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

Percentage Accurate: 99.9% → 99.9%

Time: 7.7s

Alternatives: 9

Speedup: 1.0×

• 21.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

Alternative 2: 53.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{z}{y} \cdot -4\\ t_1 := \frac{4 \cdot x}{y}\\ \mathbf{if}\;y \leq -9 \cdot 10^{+70}:\\ \;\;\;\;2\\ \mathbf{elif}\;y \leq -65:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{-94}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{-157}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+132}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (/ z y) -4.0)) (t_1 (/ (* 4.0 x) y)))
   (if (<= y -9e+70)
     2.0
     (if (<= y -65.0)
       t_1
       (if (<= y -1.2e-94)
         t_0
         (if (<= y 3.3e-157) t_1 (if (<= y 6.5e+132) t_0 2.0)))))))

C

double code(double x, double y, double z) {
	double t_0 = (z / y) * -4.0;
	double t_1 = (4.0 * x) / y;
	double tmp;
	if (y <= -9e+70) {
		tmp = 2.0;
	} else if (y <= -65.0) {
		tmp = t_1;
	} else if (y <= -1.2e-94) {
		tmp = t_0;
	} else if (y <= 3.3e-157) {
		tmp = t_1;
	} else if (y <= 6.5e+132) {
		tmp = t_0;
	} 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) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (z / y) * (-4.0d0)
    t_1 = (4.0d0 * x) / y
    if (y <= (-9d+70)) then
        tmp = 2.0d0
    else if (y <= (-65.0d0)) then
        tmp = t_1
    else if (y <= (-1.2d-94)) then
        tmp = t_0
    else if (y <= 3.3d-157) then
        tmp = t_1
    else if (y <= 6.5d+132) then
        tmp = t_0
    else
        tmp = 2.0d0
    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 t_1 = (4.0 * x) / y;
	double tmp;
	if (y <= -9e+70) {
		tmp = 2.0;
	} else if (y <= -65.0) {
		tmp = t_1;
	} else if (y <= -1.2e-94) {
		tmp = t_0;
	} else if (y <= 3.3e-157) {
		tmp = t_1;
	} else if (y <= 6.5e+132) {
		tmp = t_0;
	} else {
		tmp = 2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (z / y) * -4.0
	t_1 = (4.0 * x) / y
	tmp = 0
	if y <= -9e+70:
		tmp = 2.0
	elif y <= -65.0:
		tmp = t_1
	elif y <= -1.2e-94:
		tmp = t_0
	elif y <= 3.3e-157:
		tmp = t_1
	elif y <= 6.5e+132:
		tmp = t_0
	else:
		tmp = 2.0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(z / y) * -4.0)
	t_1 = Float64(Float64(4.0 * x) / y)
	tmp = 0.0
	if (y <= -9e+70)
		tmp = 2.0;
	elseif (y <= -65.0)
		tmp = t_1;
	elseif (y <= -1.2e-94)
		tmp = t_0;
	elseif (y <= 3.3e-157)
		tmp = t_1;
	elseif (y <= 6.5e+132)
		tmp = t_0;
	else
		tmp = 2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (z / y) * -4.0;
	t_1 = (4.0 * x) / y;
	tmp = 0.0;
	if (y <= -9e+70)
		tmp = 2.0;
	elseif (y <= -65.0)
		tmp = t_1;
	elseif (y <= -1.2e-94)
		tmp = t_0;
	elseif (y <= 3.3e-157)
		tmp = t_1;
	elseif (y <= 6.5e+132)
		tmp = t_0;
	else
		tmp = 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(z / y), $MachinePrecision] * -4.0), $MachinePrecision]}, Block[{t$95$1 = N[(N[(4.0 * x), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[y, -9e+70], 2.0, If[LessEqual[y, -65.0], t$95$1, If[LessEqual[y, -1.2e-94], t$95$0, If[LessEqual[y, 3.3e-157], t$95$1, If[LessEqual[y, 6.5e+132], t$95$0, 2.0]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.9999999999999999e70 or 6.4999999999999994e132 < 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 68.7%

