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

Percentage Accurate: 99.9% → 99.9%

Time: 7.1s

Alternatives: 11

Speedup: 1.0×

• 21.8% 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: 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: 53.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{4 \cdot x}{y}\\ t_1 := \frac{z}{y} \cdot -4\\ \mathbf{if}\;x \leq -5.5 \cdot 10^{+58}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq -2.4 \cdot 10^{-160}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{-228}:\\ \;\;\;\;2\\ \mathbf{elif}\;x \leq 0.00185:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (* 4.0 x) y)) (t_1 (* (/ z y) -4.0)))
   (if (<= x -5.5e+58)
     t_0
     (if (<= x -2.4e-160)
       t_1
       (if (<= x 6.8e-228) 2.0 (if (<= x 0.00185) t_1 t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = (4.0 * x) / y;
	double t_1 = (z / y) * -4.0;
	double tmp;
	if (x <= -5.5e+58) {
		tmp = t_0;
	} else if (x <= -2.4e-160) {
		tmp = t_1;
	} else if (x <= 6.8e-228) {
		tmp = 2.0;
	} else if (x <= 0.00185) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (4.0d0 * x) / y
    t_1 = (z / y) * (-4.0d0)
    if (x <= (-5.5d+58)) then
        tmp = t_0
    else if (x <= (-2.4d-160)) then
        tmp = t_1
    else if (x <= 6.8d-228) then
        tmp = 2.0d0
    else if (x <= 0.00185d0) then
        tmp = t_1
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (4.0 * x) / y;
	double t_1 = (z / y) * -4.0;
	double tmp;
	if (x <= -5.5e+58) {
		tmp = t_0;
	} else if (x <= -2.4e-160) {
		tmp = t_1;
	} else if (x <= 6.8e-228) {
		tmp = 2.0;
	} else if (x <= 0.00185) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (4.0 * x) / y
	t_1 = (z / y) * -4.0
	tmp = 0
	if x <= -5.5e+58:
		tmp = t_0
	elif x <= -2.4e-160:
		tmp = t_1
	elif x <= 6.8e-228:
		tmp = 2.0
	elif x <= 0.00185:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(4.0 * x) / y)
	t_1 = Float64(Float64(z / y) * -4.0)
	tmp = 0.0
	if (x <= -5.5e+58)
		tmp = t_0;
	elseif (x <= -2.4e-160)
		tmp = t_1;
	elseif (x <= 6.8e-228)
		tmp = 2.0;
	elseif (x <= 0.00185)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (4.0 * x) / y;
	t_1 = (z / y) * -4.0;
	tmp = 0.0;
	if (x <= -5.5e+58)
		tmp = t_0;
	elseif (x <= -2.4e-160)
		tmp = t_1;
	elseif (x <= 6.8e-228)
		tmp = 2.0;
	elseif (x <= 0.00185)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(4.0 * x), $MachinePrecision] / y), $MachinePrecision]}, Block[{t$95$1 = N[(N[(z / y), $MachinePrecision] * -4.0), $MachinePrecision]}, If[LessEqual[x, -5.5e+58], t$95$0, If[LessEqual[x, -2.4e-160], t$95$1, If[LessEqual[x, 6.8e-228], 2.0, If[LessEqual[x, 0.00185], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.4999999999999999e58 or 0.0018500000000000001 < 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 67.5%

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

      1. associate-*r/ 67.5%

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

   5. Simplified 67.5%

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

   if -5.4999999999999999e58 < x < -2.39999999999999991e-160 or 6.79999999999999981e-228 < x < 0.0018500000000000001

