Numeric.SpecFunctions:choose from math-functions-0.1.5.2

Percentage Accurate: 84.5% → 97.2%

Time: 8.8s

Alternatives: 7

Speedup: 0.8×

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: 84.5% 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: 97.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+19}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{x}{z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y + z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2e+19) (fma y (/ x z) x) (/ x (/ z (+ y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2e+19) {
		tmp = fma(y, (x / z), x);
	} else {
		tmp = x / (z / (y + z));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2e+19)
		tmp = fma(y, Float64(x / z), x);
	else
		tmp = Float64(x / Float64(z / Float64(y + z)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2e+19], N[(y * N[(x / z), $MachinePrecision] + x), $MachinePrecision], N[(x / N[(z / N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2e19

   1. Initial program 91.4%

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

   3. Taylor expanded in x around 0

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

      1. associate-/l* N/A

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

      2. +-commutative N/A

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

      3. *-lft-identity N/A

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

      4. metadata-eval N/A

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

      5. cancel-sign-sub-inv N/A

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

      6. div-sub N/A

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

      7. *-inverses N/A

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

      8. associate-*r/ N/A

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

      9. distribute-rgt-out-- N/A

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

      10. *-lft-identity N/A

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

      11. mul-1-neg N/A

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

      12. cancel-sign-sub N/A

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

      13. distribute-rgt1-in N/A

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

      14. distribute-lft1-in N/A

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

      15. *-commutative N/A

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

      16. lower-fma.f64 N/A

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

      17. lower-/.f64 89.9

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

   5. Applied rewrites 89.9%

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

      1. lift-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. div-inv N/A

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

      5. lift-/.f64 N/A

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

      6. associate-*l* N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lift-/.f64 N/A

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

      10. div-inv N/A

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

      11. lower-/.f64 99.8

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

   7. Applied rewrites 99.8%

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

   if -2e19 < y

   1. Initial program 84.7%

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

      1. lift-+.f64 N/A

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

      2. associate-/l* N/A

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

      3. clear-num N/A

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

      4. un-div-inv N/A

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

      5. lower-/.f64 N/A

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

      6. lower-/.f64 98.9

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

   4. Applied rewrites 98.9%

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

Alternative 2: 73.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{-8}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 1.06 \cdot 10^{+26}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.1e-8) (* y (/ x z)) (if (<= y 1.06e+26) x (/ (* y x) z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.1e-8) {
		tmp = y * (x / z);
	} else if (y <= 1.06e+26) {
		tmp = x;
	} else {
		tmp = (y * x) / z;
	}
	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 <= (-2.1d-8)) then
        tmp = y * (x / z)
    else if (y <= 1.06d+26) then
        tmp = x
    else
        tmp = (y * x) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.1e-8) {
		tmp = y * (x / z);
	} else if (y <= 1.06e+26) {
		tmp = x;
	} else {
		tmp = (y * x) / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.1e-8:
		tmp = y * (x / z)
	elif y <= 1.06e+26:
		tmp = x
	else:
		tmp = (y * x) / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.1e-8)
		tmp = Float64(y * Float64(x / z));
	elseif (y <= 1.06e+26)
		tmp = x;
	else
		tmp = Float64(Float64(y * x) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2.1e-8)
		tmp = y * (x / z);
	elseif (y <= 1.06e+26)
		tmp = x;
	else
		tmp = (y * x) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.1e-8], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.06e+26], x, N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.09999999999999994e-8

   1. Initial program 92.6%

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

   3. Taylor expanded in y around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 76.7

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

   5. Applied rewrites 76.7%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. div-inv N/A

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

      4. lift-/.f64 N/A

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

      5. associate-*l* N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lift-/.f64 N/A

