Numeric.SpecFunctions:choose from math-functions-0.1.5.2

Percentage Accurate: 84.5% → 95.7%

Time: 5.2s

Alternatives: 6

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 84.5% 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: 95.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(x, \frac{y}{z}, x\right) \end{array} \]

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 84.4%

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

   1. remove-double-neg 84.4%

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

   2. distribute-frac-neg2 84.4%

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

   3. distribute-frac-neg 84.4%

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

   4. distribute-rgt-neg-in 84.4%

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

   5. distribute-neg-in 84.4%

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

   6. distribute-lft-out 83.8%

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

   7. *-commutative 83.8%

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

   8. cancel-sign-sub-inv 83.8%

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

   9. div-sub 83.9%

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

   10. associate-*r/ 83.1%

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

   11. distribute-neg-frac 83.1%

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

   12. distribute-frac-neg2 83.1%

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

   13. remove-double-neg 83.1%

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

   14. fma-neg 83.1%

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

   15. distribute-frac-neg 83.1%

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

   16. distribute-lft-neg-out 83.1%

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

   17. *-commutative 83.1%

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

   18. associate-/l* 96.6%

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

   19. *-inverses 96.6%

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

   20. *-rgt-identity 96.6%

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

3. Simplified 96.6%

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

5. Final simplification 96.6%

   \[\leadsto \mathsf{fma}\left(x, \frac{y}{z}, x\right) \]
6. Add Preprocessing

Alternative 2: 69.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+22}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -5.6 \cdot 10^{-22} \lor \neg \left(z \leq -2.7 \cdot 10^{-66}\right) \land z \leq 4.1 \cdot 10^{+79}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -2.4e+22)
   x
   (if (or (<= z -5.6e-22) (and (not (<= z -2.7e-66)) (<= z 4.1e+79)))
     (* x (/ y z))
     x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.4e+22) {
		tmp = x;
	} else if ((z <= -5.6e-22) || (!(z <= -2.7e-66) && (z <= 4.1e+79))) {
		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 <= (-2.4d+22)) then
        tmp = x
    else if ((z <= (-5.6d-22)) .or. (.not. (z <= (-2.7d-66))) .and. (z <= 4.1d+79)) 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 <= -2.4e+22) {
		tmp = x;
	} else if ((z <= -5.6e-22) || (!(z <= -2.7e-66) && (z <= 4.1e+79))) {
		tmp = x * (y / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -2.4e+22:
		tmp = x
	elif (z <= -5.6e-22) or (not (z <= -2.7e-66) and (z <= 4.1e+79)):
		tmp = x * (y / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -2.4e+22)
		tmp = x;
	elseif ((z <= -5.6e-22) || (!(z <= -2.7e-66) && (z <= 4.1e+79)))
		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 <= -2.4e+22)
		tmp = x;
	elseif ((z <= -5.6e-22) || (~((z <= -2.7e-66)) && (z <= 4.1e+79)))
		tmp = x * (y / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -2.4e+22], x, If[Or[LessEqual[z, -5.6e-22], And[N[Not[LessEqual[z, -2.7e-66]], $MachinePrecision], LessEqual[z, 4.1e+79]]], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -2.4e22 or -5.5999999999999999e-22 < z < -2.69999999999999996e-66 or 4.1e79 < z

   1. Initial program 74.7%

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

      1. associate-/l* 99.2%

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

      2. remove-double-neg 99.2%

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

      3. distribute-frac-neg2 99.2%

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

      4. neg-sub0 99.2%

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

      5. remove-double-neg 99.2%

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

      6. unsub-neg 99.2%

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

      7. div-sub 99.2%

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

      8. *-inverses 99.2%

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

      9. metadata-eval 99.2%

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

      10. associate--r- 99.2%

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

      11. neg-sub0 99.2%

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

      12. distribute-frac-neg2 99.2%

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

      13. remove-double-neg 99.2%

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

      14. sub-neg 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in y around 0 87.1%

