Numeric.SpecFunctions:choose from math-functions-0.1.5.2

Percentage Accurate: 84.1% → 96.3%

Time: 5.8s

Alternatives: 7

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 84.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 82.7%

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

   1. associate-/l* 97.2%

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

   2. remove-double-neg 97.2%

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

   3. distribute-frac-neg2 97.2%

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

   4. neg-sub0 97.2%

      \[\leadsto x \cdot \color{blue}{\left(0 - \frac{y + z}{-z}\right)} \]

   5. remove-double-neg 97.2%

      \[\leadsto x \cdot \left(0 - \frac{y + \color{blue}{\left(-\left(-z\right)\right)}}{-z}\right) \]

   6. unsub-neg 97.2%

      \[\leadsto x \cdot \left(0 - \frac{\color{blue}{y - \left(-z\right)}}{-z}\right) \]

   7. div-sub 97.3%

      \[\leadsto x \cdot \left(0 - \color{blue}{\left(\frac{y}{-z} - \frac{-z}{-z}\right)}\right) \]

   8. *-inverses 97.3%

      \[\leadsto x \cdot \left(0 - \left(\frac{y}{-z} - \color{blue}{1}\right)\right) \]

   9. metadata-eval 97.3%

      \[\leadsto x \cdot \left(0 - \left(\frac{y}{-z} - \color{blue}{\left(--1\right)}\right)\right) \]

   10. associate--r- 97.3%

       \[\leadsto x \cdot \color{blue}{\left(\left(0 - \frac{y}{-z}\right) + \left(--1\right)\right)} \]

   11. neg-sub0 97.3%

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

   12. distribute-frac-neg2 97.3%

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

   13. remove-double-neg 97.3%

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

   14. sub-neg 97.3%

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

3. Simplified 97.3%

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

   1. sub-neg 97.3%

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

   2. metadata-eval 97.3%

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

   3. distribute-rgt-in 97.2%

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

   4. *-commutative 97.2%

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

   5. *-un-lft-identity 97.2%

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

6. Applied egg-rr 97.2%

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

   1. clear-num 97.2%

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

   2. un-div-inv 97.6%

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

8. Applied egg-rr 97.6%

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

9. Final simplification 97.6%

   \[\leadsto x + \frac{x}{\frac{z}{y}} \]
10. Add Preprocessing

Alternative 2: 69.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+43}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+29}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.7e+43) x (if (<= z 1.8e+29) (* x (/ y z)) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.7e+43) {
		tmp = x;
	} else if (z <= 1.8e+29) {
		tmp = x * (y / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-1.7d+43)) then
        tmp = x
    else if (z <= 1.8d+29) then
        tmp = x * (y / z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.7e+43) {
		tmp = x;
	} else if (z <= 1.8e+29) {
		tmp = x * (y / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.7e+43:
		tmp = x
	elif z <= 1.8e+29:
		tmp = x * (y / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.7e+43)
		tmp = x;
	elseif (z <= 1.8e+29)
		tmp = Float64(x * Float64(y / z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.7e+43)
		tmp = x;
	elseif (z <= 1.8e+29)
		tmp = x * (y / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.7e+43], x, If[LessEqual[z, 1.8e+29], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -1.70000000000000006e43 or 1.79999999999999988e29 < z

   1. Initial program 67.7%

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

      1. associate-/l* 99.9%

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

      2. remove-double-neg 99.9%

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

      3. distribute-frac-neg2 99.9%

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

      4. neg-sub0 99.9%

         \[\leadsto x \cdot \color{blue}{\left(0 - \frac{y + z}{-z}\right)} \]

      5. remove-double-neg 99.9%

         \[\leadsto x \cdot \left(0 - \frac{y + \color{blue}{\left(-\left(-z\right)\right)}}{-z}\right) \]

      6. unsub-neg 99.9%

         \[\leadsto x \cdot \left(0 - \frac{\color{blue}{y - \left(-z\right)}}{-z}\right) \]

