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

Percentage Accurate: 99.9% → 100.0%

Time: 7.5s

Alternatives: 8

Speedup: 1.4×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.4× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.2%

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

   1. +-commutative N/A

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

   2. associate-*l/ N/A

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

   3. +-commutative N/A

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

   4. associate--l+ N/A

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

   5. distribute-lft-in N/A

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

   6. +-commutative N/A

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

   7. associate-+l+ N/A

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

   8. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\frac{4}{y} \cdot \left(x - z\right)\right), \color{blue}{\left(\frac{4}{y} \cdot \left(y \cdot \frac{1}{4}\right) + 1\right)}\right) \]

3. Simplified 100.0%

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

Alternative 2: 54.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -11500:\\ \;\;\;\;x \cdot \frac{4}{y}\\ \mathbf{elif}\;x \leq -3.7 \cdot 10^{-119}:\\ \;\;\;\;\frac{-4 \cdot z}{y}\\ \mathbf{elif}\;x \leq 8 \cdot 10^{+38}:\\ \;\;\;\;2\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 4}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -11500.0)
   (* x (/ 4.0 y))
   (if (<= x -3.7e-119)
     (/ (* -4.0 z) y)
     (if (<= x 8e+38) 2.0 (/ (* x 4.0) y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -11500.0) {
		tmp = x * (4.0 / y);
	} else if (x <= -3.7e-119) {
		tmp = (-4.0 * z) / y;
	} else if (x <= 8e+38) {
		tmp = 2.0;
	} else {
		tmp = (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 <= (-11500.0d0)) then
        tmp = x * (4.0d0 / y)
    else if (x <= (-3.7d-119)) then
        tmp = ((-4.0d0) * z) / y
    else if (x <= 8d+38) then
        tmp = 2.0d0
    else
        tmp = (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 <= -11500.0) {
		tmp = x * (4.0 / y);
	} else if (x <= -3.7e-119) {
		tmp = (-4.0 * z) / y;
	} else if (x <= 8e+38) {
		tmp = 2.0;
	} else {
		tmp = (x * 4.0) / y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -11500.0:
		tmp = x * (4.0 / y)
	elif x <= -3.7e-119:
		tmp = (-4.0 * z) / y
	elif x <= 8e+38:
		tmp = 2.0
	else:
		tmp = (x * 4.0) / y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -11500.0)
		tmp = Float64(x * Float64(4.0 / y));
	elseif (x <= -3.7e-119)
		tmp = Float64(Float64(-4.0 * z) / y);
	elseif (x <= 8e+38)
		tmp = 2.0;
	else
		tmp = Float64(Float64(x * 4.0) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -11500.0)
		tmp = x * (4.0 / y);
	elseif (x <= -3.7e-119)
		tmp = (-4.0 * z) / y;
	elseif (x <= 8e+38)
		tmp = 2.0;
	else
		tmp = (x * 4.0) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -11500.0], N[(x * N[(4.0 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -3.7e-119], N[(N[(-4.0 * z), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[x, 8e+38], 2.0, N[(N[(x * 4.0), $MachinePrecision] / y), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -11500

   1. Initial program 97.3%

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

      1. +-commutative N/A

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

      2. associate-*l/ N/A

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

      3. +-commutative N/A

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

      4. associate--l+ N/A

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

      5. distribute-lft-in N/A

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

      6. +-commutative N/A

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

      7. associate-+l+ N/A

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

      8. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{4}{y} \cdot \left(x - z\right)\right), \color{blue}{\left(\frac{4}{y} \cdot \left(y \cdot \frac{1}{4}\right) + 1\right)}\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(4 \cdot x\right), \color{blue}{y}\right) \]

      3. *-lowering-*.f64 76.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(4, x\right), y\right) \]

   7. Simplified 76.9%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{4}{y}\right), \color{blue}{x}\right) \]

      5. /-lowering-/.f64 78.0%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(4, y\right), x\right) \]

   9. Applied egg-rr 78.0%

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

   if -11500 < x < -3.7000000000000001e-119

   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 N/A

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

      2. associate-*l/ N/A

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

      3. +-commutative N/A

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

      4. associate--l+ N/A

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

      5. distribute-lft-in N/A

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

      6. +-commutative N/A

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

      7. associate-+l+ N/A

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

      8. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{4}{y} \cdot \left(x - z\right)\right), \color{blue}{\left(\frac{4}{y} \cdot \left(y \cdot \frac{1}{4}\right) + 1\right)}\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(-4 \cdot z\right), \color{blue}{y}\right) \]

