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

Percentage Accurate: 99.7% → 99.8%

Time: 9.4s

Alternatives: 8

Speedup: 1.4×

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

Specification

Math

\[\begin{array}{l} \\ 1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ 1.0 (/ (* 4.0 (- (+ x (* y 0.75)) z)) y)))

C

double code(double x, double y, double z) {
	return 1.0 + ((4.0 * ((x + (y * 0.75)) - 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 * 0.75d0)) - z)) / y)
end function

Java

public static double code(double x, double y, double z) {
	return 1.0 + ((4.0 * ((x + (y * 0.75)) - z)) / y);
}

Python

def code(x, y, z):
	return 1.0 + ((4.0 * ((x + (y * 0.75)) - z)) / y)

Julia

function code(x, y, z)
	return Float64(1.0 + Float64(Float64(4.0 * Float64(Float64(x + Float64(y * 0.75)) - z)) / y))
end

MATLAB

function tmp = code(x, y, z)
	tmp = 1.0 + ((4.0 * ((x + (y * 0.75)) - z)) / y);
end

Wolfram

code[x_, y_, z_] := N[(1.0 + N[(N[(4.0 * N[(N[(x + N[(y * 0.75), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ 1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ 1.0 (/ (* 4.0 (- (+ x (* y 0.75)) z)) y)))

C

double code(double x, double y, double z) {
	return 1.0 + ((4.0 * ((x + (y * 0.75)) - 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 * 0.75d0)) - z)) / y)
end function

Java

public static double code(double x, double y, double z) {
	return 1.0 + ((4.0 * ((x + (y * 0.75)) - z)) / y);
}

Python

def code(x, y, z):
	return 1.0 + ((4.0 * ((x + (y * 0.75)) - z)) / y)

Julia

function code(x, y, z)
	return Float64(1.0 + Float64(Float64(4.0 * Float64(Float64(x + Float64(y * 0.75)) - z)) / y))
end

MATLAB

function tmp = code(x, y, z)
	tmp = 1.0 + ((4.0 * ((x + (y * 0.75)) - z)) / y);
end

Wolfram

code[x_, y_, z_] := N[(1.0 + N[(N[(4.0 * N[(N[(x + N[(y * 0.75), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.8% accurate, 1.4× speedup

Math

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

FPCore

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

C

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

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 + ((4.0d0 / y) * (x - z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.8%

   \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
2. Step-by-step derivation

   1. associate-*l/ N/A

      \[\leadsto 1 + \frac{4}{y} \cdot \color{blue}{\left(\left(x + y \cdot \frac{3}{4}\right) - z\right)} \]

   2. +-commutative N/A

      \[\leadsto 1 + \frac{4}{y} \cdot \left(\left(y \cdot \frac{3}{4} + x\right) - z\right) \]

   3. associate--l+ N/A

      \[\leadsto 1 + \frac{4}{y} \cdot \left(y \cdot \frac{3}{4} + \color{blue}{\left(x - z\right)}\right) \]

   4. distribute-lft-in N/A

      \[\leadsto 1 + \left(\frac{4}{y} \cdot \left(y \cdot \frac{3}{4}\right) + \color{blue}{\frac{4}{y} \cdot \left(x - z\right)}\right) \]

   5. associate-+r+ N/A

      \[\leadsto \left(1 + \frac{4}{y} \cdot \left(y \cdot \frac{3}{4}\right)\right) + \color{blue}{\frac{4}{y} \cdot \left(x - z\right)} \]

   6. associate-*r* N/A

      \[\leadsto \left(1 + \left(\frac{4}{y} \cdot y\right) \cdot \frac{3}{4}\right) + \frac{4}{\color{blue}{y}} \cdot \left(x - z\right) \]

   7. associate-*l/ N/A

      \[\leadsto \left(1 + \frac{4 \cdot y}{y} \cdot \frac{3}{4}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

   8. associate-/l* N/A

      \[\leadsto \left(1 + \left(4 \cdot \frac{y}{y}\right) \cdot \frac{3}{4}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

   9. *-inverses N/A

      \[\leadsto \left(1 + \left(4 \cdot 1\right) \cdot \frac{3}{4}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

   10. metadata-eval N/A

       \[\leadsto \left(1 + 4 \cdot \frac{3}{4}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

   11. metadata-eval N/A

       \[\leadsto \left(1 + 3\right) + \frac{4}{\color{blue}{y}} \cdot \left(x - z\right) \]

   12. metadata-eval N/A

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

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

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

   14. associate-*l/ N/A

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

   15. /-lowering-/.f64 N/A

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

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

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

   17. --lowering--.f64 99.3%

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

3. Simplified 99.3%

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

   1. *-commutative N/A

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

   2. associate-/l* N/A

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

   3. *-commutative N/A

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

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

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

   5. /-lowering-/.f64 N/A

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

   6. --lowering--.f64 99.8%

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

6. Applied egg-rr 99.8%

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

Alternative 2: 54.0% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 4 regimes

2. if x < -11500

   1. Initial program 97.3%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ N/A

         \[\leadsto 1 + \frac{4}{y} \cdot \color{blue}{\left(\left(x + y \cdot \frac{3}{4}\right) - z\right)} \]

      2. +-commutative N/A

         \[\leadsto 1 + \frac{4}{y} \cdot \left(\left(y \cdot \frac{3}{4} + x\right) - z\right) \]

      3. associate--l+ N/A

         \[\leadsto 1 + \frac{4}{y} \cdot \left(y \cdot \frac{3}{4} + \color{blue}{\left(x - z\right)}\right) \]

      4. distribute-lft-in N/A

         \[\leadsto 1 + \left(\frac{4}{y} \cdot \left(y \cdot \frac{3}{4}\right) + \color{blue}{\frac{4}{y} \cdot \left(x - z\right)}\right) \]

      5. associate-+r+ N/A

         \[\leadsto \left(1 + \frac{4}{y} \cdot \left(y \cdot \frac{3}{4}\right)\right) + \color{blue}{\frac{4}{y} \cdot \left(x - z\right)} \]

      6. associate-*r* N/A

         \[\leadsto \left(1 + \left(\frac{4}{y} \cdot y\right) \cdot \frac{3}{4}\right) + \frac{4}{\color{blue}{y}} \cdot \left(x - z\right) \]