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

   if -8.9999999999999999e70 < y < -65 or -1.2e-94 < y < 3.29999999999999999e-157

   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 70.0%

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

      1. associate-*r/ 70.0%

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

   5. Simplified 70.0%

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

   if -65 < y < -1.2e-94 or 3.29999999999999999e-157 < y < 6.4999999999999994e132

   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 56.4%

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

      1. *-commutative 56.4%

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

   5. Simplified 56.4%

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

Alternative 3: 53.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{z}{y} \cdot -4\\ t_1 := x \cdot \frac{4}{y}\\ \mathbf{if}\;y \leq -8.6 \cdot 10^{+70}:\\ \;\;\;\;2\\ \mathbf{elif}\;y \leq -30000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-94}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{-157}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.45 \cdot 10^{+132}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (/ z y) -4.0)) (t_1 (* x (/ 4.0 y))))
   (if (<= y -8.6e+70)
     2.0
     (if (<= y -30000.0)
       t_1
       (if (<= y -1.7e-94)
         t_0
         (if (<= y 8.8e-157) t_1 (if (<= y 2.45e+132) t_0 2.0)))))))

C

double code(double x, double y, double z) {
	double t_0 = (z / y) * -4.0;
	double t_1 = x * (4.0 / y);
	double tmp;
	if (y <= -8.6e+70) {
		tmp = 2.0;
	} else if (y <= -30000.0) {
		tmp = t_1;
	} else if (y <= -1.7e-94) {
		tmp = t_0;
	} else if (y <= 8.8e-157) {
		tmp = t_1;
	} else if (y <= 2.45e+132) {
		tmp = t_0;
	} 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) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (z / y) * (-4.0d0)
    t_1 = x * (4.0d0 / y)
    if (y <= (-8.6d+70)) then
        tmp = 2.0d0
    else if (y <= (-30000.0d0)) then
        tmp = t_1
    else if (y <= (-1.7d-94)) then
        tmp = t_0
    else if (y <= 8.8d-157) then
        tmp = t_1
    else if (y <= 2.45d+132) then
        tmp = t_0
    else
        tmp = 2.0d0
    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 t_1 = x * (4.0 / y);
	double tmp;
	if (y <= -8.6e+70) {
		tmp = 2.0;
	} else if (y <= -30000.0) {
		tmp = t_1;
	} else if (y <= -1.7e-94) {
		tmp = t_0;
	} else if (y <= 8.8e-157) {
		tmp = t_1;
	} else if (y <= 2.45e+132) {
		tmp = t_0;
	} else {
		tmp = 2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (z / y) * -4.0
	t_1 = x * (4.0 / y)
	tmp = 0
	if y <= -8.6e+70:
		tmp = 2.0
	elif y <= -30000.0:
		tmp = t_1
	elif y <= -1.7e-94:
		tmp = t_0
	elif y <= 8.8e-157:
		tmp = t_1
	elif y <= 2.45e+132:
		tmp = t_0
	else:
		tmp = 2.0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(z / y) * -4.0)
	t_1 = Float64(x * Float64(4.0 / y))
	tmp = 0.0
	if (y <= -8.6e+70)
		tmp = 2.0;
	elseif (y <= -30000.0)
		tmp = t_1;
	elseif (y <= -1.7e-94)
		tmp = t_0;
	elseif (y <= 8.8e-157)
		tmp = t_1;
	elseif (y <= 2.45e+132)
		tmp = t_0;
	else
		tmp = 2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (z / y) * -4.0;
	t_1 = x * (4.0 / y);
	tmp = 0.0;
	if (y <= -8.6e+70)
		tmp = 2.0;
	elseif (y <= -30000.0)
		tmp = t_1;
	elseif (y <= -1.7e-94)
		tmp = t_0;
	elseif (y <= 8.8e-157)
		tmp = t_1;
	elseif (y <= 2.45e+132)
		tmp = t_0;
	else
		tmp = 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(z / y), $MachinePrecision] * -4.0), $MachinePrecision]}, Block[{t$95$1 = N[(x * N[(4.0 / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -8.6e+70], 2.0, If[LessEqual[y, -30000.0], t$95$1, If[LessEqual[y, -1.7e-94], t$95$0, If[LessEqual[y, 8.8e-157], t$95$1, If[LessEqual[y, 2.45e+132], t$95$0, 2.0]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.6000000000000002e70 or 2.4500000000000001e132 < 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 68.7%

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

   if -8.6000000000000002e70 < y < -3e4 or -1.6999999999999999e-94 < y < 8.80000000000000041e-157

