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

Percentage Accurate: 85.8% → 97.4%

Time: 9.3s

Alternatives: 7

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: 85.8% 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: 97.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;x\_m \leq 7 \cdot 10^{-84}:\\ \;\;\;\;x\_m - \frac{z}{\frac{y}{x\_m}}\\ \mathbf{else}:\\ \;\;\;\;x\_m - x\_m \cdot \frac{z}{y}\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z)
 :precision binary64
 (* x_s (if (<= x_m 7e-84) (- x_m (/ z (/ y x_m))) (- x_m (* x_m (/ z y))))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if (x_m <= 7e-84) {
		tmp = x_m - (z / (y / x_m));
	} else {
		tmp = x_m - (x_m * (z / y));
	}
	return x_s * tmp;
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x_m <= 7d-84) then
        tmp = x_m - (z / (y / x_m))
    else
        tmp = x_m - (x_m * (z / y))
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if (x_m <= 7e-84) {
		tmp = x_m - (z / (y / x_m));
	} else {
		tmp = x_m - (x_m * (z / y));
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z):
	tmp = 0
	if x_m <= 7e-84:
		tmp = x_m - (z / (y / x_m))
	else:
		tmp = x_m - (x_m * (z / y))
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z)
	tmp = 0.0
	if (x_m <= 7e-84)
		tmp = Float64(x_m - Float64(z / Float64(y / x_m)));
	else
		tmp = Float64(x_m - Float64(x_m * Float64(z / y)));
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z)
	tmp = 0.0;
	if (x_m <= 7e-84)
		tmp = x_m - (z / (y / x_m));
	else
		tmp = x_m - (x_m * (z / y));
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_] := N[(x$95$s * If[LessEqual[x$95$m, 7e-84], N[(x$95$m - N[(z / N[(y / x$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x$95$m - N[(x$95$m * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if x < 7.0000000000000002e-84

   1. Initial program 87.0%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   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 94.5%

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

   3. Simplified 94.5%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{z}{y}\right)} \]
   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. flip-- N/A

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

      7. clear-num N/A

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

      8. frac-times N/A

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

      9. *-lft-identity N/A

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

      10. /-lowering-/.f64 N/A

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

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

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

      12. clear-num N/A

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

      13. flip-- N/A

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

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

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

      15. --lowering--.f64 94.9%

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

   6. Applied egg-rr 94.9%

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

      1. clear-num N/A

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

      2. associate-/l* N/A

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

      3. associate-/r* N/A

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

      4. remove-double-div N/A

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

      5. div-sub N/A

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

      6. un-div-inv N/A

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

      7. clear-num N/A

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

      8. *-commutative N/A

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

      9. associate-*l/ N/A

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

      10. associate-/l* N/A

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

      11. *-inverses N/A

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

      12. *-rgt-identity N/A

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

      13. --lowering--.f64 N/A

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

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

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

      15. /-lowering-/.f64 95.5%

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

   8. Applied egg-rr 95.5%

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

   if 7.0000000000000002e-84 < x

   1. Initial program 81.6%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   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. 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. flip-- N/A