      7. associate-*l/ N/A

         \[\leadsto \left(1 + \frac{4 \cdot y}{y} \cdot \frac{3}{4}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      8. associate-/l* N/A

         \[\leadsto \left(1 + \left(4 \cdot \frac{y}{y}\right) \cdot \frac{3}{4}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      9. *-inverses N/A

         \[\leadsto \left(1 + \left(4 \cdot 1\right) \cdot \frac{3}{4}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      10. metadata-eval N/A

          \[\leadsto \left(1 + 4 \cdot \frac{3}{4}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      11. metadata-eval N/A

          \[\leadsto \left(1 + 3\right) + \frac{4}{\color{blue}{y}} \cdot \left(x - z\right) \]

      12. metadata-eval N/A

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

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

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

      14. associate-*l/ N/A

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

      15. /-lowering-/.f64 N/A

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

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

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

      17. --lowering--.f64 97.3%

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

   3. Simplified 97.3%

      \[\leadsto \color{blue}{4 + \frac{4 \cdot \left(x - z\right)}{y}} \]
   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 76.8%

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

   7. Simplified 76.8%

      \[\leadsto \color{blue}{\frac{4 \cdot x}{y}} \]
   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. *-lowering-*.f64 N/A

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

      4. /-lowering-/.f64 77.9%

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

   9. Applied egg-rr 77.9%

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

   if -11500 < x < -3.7000000000000001e-119

   1. Initial program 96.4%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ N/A

         \[\leadsto 1 + \frac{4}{y} \cdot \color{blue}{\left(\left(x + y \cdot \frac{3}{4}\right) - z\right)} \]

      2. +-commutative N/A

         \[\leadsto 1 + \frac{4}{y} \cdot \left(\left(y \cdot \frac{3}{4} + x\right) - z\right) \]

      3. associate--l+ N/A

         \[\leadsto 1 + \frac{4}{y} \cdot \left(y \cdot \frac{3}{4} + \color{blue}{\left(x - z\right)}\right) \]

      4. distribute-lft-in N/A

         \[\leadsto 1 + \left(\frac{4}{y} \cdot \left(y \cdot \frac{3}{4}\right) + \color{blue}{\frac{4}{y} \cdot \left(x - z\right)}\right) \]

      5. associate-+r+ N/A

         \[\leadsto \left(1 + \frac{4}{y} \cdot \left(y \cdot \frac{3}{4}\right)\right) + \color{blue}{\frac{4}{y} \cdot \left(x - z\right)} \]

      6. associate-*r* N/A

         \[\leadsto \left(1 + \left(\frac{4}{y} \cdot y\right) \cdot \frac{3}{4}\right) + \frac{4}{\color{blue}{y}} \cdot \left(x - z\right) \]

      7. associate-*l/ N/A

         \[\leadsto \left(1 + \frac{4 \cdot y}{y} \cdot \frac{3}{4}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      8. associate-/l* N/A

         \[\leadsto \left(1 + \left(4 \cdot \frac{y}{y}\right) \cdot \frac{3}{4}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      9. *-inverses N/A

         \[\leadsto \left(1 + \left(4 \cdot 1\right) \cdot \frac{3}{4}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      10. metadata-eval N/A

          \[\leadsto \left(1 + 4 \cdot \frac{3}{4}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      11. metadata-eval N/A

          \[\leadsto \left(1 + 3\right) + \frac{4}{\color{blue}{y}} \cdot \left(x - z\right) \]

      12. metadata-eval N/A

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

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

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

      14. associate-*l/ N/A

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

      15. /-lowering-/.f64 N/A

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

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

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

      17. --lowering--.f64 100.0%

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

   3. Simplified 100.0%

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

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ N/A

         \[\leadsto 1 + \frac{4}{y} \cdot \color{blue}{\left(\left(x + y \cdot \frac{3}{4}\right) - z\right)} \]

      2. +-commutative N/A

         \[\leadsto 1 + \frac{4}{y} \cdot \left(\left(y \cdot \frac{3}{4} + x\right) - z\right) \]

      3. associate--l+ N/A

         \[\leadsto 1 + \frac{4}{y} \cdot \left(y \cdot \frac{3}{4} + \color{blue}{\left(x - z\right)}\right) \]

      4. distribute-lft-in N/A

         \[\leadsto 1 + \left(\frac{4}{y} \cdot \left(y \cdot \frac{3}{4}\right) + \color{blue}{\frac{4}{y} \cdot \left(x - z\right)}\right) \]

      5. associate-+r+ N/A

         \[\leadsto \left(1 + \frac{4}{y} \cdot \left(y \cdot \frac{3}{4}\right)\right) + \color{blue}{\frac{4}{y} \cdot \left(x - z\right)} \]

      6. associate-*r* N/A

         \[\leadsto \left(1 + \left(\frac{4}{y} \cdot y\right) \cdot \frac{3}{4}\right) + \frac{4}{\color{blue}{y}} \cdot \left(x - z\right) \]

      7. associate-*l/ N/A

         \[\leadsto \left(1 + \frac{4 \cdot y}{y} \cdot \frac{3}{4}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      8. associate-/l* N/A

         \[\leadsto \left(1 + \left(4 \cdot \frac{y}{y}\right) \cdot \frac{3}{4}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      9. *-inverses N/A

         \[\leadsto \left(1 + \left(4 \cdot 1\right) \cdot \frac{3}{4}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      10. metadata-eval N/A

          \[\leadsto \left(1 + 4 \cdot \frac{3}{4}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      11. metadata-eval N/A

          \[\leadsto \left(1 + 3\right) + \frac{4}{\color{blue}{y}} \cdot \left(x - z\right) \]

      12. metadata-eval N/A

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

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

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

      14. associate-*l/ N/A

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

      15. /-lowering-/.f64 N/A

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

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

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

      17. --lowering--.f64 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf

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

   7. Simplified 54.2%

      \[\leadsto \color{blue}{4} \]

   if 7.99999999999999982e38 < x

   1. Initial program 100.0%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ N/A

         \[\leadsto 1 + \frac{4}{y} \cdot \color{blue}{\left(\left(x + y \cdot \frac{3}{4}\right) - z\right)} \]

      2. +-commutative N/A

         \[\leadsto 1 + \frac{4}{y} \cdot \left(\left(y \cdot \frac{3}{4} + x\right) - z\right) \]

      3. associate--l+ N/A

         \[\leadsto 1 + \frac{4}{y} \cdot \left(y \cdot \frac{3}{4} + \color{blue}{\left(x - z\right)}\right) \]

      4. distribute-lft-in N/A

         \[\leadsto 1 + \left(\frac{4}{y} \cdot \left(y \cdot \frac{3}{4}\right) + \color{blue}{\frac{4}{y} \cdot \left(x - z\right)}\right) \]

