Diagrams.Backend.Cairo.Internal:setTexture from diagrams-cairo-1.3.0.3

Percentage Accurate: 84.8% → 96.1%

Time: 6.3s

Alternatives: 6

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 84.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 81.3%

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

   1. remove-double-neg 81.3%

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

   2. distribute-frac-neg2 81.3%

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

   3. distribute-frac-neg 81.3%

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

   4. distribute-rgt-neg-in 81.3%

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

   5. associate-/l* 96.2%

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

   6. distribute-frac-neg 96.2%

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

   7. distribute-frac-neg2 96.2%

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

   8. remove-double-neg 96.2%

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

   9. div-sub 96.2%

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

   10. *-inverses 96.2%

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

3. Simplified 96.2%

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

5. Final simplification 96.2%

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

Alternative 2: 72.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{+31} \lor \neg \left(z \leq -2.85 \cdot 10^{-6}\right) \land \left(z \leq -1.15 \cdot 10^{-44} \lor \neg \left(z \leq 1.05 \cdot 10^{-50}\right)\right):\\ \;\;\;\;z \cdot \left(-\frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -5.6e+31)
         (and (not (<= z -2.85e-6))
              (or (<= z -1.15e-44) (not (<= z 1.05e-50)))))
   (* z (- (/ x y)))
   x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5.6e+31) || (!(z <= -2.85e-6) && ((z <= -1.15e-44) || !(z <= 1.05e-50)))) {
		tmp = z * -(x / 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 <= (-5.6d+31)) .or. (.not. (z <= (-2.85d-6))) .and. (z <= (-1.15d-44)) .or. (.not. (z <= 1.05d-50))) then
        tmp = z * -(x / 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 <= -5.6e+31) || (!(z <= -2.85e-6) && ((z <= -1.15e-44) || !(z <= 1.05e-50)))) {
		tmp = z * -(x / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -5.6e+31) or (not (z <= -2.85e-6) and ((z <= -1.15e-44) or not (z <= 1.05e-50))):
		tmp = z * -(x / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -5.6e+31) || (!(z <= -2.85e-6) && ((z <= -1.15e-44) || !(z <= 1.05e-50))))
		tmp = Float64(z * Float64(-Float64(x / y)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -5.6e+31) || (~((z <= -2.85e-6)) && ((z <= -1.15e-44) || ~((z <= 1.05e-50)))))
		tmp = z * -(x / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -5.6e+31], And[N[Not[LessEqual[z, -2.85e-6]], $MachinePrecision], Or[LessEqual[z, -1.15e-44], N[Not[LessEqual[z, 1.05e-50]], $MachinePrecision]]]], N[(z * (-N[(x / y), $MachinePrecision])), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -5.60000000000000034e31 or -2.8499999999999998e-6 < z < -1.14999999999999999e-44 or 1.05e-50 < z

   1. Initial program 88.4%

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

   3. Taylor expanded in y around 0 75.6%

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

      1. associate-*r* 75.6%

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

      2. *-commutative 75.6%

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

      3. mul-1-neg 75.6%

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

   5. Simplified 75.6%

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

      1. frac-2neg 75.6%

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

      2. distribute-frac-neg 75.6%

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

      3. add-sqr-sqrt 42.8%

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

      4. sqrt-unprod 27.8%

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

      5. sqr-neg 27.8%

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

      6. sqrt-unprod 0.6%

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

      7. add-sqr-sqrt 1.7%

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

      8. remove-double-neg 1.7%

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

      9. distribute-rgt-neg-out 1.7%

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

      10. frac-2neg 1.7%

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

      11. div-inv 1.7%

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

      12. *-commutative 1.7%

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

      13. associate-*r* 1.7%

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

      14. associate-*l/ 1.7%

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

      15. *-un-lft-identity 1.7%

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

      16. add-sqr-sqrt 1.1%

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

      17. sqrt-unprod 24.0%

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

      18. sqr-neg 24.0%

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

      19. sqrt-unprod 29.6%

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

      20. add-sqr-sqrt 69.9%

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

      21. associate-/r/ 74.1%

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

      22. div-inv 74.1%

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

      23. clear-num 74.1%

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

   7. Applied egg-rr 74.1%

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

   if -5.60000000000000034e31 < z < -2.8499999999999998e-6 or -1.14999999999999999e-44 < z < 1.05e-50