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

      9. div-inv N/A

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

      10. lower-/.f64 78.0

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

   7. Applied rewrites 78.0%

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

   if -2.09999999999999994e-8 < y < 1.05999999999999997e26

   1. Initial program 80.9%

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

      1. lift-+.f64 N/A

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

      2. associate-/l* N/A

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

      3. clear-num N/A

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

      4. un-div-inv N/A

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

      5. lower-/.f64 N/A

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

      6. lower-/.f64 99.9

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

   4. Applied rewrites 99.9%

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

   5. Taylor expanded in z around inf

      \[\leadsto \frac{x}{\color{blue}{1}} \]
   6. Step-by-step derivation

   7. Applied rewrites 78.7%

      \[\leadsto \frac{x}{\color{blue}{1}} \]
   8. Step-by-step derivation

      1. /-rgt-identity 78.7

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

   9. Applied rewrites 78.7%

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

   if 1.05999999999999997e26 < y

   1. Initial program 90.6%

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

   3. Taylor expanded in y around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 77.5

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

   5. Applied rewrites 77.5%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{-8}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 1.06 \cdot 10^{+26}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 72.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{-8}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 1.06 \cdot 10^{+26}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.1e-8) (* y (/ x z)) (if (<= y 1.06e+26) x (* x (/ y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.1e-8) {
		tmp = y * (x / z);
	} else if (y <= 1.06e+26) {
		tmp = x;
	} else {
		tmp = x * (y / z);
	}
	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 <= (-2.1d-8)) then
        tmp = y * (x / z)
    else if (y <= 1.06d+26) then
        tmp = x
    else
        tmp = x * (y / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.1e-8) {
		tmp = y * (x / z);
	} else if (y <= 1.06e+26) {
		tmp = x;
	} else {
		tmp = x * (y / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.1e-8:
		tmp = y * (x / z)
	elif y <= 1.06e+26:
		tmp = x
	else:
		tmp = x * (y / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.1e-8)
		tmp = Float64(y * Float64(x / z));
	elseif (y <= 1.06e+26)
		tmp = x;
	else
		tmp = Float64(x * Float64(y / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2.1e-8)
		tmp = y * (x / z);
	elseif (y <= 1.06e+26)
		tmp = x;
	else
		tmp = x * (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.1e-8], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.06e+26], x, N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.09999999999999994e-8

   1. Initial program 92.6%

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

   3. Taylor expanded in y around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 76.7

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

   5. Applied rewrites 76.7%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. div-inv N/A

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

      4. lift-/.f64 N/A

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

      5. associate-*l* N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lift-/.f64 N/A

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

      9. div-inv N/A

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

      10. lower-/.f64 78.0

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

   7. Applied rewrites 78.0%

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

   if -2.09999999999999994e-8 < y < 1.05999999999999997e26

   1. Initial program 80.9%

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

      1. lift-+.f64 N/A

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

      2. associate-/l* N/A

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

      3. clear-num N/A

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

      4. un-div-inv N/A

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

      5. lower-/.f64 N/A

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

      6. lower-/.f64 99.9

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

   4. Applied rewrites 99.9%

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

   5. Taylor expanded in z around inf

      \[\leadsto \frac{x}{\color{blue}{1}} \]
   6. Step-by-step derivation

   7. Applied rewrites 78.7%

      \[\leadsto \frac{x}{\color{blue}{1}} \]
   8. Step-by-step derivation

      1. /-rgt-identity 78.7

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

   9. Applied rewrites 78.7%

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

   if 1.05999999999999997e26 < y

   1. Initial program 90.6%

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

   3. Taylor expanded in y around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 77.5

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

   5. Applied rewrites 77.5%

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

      1. associate-*r/ N/A

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

      2. lift-/.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 75.9

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

   7. Applied rewrites 75.9%

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

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{-8}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 1.06 \cdot 10^{+26}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 73.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \frac{x}{z}\\ \mathbf{if}\;y \leq -2.1 \cdot 10^{-8}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1.06 \cdot 10^{+26}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (/ x z))))
   (if (<= y -2.1e-8) t_0 (if (<= y 1.06e+26) x t_0))))

C

double code(double x, double y, double z) {
	double t_0 = y * (x / z);
	double tmp;
	if (y <= -2.1e-8) {
		tmp = t_0;
	} else if (y <= 1.06e+26) {
		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 <= (-2.1d-8)) then
        tmp = t_0
    else if (y <= 1.06d+26) 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 <= -2.1e-8) {
		tmp = t_0;
	} else if (y <= 1.06e+26) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (x / z)
	tmp = 0
	if y <= -2.1e-8:
		tmp = t_0
	elif y <= 1.06e+26:
		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 <= -2.1e-8)
		tmp = t_0;
	elseif (y <= 1.06e+26)
		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 <= -2.1e-8)
		tmp = t_0;
	elseif (y <= 1.06e+26)
		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, -2.1e-8], t$95$0, If[LessEqual[y, 1.06e+26], x, t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.09999999999999994e-8 or 1.05999999999999997e26 < y

   1. Initial program 91.6%

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

   3. Taylor expanded in y around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 77.1

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

   5. Applied rewrites 77.1%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. div-inv N/A

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

      4. lift-/.f64 N/A

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

      5. associate-*l* N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lift-/.f64 N/A

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

      9. div-inv N/A

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

      10. lower-/.f64 76.5

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

   7. Applied rewrites 76.5%

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

   if -2.09999999999999994e-8 < y < 1.05999999999999997e26

   1. Initial program 80.9%

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

      1. lift-+.f64 N/A

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

      2. associate-/l* N/A

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

      3. clear-num N/A

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

      4. un-div-inv N/A

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

      5. lower-/.f64 N/A

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

      6. lower-/.f64 99.9

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

   4. Applied rewrites 99.9%

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

   5. Taylor expanded in z around inf

      \[\leadsto \frac{x}{\color{blue}{1}} \]
   6. Step-by-step derivation

   7. Applied rewrites 78.7%

      \[\leadsto \frac{x}{\color{blue}{1}} \]
   8. Step-by-step derivation

      1. /-rgt-identity 78.7

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

   9. Applied rewrites 78.7%

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

Alternative 5: 97.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -500000000:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{x}{z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, \frac{y}{z}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -500000000.0) (fma y (/ x z) x) (fma x (/ y z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -500000000.0) {
		tmp = fma(y, (x / z), x);
	} else {
		tmp = fma(x, (y / z), x);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -500000000.0)
		tmp = fma(y, Float64(x / z), x);
	else
		tmp = fma(x, Float64(y / z), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -500000000.0], N[(y * N[(x / z), $MachinePrecision] + x), $MachinePrecision], N[(x * N[(y / z), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5e8

