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

Percentage Accurate: 99.9% → 100.0%

Time: 5.5s

Alternatives: 8

Speedup: 1.0×

• 20.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.0× speedup

Math

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

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(4.0 * Float64(Float64(x + Float64(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[(4.0 * N[(N[(x + N[(N[(y * 0.25), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.6%

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

   1. associate-/l* 100.0%

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

   2. associate--l+ 100.0%

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

3. Simplified 100.0%

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

Alternative 2: 53.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{z}{y} \cdot -4\\ \mathbf{if}\;z \leq -2.4 \cdot 10^{+61}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-55}:\\ \;\;\;\;4 \cdot \frac{x}{y}\\ \mathbf{elif}\;z \leq 3.15 \cdot 10^{-46}:\\ \;\;\;\;2\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (/ z y) -4.0)))
   (if (<= z -2.4e+61)
     t_0
     (if (<= z -1.25e-55) (* 4.0 (/ x y)) (if (<= z 3.15e-46) 2.0 t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = (z / y) * -4.0;
	double tmp;
	if (z <= -2.4e+61) {
		tmp = t_0;
	} else if (z <= -1.25e-55) {
		tmp = 4.0 * (x / y);
	} else if (z <= 3.15e-46) {
		tmp = 2.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (z / y) * (-4.0d0)
    if (z <= (-2.4d+61)) then
        tmp = t_0
    else if (z <= (-1.25d-55)) then
        tmp = 4.0d0 * (x / y)
    else if (z <= 3.15d-46) then
        tmp = 2.0d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (z / y) * -4.0;
	double tmp;
	if (z <= -2.4e+61) {
		tmp = t_0;
	} else if (z <= -1.25e-55) {
		tmp = 4.0 * (x / y);
	} else if (z <= 3.15e-46) {
		tmp = 2.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (z / y) * -4.0
	tmp = 0
	if z <= -2.4e+61:
		tmp = t_0
	elif z <= -1.25e-55:
		tmp = 4.0 * (x / y)
	elif z <= 3.15e-46:
		tmp = 2.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(z / y) * -4.0)
	tmp = 0.0
	if (z <= -2.4e+61)
		tmp = t_0;
	elseif (z <= -1.25e-55)
		tmp = Float64(4.0 * Float64(x / y));
	elseif (z <= 3.15e-46)
		tmp = 2.0;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (z / y) * -4.0;
	tmp = 0.0;
	if (z <= -2.4e+61)
		tmp = t_0;
	elseif (z <= -1.25e-55)
		tmp = 4.0 * (x / y);
	elseif (z <= 3.15e-46)
		tmp = 2.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(z / y), $MachinePrecision] * -4.0), $MachinePrecision]}, If[LessEqual[z, -2.4e+61], t$95$0, If[LessEqual[z, -1.25e-55], N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.15e-46], 2.0, t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.3999999999999999e61 or 3.15e-46 < z

   1. Initial program 99.1%

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

      1. associate-/l* 99.9%

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

      2. associate--l+ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 63.7%

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

      1. *-commutative 63.7%

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

   7. Simplified 63.7%

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

   if -2.3999999999999999e61 < z < -1.25e-55

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. associate--l+ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 67.9%

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

   if -1.25e-55 < z < 3.15e-46

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. associate--l+ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 56.3%

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

Alternative 3: 85.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.00033 \lor \neg \left(z \leq 2.2 \cdot 10^{+79}\right):\\ \;\;\;\;\left(z - x\right) \cdot \frac{-4}{y}\\ \mathbf{else}:\\ \;\;\;\;2 + 4 \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.00033) (not (<= z 2.2e+79)))
   (* (- z x) (/ -4.0 y))
   (+ 2.0 (* 4.0 (/ x y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.00033) || !(z <= 2.2e+79)) {
		tmp = (z - x) * (-4.0 / y);
	} else {
		tmp = 2.0 + (4.0 * (x / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-0.00033d0)) .or. (.not. (z <= 2.2d+79))) then
        tmp = (z - x) * ((-4.0d0) / y)
    else
        tmp = 2.0d0 + (4.0d0 * (x / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.00033) || !(z <= 2.2e+79)) {
		tmp = (z - x) * (-4.0 / y);
	} else {
		tmp = 2.0 + (4.0 * (x / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.00033) or not (z <= 2.2e+79):
		tmp = (z - x) * (-4.0 / y)
	else:
		tmp = 2.0 + (4.0 * (x / y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.00033) || !(z <= 2.2e+79))
		tmp = Float64(Float64(z - x) * Float64(-4.0 / y));
	else
		tmp = Float64(2.0 + Float64(4.0 * Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -0.00033) || ~((z <= 2.2e+79)))
		tmp = (z - x) * (-4.0 / y);
	else
		tmp = 2.0 + (4.0 * (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.00033], N[Not[LessEqual[z, 2.2e+79]], $MachinePrecision]], N[(N[(z - x), $MachinePrecision] * N[(-4.0 / y), $MachinePrecision]), $MachinePrecision], N[(2.0 + N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.3e-4 or 2.1999999999999999e79 < z

