Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, D

Percentage Accurate: 99.5% → 99.7%

Time: 12.2s

Alternatives: 13

Speedup: 1.2×

• 21.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ x (* (* (- y x) 6.0) (- (/ 2.0 3.0) z))))

C

double code(double x, double y, double z) {
	return x + (((y - x) * 6.0) * ((2.0 / 3.0) - z));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + (((y - x) * 6.0d0) * ((2.0d0 / 3.0d0) - z))
end function

Java

public static double code(double x, double y, double z) {
	return x + (((y - x) * 6.0) * ((2.0 / 3.0) - z));
}

Python

def code(x, y, z):
	return x + (((y - x) * 6.0) * ((2.0 / 3.0) - z))

Julia

function code(x, y, z)
	return Float64(x + Float64(Float64(Float64(y - x) * 6.0) * Float64(Float64(2.0 / 3.0) - z)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + (((y - x) * 6.0) * ((2.0 / 3.0) - z));
end

Wolfram

code[x_, y_, z_] := N[(x + N[(N[(N[(y - x), $MachinePrecision] * 6.0), $MachinePrecision] * N[(N[(2.0 / 3.0), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ x (* (* (- y x) 6.0) (- (/ 2.0 3.0) z))))

C

double code(double x, double y, double z) {
	return x + (((y - x) * 6.0) * ((2.0 / 3.0) - z));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + (((y - x) * 6.0d0) * ((2.0d0 / 3.0d0) - z))
end function

Java

public static double code(double x, double y, double z) {
	return x + (((y - x) * 6.0) * ((2.0 / 3.0) - z));
}

Python

def code(x, y, z):
	return x + (((y - x) * 6.0) * ((2.0 / 3.0) - z))

Julia

function code(x, y, z)
	return Float64(x + Float64(Float64(Float64(y - x) * 6.0) * Float64(Float64(2.0 / 3.0) - z)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + (((y - x) * 6.0) * ((2.0 / 3.0) - z));
end

Wolfram

code[x_, y_, z_] := N[(x + N[(N[(N[(y - x), $MachinePrecision] * 6.0), $MachinePrecision] * N[(N[(2.0 / 3.0), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ x + \left(y - x\right) \cdot \left(4 + z \cdot -6\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ x (* (- y x) (+ 4.0 (* z -6.0)))))

C

double code(double x, double y, double z) {
	return x + ((y - x) * (4.0 + (z * -6.0)));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + ((y - x) * (4.0d0 + (z * (-6.0d0))))
end function

Java

public static double code(double x, double y, double z) {
	return x + ((y - x) * (4.0 + (z * -6.0)));
}

Python

def code(x, y, z):
	return x + ((y - x) * (4.0 + (z * -6.0)))

Julia

function code(x, y, z)
	return Float64(x + Float64(Float64(y - x) * Float64(4.0 + Float64(z * -6.0))))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + ((y - x) * (4.0 + (z * -6.0)));
end

Wolfram

code[x_, y_, z_] := N[(x + N[(N[(y - x), $MachinePrecision] * N[(4.0 + N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.6%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
2. Step-by-step derivation

   1. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)\right)}\right) \]

   2. associate-*l* N/A

      \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - x\right) \cdot \color{blue}{\left(6 \cdot \left(\frac{2}{3} - z\right)\right)}\right)\right) \]

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

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(y - x\right), \color{blue}{\left(6 \cdot \left(\frac{2}{3} - z\right)\right)}\right)\right) \]

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

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(\color{blue}{6} \cdot \left(\frac{2}{3} - z\right)\right)\right)\right) \]

   5. sub-neg N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(6 \cdot \left(\frac{2}{3} + \color{blue}{\left(\mathsf{neg}\left(z\right)\right)}\right)\right)\right)\right) \]

   6. distribute-lft-in N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(6 \cdot \frac{2}{3} + \color{blue}{6 \cdot \left(\mathsf{neg}\left(z\right)\right)}\right)\right)\right) \]

   7. *-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(6 \cdot \frac{2}{3} + \left(\mathsf{neg}\left(z\right)\right) \cdot \color{blue}{6}\right)\right)\right) \]

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

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(\left(6 \cdot \frac{2}{3}\right), \color{blue}{\left(\left(\mathsf{neg}\left(z\right)\right) \cdot 6\right)}\right)\right)\right) \]

   9. metadata-eval N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(\left(6 \cdot \frac{2}{3}\right), \left(\left(\mathsf{neg}\left(z\right)\right) \cdot 6\right)\right)\right)\right) \]

