Numeric.SpecFunctions:choose from math-functions-0.1.5.2

Percentage Accurate: 84.3% → 96.1%

Time: 4.5s

Alternatives: 6

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return (x * (y + z)) / 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 = (x * (y + z)) / z
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 84.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return (x * (y + z)) / 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 = (x * (y + z)) / z
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 83.5%

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

   1. associate-/l* N/A

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

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

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

   3. *-lft-identity N/A

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

   4. *-inverses N/A

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

   5. associate-*l/ N/A

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

   6. distribute-lft-in N/A

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

   7. associate-*l/ N/A

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

   8. *-inverses N/A

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

   9. *-lft-identity N/A

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

   10. *-inverses N/A

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

   11. lft-mult-inverse N/A

       \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{y}{z} + 1\right)\right) \]

   12. *-inverses N/A

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

   13. +-commutative N/A

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

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

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

   15. *-inverses N/A

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

   16. *-rgt-identity N/A

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

   17. *-inverses N/A

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

   18. associate-/l* N/A

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

   19. associate-*l/ N/A

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

   20. *-commutative N/A

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

   21. /-lowering-/.f64 N/A

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

   22. *-commutative N/A

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

   23. associate-*l/ N/A

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

   24. associate-/l* N/A

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

   25. *-inverses N/A

       \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\left(y \cdot 1\right), z\right)\right)\right) \]

   26. *-rgt-identity 97.7%

       \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(y, z\right)\right)\right) \]

3. Simplified 97.7%

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

Alternative 2: 71.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+69}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+15}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2e+69) (/ (* x y) z) (if (<= y 1.6e+15) x (/ y (/ z x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2e+69) {
		tmp = (x * y) / z;
	} else if (y <= 1.6e+15) {
		tmp = x;
	} else {
		tmp = y / (z / x);
	}
	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 <= (-2d+69)) then
        tmp = (x * y) / z
    else if (y <= 1.6d+15) then
        tmp = x
    else
        tmp = y / (z / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -2e+69) {
		tmp = (x * y) / z;
	} else if (y <= 1.6e+15) {
		tmp = x;
	} else {
		tmp = y / (z / x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2e+69:
		tmp = (x * y) / z
	elif y <= 1.6e+15:
		tmp = x
	else:
		tmp = y / (z / x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2e+69)
		tmp = Float64(Float64(x * y) / z);
	elseif (y <= 1.6e+15)
		tmp = x;
	else
		tmp = Float64(y / Float64(z / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2e+69)
		tmp = (x * y) / z;
	elseif (y <= 1.6e+15)
		tmp = x;
	else
		tmp = y / (z / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2e+69], N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, 1.6e+15], x, N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.0000000000000001e69

   1. Initial program 89.2%

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

   3. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 72.5%

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

   5. Simplified 72.5%

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

   if -2.0000000000000001e69 < y < 1.6e15

   1. Initial program 79.1%

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

      1. associate-/l* N/A

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

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

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

      3. *-lft-identity N/A

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

      4. *-inverses N/A

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

      5. associate-*l/ N/A

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

      6. distribute-lft-in N/A

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

      7. associate-*l/ N/A

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

      8. *-inverses N/A

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

      9. *-lft-identity N/A

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

      10. *-inverses N/A

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

      11. lft-mult-inverse N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{y}{z} + 1\right)\right) \]

      12. *-inverses N/A

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

      13. +-commutative N/A

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

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

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

      15. *-inverses N/A

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

      16. *-rgt-identity N/A

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

      17. *-inverses N/A

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

      18. associate-/l* N/A

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

      19. associate-*l/ N/A

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

      20. *-commutative N/A

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

      21. /-lowering-/.f64 N/A

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

      22. *-commutative N/A

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

      23. associate-*l/ N/A

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

      24. associate-/l* N/A

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

      25. *-inverses N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\left(y \cdot 1\right), z\right)\right)\right) \]

      26. *-rgt-identity 100.0%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(y, z\right)\right)\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0

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

   7. Simplified 78.2%

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

   if 1.6e15 < y

   1. Initial program 88.8%

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

      1. associate-/l* N/A

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

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

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

      3. *-lft-identity N/A

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

      4. *-inverses N/A

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

      5. associate-*l/ N/A

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

      6. distribute-lft-in N/A

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

      7. associate-*l/ N/A

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

      8. *-inverses N/A

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

      9. *-lft-identity N/A

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

      10. *-inverses N/A

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

      11. lft-mult-inverse N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{y}{z} + 1\right)\right) \]

