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

Percentage Accurate: 99.8% → 100.0%

Time: 6.6s

Alternatives: 12

Speedup: 1.4×

• 21.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.8% 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

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

FPCore

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

C

double code(double x, double y, double z) {
	return ((x - z) / (y * 0.25)) + 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) / (y * 0.25d0)) + 2.0d0
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(N[(N[(x - z), $MachinePrecision] / N[(y * 0.25), $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/ 99.4%

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

   3. +-commutative 99.4%

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

   4. associate--l+ 99.4%

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

   5. +-commutative 99.4%

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

   6. distribute-lft-in 99.4%

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

   7. associate-+l+ 99.4%

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

   8. associate-*l/ 99.4%

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

   9. *-commutative 99.4%

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

   10. associate-*l* 99.4%

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

   11. metadata-eval 99.4%

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

   12. *-rgt-identity 99.4%

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

   13. *-inverses 99.4%

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

   14. metadata-eval 99.4%

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

3. Simplified 99.4%

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

   1. clear-num 99.4%

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

   2. div-inv 99.4%

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

   3. metadata-eval 99.4%

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

   4. associate-*l/ 100.0%

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

   5. *-un-lft-identity 100.0%

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

6. Applied egg-rr 100.0%

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

Alternative 2: 54.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+119}:\\ \;\;\;\;2\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-184}:\\ \;\;\;\;-4 \cdot \frac{z}{y} + 1\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+91}:\\ \;\;\;\;1 + \frac{x \cdot 4}{y}\\ \mathbf{else}:\\ \;\;\;\;2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3.4e+119)
   2.0
   (if (<= y 2.3e-184)
     (+ (* -4.0 (/ z y)) 1.0)
     (if (<= y 1.35e+91) (+ 1.0 (/ (* x 4.0) y)) 2.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.4e+119) {
		tmp = 2.0;
	} else if (y <= 2.3e-184) {
		tmp = (-4.0 * (z / y)) + 1.0;
	} else if (y <= 1.35e+91) {
		tmp = 1.0 + ((x * 4.0) / y);
	} else {
		tmp = 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-3.4d+119)) then
        tmp = 2.0d0
    else if (y <= 2.3d-184) then
        tmp = ((-4.0d0) * (z / y)) + 1.0d0
    else if (y <= 1.35d+91) then
        tmp = 1.0d0 + ((x * 4.0d0) / y)
    else
        tmp = 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.4e+119) {
		tmp = 2.0;
	} else if (y <= 2.3e-184) {
		tmp = (-4.0 * (z / y)) + 1.0;
	} else if (y <= 1.35e+91) {
		tmp = 1.0 + ((x * 4.0) / y);
	} else {
		tmp = 2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -3.4e+119:
		tmp = 2.0
	elif y <= 2.3e-184:
		tmp = (-4.0 * (z / y)) + 1.0
	elif y <= 1.35e+91:
		tmp = 1.0 + ((x * 4.0) / y)
	else:
		tmp = 2.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3.4e+119)
		tmp = 2.0;
	elseif (y <= 2.3e-184)
		tmp = Float64(Float64(-4.0 * Float64(z / y)) + 1.0);
	elseif (y <= 1.35e+91)
		tmp = Float64(1.0 + Float64(Float64(x * 4.0) / y));
	else
		tmp = 2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -3.4e+119)
		tmp = 2.0;
	elseif (y <= 2.3e-184)
		tmp = (-4.0 * (z / y)) + 1.0;
	elseif (y <= 1.35e+91)
		tmp = 1.0 + ((x * 4.0) / y);
	else
		tmp = 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3.4e+119], 2.0, If[LessEqual[y, 2.3e-184], N[(N[(-4.0 * N[(z / y), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision], If[LessEqual[y, 1.35e+91], N[(1.0 + N[(N[(x * 4.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], 2.0]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.40000000000000013e119 or 1.35e91 < 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 78.9%