   10. metadata-eval N/A

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(\color{blue}{\left(\mathsf{neg}\left(z\right)\right)} \cdot 6\right)\right)\right)\right) \]

   11. distribute-lft-neg-out N/A

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(\mathsf{neg}\left(z \cdot 6\right)\right)\right)\right)\right) \]

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

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(z \cdot \color{blue}{\left(\mathsf{neg}\left(6\right)\right)}\right)\right)\right)\right) \]

   13. metadata-eval N/A

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(z \cdot -6\right)\right)\right)\right) \]

   14. metadata-eval N/A

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(z \cdot \left(6 \cdot \color{blue}{-1}\right)\right)\right)\right)\right) \]

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

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \mathsf{*.f64}\left(z, \color{blue}{\left(6 \cdot -1\right)}\right)\right)\right)\right) \]

   16. metadata-eval 99.8%

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \mathsf{*.f64}\left(z, -6\right)\right)\right)\right) \]

3. Simplified 99.8%

   \[\leadsto \color{blue}{x + \left(y - x\right) \cdot \left(4 + z \cdot -6\right)} \]
4. Add Preprocessing
5. Add Preprocessing

Alternative 2: 50.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(z \cdot -6\right)\\ \mathbf{if}\;z \leq -5.2 \cdot 10^{-16}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-285}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-147}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.56:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+159}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (* z -6.0))))
   (if (<= z -5.2e-16)
     t_0
     (if (<= z 3.1e-285)
       (* y 4.0)
       (if (<= z 4.2e-147)
         (* x -3.0)
         (if (<= z 0.56)
           (* y 4.0)
           (if (<= z 5.2e+159) (* x (* z 6.0)) t_0)))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (z * -6.0);
	double tmp;
	if (z <= -5.2e-16) {
		tmp = t_0;
	} else if (z <= 3.1e-285) {
		tmp = y * 4.0;
	} else if (z <= 4.2e-147) {
		tmp = x * -3.0;
	} else if (z <= 0.56) {
		tmp = y * 4.0;
	} else if (z <= 5.2e+159) {
		tmp = x * (z * 6.0);
	} 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 = y * (z * (-6.0d0))
    if (z <= (-5.2d-16)) then
        tmp = t_0
    else if (z <= 3.1d-285) then
        tmp = y * 4.0d0
    else if (z <= 4.2d-147) then
        tmp = x * (-3.0d0)
    else if (z <= 0.56d0) then
        tmp = y * 4.0d0
    else if (z <= 5.2d+159) then
        tmp = x * (z * 6.0d0)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * (z * -6.0);
	double tmp;
	if (z <= -5.2e-16) {
		tmp = t_0;
	} else if (z <= 3.1e-285) {
		tmp = y * 4.0;
	} else if (z <= 4.2e-147) {
		tmp = x * -3.0;
	} else if (z <= 0.56) {
		tmp = y * 4.0;
	} else if (z <= 5.2e+159) {
		tmp = x * (z * 6.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (z * -6.0)
	tmp = 0
	if z <= -5.2e-16:
		tmp = t_0
	elif z <= 3.1e-285:
		tmp = y * 4.0
	elif z <= 4.2e-147:
		tmp = x * -3.0
	elif z <= 0.56:
		tmp = y * 4.0
	elif z <= 5.2e+159:
		tmp = x * (z * 6.0)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(z * -6.0))
	tmp = 0.0
	if (z <= -5.2e-16)
		tmp = t_0;
	elseif (z <= 3.1e-285)
		tmp = Float64(y * 4.0);
	elseif (z <= 4.2e-147)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.56)
		tmp = Float64(y * 4.0);
	elseif (z <= 5.2e+159)
		tmp = Float64(x * Float64(z * 6.0));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (z * -6.0);
	tmp = 0.0;
	if (z <= -5.2e-16)
		tmp = t_0;
	elseif (z <= 3.1e-285)
		tmp = y * 4.0;
	elseif (z <= 4.2e-147)
		tmp = x * -3.0;
	elseif (z <= 0.56)
		tmp = y * 4.0;
	elseif (z <= 5.2e+159)
		tmp = x * (z * 6.0);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(z * -6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.2e-16], t$95$0, If[LessEqual[z, 3.1e-285], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 4.2e-147], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.56], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 5.2e+159], N[(x * N[(z * 6.0), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.1999999999999997e-16 or 5.2000000000000001e159 < z

