 2.0;
	elseif (z <= 5e+88)
		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[(x * 4.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(1.0 + N[(z * N[(-4.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -64000.0], t$95$1, If[LessEqual[z, -2.05e-56], t$95$0, If[LessEqual[z, -2.9e-165], 2.0, If[LessEqual[z, -3.7e-259], t$95$0, If[LessEqual[z, 5.7e-84], 2.0, If[LessEqual[z, 5e+88], t$95$0, t$95$1]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -64000 or 4.99999999999999997e88 < 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 74.4%

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

      1. associate-*r/ 74.4%

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

      2. metadata-eval 74.4%

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

      3. associate-*r* 74.4%

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

      4. neg-mul-1 74.4%

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

      5. associate-*l/ 74.3%

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

      6. distribute-rgt-neg-out 74.3%

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

      7. *-commutative 74.3%

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

      8. distribute-rgt-neg-in 74.3%

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

      9. distribute-neg-frac 74.3%

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

      10. metadata-eval 74.3%

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

   5. Simplified 74.3%

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

   if -64000 < z < -2.0500000000000001e-56 or -2.9e-165 < z < -3.69999999999999991e-259 or 5.7e-84 < z < 4.99999999999999997e88

   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 60.3%

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

      1. associate-*r/ 60.3%

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

   5. Simplified 60.3%

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

   if -2.0500000000000001e-56 < z < -2.9e-165 or -3.69999999999999991e-259 < z < 5.7e-84

   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 68.5%

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

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -64000:\\ \;\;\;\;1 + z \cdot \frac{-4}{y}\\ \mathbf{elif}\;z \leq -2.05 \cdot 10^{-56}:\\ \;\;\;\;1 + \frac{x \cdot 4}{y}\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-165}:\\ \;\;\;\;2\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{-259}:\\ \;\;\;\;1 + \frac{x \cdot 4}{y}\\ \mathbf{elif}\;z \leq 5.7 \cdot 10^{-84}:\\ \;\;\;\;2\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+88}:\\ \;\;\;\;1 + \frac{x \cdot 4}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + z \cdot \frac{-4}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 57.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + \frac{x \cdot 4}{y}\\ t_1 := 1 + \frac{z \cdot -4}{y}\\ \mathbf{if}\;z \leq -116000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -6.3 \cdot 10^{-56}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-165}:\\ \;\;\;\;2\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-262}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1.46 \cdot 10^{-83}:\\ \;\;\;\;2\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+88}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ 1.0 (/ (* x 4.0) y))) (t_1 (+ 1.0 (/ (* z -4.0) y))))
   (if (<= z -116000.0)
     t_1
     (if (<= z -6.3e-56)
       t_0
       (if (<= z -6.2e-165)
         2.0
         (if (<= z -1.4e-262)
           t_0
           (if (<= z 1.46e-83) 2.0 (if (<= z 8.5e+88) t_0 t_1))))))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 + ((x * 4.0) / y);
	double t_1 = 1.0 + ((z * -4.0) / y);
	double tmp;
	if (z <= -116000.0) {
		tmp = t_1;
	} else if (z <= -6.3e-56) {
		tmp = t_0;
	} else if (z <= -6.2e-165) {
		tmp = 2.0;
	} else if (z <= -1.4e-262) {
		tmp = t_0;
	} else if (z <= 1.46e-83) {
		tmp = 2.0;
	} else if (z <= 8.5e+88) {
		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 + ((x * 4.0d0) / y)
    t_1 = 1.0d0 + ((z * (-4.0d0)) / y)
    if (z <= (-116000.0d0)) then
        tmp = t_1
    else if (z <= (-6.3d-56)) then
        tmp = t_0
    else if (z <= (-6.2d-165)) then
        tmp = 2.0d0
    else if (z <= (-1.4d-262)) then
        tmp = t_0
    else if (z <= 1.46d-83) then
        tmp = 2.0d0
    else if (z <= 8.5d+88) 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 + ((x * 4.0) / y);
	double t_1 = 1.0 + ((z * -4.0) / y);
	double tmp;
	if (z <= -116000.0) {
		tmp = t_1;
	} else if (z <= -6.3e-56) {
		tmp = t_0;
	} else if (z <= -6.2e-165) {
		tmp = 2.0;
	} else if (z <= -1.4e-262) {
		tmp = t_0;
	} else if (z <= 1.46e-83) {
		tmp = 2.0;
	} else if (z <= 8.5e+88) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 + ((x * 4.0) / y)
	t_1 = 1.0 + ((z * -4.0) / y)
	tmp = 0
	if z <= -116000.0:
		tmp = t_1
	elif z <= -6.3e-56:
		tmp = t_0
	elif z <= -6.2e-165:
		tmp = 2.0
	elif z <= -1.4e-262:
		tmp = t_0
	elif z <= 1.46e-83:
		tmp = 2.0
	elif z <= 8.5e+88:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 + Float64(Float64(x * 4.0) / y))
	t_1 = Float64(1.0 + Float64(Float64(z * -4.0) / y))
	tmp = 0.0
	if (z <= -116000.0)
		tmp = t_1;
	elseif (z <= -6.3e-56)
		tmp = t_0;
	elseif (z <= -6.2e-165)
		tmp = 2.0;
	elseif (z <= -1.4e-262)
		tmp = t_0;
	elseif (z <= 1.46e-83)
		tmp = 2.0;
	elseif (z <= 8.5e+88)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 + ((x * 4.0) / y);
	t_1 = 1.0 + ((z * -4.0) / y);
	tmp = 0.0;
	if (z <= -116000.0)
		tmp = t_1;
	elseif (z <= -6.3e-56)
		tmp = t_0;
	elseif (z <= -6.2e-165)
		tmp = 2.0;
	elseif (z <= -1.4e-262)
		tmp = t_0;
	elseif (z <= 1.46e-83)
		tmp = 2.0;
	elseif (z <= 8.5e+88)
		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[(x * 4.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(1.0 + N[(N[(z * -4.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -116000.0], t$95$1, If[LessEqual[z, -6.3e-56], t$95$0, If[LessEqual[z, -6.2e-165], 2.0, If[LessEqual[z, -1.4e-262], t$95$0, If[LessEqual[z, 1.46e-83], 2.0, If[LessEqual[z, 8.5e+88], t$95$0, t$95$1]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -116000 or 8.5000000000000005e88 < 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 74.4%