      3. *-lowering-*.f64 61.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(-4, z\right), y\right) \]

   7. Simplified 61.3%

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

   if -3.7000000000000001e-119 < x < 7.99999999999999982e38

   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 N/A

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

      2. associate-*l/ N/A

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

      3. +-commutative N/A

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

      4. associate--l+ N/A

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

      5. distribute-lft-in N/A

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

      6. +-commutative N/A

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

      7. associate-+l+ N/A

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

      8. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{4}{y} \cdot \left(x - z\right)\right), \color{blue}{\left(\frac{4}{y} \cdot \left(y \cdot \frac{1}{4}\right) + 1\right)}\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf

      \[\leadsto \color{blue}{2} \]
   6. Step-by-step derivation

   7. Simplified 54.1%

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

   if 7.99999999999999982e38 < x

   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 N/A

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

      2. associate-*l/ N/A

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

      3. +-commutative N/A

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

      4. associate--l+ N/A

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

      5. distribute-lft-in N/A

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

      6. +-commutative N/A

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

      7. associate-+l+ N/A

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

      8. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{4}{y} \cdot \left(x - z\right)\right), \color{blue}{\left(\frac{4}{y} \cdot \left(y \cdot \frac{1}{4}\right) + 1\right)}\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(4 \cdot x\right), \color{blue}{y}\right) \]

      3. *-lowering-*.f64 78.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(4, x\right), y\right) \]

   7. Simplified 78.5%

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

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -11500:\\ \;\;\;\;x \cdot \frac{4}{y}\\ \mathbf{elif}\;x \leq -3.7 \cdot 10^{-119}:\\ \;\;\;\;\frac{-4 \cdot z}{y}\\ \mathbf{elif}\;x \leq 8 \cdot 10^{+38}:\\ \;\;\;\;2\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 4}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 54.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \frac{4}{y}\\ \mathbf{if}\;x \leq -6200:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq -4.8 \cdot 10^{-123}:\\ \;\;\;\;\frac{-4 \cdot z}{y}\\ \mathbf{elif}\;x \leq 10^{+39}:\\ \;\;\;\;2\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (/ 4.0 y))))
   (if (<= x -6200.0)
     t_0
     (if (<= x -4.8e-123) (/ (* -4.0 z) y) (if (<= x 1e+39) 2.0 t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = x * (4.0 / y);
	double tmp;
	if (x <= -6200.0) {
		tmp = t_0;
	} else if (x <= -4.8e-123) {
		tmp = (-4.0 * z) / y;
	} else if (x <= 1e+39) {
		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 = x * (4.0d0 / y)
    if (x <= (-6200.0d0)) then
        tmp = t_0
    else if (x <= (-4.8d-123)) then
        tmp = ((-4.0d0) * z) / y
    else if (x <= 1d+39) 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 = x * (4.0 / y);
	double tmp;
	if (x <= -6200.0) {
		tmp = t_0;
	} else if (x <= -4.8e-123) {
		tmp = (-4.0 * z) / y;
	} else if (x <= 1e+39) {
		tmp = 2.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (4.0 / y)
	tmp = 0
	if x <= -6200.0:
		tmp = t_0
	elif x <= -4.8e-123:
		tmp = (-4.0 * z) / y
	elif x <= 1e+39:
		tmp = 2.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(4.0 / y))
	tmp = 0.0
	if (x <= -6200.0)
		tmp = t_0;
	elseif (x <= -4.8e-123)
		tmp = Float64(Float64(-4.0 * z) / y);
	elseif (x <= 1e+39)
		tmp = 2.0;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (4.0 / y);
	tmp = 0.0;
	if (x <= -6200.0)
		tmp = t_0;
	elseif (x <= -4.8e-123)
		tmp = (-4.0 * z) / y;
	elseif (x <= 1e+39)
		tmp = 2.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(4.0 / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -6200.0], t$95$0, If[LessEqual[x, -4.8e-123], N[(N[(-4.0 * z), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[x, 1e+39], 2.0, t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if x < -6200 or 9.9999999999999994e38 < x