   1. Initial program 99.9%

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

   3. Taylor expanded in 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%

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

   if -2.39999999999999991e-160 < x < 6.79999999999999981e-228

   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 59.5%

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

Alternative 3: 53.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{4}{\frac{y}{x}}\\ t_1 := \frac{z}{y} \cdot -4\\ \mathbf{if}\;x \leq -1.7 \cdot 10^{+59}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq -2.15 \cdot 10^{-156}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 2 \cdot 10^{-226}:\\ \;\;\;\;2\\ \mathbf{elif}\;x \leq 0.025:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ 4.0 (/ y x))) (t_1 (* (/ z y) -4.0)))
   (if (<= x -1.7e+59)
     t_0
     (if (<= x -2.15e-156)
       t_1
       (if (<= x 2e-226) 2.0 (if (<= x 0.025) t_1 t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = 4.0 / (y / x);
	double t_1 = (z / y) * -4.0;
	double tmp;
	if (x <= -1.7e+59) {
		tmp = t_0;
	} else if (x <= -2.15e-156) {
		tmp = t_1;
	} else if (x <= 2e-226) {
		tmp = 2.0;
	} else if (x <= 0.025) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = 4.0d0 / (y / x)
    t_1 = (z / y) * (-4.0d0)
    if (x <= (-1.7d+59)) then
        tmp = t_0
    else if (x <= (-2.15d-156)) then
        tmp = t_1
    else if (x <= 2d-226) then
        tmp = 2.0d0
    else if (x <= 0.025d0) then
        tmp = t_1
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 4.0 / (y / x);
	double t_1 = (z / y) * -4.0;
	double tmp;
	if (x <= -1.7e+59) {
		tmp = t_0;
	} else if (x <= -2.15e-156) {
		tmp = t_1;
	} else if (x <= 2e-226) {
		tmp = 2.0;
	} else if (x <= 0.025) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 4.0 / (y / x)
	t_1 = (z / y) * -4.0
	tmp = 0
	if x <= -1.7e+59:
		tmp = t_0
	elif x <= -2.15e-156:
		tmp = t_1
	elif x <= 2e-226:
		tmp = 2.0
	elif x <= 0.025:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(4.0 / Float64(y / x))
	t_1 = Float64(Float64(z / y) * -4.0)
	tmp = 0.0
	if (x <= -1.7e+59)
		tmp = t_0;
	elseif (x <= -2.15e-156)
		tmp = t_1;
	elseif (x <= 2e-226)
		tmp = 2.0;
	elseif (x <= 0.025)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 4.0 / (y / x);
	t_1 = (z / y) * -4.0;
	tmp = 0.0;
	if (x <= -1.7e+59)
		tmp = t_0;
	elseif (x <= -2.15e-156)
		tmp = t_1;
	elseif (x <= 2e-226)
		tmp = 2.0;
	elseif (x <= 0.025)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(4.0 / N[(y / x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(z / y), $MachinePrecision] * -4.0), $MachinePrecision]}, If[LessEqual[x, -1.7e+59], t$95$0, If[LessEqual[x, -2.15e-156], t$95$1, If[LessEqual[x, 2e-226], 2.0, If[LessEqual[x, 0.025], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.70000000000000003e59 or 0.025000000000000001 < 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 y around 0 80.8%

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

      1. clear-num 80.6%

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

      2. un-div-inv 80.6%

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

   5. Applied egg-rr 80.6%

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

   6. Taylor expanded in x around inf 67.5%

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

      1. associate-*r/ 67.5%

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

      2. associate-*l/ 67.3%

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

      3. associate-/r/ 67.3%

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

   8. Simplified 67.3%

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

   if -1.70000000000000003e59 < x < -2.14999999999999989e-156 or 1.99999999999999984e-226 < x < 0.025000000000000001

   1. Initial program 99.9%

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

   3. Taylor expanded in 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%

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

   if -2.14999999999999989e-156 < x < 1.99999999999999984e-226

   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 59.5%

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

Alternative 4: 86.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{+59} \lor \neg \left(x \leq 0.032\right):\\ \;\;\;\;2 + 4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;2 + \frac{z}{y} \cdot -4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.9e+59) (not (<= x 0.032)))
   (+ 2.0 (* 4.0 (/ x y)))
   (+ 2.0 (* (/ z y) -4.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.9e+59) || !(x <= 0.032)) {
		tmp = 2.0 + (4.0 * (x / y));
	} else {
		tmp = 2.0 + ((z / y) * -4.0);
	}
	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 ((x <= (-1.9d+59)) .or. (.not. (x <= 0.032d0))) then
        tmp = 2.0d0 + (4.0d0 * (x / y))
    else
        tmp = 2.0d0 + ((z / y) * (-4.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.9e+59) || !(x <= 0.032)) {
		tmp = 2.0 + (4.0 * (x / y));
	} else {
		tmp = 2.0 + ((z / y) * -4.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.9e+59) or not (x <= 0.032):
		tmp = 2.0 + (4.0 * (x / y))
	else:
		tmp = 2.0 + ((z / y) * -4.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.9e+59) || !(x <= 0.032))
		tmp = Float64(2.0 + Float64(4.0 * Float64(x / y)));
	else
		tmp = Float64(2.0 + Float64(Float64(z / y) * -4.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.9e+59) || ~((x <= 0.032)))
		tmp = 2.0 + (4.0 * (x / y));
	else
		tmp = 2.0 + ((z / y) * -4.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.9e+59], N[Not[LessEqual[x, 0.032]], $MachinePrecision]], N[(2.0 + N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 + N[(N[(z / y), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.9e59 or 0.032000000000000001 < 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%