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)\right)}\right) \]

      2. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - x\right) \cdot \color{blue}{\left(6 \cdot \left(\frac{2}{3} - z\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(y - x\right), \color{blue}{\left(6 \cdot \left(\frac{2}{3} - z\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(\color{blue}{6} \cdot \left(\frac{2}{3} - z\right)\right)\right)\right) \]

      5. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(6 \cdot \left(\frac{2}{3} + \color{blue}{\left(\mathsf{neg}\left(z\right)\right)}\right)\right)\right)\right) \]

      6. distribute-lft-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(6 \cdot \frac{2}{3} + \color{blue}{6 \cdot \left(\mathsf{neg}\left(z\right)\right)}\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(6 \cdot \frac{2}{3} + \left(\mathsf{neg}\left(z\right)\right) \cdot \color{blue}{6}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(\left(6 \cdot \frac{2}{3}\right), \color{blue}{\left(\left(\mathsf{neg}\left(z\right)\right) \cdot 6\right)}\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(\left(6 \cdot \frac{2}{3}\right), \left(\left(\mathsf{neg}\left(z\right)\right) \cdot 6\right)\right)\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(\color{blue}{\left(\mathsf{neg}\left(z\right)\right)} \cdot 6\right)\right)\right)\right) \]

      11. distribute-lft-neg-out N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(\mathsf{neg}\left(z \cdot 6\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(z \cdot \color{blue}{\left(\mathsf{neg}\left(6\right)\right)}\right)\right)\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(z \cdot -6\right)\right)\right)\right) \]

      14. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(z \cdot \left(6 \cdot \color{blue}{-1}\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \mathsf{*.f64}\left(z, \color{blue}{\left(6 \cdot -1\right)}\right)\right)\right)\right) \]

      16. metadata-eval 99.8%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \mathsf{*.f64}\left(z, -6\right)\right)\right)\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x + \left(y - x\right) \cdot \left(4 + z \cdot -6\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. flip3-+ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - x\right) \cdot \frac{{4}^{3} + {\left(z \cdot -6\right)}^{3}}{\color{blue}{4 \cdot 4 + \left(\left(z \cdot -6\right) \cdot \left(z \cdot -6\right) - 4 \cdot \left(z \cdot -6\right)\right)}}\right)\right) \]

      2. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - x\right) \cdot \frac{1}{\color{blue}{\frac{4 \cdot 4 + \left(\left(z \cdot -6\right) \cdot \left(z \cdot -6\right) - 4 \cdot \left(z \cdot -6\right)\right)}{{4}^{3} + {\left(z \cdot -6\right)}^{3}}}}\right)\right) \]

      3. un-div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y - x}{\color{blue}{\frac{4 \cdot 4 + \left(\left(z \cdot -6\right) \cdot \left(z \cdot -6\right) - 4 \cdot \left(z \cdot -6\right)\right)}{{4}^{3} + {\left(z \cdot -6\right)}^{3}}}}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(y - x\right), \color{blue}{\left(\frac{4 \cdot 4 + \left(\left(z \cdot -6\right) \cdot \left(z \cdot -6\right) - 4 \cdot \left(z \cdot -6\right)\right)}{{4}^{3} + {\left(z \cdot -6\right)}^{3}}\right)}\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(\frac{\color{blue}{4 \cdot 4 + \left(\left(z \cdot -6\right) \cdot \left(z \cdot -6\right) - 4 \cdot \left(z \cdot -6\right)\right)}}{{4}^{3} + {\left(z \cdot -6\right)}^{3}}\right)\right)\right) \]

      6. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(\frac{1}{\color{blue}{\frac{{4}^{3} + {\left(z \cdot -6\right)}^{3}}{4 \cdot 4 + \left(\left(z \cdot -6\right) \cdot \left(z \cdot -6\right) - 4 \cdot \left(z \cdot -6\right)\right)}}}\right)\right)\right) \]

      7. flip3-+ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(\frac{1}{4 + \color{blue}{z \cdot -6}}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{/.f64}\left(1, \color{blue}{\left(4 + z \cdot -6\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(4, \color{blue}{\left(z \cdot -6\right)}\right)\right)\right)\right) \]

      10. *-lowering-*.f64 99.7%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(4, \mathsf{*.f64}\left(z, \color{blue}{-6}\right)\right)\right)\right)\right) \]

   6. Applied egg-rr 99.7%

      \[\leadsto x + \color{blue}{\frac{y - x}{\frac{1}{4 + z \cdot -6}}} \]

