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

Percentage Accurate: 84.0% → 96.7%

Time: 9.3s

Alternatives: 9

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: 84.0% 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: 96.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+48}:\\ \;\;\;\;x - \frac{z}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -2e+48) (- x (/ z (/ y x))) (* x (- 1.0 (/ z y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -2e+48) {
		tmp = x - (z / (y / x));
	} else {
		tmp = x * (1.0 - (z / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-2d+48)) then
        tmp = x - (z / (y / x))
    else
        tmp = x * (1.0d0 - (z / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -2e+48) {
		tmp = x - (z / (y / x));
	} else {
		tmp = x * (1.0 - (z / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -2e+48:
		tmp = x - (z / (y / x))
	else:
		tmp = x * (1.0 - (z / y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -2e+48)
		tmp = Float64(x - Float64(z / Float64(y / x)));
	else
		tmp = Float64(x * Float64(1.0 - Float64(z / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -2e+48)
		tmp = x - (z / (y / x));
	else
		tmp = x * (1.0 - (z / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -2e+48], N[(x - N[(z / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.00000000000000009e48

   1. Initial program 94.2%

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

      1. associate-/l* N/A

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

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

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

      3. div-sub N/A

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

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

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

      5. *-inverses N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \left(\frac{\color{blue}{z}}{y}\right)\right)\right) \]

      6. /-lowering-/.f64 90.1%

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

   3. Simplified 90.1%

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

      1. flip3-- N/A

         \[\leadsto x \cdot \frac{{1}^{3} - {\left(\frac{z}{y}\right)}^{3}}{\color{blue}{1 \cdot 1 + \left(\frac{z}{y} \cdot \frac{z}{y} + 1 \cdot \frac{z}{y}\right)}} \]

      2. clear-num N/A

         \[\leadsto x \cdot \frac{1}{\color{blue}{\frac{1 \cdot 1 + \left(\frac{z}{y} \cdot \frac{z}{y} + 1 \cdot \frac{z}{y}\right)}{{1}^{3} - {\left(\frac{z}{y}\right)}^{3}}}} \]

      3. un-div-inv N/A

         \[\leadsto \frac{x}{\color{blue}{\frac{1 \cdot 1 + \left(\frac{z}{y} \cdot \frac{z}{y} + 1 \cdot \frac{z}{y}\right)}{{1}^{3} - {\left(\frac{z}{y}\right)}^{3}}}} \]

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

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(\frac{1 \cdot 1 + \left(\frac{z}{y} \cdot \frac{z}{y} + 1 \cdot \frac{z}{y}\right)}{{1}^{3} - {\left(\frac{z}{y}\right)}^{3}}\right)}\right) \]

      5. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(\frac{1}{\color{blue}{\frac{{1}^{3} - {\left(\frac{z}{y}\right)}^{3}}{1 \cdot 1 + \left(\frac{z}{y} \cdot \frac{z}{y} + 1 \cdot \frac{z}{y}\right)}}}\right)\right) \]

      6. flip3-- N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(\frac{1}{1 - \color{blue}{\frac{z}{y}}}\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(1, \color{blue}{\left(1 - \frac{z}{y}\right)}\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(1, \color{blue}{\left(\frac{z}{y}\right)}\right)\right)\right) \]

      9. /-lowering-/.f64 90.1%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(z, \color{blue}{y}\right)\right)\right)\right) \]

   6. Applied egg-rr 90.1%

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

      1. associate-/r/ N/A

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

      2. /-rgt-identity N/A

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

      3. *-commutative N/A

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

      4. *-inverses N/A

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

      5. div-sub N/A

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

      6. associate-/r/ N/A

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

      7. div-sub N/A

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

      8. un-div-inv N/A

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

      9. associate-/r/ N/A

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

      10. associate-*r* N/A

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

      11. div-inv N/A

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

      12. *-inverses N/A

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

      13. *-lft-identity N/A

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

      14. --lowering--.f64 N/A

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

      15. /-lowering-/.f64 N/A

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

      16. /-lowering-/.f64 99.8%

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

   8. Applied egg-rr 99.8%

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

   if -2.00000000000000009e48 < z

   1. Initial program 84.4%

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

      1. associate-/l* N/A

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

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

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

      3. div-sub N/A

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

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

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

      5. *-inverses N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \left(\frac{\color{blue}{z}}{y}\right)\right)\right) \]

      6. /-lowering-/.f64 97.9%

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

   3. Simplified 97.9%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{z}{y}\right)} \]
   4. Add Preprocessing
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 2: 73.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{-37}:\\ \;\;\;\;z \cdot \frac{x}{0 - y}\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+23}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;0 - \frac{z \cdot x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -5e-37)
   (* z (/ x (- 0.0 y)))
   (if (<= z 1.05e+23) x (- 0.0 (/ (* z x) y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -5e-37) {
		tmp = z * (x / (0.0 - y));
	} else if (z <= 1.05e+23) {
		tmp = x;
	} else {
		tmp = 0.0 - ((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 <= (-5d-37)) then
        tmp = z * (x / (0.0d0 - y))
    else if (z <= 1.05d+23) then
        tmp = x
    else
        tmp = 0.0d0 - ((z * x) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -5e-37) {
		tmp = z * (x / (0.0 - y));
	} else if (z <= 1.05e+23) {
		tmp = x;
	} else {
		tmp = 0.0 - ((z * x) / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -5e-37:
		tmp = z * (x / (0.0 - y))
	elif z <= 1.05e+23:
		tmp = x
	else:
		tmp = 0.0 - ((z * x) / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -5e-37)
		tmp = Float64(z * Float64(x / Float64(0.0 - y)));
	elseif (z <= 1.05e+23)
		tmp = x;
	else
		tmp = Float64(0.0 - Float64(Float64(z * x) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -5e-37)
		tmp = z * (x / (0.0 - y));
	elseif (z <= 1.05e+23)
		tmp = x;
	else
		tmp = 0.0 - ((z * x) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -5e-37], N[(z * N[(x / N[(0.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.05e+23], x, N[(0.0 - N[(N[(z * x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.9999999999999997e-37