      12. *-inverses N/A

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

      13. +-commutative N/A

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

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

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

      15. *-inverses N/A

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

      16. *-rgt-identity N/A

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

      17. *-inverses N/A

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

      18. associate-/l* N/A

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

      19. associate-*l/ N/A

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

      20. *-commutative N/A

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

      21. /-lowering-/.f64 N/A

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

      22. *-commutative N/A

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

      23. associate-*l/ N/A

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

      24. associate-/l* N/A

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

      25. *-inverses N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\left(y \cdot 1\right), z\right)\right)\right) \]

      26. *-rgt-identity 96.8%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(y, z\right)\right)\right) \]

   3. Simplified 96.8%

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

   5. Taylor expanded in y around inf

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

      1. *-rgt-identity N/A

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

      2. rgt-mult-inverse N/A

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

      3. associate-*r/ N/A

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

      4. *-rgt-identity N/A

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

      5. associate-/l* N/A

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

      6. associate-*l/ N/A

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

      7. *-commutative N/A

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

      8. associate-/r* N/A

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

      9. associate-/l* N/A

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

      10. *-rgt-identity N/A

          \[\leadsto \frac{x \cdot \frac{y \cdot 1}{y}}{\frac{z}{y}} \]

      11. associate-*r/ N/A

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

      12. rgt-mult-inverse N/A

          \[\leadsto \frac{x \cdot 1}{\frac{z}{y}} \]

      13. *-rgt-identity N/A

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

      14. /-lowering-/.f64 N/A

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

      15. /-lowering-/.f64 65.7%

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

   7. Simplified 65.7%

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

      1. associate-/r/ N/A

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

      2. *-commutative N/A

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

      3. clear-num N/A

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

      4. un-div-inv N/A

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

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

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

      6. /-lowering-/.f64 68.9%

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

   9. Applied egg-rr 68.9%

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

Alternative 3: 71.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y}{\frac{z}{x}}\\ \mathbf{if}\;y \leq -5.2 \cdot 10^{+70}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+15}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ y (/ z x))))
   (if (<= y -5.2e+70) t_0 (if (<= y 1.45e+15) x t_0))))

C

double code(double x, double y, double z) {
	double t_0 = y / (z / x);
	double tmp;
	if (y <= -5.2e+70) {
		tmp = t_0;
	} else if (y <= 1.45e+15) {
		tmp = x;
	} 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 = y / (z / x)
    if (y <= (-5.2d+70)) then
        tmp = t_0
    else if (y <= 1.45d+15) then
        tmp = x
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y / (z / x);
	double tmp;
	if (y <= -5.2e+70) {
		tmp = t_0;
	} else if (y <= 1.45e+15) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y / (z / x)
	tmp = 0
	if y <= -5.2e+70:
		tmp = t_0
	elif y <= 1.45e+15:
		tmp = x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y / Float64(z / x))
	tmp = 0.0
	if (y <= -5.2e+70)
		tmp = t_0;
	elseif (y <= 1.45e+15)
		tmp = x;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y / (z / x);
	tmp = 0.0;
	if (y <= -5.2e+70)
		tmp = t_0;
	elseif (y <= 1.45e+15)
		tmp = x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.2e+70], t$95$0, If[LessEqual[y, 1.45e+15], x, t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -5.2000000000000001e70 or 1.45e15 < y

   1. Initial program 89.0%

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

      1. associate-/l* N/A

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

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

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

      3. *-lft-identity N/A

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

      4. *-inverses N/A

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

      5. associate-*l/ N/A

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

      6. distribute-lft-in N/A

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

      7. associate-*l/ N/A

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

      8. *-inverses N/A

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

      9. *-lft-identity N/A

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

      10. *-inverses N/A

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

      11. lft-mult-inverse N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{y}{z} + 1\right)\right) \]

      12. *-inverses N/A

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

      13. +-commutative N/A

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

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

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

      15. *-inverses N/A

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

      16. *-rgt-identity N/A

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

      17. *-inverses N/A

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

      18. associate-/l* N/A

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

      19. associate-*l/ N/A

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

      20. *-commutative N/A

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

      21. /-lowering-/.f64 N/A

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

      22. *-commutative N/A

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

      23. associate-*l/ N/A

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

      24. associate-/l* N/A

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

      25. *-inverses N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\left(y \cdot 1\right), z\right)\right)\right) \]