      7. div-sub 99.9%

         \[\leadsto x \cdot \left(0 - \color{blue}{\left(\frac{y}{-z} - \frac{-z}{-z}\right)}\right) \]

      8. *-inverses 99.9%

         \[\leadsto x \cdot \left(0 - \left(\frac{y}{-z} - \color{blue}{1}\right)\right) \]

      9. metadata-eval 99.9%

         \[\leadsto x \cdot \left(0 - \left(\frac{y}{-z} - \color{blue}{\left(--1\right)}\right)\right) \]

      10. associate--r- 99.9%

          \[\leadsto x \cdot \color{blue}{\left(\left(0 - \frac{y}{-z}\right) + \left(--1\right)\right)} \]

      11. neg-sub0 99.9%

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

      12. distribute-frac-neg2 99.9%

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

      13. remove-double-neg 99.9%

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

      14. sub-neg 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 76.0%

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

   if -1.70000000000000006e43 < z < 1.79999999999999988e29

   1. Initial program 95.1%

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

      1. associate-/l* 95.1%

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

      2. remove-double-neg 95.1%

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

      3. distribute-frac-neg2 95.1%

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

      4. neg-sub0 95.1%

         \[\leadsto x \cdot \color{blue}{\left(0 - \frac{y + z}{-z}\right)} \]

      5. remove-double-neg 95.1%

         \[\leadsto x \cdot \left(0 - \frac{y + \color{blue}{\left(-\left(-z\right)\right)}}{-z}\right) \]

      6. unsub-neg 95.1%

         \[\leadsto x \cdot \left(0 - \frac{\color{blue}{y - \left(-z\right)}}{-z}\right) \]

      7. div-sub 95.1%

         \[\leadsto x \cdot \left(0 - \color{blue}{\left(\frac{y}{-z} - \frac{-z}{-z}\right)}\right) \]

      8. *-inverses 95.1%

         \[\leadsto x \cdot \left(0 - \left(\frac{y}{-z} - \color{blue}{1}\right)\right) \]

      9. metadata-eval 95.1%

         \[\leadsto x \cdot \left(0 - \left(\frac{y}{-z} - \color{blue}{\left(--1\right)}\right)\right) \]

      10. associate--r- 95.1%

          \[\leadsto x \cdot \color{blue}{\left(\left(0 - \frac{y}{-z}\right) + \left(--1\right)\right)} \]

      11. neg-sub0 95.1%

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

      12. distribute-frac-neg2 95.1%

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

      13. remove-double-neg 95.1%

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

      14. sub-neg 95.1%

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

   3. Simplified 95.1%

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

   5. Taylor expanded in y around inf 74.6%

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

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+43}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+29}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 72.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+28}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+25}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.1e+28) x (if (<= z 1.4e+25) (* y (/ x z)) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.1e+28) {
		tmp = x;
	} else if (z <= 1.4e+25) {
		tmp = y * (x / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-1.1d+28)) then
        tmp = x
    else if (z <= 1.4d+25) then
        tmp = y * (x / z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.1e+28) {
		tmp = x;
	} else if (z <= 1.4e+25) {
		tmp = y * (x / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.1e+28:
		tmp = x
	elif z <= 1.4e+25:
		tmp = y * (x / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.1e+28)
		tmp = x;
	elseif (z <= 1.4e+25)
		tmp = Float64(y * Float64(x / z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.1e+28)
		tmp = x;
	elseif (z <= 1.4e+25)
		tmp = y * (x / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.1e+28], x, If[LessEqual[z, 1.4e+25], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -1.09999999999999993e28 or 1.4000000000000001e25 < z

   1. Initial program 68.7%

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

      1. associate-/l* 99.9%

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

      2. remove-double-neg 99.9%

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

      3. distribute-frac-neg2 99.9%

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

      4. neg-sub0 99.9%

         \[\leadsto x \cdot \color{blue}{\left(0 - \frac{y + z}{-z}\right)} \]