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

   if -2.4e22 < z < -5.5999999999999999e-22 or -2.69999999999999996e-66 < z < 4.1e79

   1. Initial program 93.4%

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

      1. associate-/l* 94.2%

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

      2. remove-double-neg 94.2%

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

      3. distribute-frac-neg2 94.2%

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

      4. neg-sub0 94.2%

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

      5. remove-double-neg 94.2%

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

      6. unsub-neg 94.2%

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

      7. div-sub 94.2%

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

      8. *-inverses 94.2%

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

      9. metadata-eval 94.2%

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

      10. associate--r- 94.2%

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

      11. neg-sub0 94.2%

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

      12. distribute-frac-neg2 94.2%

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

      13. remove-double-neg 94.2%

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

      14. sub-neg 94.2%

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

   3. Simplified 94.2%

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

   5. Taylor expanded in y around inf 74.7%

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

      1. associate-*r/ 72.3%

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

   7. Simplified 72.3%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+22}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -5.6 \cdot 10^{-22} \lor \neg \left(z \leq -2.7 \cdot 10^{-66}\right) \land z \leq 4.1 \cdot 10^{+79}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 71.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+25}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-22}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -2.15 \cdot 10^{-66}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{+79}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -2.4e+25)
   x
   (if (<= z -6e-22)
     (* x (/ y z))
     (if (<= z -2.15e-66) x (if (<= z 4.1e+79) (* y (/ x z)) x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.4e+25) {
		tmp = x;
	} else if (z <= -6e-22) {
		tmp = x * (y / z);
	} else if (z <= -2.15e-66) {
		tmp = x;
	} else if (z <= 4.1e+79) {
		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 <= (-2.4d+25)) then
        tmp = x
    else if (z <= (-6d-22)) then
        tmp = x * (y / z)
    else if (z <= (-2.15d-66)) then
        tmp = x
    else if (z <= 4.1d+79) 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 <= -2.4e+25) {
		tmp = x;
	} else if (z <= -6e-22) {
		tmp = x * (y / z);
	} else if (z <= -2.15e-66) {
		tmp = x;
	} else if (z <= 4.1e+79) {
		tmp = y * (x / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -2.4e+25:
		tmp = x
	elif z <= -6e-22:
		tmp = x * (y / z)
	elif z <= -2.15e-66:
		tmp = x
	elif z <= 4.1e+79:
		tmp = y * (x / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -2.4e+25)
		tmp = x;
	elseif (z <= -6e-22)
		tmp = Float64(x * Float64(y / z));
	elseif (z <= -2.15e-66)
		tmp = x;
	elseif (z <= 4.1e+79)
		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 <= -2.4e+25)
		tmp = x;
	elseif (z <= -6e-22)
		tmp = x * (y / z);
	elseif (z <= -2.15e-66)
		tmp = x;
	elseif (z <= 4.1e+79)
		tmp = y * (x / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -2.4e+25], x, If[LessEqual[z, -6e-22], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.15e-66], x, If[LessEqual[z, 4.1e+79], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], x]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.39999999999999996e25 or -5.9999999999999998e-22 < z < -2.15000000000000007e-66 or 4.1e79 < z

   1. Initial program 74.7%

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

      1. associate-/l* 99.2%

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

      2. remove-double-neg 99.2%

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

      3. distribute-frac-neg2 99.2%

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

      4. neg-sub0 99.2%

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

      5. remove-double-neg 99.2%

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

      6. unsub-neg 99.2%

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

      7. div-sub 99.2%

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

      8. *-inverses 99.2%

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

      9. metadata-eval 99.2%

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

      10. associate--r- 99.2%

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

      11. neg-sub0 99.2%

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

      12. distribute-frac-neg2 99.2%

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

      13. remove-double-neg 99.2%

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

      14. sub-neg 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in y around 0 87.1%

