Numeric.SpecFunctions:choose from math-functions-0.1.5.2

Percentage Accurate: 84.9% → 94.8%

Time: 6.2s

Alternatives: 7

Speedup: 0.6×

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: 84.9% 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: 94.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + \frac{x}{\frac{z}{y}}\\ \mathbf{if}\;z \leq -1.28 \cdot 10^{-245}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-148}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ x (/ x (/ z y)))))
   (if (<= z -1.28e-245) t_0 (if (<= z 9.2e-148) (/ (* x y) z) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x + (x / (z / y));
	double tmp;
	if (z <= -1.28e-245) {
		tmp = t_0;
	} else if (z <= 9.2e-148) {
		tmp = (x * y) / z;
	} 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 + (x / (z / y))
    if (z <= (-1.28d-245)) then
        tmp = t_0
    else if (z <= 9.2d-148) then
        tmp = (x * y) / z
    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 + (x / (z / y));
	double tmp;
	if (z <= -1.28e-245) {
		tmp = t_0;
	} else if (z <= 9.2e-148) {
		tmp = (x * y) / z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x + (x / (z / y))
	tmp = 0
	if z <= -1.28e-245:
		tmp = t_0
	elif z <= 9.2e-148:
		tmp = (x * y) / z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x + Float64(x / Float64(z / y)))
	tmp = 0.0
	if (z <= -1.28e-245)
		tmp = t_0;
	elseif (z <= 9.2e-148)
		tmp = Float64(Float64(x * y) / z);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x + (x / (z / y));
	tmp = 0.0;
	if (z <= -1.28e-245)
		tmp = t_0;
	elseif (z <= 9.2e-148)
		tmp = (x * y) / z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x + N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.28e-245], t$95$0, If[LessEqual[z, 9.2e-148], N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.28e-245 or 9.1999999999999999e-148 < z

   1. Initial program 83.1%

      \[\frac{x \cdot \left(y + z\right)}{z} \]
   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 98.1%

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

   3. Simplified 98.1%

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

      1. +-commutative N/A

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

      2. distribute-rgt-in N/A

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

      3. *-lft-identity N/A

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

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

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

      5. clear-num N/A

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

      6. associate-*l/ N/A

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

      7. *-lft-identity N/A

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

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

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

      9. /-lowering-/.f64 98.2%

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

   6. Applied egg-rr 98.2%

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

   if -1.28e-245 < z < 9.1999999999999999e-148

   1. Initial program 98.0%

      \[\frac{x \cdot \left(y + z\right)}{z} \]
   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 98.0%

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

   5. Simplified 98.0%

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

4. Final simplification 98.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.28 \cdot 10^{-245}:\\ \;\;\;\;x + \frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-148}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{x}{\frac{z}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 94.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(1 + \frac{y}{z}\right)\\ \mathbf{if}\;z \leq -1.38 \cdot 10^{-245}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-148}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ 1.0 (/ y z)))))
   (if (<= z -1.38e-245) t_0 (if (<= z 9.2e-148) (/ (* x y) z) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x * (1.0 + (y / z));
	double tmp;
	if (z <= -1.38e-245) {
		tmp = t_0;
	} else if (z <= 9.2e-148) {
		tmp = (x * y) / z;
	} 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 * (1.0d0 + (y / z))
    if (z <= (-1.38d-245)) then
        tmp = t_0
    else if (z <= 9.2d-148) then
        tmp = (x * y) / z
    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 * (1.0 + (y / z));
	double tmp;
	if (z <= -1.38e-245) {
		tmp = t_0;
	} else if (z <= 9.2e-148) {
		tmp = (x * y) / z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (1.0 + (y / z))
	tmp = 0
	if z <= -1.38e-245:
		tmp = t_0
	elif z <= 9.2e-148:
		tmp = (x * y) / z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(1.0 + Float64(y / z)))
	tmp = 0.0
	if (z <= -1.38e-245)
		tmp = t_0;
	elseif (z <= 9.2e-148)
		tmp = Float64(Float64(x * y) / z);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (1.0 + (y / z));
	tmp = 0.0;
	if (z <= -1.38e-245)
		tmp = t_0;
	elseif (z <= 9.2e-148)
		tmp = (x * y) / z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(1.0 + N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.38e-245], t$95$0, If[LessEqual[z, 9.2e-148], N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.38000000000000006e-245 or 9.1999999999999999e-148 < z