   1. Initial program 73.8%

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

      1. remove-double-neg 73.8%

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

      2. distribute-frac-neg2 73.8%

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

      3. distribute-frac-neg 73.8%

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

      4. distribute-rgt-neg-in 73.8%

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

      5. associate-/l* 99.9%

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

      6. distribute-frac-neg 99.9%

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

      7. distribute-frac-neg2 99.9%

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

      8. remove-double-neg 99.9%

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

      9. div-sub 99.9%

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

      10. *-inverses 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0 83.9%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{+31} \lor \neg \left(z \leq -2.85 \cdot 10^{-6}\right) \land \left(z \leq -1.15 \cdot 10^{-44} \lor \neg \left(z \leq 1.05 \cdot 10^{-50}\right)\right):\\ \;\;\;\;z \cdot \left(-\frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 72.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(-\frac{x}{y}\right)\\ \mathbf{if}\;z \leq -8.4 \cdot 10^{+30}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-7}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-45}:\\ \;\;\;\;\frac{-z}{\frac{y}{x}}\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{-53}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (- (/ x y)))))
   (if (<= z -8.4e+30)
     t_0
     (if (<= z -7.5e-7)
       x
       (if (<= z -9.5e-45) (/ (- z) (/ y x)) (if (<= z 6.4e-53) x t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = z * -(x / y);
	double tmp;
	if (z <= -8.4e+30) {
		tmp = t_0;
	} else if (z <= -7.5e-7) {
		tmp = x;
	} else if (z <= -9.5e-45) {
		tmp = -z / (y / x);
	} else if (z <= 6.4e-53) {
		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 = z * -(x / y)
    if (z <= (-8.4d+30)) then
        tmp = t_0
    else if (z <= (-7.5d-7)) then
        tmp = x
    else if (z <= (-9.5d-45)) then
        tmp = -z / (y / x)
    else if (z <= 6.4d-53) 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 = z * -(x / y);
	double tmp;
	if (z <= -8.4e+30) {
		tmp = t_0;
	} else if (z <= -7.5e-7) {
		tmp = x;
	} else if (z <= -9.5e-45) {
		tmp = -z / (y / x);
	} else if (z <= 6.4e-53) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * -(x / y)
	tmp = 0
	if z <= -8.4e+30:
		tmp = t_0
	elif z <= -7.5e-7:
		tmp = x
	elif z <= -9.5e-45:
		tmp = -z / (y / x)
	elif z <= 6.4e-53:
		tmp = x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(-Float64(x / y)))
	tmp = 0.0
	if (z <= -8.4e+30)
		tmp = t_0;
	elseif (z <= -7.5e-7)
		tmp = x;
	elseif (z <= -9.5e-45)
		tmp = Float64(Float64(-z) / Float64(y / x));
	elseif (z <= 6.4e-53)
		tmp = x;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * -(x / y);
	tmp = 0.0;
	if (z <= -8.4e+30)
		tmp = t_0;
	elseif (z <= -7.5e-7)
		tmp = x;
	elseif (z <= -9.5e-45)
		tmp = -z / (y / x);
	elseif (z <= 6.4e-53)
		tmp = x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * (-N[(x / y), $MachinePrecision])), $MachinePrecision]}, If[LessEqual[z, -8.4e+30], t$95$0, If[LessEqual[z, -7.5e-7], x, If[LessEqual[z, -9.5e-45], N[((-z) / N[(y / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.4e-53], x, t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.4000000000000001e30 or 6.4000000000000002e-53 < z

   1. Initial program 87.8%

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

   3. Taylor expanded in y around 0 75.0%

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

      1. associate-*r* 75.0%

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

      2. *-commutative 75.0%

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

      3. mul-1-neg 75.0%

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

   5. Simplified 75.0%

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

      1. frac-2neg 75.0%

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

      2. distribute-frac-neg 75.0%

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

      3. add-sqr-sqrt 42.1%

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

      4. sqrt-unprod 27.7%

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

      5. sqr-neg 27.7%

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

      6. sqrt-unprod 0.6%

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

      7. add-sqr-sqrt 1.7%

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

      8. remove-double-neg 1.7%

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

      9. distribute-rgt-neg-out 1.7%

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

      10. frac-2neg 1.7%

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

      11. div-inv 1.7%

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

      12. *-commutative 1.7%

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

      13. associate-*r* 1.7%

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

      14. associate-*l/ 1.7%

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

      15. *-un-lft-identity 1.7%

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

      16. add-sqr-sqrt 1.2%

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

      17. sqrt-unprod 23.7%

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

      18. sqr-neg 23.7%

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

      19. sqrt-unprod 29.7%

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

      20. add-sqr-sqrt 69.1%

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

      21. associate-/r/ 73.4%

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

      22. div-inv 73.4%

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

      23. clear-num 73.4%

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

   7. Applied egg-rr 73.4%

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

   if -8.4000000000000001e30 < z < -7.5000000000000002e-7 or -9.5000000000000002e-45 < z < 6.4000000000000002e-53