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

   if -2.39999999999999996e25 < z < -5.9999999999999998e-22

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. remove-double-neg 100.0%

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

      3. distribute-frac-neg2 100.0%

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

      4. neg-sub0 100.0%

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

      5. remove-double-neg 100.0%

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

      6. unsub-neg 100.0%

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

      7. div-sub 100.0%

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

      8. *-inverses 100.0%

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

      9. metadata-eval 100.0%

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

      10. associate--r- 100.0%

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

      11. neg-sub0 100.0%

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

      12. distribute-frac-neg2 100.0%

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

      13. remove-double-neg 100.0%

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

      14. sub-neg 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 90.3%

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

      1. associate-*r/ 90.3%

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

   7. Simplified 90.3%

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

   if -2.15000000000000007e-66 < z < 4.1e79

   1. Initial program 92.9%

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

      1. associate-/l* 93.7%

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

      2. remove-double-neg 93.7%

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

      3. distribute-frac-neg2 93.7%

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

      4. neg-sub0 93.7%

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

      5. remove-double-neg 93.7%

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

      6. unsub-neg 93.7%

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

      7. div-sub 93.7%

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

      8. *-inverses 93.7%

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

      9. metadata-eval 93.7%

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

      10. associate--r- 93.7%

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

      11. neg-sub0 93.7%

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

      12. distribute-frac-neg2 93.7%

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

      13. remove-double-neg 93.7%

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

      14. sub-neg 93.7%

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

   3. Simplified 93.7%

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

   5. Taylor expanded in y around inf 73.4%

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

      1. associate-*l/ 72.6%

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

      2. *-commutative 72.6%

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

   7. Simplified 72.6%

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

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+25}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-22}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -2.15 \cdot 10^{-66}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{+79}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 71.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+22}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{-22}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-66}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+79}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.25e+22)
   x
   (if (<= z -4.1e-22)
     (* x (/ y z))
     (if (<= z -2.4e-66) x (if (<= z 4.6e+79) (/ (* x y) z) x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.25e+22) {
		tmp = x;
	} else if (z <= -4.1e-22) {
		tmp = x * (y / z);
	} else if (z <= -2.4e-66) {
		tmp = x;
	} else if (z <= 4.6e+79) {
		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 <= (-1.25d+22)) then
        tmp = x
    else if (z <= (-4.1d-22)) then
        tmp = x * (y / z)
    else if (z <= (-2.4d-66)) then
        tmp = x
    else if (z <= 4.6d+79) 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 <= -1.25e+22) {
		tmp = x;
	} else if (z <= -4.1e-22) {
		tmp = x * (y / z);
	} else if (z <= -2.4e-66) {
		tmp = x;
	} else if (z <= 4.6e+79) {
		tmp = (x * y) / z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.25e+22:
		tmp = x
	elif z <= -4.1e-22:
		tmp = x * (y / z)
	elif z <= -2.4e-66:
		tmp = x
	elif z <= 4.6e+79:
		tmp = (x * y) / z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.25e+22)
		tmp = x;
	elseif (z <= -4.1e-22)
		tmp = Float64(x * Float64(y / z));
	elseif (z <= -2.4e-66)
		tmp = x;
	elseif (z <= 4.6e+79)
		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 <= -1.25e+22)
		tmp = x;
	elseif (z <= -4.1e-22)
		tmp = x * (y / z);
	elseif (z <= -2.4e-66)
		tmp = x;
	elseif (z <= 4.6e+79)
		tmp = (x * y) / z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.25e+22], x, If[LessEqual[z, -4.1e-22], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.4e-66], x, If[LessEqual[z, 4.6e+79], N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision], x]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.2499999999999999e22 or -4.0999999999999999e-22 < z < -2.40000000000000026e-66 or 4.6000000000000001e79 < z