   1. Initial program 95.1%

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

      1. associate-/l* N/A

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

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

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

      3. div-sub N/A

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

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

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

      5. *-inverses N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \left(\frac{\color{blue}{z}}{y}\right)\right)\right) \]

      6. /-lowering-/.f64 91.8%

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

   3. Simplified 91.8%

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

      1. flip3-- N/A

         \[\leadsto x \cdot \frac{{1}^{3} - {\left(\frac{z}{y}\right)}^{3}}{\color{blue}{1 \cdot 1 + \left(\frac{z}{y} \cdot \frac{z}{y} + 1 \cdot \frac{z}{y}\right)}} \]

      2. clear-num N/A

         \[\leadsto x \cdot \frac{1}{\color{blue}{\frac{1 \cdot 1 + \left(\frac{z}{y} \cdot \frac{z}{y} + 1 \cdot \frac{z}{y}\right)}{{1}^{3} - {\left(\frac{z}{y}\right)}^{3}}}} \]

      3. un-div-inv N/A

         \[\leadsto \frac{x}{\color{blue}{\frac{1 \cdot 1 + \left(\frac{z}{y} \cdot \frac{z}{y} + 1 \cdot \frac{z}{y}\right)}{{1}^{3} - {\left(\frac{z}{y}\right)}^{3}}}} \]

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

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(\frac{1 \cdot 1 + \left(\frac{z}{y} \cdot \frac{z}{y} + 1 \cdot \frac{z}{y}\right)}{{1}^{3} - {\left(\frac{z}{y}\right)}^{3}}\right)}\right) \]

      5. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(\frac{1}{\color{blue}{\frac{{1}^{3} - {\left(\frac{z}{y}\right)}^{3}}{1 \cdot 1 + \left(\frac{z}{y} \cdot \frac{z}{y} + 1 \cdot \frac{z}{y}\right)}}}\right)\right) \]

      6. flip3-- N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(\frac{1}{1 - \color{blue}{\frac{z}{y}}}\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(1, \color{blue}{\left(1 - \frac{z}{y}\right)}\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(1, \color{blue}{\left(\frac{z}{y}\right)}\right)\right)\right) \]

      9. /-lowering-/.f64 91.7%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(z, \color{blue}{y}\right)\right)\right)\right) \]

   6. Applied egg-rr 91.7%

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

   7. Taylor expanded in z around inf

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(-1 \cdot \frac{y}{z}\right)}\right) \]
   8. Step-by-step derivation

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(0 - \color{blue}{\frac{y}{z}}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(0, \color{blue}{\left(\frac{y}{z}\right)}\right)\right) \]

      4. /-lowering-/.f64 64.4%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(0, \mathsf{/.f64}\left(y, \color{blue}{z}\right)\right)\right) \]

   9. Simplified 64.4%

      \[\leadsto \frac{x}{\color{blue}{0 - \frac{y}{z}}} \]
   10. Step-by-step derivation

       1. clear-num N/A

          \[\leadsto \frac{1}{\color{blue}{\frac{0 - \frac{y}{z}}{x}}} \]

       2. associate-/r/ N/A

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

       3. sub0-neg N/A

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

       4. distribute-frac-neg2 N/A

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

       5. clear-num N/A

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

       6. distribute-lft-neg-in N/A

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

       7. associate-/r/ N/A

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

       8. div-inv N/A

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

       9. clear-num N/A

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

       10. distribute-rgt-neg-in N/A

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

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

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

       12. neg-lowering-neg.f64 N/A

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

       13. /-lowering-/.f64 81.5%

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

   11. Applied egg-rr 81.5%

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

   if -4.9999999999999997e-37 < z < 1.0500000000000001e23

   1. Initial program 80.5%

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

      1. associate-/l* N/A

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

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

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

      3. div-sub N/A

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

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

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

      5. *-inverses N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \left(\frac{\color{blue}{z}}{y}\right)\right)\right) \]

      6. /-lowering-/.f64 99.9%

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

   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

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

   7. Simplified 74.6%

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

   if 1.0500000000000001e23 < z

   1. Initial program 88.5%

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

      1. associate-/l* N/A

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

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

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

      3. div-sub N/A

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

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

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

      5. *-inverses N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \left(\frac{\color{blue}{z}}{y}\right)\right)\right) \]

      6. /-lowering-/.f64 93.4%

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

   3. Simplified 93.4%

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

      1. flip3-- N/A

         \[\leadsto x \cdot \frac{{1}^{3} - {\left(\frac{z}{y}\right)}^{3}}{\color{blue}{1 \cdot 1 + \left(\frac{z}{y} \cdot \frac{z}{y} + 1 \cdot \frac{z}{y}\right)}} \]