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

   if -3.40000000000000013e119 < y < 2.2999999999999999e-184

   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 53.5%

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

      1. *-commutative 53.5%

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

   5. Simplified 53.5%

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

   if 2.2999999999999999e-184 < y < 1.35e91

   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 59.3%

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

      1. *-commutative 59.3%

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

      2. associate-*l/ 59.3%

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

   5. Simplified 59.3%

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

4. Final simplification 63.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+119}:\\ \;\;\;\;2\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-184}:\\ \;\;\;\;-4 \cdot \frac{z}{y} + 1\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+91}:\\ \;\;\;\;1 + \frac{x \cdot 4}{y}\\ \mathbf{else}:\\ \;\;\;\;2\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 54.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+124}:\\ \;\;\;\;2\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-187}:\\ \;\;\;\;-4 \cdot \frac{z}{y} + 1\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+91}:\\ \;\;\;\;1 + x \cdot \frac{4}{y}\\ \mathbf{else}:\\ \;\;\;\;2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -8e+124)
   2.0
   (if (<= y 1.9e-187)
     (+ (* -4.0 (/ z y)) 1.0)
     (if (<= y 1.45e+91) (+ 1.0 (* x (/ 4.0 y))) 2.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -8e+124) {
		tmp = 2.0;
	} else if (y <= 1.9e-187) {
		tmp = (-4.0 * (z / y)) + 1.0;
	} else if (y <= 1.45e+91) {
		tmp = 1.0 + (x * (4.0 / y));
	} else {
		tmp = 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-8d+124)) then
        tmp = 2.0d0
    else if (y <= 1.9d-187) then
        tmp = ((-4.0d0) * (z / y)) + 1.0d0
    else if (y <= 1.45d+91) then
        tmp = 1.0d0 + (x * (4.0d0 / y))
    else
        tmp = 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -8e+124) {
		tmp = 2.0;
	} else if (y <= 1.9e-187) {
		tmp = (-4.0 * (z / y)) + 1.0;
	} else if (y <= 1.45e+91) {
		tmp = 1.0 + (x * (4.0 / y));
	} else {
		tmp = 2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -8e+124:
		tmp = 2.0
	elif y <= 1.9e-187:
		tmp = (-4.0 * (z / y)) + 1.0
	elif y <= 1.45e+91:
		tmp = 1.0 + (x * (4.0 / y))
	else:
		tmp = 2.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -8e+124)
		tmp = 2.0;
	elseif (y <= 1.9e-187)
		tmp = Float64(Float64(-4.0 * Float64(z / y)) + 1.0);
	elseif (y <= 1.45e+91)
		tmp = Float64(1.0 + Float64(x * Float64(4.0 / y)));
	else
		tmp = 2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -8e+124)
		tmp = 2.0;
	elseif (y <= 1.9e-187)
		tmp = (-4.0 * (z / y)) + 1.0;
	elseif (y <= 1.45e+91)
		tmp = 1.0 + (x * (4.0 / y));
	else
		tmp = 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -8e+124], 2.0, If[LessEqual[y, 1.9e-187], N[(N[(-4.0 * N[(z / y), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision], If[LessEqual[y, 1.45e+91], N[(1.0 + N[(x * N[(4.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 2.0]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.99999999999999959e124 or 1.45000000000000007e91 < 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 78.9%