   1. Initial program 99.1%

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

      1. associate-/l* 99.9%

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

      2. associate--l+ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 84.6%

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

      1. associate-*r/ 83.8%

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

      2. associate-*l/ 84.4%

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

      3. *-commutative 84.4%

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

      4. metadata-eval 84.4%

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

      5. associate-*r/ 84.4%

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

      6. associate-*r* 84.4%

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

      7. *-commutative 84.4%

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

      8. neg-mul-1 84.4%

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

      9. sub-neg 84.4%

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

      10. +-commutative 84.4%

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

      11. distribute-neg-in 84.4%

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

      12. remove-double-neg 84.4%

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

      13. sub-neg 84.4%

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

   7. Simplified 84.4%

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

   if -3.3e-4 < z < 2.1999999999999999e79

   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 90.8%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.00033 \lor \neg \left(z \leq 2.2 \cdot 10^{+79}\right):\\ \;\;\;\;\left(z - x\right) \cdot \frac{-4}{y}\\ \mathbf{else}:\\ \;\;\;\;2 + 4 \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{+40}:\\ \;\;\;\;2 + 4 \cdot \frac{x}{y}\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{+36}:\\ \;\;\;\;2 + \frac{z}{y} \cdot -4\\ \mathbf{else}:\\ \;\;\;\;\left(z - x\right) \cdot \frac{-4}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.45e+40)
   (+ 2.0 (* 4.0 (/ x y)))
   (if (<= x 1.5e+36) (+ 2.0 (* (/ z y) -4.0)) (* (- z x) (/ -4.0 y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.45e+40) {
		tmp = 2.0 + (4.0 * (x / y));
	} else if (x <= 1.5e+36) {
		tmp = 2.0 + ((z / y) * -4.0);
	} else {
		tmp = (z - x) * (-4.0 / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-1.45d+40)) then
        tmp = 2.0d0 + (4.0d0 * (x / y))
    else if (x <= 1.5d+36) then
        tmp = 2.0d0 + ((z / y) * (-4.0d0))
    else
        tmp = (z - x) * ((-4.0d0) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.45e+40) {
		tmp = 2.0 + (4.0 * (x / y));
	} else if (x <= 1.5e+36) {
		tmp = 2.0 + ((z / y) * -4.0);
	} else {
		tmp = (z - x) * (-4.0 / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.45e+40:
		tmp = 2.0 + (4.0 * (x / y))
	elif x <= 1.5e+36:
		tmp = 2.0 + ((z / y) * -4.0)
	else:
		tmp = (z - x) * (-4.0 / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.45e+40)
		tmp = Float64(2.0 + Float64(4.0 * Float64(x / y)));
	elseif (x <= 1.5e+36)
		tmp = Float64(2.0 + Float64(Float64(z / y) * -4.0));
	else
		tmp = Float64(Float64(z - x) * Float64(-4.0 / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.45e+40)
		tmp = 2.0 + (4.0 * (x / y));
	elseif (x <= 1.5e+36)
		tmp = 2.0 + ((z / y) * -4.0);
	else
		tmp = (z - x) * (-4.0 / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.45e+40], N[(2.0 + N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.5e+36], N[(2.0 + N[(N[(z / y), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision], N[(N[(z - x), $MachinePrecision] * N[(-4.0 / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.45000000000000009e40