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

      10. associate-*r* 99.8%

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

      11. metadata-eval 99.8%

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

      12. *-lft-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 z around 0 86.5%

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

   if -1.9e59 < x < 0.032000000000000001

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      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%

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

      10. associate-*r* 99.8%

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

      11. metadata-eval 99.8%

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

      12. *-lft-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 93.4%

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

      1. *-commutative 93.4%

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

   7. Simplified 93.4%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{+59} \lor \neg \left(x \leq 0.032\right):\\ \;\;\;\;2 + 4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;2 + \frac{z}{y} \cdot -4\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 85.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+83} \lor \neg \left(y \leq 1.1 \cdot 10^{+94}\right):\\ \;\;\;\;2 + 4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \frac{x - z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -4.4e+83) (not (<= y 1.1e+94)))
   (+ 2.0 (* 4.0 (/ x y)))
   (* 4.0 (/ (- x z) y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4.4e+83) || !(y <= 1.1e+94)) {
		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 <= (-4.4d+83)) .or. (.not. (y <= 1.1d+94))) 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 <= -4.4e+83) || !(y <= 1.1e+94)) {
		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 <= -4.4e+83) or not (y <= 1.1e+94):
		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 <= -4.4e+83) || !(y <= 1.1e+94))
		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 <= -4.4e+83) || ~((y <= 1.1e+94)))
		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, -4.4e+83], N[Not[LessEqual[y, 1.1e+94]], $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 < -4.39999999999999997e83 or 1.10000000000000006e94 < y

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      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%

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

      10. associate-*r* 99.9%

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

      11. metadata-eval 99.9%

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

      12. *-lft-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 88.1%

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

   if -4.39999999999999997e83 < y < 1.10000000000000006e94

   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 88.7%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+83} \lor \neg \left(y \leq 1.1 \cdot 10^{+94}\right):\\ \;\;\;\;2 + 4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \frac{x - z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 79.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+185}:\\ \;\;\;\;2\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+95}:\\ \;\;\;\;4 \cdot \frac{x - z}{y}\\ \mathbf{else}:\\ \;\;\;\;2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.25e+185) 2.0 (if (<= y 7.2e+95) (* 4.0 (/ (- x z) y)) 2.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.25e+185) {
		tmp = 2.0;
	} else if (y <= 7.2e+95) {
		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 <= (-1.25d+185)) then
        tmp = 2.0d0
    else if (y <= 7.2d+95) 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 <= -1.25e+185) {
		tmp = 2.0;
	} else if (y <= 7.2e+95) {
		tmp = 4.0 * ((x - z) / y);
	} else {
		tmp = 2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.25e+185:
		tmp = 2.0
	elif y <= 7.2e+95:
		tmp = 4.0 * ((x - z) / y)
	else:
		tmp = 2.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.25e+185)
		tmp = 2.0;
	elseif (y <= 7.2e+95)
		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 <= -1.25e+185)
		tmp = 2.0;
	elseif (y <= 7.2e+95)
		tmp = 4.0 * ((x - z) / y);
	else
		tmp = 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.25e+185], 2.0, If[LessEqual[y, 7.2e+95], N[(4.0 * N[(N[(x - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], 2.0]]

Derivation

1. Split input into 2 regimes

2. if y < -1.24999999999999997e185 or 7.19999999999999955e95 < 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 79.3%

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

   if -1.24999999999999997e185 < y < 7.19999999999999955e95

   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 83.6%

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

Alternative 7: 53.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{+79}:\\ \;\;\;\;2\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{+94}:\\ \;\;\;\;\frac{z}{y} \cdot -4\\ \mathbf{else}:\\ \;\;\;\;2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.35e+79) 2.0 (if (<= y 1.12e+94) (* (/ z y) -4.0) 2.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.35e+79) {
		tmp = 2.0;
	} else if (y <= 1.12e+94) {
		tmp = (z / y) * -4.0;
	} 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) :: tmp
    if (y <= (-1.35d+79)) then
        tmp = 2.0d0
    else if (y <= 1.12d+94) then
        tmp = (z / y) * (-4.0d0)
    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 <= -1.35e+79) {
		tmp = 2.0;
	} else if (y <= 1.12e+94) {
		tmp = (z / y) * -4.0;
	} else {
		tmp = 2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.35e+79:
		tmp = 2.0
	elif y <= 1.12e+94:
		tmp = (z / y) * -4.0
	else:
		tmp = 2.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.35e+79)
		tmp = 2.0;
	elseif (y <= 1.12e+94)
		tmp = Float64(Float64(z / y) * -4.0);
	else
		tmp = 2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.35e+79)
		tmp = 2.0;
	elseif (y <= 1.12e+94)
		tmp = (z / y) * -4.0;
	else
		tmp = 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.35e+79], 2.0, If[LessEqual[y, 1.12e+94], N[(N[(z / y), $MachinePrecision] * -4.0), $MachinePrecision], 2.0]]