      5. associate-+r+ N/A

         \[\leadsto \left(1 + \frac{4}{y} \cdot \left(y \cdot \frac{3}{4}\right)\right) + \color{blue}{\frac{4}{y} \cdot \left(x - z\right)} \]

      6. associate-*r* N/A

         \[\leadsto \left(1 + \left(\frac{4}{y} \cdot y\right) \cdot \frac{3}{4}\right) + \frac{4}{\color{blue}{y}} \cdot \left(x - z\right) \]

      7. associate-*l/ N/A

         \[\leadsto \left(1 + \frac{4 \cdot y}{y} \cdot \frac{3}{4}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      8. associate-/l* N/A

         \[\leadsto \left(1 + \left(4 \cdot \frac{y}{y}\right) \cdot \frac{3}{4}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      9. *-inverses N/A

         \[\leadsto \left(1 + \left(4 \cdot 1\right) \cdot \frac{3}{4}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      10. metadata-eval N/A

          \[\leadsto \left(1 + 4 \cdot \frac{3}{4}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      11. metadata-eval N/A

          \[\leadsto \left(1 + 3\right) + \frac{4}{\color{blue}{y}} \cdot \left(x - z\right) \]

      12. metadata-eval N/A

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

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

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

      14. associate-*l/ N/A

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

      15. /-lowering-/.f64 N/A

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

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

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

      17. --lowering--.f64 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{4 + \frac{4 \cdot \left(x - z\right)}{y}} \]
   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 78.4%

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

   7. Simplified 78.4%

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

4. Final simplification 66.1%

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

Alternative 3: 54.0% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 3 regimes

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

   1. Initial program 98.4%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ N/A

         \[\leadsto 1 + \frac{4}{y} \cdot \color{blue}{\left(\left(x + y \cdot \frac{3}{4}\right) - z\right)} \]

      2. +-commutative N/A

         \[\leadsto 1 + \frac{4}{y} \cdot \left(\left(y \cdot \frac{3}{4} + x\right) - z\right) \]

      3. associate--l+ N/A

         \[\leadsto 1 + \frac{4}{y} \cdot \left(y \cdot \frac{3}{4} + \color{blue}{\left(x - z\right)}\right) \]

      4. distribute-lft-in N/A

         \[\leadsto 1 + \left(\frac{4}{y} \cdot \left(y \cdot \frac{3}{4}\right) + \color{blue}{\frac{4}{y} \cdot \left(x - z\right)}\right) \]

      5. associate-+r+ N/A

         \[\leadsto \left(1 + \frac{4}{y} \cdot \left(y \cdot \frac{3}{4}\right)\right) + \color{blue}{\frac{4}{y} \cdot \left(x - z\right)} \]

      6. associate-*r* N/A

         \[\leadsto \left(1 + \left(\frac{4}{y} \cdot y\right) \cdot \frac{3}{4}\right) + \frac{4}{\color{blue}{y}} \cdot \left(x - z\right) \]

      7. associate-*l/ N/A

         \[\leadsto \left(1 + \frac{4 \cdot y}{y} \cdot \frac{3}{4}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      8. associate-/l* N/A

         \[\leadsto \left(1 + \left(4 \cdot \frac{y}{y}\right) \cdot \frac{3}{4}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      9. *-inverses N/A

         \[\leadsto \left(1 + \left(4 \cdot 1\right) \cdot \frac{3}{4}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      10. metadata-eval N/A

          \[\leadsto \left(1 + 4 \cdot \frac{3}{4}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      11. metadata-eval N/A

          \[\leadsto \left(1 + 3\right) + \frac{4}{\color{blue}{y}} \cdot \left(x - z\right) \]

      12. metadata-eval N/A

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

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

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

      14. associate-*l/ N/A

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

      15. /-lowering-/.f64 N/A

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

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

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

      17. --lowering--.f64 98.4%

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

   3. Simplified 98.4%

      \[\leadsto \color{blue}{4 + \frac{4 \cdot \left(x - z\right)}{y}} \]
   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. *-lowering-*.f64 N/A

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

      4. /-lowering-/.f64 78.1%

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

   9. Applied egg-rr 78.1%

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

   if -6200 < x < -4.8e-123

   1. Initial program 96.4%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ N/A

         \[\leadsto 1 + \frac{4}{y} \cdot \color{blue}{\left(\left(x + y \cdot \frac{3}{4}\right) - z\right)} \]

      2. +-commutative N/A

         \[\leadsto 1 + \frac{4}{y} \cdot \left(\left(y \cdot \frac{3}{4} + x\right) - z\right) \]

      3. associate--l+ N/A

         \[\leadsto 1 + \frac{4}{y} \cdot \left(y \cdot \frac{3}{4} + \color{blue}{\left(x - z\right)}\right) \]

      4. distribute-lft-in N/A

         \[\leadsto 1 + \left(\frac{4}{y} \cdot \left(y \cdot \frac{3}{4}\right) + \color{blue}{\frac{4}{y} \cdot \left(x - z\right)}\right) \]

      5. associate-+r+ N/A

         \[\leadsto \left(1 + \frac{4}{y} \cdot \left(y \cdot \frac{3}{4}\right)\right) + \color{blue}{\frac{4}{y} \cdot \left(x - z\right)} \]

      6. associate-*r* N/A

         \[\leadsto \left(1 + \left(\frac{4}{y} \cdot y\right) \cdot \frac{3}{4}\right) + \frac{4}{\color{blue}{y}} \cdot \left(x - z\right) \]

      7. associate-*l/ N/A

         \[\leadsto \left(1 + \frac{4 \cdot y}{y} \cdot \frac{3}{4}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      8. associate-/l* N/A

         \[\leadsto \left(1 + \left(4 \cdot \frac{y}{y}\right) \cdot \frac{3}{4}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      9. *-inverses N/A

         \[\leadsto \left(1 + \left(4 \cdot 1\right) \cdot \frac{3}{4}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      10. metadata-eval N/A

          \[\leadsto \left(1 + 4 \cdot \frac{3}{4}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      11. metadata-eval N/A

          \[\leadsto \left(1 + 3\right) + \frac{4}{\color{blue}{y}} \cdot \left(x - z\right) \]

      12. metadata-eval N/A

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

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

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

      14. associate-*l/ N/A

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

      15. /-lowering-/.f64 N/A

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

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

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

      17. --lowering--.f64 100.0%

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

   3. Simplified 100.0%

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

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ N/A

         \[\leadsto 1 + \frac{4}{y} \cdot \color{blue}{\left(\left(x + y \cdot \frac{3}{4}\right) - z\right)} \]