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

   if -7.99999999999999959e124 < y < 1.90000000000000013e-187

   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 53.5%

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

      1. *-commutative 53.5%

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

   5. Simplified 53.5%

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

   if 1.90000000000000013e-187 < y < 1.45000000000000007e91

   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 59.3%

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

      1. associate-*r/ 59.3%

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

      2. associate-*l/ 59.1%

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

      3. *-commutative 59.1%

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

   5. Simplified 59.1%

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

4. Final simplification 63.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+124}:\\ \;\;\;\;2\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-187}:\\ \;\;\;\;-4 \cdot \frac{z}{y} + 1\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+91}:\\ \;\;\;\;1 + x \cdot \frac{4}{y}\\ \mathbf{else}:\\ \;\;\;\;2\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 54.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+118}:\\ \;\;\;\;2\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-190}:\\ \;\;\;\;1 + z \cdot \frac{-4}{y}\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+91}:\\ \;\;\;\;1 + x \cdot \frac{4}{y}\\ \mathbf{else}:\\ \;\;\;\;2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.2e+118)
   2.0
   (if (<= y 2e-190)
     (+ 1.0 (* z (/ -4.0 y)))
     (if (<= y 4.5e+91) (+ 1.0 (* x (/ 4.0 y))) 2.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.2e+118) {
		tmp = 2.0;
	} else if (y <= 2e-190) {
		tmp = 1.0 + (z * (-4.0 / y));
	} else if (y <= 4.5e+91) {
		tmp = 1.0 + (x * (4.0 / y));
	} else {
		tmp = 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-1.2d+118)) then
        tmp = 2.0d0
    else if (y <= 2d-190) then
        tmp = 1.0d0 + (z * ((-4.0d0) / y))
    else if (y <= 4.5d+91) then
        tmp = 1.0d0 + (x * (4.0d0 / y))
    else
        tmp = 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.2e+118) {
		tmp = 2.0;
	} else if (y <= 2e-190) {
		tmp = 1.0 + (z * (-4.0 / y));
	} else if (y <= 4.5e+91) {
		tmp = 1.0 + (x * (4.0 / y));
	} else {
		tmp = 2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.2e+118:
		tmp = 2.0
	elif y <= 2e-190:
		tmp = 1.0 + (z * (-4.0 / y))
	elif y <= 4.5e+91:
		tmp = 1.0 + (x * (4.0 / y))
	else:
		tmp = 2.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.2e+118)
		tmp = 2.0;
	elseif (y <= 2e-190)
		tmp = Float64(1.0 + Float64(z * Float64(-4.0 / y)));
	elseif (y <= 4.5e+91)
		tmp = Float64(1.0 + Float64(x * Float64(4.0 / y)));
	else
		tmp = 2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.2e+118)
		tmp = 2.0;
	elseif (y <= 2e-190)
		tmp = 1.0 + (z * (-4.0 / y));
	elseif (y <= 4.5e+91)
		tmp = 1.0 + (x * (4.0 / y));
	else
		tmp = 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.2e+118], 2.0, If[LessEqual[y, 2e-190], N[(1.0 + N[(z * N[(-4.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.5e+91], N[(1.0 + N[(x * N[(4.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 2.0]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.2e118 or 4.5e91 < 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 78.9%

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

   if -1.2e118 < y < 2e-190

   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 53.5%

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

      1. associate-*r/ 53.5%

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

      2. metadata-eval 53.5%

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

      3. associate-*r* 53.5%

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

      4. neg-mul-1 53.5%

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

      5. *-commutative 53.5%

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

      6. associate-*r/ 53.4%

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

      7. distribute-lft-neg-out 53.4%

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

      8. distribute-rgt-neg-in 53.4%

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

      9. distribute-neg-frac 53.4%

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

      10. metadata-eval 53.4%

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

   5. Simplified 53.4%

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

   if 2e-190 < y < 4.5e91

   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 59.3%

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

      1. associate-*r/ 59.3%

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

      2. associate-*l/ 59.1%

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

      3. *-commutative 59.1%

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

   5. Simplified 59.1%

      \[\leadsto 1 + \color{blue}{x \cdot \frac{4}{y}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 5: 54.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.9 \cdot 10^{+74}:\\ \;\;\;\;2\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-190}:\\ \;\;\;\;-4 \cdot \frac{z}{y}\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+91}:\\ \;\;\;\;1 + x \cdot \frac{4}{y}\\ \mathbf{else}:\\ \;\;\;\;2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -6.9e+74)
   2.0
   (if (<= y 9.5e-190)
     (* -4.0 (/ z y))
     (if (<= y 1.5e+91) (+ 1.0 (* x (/ 4.0 y))) 2.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -6.9e+74) {
		tmp = 2.0;
	} else if (y <= 9.5e-190) {
		tmp = -4.0 * (z / y);
	} else if (y <= 1.5e+91) {
		tmp = 1.0 + (x * (4.0 / y));
	} else {
		tmp = 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-6.9d+74)) then
        tmp = 2.0d0
    else if (y <= 9.5d-190) then
        tmp = (-4.0d0) * (z / y)
    else if (y <= 1.5d+91) then
        tmp = 1.0d0 + (x * (4.0d0 / y))
    else
        tmp = 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -6.9e+74) {
		tmp = 2.0;
	} else if (y <= 9.5e-190) {
		tmp = -4.0 * (z / y);
	} else if (y <= 1.5e+91) {
		tmp = 1.0 + (x * (4.0 / y));
	} else {
		tmp = 2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -6.9e+74:
		tmp = 2.0
	elif y <= 9.5e-190:
		tmp = -4.0 * (z / y)
	elif y <= 1.5e+91:
		tmp = 1.0 + (x * (4.0 / y))
	else:
		tmp = 2.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -6.9e+74)
		tmp = 2.0;
	elseif (y <= 9.5e-190)
		tmp = Float64(-4.0 * Float64(z / y));
	elseif (y <= 1.5e+91)
		tmp = Float64(1.0 + Float64(x * Float64(4.0 / y)));
	else
		tmp = 2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -6.9e+74)
		tmp = 2.0;
	elseif (y <= 9.5e-190)
		tmp = -4.0 * (z / y);
	elseif (y <= 1.5e+91)
		tmp = 1.0 + (x * (4.0 / y));
	else
		tmp = 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -6.9e+74], 2.0, If[LessEqual[y, 9.5e-190], N[(-4.0 * N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.5e+91], N[(1.0 + N[(x * N[(4.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 2.0]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.8999999999999996e74 or 1.50000000000000003e91 < 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 75.7%