      5. remove-double-neg 99.9%

         \[\leadsto x \cdot \left(0 - \frac{y + \color{blue}{\left(-\left(-z\right)\right)}}{-z}\right) \]

      6. unsub-neg 99.9%

         \[\leadsto x \cdot \left(0 - \frac{\color{blue}{y - \left(-z\right)}}{-z}\right) \]

      7. div-sub 99.9%

         \[\leadsto x \cdot \left(0 - \color{blue}{\left(\frac{y}{-z} - \frac{-z}{-z}\right)}\right) \]

      8. *-inverses 99.9%

         \[\leadsto x \cdot \left(0 - \left(\frac{y}{-z} - \color{blue}{1}\right)\right) \]

      9. metadata-eval 99.9%

         \[\leadsto x \cdot \left(0 - \left(\frac{y}{-z} - \color{blue}{\left(--1\right)}\right)\right) \]

      10. associate--r- 99.9%

          \[\leadsto x \cdot \color{blue}{\left(\left(0 - \frac{y}{-z}\right) + \left(--1\right)\right)} \]

      11. neg-sub0 99.9%

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

      12. distribute-frac-neg2 99.9%

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

      13. remove-double-neg 99.9%

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

      14. sub-neg 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 75.3%

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

   if -1.09999999999999993e28 < z < 1.4000000000000001e25

   1. Initial program 95.0%

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

      1. associate-/l* 94.9%

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

      2. remove-double-neg 94.9%

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

      3. distribute-frac-neg2 94.9%

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

      4. neg-sub0 94.9%

         \[\leadsto x \cdot \color{blue}{\left(0 - \frac{y + z}{-z}\right)} \]

      5. remove-double-neg 94.9%

         \[\leadsto x \cdot \left(0 - \frac{y + \color{blue}{\left(-\left(-z\right)\right)}}{-z}\right) \]

      6. unsub-neg 94.9%

         \[\leadsto x \cdot \left(0 - \frac{\color{blue}{y - \left(-z\right)}}{-z}\right) \]

      7. div-sub 94.9%

         \[\leadsto x \cdot \left(0 - \color{blue}{\left(\frac{y}{-z} - \frac{-z}{-z}\right)}\right) \]

      8. *-inverses 94.9%

         \[\leadsto x \cdot \left(0 - \left(\frac{y}{-z} - \color{blue}{1}\right)\right) \]

      9. metadata-eval 94.9%

         \[\leadsto x \cdot \left(0 - \left(\frac{y}{-z} - \color{blue}{\left(--1\right)}\right)\right) \]

      10. associate--r- 94.9%

          \[\leadsto x \cdot \color{blue}{\left(\left(0 - \frac{y}{-z}\right) + \left(--1\right)\right)} \]

      11. neg-sub0 94.9%

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

      12. distribute-frac-neg2 94.9%

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

      13. remove-double-neg 94.9%

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

      14. sub-neg 94.9%

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

   3. Simplified 94.9%

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

   5. Taylor expanded in y around inf 78.0%

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

      1. associate-*l/ 75.3%

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

      2. *-commutative 75.3%

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

   7. Simplified 75.3%

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

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+28}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+25}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 70.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+40}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+28}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -2e+40) x (if (<= z 3.6e+28) (/ x (/ z y)) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -2e+40) {
		tmp = x;
	} else if (z <= 3.6e+28) {
		tmp = x / (z / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-2d+40)) then
        tmp = x
    else if (z <= 3.6d+28) then
        tmp = x / (z / y)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -2e+40) {
		tmp = x;
	} else if (z <= 3.6e+28) {
		tmp = x / (z / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -2e+40:
		tmp = x
	elif z <= 3.6e+28:
		tmp = x / (z / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -2e+40)
		tmp = x;
	elseif (z <= 3.6e+28)
		tmp = Float64(x / Float64(z / y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -2e+40)
		tmp = x;
	elseif (z <= 3.6e+28)
		tmp = x / (z / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -2e+40], x, If[LessEqual[z, 3.6e+28], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -2.00000000000000006e40 or 3.5999999999999999e28 < z