      2. clear-num N/A

         \[\leadsto x \cdot \frac{1}{\color{blue}{\frac{1 \cdot 1 + \left(\frac{z}{y} \cdot \frac{z}{y} + 1 \cdot \frac{z}{y}\right)}{{1}^{3} - {\left(\frac{z}{y}\right)}^{3}}}} \]

      3. un-div-inv N/A

         \[\leadsto \frac{x}{\color{blue}{\frac{1 \cdot 1 + \left(\frac{z}{y} \cdot \frac{z}{y} + 1 \cdot \frac{z}{y}\right)}{{1}^{3} - {\left(\frac{z}{y}\right)}^{3}}}} \]

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

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(\frac{1 \cdot 1 + \left(\frac{z}{y} \cdot \frac{z}{y} + 1 \cdot \frac{z}{y}\right)}{{1}^{3} - {\left(\frac{z}{y}\right)}^{3}}\right)}\right) \]

      5. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(\frac{1}{\color{blue}{\frac{{1}^{3} - {\left(\frac{z}{y}\right)}^{3}}{1 \cdot 1 + \left(\frac{z}{y} \cdot \frac{z}{y} + 1 \cdot \frac{z}{y}\right)}}}\right)\right) \]

      6. flip3-- N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(\frac{1}{1 - \color{blue}{\frac{z}{y}}}\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(1, \color{blue}{\left(1 - \frac{z}{y}\right)}\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(1, \color{blue}{\left(\frac{z}{y}\right)}\right)\right)\right) \]

      9. /-lowering-/.f64 93.2%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(z, \color{blue}{y}\right)\right)\right)\right) \]

   6. Applied egg-rr 93.2%

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

   7. Taylor expanded in z around inf

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(-1 \cdot \frac{y}{z}\right)}\right) \]
   8. Step-by-step derivation

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(0 - \color{blue}{\frac{y}{z}}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(0, \color{blue}{\left(\frac{y}{z}\right)}\right)\right) \]

      4. /-lowering-/.f64 66.2%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(0, \mathsf{/.f64}\left(y, \color{blue}{z}\right)\right)\right) \]

   9. Simplified 66.2%

      \[\leadsto \frac{x}{\color{blue}{0 - \frac{y}{z}}} \]
   10. Step-by-step derivation

       1. clear-num N/A

          \[\leadsto \frac{1}{\color{blue}{\frac{0 - \frac{y}{z}}{x}}} \]

       2. associate-/r/ N/A

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

       3. sub0-neg N/A

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

       4. distribute-frac-neg2 N/A

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

       5. clear-num N/A

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

       6. distribute-lft-neg-in N/A

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

       7. associate-/r/ N/A

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

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

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

       9. /-lowering-/.f64 N/A

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

       10. /-lowering-/.f64 74.2%

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

   11. Applied egg-rr 74.2%

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

       1. associate-/r/ N/A

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

       2. associate-*l/ N/A

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

       3. /-lowering-/.f64 N/A

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

       4. *-lowering-*.f64 76.0%

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

   13. Applied egg-rr 76.0%

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

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{-37}:\\ \;\;\;\;z \cdot \frac{x}{0 - y}\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+23}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;0 - \frac{z \cdot x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 73.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.9 \cdot 10^{-36}:\\ \;\;\;\;\frac{z}{\frac{0 - y}{x}}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+21}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;0 - \frac{z \cdot x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -5.9e-36)
   (/ z (/ (- 0.0 y) x))
   (if (<= z 6.8e+21) x (- 0.0 (/ (* z x) y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -5.9e-36) {
		tmp = z / ((0.0 - y) / x);
	} else if (z <= 6.8e+21) {
		tmp = x;
	} else {
		tmp = 0.0 - ((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 <= (-5.9d-36)) then
        tmp = z / ((0.0d0 - y) / x)
    else if (z <= 6.8d+21) then
        tmp = x
    else
        tmp = 0.0d0 - ((z * x) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -5.9e-36) {
		tmp = z / ((0.0 - y) / x);
	} else if (z <= 6.8e+21) {
		tmp = x;
	} else {
		tmp = 0.0 - ((z * x) / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -5.9e-36:
		tmp = z / ((0.0 - y) / x)
	elif z <= 6.8e+21:
		tmp = x
	else:
		tmp = 0.0 - ((z * x) / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -5.9e-36)
		tmp = Float64(z / Float64(Float64(0.0 - y) / x));
	elseif (z <= 6.8e+21)
		tmp = x;
	else
		tmp = Float64(0.0 - Float64(Float64(z * x) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -5.9e-36)
		tmp = z / ((0.0 - y) / x);
	elseif (z <= 6.8e+21)
		tmp = x;
	else
		tmp = 0.0 - ((z * x) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -5.9e-36], N[(z / N[(N[(0.0 - y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.8e+21], x, N[(0.0 - N[(N[(z * x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.89999999999999995e-36

   1. Initial program 95.1%

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

      1. associate-/l* N/A

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

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

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

      3. div-sub N/A

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

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

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

      5. *-inverses N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \left(\frac{\color{blue}{z}}{y}\right)\right)\right) \]