   1. Initial program 98.4%

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

      1. +-commutative N/A

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

      2. associate-*l/ N/A

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

      3. +-commutative N/A

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

      4. associate--l+ N/A

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

      5. distribute-lft-in N/A

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

      6. +-commutative N/A

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

      7. associate-+l+ N/A

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

      8. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{4}{y} \cdot \left(x - z\right)\right), \color{blue}{\left(\frac{4}{y} \cdot \left(y \cdot \frac{1}{4}\right) + 1\right)}\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(4 \cdot x\right), \color{blue}{y}\right) \]

      3. *-lowering-*.f64 77.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(4, x\right), y\right) \]

   7. Simplified 77.5%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{4}{y}\right), \color{blue}{x}\right) \]

      5. /-lowering-/.f64 78.1%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(4, y\right), x\right) \]

   9. Applied egg-rr 78.1%

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

   if -6200 < x < -4.8e-123

   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 N/A

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

      2. associate-*l/ N/A

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

      3. +-commutative N/A

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

      4. associate--l+ N/A

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

      5. distribute-lft-in N/A

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

      6. +-commutative N/A

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

      7. associate-+l+ N/A

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

      8. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{4}{y} \cdot \left(x - z\right)\right), \color{blue}{\left(\frac{4}{y} \cdot \left(y \cdot \frac{1}{4}\right) + 1\right)}\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(-4 \cdot z\right), \color{blue}{y}\right) \]

      3. *-lowering-*.f64 61.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(-4, z\right), y\right) \]

   7. Simplified 61.3%

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

   if -4.8e-123 < x < 9.9999999999999994e38

   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 N/A

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

      2. associate-*l/ N/A

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

      3. +-commutative N/A

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

      4. associate--l+ N/A

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

      5. distribute-lft-in N/A

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

      6. +-commutative N/A

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

      7. associate-+l+ N/A

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

      8. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{4}{y} \cdot \left(x - z\right)\right), \color{blue}{\left(\frac{4}{y} \cdot \left(y \cdot \frac{1}{4}\right) + 1\right)}\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf

      \[\leadsto \color{blue}{2} \]
   6. Step-by-step derivation

   7. Simplified 54.1%

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

4. Final simplification 66.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6200:\\ \;\;\;\;x \cdot \frac{4}{y}\\ \mathbf{elif}\;x \leq -4.8 \cdot 10^{-123}:\\ \;\;\;\;\frac{-4 \cdot z}{y}\\ \mathbf{elif}\;x \leq 10^{+39}:\\ \;\;\;\;2\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{4}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 54.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \frac{4}{y}\\ \mathbf{if}\;x \leq -19000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq -3.6 \cdot 10^{-123}:\\ \;\;\;\;z \cdot \frac{-4}{y}\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{+40}:\\ \;\;\;\;2\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (/ 4.0 y))))
   (if (<= x -19000.0)
     t_0
     (if (<= x -3.6e-123) (* z (/ -4.0 y)) (if (<= x 4.2e+40) 2.0 t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = x * (4.0 / y);
	double tmp;
	if (x <= -19000.0) {
		tmp = t_0;
	} else if (x <= -3.6e-123) {
		tmp = z * (-4.0 / y);
	} else if (x <= 4.2e+40) {
		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 = x * (4.0d0 / y)
    if (x <= (-19000.0d0)) then
        tmp = t_0
    else if (x <= (-3.6d-123)) then
        tmp = z * ((-4.0d0) / y)
    else if (x <= 4.2d+40) 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 = x * (4.0 / y);
	double tmp;
	if (x <= -19000.0) {
		tmp = t_0;
	} else if (x <= -3.6e-123) {
		tmp = z * (-4.0 / y);
	} else if (x <= 4.2e+40) {
		tmp = 2.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (4.0 / y)
	tmp = 0
	if x <= -19000.0:
		tmp = t_0
	elif x <= -3.6e-123:
		tmp = z * (-4.0 / y)
	elif x <= 4.2e+40:
		tmp = 2.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(4.0 / y))
	tmp = 0.0
	if (x <= -19000.0)
		tmp = t_0;
	elseif (x <= -3.6e-123)
		tmp = Float64(z * Float64(-4.0 / y));
	elseif (x <= 4.2e+40)
		tmp = 2.0;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (4.0 / y);
	tmp = 0.0;
	if (x <= -19000.0)
		tmp = t_0;
	elseif (x <= -3.6e-123)
		tmp = z * (-4.0 / y);
	elseif (x <= 4.2e+40)
		tmp = 2.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(4.0 / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -19000.0], t$95$0, If[LessEqual[x, -3.6e-123], N[(z * N[(-4.0 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.2e+40], 2.0, t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if x < -19000 or 4.2000000000000002e40 < x