   1. Initial program 73.8%

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

      1. remove-double-neg 73.8%

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

      2. distribute-frac-neg2 73.8%

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

      3. distribute-frac-neg 73.8%

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

      4. distribute-rgt-neg-in 73.8%

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

      5. associate-/l* 99.9%

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

      6. distribute-frac-neg 99.9%

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

      7. distribute-frac-neg2 99.9%

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

      8. remove-double-neg 99.9%

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

      9. div-sub 99.9%

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

      10. *-inverses 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0 83.9%

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

   if -7.5000000000000002e-7 < z < -9.5000000000000002e-45

   1. Initial program 99.6%

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

      1. clear-num 99.3%

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

      2. associate-/r/ 99.1%

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

   4. Applied egg-rr 99.1%

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

   5. Taylor expanded in y around 0 85.1%

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

      1. associate-*r* 85.3%

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

      2. *-commutative 85.3%

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

      3. mul-1-neg 85.3%

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

   7. Simplified 85.1%

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

      1. associate-*r* 85.3%

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

      2. associate-*l/ 85.5%

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

      3. *-un-lft-identity 85.5%

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

      4. add-sqr-sqrt 56.1%

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

      5. sqrt-unprod 29.7%

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

      6. sqr-neg 29.7%

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

      7. sqrt-unprod 0.8%

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

      8. add-sqr-sqrt 1.5%

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

      9. associate-/r/ 1.5%

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

      10. frac-2neg 1.5%

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

      11. distribute-neg-frac2 1.5%

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

      12. add-sqr-sqrt 0.7%

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

      13. sqrt-unprod 30.3%

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

      14. sqr-neg 30.3%

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

      15. sqrt-unprod 28.9%

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

      16. add-sqr-sqrt 85.8%

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

   9. Applied egg-rr 85.8%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.4 \cdot 10^{+30}:\\ \;\;\;\;z \cdot \left(-\frac{x}{y}\right)\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-7}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-45}:\\ \;\;\;\;\frac{-z}{\frac{y}{x}}\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{-53}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-\frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 72.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+31}:\\ \;\;\;\;\frac{x \cdot \left(-z\right)}{y}\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-8}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-45}:\\ \;\;\;\;\frac{-z}{\frac{y}{x}}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-53}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-\frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -3.3e+31)
   (/ (* x (- z)) y)
   (if (<= z -7e-8)
     x
     (if (<= z -5e-45)
       (/ (- z) (/ y x))
       (if (<= z 6.5e-53) x (* z (- (/ x y))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -3.3e+31) {
		tmp = (x * -z) / y;
	} else if (z <= -7e-8) {
		tmp = x;
	} else if (z <= -5e-45) {
		tmp = -z / (y / x);
	} else if (z <= 6.5e-53) {
		tmp = x;
	} else {
		tmp = z * -(x / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-3.3d+31)) then
        tmp = (x * -z) / y
    else if (z <= (-7d-8)) then
        tmp = x
    else if (z <= (-5d-45)) then
        tmp = -z / (y / x)
    else if (z <= 6.5d-53) then
        tmp = x
    else
        tmp = z * -(x / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -3.3e+31) {
		tmp = (x * -z) / y;
	} else if (z <= -7e-8) {
		tmp = x;
	} else if (z <= -5e-45) {
		tmp = -z / (y / x);
	} else if (z <= 6.5e-53) {
		tmp = x;
	} else {
		tmp = z * -(x / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -3.3e+31:
		tmp = (x * -z) / y
	elif z <= -7e-8:
		tmp = x
	elif z <= -5e-45:
		tmp = -z / (y / x)
	elif z <= 6.5e-53:
		tmp = x
	else:
		tmp = z * -(x / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -3.3e+31)
		tmp = Float64(Float64(x * Float64(-z)) / y);
	elseif (z <= -7e-8)
		tmp = x;
	elseif (z <= -5e-45)
		tmp = Float64(Float64(-z) / Float64(y / x));
	elseif (z <= 6.5e-53)
		tmp = x;
	else
		tmp = Float64(z * Float64(-Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -3.3e+31)
		tmp = (x * -z) / y;
	elseif (z <= -7e-8)
		tmp = x;
	elseif (z <= -5e-45)
		tmp = -z / (y / x);
	elseif (z <= 6.5e-53)
		tmp = x;
	else
		tmp = z * -(x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -3.3e+31], N[(N[(x * (-z)), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[z, -7e-8], x, If[LessEqual[z, -5e-45], N[((-z) / N[(y / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.5e-53], x, N[(z * (-N[(x / y), $MachinePrecision])), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.29999999999999992e31