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

   if -6.8999999999999996e74 < y < 9.50000000000000055e-190

   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 86.2%

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

      1. mul-1-neg 86.2%

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

      2. *-commutative 86.2%

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

      3. distribute-rgt-neg-in 86.2%

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

   5. Simplified 86.2%

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

   6. Taylor expanded in z around inf 52.9%

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

   if 9.50000000000000055e-190 < y < 1.50000000000000003e91

   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 59.3%

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

      1. associate-*r/ 59.3%

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

      2. associate-*l/ 59.1%

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

      3. *-commutative 59.1%

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

   5. Simplified 59.1%

      \[\leadsto 1 + \color{blue}{x \cdot \frac{4}{y}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 6: 53.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.12 \cdot 10^{+78}:\\ \;\;\;\;2\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{-184}:\\ \;\;\;\;-4 \cdot \frac{z}{y}\\ \mathbf{elif}\;y \leq 8.6 \cdot 10^{+91}:\\ \;\;\;\;4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.12e+78)
   2.0
   (if (<= y 5.6e-184)
     (* -4.0 (/ z y))
     (if (<= y 8.6e+91) (* 4.0 (/ x y)) 2.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.12e+78) {
		tmp = 2.0;
	} else if (y <= 5.6e-184) {
		tmp = -4.0 * (z / y);
	} else if (y <= 8.6e+91) {
		tmp = 4.0 * (x / 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 <= (-1.12d+78)) then
        tmp = 2.0d0
    else if (y <= 5.6d-184) then
        tmp = (-4.0d0) * (z / y)
    else if (y <= 8.6d+91) then
        tmp = 4.0d0 * (x / 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 <= -1.12e+78) {
		tmp = 2.0;
	} else if (y <= 5.6e-184) {
		tmp = -4.0 * (z / y);
	} else if (y <= 8.6e+91) {
		tmp = 4.0 * (x / y);
	} else {
		tmp = 2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.12e+78:
		tmp = 2.0
	elif y <= 5.6e-184:
		tmp = -4.0 * (z / y)
	elif y <= 8.6e+91:
		tmp = 4.0 * (x / y)
	else:
		tmp = 2.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.12e+78)
		tmp = 2.0;
	elseif (y <= 5.6e-184)
		tmp = Float64(-4.0 * Float64(z / y));
	elseif (y <= 8.6e+91)
		tmp = Float64(4.0 * Float64(x / y));
	else
		tmp = 2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.12e+78)
		tmp = 2.0;
	elseif (y <= 5.6e-184)
		tmp = -4.0 * (z / y);
	elseif (y <= 8.6e+91)
		tmp = 4.0 * (x / y);
	else
		tmp = 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.12e+78], 2.0, If[LessEqual[y, 5.6e-184], N[(-4.0 * N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.6e+91], N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision], 2.0]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.12e78 or 8.6000000000000001e91 < 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 75.7%