      6. /-lowering-/.f64 91.8%

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

   3. Simplified 91.8%

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

      1. flip3-- N/A

         \[\leadsto x \cdot \frac{{1}^{3} - {\left(\frac{z}{y}\right)}^{3}}{\color{blue}{1 \cdot 1 + \left(\frac{z}{y} \cdot \frac{z}{y} + 1 \cdot \frac{z}{y}\right)}} \]

      2. clear-num N/A

         \[\leadsto x \cdot \frac{1}{\color{blue}{\frac{1 \cdot 1 + \left(\frac{z}{y} \cdot \frac{z}{y} + 1 \cdot \frac{z}{y}\right)}{{1}^{3} - {\left(\frac{z}{y}\right)}^{3}}}} \]

      3. un-div-inv N/A

         \[\leadsto \frac{x}{\color{blue}{\frac{1 \cdot 1 + \left(\frac{z}{y} \cdot \frac{z}{y} + 1 \cdot \frac{z}{y}\right)}{{1}^{3} - {\left(\frac{z}{y}\right)}^{3}}}} \]

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

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(\frac{1 \cdot 1 + \left(\frac{z}{y} \cdot \frac{z}{y} + 1 \cdot \frac{z}{y}\right)}{{1}^{3} - {\left(\frac{z}{y}\right)}^{3}}\right)}\right) \]

      5. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(\frac{1}{\color{blue}{\frac{{1}^{3} - {\left(\frac{z}{y}\right)}^{3}}{1 \cdot 1 + \left(\frac{z}{y} \cdot \frac{z}{y} + 1 \cdot \frac{z}{y}\right)}}}\right)\right) \]

      6. flip3-- N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(\frac{1}{1 - \color{blue}{\frac{z}{y}}}\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(1, \color{blue}{\left(1 - \frac{z}{y}\right)}\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(1, \color{blue}{\left(\frac{z}{y}\right)}\right)\right)\right) \]

      9. /-lowering-/.f64 91.7%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(z, \color{blue}{y}\right)\right)\right)\right) \]

   6. Applied egg-rr 91.7%

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

   7. Taylor expanded in z around inf

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(-1 \cdot \frac{y}{z}\right)}\right) \]
   8. Step-by-step derivation

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(0 - \color{blue}{\frac{y}{z}}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(0, \color{blue}{\left(\frac{y}{z}\right)}\right)\right) \]

      4. /-lowering-/.f64 64.4%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(0, \mathsf{/.f64}\left(y, \color{blue}{z}\right)\right)\right) \]

   9. Simplified 64.4%

      \[\leadsto \frac{x}{\color{blue}{0 - \frac{y}{z}}} \]
   10. Step-by-step derivation

       1. clear-num N/A

          \[\leadsto \frac{1}{\color{blue}{\frac{0 - \frac{y}{z}}{x}}} \]

       2. associate-/r/ N/A

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

       3. sub0-neg N/A

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

       4. distribute-frac-neg2 N/A

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

       5. clear-num N/A

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

       6. distribute-lft-neg-in N/A

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

       7. associate-/r/ N/A

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

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

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

       9. /-lowering-/.f64 N/A

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

       10. /-lowering-/.f64 81.5%

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

   11. Applied egg-rr 81.5%

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

   if -5.89999999999999995e-36 < z < 6.8e21

   1. Initial program 80.5%

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

      1. associate-/l* N/A

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

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

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

      3. div-sub N/A

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

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

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

      5. *-inverses N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \left(\frac{\color{blue}{z}}{y}\right)\right)\right) \]

      6. /-lowering-/.f64 99.9%

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

   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

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

   7. Simplified 74.6%

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

   if 6.8e21 < z

   1. Initial program 88.5%

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

      1. associate-/l* N/A

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

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

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

      3. div-sub N/A

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

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

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

      5. *-inverses N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \left(\frac{\color{blue}{z}}{y}\right)\right)\right) \]

      6. /-lowering-/.f64 93.4%

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

   3. Simplified 93.4%

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

      1. flip3-- N/A

         \[\leadsto x \cdot \frac{{1}^{3} - {\left(\frac{z}{y}\right)}^{3}}{\color{blue}{1 \cdot 1 + \left(\frac{z}{y} \cdot \frac{z}{y} + 1 \cdot \frac{z}{y}\right)}} \]

      2. clear-num N/A

         \[\leadsto x \cdot \frac{1}{\color{blue}{\frac{1 \cdot 1 + \left(\frac{z}{y} \cdot \frac{z}{y} + 1 \cdot \frac{z}{y}\right)}{{1}^{3} - {\left(\frac{z}{y}\right)}^{3}}}} \]

      3. un-div-inv N/A

         \[\leadsto \frac{x}{\color{blue}{\frac{1 \cdot 1 + \left(\frac{z}{y} \cdot \frac{z}{y} + 1 \cdot \frac{z}{y}\right)}{{1}^{3} - {\left(\frac{z}{y}\right)}^{3}}}} \]

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

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(\frac{1 \cdot 1 + \left(\frac{z}{y} \cdot \frac{z}{y} + 1 \cdot \frac{z}{y}\right)}{{1}^{3} - {\left(\frac{z}{y}\right)}^{3}}\right)}\right) \]

      5. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(\frac{1}{\color{blue}{\frac{{1}^{3} - {\left(\frac{z}{y}\right)}^{3}}{1 \cdot 1 + \left(\frac{z}{y} \cdot \frac{z}{y} + 1 \cdot \frac{z}{y}\right)}}}\right)\right) \]