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

      7. clear-num N/A

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

      8. frac-times N/A

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

      9. *-lft-identity N/A

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

      10. /-lowering-/.f64 N/A

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

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

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

      12. clear-num N/A

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

      13. flip-- N/A

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

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

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

      15. --lowering--.f64 99.8%

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

   6. Applied egg-rr 99.8%

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

      1. clear-num N/A

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

      2. associate-/l* N/A

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

      3. associate-/r* N/A

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

      4. remove-double-div N/A

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

      5. div-sub N/A

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

      6. un-div-inv N/A

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

      7. clear-num N/A

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

      8. *-commutative N/A

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

      9. associate-*l/ N/A

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

      10. associate-/l* N/A

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

      11. *-inverses N/A

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

      12. *-rgt-identity N/A

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

      13. --lowering--.f64 N/A

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

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

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

      15. /-lowering-/.f64 95.0%

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

   8. Applied egg-rr 95.0%

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

      1. associate-/r/ N/A

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

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

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

      3. /-lowering-/.f64 99.9%

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

   10. Applied egg-rr 99.9%

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

4. Final simplification 96.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 7 \cdot 10^{-84}:\\ \;\;\;\;x - \frac{z}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \frac{z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 73.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+17}:\\ \;\;\;\;x\_m\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{-7}:\\ \;\;\;\;0 - z \cdot \frac{x\_m}{y}\\ \mathbf{else}:\\ \;\;\;\;x\_m\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z)
 :precision binary64
 (*
  x_s
  (if (<= y -6.5e+17) x_m (if (<= y 3.3e-7) (- 0.0 (* z (/ x_m y))) x_m))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if (y <= -6.5e+17) {
		tmp = x_m;
	} else if (y <= 3.3e-7) {
		tmp = 0.0 - (z * (x_m / y));
	} else {
		tmp = x_m;
	}
	return x_s * tmp;
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-6.5d+17)) then
        tmp = x_m
    else if (y <= 3.3d-7) then
        tmp = 0.0d0 - (z * (x_m / y))
    else
        tmp = x_m
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if (y <= -6.5e+17) {
		tmp = x_m;
	} else if (y <= 3.3e-7) {
		tmp = 0.0 - (z * (x_m / y));
	} else {
		tmp = x_m;
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z):
	tmp = 0
	if y <= -6.5e+17:
		tmp = x_m
	elif y <= 3.3e-7:
		tmp = 0.0 - (z * (x_m / y))
	else:
		tmp = x_m
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z)
	tmp = 0.0
	if (y <= -6.5e+17)
		tmp = x_m;
	elseif (y <= 3.3e-7)
		tmp = Float64(0.0 - Float64(z * Float64(x_m / y)));
	else
		tmp = x_m;
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z)
	tmp = 0.0;
	if (y <= -6.5e+17)
		tmp = x_m;
	elseif (y <= 3.3e-7)
		tmp = 0.0 - (z * (x_m / y));
	else
		tmp = x_m;
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_] := N[(x$95$s * If[LessEqual[y, -6.5e+17], x$95$m, If[LessEqual[y, 3.3e-7], N[(0.0 - N[(z * N[(x$95$m / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x$95$m]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if y < -6.5e17 or 3.3000000000000002e-7 < y

   1. Initial program 74.7%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   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 73.7%

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

   if -6.5e17 < y < 3.3000000000000002e-7

   1. Initial program 95.2%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   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 92.7%

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

   3. Simplified 92.7%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{z}{y}\right)} \]
   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. flip-- N/A

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

      7. clear-num N/A

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

      8. frac-times N/A

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

      9. *-lft-identity N/A

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

      10. /-lowering-/.f64 N/A

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

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

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

      12. clear-num N/A

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

      13. flip-- N/A

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

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

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

      15. --lowering--.f64 93.3%

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

   6. Applied egg-rr 93.3%

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

   7. Taylor expanded in y around 0

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

      1. /-lowering-/.f64 72.1%

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

   9. Simplified 72.1%

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

       1. frac-2neg N/A

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

       2. distribute-frac-neg2 N/A

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

       3. *-lft-identity N/A

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

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

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

       5. times-frac N/A

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

       6. clear-num N/A

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

       7. times-frac N/A

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

       8. neg-mul-1 N/A

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

       9. associate-*r/ N/A

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

       10. frac-2neg N/A

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

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

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

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

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

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

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

       14. /-lowering-/.f64 76.0%

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

   11. Applied egg-rr 76.0%

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

4. Final simplification 74.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+17}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{-7}:\\ \;\;\;\;0 - z \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 73.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+18}:\\ \;\;\;\;x\_m\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-13}:\\ \;\;\;\;\frac{z}{\frac{y}{0 - x\_m}}\\ \mathbf{else}:\\ \;\;\;\;x\_m\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z)
 :precision binary64
 (*
  x_s
  (if (<= y -1.7e+18) x_m (if (<= y 1.05e-13) (/ z (/ y (- 0.0 x_m))) x_m))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if (y <= -1.7e+18) {
		tmp = x_m;
	} else if (y <= 1.05e-13) {
		tmp = z / (y / (0.0 - x_m));
	} else {
		tmp = x_m;
	}
	return x_s * tmp;
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-1.7d+18)) then
        tmp = x_m
    else if (y <= 1.05d-13) then
        tmp = z / (y / (0.0d0 - x_m))
    else
        tmp = x_m
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if (y <= -1.7e+18) {
		tmp = x_m;
	} else if (y <= 1.05e-13) {
		tmp = z / (y / (0.0 - x_m));
	} else {
		tmp = x_m;
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z):
	tmp = 0
	if y <= -1.7e+18:
		tmp = x_m
	elif y <= 1.05e-13:
		tmp = z / (y / (0.0 - x_m))
	else:
		tmp = x_m
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z)
	tmp = 0.0
	if (y <= -1.7e+18)
		tmp = x_m;
	elseif (y <= 1.05e-13)
		tmp = Float64(z / Float64(y / Float64(0.0 - x_m)));
	else
		tmp = x_m;
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z)
	tmp = 0.0;
	if (y <= -1.7e+18)
		tmp = x_m;
	elseif (y <= 1.05e-13)
		tmp = z / (y / (0.0 - x_m));
	else
		tmp = x_m;
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_] := N[(x$95$s * If[LessEqual[y, -1.7e+18], x$95$m, If[LessEqual[y, 1.05e-13], N[(z / N[(y / N[(0.0 - x$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x$95$m]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if y < -1.7e18 or 1.04999999999999994e-13 < y