Derivation

1. Split input into 2 regimes

2. if y < -1.35e79 or 1.11999999999999996e94 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 70.8%

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

   if -1.35e79 < y < 1.11999999999999996e94

   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 49.6%

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

      1. *-commutative 49.6%

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

   5. Simplified 49.6%

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

Alternative 8: 53.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.95 \cdot 10^{+80}:\\ \;\;\;\;2\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+95}:\\ \;\;\;\;z \cdot \frac{-4}{y}\\ \mathbf{else}:\\ \;\;\;\;2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.95e+80) 2.0 (if (<= y 1.15e+95) (* z (/ -4.0 y)) 2.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.95e+80) {
		tmp = 2.0;
	} else if (y <= 1.15e+95) {
		tmp = 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 (y <= (-2.95d+80)) then
        tmp = 2.0d0
    else if (y <= 1.15d+95) then
        tmp = 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 (y <= -2.95e+80) {
		tmp = 2.0;
	} else if (y <= 1.15e+95) {
		tmp = z * (-4.0 / y);
	} else {
		tmp = 2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.95e+80:
		tmp = 2.0
	elif y <= 1.15e+95:
		tmp = z * (-4.0 / y)
	else:
		tmp = 2.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.95e+80)
		tmp = 2.0;
	elseif (y <= 1.15e+95)
		tmp = 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 (y <= -2.95e+80)
		tmp = 2.0;
	elseif (y <= 1.15e+95)
		tmp = z * (-4.0 / y);
	else
		tmp = 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.95e+80], 2.0, If[LessEqual[y, 1.15e+95], N[(z * N[(-4.0 / y), $MachinePrecision]), $MachinePrecision], 2.0]]

Derivation

1. Split input into 2 regimes

2. if y < -2.94999999999999986e80 or 1.14999999999999999e95 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 70.8%

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

   if -2.94999999999999986e80 < y < 1.14999999999999999e95

   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 49.6%

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

      1. associate-*r/ 49.6%

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

      2. *-commutative 49.6%

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

      3. associate-/l* 49.5%

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

   5. Simplified 49.5%

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

Alternative 9: 99.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \frac{1}{\frac{y}{4 \cdot \left(x - z\right)}} + 2 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ (/ 1.0 (/ y (* 4.0 (- x z)))) 2.0))

C

double code(double x, double y, double z) {
	return (1.0 / (y / (4.0 * (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 = (1.0d0 / (y / (4.0d0 * (x - z)))) + 2.0d0
end function

Java

public static double code(double x, double y, double z) {
	return (1.0 / (y / (4.0 * (x - z)))) + 2.0;
}

Python

def code(x, y, z):
	return (1.0 / (y / (4.0 * (x - z)))) + 2.0

Julia

function code(x, y, z)
	return Float64(Float64(1.0 / Float64(y / Float64(4.0 * Float64(x - z)))) + 2.0)
end

MATLAB

function tmp = code(x, y, z)
	tmp = (1.0 / (y / (4.0 * (x - z)))) + 2.0;
end

Wolfram

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

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

   10. associate-*r* 99.8%

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

   11. metadata-eval 99.8%

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

   12. *-lft-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. associate-*l/ 100.0%

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

   2. clear-num 99.8%

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

6. Applied egg-rr 99.8%

   \[\leadsto \color{blue}{\frac{1}{\frac{y}{4 \cdot \left(x - z\right)}}} + 2 \]
7. 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/ 99.8%

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

   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%

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

   10. associate-*r* 99.8%

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

   11. metadata-eval 99.8%

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

   12. *-lft-identity 99.8%

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

   13. *-inverses 99.8%

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

   14. metadata-eval 99.8%

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

3. Simplified 99.8%

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

5. Final simplification 99.8%

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

Alternative 11: 33.6% 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 33.1%

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

Reproduce

herbie shell --seed 2024185 
(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)))