   7. Taylor expanded in x around 0

      \[\leadsto \color{blue}{y \cdot \left(4 + -6 \cdot z\right)} \]
   8. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(4 + -6 \cdot z\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(4, \color{blue}{\left(-6 \cdot z\right)}\right)\right) \]

      3. *-lowering-*.f64 57.9%

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(4, \mathsf{*.f64}\left(-6, \color{blue}{z}\right)\right)\right) \]

   9. Simplified 57.9%

      \[\leadsto \color{blue}{y \cdot \left(4 + -6 \cdot z\right)} \]

   10. Taylor expanded in z around inf

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

       1. associate-*r* N/A

          \[\leadsto \left(-6 \cdot y\right) \cdot \color{blue}{z} \]

       2. *-commutative N/A

          \[\leadsto \left(y \cdot -6\right) \cdot z \]

       3. associate-*r* N/A

          \[\leadsto y \cdot \color{blue}{\left(-6 \cdot z\right)} \]

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

          \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(-6 \cdot z\right)}\right) \]

       5. *-lowering-*.f64 57.6%

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(-6, \color{blue}{z}\right)\right) \]

   12. Simplified 57.6%

       \[\leadsto \color{blue}{y \cdot \left(-6 \cdot z\right)} \]

   if -5.1999999999999997e-16 < z < 3.1000000000000001e-285 or 4.2e-147 < z < 0.56000000000000005

   1. Initial program 99.5%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{6 \cdot \left(y \cdot \left(\frac{2}{3} - z\right)\right)} \]
   4. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(6, \color{blue}{\left(y \cdot \left(\frac{2}{3} - z\right)\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{2}{3} - z\right)}\right)\right) \]

      3. --lowering--.f64 62.9%

         \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\frac{2}{3}, \color{blue}{z}\right)\right)\right) \]

   5. Simplified 62.9%

      \[\leadsto \color{blue}{6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)} \]

   6. Taylor expanded in z around 0

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

      1. *-commutative N/A

         \[\leadsto y \cdot \color{blue}{4} \]

      2. *-lowering-*.f64 62.7%

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{4}\right) \]

   8. Simplified 62.7%

      \[\leadsto \color{blue}{y \cdot 4} \]

   if 3.1000000000000001e-285 < z < 4.2e-147

   1. Initial program 99.4%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)\right)}\right) \]

      2. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - x\right) \cdot \color{blue}{\left(6 \cdot \left(\frac{2}{3} - z\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(y - x\right), \color{blue}{\left(6 \cdot \left(\frac{2}{3} - z\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(\color{blue}{6} \cdot \left(\frac{2}{3} - z\right)\right)\right)\right) \]

      5. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(6 \cdot \left(\frac{2}{3} + \color{blue}{\left(\mathsf{neg}\left(z\right)\right)}\right)\right)\right)\right) \]

      6. distribute-lft-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(6 \cdot \frac{2}{3} + \color{blue}{6 \cdot \left(\mathsf{neg}\left(z\right)\right)}\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(6 \cdot \frac{2}{3} + \left(\mathsf{neg}\left(z\right)\right) \cdot \color{blue}{6}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(\left(6 \cdot \frac{2}{3}\right), \color{blue}{\left(\left(\mathsf{neg}\left(z\right)\right) \cdot 6\right)}\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(\left(6 \cdot \frac{2}{3}\right), \left(\left(\mathsf{neg}\left(z\right)\right) \cdot 6\right)\right)\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(\color{blue}{\left(\mathsf{neg}\left(z\right)\right)} \cdot 6\right)\right)\right)\right) \]

      11. distribute-lft-neg-out N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(\mathsf{neg}\left(z \cdot 6\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(z \cdot \color{blue}{\left(\mathsf{neg}\left(6\right)\right)}\right)\right)\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(z \cdot -6\right)\right)\right)\right) \]

      14. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(z \cdot \left(6 \cdot \color{blue}{-1}\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \mathsf{*.f64}\left(z, \color{blue}{\left(6 \cdot -1\right)}\right)\right)\right)\right) \]

      16. metadata-eval 99.6%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \mathsf{*.f64}\left(z, -6\right)\right)\right)\right) \]

   3. Simplified 99.6%

      \[\leadsto \color{blue}{x + \left(y - x\right) \cdot \left(4 + z \cdot -6\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0

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

   7. Simplified 99.6%

      \[\leadsto x + \left(y - x\right) \cdot \color{blue}{4} \]