   1. Initial program 74.7%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   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 73.7%

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

   if -1.7e18 < y < 1.04999999999999994e-13

   1. Initial program 95.2%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   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 92.7%

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

   3. Simplified 92.7%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{z}{y}\right)} \]
   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. flip-- N/A

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

      7. clear-num N/A

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

      8. frac-times N/A

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

      9. *-lft-identity N/A

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

      10. /-lowering-/.f64 N/A

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

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

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

      12. clear-num N/A

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

      13. flip-- N/A

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

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

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

      15. --lowering--.f64 93.3%

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

   6. Applied egg-rr 93.3%

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

   7. Taylor expanded in y around 0

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

      1. /-lowering-/.f64 72.1%

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

   9. Simplified 72.1%

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

       1. frac-2neg N/A

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

       2. distribute-frac-neg2 N/A

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

       3. *-lft-identity N/A

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

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

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

       5. times-frac N/A

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

       6. clear-num N/A

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

       7. times-frac N/A

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

       8. neg-mul-1 N/A

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

       9. associate-*r/ N/A

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

       10. frac-2neg N/A

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

       11. clear-num N/A

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

       12. div-inv N/A

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

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

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

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

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

       15. /-lowering-/.f64 75.9%

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

   11. Applied egg-rr 75.9%

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

4. Final simplification 74.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+18}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-13}:\\ \;\;\;\;\frac{z}{\frac{y}{0 - x}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 52.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -2.15 \cdot 10^{-107}:\\ \;\;\;\;x\_m\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-145}:\\ \;\;\;\;y \cdot \frac{x\_m}{y}\\ \mathbf{else}:\\ \;\;\;\;x\_m\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z)
 :precision binary64
 (* x_s (if (<= y -2.15e-107) x_m (if (<= y 2.6e-145) (* y (/ x_m y)) x_m))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if (y <= -2.15e-107) {
		tmp = x_m;
	} else if (y <= 2.6e-145) {
		tmp = y * (x_m / y);
	} else {
		tmp = x_m;
	}
	return x_s * tmp;
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-2.15d-107)) then
        tmp = x_m
    else if (y <= 2.6d-145) then
        tmp = y * (x_m / y)
    else
        tmp = x_m
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if (y <= -2.15e-107) {
		tmp = x_m;
	} else if (y <= 2.6e-145) {
		tmp = y * (x_m / y);
	} else {
		tmp = x_m;
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z):
	tmp = 0
	if y <= -2.15e-107:
		tmp = x_m
	elif y <= 2.6e-145:
		tmp = y * (x_m / y)
	else:
		tmp = x_m
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z)
	tmp = 0.0
	if (y <= -2.15e-107)
		tmp = x_m;
	elseif (y <= 2.6e-145)
		tmp = Float64(y * Float64(x_m / y));
	else
		tmp = x_m;
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z)
	tmp = 0.0;
	if (y <= -2.15e-107)
		tmp = x_m;
	elseif (y <= 2.6e-145)
		tmp = y * (x_m / y);
	else
		tmp = x_m;
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_] := N[(x$95$s * If[LessEqual[y, -2.15e-107], x$95$m, If[LessEqual[y, 2.6e-145], N[(y * N[(x$95$m / y), $MachinePrecision]), $MachinePrecision], x$95$m]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if y < -2.1499999999999999e-107 or 2.6e-145 < y

   1. Initial program 83.6%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   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 97.8%