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

      1. *-commutative 74.4%

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

      2. associate-*l/ 74.4%

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

   5. Simplified 74.4%

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

   if -116000 < z < -6.2999999999999997e-56 or -6.19999999999999992e-165 < z < -1.39999999999999988e-262 or 1.4600000000000001e-83 < z < 8.5000000000000005e88

   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 60.3%

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

      1. associate-*r/ 60.3%

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

   5. Simplified 60.3%

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

   if -6.2999999999999997e-56 < z < -6.19999999999999992e-165 or -1.39999999999999988e-262 < z < 1.4600000000000001e-83

   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 68.5%

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

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -116000:\\ \;\;\;\;1 + \frac{z \cdot -4}{y}\\ \mathbf{elif}\;z \leq -6.3 \cdot 10^{-56}:\\ \;\;\;\;1 + \frac{x \cdot 4}{y}\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-165}:\\ \;\;\;\;2\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-262}:\\ \;\;\;\;1 + \frac{x \cdot 4}{y}\\ \mathbf{elif}\;z \leq 1.46 \cdot 10^{-83}:\\ \;\;\;\;2\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+88}:\\ \;\;\;\;1 + \frac{x \cdot 4}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{z \cdot -4}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 81.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{+163} \lor \neg \left(x \leq 1.4 \cdot 10^{+141}\right) \land \left(x \leq 3.5 \cdot 10^{+170} \lor \neg \left(x \leq 4.2 \cdot 10^{+187}\right)\right):\\ \;\;\;\;1 + \frac{x \cdot 4}{y}\\ \mathbf{else}:\\ \;\;\;\;2 + -4 \cdot \frac{z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -5.8e+163)
         (and (not (<= x 1.4e+141))
              (or (<= x 3.5e+170) (not (<= x 4.2e+187)))))
   (+ 1.0 (/ (* x 4.0) y))
   (+ 2.0 (* -4.0 (/ z y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5.8e+163) || (!(x <= 1.4e+141) && ((x <= 3.5e+170) || !(x <= 4.2e+187)))) {
		tmp = 1.0 + ((x * 4.0) / 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 <= (-5.8d+163)) .or. (.not. (x <= 1.4d+141)) .and. (x <= 3.5d+170) .or. (.not. (x <= 4.2d+187))) then
        tmp = 1.0d0 + ((x * 4.0d0) / 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 <= -5.8e+163) || (!(x <= 1.4e+141) && ((x <= 3.5e+170) || !(x <= 4.2e+187)))) {
		tmp = 1.0 + ((x * 4.0) / y);
	} else {
		tmp = 2.0 + (-4.0 * (z / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -5.8e+163) or (not (x <= 1.4e+141) and ((x <= 3.5e+170) or not (x <= 4.2e+187))):
		tmp = 1.0 + ((x * 4.0) / y)
	else:
		tmp = 2.0 + (-4.0 * (z / y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -5.8e+163) || (!(x <= 1.4e+141) && ((x <= 3.5e+170) || !(x <= 4.2e+187))))
		tmp = Float64(1.0 + Float64(Float64(x * 4.0) / 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 <= -5.8e+163) || (~((x <= 1.4e+141)) && ((x <= 3.5e+170) || ~((x <= 4.2e+187)))))
		tmp = 1.0 + ((x * 4.0) / y);
	else
		tmp = 2.0 + (-4.0 * (z / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -5.8e+163], And[N[Not[LessEqual[x, 1.4e+141]], $MachinePrecision], Or[LessEqual[x, 3.5e+170], N[Not[LessEqual[x, 4.2e+187]], $MachinePrecision]]]], N[(1.0 + N[(N[(x * 4.0), $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 < -5.79999999999999996e163 or 1.39999999999999996e141 < x < 3.50000000000000005e170 or 4.2e187 < x