      26. *-rgt-identity 94.9%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(y, z\right)\right)\right) \]

   3. Simplified 94.9%

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

   5. Taylor expanded in y around inf

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

      1. *-rgt-identity N/A

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

      2. rgt-mult-inverse N/A

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

      3. associate-*r/ N/A

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

      4. *-rgt-identity N/A

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

      5. associate-/l* N/A

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

      6. associate-*l/ N/A

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

      7. *-commutative N/A

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

      8. associate-/r* N/A

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

      9. associate-/l* N/A

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

      10. *-rgt-identity N/A

          \[\leadsto \frac{x \cdot \frac{y \cdot 1}{y}}{\frac{z}{y}} \]

      11. associate-*r/ N/A

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

      12. rgt-mult-inverse N/A

          \[\leadsto \frac{x \cdot 1}{\frac{z}{y}} \]

      13. *-rgt-identity N/A

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

      14. /-lowering-/.f64 N/A

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

      15. /-lowering-/.f64 66.9%

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

   7. Simplified 66.9%

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

      1. associate-/r/ N/A

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

      2. *-commutative N/A

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

      3. clear-num N/A

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

      4. un-div-inv N/A

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

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

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

      6. /-lowering-/.f64 69.8%

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

   9. Applied egg-rr 69.8%

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

   if -5.2000000000000001e70 < y < 1.45e15

   1. Initial program 79.1%

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

      1. associate-/l* N/A

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

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

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

      3. *-lft-identity N/A

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

      4. *-inverses N/A

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

      5. associate-*l/ N/A

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

      6. distribute-lft-in N/A

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

      7. associate-*l/ N/A

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

      8. *-inverses N/A

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

      9. *-lft-identity N/A

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

      10. *-inverses N/A

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

      11. lft-mult-inverse N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{y}{z} + 1\right)\right) \]

      12. *-inverses N/A

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

      13. +-commutative N/A

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

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

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

      15. *-inverses N/A

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

      16. *-rgt-identity N/A

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

      17. *-inverses N/A

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

      18. associate-/l* N/A

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

      19. associate-*l/ N/A

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

      20. *-commutative N/A

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

      21. /-lowering-/.f64 N/A

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

      22. *-commutative N/A

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

      23. associate-*l/ N/A

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

      24. associate-/l* N/A

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

      25. *-inverses N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\left(y \cdot 1\right), z\right)\right)\right) \]

      26. *-rgt-identity 100.0%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(y, z\right)\right)\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0

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

   7. Simplified 78.2%

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

Alternative 4: 72.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \frac{x}{z}\\ \mathbf{if}\;y \leq -2 \cdot 10^{+71}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+15}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (/ x z)))) (if (<= y -2e+71) t_0 (if (<= y 2.6e+15) x t_0))))

C

double code(double x, double y, double z) {
	double t_0 = y * (x / z);
	double tmp;
	if (y <= -2e+71) {
		tmp = t_0;
	} else if (y <= 2.6e+15) {
		tmp = x;
	} 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 = y * (x / z)
    if (y <= (-2d+71)) then
        tmp = t_0
    else if (y <= 2.6d+15) then
        tmp = x
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * (x / z);
	double tmp;
	if (y <= -2e+71) {
		tmp = t_0;
	} else if (y <= 2.6e+15) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (x / z)
	tmp = 0
	if y <= -2e+71:
		tmp = t_0
	elif y <= 2.6e+15:
		tmp = x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(x / z))
	tmp = 0.0
	if (y <= -2e+71)
		tmp = t_0;
	elseif (y <= 2.6e+15)
		tmp = x;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (x / z);
	tmp = 0.0;
	if (y <= -2e+71)
		tmp = t_0;
	elseif (y <= 2.6e+15)
		tmp = x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2e+71], t$95$0, If[LessEqual[y, 2.6e+15], x, t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.0000000000000001e71 or 2.6e15 < y

   1. Initial program 89.0%

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

      1. associate-/l* N/A

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

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

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

      3. *-lft-identity N/A

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

      4. *-inverses N/A

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

      5. associate-*l/ N/A

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

      6. distribute-lft-in N/A

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

      7. associate-*l/ N/A

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

      8. *-inverses N/A

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

      9. *-lft-identity N/A

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

      10. *-inverses N/A

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

      11. lft-mult-inverse N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{y}{z} + 1\right)\right) \]