      2. +-commutative N/A

         \[\leadsto 1 + \frac{4}{y} \cdot \left(\left(y \cdot \frac{3}{4} + x\right) - z\right) \]

      3. associate--l+ N/A

         \[\leadsto 1 + \frac{4}{y} \cdot \left(y \cdot \frac{3}{4} + \color{blue}{\left(x - z\right)}\right) \]

      4. distribute-lft-in N/A

         \[\leadsto 1 + \left(\frac{4}{y} \cdot \left(y \cdot \frac{3}{4}\right) + \color{blue}{\frac{4}{y} \cdot \left(x - z\right)}\right) \]

      5. associate-+r+ N/A

         \[\leadsto \left(1 + \frac{4}{y} \cdot \left(y \cdot \frac{3}{4}\right)\right) + \color{blue}{\frac{4}{y} \cdot \left(x - z\right)} \]

      6. associate-*r* N/A

         \[\leadsto \left(1 + \left(\frac{4}{y} \cdot y\right) \cdot \frac{3}{4}\right) + \frac{4}{\color{blue}{y}} \cdot \left(x - z\right) \]

      7. associate-*l/ N/A

         \[\leadsto \left(1 + \frac{4 \cdot y}{y} \cdot \frac{3}{4}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      8. associate-/l* N/A

         \[\leadsto \left(1 + \left(4 \cdot \frac{y}{y}\right) \cdot \frac{3}{4}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      9. *-inverses N/A

         \[\leadsto \left(1 + \left(4 \cdot 1\right) \cdot \frac{3}{4}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      10. metadata-eval N/A

          \[\leadsto \left(1 + 4 \cdot \frac{3}{4}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      11. metadata-eval N/A

          \[\leadsto \left(1 + 3\right) + \frac{4}{\color{blue}{y}} \cdot \left(x - z\right) \]

      12. metadata-eval N/A

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

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

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

      14. associate-*l/ N/A

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

      15. /-lowering-/.f64 N/A

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

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

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

      17. --lowering--.f64 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf

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

   7. Simplified 54.2%

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

4. Final simplification 66.0%

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

Alternative 4: 54.1% accurate, 0.6× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	double t_0 = (4.0 / y) * x;
	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 = 4.0;
	} 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 = (4.0d0 / y) * x
    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 = 4.0d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (4.0 / y) * x;
	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 = 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (4.0 / y) * x
	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 = 4.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(4.0 / y) * x)
	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 = 4.0;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (4.0 / y) * x;
	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 = 4.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(4.0 / y), $MachinePrecision] * x), $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], 4.0, t$95$0]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 98.4%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ N/A

         \[\leadsto 1 + \frac{4}{y} \cdot \color{blue}{\left(\left(x + y \cdot \frac{3}{4}\right) - z\right)} \]

      2. +-commutative N/A

         \[\leadsto 1 + \frac{4}{y} \cdot \left(\left(y \cdot \frac{3}{4} + x\right) - z\right) \]

      3. associate--l+ N/A

         \[\leadsto 1 + \frac{4}{y} \cdot \left(y \cdot \frac{3}{4} + \color{blue}{\left(x - z\right)}\right) \]

      4. distribute-lft-in N/A

         \[\leadsto 1 + \left(\frac{4}{y} \cdot \left(y \cdot \frac{3}{4}\right) + \color{blue}{\frac{4}{y} \cdot \left(x - z\right)}\right) \]

      5. associate-+r+ N/A

         \[\leadsto \left(1 + \frac{4}{y} \cdot \left(y \cdot \frac{3}{4}\right)\right) + \color{blue}{\frac{4}{y} \cdot \left(x - z\right)} \]

      6. associate-*r* N/A

         \[\leadsto \left(1 + \left(\frac{4}{y} \cdot y\right) \cdot \frac{3}{4}\right) + \frac{4}{\color{blue}{y}} \cdot \left(x - z\right) \]

      7. associate-*l/ N/A

         \[\leadsto \left(1 + \frac{4 \cdot y}{y} \cdot \frac{3}{4}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      8. associate-/l* N/A

         \[\leadsto \left(1 + \left(4 \cdot \frac{y}{y}\right) \cdot \frac{3}{4}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      9. *-inverses N/A

         \[\leadsto \left(1 + \left(4 \cdot 1\right) \cdot \frac{3}{4}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      10. metadata-eval N/A

          \[\leadsto \left(1 + 4 \cdot \frac{3}{4}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      11. metadata-eval N/A

          \[\leadsto \left(1 + 3\right) + \frac{4}{\color{blue}{y}} \cdot \left(x - z\right) \]

      12. metadata-eval N/A

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

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

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

      14. associate-*l/ N/A

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

      15. /-lowering-/.f64 N/A

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

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

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

      17. --lowering--.f64 98.4%

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

   3. Simplified 98.4%

      \[\leadsto \color{blue}{4 + \frac{4 \cdot \left(x - z\right)}{y}} \]
   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. *-lowering-*.f64 N/A

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

      4. /-lowering-/.f64 78.1%

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

   9. Applied egg-rr 78.1%

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

   if -19000 < x < -3.5999999999999997e-123

   1. Initial program 96.4%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ N/A

         \[\leadsto 1 + \frac{4}{y} \cdot \color{blue}{\left(\left(x + y \cdot \frac{3}{4}\right) - z\right)} \]

      2. +-commutative N/A

         \[\leadsto 1 + \frac{4}{y} \cdot \left(\left(y \cdot \frac{3}{4} + x\right) - z\right) \]

      3. associate--l+ N/A

         \[\leadsto 1 + \frac{4}{y} \cdot \left(y \cdot \frac{3}{4} + \color{blue}{\left(x - z\right)}\right) \]

      4. distribute-lft-in N/A

         \[\leadsto 1 + \left(\frac{4}{y} \cdot \left(y \cdot \frac{3}{4}\right) + \color{blue}{\frac{4}{y} \cdot \left(x - z\right)}\right) \]

      5. associate-+r+ N/A

         \[\leadsto \left(1 + \frac{4}{y} \cdot \left(y \cdot \frac{3}{4}\right)\right) + \color{blue}{\frac{4}{y} \cdot \left(x - z\right)} \]

      6. associate-*r* N/A

         \[\leadsto \left(1 + \left(\frac{4}{y} \cdot y\right) \cdot \frac{3}{4}\right) + \frac{4}{\color{blue}{y}} \cdot \left(x - z\right) \]