   1. Initial program 98.4%

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

      1. +-commutative N/A

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

      2. associate-*l/ N/A

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

      3. +-commutative N/A

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

      4. associate--l+ N/A

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

      5. distribute-lft-in N/A

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

      6. +-commutative N/A

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

      7. associate-+l+ N/A

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

      8. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{4}{y} \cdot \left(x - z\right)\right), \color{blue}{\left(\frac{4}{y} \cdot \left(y \cdot \frac{1}{4}\right) + 1\right)}\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(4 \cdot x\right), \color{blue}{y}\right) \]

      3. *-lowering-*.f64 77.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(4, x\right), y\right) \]

   7. Simplified 77.5%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{4}{y}\right), \color{blue}{x}\right) \]

      5. /-lowering-/.f64 78.1%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(4, y\right), x\right) \]

   9. Applied egg-rr 78.1%

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

   if -19000 < x < -3.5999999999999997e-123

   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 N/A

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

      2. associate-*l/ N/A

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

      3. +-commutative N/A

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

      4. associate--l+ N/A

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

      5. distribute-lft-in N/A

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

      6. +-commutative N/A

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

      7. associate-+l+ N/A

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

      8. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{4}{y} \cdot \left(x - z\right)\right), \color{blue}{\left(\frac{4}{y} \cdot \left(y \cdot \frac{1}{4}\right) + 1\right)}\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(-4 \cdot z\right), \color{blue}{y}\right) \]

      3. *-lowering-*.f64 61.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(-4, z\right), y\right) \]

   7. Simplified 61.3%

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

      1. associate-*l/ N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{-4}{y}\right), \color{blue}{z}\right) \]

      3. /-lowering-/.f64 61.1%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(-4, y\right), z\right) \]

   9. Applied egg-rr 61.1%

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

   if -3.5999999999999997e-123 < x < 4.2000000000000002e40

   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 N/A

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

      2. associate-*l/ N/A

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

      3. +-commutative N/A

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

      4. associate--l+ N/A

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

      5. distribute-lft-in N/A

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

      6. +-commutative N/A

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

      7. associate-+l+ N/A

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

      8. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{4}{y} \cdot \left(x - z\right)\right), \color{blue}{\left(\frac{4}{y} \cdot \left(y \cdot \frac{1}{4}\right) + 1\right)}\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf

      \[\leadsto \color{blue}{2} \]
   6. Step-by-step derivation

   7. Simplified 54.1%

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

4. Final simplification 66.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -19000:\\ \;\;\;\;x \cdot \frac{4}{y}\\ \mathbf{elif}\;x \leq -3.6 \cdot 10^{-123}:\\ \;\;\;\;z \cdot \frac{-4}{y}\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{+40}:\\ \;\;\;\;2\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{4}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 86.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -4 \cdot \frac{z - x}{y}\\ \mathbf{if}\;x \leq -2.85 \cdot 10^{+35}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 3.05 \cdot 10^{+40}:\\ \;\;\;\;2 + -4 \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -4.0 (/ (- z x) y))))
   (if (<= x -2.85e+35)
     t_0
     (if (<= x 3.05e+40) (+ 2.0 (* -4.0 (/ z y))) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = -4.0 * ((z - x) / y);
	double tmp;
	if (x <= -2.85e+35) {
		tmp = t_0;
	} else if (x <= 3.05e+40) {
		tmp = 2.0 + (-4.0 * (z / y));
	} 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 = (-4.0d0) * ((z - x) / y)
    if (x <= (-2.85d+35)) then
        tmp = t_0
    else if (x <= 3.05d+40) then
        tmp = 2.0d0 + ((-4.0d0) * (z / y))
    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 * ((z - x) / y);
	double tmp;
	if (x <= -2.85e+35) {
		tmp = t_0;
	} else if (x <= 3.05e+40) {
		tmp = 2.0 + (-4.0 * (z / y));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -4.0 * ((z - x) / y)
	tmp = 0
	if x <= -2.85e+35:
		tmp = t_0
	elif x <= 3.05e+40:
		tmp = 2.0 + (-4.0 * (z / y))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-4.0 * Float64(Float64(z - x) / y))
	tmp = 0.0
	if (x <= -2.85e+35)
		tmp = t_0;
	elseif (x <= 3.05e+40)
		tmp = Float64(2.0 + Float64(-4.0 * Float64(z / y)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -4.0 * ((z - x) / y);
	tmp = 0.0;
	if (x <= -2.85e+35)
		tmp = t_0;
	elseif (x <= 3.05e+40)
		tmp = 2.0 + (-4.0 * (z / y));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-4.0 * N[(N[(z - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.85e+35], t$95$0, If[LessEqual[x, 3.05e+40], N[(2.0 + N[(-4.0 * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.84999999999999997e35 or 3.05e40 < 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. +-commutative N/A