   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 87.1%

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

      1. associate-*r/ 87.1%

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

   5. Simplified 87.1%

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

   if -5.79999999999999996e163 < x < 1.39999999999999996e141 or 3.50000000000000005e170 < x < 4.2e187

   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 99.9%

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

      5. associate-+r+ 99.9%

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

   3. Simplified 99.9%

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

      1. clear-num 99.9%

         \[\leadsto 2 + \color{blue}{\frac{1}{\frac{y}{4}}} \cdot \left(x - z\right) \]

      2. div-inv 99.9%

         \[\leadsto 2 + \frac{1}{\color{blue}{y \cdot \frac{1}{4}}} \cdot \left(x - z\right) \]

      3. metadata-eval 99.9%

         \[\leadsto 2 + \frac{1}{y \cdot \color{blue}{0.25}} \cdot \left(x - z\right) \]

      4. associate-*l/ 100.0%

         \[\leadsto 2 + \color{blue}{\frac{1 \cdot \left(x - z\right)}{y \cdot 0.25}} \]

      5. *-un-lft-identity 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in x around 0 85.4%

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

4. Final simplification 85.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{+163} \lor \neg \left(x \leq 1.4 \cdot 10^{+141}\right) \land \left(x \leq 3.5 \cdot 10^{+170} \lor \neg \left(x \leq 4.2 \cdot 10^{+187}\right)\right):\\ \;\;\;\;1 + \frac{x \cdot 4}{y}\\ \mathbf{else}:\\ \;\;\;\;2 + -4 \cdot \frac{z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 55.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{-17} \lor \neg \left(z \leq 1.35 \cdot 10^{+14}\right):\\ \;\;\;\;1 + z \cdot \frac{-4}{y}\\ \mathbf{else}:\\ \;\;\;\;2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.55e-17) (not (<= z 1.35e+14))) (+ 1.0 (* z (/ -4.0 y))) 2.0))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.55e-17) || !(z <= 1.35e+14)) {
		tmp = 1.0 + (z * (-4.0 / y));
	} else {
		tmp = 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-1.55d-17)) .or. (.not. (z <= 1.35d+14))) then
        tmp = 1.0d0 + (z * ((-4.0d0) / y))
    else
        tmp = 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.55e-17) || !(z <= 1.35e+14)) {
		tmp = 1.0 + (z * (-4.0 / y));
	} else {
		tmp = 2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.55e-17) or not (z <= 1.35e+14):
		tmp = 1.0 + (z * (-4.0 / y))
	else:
		tmp = 2.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.55e-17) || !(z <= 1.35e+14))
		tmp = Float64(1.0 + Float64(z * Float64(-4.0 / y)));
	else
		tmp = 2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.55e-17) || ~((z <= 1.35e+14)))
		tmp = 1.0 + (z * (-4.0 / y));
	else
		tmp = 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.55e-17], N[Not[LessEqual[z, 1.35e+14]], $MachinePrecision]], N[(1.0 + N[(z * N[(-4.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 2.0]

Derivation

1. Split input into 2 regimes

2. if z < -1.5499999999999999e-17 or 1.35e14 < 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 68.5%