   1. Initial program 67.7%

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

      1. associate-/l* 99.9%

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

      2. remove-double-neg 99.9%

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

      3. distribute-frac-neg2 99.9%

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

      4. neg-sub0 99.9%

         \[\leadsto x \cdot \color{blue}{\left(0 - \frac{y + z}{-z}\right)} \]

      5. remove-double-neg 99.9%

         \[\leadsto x \cdot \left(0 - \frac{y + \color{blue}{\left(-\left(-z\right)\right)}}{-z}\right) \]

      6. unsub-neg 99.9%

         \[\leadsto x \cdot \left(0 - \frac{\color{blue}{y - \left(-z\right)}}{-z}\right) \]

      7. div-sub 99.9%

         \[\leadsto x \cdot \left(0 - \color{blue}{\left(\frac{y}{-z} - \frac{-z}{-z}\right)}\right) \]

      8. *-inverses 99.9%

         \[\leadsto x \cdot \left(0 - \left(\frac{y}{-z} - \color{blue}{1}\right)\right) \]

      9. metadata-eval 99.9%

         \[\leadsto x \cdot \left(0 - \left(\frac{y}{-z} - \color{blue}{\left(--1\right)}\right)\right) \]

      10. associate--r- 99.9%

          \[\leadsto x \cdot \color{blue}{\left(\left(0 - \frac{y}{-z}\right) + \left(--1\right)\right)} \]

      11. neg-sub0 99.9%

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

      12. distribute-frac-neg2 99.9%

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

      13. remove-double-neg 99.9%

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

      14. sub-neg 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 76.0%

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

   if -2.00000000000000006e40 < z < 3.5999999999999999e28

   1. Initial program 95.1%

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

      1. associate-/l* 95.1%

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

      2. remove-double-neg 95.1%

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

      3. distribute-frac-neg2 95.1%

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

      4. neg-sub0 95.1%

         \[\leadsto x \cdot \color{blue}{\left(0 - \frac{y + z}{-z}\right)} \]

      5. remove-double-neg 95.1%

         \[\leadsto x \cdot \left(0 - \frac{y + \color{blue}{\left(-\left(-z\right)\right)}}{-z}\right) \]

      6. unsub-neg 95.1%

         \[\leadsto x \cdot \left(0 - \frac{\color{blue}{y - \left(-z\right)}}{-z}\right) \]

      7. div-sub 95.1%

         \[\leadsto x \cdot \left(0 - \color{blue}{\left(\frac{y}{-z} - \frac{-z}{-z}\right)}\right) \]

      8. *-inverses 95.1%

         \[\leadsto x \cdot \left(0 - \left(\frac{y}{-z} - \color{blue}{1}\right)\right) \]

      9. metadata-eval 95.1%

         \[\leadsto x \cdot \left(0 - \left(\frac{y}{-z} - \color{blue}{\left(--1\right)}\right)\right) \]

      10. associate--r- 95.1%

          \[\leadsto x \cdot \color{blue}{\left(\left(0 - \frac{y}{-z}\right) + \left(--1\right)\right)} \]