   1. Initial program 92.1%

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

   3. Taylor expanded in x around 0

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

      1. associate-/l* N/A

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

      2. +-commutative N/A

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

      3. *-lft-identity N/A

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

      4. metadata-eval N/A

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

      5. cancel-sign-sub-inv N/A

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

      6. div-sub N/A

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

      7. *-inverses N/A

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

      8. associate-*r/ N/A

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

      9. distribute-rgt-out-- N/A

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

      10. *-lft-identity N/A

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

      11. mul-1-neg N/A

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

      12. cancel-sign-sub N/A

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

      13. distribute-rgt1-in N/A

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

      14. distribute-lft1-in N/A

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

      15. *-commutative N/A

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

      16. lower-fma.f64 N/A

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

      17. lower-/.f64 90.7

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

   5. Applied rewrites 90.7%

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

      1. lift-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. div-inv N/A

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

      5. lift-/.f64 N/A

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

      6. associate-*l* N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lift-/.f64 N/A

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

      10. div-inv N/A

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

      11. lower-/.f64 99.8

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

   7. Applied rewrites 99.8%

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

   if -5e8 < y

   1. Initial program 84.3%

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

   3. Taylor expanded in x around 0

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

      1. associate-/l* N/A

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

      2. +-commutative N/A

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

      3. *-lft-identity N/A

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

      4. metadata-eval N/A

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

      5. cancel-sign-sub-inv N/A

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

      6. div-sub N/A

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

      7. *-inverses N/A

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

      8. associate-*r/ N/A

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

      9. distribute-rgt-out-- N/A

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

      10. *-lft-identity N/A

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

      11. mul-1-neg N/A

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

      12. cancel-sign-sub N/A

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

      13. distribute-rgt1-in N/A

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

      14. distribute-lft1-in N/A

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

      15. *-commutative N/A

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

      16. lower-fma.f64 N/A

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

      17. lower-/.f64 98.4

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

   5. Applied rewrites 98.4%

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

Alternative 6: 95.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+197}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, \frac{y}{z}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3.2e+197) (* y (/ x z)) (fma x (/ y z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.2e+197) {
		tmp = y * (x / z);
	} else {
		tmp = fma(x, (y / z), x);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3.2e+197)
		tmp = Float64(y * Float64(x / z));
	else
		tmp = fma(x, Float64(y / z), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3.2e+197], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(x * N[(y / z), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.1999999999999998e197

   1. Initial program 91.1%

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

   3. Taylor expanded in y around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 91.1

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

   5. Applied rewrites 91.1%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. div-inv N/A

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

      4. lift-/.f64 N/A

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

      5. associate-*l* N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lift-/.f64 N/A

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

      9. div-inv N/A

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

      10. lower-/.f64 99.3

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

   7. Applied rewrites 99.3%

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

   if -3.1999999999999998e197 < y

   1. Initial program 85.8%

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

   3. Taylor expanded in x around 0

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

      1. associate-/l* N/A

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

      2. +-commutative N/A

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

      3. *-lft-identity N/A

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

      4. metadata-eval N/A

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

      5. cancel-sign-sub-inv N/A

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

      6. div-sub N/A

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

      7. *-inverses N/A

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

      8. associate-*r/ N/A

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

      9. distribute-rgt-out-- N/A

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

      10. *-lft-identity N/A

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

      11. mul-1-neg N/A

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

      12. cancel-sign-sub N/A

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

      13. distribute-rgt1-in N/A

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

      14. distribute-lft1-in N/A

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

      15. *-commutative N/A

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

      16. lower-fma.f64 N/A

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

      17. lower-/.f64 98.2

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

   5. Applied rewrites 98.2%

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

Alternative 7: 51.9% accurate, 20.0× 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. Add Preprocessing
3. Step-by-step derivation

   1. lift-+.f64 N/A

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

   2. associate-/l* N/A

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

   3. clear-num N/A

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

   4. un-div-inv N/A

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

   5. lower-/.f64 N/A

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

   6. lower-/.f64 97.2

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

4. Applied rewrites 97.2%

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

5. Taylor expanded in z around inf

   \[\leadsto \frac{x}{\color{blue}{1}} \]
6. Step-by-step derivation

7. Applied rewrites 50.9%

   \[\leadsto \frac{x}{\color{blue}{1}} \]
8. Step-by-step derivation

   1. /-rgt-identity 50.9

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

9. Applied rewrites 50.9%

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

Developer Target 1: 96.6% accurate, 0.8× 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 2024214 
(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))