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

      2. associate-*l/ N/A

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

      3. +-commutative N/A

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

      4. associate--l+ N/A

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

      5. distribute-lft-in N/A

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

      6. +-commutative N/A

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

      7. associate-+l+ N/A

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

      8. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{4}{y} \cdot \left(x - z\right)\right), \color{blue}{\left(\frac{4}{y} \cdot \left(y \cdot \frac{1}{4}\right) + 1\right)}\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0

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

   7. Simplified 93.0%

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

   if -2.84999999999999997e35 < x < 3.05e40

   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 N/A

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

      2. associate-*l/ N/A

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

      3. +-commutative N/A

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

      4. associate--l+ N/A

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

      5. distribute-lft-in N/A

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

      6. +-commutative N/A

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

      7. associate-+l+ N/A

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

      8. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{4}{y} \cdot \left(x - z\right)\right), \color{blue}{\left(\frac{4}{y} \cdot \left(y \cdot \frac{1}{4}\right) + 1\right)}\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, \color{blue}{\left(\frac{z}{y}\right)}\right), 2\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 90.8%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, \mathsf{/.f64}\left(z, y\right)\right), 2\right) \]

   7. Simplified 90.8%

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

4. Final simplification 91.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.85 \cdot 10^{+35}:\\ \;\;\;\;-4 \cdot \frac{z - x}{y}\\ \mathbf{elif}\;x \leq 3.05 \cdot 10^{+40}:\\ \;\;\;\;2 + -4 \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{z - x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 80.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+137}:\\ \;\;\;\;2\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+111}:\\ \;\;\;\;-4 \cdot \frac{z - x}{y}\\ \mathbf{else}:\\ \;\;\;\;2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -5.8e+137) 2.0 (if (<= y 4.5e+111) (* -4.0 (/ (- z x) y)) 2.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -5.8e+137) {
		tmp = 2.0;
	} else if (y <= 4.5e+111) {
		tmp = -4.0 * ((z - x) / y);
	} else {
		tmp = 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-5.8d+137)) then
        tmp = 2.0d0
    else if (y <= 4.5d+111) then
        tmp = (-4.0d0) * ((z - x) / y)
    else
        tmp = 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -5.8e+137) {
		tmp = 2.0;
	} else if (y <= 4.5e+111) {
		tmp = -4.0 * ((z - x) / y);
	} else {
		tmp = 2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -5.8e+137:
		tmp = 2.0
	elif y <= 4.5e+111:
		tmp = -4.0 * ((z - x) / y)
	else:
		tmp = 2.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -5.8e+137)
		tmp = 2.0;
	elseif (y <= 4.5e+111)
		tmp = Float64(-4.0 * Float64(Float64(z - x) / y));
	else
		tmp = 2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -5.8e+137)
		tmp = 2.0;
	elseif (y <= 4.5e+111)
		tmp = -4.0 * ((z - x) / y);
	else
		tmp = 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -5.8e+137], 2.0, If[LessEqual[y, 4.5e+111], N[(-4.0 * N[(N[(z - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], 2.0]]

Derivation

1. Split input into 2 regimes

2. if y < -5.79999999999999969e137 or 4.50000000000000001e111 < 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 N/A

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

      2. associate-*l/ N/A

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

      3. +-commutative N/A

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

      4. associate--l+ N/A

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

      5. distribute-lft-in N/A

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

      6. +-commutative N/A

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

      7. associate-+l+ N/A

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

      8. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{4}{y} \cdot \left(x - z\right)\right), \color{blue}{\left(\frac{4}{y} \cdot \left(y \cdot \frac{1}{4}\right) + 1\right)}\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf

      \[\leadsto \color{blue}{2} \]
   6. Step-by-step derivation

   7. Simplified 70.0%

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

   if -5.79999999999999969e137 < y < 4.50000000000000001e111

   1. Initial program 99.0%

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

      1. +-commutative N/A

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

      2. associate-*l/ N/A

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

      3. +-commutative N/A

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

      4. associate--l+ N/A

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

      5. distribute-lft-in N/A

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

      6. +-commutative N/A

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

      7. associate-+l+ N/A

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

      8. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{4}{y} \cdot \left(x - z\right)\right), \color{blue}{\left(\frac{4}{y} \cdot \left(y \cdot \frac{1}{4}\right) + 1\right)}\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0