   8. Taylor expanded in x around inf

      \[\leadsto \color{blue}{-3 \cdot x} \]
   9. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto x \cdot \color{blue}{-3} \]

      2. *-lowering-*.f64 63.0%

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{-3}\right) \]

   10. Simplified 63.0%

       \[\leadsto \color{blue}{x \cdot -3} \]

   if 0.56000000000000005 < z < 5.2000000000000001e159

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)\right)}\right) \]

      2. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - x\right) \cdot \color{blue}{\left(6 \cdot \left(\frac{2}{3} - z\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(y - x\right), \color{blue}{\left(6 \cdot \left(\frac{2}{3} - z\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(\color{blue}{6} \cdot \left(\frac{2}{3} - z\right)\right)\right)\right) \]

      5. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(6 \cdot \left(\frac{2}{3} + \color{blue}{\left(\mathsf{neg}\left(z\right)\right)}\right)\right)\right)\right) \]

      6. distribute-lft-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(6 \cdot \frac{2}{3} + \color{blue}{6 \cdot \left(\mathsf{neg}\left(z\right)\right)}\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(6 \cdot \frac{2}{3} + \left(\mathsf{neg}\left(z\right)\right) \cdot \color{blue}{6}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(\left(6 \cdot \frac{2}{3}\right), \color{blue}{\left(\left(\mathsf{neg}\left(z\right)\right) \cdot 6\right)}\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(\left(6 \cdot \frac{2}{3}\right), \left(\left(\mathsf{neg}\left(z\right)\right) \cdot 6\right)\right)\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(\color{blue}{\left(\mathsf{neg}\left(z\right)\right)} \cdot 6\right)\right)\right)\right) \]

      11. distribute-lft-neg-out N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(\mathsf{neg}\left(z \cdot 6\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(z \cdot \color{blue}{\left(\mathsf{neg}\left(6\right)\right)}\right)\right)\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(z \cdot -6\right)\right)\right)\right) \]

      14. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(z \cdot \left(6 \cdot \color{blue}{-1}\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \mathsf{*.f64}\left(z, \color{blue}{\left(6 \cdot -1\right)}\right)\right)\right)\right) \]

      16. metadata-eval 99.8%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \mathsf{*.f64}\left(z, -6\right)\right)\right)\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x + \left(y - x\right) \cdot \left(4 + z \cdot -6\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. flip3-+ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - x\right) \cdot \frac{{4}^{3} + {\left(z \cdot -6\right)}^{3}}{\color{blue}{4 \cdot 4 + \left(\left(z \cdot -6\right) \cdot \left(z \cdot -6\right) - 4 \cdot \left(z \cdot -6\right)\right)}}\right)\right) \]

      2. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - x\right) \cdot \frac{1}{\color{blue}{\frac{4 \cdot 4 + \left(\left(z \cdot -6\right) \cdot \left(z \cdot -6\right) - 4 \cdot \left(z \cdot -6\right)\right)}{{4}^{3} + {\left(z \cdot -6\right)}^{3}}}}\right)\right) \]

      3. un-div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y - x}{\color{blue}{\frac{4 \cdot 4 + \left(\left(z \cdot -6\right) \cdot \left(z \cdot -6\right) - 4 \cdot \left(z \cdot -6\right)\right)}{{4}^{3} + {\left(z \cdot -6\right)}^{3}}}}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(y - x\right), \color{blue}{\left(\frac{4 \cdot 4 + \left(\left(z \cdot -6\right) \cdot \left(z \cdot -6\right) - 4 \cdot \left(z \cdot -6\right)\right)}{{4}^{3} + {\left(z \cdot -6\right)}^{3}}\right)}\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(\frac{\color{blue}{4 \cdot 4 + \left(\left(z \cdot -6\right) \cdot \left(z \cdot -6\right) - 4 \cdot \left(z \cdot -6\right)\right)}}{{4}^{3} + {\left(z \cdot -6\right)}^{3}}\right)\right)\right) \]

      6. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(\frac{1}{\color{blue}{\frac{{4}^{3} + {\left(z \cdot -6\right)}^{3}}{4 \cdot 4 + \left(\left(z \cdot -6\right) \cdot \left(z \cdot -6\right) - 4 \cdot \left(z \cdot -6\right)\right)}}}\right)\right)\right) \]

      7. flip3-+ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(\frac{1}{4 + \color{blue}{z \cdot -6}}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{/.f64}\left(1, \color{blue}{\left(4 + z \cdot -6\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(4, \color{blue}{\left(z \cdot -6\right)}\right)\right)\right)\right) \]