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

   if -1.12e78 < y < 5.5999999999999997e-184

   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 86.2%

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

      1. mul-1-neg 86.2%

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

      2. *-commutative 86.2%

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

      3. distribute-rgt-neg-in 86.2%

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

   5. Simplified 86.2%

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

   6. Taylor expanded in z around inf 52.9%

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

   if 5.5999999999999997e-184 < y < 8.6000000000000001e91

   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 88.9%

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

      1. mul-1-neg 88.9%

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

      2. *-commutative 88.9%

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

      3. distribute-rgt-neg-in 88.9%

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

   5. Simplified 88.8%

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

   6. Taylor expanded in x around inf 57.2%

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

Alternative 7: 84.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{+46} \lor \neg \left(x \leq 1.75 \cdot 10^{-106}\right):\\ \;\;\;\;2 + 4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;2 + -4 \cdot \frac{z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -7.5e+46) (not (<= x 1.75e-106)))
   (+ 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 <= -7.5e+46) || !(x <= 1.75e-106)) {
		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 <= (-7.5d+46)) .or. (.not. (x <= 1.75d-106))) 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 <= -7.5e+46) || !(x <= 1.75e-106)) {
		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 <= -7.5e+46) or not (x <= 1.75e-106):
		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 <= -7.5e+46) || !(x <= 1.75e-106))
		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 <= -7.5e+46) || ~((x <= 1.75e-106)))
		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, -7.5e+46], N[Not[LessEqual[x, 1.75e-106]], $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 < -7.5000000000000003e46 or 1.75e-106 < 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. +-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. Step-by-step derivation

      1. clear-num 99.8%

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

      2. div-inv 99.8%

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

      3. metadata-eval 99.8%

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

      4. associate-*l/ 100.0%

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

      5. *-un-lft-identity 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in x around inf 84.2%

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

   if -7.5000000000000003e46 < x < 1.75e-106

   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/ 99.0%

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

      3. +-commutative 99.0%

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

      4. associate--l+ 99.0%

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

      5. +-commutative 99.0%

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

      6. distribute-lft-in 99.0%

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

      7. associate-+l+ 99.0%

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

      8. associate-*l/ 99.0%

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

      9. *-commutative 99.0%

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

      10. associate-*l* 99.0%

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

      11. metadata-eval 99.0%

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

      12. *-rgt-identity 99.0%

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

      13. *-inverses 99.0%

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

      14. metadata-eval 99.0%

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

   3. Simplified 99.0%

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

      1. clear-num 99.0%

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

      2. div-inv 99.0%

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

      3. metadata-eval 99.0%

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

      4. associate-*l/ 100.0%

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

      5. *-un-lft-identity 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in x around 0 94.5%

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

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{+46} \lor \neg \left(x \leq 1.75 \cdot 10^{-106}\right):\\ \;\;\;\;2 + 4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;2 + -4 \cdot \frac{z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 81.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{+100} \lor \neg \left(x \leq 1.26 \cdot 10^{+61}\right):\\ \;\;\;\;1 + \frac{x \cdot 4}{y}\\ \mathbf{else}:\\ \;\;\;\;2 + -4 \cdot \frac{z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.45e+100) (not (<= x 1.26e+61)))
   (+ 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 <= -1.45e+100) || !(x <= 1.26e+61)) {
		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 <= (-1.45d+100)) .or. (.not. (x <= 1.26d+61))) 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 <= -1.45e+100) || !(x <= 1.26e+61)) {
		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 <= -1.45e+100) or not (x <= 1.26e+61):
		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 <= -1.45e+100) || !(x <= 1.26e+61))
		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 <= -1.45e+100) || ~((x <= 1.26e+61)))
		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, -1.45e+100], N[Not[LessEqual[x, 1.26e+61]], $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 < -1.45e100 or 1.2600000000000001e61 < 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 77.7%