   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+ 99.9%

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

      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 84.2%

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

   if -1.45000000000000009e40 < x < 1.5e36

   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+ 99.9%

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

      8. associate-*l/ 99.9%

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

      9. *-commutative 99.9%

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

      10. associate-*l* 99.9%

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

      11. metadata-eval 99.9%

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

      12. *-rgt-identity 99.9%

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

      13. *-inverses 99.9%

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

      14. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 94.4%

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

      1. *-commutative 94.4%

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

   7. Simplified 94.4%

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

   if 1.5e36 < x

   1. Initial program 98.3%

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

      1. associate-/l* 100.0%

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

      2. associate--l+ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 88.4%

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

      1. associate-*r/ 86.7%

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

      2. associate-*l/ 88.1%

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

      3. *-commutative 88.1%

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

      4. metadata-eval 88.1%

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

      5. associate-*r/ 88.1%

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

      6. associate-*r* 88.1%

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

      7. *-commutative 88.1%

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

      8. neg-mul-1 88.1%

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

      9. sub-neg 88.1%

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

      10. +-commutative 88.1%

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

      11. distribute-neg-in 88.1%

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

      12. remove-double-neg 88.1%

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

      13. sub-neg 88.1%

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

   7. Simplified 88.1%

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

Alternative 5: 78.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{+170}:\\ \;\;\;\;2\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+203}:\\ \;\;\;\;\left(z - x\right) \cdot \frac{-4}{y}\\ \mathbf{else}:\\ \;\;\;\;2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -5.2e+170) 2.0 (if (<= y 1.5e+203) (* (- z x) (/ -4.0 y)) 2.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -5.2e+170) {
		tmp = 2.0;
	} else if (y <= 1.5e+203) {
		tmp = (z - 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 <= (-5.2d+170)) then
        tmp = 2.0d0
    else if (y <= 1.5d+203) then
        tmp = (z - 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 <= -5.2e+170) {
		tmp = 2.0;
	} else if (y <= 1.5e+203) {
		tmp = (z - x) * (-4.0 / y);
	} else {
		tmp = 2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -5.2e+170:
		tmp = 2.0
	elif y <= 1.5e+203:
		tmp = (z - x) * (-4.0 / y)
	else:
		tmp = 2.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -5.2e+170)
		tmp = 2.0;
	elseif (y <= 1.5e+203)
		tmp = Float64(Float64(z - 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 <= -5.2e+170)
		tmp = 2.0;
	elseif (y <= 1.5e+203)
		tmp = (z - x) * (-4.0 / y);
	else
		tmp = 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -5.2e+170], 2.0, If[LessEqual[y, 1.5e+203], N[(N[(z - x), $MachinePrecision] * N[(-4.0 / y), $MachinePrecision]), $MachinePrecision], 2.0]]

Derivation

1. Split input into 2 regimes

2. if y < -5.1999999999999996e170 or 1.5e203 < 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. associate-/l* 99.9%

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

      2. associate--l+ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 83.5%

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

   if -5.1999999999999996e170 < y < 1.5e203

   1. Initial program 99.6%

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

      1. associate-/l* 100.0%

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

      2. associate--l+ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 77.5%

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

      1. associate-*r/ 77.1%

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

      2. associate-*l/ 77.3%

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

      3. *-commutative 77.3%

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

      4. metadata-eval 77.3%

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

      5. associate-*r/ 77.3%

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

      6. associate-*r* 77.3%

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

      7. *-commutative 77.3%

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

      8. neg-mul-1 77.3%

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

      9. sub-neg 77.3%

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

      10. +-commutative 77.3%

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

      11. distribute-neg-in 77.3%

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

      12. remove-double-neg 77.3%

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

      13. sub-neg 77.3%

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

   7. Simplified 77.3%

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

Alternative 6: 53.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.3 \cdot 10^{+81} \lor \neg \left(x \leq 1.48 \cdot 10^{+35}\right):\\ \;\;\;\;4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -5.3e+81) (not (<= x 1.48e+35))) (* 4.0 (/ x y)) 2.0))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5.3e+81) || !(x <= 1.48e+35)) {
		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 ((x <= (-5.3d+81)) .or. (.not. (x <= 1.48d+35))) 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 ((x <= -5.3e+81) || !(x <= 1.48e+35)) {
		tmp = 4.0 * (x / y);
	} else {
		tmp = 2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -5.3e+81) or not (x <= 1.48e+35):
		tmp = 4.0 * (x / y)
	else:
		tmp = 2.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -5.3e+81) || !(x <= 1.48e+35))
		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 ((x <= -5.3e+81) || ~((x <= 1.48e+35)))
		tmp = 4.0 * (x / y);
	else
		tmp = 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -5.3e+81], N[Not[LessEqual[x, 1.48e+35]], $MachinePrecision]], N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision], 2.0]

Derivation

1. Split input into 2 regimes

2. if x < -5.30000000000000028e81 or 1.48000000000000003e35 < x

   1. Initial program 99.1%

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

      1. associate-/l* 99.9%

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

      2. associate--l+ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 67.7%

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

   if -5.30000000000000028e81 < x < 1.48000000000000003e35

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. associate--l+ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 51.7%

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

4. Final simplification 58.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.3 \cdot 10^{+81} \lor \neg \left(x \leq 1.48 \cdot 10^{+35}\right):\\ \;\;\;\;4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;2\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 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 99.6%

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

   1. +-commutative 99.6%

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

   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 8: 33.7% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := 2.0

Derivation

1. Initial program 99.6%

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

   1. associate-/l* 100.0%

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

   2. associate--l+ 100.0%

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

3. Simplified 100.0%

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

5. Taylor expanded in y around inf 35.9%

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

Reproduce

herbie shell --seed 2024141 
(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)))