   1. Initial program 83.1%

      \[\frac{x \cdot \left(y + z\right)}{z} \]
   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 98.1%

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

   3. Simplified 98.1%

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

   if -1.38000000000000006e-245 < z < 9.1999999999999999e-148

   1. Initial program 98.0%

      \[\frac{x \cdot \left(y + z\right)}{z} \]
   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 98.0%

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

   5. Simplified 98.0%

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

Alternative 3: 73.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x \cdot y}{z}\\ \mathbf{if}\;y \leq -7.5 \cdot 10^{-9}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 0.0265:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (* x y) z))) (if (<= y -7.5e-9) t_0 (if (<= y 0.0265) x t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (x * y) / z;
	double tmp;
	if (y <= -7.5e-9) {
		tmp = t_0;
	} else if (y <= 0.0265) {
		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 <= (-7.5d-9)) then
        tmp = t_0
    else if (y <= 0.0265d0) 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 <= -7.5e-9) {
		tmp = t_0;
	} else if (y <= 0.0265) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x * y) / z
	tmp = 0
	if y <= -7.5e-9:
		tmp = t_0
	elif y <= 0.0265:
		tmp = x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x * y) / z)
	tmp = 0.0
	if (y <= -7.5e-9)
		tmp = t_0;
	elseif (y <= 0.0265)
		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 <= -7.5e-9)
		tmp = t_0;
	elseif (y <= 0.0265)
		tmp = x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[y, -7.5e-9], t$95$0, If[LessEqual[y, 0.0265], x, t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -7.49999999999999933e-9 or 0.0264999999999999993 < y

   1. Initial program 90.6%

      \[\frac{x \cdot \left(y + z\right)}{z} \]
   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 76.2%

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

   5. Simplified 76.2%

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

   if -7.49999999999999933e-9 < y < 0.0264999999999999993

   1. Initial program 80.6%

      \[\frac{x \cdot \left(y + z\right)}{z} \]
   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 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0

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

   7. Simplified 77.2%

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

Alternative 4: 73.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \frac{x}{z}\\ \mathbf{if}\;y \leq -4.4 \cdot 10^{-8}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 0.04:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (/ x z)))) (if (<= y -4.4e-8) t_0 (if (<= y 0.04) x t_0))))

C

double code(double x, double y, double z) {
	double t_0 = y * (x / z);
	double tmp;
	if (y <= -4.4e-8) {
		tmp = t_0;
	} else if (y <= 0.04) {
		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 <= (-4.4d-8)) then
        tmp = t_0
    else if (y <= 0.04d0) 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 <= -4.4e-8) {
		tmp = t_0;
	} else if (y <= 0.04) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (x / z)
	tmp = 0
	if y <= -4.4e-8:
		tmp = t_0
	elif y <= 0.04:
		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 <= -4.4e-8)
		tmp = t_0;
	elseif (y <= 0.04)
		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 <= -4.4e-8)
		tmp = t_0;
	elseif (y <= 0.04)
		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, -4.4e-8], t$95$0, If[LessEqual[y, 0.04], x, t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -4.3999999999999997e-8 or 0.0400000000000000008 < y

   1. Initial program 90.6%

      \[\frac{x \cdot \left(y + z\right)}{z} \]
   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 90.1%

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

   3. Simplified 90.1%

      \[\leadsto \color{blue}{x \cdot \left(1 + \frac{y}{z}\right)} \]
   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 70.7%