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

      1. associate-*r/ 68.5%

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

      2. metadata-eval 68.5%

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

      3. associate-*r* 68.5%

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

      4. neg-mul-1 68.5%

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

      5. associate-*l/ 68.4%

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

      6. distribute-rgt-neg-out 68.4%

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

      7. *-commutative 68.4%

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

      8. distribute-rgt-neg-in 68.4%

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

      9. distribute-neg-frac 68.4%

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

      10. metadata-eval 68.4%

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

   5. Simplified 68.4%

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

   if -1.5499999999999999e-17 < z < 1.35e14

   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 53.8%

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

4. Final simplification 61.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{-17} \lor \neg \left(z \leq 1.35 \cdot 10^{+14}\right):\\ \;\;\;\;1 + z \cdot \frac{-4}{y}\\ \mathbf{else}:\\ \;\;\;\;2\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 86.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -96000 \lor \neg \left(z \leq 5.3 \cdot 10^{+88}\right):\\ \;\;\;\;2 + -4 \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;2 + 4 \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -96000.0) (not (<= z 5.3e+88)))
   (+ 2.0 (* -4.0 (/ z y)))
   (+ 2.0 (* 4.0 (/ x y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -96000.0) || !(z <= 5.3e+88)) {
		tmp = 2.0 + (-4.0 * (z / y));
	} else {
		tmp = 2.0 + (4.0 * (x / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-96000.0d0)) .or. (.not. (z <= 5.3d+88))) then
        tmp = 2.0d0 + ((-4.0d0) * (z / y))
    else
        tmp = 2.0d0 + (4.0d0 * (x / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -96000.0) || !(z <= 5.3e+88)) {
		tmp = 2.0 + (-4.0 * (z / y));
	} else {
		tmp = 2.0 + (4.0 * (x / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -96000.0) or not (z <= 5.3e+88):
		tmp = 2.0 + (-4.0 * (z / y))
	else:
		tmp = 2.0 + (4.0 * (x / y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -96000.0) || !(z <= 5.3e+88))
		tmp = Float64(2.0 + Float64(-4.0 * Float64(z / y)));
	else
		tmp = Float64(2.0 + Float64(4.0 * Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -96000.0) || ~((z <= 5.3e+88)))
		tmp = 2.0 + (-4.0 * (z / y));
	else
		tmp = 2.0 + (4.0 * (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -96000.0], N[Not[LessEqual[z, 5.3e+88]], $MachinePrecision]], N[(2.0 + N[(-4.0 * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 + N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -96000 or 5.29999999999999987e88 < 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/ 99.8%

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

      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%

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

   3. Simplified 99.9%

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

      1. clear-num 99.9%

         \[\leadsto 2 + \color{blue}{\frac{1}{\frac{y}{4}}} \cdot \left(x - z\right) \]

      2. div-inv 99.9%

         \[\leadsto 2 + \frac{1}{\color{blue}{y \cdot \frac{1}{4}}} \cdot \left(x - z\right) \]

      3. metadata-eval 99.9%

         \[\leadsto 2 + \frac{1}{y \cdot \color{blue}{0.25}} \cdot \left(x - z\right) \]

      4. associate-*l/ 100.0%

         \[\leadsto 2 + \color{blue}{\frac{1 \cdot \left(x - z\right)}{y \cdot 0.25}} \]

      5. *-un-lft-identity 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in x around 0 86.9%

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

   if -96000 < z < 5.29999999999999987e88

   1. Initial program 100.0%

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

      1. associate-*l/ 99.8%

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

      2. +-commutative 99.8%

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

      3. associate--l+ 99.8%

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

      4. distribute-lft-in 99.8%

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

      5. associate-+r+ 99.8%

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

   3. Simplified 99.8%

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

      1. clear-num 99.8%

         \[\leadsto 2 + \color{blue}{\frac{1}{\frac{y}{4}}} \cdot \left(x - z\right) \]

      2. div-inv 99.8%

         \[\leadsto 2 + \frac{1}{\color{blue}{y \cdot \frac{1}{4}}} \cdot \left(x - z\right) \]

      3. metadata-eval 99.8%

         \[\leadsto 2 + \frac{1}{y \cdot \color{blue}{0.25}} \cdot \left(x - z\right) \]

      4. associate-*l/ 100.0%

         \[\leadsto 2 + \color{blue}{\frac{1 \cdot \left(x - z\right)}{y \cdot 0.25}} \]

      5. *-un-lft-identity 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in x around inf 92.7%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -96000 \lor \neg \left(z \leq 5.3 \cdot 10^{+88}\right):\\ \;\;\;\;2 + -4 \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;2 + 4 \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 99.8% accurate, 1.4× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = 2.0d0 + ((x - z) * (4.0d0 / y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. associate-*l/ 99.8%

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

   2. +-commutative 99.8%

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

   3. associate--l+ 99.8%

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

   4. distribute-lft-in 99.8%

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

   5. associate-+r+ 99.9%

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

3. Simplified 99.9%

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

5. Final simplification 99.9%

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

Alternative 8: 33.7% 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 34.6%

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

4. Final simplification 34.6%

   \[\leadsto 2 \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024031 
(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)))