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

   3. Simplified 97.8%

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

   5. Taylor expanded in z around 0

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

   7. Simplified 59.0%

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

   if -2.1499999999999999e-107 < y < 2.6e-145

   1. Initial program 90.5%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   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 11.1%

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

   5. Simplified 11.1%

      \[\leadsto \frac{\color{blue}{x \cdot y}}{y} \]
   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 27.0%

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

   7. Applied egg-rr 27.0%

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

4. Final simplification 50.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.15 \cdot 10^{-107}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-145}:\\ \;\;\;\;y \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 95.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \left(x\_m - x\_m \cdot \frac{z}{y}\right) \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z) :precision binary64 (* x_s (- x_m (* x_m (/ z y)))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z) {
	return x_s * (x_m - (x_m * (z / y)));
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x_s * (x_m - (x_m * (z / y)))
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z) {
	return x_s * (x_m - (x_m * (z / y)));
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z):
	return x_s * (x_m - (x_m * (z / y)))

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z)
	return Float64(x_s * Float64(x_m - Float64(x_m * Float64(z / y))))
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
function tmp = code(x_s, x_m, y, z)
	tmp = x_s * (x_m - (x_m * (z / y)));
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_] := N[(x$95$s * N[(x$95$m - N[(x$95$m * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 85.3%

   \[\frac{x \cdot \left(y - z\right)}{y} \]
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 96.1%

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

3. Simplified 96.1%

   \[\leadsto \color{blue}{x \cdot \left(1 - \frac{z}{y}\right)} \]
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. flip-- N/A

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

   7. clear-num N/A

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

   8. frac-times N/A

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

   9. *-lft-identity N/A

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

   10. /-lowering-/.f64 N/A

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

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

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

   12. clear-num N/A

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

   13. flip-- N/A

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

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

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

   15. --lowering--.f64 96.4%

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

6. Applied egg-rr 96.4%

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

   1. clear-num N/A

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

   2. associate-/l* N/A

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

   3. associate-/r* N/A

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

   4. remove-double-div N/A

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

   5. div-sub N/A

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

   6. un-div-inv N/A

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

   7. clear-num N/A

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

   8. *-commutative N/A

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

   9. associate-*l/ N/A

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

   10. associate-/l* N/A

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

   11. *-inverses N/A

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

   12. *-rgt-identity N/A

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

   13. --lowering--.f64 N/A

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

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

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

   15. /-lowering-/.f64 95.4%

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

8. Applied egg-rr 95.4%

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

   1. associate-/r/ N/A

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

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

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

   3. /-lowering-/.f64 96.2%

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

10. Applied egg-rr 96.2%

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

11. Final simplification 96.2%

    \[\leadsto x - x \cdot \frac{z}{y} \]
12. Add Preprocessing

Alternative 6: 95.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \left(x\_m \cdot \left(1 - \frac{z}{y}\right)\right) \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z) :precision binary64 (* x_s (* x_m (- 1.0 (/ z y)))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z) {
	return x_s * (x_m * (1.0 - (z / y)));
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x_s * (x_m * (1.0d0 - (z / y)))
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z) {
	return x_s * (x_m * (1.0 - (z / y)));
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z):
	return x_s * (x_m * (1.0 - (z / y)))

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z)
	return Float64(x_s * Float64(x_m * Float64(1.0 - Float64(z / y))))
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
function tmp = code(x_s, x_m, y, z)
	tmp = x_s * (x_m * (1.0 - (z / y)));
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_] := N[(x$95$s * N[(x$95$m * N[(1.0 - N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 85.3%

   \[\frac{x \cdot \left(y - z\right)}{y} \]
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 96.1%

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

3. Simplified 96.1%

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

Alternative 7: 50.4% accurate, 7.0× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot x\_m \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z) :precision binary64 (* x_s x_m))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z) {
	return x_s * x_m;
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x_s * x_m
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z) {
	return x_s * x_m;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z):
	return x_s * x_m

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z)
	return Float64(x_s * x_m)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
function tmp = code(x_s, x_m, y, z)
	tmp = x_s * x_m;
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_] := N[(x$95$s * x$95$m), $MachinePrecision]

Derivation

1. Initial program 85.3%

   \[\frac{x \cdot \left(y - z\right)}{y} \]
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 96.1%

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

3. Simplified 96.1%

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

5. Taylor expanded in z around 0

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

7. Simplified 47.3%

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

Developer Target 1: 96.1% 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 2024163 
(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))