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

   7. Simplified 70.7%

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

      1. associate-/r/ N/A

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

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

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

      3. /-lowering-/.f64 75.9%

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

   9. Applied egg-rr 75.9%

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

   if -4.3999999999999997e-8 < y < 0.0400000000000000008

   1. Initial program 80.6%

      \[\frac{x \cdot \left(y + z\right)}{z} \]
   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 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0

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

   7. Simplified 77.2%

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

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{-8}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 0.04:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 70.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \frac{y}{z}\\ \mathbf{if}\;y \leq -2.3 \cdot 10^{-7}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 0.045:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (/ y z)))) (if (<= y -2.3e-7) t_0 (if (<= y 0.045) x t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x * (y / z);
	double tmp;
	if (y <= -2.3e-7) {
		tmp = t_0;
	} else if (y <= 0.045) {
		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-7)) then
        tmp = t_0
    else if (y <= 0.045d0) 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-7) {
		tmp = t_0;
	} else if (y <= 0.045) {
		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-7:
		tmp = t_0
	elif y <= 0.045:
		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-7)
		tmp = t_0;
	elseif (y <= 0.045)
		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-7)
		tmp = t_0;
	elseif (y <= 0.045)
		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-7], t$95$0, If[LessEqual[y, 0.045], x, t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.29999999999999995e-7 or 0.044999999999999998 < y

   1. Initial program 90.6%

      \[\frac{x \cdot \left(y + z\right)}{z} \]
   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 90.1%

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

   3. Simplified 90.1%

      \[\leadsto \color{blue}{x \cdot \left(1 + \frac{y}{z}\right)} \]
   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 69.7%

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

   7. Simplified 69.7%

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

   if -2.29999999999999995e-7 < y < 0.044999999999999998

   1. Initial program 80.6%

      \[\frac{x \cdot \left(y + z\right)}{z} \]
   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 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0

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

   7. Simplified 77.2%

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

Alternative 6: 90.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 2 \cdot 10^{-13}:\\ \;\;\;\;\frac{x \cdot \left(y + z\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{x}{\frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 2e-13) (/ (* x (+ y z)) z) (+ x (/ x (/ z y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 2e-13) {
		tmp = (x * (y + z)) / z;
	} else {
		tmp = x + (x / (z / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= 2d-13) then
        tmp = (x * (y + z)) / z
    else
        tmp = x + (x / (z / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 2e-13) {
		tmp = (x * (y + z)) / z;
	} else {
		tmp = x + (x / (z / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 2e-13:
		tmp = (x * (y + z)) / z
	else:
		tmp = x + (x / (z / y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 2e-13)
		tmp = Float64(Float64(x * Float64(y + z)) / z);
	else
		tmp = Float64(x + Float64(x / Float64(z / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 2e-13)
		tmp = (x * (y + z)) / z;
	else
		tmp = x + (x / (z / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 2e-13], N[(N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], N[(x + N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 2.0000000000000001e-13

   1. Initial program 88.8%

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

   if 2.0000000000000001e-13 < x

   1. Initial program 76.9%

      \[\frac{x \cdot \left(y + z\right)}{z} \]
   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 99.9%

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

   3. Simplified 99.9%

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

      1. +-commutative N/A

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

      2. distribute-rgt-in N/A

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

      3. *-lft-identity N/A

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

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

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

      5. clear-num N/A

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

      6. associate-*l/ N/A

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

      7. *-lft-identity N/A

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

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

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

      9. /-lowering-/.f64 99.9%

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

   6. Applied egg-rr 99.9%

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

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 2 \cdot 10^{-13}:\\ \;\;\;\;\frac{x \cdot \left(y + z\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{x}{\frac{z}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 50.8% 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 86.2%

   \[\frac{x \cdot \left(y + z\right)}{z} \]
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 94.4%

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

3. Simplified 94.4%

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

5. Taylor expanded in y around 0

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

7. Simplified 46.0%

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

Developer Target 1: 96.4% 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 2024152 
(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))