      6. flip3-- N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(\frac{1}{1 - \color{blue}{\frac{z}{y}}}\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(1, \color{blue}{\left(1 - \frac{z}{y}\right)}\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(1, \color{blue}{\left(\frac{z}{y}\right)}\right)\right)\right) \]

      9. /-lowering-/.f64 93.2%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(z, \color{blue}{y}\right)\right)\right)\right) \]

   6. Applied egg-rr 93.2%

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

   7. Taylor expanded in z around inf

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(-1 \cdot \frac{y}{z}\right)}\right) \]
   8. Step-by-step derivation

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(0 - \color{blue}{\frac{y}{z}}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(0, \color{blue}{\left(\frac{y}{z}\right)}\right)\right) \]

      4. /-lowering-/.f64 66.2%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(0, \mathsf{/.f64}\left(y, \color{blue}{z}\right)\right)\right) \]

   9. Simplified 66.2%

      \[\leadsto \frac{x}{\color{blue}{0 - \frac{y}{z}}} \]
   10. Step-by-step derivation

       1. clear-num N/A

          \[\leadsto \frac{1}{\color{blue}{\frac{0 - \frac{y}{z}}{x}}} \]

       2. associate-/r/ N/A

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

       3. sub0-neg N/A

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

       4. distribute-frac-neg2 N/A

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

       5. clear-num N/A

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

       6. distribute-lft-neg-in N/A

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

       7. associate-/r/ N/A

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

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

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

       9. /-lowering-/.f64 N/A

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

       10. /-lowering-/.f64 74.2%

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

   11. Applied egg-rr 74.2%

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

       1. associate-/r/ N/A

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

       2. associate-*l/ N/A

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

       3. /-lowering-/.f64 N/A

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

       4. *-lowering-*.f64 76.0%

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

   13. Applied egg-rr 76.0%

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

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.9 \cdot 10^{-36}:\\ \;\;\;\;\frac{z}{\frac{0 - y}{x}}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+21}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;0 - \frac{z \cdot x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 72.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{-36}:\\ \;\;\;\;\frac{z}{\frac{0 - y}{x}}\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+22}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;0 - x \cdot \frac{z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -8.5e-36)
   (/ z (/ (- 0.0 y) x))
   (if (<= z 3.3e+22) x (- 0.0 (* x (/ z y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -8.5e-36) {
		tmp = z / ((0.0 - y) / x);
	} else if (z <= 3.3e+22) {
		tmp = x;
	} else {
		tmp = 0.0 - (x * (z / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-8.5d-36)) then
        tmp = z / ((0.0d0 - y) / x)
    else if (z <= 3.3d+22) then
        tmp = x
    else
        tmp = 0.0d0 - (x * (z / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -8.5e-36) {
		tmp = z / ((0.0 - y) / x);
	} else if (z <= 3.3e+22) {
		tmp = x;
	} else {
		tmp = 0.0 - (x * (z / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -8.5e-36:
		tmp = z / ((0.0 - y) / x)
	elif z <= 3.3e+22:
		tmp = x
	else:
		tmp = 0.0 - (x * (z / y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -8.5e-36)
		tmp = Float64(z / Float64(Float64(0.0 - y) / x));
	elseif (z <= 3.3e+22)
		tmp = x;
	else
		tmp = Float64(0.0 - Float64(x * Float64(z / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -8.5e-36)
		tmp = z / ((0.0 - y) / x);
	elseif (z <= 3.3e+22)
		tmp = x;
	else
		tmp = 0.0 - (x * (z / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -8.5e-36], N[(z / N[(N[(0.0 - y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.3e+22], x, N[(0.0 - N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.5000000000000007e-36

   1. Initial program 95.1%

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

      1. associate-/l* N/A

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

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

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

      3. div-sub N/A

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

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

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

      5. *-inverses N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \left(\frac{\color{blue}{z}}{y}\right)\right)\right) \]

      6. /-lowering-/.f64 91.8%

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

   3. Simplified 91.8%

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

      1. flip3-- N/A

         \[\leadsto x \cdot \frac{{1}^{3} - {\left(\frac{z}{y}\right)}^{3}}{\color{blue}{1 \cdot 1 + \left(\frac{z}{y} \cdot \frac{z}{y} + 1 \cdot \frac{z}{y}\right)}} \]

      2. clear-num N/A

         \[\leadsto x \cdot \frac{1}{\color{blue}{\frac{1 \cdot 1 + \left(\frac{z}{y} \cdot \frac{z}{y} + 1 \cdot \frac{z}{y}\right)}{{1}^{3} - {\left(\frac{z}{y}\right)}^{3}}}} \]

      3. un-div-inv N/A

         \[\leadsto \frac{x}{\color{blue}{\frac{1 \cdot 1 + \left(\frac{z}{y} \cdot \frac{z}{y} + 1 \cdot \frac{z}{y}\right)}{{1}^{3} - {\left(\frac{z}{y}\right)}^{3}}}} \]

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

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(\frac{1 \cdot 1 + \left(\frac{z}{y} \cdot \frac{z}{y} + 1 \cdot \frac{z}{y}\right)}{{1}^{3} - {\left(\frac{z}{y}\right)}^{3}}\right)}\right) \]