      7. associate-*l/ N/A

         \[\leadsto \left(1 + \frac{4 \cdot y}{y} \cdot \frac{3}{4}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      8. associate-/l* N/A

         \[\leadsto \left(1 + \left(4 \cdot \frac{y}{y}\right) \cdot \frac{3}{4}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      9. *-inverses N/A

         \[\leadsto \left(1 + \left(4 \cdot 1\right) \cdot \frac{3}{4}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      10. metadata-eval N/A

          \[\leadsto \left(1 + 4 \cdot \frac{3}{4}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      11. metadata-eval N/A

          \[\leadsto \left(1 + 3\right) + \frac{4}{\color{blue}{y}} \cdot \left(x - z\right) \]

      12. metadata-eval N/A

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

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

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

      14. associate-*l/ N/A

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

      15. /-lowering-/.f64 N/A

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

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

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

      17. --lowering--.f64 100.0%

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

   3. Simplified 100.0%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

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

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

      5. /-lowering-/.f64 N/A

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

      6. --lowering--.f64 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in z around inf

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. metadata-eval N/A

         \[\leadsto z \cdot \frac{\mathsf{neg}\left(4\right)}{y} \]

      5. distribute-neg-frac N/A

         \[\leadsto z \cdot \left(\mathsf{neg}\left(\frac{4}{y}\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto z \cdot \left(\mathsf{neg}\left(\frac{4 \cdot 1}{y}\right)\right) \]

      7. associate-*r/ N/A

         \[\leadsto z \cdot \left(\mathsf{neg}\left(4 \cdot \frac{1}{y}\right)\right) \]

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

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

      9. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(\frac{4 \cdot 1}{y}\right)\right)\right) \]

      10. metadata-eval N/A

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

      11. distribute-neg-frac N/A

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

      12. metadata-eval N/A

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

      13. /-lowering-/.f64 61.1%

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

   9. Simplified 61.1%

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

   if -3.5999999999999997e-123 < x < 4.2000000000000002e40

   1. Initial program 99.8%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ N/A

         \[\leadsto 1 + \frac{4}{y} \cdot \color{blue}{\left(\left(x + y \cdot \frac{3}{4}\right) - z\right)} \]

      2. +-commutative N/A

         \[\leadsto 1 + \frac{4}{y} \cdot \left(\left(y \cdot \frac{3}{4} + x\right) - z\right) \]

      3. associate--l+ N/A

         \[\leadsto 1 + \frac{4}{y} \cdot \left(y \cdot \frac{3}{4} + \color{blue}{\left(x - z\right)}\right) \]

      4. distribute-lft-in N/A

         \[\leadsto 1 + \left(\frac{4}{y} \cdot \left(y \cdot \frac{3}{4}\right) + \color{blue}{\frac{4}{y} \cdot \left(x - z\right)}\right) \]

      5. associate-+r+ N/A

         \[\leadsto \left(1 + \frac{4}{y} \cdot \left(y \cdot \frac{3}{4}\right)\right) + \color{blue}{\frac{4}{y} \cdot \left(x - z\right)} \]

      6. associate-*r* N/A

         \[\leadsto \left(1 + \left(\frac{4}{y} \cdot y\right) \cdot \frac{3}{4}\right) + \frac{4}{\color{blue}{y}} \cdot \left(x - z\right) \]

      7. associate-*l/ N/A

         \[\leadsto \left(1 + \frac{4 \cdot y}{y} \cdot \frac{3}{4}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      8. associate-/l* N/A

         \[\leadsto \left(1 + \left(4 \cdot \frac{y}{y}\right) \cdot \frac{3}{4}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      9. *-inverses N/A

         \[\leadsto \left(1 + \left(4 \cdot 1\right) \cdot \frac{3}{4}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      10. metadata-eval N/A

          \[\leadsto \left(1 + 4 \cdot \frac{3}{4}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      11. metadata-eval N/A

          \[\leadsto \left(1 + 3\right) + \frac{4}{\color{blue}{y}} \cdot \left(x - z\right) \]

      12. metadata-eval N/A

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

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

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

      14. associate-*l/ N/A

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

      15. /-lowering-/.f64 N/A

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

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

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

      17. --lowering--.f64 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf

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

   7. Simplified 54.2%

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

4. Final simplification 66.0%

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

Alternative 5: 86.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 4 \cdot \frac{x - z}{y}\\ \mathbf{if}\;x \leq -1.65 \cdot 10^{+35}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 3.05 \cdot 10^{+40}:\\ \;\;\;\;4 + \frac{z \cdot -4}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 4.0 (/ (- x z) y))))
   (if (<= x -1.65e+35)
     t_0
     (if (<= x 3.05e+40) (+ 4.0 (/ (* z -4.0) y)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = 4.0 * ((x - z) / y);
	double tmp;
	if (x <= -1.65e+35) {
		tmp = t_0;
	} else if (x <= 3.05e+40) {
		tmp = 4.0 + ((z * -4.0) / 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 * ((x - z) / y)
    if (x <= (-1.65d+35)) then
        tmp = t_0
    else if (x <= 3.05d+40) then
        tmp = 4.0d0 + ((z * (-4.0d0)) / 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 * ((x - z) / y);
	double tmp;
	if (x <= -1.65e+35) {
		tmp = t_0;
	} else if (x <= 3.05e+40) {
		tmp = 4.0 + ((z * -4.0) / y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 4.0 * ((x - z) / y)
	tmp = 0
	if x <= -1.65e+35:
		tmp = t_0
	elif x <= 3.05e+40:
		tmp = 4.0 + ((z * -4.0) / y)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(4.0 * Float64(Float64(x - z) / y))
	tmp = 0.0
	if (x <= -1.65e+35)
		tmp = t_0;
	elseif (x <= 3.05e+40)
		tmp = Float64(4.0 + Float64(Float64(z * -4.0) / y));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 4.0 * ((x - z) / y);
	tmp = 0.0;
	if (x <= -1.65e+35)
		tmp = t_0;
	elseif (x <= 3.05e+40)
		tmp = 4.0 + ((z * -4.0) / y);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(4.0 * N[(N[(x - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.65e+35], t$95$0, If[LessEqual[x, 3.05e+40], N[(4.0 + N[(N[(z * -4.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.6500000000000001e35 or 3.05e40 < x

   1. Initial program 98.3%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ N/A

         \[\leadsto 1 + \frac{4}{y} \cdot \color{blue}{\left(\left(x + y \cdot \frac{3}{4}\right) - z\right)} \]

      2. +-commutative N/A

         \[\leadsto 1 + \frac{4}{y} \cdot \left(\left(y \cdot \frac{3}{4} + x\right) - z\right) \]