      12. *-inverses N/A

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

      13. +-commutative N/A

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

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

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

      15. *-inverses N/A

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

      16. *-rgt-identity N/A

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

      17. *-inverses N/A

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

      18. associate-/l* N/A

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

      19. associate-*l/ N/A

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

      20. *-commutative N/A

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

      21. /-lowering-/.f64 N/A

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

      22. *-commutative N/A

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

      23. associate-*l/ N/A

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

      24. associate-/l* N/A

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

      25. *-inverses N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\left(y \cdot 1\right), z\right)\right)\right) \]

      26. *-rgt-identity 94.9%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(y, z\right)\right)\right) \]

   3. Simplified 94.9%

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

   5. Taylor expanded in y around inf

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

      1. *-rgt-identity N/A

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

      2. rgt-mult-inverse N/A

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

      3. associate-*r/ N/A

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

      4. *-rgt-identity N/A

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

      5. associate-/l* N/A

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

      6. associate-*l/ N/A

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

      7. *-commutative N/A

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

      8. associate-/r* N/A

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

      9. associate-/l* N/A

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

      10. *-rgt-identity N/A

          \[\leadsto \frac{x \cdot \frac{y \cdot 1}{y}}{\frac{z}{y}} \]

      11. associate-*r/ N/A

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

      12. rgt-mult-inverse N/A

          \[\leadsto \frac{x \cdot 1}{\frac{z}{y}} \]

      13. *-rgt-identity N/A

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

      14. /-lowering-/.f64 N/A

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

      15. /-lowering-/.f64 66.9%

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

   7. Simplified 66.9%

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

      1. associate-/r/ N/A

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

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

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

      3. /-lowering-/.f64 69.8%

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

   9. Applied egg-rr 69.8%

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

   if -2.0000000000000001e71 < y < 2.6e15

   1. Initial program 79.1%

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

      1. associate-/l* N/A

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

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

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

      3. *-lft-identity N/A

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

      4. *-inverses N/A

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

      5. associate-*l/ N/A

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

      6. distribute-lft-in N/A

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

      7. associate-*l/ N/A

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

      8. *-inverses N/A

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

      9. *-lft-identity N/A

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

      10. *-inverses N/A

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

      11. lft-mult-inverse N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{y}{z} + 1\right)\right) \]

      12. *-inverses N/A

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

      13. +-commutative N/A

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

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

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

      15. *-inverses N/A

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

      16. *-rgt-identity N/A

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

      17. *-inverses N/A

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

      18. associate-/l* N/A

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

      19. associate-*l/ N/A

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

      20. *-commutative N/A

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

      21. /-lowering-/.f64 N/A

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

      22. *-commutative N/A

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

      23. associate-*l/ N/A

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

      24. associate-/l* N/A

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

      25. *-inverses N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\left(y \cdot 1\right), z\right)\right)\right) \]

      26. *-rgt-identity 100.0%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(y, z\right)\right)\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0

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

   7. Simplified 78.2%

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

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+71}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+15}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 69.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \frac{y}{z}\\ \mathbf{if}\;y \leq -2.3 \cdot 10^{+72}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{+15}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (/ y z))))
   (if (<= y -2.3e+72) t_0 (if (<= y 1.85e+15) x t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x * (y / z);
	double tmp;
	if (y <= -2.3e+72) {
		tmp = t_0;
	} else if (y <= 1.85e+15) {
		tmp = x;
	} 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 * (y / z)
    if (y <= (-2.3d+72)) then
        tmp = t_0
    else if (y <= 1.85d+15) then
        tmp = x
    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 * (y / z);
	double tmp;
	if (y <= -2.3e+72) {
		tmp = t_0;
	} else if (y <= 1.85e+15) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (y / z)
	tmp = 0
	if y <= -2.3e+72:
		tmp = t_0
	elif y <= 1.85e+15:
		tmp = x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(y / z))
	tmp = 0.0
	if (y <= -2.3e+72)
		tmp = t_0;
	elseif (y <= 1.85e+15)
		tmp = x;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (y / z);
	tmp = 0.0;
	if (y <= -2.3e+72)
		tmp = t_0;
	elseif (y <= 1.85e+15)
		tmp = x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.3e+72], t$95$0, If[LessEqual[y, 1.85e+15], x, t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.3e72 or 1.85e15 < y