      5. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(\frac{1}{\color{blue}{\frac{{1}^{3} - {\left(\frac{z}{y}\right)}^{3}}{1 \cdot 1 + \left(\frac{z}{y} \cdot \frac{z}{y} + 1 \cdot \frac{z}{y}\right)}}}\right)\right) \]

      6. flip3-- N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(\frac{1}{1 - \color{blue}{\frac{z}{y}}}\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(1, \color{blue}{\left(1 - \frac{z}{y}\right)}\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(1, \color{blue}{\left(\frac{z}{y}\right)}\right)\right)\right) \]

      9. /-lowering-/.f64 91.7%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(z, \color{blue}{y}\right)\right)\right)\right) \]

   6. Applied egg-rr 91.7%

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

   7. Taylor expanded in z around inf

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(-1 \cdot \frac{y}{z}\right)}\right) \]
   8. Step-by-step derivation

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(0 - \color{blue}{\frac{y}{z}}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(0, \color{blue}{\left(\frac{y}{z}\right)}\right)\right) \]

      4. /-lowering-/.f64 64.4%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(0, \mathsf{/.f64}\left(y, \color{blue}{z}\right)\right)\right) \]

   9. Simplified 64.4%

      \[\leadsto \frac{x}{\color{blue}{0 - \frac{y}{z}}} \]
   10. Step-by-step derivation

       1. clear-num N/A

          \[\leadsto \frac{1}{\color{blue}{\frac{0 - \frac{y}{z}}{x}}} \]

       2. associate-/r/ N/A

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

       3. sub0-neg N/A

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

       4. distribute-frac-neg2 N/A

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

       5. clear-num N/A

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

       6. distribute-lft-neg-in N/A

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

       7. associate-/r/ N/A

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

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

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

       9. /-lowering-/.f64 N/A

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

       10. /-lowering-/.f64 81.5%

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

   11. Applied egg-rr 81.5%

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

   if -8.5000000000000007e-36 < z < 3.2999999999999998e22

   1. Initial program 80.5%

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

      1. associate-/l* N/A

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

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

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

      3. div-sub N/A

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

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

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

      5. *-inverses N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \left(\frac{\color{blue}{z}}{y}\right)\right)\right) \]

      6. /-lowering-/.f64 99.9%

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

   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

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

   7. Simplified 74.6%

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

   if 3.2999999999999998e22 < z

   1. Initial program 88.5%

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

      1. associate-/l* N/A

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

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

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

      3. div-sub N/A

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

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

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

      5. *-inverses N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \left(\frac{\color{blue}{z}}{y}\right)\right)\right) \]

      6. /-lowering-/.f64 93.4%

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

   3. Simplified 93.4%

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

      1. flip3-- N/A

         \[\leadsto x \cdot \frac{{1}^{3} - {\left(\frac{z}{y}\right)}^{3}}{\color{blue}{1 \cdot 1 + \left(\frac{z}{y} \cdot \frac{z}{y} + 1 \cdot \frac{z}{y}\right)}} \]

      2. clear-num N/A

         \[\leadsto x \cdot \frac{1}{\color{blue}{\frac{1 \cdot 1 + \left(\frac{z}{y} \cdot \frac{z}{y} + 1 \cdot \frac{z}{y}\right)}{{1}^{3} - {\left(\frac{z}{y}\right)}^{3}}}} \]

      3. un-div-inv N/A

         \[\leadsto \frac{x}{\color{blue}{\frac{1 \cdot 1 + \left(\frac{z}{y} \cdot \frac{z}{y} + 1 \cdot \frac{z}{y}\right)}{{1}^{3} - {\left(\frac{z}{y}\right)}^{3}}}} \]

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

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(\frac{1 \cdot 1 + \left(\frac{z}{y} \cdot \frac{z}{y} + 1 \cdot \frac{z}{y}\right)}{{1}^{3} - {\left(\frac{z}{y}\right)}^{3}}\right)}\right) \]

      5. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(\frac{1}{\color{blue}{\frac{{1}^{3} - {\left(\frac{z}{y}\right)}^{3}}{1 \cdot 1 + \left(\frac{z}{y} \cdot \frac{z}{y} + 1 \cdot \frac{z}{y}\right)}}}\right)\right) \]

      6. flip3-- N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(\frac{1}{1 - \color{blue}{\frac{z}{y}}}\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(1, \color{blue}{\left(1 - \frac{z}{y}\right)}\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(1, \color{blue}{\left(\frac{z}{y}\right)}\right)\right)\right) \]

      9. /-lowering-/.f64 93.2%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(z, \color{blue}{y}\right)\right)\right)\right) \]

   6. Applied egg-rr 93.2%

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

   7. Taylor expanded in z around inf

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(-1 \cdot \frac{y}{z}\right)}\right) \]
   8. Step-by-step derivation

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(0 - \color{blue}{\frac{y}{z}}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(0, \color{blue}{\left(\frac{y}{z}\right)}\right)\right) \]

      4. /-lowering-/.f64 66.2%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(0, \mathsf{/.f64}\left(y, \color{blue}{z}\right)\right)\right) \]

   9. Simplified 66.2%

      \[\leadsto \frac{x}{\color{blue}{0 - \frac{y}{z}}} \]
   10. Step-by-step derivation

       1. clear-num N/A

          \[\leadsto \frac{1}{\color{blue}{\frac{0 - \frac{y}{z}}{x}}} \]