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

   7. Simplified 83.6%

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

Alternative 7: 53.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \frac{-4}{y}\\ \mathbf{if}\;z \leq -9 \cdot 10^{+81}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+21}:\\ \;\;\;\;2\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (/ -4.0 y))))
   (if (<= z -9e+81) t_0 (if (<= z 6.2e+21) 2.0 t_0))))

C

double code(double x, double y, double z) {
	double t_0 = z * (-4.0 / y);
	double tmp;
	if (z <= -9e+81) {
		tmp = t_0;
	} else if (z <= 6.2e+21) {
		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 * ((-4.0d0) / y)
    if (z <= (-9d+81)) then
        tmp = t_0
    else if (z <= 6.2d+21) 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 * (-4.0 / y);
	double tmp;
	if (z <= -9e+81) {
		tmp = t_0;
	} else if (z <= 6.2e+21) {
		tmp = 2.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * (-4.0 / y)
	tmp = 0
	if z <= -9e+81:
		tmp = t_0
	elif z <= 6.2e+21:
		tmp = 2.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(-4.0 / y))
	tmp = 0.0
	if (z <= -9e+81)
		tmp = t_0;
	elseif (z <= 6.2e+21)
		tmp = 2.0;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * (-4.0 / y);
	tmp = 0.0;
	if (z <= -9e+81)
		tmp = t_0;
	elseif (z <= 6.2e+21)
		tmp = 2.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(-4.0 / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9e+81], t$95$0, If[LessEqual[z, 6.2e+21], 2.0, t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -9.00000000000000034e81 or 6.2e21 < z

   1. Initial program 98.2%

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

      1. +-commutative N/A

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

      2. associate-*l/ N/A

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

      3. +-commutative N/A

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

      4. associate--l+ N/A

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

      5. distribute-lft-in N/A

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

      6. +-commutative N/A

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

      7. associate-+l+ N/A

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

      8. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{4}{y} \cdot \left(x - z\right)\right), \color{blue}{\left(\frac{4}{y} \cdot \left(y \cdot \frac{1}{4}\right) + 1\right)}\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(-4 \cdot z\right), \color{blue}{y}\right) \]

      3. *-lowering-*.f64 60.8%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(-4, z\right), y\right) \]

   7. Simplified 60.8%

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

      1. associate-*l/ N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{-4}{y}\right), \color{blue}{z}\right) \]

      3. /-lowering-/.f64 61.4%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(-4, y\right), z\right) \]

   9. Applied egg-rr 61.4%

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

   if -9.00000000000000034e81 < z < 6.2e21

   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 N/A

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

      2. associate-*l/ N/A

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

      3. +-commutative N/A

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

      4. associate--l+ N/A

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

      5. distribute-lft-in N/A

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

      6. +-commutative N/A

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

      7. associate-+l+ N/A

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

      8. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{4}{y} \cdot \left(x - z\right)\right), \color{blue}{\left(\frac{4}{y} \cdot \left(y \cdot \frac{1}{4}\right) + 1\right)}\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf

      \[\leadsto \color{blue}{2} \]
   6. Step-by-step derivation

   7. Simplified 43.8%

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

4. Final simplification 51.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+81}:\\ \;\;\;\;z \cdot \frac{-4}{y}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+21}:\\ \;\;\;\;2\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{-4}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 33.8% 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 99.2%

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

   1. +-commutative N/A

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

   2. associate-*l/ N/A

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

   3. +-commutative N/A

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

   4. associate--l+ N/A

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

   5. distribute-lft-in N/A

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

   6. +-commutative N/A

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

   7. associate-+l+ N/A

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

   8. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\frac{4}{y} \cdot \left(x - z\right)\right), \color{blue}{\left(\frac{4}{y} \cdot \left(y \cdot \frac{1}{4}\right) + 1\right)}\right) \]

3. Simplified 100.0%

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

5. Taylor expanded in y around inf

   \[\leadsto \color{blue}{2} \]
6. Step-by-step derivation

7. Simplified 31.8%

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

Reproduce

herbie shell --seed 2024138 
(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)))