      3. associate--l+ N/A

         \[\leadsto 1 + \frac{4}{y} \cdot \left(y \cdot \frac{3}{4} + \color{blue}{\left(x - z\right)}\right) \]

      4. distribute-lft-in N/A

         \[\leadsto 1 + \left(\frac{4}{y} \cdot \left(y \cdot \frac{3}{4}\right) + \color{blue}{\frac{4}{y} \cdot \left(x - z\right)}\right) \]

      5. associate-+r+ N/A

         \[\leadsto \left(1 + \frac{4}{y} \cdot \left(y \cdot \frac{3}{4}\right)\right) + \color{blue}{\frac{4}{y} \cdot \left(x - z\right)} \]

      6. associate-*r* N/A

         \[\leadsto \left(1 + \left(\frac{4}{y} \cdot y\right) \cdot \frac{3}{4}\right) + \frac{4}{\color{blue}{y}} \cdot \left(x - z\right) \]

      7. associate-*l/ N/A

         \[\leadsto \left(1 + \frac{4 \cdot y}{y} \cdot \frac{3}{4}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      8. associate-/l* N/A

         \[\leadsto \left(1 + \left(4 \cdot \frac{y}{y}\right) \cdot \frac{3}{4}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      9. *-inverses N/A

         \[\leadsto \left(1 + \left(4 \cdot 1\right) \cdot \frac{3}{4}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      10. metadata-eval N/A

          \[\leadsto \left(1 + 4 \cdot \frac{3}{4}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      11. metadata-eval N/A

          \[\leadsto \left(1 + 3\right) + \frac{4}{\color{blue}{y}} \cdot \left(x - z\right) \]

      12. metadata-eval N/A

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

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

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

      14. associate-*l/ N/A

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

      15. /-lowering-/.f64 N/A

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

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

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

      17. --lowering--.f64 98.3%

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

   3. Simplified 98.3%

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

   5. Taylor expanded in y around 0

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

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

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

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

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

      3. --lowering--.f64 93.0%

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

   7. Simplified 93.0%

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

   if -1.6500000000000001e35 < x < 3.05e40

   1. Initial program 99.2%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ N/A

         \[\leadsto 1 + \frac{4}{y} \cdot \color{blue}{\left(\left(x + y \cdot \frac{3}{4}\right) - z\right)} \]

      2. +-commutative N/A

         \[\leadsto 1 + \frac{4}{y} \cdot \left(\left(y \cdot \frac{3}{4} + x\right) - z\right) \]

      3. associate--l+ N/A

         \[\leadsto 1 + \frac{4}{y} \cdot \left(y \cdot \frac{3}{4} + \color{blue}{\left(x - z\right)}\right) \]

      4. distribute-lft-in N/A

         \[\leadsto 1 + \left(\frac{4}{y} \cdot \left(y \cdot \frac{3}{4}\right) + \color{blue}{\frac{4}{y} \cdot \left(x - z\right)}\right) \]

      5. associate-+r+ N/A

         \[\leadsto \left(1 + \frac{4}{y} \cdot \left(y \cdot \frac{3}{4}\right)\right) + \color{blue}{\frac{4}{y} \cdot \left(x - z\right)} \]

      6. associate-*r* N/A

         \[\leadsto \left(1 + \left(\frac{4}{y} \cdot y\right) \cdot \frac{3}{4}\right) + \frac{4}{\color{blue}{y}} \cdot \left(x - z\right) \]

      7. associate-*l/ N/A

         \[\leadsto \left(1 + \frac{4 \cdot y}{y} \cdot \frac{3}{4}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      8. associate-/l* N/A

         \[\leadsto \left(1 + \left(4 \cdot \frac{y}{y}\right) \cdot \frac{3}{4}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      9. *-inverses N/A

         \[\leadsto \left(1 + \left(4 \cdot 1\right) \cdot \frac{3}{4}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      10. metadata-eval N/A

          \[\leadsto \left(1 + 4 \cdot \frac{3}{4}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      11. metadata-eval N/A

          \[\leadsto \left(1 + 3\right) + \frac{4}{\color{blue}{y}} \cdot \left(x - z\right) \]

      12. metadata-eval N/A

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

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

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

      14. associate-*l/ N/A

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

      15. /-lowering-/.f64 N/A

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

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

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

      17. --lowering--.f64 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0

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

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

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

      2. associate-*r/ N/A

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

      3. /-lowering-/.f64 N/A

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

      4. *-lowering-*.f64 90.8%

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

   7. Simplified 90.8%

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

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{+35}:\\ \;\;\;\;4 \cdot \frac{x - z}{y}\\ \mathbf{elif}\;x \leq 3.05 \cdot 10^{+40}:\\ \;\;\;\;4 + \frac{z \cdot -4}{y}\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \frac{x - z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 80.1% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if y < -5.79999999999999969e137 or 4.50000000000000001e111 < y

   1. Initial program 98.5%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ N/A

         \[\leadsto 1 + \frac{4}{y} \cdot \color{blue}{\left(\left(x + y \cdot \frac{3}{4}\right) - z\right)} \]

      2. +-commutative N/A

         \[\leadsto 1 + \frac{4}{y} \cdot \left(\left(y \cdot \frac{3}{4} + x\right) - z\right) \]

      3. associate--l+ N/A

         \[\leadsto 1 + \frac{4}{y} \cdot \left(y \cdot \frac{3}{4} + \color{blue}{\left(x - z\right)}\right) \]

      4. distribute-lft-in N/A

         \[\leadsto 1 + \left(\frac{4}{y} \cdot \left(y \cdot \frac{3}{4}\right) + \color{blue}{\frac{4}{y} \cdot \left(x - z\right)}\right) \]

      5. associate-+r+ N/A

         \[\leadsto \left(1 + \frac{4}{y} \cdot \left(y \cdot \frac{3}{4}\right)\right) + \color{blue}{\frac{4}{y} \cdot \left(x - z\right)} \]

      6. associate-*r* N/A

         \[\leadsto \left(1 + \left(\frac{4}{y} \cdot y\right) \cdot \frac{3}{4}\right) + \frac{4}{\color{blue}{y}} \cdot \left(x - z\right) \]

      7. associate-*l/ N/A

         \[\leadsto \left(1 + \frac{4 \cdot y}{y} \cdot \frac{3}{4}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      8. associate-/l* N/A

         \[\leadsto \left(1 + \left(4 \cdot \frac{y}{y}\right) \cdot \frac{3}{4}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      9. *-inverses N/A

         \[\leadsto \left(1 + \left(4 \cdot 1\right) \cdot \frac{3}{4}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      10. metadata-eval N/A

          \[\leadsto \left(1 + 4 \cdot \frac{3}{4}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      11. metadata-eval N/A

          \[\leadsto \left(1 + 3\right) + \frac{4}{\color{blue}{y}} \cdot \left(x - z\right) \]