       2. associate-/r/ N/A

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

       3. sub0-neg N/A

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

       4. distribute-frac-neg2 N/A

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

       5. clear-num N/A

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

       6. distribute-lft-neg-in N/A

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

       7. associate-/r/ N/A

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

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

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

       9. /-lowering-/.f64 N/A

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

       10. /-lowering-/.f64 74.2%

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

   11. Applied egg-rr 74.2%

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

       1. associate-/r/ N/A

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

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

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

       3. /-lowering-/.f64 74.5%

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

   13. Applied egg-rr 74.5%

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

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{-36}:\\ \;\;\;\;\frac{z}{\frac{0 - y}{x}}\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+22}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;0 - x \cdot \frac{z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 71.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 0 - x \cdot \frac{z}{y}\\ \mathbf{if}\;z \leq -1.15 \cdot 10^{-36}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+21}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 0.0 (* x (/ z y)))))
   (if (<= z -1.15e-36) t_0 (if (<= z 7.5e+21) x t_0))))

C

double code(double x, double y, double z) {
	double t_0 = 0.0 - (x * (z / y));
	double tmp;
	if (z <= -1.15e-36) {
		tmp = t_0;
	} else if (z <= 7.5e+21) {
		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 = 0.0d0 - (x * (z / y))
    if (z <= (-1.15d-36)) then
        tmp = t_0
    else if (z <= 7.5d+21) 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 = 0.0 - (x * (z / y));
	double tmp;
	if (z <= -1.15e-36) {
		tmp = t_0;
	} else if (z <= 7.5e+21) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 0.0 - (x * (z / y))
	tmp = 0
	if z <= -1.15e-36:
		tmp = t_0
	elif z <= 7.5e+21:
		tmp = x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(0.0 - Float64(x * Float64(z / y)))
	tmp = 0.0
	if (z <= -1.15e-36)
		tmp = t_0;
	elseif (z <= 7.5e+21)
		tmp = x;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 0.0 - (x * (z / y));
	tmp = 0.0;
	if (z <= -1.15e-36)
		tmp = t_0;
	elseif (z <= 7.5e+21)
		tmp = x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(0.0 - N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.15e-36], t$95$0, If[LessEqual[z, 7.5e+21], x, t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.14999999999999998e-36 or 7.5e21 < z

   1. Initial program 92.3%

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

      1. associate-/l* N/A

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

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

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

      3. div-sub N/A

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

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

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

      5. *-inverses N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \left(\frac{\color{blue}{z}}{y}\right)\right)\right) \]

      6. /-lowering-/.f64 92.4%

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

   3. Simplified 92.4%

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

      1. flip3-- N/A

         \[\leadsto x \cdot \frac{{1}^{3} - {\left(\frac{z}{y}\right)}^{3}}{\color{blue}{1 \cdot 1 + \left(\frac{z}{y} \cdot \frac{z}{y} + 1 \cdot \frac{z}{y}\right)}} \]

      2. clear-num N/A

         \[\leadsto x \cdot \frac{1}{\color{blue}{\frac{1 \cdot 1 + \left(\frac{z}{y} \cdot \frac{z}{y} + 1 \cdot \frac{z}{y}\right)}{{1}^{3} - {\left(\frac{z}{y}\right)}^{3}}}} \]

      3. un-div-inv N/A

         \[\leadsto \frac{x}{\color{blue}{\frac{1 \cdot 1 + \left(\frac{z}{y} \cdot \frac{z}{y} + 1 \cdot \frac{z}{y}\right)}{{1}^{3} - {\left(\frac{z}{y}\right)}^{3}}}} \]

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

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(\frac{1 \cdot 1 + \left(\frac{z}{y} \cdot \frac{z}{y} + 1 \cdot \frac{z}{y}\right)}{{1}^{3} - {\left(\frac{z}{y}\right)}^{3}}\right)}\right) \]

      5. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(\frac{1}{\color{blue}{\frac{{1}^{3} - {\left(\frac{z}{y}\right)}^{3}}{1 \cdot 1 + \left(\frac{z}{y} \cdot \frac{z}{y} + 1 \cdot \frac{z}{y}\right)}}}\right)\right) \]

      6. flip3-- N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(\frac{1}{1 - \color{blue}{\frac{z}{y}}}\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(1, \color{blue}{\left(1 - \frac{z}{y}\right)}\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(1, \color{blue}{\left(\frac{z}{y}\right)}\right)\right)\right) \]

      9. /-lowering-/.f64 92.4%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(z, \color{blue}{y}\right)\right)\right)\right) \]

   6. Applied egg-rr 92.4%

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

   7. Taylor expanded in z around inf

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(-1 \cdot \frac{y}{z}\right)}\right) \]
   8. Step-by-step derivation

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(0 - \color{blue}{\frac{y}{z}}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(0, \color{blue}{\left(\frac{y}{z}\right)}\right)\right) \]

      4. /-lowering-/.f64 65.2%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(0, \mathsf{/.f64}\left(y, \color{blue}{z}\right)\right)\right) \]

   9. Simplified 65.2%

      \[\leadsto \frac{x}{\color{blue}{0 - \frac{y}{z}}} \]
   10. Step-by-step derivation

       1. clear-num N/A

          \[\leadsto \frac{1}{\color{blue}{\frac{0 - \frac{y}{z}}{x}}} \]