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

      1. *-commutative 77.7%

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

      2. associate-*l/ 77.7%

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

   5. Simplified 77.7%

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

   if -1.45e100 < x < 1.2600000000000001e61

   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/ 99.2%

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

      3. +-commutative 99.2%

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

      4. associate--l+ 99.2%

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

      5. +-commutative 99.2%

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

      6. distribute-lft-in 99.2%

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

      7. associate-+l+ 99.2%

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

      8. associate-*l/ 99.2%

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

      9. *-commutative 99.2%

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

      10. associate-*l* 99.2%

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

      11. metadata-eval 99.2%

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

      12. *-rgt-identity 99.2%

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

      13. *-inverses 99.2%

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

      14. metadata-eval 99.2%

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

   3. Simplified 99.2%

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

      1. clear-num 99.2%

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

      2. div-inv 99.2%

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

      3. metadata-eval 99.2%

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

      4. associate-*l/ 100.0%

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

      5. *-un-lft-identity 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in x around 0 86.6%

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

4. Final simplification 83.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{+100} \lor \neg \left(x \leq 1.26 \cdot 10^{+61}\right):\\ \;\;\;\;1 + \frac{x \cdot 4}{y}\\ \mathbf{else}:\\ \;\;\;\;2 + -4 \cdot \frac{z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 54.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+75}:\\ \;\;\;\;2\\ \mathbf{elif}\;y \leq 1550000000000:\\ \;\;\;\;-4 \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -4e+75) 2.0 (if (<= y 1550000000000.0) (* -4.0 (/ z y)) 2.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -4e+75) {
		tmp = 2.0;
	} else if (y <= 1550000000000.0) {
		tmp = -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 (y <= (-4d+75)) then
        tmp = 2.0d0
    else if (y <= 1550000000000.0d0) then
        tmp = (-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 (y <= -4e+75) {
		tmp = 2.0;
	} else if (y <= 1550000000000.0) {
		tmp = -4.0 * (z / y);
	} else {
		tmp = 2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -4e+75:
		tmp = 2.0
	elif y <= 1550000000000.0:
		tmp = -4.0 * (z / y)
	else:
		tmp = 2.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -4e+75)
		tmp = 2.0;
	elseif (y <= 1550000000000.0)
		tmp = 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 (y <= -4e+75)
		tmp = 2.0;
	elseif (y <= 1550000000000.0)
		tmp = -4.0 * (z / y);
	else
		tmp = 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -4e+75], 2.0, If[LessEqual[y, 1550000000000.0], N[(-4.0 * N[(z / y), $MachinePrecision]), $MachinePrecision], 2.0]]

Derivation

1. Split input into 2 regimes

2. if y < -3.99999999999999971e75 or 1.55e12 < 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 70.4%

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

   if -3.99999999999999971e75 < y < 1.55e12

   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 87.1%

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

      1. mul-1-neg 87.1%

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

      2. *-commutative 87.1%

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

      3. distribute-rgt-neg-in 87.1%

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

   5. Simplified 87.0%

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

   6. Taylor expanded in z around inf 49.1%

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

Alternative 10: 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. +-commutative 100.0%

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

   2. associate-*l/ 99.4%

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

   3. +-commutative 99.4%

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

   4. associate--l+ 99.4%

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

   5. +-commutative 99.4%

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

   6. distribute-lft-in 99.4%

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

   7. associate-+l+ 99.4%

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

   8. associate-*l/ 99.4%

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

   9. *-commutative 99.4%

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

   10. associate-*l* 99.4%

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

   11. metadata-eval 99.4%

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

   12. *-rgt-identity 99.4%

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

   13. *-inverses 99.4%

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

   14. metadata-eval 99.4%

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

3. Simplified 99.4%

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

5. Final simplification 99.4%

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

Alternative 11: 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. Add Preprocessing

3. Taylor expanded in y around inf 36.8%

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

Alternative 12: 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. Add Preprocessing

3. Taylor expanded in z around inf 39.4%

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

   1. associate-*r/ 39.4%

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

   2. metadata-eval 39.4%

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

   3. associate-*r* 39.4%

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

   4. neg-mul-1 39.4%

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

   5. *-commutative 39.4%

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

   6. associate-*r/ 39.3%

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

   7. distribute-lft-neg-out 39.3%

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

   8. distribute-rgt-neg-in 39.3%

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

   9. distribute-neg-frac 39.3%

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

   10. metadata-eval 39.3%

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

5. Simplified 39.3%

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

6. Taylor expanded in z around 0 8.6%

   \[\leadsto \color{blue}{1} \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024106 
(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)))