   1. Initial program 90.6%

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

   3. Taylor expanded in y around 0 77.4%

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

      1. associate-*r* 77.4%

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

      2. *-commutative 77.4%

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

      3. mul-1-neg 77.4%

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

   5. Simplified 77.4%

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

   if -3.29999999999999992e31 < z < -7.00000000000000048e-8 or -4.99999999999999976e-45 < z < 6.4999999999999997e-53

   1. Initial program 73.8%

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

      1. remove-double-neg 73.8%

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

      2. distribute-frac-neg2 73.8%

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

      3. distribute-frac-neg 73.8%

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

      4. distribute-rgt-neg-in 73.8%

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

      5. associate-/l* 99.9%

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

      6. distribute-frac-neg 99.9%

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

      7. distribute-frac-neg2 99.9%

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

      8. remove-double-neg 99.9%

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

      9. div-sub 99.9%

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

      10. *-inverses 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0 83.9%

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

   if -7.00000000000000048e-8 < z < -4.99999999999999976e-45

   1. Initial program 99.6%

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

      1. clear-num 99.3%

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

      2. associate-/r/ 99.1%

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

   4. Applied egg-rr 99.1%

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

   5. Taylor expanded in y around 0 85.1%

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

      1. associate-*r* 85.3%

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

      2. *-commutative 85.3%

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

      3. mul-1-neg 85.3%

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

   7. Simplified 85.1%

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

      1. associate-*r* 85.3%

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

      2. associate-*l/ 85.5%

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

      3. *-un-lft-identity 85.5%

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

      4. add-sqr-sqrt 56.1%

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

      5. sqrt-unprod 29.7%

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

      6. sqr-neg 29.7%

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

      7. sqrt-unprod 0.8%

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

      8. add-sqr-sqrt 1.5%

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

      9. associate-/r/ 1.5%

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

      10. frac-2neg 1.5%

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

      11. distribute-neg-frac2 1.5%

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

      12. add-sqr-sqrt 0.7%

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

      13. sqrt-unprod 30.3%

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

      14. sqr-neg 30.3%

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

      15. sqrt-unprod 28.9%

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

      16. add-sqr-sqrt 85.8%

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

   9. Applied egg-rr 85.8%

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

   if 6.4999999999999997e-53 < z

   1. Initial program 85.8%

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

   3. Taylor expanded in y around 0 73.4%

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

      1. associate-*r* 73.4%

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

      2. *-commutative 73.4%

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

      3. mul-1-neg 73.4%

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

   5. Simplified 73.4%

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

      1. frac-2neg 73.4%

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

      2. distribute-frac-neg 73.4%

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

      3. add-sqr-sqrt 35.8%

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

      4. sqrt-unprod 21.1%

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

      5. sqr-neg 21.1%

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

      6. sqrt-unprod 0.4%

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

      7. add-sqr-sqrt 1.5%

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

      8. remove-double-neg 1.5%

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

      9. distribute-rgt-neg-out 1.5%

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

      10. frac-2neg 1.5%

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

      11. div-inv 1.5%

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

      12. *-commutative 1.5%

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

      13. associate-*r* 1.6%

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

      14. associate-*l/ 1.6%

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

      15. *-un-lft-identity 1.6%

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

      16. add-sqr-sqrt 1.2%

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

      17. sqrt-unprod 30.4%

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

      18. sqr-neg 30.4%

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

      19. sqrt-unprod 34.9%

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

      20. add-sqr-sqrt 69.7%

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

      21. associate-/r/ 74.6%

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

      22. div-inv 74.6%

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

      23. clear-num 74.6%

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

   7. Applied egg-rr 74.6%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+31}:\\ \;\;\;\;\frac{x \cdot \left(-z\right)}{y}\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-8}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-45}:\\ \;\;\;\;\frac{-z}{\frac{y}{x}}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-53}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-\frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 52.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 2 \cdot 10^{+25}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= x 2e+25) x (* y (/ x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 2e+25) {
		tmp = x;
	} else {
		tmp = y * (x / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= 2d+25) then
        tmp = x
    else
        tmp = y * (x / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 2e+25) {
		tmp = x;
	} else {
		tmp = y * (x / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 2e+25:
		tmp = x
	else:
		tmp = y * (x / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 2e+25)
		tmp = x;
	else
		tmp = Float64(y * Float64(x / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 2e+25)
		tmp = x;
	else
		tmp = y * (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 2e+25], x, N[(y * N[(x / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 2.00000000000000018e25