      10. *-lowering-*.f64 99.6%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(4, \mathsf{*.f64}\left(z, \color{blue}{-6}\right)\right)\right)\right)\right) \]

   6. Applied egg-rr 99.6%

      \[\leadsto x + \color{blue}{\frac{y - x}{\frac{1}{4 + z \cdot -6}}} \]

   7. Taylor expanded in z around inf

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

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

         \[\leadsto \mathsf{*.f64}\left(-6, \color{blue}{\left(z \cdot \left(y - x\right)\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(-6, \mathsf{*.f64}\left(z, \color{blue}{\left(y - x\right)}\right)\right) \]

      3. --lowering--.f64 98.0%

         \[\leadsto \mathsf{*.f64}\left(-6, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(y, \color{blue}{x}\right)\right)\right) \]

   9. Simplified 98.0%

      \[\leadsto \color{blue}{-6 \cdot \left(z \cdot \left(y - x\right)\right)} \]

   10. Taylor expanded in y around 0

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

       1. *-commutative N/A

          \[\leadsto \left(x \cdot z\right) \cdot \color{blue}{6} \]

       2. associate-*r* N/A

          \[\leadsto x \cdot \color{blue}{\left(z \cdot 6\right)} \]

       3. *-commutative N/A

          \[\leadsto x \cdot \left(6 \cdot \color{blue}{z}\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(6 \cdot z\right)}\right) \]

       5. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(z \cdot \color{blue}{6}\right)\right) \]

       6. *-lowering-*.f64 60.5%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(z, \color{blue}{6}\right)\right) \]

   12. Simplified 60.5%

       \[\leadsto \color{blue}{x \cdot \left(z \cdot 6\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 60.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{-16}:\\ \;\;\;\;y \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-285}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-147}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.56:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+159}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot -6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 50.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -5.2 \cdot 10^{-16}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-284}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 6.1 \cdot 10^{-148}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{+154}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* y z))))
   (if (<= z -5.2e-16)
     t_0
     (if (<= z 1.25e-284)
       (* y 4.0)
       (if (<= z 6.1e-148)
         (* x -3.0)
         (if (<= z 0.5)
           (* y 4.0)
           (if (<= z 2.25e+154) (* x (* z 6.0)) t_0)))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double tmp;
	if (z <= -5.2e-16) {
		tmp = t_0;
	} else if (z <= 1.25e-284) {
		tmp = y * 4.0;
	} else if (z <= 6.1e-148) {
		tmp = x * -3.0;
	} else if (z <= 0.5) {
		tmp = y * 4.0;
	} else if (z <= 2.25e+154) {
		tmp = x * (z * 6.0);
	} 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 = (-6.0d0) * (y * z)
    if (z <= (-5.2d-16)) then
        tmp = t_0
    else if (z <= 1.25d-284) then
        tmp = y * 4.0d0
    else if (z <= 6.1d-148) then
        tmp = x * (-3.0d0)
    else if (z <= 0.5d0) then
        tmp = y * 4.0d0
    else if (z <= 2.25d+154) then
        tmp = x * (z * 6.0d0)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double tmp;
	if (z <= -5.2e-16) {
		tmp = t_0;
	} else if (z <= 1.25e-284) {
		tmp = y * 4.0;
	} else if (z <= 6.1e-148) {
		tmp = x * -3.0;
	} else if (z <= 0.5) {
		tmp = y * 4.0;
	} else if (z <= 2.25e+154) {
		tmp = x * (z * 6.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (y * z)
	tmp = 0
	if z <= -5.2e-16:
		tmp = t_0
	elif z <= 1.25e-284:
		tmp = y * 4.0
	elif z <= 6.1e-148:
		tmp = x * -3.0
	elif z <= 0.5:
		tmp = y * 4.0
	elif z <= 2.25e+154:
		tmp = x * (z * 6.0)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(y * z))
	tmp = 0.0
	if (z <= -5.2e-16)
		tmp = t_0;
	elseif (z <= 1.25e-284)
		tmp = Float64(y * 4.0);
	elseif (z <= 6.1e-148)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.5)
		tmp = Float64(y * 4.0);
	elseif (z <= 2.25e+154)
		tmp = Float64(x * Float64(z * 6.0));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (y * z);
	tmp = 0.0;
	if (z <= -5.2e-16)
		tmp = t_0;
	elseif (z <= 1.25e-284)
		tmp = y * 4.0;
	elseif (z <= 6.1e-148)
		tmp = x * -3.0;
	elseif (z <= 0.5)
		tmp = y * 4.0;
	elseif (z <= 2.25e+154)
		tmp = x * (z * 6.0);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.2e-16], t$95$0, If[LessEqual[z, 1.25e-284], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 6.1e-148], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.5], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 2.25e+154], N[(x * N[(z * 6.0), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.1999999999999997e-16 or 2.25000000000000005e154 < z