   1. Initial program 89.0%

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

      1. associate-/l* N/A

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

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

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

      3. *-lft-identity N/A

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

      4. *-inverses N/A

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

      5. associate-*l/ N/A

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

      6. distribute-lft-in N/A

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

      7. associate-*l/ N/A

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

      8. *-inverses N/A

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

      9. *-lft-identity N/A

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

      10. *-inverses N/A

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

      11. lft-mult-inverse N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{y}{z} + 1\right)\right) \]

      12. *-inverses N/A

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

      13. +-commutative N/A

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

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

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

      15. *-inverses N/A

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

      16. *-rgt-identity N/A

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

      17. *-inverses N/A

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

      18. associate-/l* N/A

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

      19. associate-*l/ N/A

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

      20. *-commutative N/A

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

      21. /-lowering-/.f64 N/A

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

      22. *-commutative N/A

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

      23. associate-*l/ N/A

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

      24. associate-/l* N/A

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

      25. *-inverses N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\left(y \cdot 1\right), z\right)\right)\right) \]

      26. *-rgt-identity 94.9%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(y, z\right)\right)\right) \]

   3. Simplified 94.9%

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

   5. Taylor expanded in y around inf

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

      1. /-lowering-/.f64 67.0%

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

   7. Simplified 67.0%

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

   if -2.3e72 < y < 1.85e15

   1. Initial program 79.1%

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

      1. associate-/l* N/A

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

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

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

      3. *-lft-identity N/A

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

      4. *-inverses N/A

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

      5. associate-*l/ N/A

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

      6. distribute-lft-in N/A

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

      7. associate-*l/ N/A

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

      8. *-inverses N/A

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

      9. *-lft-identity N/A

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

      10. *-inverses N/A

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

      11. lft-mult-inverse N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{y}{z} + 1\right)\right) \]

      12. *-inverses N/A

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

      13. +-commutative N/A

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

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

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

      15. *-inverses N/A

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

      16. *-rgt-identity N/A

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

      17. *-inverses N/A

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

      18. associate-/l* N/A

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

      19. associate-*l/ N/A

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

      20. *-commutative N/A

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

      21. /-lowering-/.f64 N/A

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

      22. *-commutative N/A

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

      23. associate-*l/ N/A

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

      24. associate-/l* N/A

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

      25. *-inverses N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\left(y \cdot 1\right), z\right)\right)\right) \]

      26. *-rgt-identity 100.0%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(y, z\right)\right)\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0

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

   7. Simplified 78.2%

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

Alternative 6: 50.9% accurate, 7.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 83.5%

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

   1. associate-/l* N/A

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

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

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

   3. *-lft-identity N/A

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

   4. *-inverses N/A

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

   5. associate-*l/ N/A

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

   6. distribute-lft-in N/A

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

   7. associate-*l/ N/A

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

   8. *-inverses N/A

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

   9. *-lft-identity N/A

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

   10. *-inverses N/A

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

   11. lft-mult-inverse N/A

       \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{y}{z} + 1\right)\right) \]

   12. *-inverses N/A

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

   13. +-commutative N/A

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

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

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

   15. *-inverses N/A

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

   16. *-rgt-identity N/A

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

   17. *-inverses N/A

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

   18. associate-/l* N/A

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

   19. associate-*l/ N/A

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

   20. *-commutative N/A

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

   21. /-lowering-/.f64 N/A

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

   22. *-commutative N/A

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

   23. associate-*l/ N/A

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

   24. associate-/l* N/A

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

   25. *-inverses N/A

       \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\left(y \cdot 1\right), z\right)\right)\right) \]

   26. *-rgt-identity 97.7%

       \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(y, z\right)\right)\right) \]

3. Simplified 97.7%

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

5. Taylor expanded in y around 0

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

7. Simplified 56.1%

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

Developer Target 1: 96.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x}{\frac{z}{y + z}} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (/ x (/ z (+ y z))))

C

double code(double x, double y, double z) {
	return x / (z / (y + 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 = x / (z / (y + z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024140 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:choose from math-functions-0.1.5.2"
  :precision binary64

  :alt
  (! :herbie-platform default (/ x (/ z (+ y z))))

  (/ (* x (+ y z)) z))