   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 70.0%

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

      1. associate-*r/ 70.0%

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

      2. associate-*l/ 69.9%

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

      3. *-commutative 69.9%

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

   5. Simplified 69.9%

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

   if -3e4 < y < -1.6999999999999999e-94 or 8.80000000000000041e-157 < y < 2.4500000000000001e132

   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 56.4%

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

      1. *-commutative 56.4%

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

   5. Simplified 56.4%

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

Alternative 4: 85.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{+82} \lor \neg \left(y \leq 2.4 \cdot 10^{+132}\right):\\ \;\;\;\;2 + 4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \frac{x - z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -5.2e+82) (not (<= y 2.4e+132)))
   (+ 2.0 (* 4.0 (/ x y)))
   (* 4.0 (/ (- x z) y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -5.2e+82) || !(y <= 2.4e+132)) {
		tmp = 2.0 + (4.0 * (x / y));
	} 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 <= (-5.2d+82)) .or. (.not. (y <= 2.4d+132))) then
        tmp = 2.0d0 + (4.0d0 * (x / y))
    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 <= -5.2e+82) || !(y <= 2.4e+132)) {
		tmp = 2.0 + (4.0 * (x / y));
	} else {
		tmp = 4.0 * ((x - z) / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -5.2e+82) or not (y <= 2.4e+132):
		tmp = 2.0 + (4.0 * (x / y))
	else:
		tmp = 4.0 * ((x - z) / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -5.2e+82) || !(y <= 2.4e+132))
		tmp = Float64(2.0 + Float64(4.0 * Float64(x / y)));
	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 <= -5.2e+82) || ~((y <= 2.4e+132)))
		tmp = 2.0 + (4.0 * (x / y));
	else
		tmp = 4.0 * ((x - z) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -5.2e+82], N[Not[LessEqual[y, 2.4e+132]], $MachinePrecision]], N[(2.0 + N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(4.0 * N[(N[(x - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.1999999999999997e82 or 2.4000000000000001e132 < 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 99.8%

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

      7. associate-+l+ 99.9%

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

      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 z around 0 87.9%

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

   if -5.1999999999999997e82 < y < 2.4000000000000001e132

   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 90.2%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{+82} \lor \neg \left(y \leq 2.4 \cdot 10^{+132}\right):\\ \;\;\;\;2 + 4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \frac{x - z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 85.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.6 \cdot 10^{+70}:\\ \;\;\;\;2 + \frac{z}{y} \cdot -4\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+132}:\\ \;\;\;\;4 \cdot \frac{x - z}{y}\\ \mathbf{else}:\\ \;\;\;\;2 + 4 \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -5.6e+70)
   (+ 2.0 (* (/ z y) -4.0))
   (if (<= y 6.5e+132) (* 4.0 (/ (- x z) y)) (+ 2.0 (* 4.0 (/ x y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -5.6e+70) {
		tmp = 2.0 + ((z / y) * -4.0);
	} else if (y <= 6.5e+132) {
		tmp = 4.0 * ((x - 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 (y <= (-5.6d+70)) then
        tmp = 2.0d0 + ((z / y) * (-4.0d0))
    else if (y <= 6.5d+132) then
        tmp = 4.0d0 * ((x - 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 (y <= -5.6e+70) {
		tmp = 2.0 + ((z / y) * -4.0);
	} else if (y <= 6.5e+132) {
		tmp = 4.0 * ((x - z) / y);
	} else {
		tmp = 2.0 + (4.0 * (x / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -5.6e+70:
		tmp = 2.0 + ((z / y) * -4.0)
	elif y <= 6.5e+132:
		tmp = 4.0 * ((x - z) / y)
	else:
		tmp = 2.0 + (4.0 * (x / y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -5.6e+70)
		tmp = Float64(2.0 + Float64(Float64(z / y) * -4.0));
	elseif (y <= 6.5e+132)
		tmp = Float64(4.0 * Float64(Float64(x - 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 (y <= -5.6e+70)
		tmp = 2.0 + ((z / y) * -4.0);
	elseif (y <= 6.5e+132)
		tmp = 4.0 * ((x - z) / y);
	else
		tmp = 2.0 + (4.0 * (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -5.6e+70], N[(2.0 + N[(N[(z / y), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.5e+132], N[(4.0 * N[(N[(x - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(2.0 + N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.59999999999999979e70