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{6 \cdot \left(y \cdot \left(\frac{2}{3} - z\right)\right)} \]
   4. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(6, \color{blue}{\left(y \cdot \left(\frac{2}{3} - z\right)\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{2}{3} - z\right)}\right)\right) \]

      3. --lowering--.f64 57.8%

         \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\frac{2}{3}, \color{blue}{z}\right)\right)\right) \]

   5. Simplified 57.8%

      \[\leadsto \color{blue}{6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)} \]

   6. Taylor expanded in z around inf

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

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

         \[\leadsto \mathsf{*.f64}\left(-6, \color{blue}{\left(y \cdot z\right)}\right) \]

      2. *-lowering-*.f64 57.5%

         \[\leadsto \mathsf{*.f64}\left(-6, \mathsf{*.f64}\left(y, \color{blue}{z}\right)\right) \]

   8. Simplified 57.5%

      \[\leadsto \color{blue}{-6 \cdot \left(y \cdot z\right)} \]

   if -5.1999999999999997e-16 < z < 1.24999999999999993e-284 or 6.09999999999999976e-148 < z < 0.5

   1. Initial program 99.5%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{6 \cdot \left(y \cdot \left(\frac{2}{3} - z\right)\right)} \]
   4. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(6, \color{blue}{\left(y \cdot \left(\frac{2}{3} - z\right)\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{2}{3} - z\right)}\right)\right) \]

      3. --lowering--.f64 62.9%

         \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\frac{2}{3}, \color{blue}{z}\right)\right)\right) \]

   5. Simplified 62.9%

      \[\leadsto \color{blue}{6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)} \]

   6. Taylor expanded in z around 0

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

      1. *-commutative N/A

         \[\leadsto y \cdot \color{blue}{4} \]

      2. *-lowering-*.f64 62.7%

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{4}\right) \]

   8. Simplified 62.7%

      \[\leadsto \color{blue}{y \cdot 4} \]

   if 1.24999999999999993e-284 < z < 6.09999999999999976e-148

   1. Initial program 99.4%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)\right)}\right) \]

      2. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - x\right) \cdot \color{blue}{\left(6 \cdot \left(\frac{2}{3} - z\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(y - x\right), \color{blue}{\left(6 \cdot \left(\frac{2}{3} - z\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(\color{blue}{6} \cdot \left(\frac{2}{3} - z\right)\right)\right)\right) \]

      5. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(6 \cdot \left(\frac{2}{3} + \color{blue}{\left(\mathsf{neg}\left(z\right)\right)}\right)\right)\right)\right) \]

      6. distribute-lft-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(6 \cdot \frac{2}{3} + \color{blue}{6 \cdot \left(\mathsf{neg}\left(z\right)\right)}\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(6 \cdot \frac{2}{3} + \left(\mathsf{neg}\left(z\right)\right) \cdot \color{blue}{6}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(\left(6 \cdot \frac{2}{3}\right), \color{blue}{\left(\left(\mathsf{neg}\left(z\right)\right) \cdot 6\right)}\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(\left(6 \cdot \frac{2}{3}\right), \left(\left(\mathsf{neg}\left(z\right)\right) \cdot 6\right)\right)\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(\color{blue}{\left(\mathsf{neg}\left(z\right)\right)} \cdot 6\right)\right)\right)\right) \]

      11. distribute-lft-neg-out N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(\mathsf{neg}\left(z \cdot 6\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(z \cdot \color{blue}{\left(\mathsf{neg}\left(6\right)\right)}\right)\right)\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(z \cdot -6\right)\right)\right)\right) \]

      14. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(z \cdot \left(6 \cdot \color{blue}{-1}\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \mathsf{*.f64}\left(z, \color{blue}{\left(6 \cdot -1\right)}\right)\right)\right)\right) \]

      16. metadata-eval 99.6%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \mathsf{*.f64}\left(z, -6\right)\right)\right)\right) \]