      12. metadata-eval N/A

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

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

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

      14. associate-*l/ N/A

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

      15. /-lowering-/.f64 N/A

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

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

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

      17. --lowering--.f64 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf

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

   7. Simplified 70.1%

      \[\leadsto \color{blue}{4} \]

   if -5.79999999999999969e137 < y < 4.50000000000000001e111

   1. Initial program 99.0%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ N/A

         \[\leadsto 1 + \frac{4}{y} \cdot \color{blue}{\left(\left(x + y \cdot \frac{3}{4}\right) - z\right)} \]

      2. +-commutative N/A

         \[\leadsto 1 + \frac{4}{y} \cdot \left(\left(y \cdot \frac{3}{4} + x\right) - z\right) \]

      3. associate--l+ N/A

         \[\leadsto 1 + \frac{4}{y} \cdot \left(y \cdot \frac{3}{4} + \color{blue}{\left(x - z\right)}\right) \]

      4. distribute-lft-in N/A

         \[\leadsto 1 + \left(\frac{4}{y} \cdot \left(y \cdot \frac{3}{4}\right) + \color{blue}{\frac{4}{y} \cdot \left(x - z\right)}\right) \]

      5. associate-+r+ N/A

         \[\leadsto \left(1 + \frac{4}{y} \cdot \left(y \cdot \frac{3}{4}\right)\right) + \color{blue}{\frac{4}{y} \cdot \left(x - z\right)} \]

      6. associate-*r* N/A

         \[\leadsto \left(1 + \left(\frac{4}{y} \cdot y\right) \cdot \frac{3}{4}\right) + \frac{4}{\color{blue}{y}} \cdot \left(x - z\right) \]

      7. associate-*l/ N/A

         \[\leadsto \left(1 + \frac{4 \cdot y}{y} \cdot \frac{3}{4}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      8. associate-/l* N/A

         \[\leadsto \left(1 + \left(4 \cdot \frac{y}{y}\right) \cdot \frac{3}{4}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      9. *-inverses N/A

         \[\leadsto \left(1 + \left(4 \cdot 1\right) \cdot \frac{3}{4}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      10. metadata-eval N/A

          \[\leadsto \left(1 + 4 \cdot \frac{3}{4}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      11. metadata-eval N/A

          \[\leadsto \left(1 + 3\right) + \frac{4}{\color{blue}{y}} \cdot \left(x - z\right) \]

      12. metadata-eval N/A

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

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

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

      14. associate-*l/ N/A

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

      15. /-lowering-/.f64 N/A

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

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

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

      17. --lowering--.f64 99.0%

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

   3. Simplified 99.0%

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

   5. Taylor expanded in y around 0

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

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

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

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

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

      3. --lowering--.f64 83.6%

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

   7. Simplified 83.6%

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

Alternative 7: 54.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{4}{y} \cdot x\\ \mathbf{if}\;x \leq -7 \cdot 10^{+35}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 7.4 \cdot 10^{+37}:\\ \;\;\;\;4\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (/ 4.0 y) x)))
   (if (<= x -7e+35) t_0 (if (<= x 7.4e+37) 4.0 t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (4.0 / y) * x;
	double tmp;
	if (x <= -7e+35) {
		tmp = t_0;
	} else if (x <= 7.4e+37) {
		tmp = 4.0;
	} 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 = (4.0d0 / y) * x
    if (x <= (-7d+35)) then
        tmp = t_0
    else if (x <= 7.4d+37) then
        tmp = 4.0d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (4.0 / y) * x;
	double tmp;
	if (x <= -7e+35) {
		tmp = t_0;
	} else if (x <= 7.4e+37) {
		tmp = 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (4.0 / y) * x
	tmp = 0
	if x <= -7e+35:
		tmp = t_0
	elif x <= 7.4e+37:
		tmp = 4.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(4.0 / y) * x)
	tmp = 0.0
	if (x <= -7e+35)
		tmp = t_0;
	elseif (x <= 7.4e+37)
		tmp = 4.0;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (4.0 / y) * x;
	tmp = 0.0;
	if (x <= -7e+35)
		tmp = t_0;
	elseif (x <= 7.4e+37)
		tmp = 4.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(4.0 / y), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[x, -7e+35], t$95$0, If[LessEqual[x, 7.4e+37], 4.0, t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -7.0000000000000001e35 or 7.3999999999999999e37 < x

   1. Initial program 98.3%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ N/A

         \[\leadsto 1 + \frac{4}{y} \cdot \color{blue}{\left(\left(x + y \cdot \frac{3}{4}\right) - z\right)} \]

      2. +-commutative N/A

         \[\leadsto 1 + \frac{4}{y} \cdot \left(\left(y \cdot \frac{3}{4} + x\right) - z\right) \]

      3. associate--l+ N/A

         \[\leadsto 1 + \frac{4}{y} \cdot \left(y \cdot \frac{3}{4} + \color{blue}{\left(x - z\right)}\right) \]

      4. distribute-lft-in N/A

         \[\leadsto 1 + \left(\frac{4}{y} \cdot \left(y \cdot \frac{3}{4}\right) + \color{blue}{\frac{4}{y} \cdot \left(x - z\right)}\right) \]

      5. associate-+r+ N/A

         \[\leadsto \left(1 + \frac{4}{y} \cdot \left(y \cdot \frac{3}{4}\right)\right) + \color{blue}{\frac{4}{y} \cdot \left(x - z\right)} \]

      6. associate-*r* N/A

         \[\leadsto \left(1 + \left(\frac{4}{y} \cdot y\right) \cdot \frac{3}{4}\right) + \frac{4}{\color{blue}{y}} \cdot \left(x - z\right) \]

      7. associate-*l/ N/A

         \[\leadsto \left(1 + \frac{4 \cdot y}{y} \cdot \frac{3}{4}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      8. associate-/l* N/A

         \[\leadsto \left(1 + \left(4 \cdot \frac{y}{y}\right) \cdot \frac{3}{4}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      9. *-inverses N/A

         \[\leadsto \left(1 + \left(4 \cdot 1\right) \cdot \frac{3}{4}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      10. metadata-eval N/A

          \[\leadsto \left(1 + 4 \cdot \frac{3}{4}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      11. metadata-eval N/A

          \[\leadsto \left(1 + 3\right) + \frac{4}{\color{blue}{y}} \cdot \left(x - z\right) \]