      11. neg-sub0 95.1%

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

      12. distribute-frac-neg2 95.1%

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

      13. remove-double-neg 95.1%

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

      14. sub-neg 95.1%

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

   3. Simplified 95.1%

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

   5. Taylor expanded in y around inf 74.6%

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

      1. clear-num 95.0%

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

      2. un-div-inv 95.7%

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

   7. Applied egg-rr 75.2%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+40}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+28}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 72.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+46}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{+28}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.9e+46) x (if (<= z 7.8e+28) (/ (* x y) z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.9e+46) {
		tmp = x;
	} else if (z <= 7.8e+28) {
		tmp = (x * y) / z;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-1.9d+46)) then
        tmp = x
    else if (z <= 7.8d+28) then
        tmp = (x * y) / z
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.9e+46) {
		tmp = x;
	} else if (z <= 7.8e+28) {
		tmp = (x * y) / z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.9e+46:
		tmp = x
	elif z <= 7.8e+28:
		tmp = (x * y) / z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.9e+46)
		tmp = x;
	elseif (z <= 7.8e+28)
		tmp = Float64(Float64(x * y) / z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.9e+46)
		tmp = x;
	elseif (z <= 7.8e+28)
		tmp = (x * y) / z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.9e+46], x, If[LessEqual[z, 7.8e+28], N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -1.9e46 or 7.7999999999999997e28 < z

   1. Initial program 67.7%

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

      1. associate-/l* 99.9%

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

      2. remove-double-neg 99.9%

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

      3. distribute-frac-neg2 99.9%

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

      4. neg-sub0 99.9%

         \[\leadsto x \cdot \color{blue}{\left(0 - \frac{y + z}{-z}\right)} \]

      5. remove-double-neg 99.9%

         \[\leadsto x \cdot \left(0 - \frac{y + \color{blue}{\left(-\left(-z\right)\right)}}{-z}\right) \]

      6. unsub-neg 99.9%

         \[\leadsto x \cdot \left(0 - \frac{\color{blue}{y - \left(-z\right)}}{-z}\right) \]

      7. div-sub 99.9%

         \[\leadsto x \cdot \left(0 - \color{blue}{\left(\frac{y}{-z} - \frac{-z}{-z}\right)}\right) \]

      8. *-inverses 99.9%

         \[\leadsto x \cdot \left(0 - \left(\frac{y}{-z} - \color{blue}{1}\right)\right) \]

      9. metadata-eval 99.9%

         \[\leadsto x \cdot \left(0 - \left(\frac{y}{-z} - \color{blue}{\left(--1\right)}\right)\right) \]

      10. associate--r- 99.9%

          \[\leadsto x \cdot \color{blue}{\left(\left(0 - \frac{y}{-z}\right) + \left(--1\right)\right)} \]

      11. neg-sub0 99.9%

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

      12. distribute-frac-neg2 99.9%

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

      13. remove-double-neg 99.9%

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

      14. sub-neg 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 76.0%

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

   if -1.9e46 < z < 7.7999999999999997e28

   1. Initial program 95.1%

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

      1. associate-/l* 95.1%

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

      2. remove-double-neg 95.1%

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

      3. distribute-frac-neg2 95.1%

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

      4. neg-sub0 95.1%

         \[\leadsto x \cdot \color{blue}{\left(0 - \frac{y + z}{-z}\right)} \]

      5. remove-double-neg 95.1%

         \[\leadsto x \cdot \left(0 - \frac{y + \color{blue}{\left(-\left(-z\right)\right)}}{-z}\right) \]

      6. unsub-neg 95.1%

         \[\leadsto x \cdot \left(0 - \frac{\color{blue}{y - \left(-z\right)}}{-z}\right) \]

      7. div-sub 95.1%

         \[\leadsto x \cdot \left(0 - \color{blue}{\left(\frac{y}{-z} - \frac{-z}{-z}\right)}\right) \]

      8. *-inverses 95.1%

         \[\leadsto x \cdot \left(0 - \left(\frac{y}{-z} - \color{blue}{1}\right)\right) \]

      9. metadata-eval 95.1%

         \[\leadsto x \cdot \left(0 - \left(\frac{y}{-z} - \color{blue}{\left(--1\right)}\right)\right) \]

      10. associate--r- 95.1%

          \[\leadsto x \cdot \color{blue}{\left(\left(0 - \frac{y}{-z}\right) + \left(--1\right)\right)} \]