   1. Initial program 74.7%

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

      1. associate-/l* 99.2%

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

      2. remove-double-neg 99.2%

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

      3. distribute-frac-neg2 99.2%

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

      4. neg-sub0 99.2%

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

      5. remove-double-neg 99.2%

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

      6. unsub-neg 99.2%

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

      7. div-sub 99.2%

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

      8. *-inverses 99.2%

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

      9. metadata-eval 99.2%

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

      10. associate--r- 99.2%

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

      11. neg-sub0 99.2%

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

      12. distribute-frac-neg2 99.2%

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

      13. remove-double-neg 99.2%

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

      14. sub-neg 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in y around 0 87.1%

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

   if -1.2499999999999999e22 < z < -4.0999999999999999e-22

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. remove-double-neg 100.0%

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

      3. distribute-frac-neg2 100.0%

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

      4. neg-sub0 100.0%

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

      5. remove-double-neg 100.0%

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

      6. unsub-neg 100.0%

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

      7. div-sub 100.0%

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

      8. *-inverses 100.0%

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

      9. metadata-eval 100.0%

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

      10. associate--r- 100.0%

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

      11. neg-sub0 100.0%

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

      12. distribute-frac-neg2 100.0%

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

      13. remove-double-neg 100.0%

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

      14. sub-neg 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 90.3%

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

      1. associate-*r/ 90.3%

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

   7. Simplified 90.3%

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

   if -2.40000000000000026e-66 < z < 4.6000000000000001e79

   1. Initial program 92.9%

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

      1. associate-/l* 93.7%

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

      2. remove-double-neg 93.7%

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

      3. distribute-frac-neg2 93.7%

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

      4. neg-sub0 93.7%

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

      5. remove-double-neg 93.7%

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

      6. unsub-neg 93.7%

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

      7. div-sub 93.7%

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

      8. *-inverses 93.7%

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

      9. metadata-eval 93.7%

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

      10. associate--r- 93.7%

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

      11. neg-sub0 93.7%

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

      12. distribute-frac-neg2 93.7%

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

      13. remove-double-neg 93.7%

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

      14. sub-neg 93.7%

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

   3. Simplified 93.7%

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

   5. Taylor expanded in y around inf 73.4%

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

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+22}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{-22}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-66}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+79}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 95.7% 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 84.4%

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

   1. associate-/l* 96.6%

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

   2. remove-double-neg 96.6%

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

   3. distribute-frac-neg2 96.6%

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

   4. neg-sub0 96.6%

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

   5. remove-double-neg 96.6%

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

   6. unsub-neg 96.6%

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

   7. div-sub 96.6%

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

   8. *-inverses 96.6%

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

   9. metadata-eval 96.6%

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

   10. associate--r- 96.6%

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

   11. neg-sub0 96.6%

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

   12. distribute-frac-neg2 96.6%

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

   13. remove-double-neg 96.6%

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

   14. sub-neg 96.6%

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

3. Simplified 96.6%

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

5. Final simplification 96.6%

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

Alternative 6: 50.3% 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 84.4%

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

   1. associate-/l* 96.6%

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

   2. remove-double-neg 96.6%

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

   3. distribute-frac-neg2 96.6%

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

   4. neg-sub0 96.6%

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

   5. remove-double-neg 96.6%

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

   6. unsub-neg 96.6%

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

   7. div-sub 96.6%

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

   8. *-inverses 96.6%

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

   9. metadata-eval 96.6%

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

   10. associate--r- 96.6%

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

   11. neg-sub0 96.6%

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

   12. distribute-frac-neg2 96.6%

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

   13. remove-double-neg 96.6%

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

   14. sub-neg 96.6%

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

3. Simplified 96.6%

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

5. Taylor expanded in y around 0 54.5%

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

6. Final simplification 54.5%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 96.0% 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 2024043 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:choose from math-functions-0.1.5.2"
  :precision binary64

  :alt
  (/ x (/ z (+ y z)))

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