      12. metadata-eval N/A

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

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

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

      14. associate-*l/ N/A

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

      15. /-lowering-/.f64 N/A

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

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

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

      17. --lowering--.f64 98.3%

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

   3. Simplified 98.3%

      \[\leadsto \color{blue}{4 + \frac{4 \cdot \left(x - z\right)}{y}} \]
   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 81.0%

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

   7. Simplified 81.0%

      \[\leadsto \color{blue}{\frac{4 \cdot x}{y}} \]
   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. *-lowering-*.f64 N/A

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

      4. /-lowering-/.f64 81.7%

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

   9. Applied egg-rr 81.7%

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

   if -7.0000000000000001e35 < x < 7.3999999999999999e37

   1. Initial program 99.2%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ N/A

         \[\leadsto 1 + \frac{4}{y} \cdot \color{blue}{\left(\left(x + y \cdot \frac{3}{4}\right) - z\right)} \]

      2. +-commutative N/A

         \[\leadsto 1 + \frac{4}{y} \cdot \left(\left(y \cdot \frac{3}{4} + x\right) - z\right) \]

      3. associate--l+ N/A

         \[\leadsto 1 + \frac{4}{y} \cdot \left(y \cdot \frac{3}{4} + \color{blue}{\left(x - z\right)}\right) \]

      4. distribute-lft-in N/A

         \[\leadsto 1 + \left(\frac{4}{y} \cdot \left(y \cdot \frac{3}{4}\right) + \color{blue}{\frac{4}{y} \cdot \left(x - z\right)}\right) \]

      5. associate-+r+ N/A

         \[\leadsto \left(1 + \frac{4}{y} \cdot \left(y \cdot \frac{3}{4}\right)\right) + \color{blue}{\frac{4}{y} \cdot \left(x - z\right)} \]

      6. associate-*r* N/A

         \[\leadsto \left(1 + \left(\frac{4}{y} \cdot y\right) \cdot \frac{3}{4}\right) + \frac{4}{\color{blue}{y}} \cdot \left(x - z\right) \]

      7. associate-*l/ N/A

         \[\leadsto \left(1 + \frac{4 \cdot y}{y} \cdot \frac{3}{4}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      8. associate-/l* N/A

         \[\leadsto \left(1 + \left(4 \cdot \frac{y}{y}\right) \cdot \frac{3}{4}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      9. *-inverses N/A

         \[\leadsto \left(1 + \left(4 \cdot 1\right) \cdot \frac{3}{4}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      10. metadata-eval N/A

          \[\leadsto \left(1 + 4 \cdot \frac{3}{4}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

      11. metadata-eval N/A

          \[\leadsto \left(1 + 3\right) + \frac{4}{\color{blue}{y}} \cdot \left(x - z\right) \]

      12. metadata-eval N/A

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

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

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

      14. associate-*l/ N/A

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

      15. /-lowering-/.f64 N/A

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

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

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

      17. --lowering--.f64 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf

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

   7. Simplified 50.3%

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

4. Final simplification 63.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{+35}:\\ \;\;\;\;\frac{4}{y} \cdot x\\ \mathbf{elif}\;x \leq 7.4 \cdot 10^{+37}:\\ \;\;\;\;4\\ \mathbf{else}:\\ \;\;\;\;\frac{4}{y} \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 33.9% accurate, 13.0× speedup

Math

\[\begin{array}{l} \\ 4 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 4.0)

C

double code(double x, double y, double z) {
	return 4.0;
}

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
end function

Java

public static double code(double x, double y, double z) {
	return 4.0;
}

Python

def code(x, y, z):
	return 4.0

Julia

function code(x, y, z)
	return 4.0
end

MATLAB

function tmp = code(x, y, z)
	tmp = 4.0;
end

Wolfram

code[x_, y_, z_] := 4.0

Derivation

1. Initial program 98.8%

   \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
2. Step-by-step derivation

   1. associate-*l/ N/A

      \[\leadsto 1 + \frac{4}{y} \cdot \color{blue}{\left(\left(x + y \cdot \frac{3}{4}\right) - z\right)} \]

   2. +-commutative N/A

      \[\leadsto 1 + \frac{4}{y} \cdot \left(\left(y \cdot \frac{3}{4} + x\right) - z\right) \]

   3. associate--l+ N/A

      \[\leadsto 1 + \frac{4}{y} \cdot \left(y \cdot \frac{3}{4} + \color{blue}{\left(x - z\right)}\right) \]

   4. distribute-lft-in N/A

      \[\leadsto 1 + \left(\frac{4}{y} \cdot \left(y \cdot \frac{3}{4}\right) + \color{blue}{\frac{4}{y} \cdot \left(x - z\right)}\right) \]

   5. associate-+r+ N/A

      \[\leadsto \left(1 + \frac{4}{y} \cdot \left(y \cdot \frac{3}{4}\right)\right) + \color{blue}{\frac{4}{y} \cdot \left(x - z\right)} \]

   6. associate-*r* N/A

      \[\leadsto \left(1 + \left(\frac{4}{y} \cdot y\right) \cdot \frac{3}{4}\right) + \frac{4}{\color{blue}{y}} \cdot \left(x - z\right) \]

   7. associate-*l/ N/A

      \[\leadsto \left(1 + \frac{4 \cdot y}{y} \cdot \frac{3}{4}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

   8. associate-/l* N/A

      \[\leadsto \left(1 + \left(4 \cdot \frac{y}{y}\right) \cdot \frac{3}{4}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

   9. *-inverses N/A

      \[\leadsto \left(1 + \left(4 \cdot 1\right) \cdot \frac{3}{4}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

   10. metadata-eval N/A

       \[\leadsto \left(1 + 4 \cdot \frac{3}{4}\right) + \frac{4}{y} \cdot \left(x - z\right) \]

   11. metadata-eval N/A

       \[\leadsto \left(1 + 3\right) + \frac{4}{\color{blue}{y}} \cdot \left(x - z\right) \]

   12. metadata-eval N/A

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

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

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

   14. associate-*l/ N/A

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

   15. /-lowering-/.f64 N/A

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

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

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

   17. --lowering--.f64 99.3%

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

3. Simplified 99.3%

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

5. Taylor expanded in y around inf

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

7. Simplified 31.9%

   \[\leadsto \color{blue}{4} \]
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, A"
  :precision binary64
  (+ 1.0 (/ (* 4.0 (- (+ x (* y 0.75)) z)) y)))