   1. Initial program 82.7%

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

      1. remove-double-neg 82.7%

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

      2. distribute-frac-neg2 82.7%

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

      3. distribute-frac-neg 82.7%

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

      4. distribute-rgt-neg-in 82.7%

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

      5. associate-/l* 95.2%

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

      6. distribute-frac-neg 95.2%

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

      7. distribute-frac-neg2 95.2%

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

      8. remove-double-neg 95.2%

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

      9. div-sub 95.2%

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

      10. *-inverses 95.2%

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

   3. Simplified 95.2%

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

   5. Taylor expanded in z around 0 53.0%

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

   if 2.00000000000000018e25 < x

   1. Initial program 76.1%

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

   3. Taylor expanded in y around inf 28.4%

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

      1. *-commutative 28.4%

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

      2. associate-/l* 63.7%

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

   5. Applied egg-rr 63.7%

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

4. Final simplification 55.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 2 \cdot 10^{+25}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 51.1% 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 81.3%

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

   1. remove-double-neg 81.3%

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

   2. distribute-frac-neg2 81.3%

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

   3. distribute-frac-neg 81.3%

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

   4. distribute-rgt-neg-in 81.3%

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

   5. associate-/l* 96.2%

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

   6. distribute-frac-neg 96.2%

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

   7. distribute-frac-neg2 96.2%

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

   8. remove-double-neg 96.2%

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

   9. div-sub 96.2%

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

   10. *-inverses 96.2%

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

3. Simplified 96.2%

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

5. Taylor expanded in z around 0 52.9%

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

6. Final simplification 52.9%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 96.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z < -2.060202331921739 \cdot 10^{+104}:\\ \;\;\;\;x - \frac{z \cdot x}{y}\\ \mathbf{elif}\;z < 1.6939766013828526 \cdot 10^{+213}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (< z -2.060202331921739e+104)
   (- x (/ (* z x) y))
   (if (< z 1.6939766013828526e+213) (/ x (/ y (- y z))) (* (- y z) (/ x y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z < -2.060202331921739e+104) {
		tmp = x - ((z * x) / y);
	} else if (z < 1.6939766013828526e+213) {
		tmp = x / (y / (y - z));
	} else {
		tmp = (y - z) * (x / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z < (-2.060202331921739d+104)) then
        tmp = x - ((z * x) / y)
    else if (z < 1.6939766013828526d+213) then
        tmp = x / (y / (y - z))
    else
        tmp = (y - z) * (x / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z < -2.060202331921739e+104) {
		tmp = x - ((z * x) / y);
	} else if (z < 1.6939766013828526e+213) {
		tmp = x / (y / (y - z));
	} else {
		tmp = (y - z) * (x / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z < -2.060202331921739e+104:
		tmp = x - ((z * x) / y)
	elif z < 1.6939766013828526e+213:
		tmp = x / (y / (y - z))
	else:
		tmp = (y - z) * (x / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z < -2.060202331921739e+104)
		tmp = Float64(x - Float64(Float64(z * x) / y));
	elseif (z < 1.6939766013828526e+213)
		tmp = Float64(x / Float64(y / Float64(y - z)));
	else
		tmp = Float64(Float64(y - z) * Float64(x / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z < -2.060202331921739e+104)
		tmp = x - ((z * x) / y);
	elseif (z < 1.6939766013828526e+213)
		tmp = x / (y / (y - z));
	else
		tmp = (y - z) * (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Less[z, -2.060202331921739e+104], N[(x - N[(N[(z * x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[Less[z, 1.6939766013828526e+213], N[(x / N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y - z), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]]]

Reproduce

herbie shell --seed 2024059 
(FPCore (x y z)
  :name "Diagrams.Backend.Cairo.Internal:setTexture from diagrams-cairo-1.3.0.3"
  :precision binary64

  :herbie-target
  (if (< z -2.060202331921739e+104) (- x (/ (* z x) y)) (if (< z 1.6939766013828526e+213) (/ x (/ y (- y z))) (* (- y z) (/ x y))))

  (/ (* x (- y z)) y))