      11. neg-sub0 95.1%

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

      12. distribute-frac-neg2 95.1%

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

      13. remove-double-neg 95.1%

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

      14. sub-neg 95.1%

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

   3. Simplified 95.1%

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

   5. Taylor expanded in y around inf 77.3%

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

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+46}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{+28}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 95.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 82.7%

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

   1. associate-/l* 97.2%

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

   2. remove-double-neg 97.2%

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

   3. distribute-frac-neg2 97.2%

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

   4. neg-sub0 97.2%

      \[\leadsto x \cdot \color{blue}{\left(0 - \frac{y + z}{-z}\right)} \]

   5. remove-double-neg 97.2%

      \[\leadsto x \cdot \left(0 - \frac{y + \color{blue}{\left(-\left(-z\right)\right)}}{-z}\right) \]

   6. unsub-neg 97.2%

      \[\leadsto x \cdot \left(0 - \frac{\color{blue}{y - \left(-z\right)}}{-z}\right) \]

   7. div-sub 97.3%

      \[\leadsto x \cdot \left(0 - \color{blue}{\left(\frac{y}{-z} - \frac{-z}{-z}\right)}\right) \]

   8. *-inverses 97.3%

      \[\leadsto x \cdot \left(0 - \left(\frac{y}{-z} - \color{blue}{1}\right)\right) \]

   9. metadata-eval 97.3%

      \[\leadsto x \cdot \left(0 - \left(\frac{y}{-z} - \color{blue}{\left(--1\right)}\right)\right) \]

   10. associate--r- 97.3%

       \[\leadsto x \cdot \color{blue}{\left(\left(0 - \frac{y}{-z}\right) + \left(--1\right)\right)} \]

   11. neg-sub0 97.3%

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

   12. distribute-frac-neg2 97.3%

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

   13. remove-double-neg 97.3%

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

   14. sub-neg 97.3%

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

3. Simplified 97.3%

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

5. Final simplification 97.3%

   \[\leadsto x \cdot \left(\frac{y}{z} - -1\right) \]
6. Add Preprocessing

Alternative 7: 50.6% 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 82.7%

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

   1. associate-/l* 97.2%

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

   2. remove-double-neg 97.2%

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

   3. distribute-frac-neg2 97.2%

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

   4. neg-sub0 97.2%

      \[\leadsto x \cdot \color{blue}{\left(0 - \frac{y + z}{-z}\right)} \]

   5. remove-double-neg 97.2%

      \[\leadsto x \cdot \left(0 - \frac{y + \color{blue}{\left(-\left(-z\right)\right)}}{-z}\right) \]

   6. unsub-neg 97.2%

      \[\leadsto x \cdot \left(0 - \frac{\color{blue}{y - \left(-z\right)}}{-z}\right) \]

   7. div-sub 97.3%

      \[\leadsto x \cdot \left(0 - \color{blue}{\left(\frac{y}{-z} - \frac{-z}{-z}\right)}\right) \]

   8. *-inverses 97.3%

      \[\leadsto x \cdot \left(0 - \left(\frac{y}{-z} - \color{blue}{1}\right)\right) \]

   9. metadata-eval 97.3%

      \[\leadsto x \cdot \left(0 - \left(\frac{y}{-z} - \color{blue}{\left(--1\right)}\right)\right) \]

   10. associate--r- 97.3%

       \[\leadsto x \cdot \color{blue}{\left(\left(0 - \frac{y}{-z}\right) + \left(--1\right)\right)} \]

   11. neg-sub0 97.3%

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

   12. distribute-frac-neg2 97.3%

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

   13. remove-double-neg 97.3%

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

   14. sub-neg 97.3%

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

3. Simplified 97.3%

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

5. Taylor expanded in y around 0 47.1%

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

6. Final simplification 47.1%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 96.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024052 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:choose from math-functions-0.1.5.2"
  :precision binary64

  :herbie-target
  (/ x (/ z (+ y z)))

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