       2. associate-/r/ N/A

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

       3. sub0-neg N/A

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

       4. distribute-frac-neg2 N/A

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

       5. clear-num N/A

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

       6. distribute-lft-neg-in N/A

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

       7. associate-/r/ N/A

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

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

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

       9. /-lowering-/.f64 N/A

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

       10. /-lowering-/.f64 78.4%

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

   11. Applied egg-rr 78.4%

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

       1. associate-/r/ N/A

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

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

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

       3. /-lowering-/.f64 73.9%

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

   13. Applied egg-rr 73.9%

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

   if -1.14999999999999998e-36 < z < 7.5e21

   1. Initial program 80.5%

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

      1. associate-/l* N/A

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

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

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

      3. div-sub N/A

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

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

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

      5. *-inverses N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \left(\frac{\color{blue}{z}}{y}\right)\right)\right) \]

      6. /-lowering-/.f64 99.9%

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

   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

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

   7. Simplified 74.6%

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

4. Final simplification 74.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{-36}:\\ \;\;\;\;0 - x \cdot \frac{z}{y}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+21}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;0 - x \cdot \frac{z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 95.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+47}:\\ \;\;\;\;\frac{x}{y} \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -2.1e+47) (* (/ x y) (- y z)) (* x (- 1.0 (/ z y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.1e+47) {
		tmp = (x / y) * (y - z);
	} else {
		tmp = x * (1.0 - (z / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-2.1d+47)) then
        tmp = (x / y) * (y - z)
    else
        tmp = x * (1.0d0 - (z / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.1e+47) {
		tmp = (x / y) * (y - z);
	} else {
		tmp = x * (1.0 - (z / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -2.1e+47:
		tmp = (x / y) * (y - z)
	else:
		tmp = x * (1.0 - (z / y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -2.1e+47)
		tmp = Float64(Float64(x / y) * Float64(y - z));
	else
		tmp = Float64(x * Float64(1.0 - Float64(z / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -2.1e+47)
		tmp = (x / y) * (y - z);
	else
		tmp = x * (1.0 - (z / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -2.1e+47], N[(N[(x / y), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.1e47

   1. Initial program 94.2%

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

      1. associate-/l* N/A

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

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

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

      3. div-sub N/A

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

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

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

      5. *-inverses N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \left(\frac{\color{blue}{z}}{y}\right)\right)\right) \]

      6. /-lowering-/.f64 90.1%

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

   3. Simplified 90.1%

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

      1. *-inverses N/A

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

      2. div-sub N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

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

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

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

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

      9. --lowering--.f64 96.3%

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

   6. Applied egg-rr 96.3%

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

   if -2.1e47 < z

   1. Initial program 84.4%

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

      1. associate-/l* N/A

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

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

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

      3. div-sub N/A

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

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

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

      5. *-inverses N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \left(\frac{\color{blue}{z}}{y}\right)\right)\right) \]

      6. /-lowering-/.f64 97.9%

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

   3. Simplified 97.9%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{z}{y}\right)} \]
   4. Add Preprocessing
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 52.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 2 \cdot 10^{+34}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= x 2e+34) x (* y (/ x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 2e+34) {
		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+34) 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+34) {
		tmp = x;
	} else {
		tmp = y * (x / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 2e+34:
		tmp = x
	else:
		tmp = y * (x / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 2e+34)
		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+34)
		tmp = x;
	else
		tmp = y * (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 2e+34], x, N[(y * N[(x / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 1.99999999999999989e34

   1. Initial program 88.9%

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

      1. associate-/l* N/A

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

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

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

      3. div-sub N/A

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

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

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

      5. *-inverses N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \left(\frac{\color{blue}{z}}{y}\right)\right)\right) \]

      6. /-lowering-/.f64 94.7%

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

   3. Simplified 94.7%

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

   5. Taylor expanded in z around 0

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

   7. Simplified 45.8%

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

   if 1.99999999999999989e34 < x

   1. Initial program 80.3%

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

   3. Taylor expanded in y around inf

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(x \cdot y\right)}, y\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 28.6%

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

   5. Simplified 28.6%

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

      1. associate-*l/ N/A

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

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

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

      3. /-lowering-/.f64 50.0%

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

   7. Applied egg-rr 50.0%

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

4. Final simplification 46.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 2 \cdot 10^{+34}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 96.0% 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 86.9%

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

   1. associate-/l* N/A

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

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

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

   3. div-sub N/A

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

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

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

   5. *-inverses N/A

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \left(\frac{\color{blue}{z}}{y}\right)\right)\right) \]

   6. /-lowering-/.f64 95.9%

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

3. Simplified 95.9%

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

Alternative 9: 50.8% accurate, 7.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

function code(x, y, z)
	return x
end

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 86.9%

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

   1. associate-/l* N/A

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

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

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

   3. div-sub N/A

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

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

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

   5. *-inverses N/A

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \left(\frac{\color{blue}{z}}{y}\right)\right)\right) \]

   6. /-lowering-/.f64 95.9%

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

3. Simplified 95.9%

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

5. Taylor expanded in z around 0

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

7. Simplified 45.6%

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

Developer Target 1: 96.2% 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 2024161 
(FPCore (x y z)
  :name "Diagrams.Backend.Cairo.Internal:setTexture from diagrams-cairo-1.3.0.3"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< z -206020233192173900000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- x (/ (* z x) y)) (if (< z 1693976601382852600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (/ x (/ y (- y z))) (* (- y z) (/ x y)))))

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