   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 99.7%

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

      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 84.9%

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

      1. *-commutative 84.9%

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

   7. Simplified 84.9%

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

   if -5.59999999999999979e70 < y < 6.4999999999999994e132

   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 91.0%

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

   if 6.4999999999999994e132 < 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 z around 0 100.0%

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

Alternative 6: 79.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{+178}:\\ \;\;\;\;2\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+158}:\\ \;\;\;\;4 \cdot \frac{x - z}{y}\\ \mathbf{else}:\\ \;\;\;\;2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.2e+178) 2.0 (if (<= y 9e+158) (* 4.0 (/ (- x z) y)) 2.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.2e+178) {
		tmp = 2.0;
	} else if (y <= 9e+158) {
		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 <= (-2.2d+178)) then
        tmp = 2.0d0
    else if (y <= 9d+158) 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 <= -2.2e+178) {
		tmp = 2.0;
	} else if (y <= 9e+158) {
		tmp = 4.0 * ((x - z) / y);
	} else {
		tmp = 2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.2e+178:
		tmp = 2.0
	elif y <= 9e+158:
		tmp = 4.0 * ((x - z) / y)
	else:
		tmp = 2.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.2e+178)
		tmp = 2.0;
	elseif (y <= 9e+158)
		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 <= -2.2e+178)
		tmp = 2.0;
	elseif (y <= 9e+158)
		tmp = 4.0 * ((x - z) / y);
	else
		tmp = 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.2e+178], 2.0, If[LessEqual[y, 9e+158], N[(4.0 * N[(N[(x - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], 2.0]]

Derivation

1. Split input into 2 regimes

2. if y < -2.19999999999999997e178 or 9.00000000000000092e158 < 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 80.7%

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

   if -2.19999999999999997e178 < y < 9.00000000000000092e158

   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 86.5%

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

Alternative 7: 54.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+70}:\\ \;\;\;\;2\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+89}:\\ \;\;\;\;x \cdot \frac{4}{y}\\ \mathbf{else}:\\ \;\;\;\;2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -9.5e+70) 2.0 (if (<= y 7e+89) (* x (/ 4.0 y)) 2.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -9.5e+70) {
		tmp = 2.0;
	} else if (y <= 7e+89) {
		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 <= (-9.5d+70)) then
        tmp = 2.0d0
    else if (y <= 7d+89) 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 <= -9.5e+70) {
		tmp = 2.0;
	} else if (y <= 7e+89) {
		tmp = x * (4.0 / y);
	} else {
		tmp = 2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -9.5e+70:
		tmp = 2.0
	elif y <= 7e+89:
		tmp = x * (4.0 / y)
	else:
		tmp = 2.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -9.5e+70)
		tmp = 2.0;
	elseif (y <= 7e+89)
		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 <= -9.5e+70)
		tmp = 2.0;
	elseif (y <= 7e+89)
		tmp = x * (4.0 / y);
	else
		tmp = 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -9.5e+70], 2.0, If[LessEqual[y, 7e+89], N[(x * N[(4.0 / y), $MachinePrecision]), $MachinePrecision], 2.0]]

Derivation

1. Split input into 2 regimes

2. if y < -9.5000000000000002e70 or 7.0000000000000001e89 < 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 64.7%

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

   if -9.5000000000000002e70 < y < 7.0000000000000001e89

   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 54.8%

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

      1. associate-*r/ 54.8%

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

      2. associate-*l/ 54.6%

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

      3. *-commutative 54.6%

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

   5. Simplified 54.6%

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

Alternative 8: 99.8% accurate, 1.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 9: 33.9% accurate, 13.0× speedup

Math

\[\begin{array}{l} \\ 2 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 2.0)

C

double code(double x, double y, double z) {
	return 2.0;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = 2.0d0
end function

Java

public static double code(double x, double y, double z) {
	return 2.0;
}

Python

def code(x, y, z):
	return 2.0

Julia

function code(x, y, z)
	return 2.0
end

MATLAB

function tmp = code(x, y, z)
	tmp = 2.0;
end

Wolfram

code[x_, y_, z_] := 2.0

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in y around inf 29.0%

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

Reproduce

herbie shell --seed 2024129 
(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)))