   3. Simplified 99.6%

      \[\leadsto \color{blue}{x + \left(y - x\right) \cdot \left(4 + z \cdot -6\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0

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

   7. Simplified 99.6%

      \[\leadsto x + \left(y - x\right) \cdot \color{blue}{4} \]

   8. Taylor expanded in x around inf

      \[\leadsto \color{blue}{-3 \cdot x} \]
   9. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto x \cdot \color{blue}{-3} \]

      2. *-lowering-*.f64 63.0%

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{-3}\right) \]

   10. Simplified 63.0%

       \[\leadsto \color{blue}{x \cdot -3} \]

   if 0.5 < z < 2.25000000000000005e154

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)\right)}\right) \]

      2. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - x\right) \cdot \color{blue}{\left(6 \cdot \left(\frac{2}{3} - z\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(y - x\right), \color{blue}{\left(6 \cdot \left(\frac{2}{3} - z\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(\color{blue}{6} \cdot \left(\frac{2}{3} - z\right)\right)\right)\right) \]

      5. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(6 \cdot \left(\frac{2}{3} + \color{blue}{\left(\mathsf{neg}\left(z\right)\right)}\right)\right)\right)\right) \]

      6. distribute-lft-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(6 \cdot \frac{2}{3} + \color{blue}{6 \cdot \left(\mathsf{neg}\left(z\right)\right)}\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(6 \cdot \frac{2}{3} + \left(\mathsf{neg}\left(z\right)\right) \cdot \color{blue}{6}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(\left(6 \cdot \frac{2}{3}\right), \color{blue}{\left(\left(\mathsf{neg}\left(z\right)\right) \cdot 6\right)}\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(\left(6 \cdot \frac{2}{3}\right), \left(\left(\mathsf{neg}\left(z\right)\right) \cdot 6\right)\right)\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(\color{blue}{\left(\mathsf{neg}\left(z\right)\right)} \cdot 6\right)\right)\right)\right) \]

      11. distribute-lft-neg-out N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(\mathsf{neg}\left(z \cdot 6\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(z \cdot \color{blue}{\left(\mathsf{neg}\left(6\right)\right)}\right)\right)\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(z \cdot -6\right)\right)\right)\right) \]

      14. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(z \cdot \left(6 \cdot \color{blue}{-1}\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \mathsf{*.f64}\left(z, \color{blue}{\left(6 \cdot -1\right)}\right)\right)\right)\right) \]

      16. metadata-eval 99.8%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \mathsf{*.f64}\left(z, -6\right)\right)\right)\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x + \left(y - x\right) \cdot \left(4 + z \cdot -6\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. flip3-+ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - x\right) \cdot \frac{{4}^{3} + {\left(z \cdot -6\right)}^{3}}{\color{blue}{4 \cdot 4 + \left(\left(z \cdot -6\right) \cdot \left(z \cdot -6\right) - 4 \cdot \left(z \cdot -6\right)\right)}}\right)\right) \]

      2. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - x\right) \cdot \frac{1}{\color{blue}{\frac{4 \cdot 4 + \left(\left(z \cdot -6\right) \cdot \left(z \cdot -6\right) - 4 \cdot \left(z \cdot -6\right)\right)}{{4}^{3} + {\left(z \cdot -6\right)}^{3}}}}\right)\right) \]

      3. un-div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y - x}{\color{blue}{\frac{4 \cdot 4 + \left(\left(z \cdot -6\right) \cdot \left(z \cdot -6\right) - 4 \cdot \left(z \cdot -6\right)\right)}{{4}^{3} + {\left(z \cdot -6\right)}^{3}}}}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(y - x\right), \color{blue}{\left(\frac{4 \cdot 4 + \left(\left(z \cdot -6\right) \cdot \left(z \cdot -6\right) - 4 \cdot \left(z \cdot -6\right)\right)}{{4}^{3} + {\left(z \cdot -6\right)}^{3}}\right)}\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(\frac{\color{blue}{4 \cdot 4 + \left(\left(z \cdot -6\right) \cdot \left(z \cdot -6\right) - 4 \cdot \left(z \cdot -6\right)\right)}}{{4}^{3} + {\left(z \cdot -6\right)}^{3}}\right)\right)\right) \]

      6. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(\frac{1}{\color{blue}{\frac{{4}^{3} + {\left(z \cdot -6\right)}^{3}}{4 \cdot 4 + \left(\left(z \cdot -6\right) \cdot \left(z \cdot -6\right) - 4 \cdot \left(z \cdot -6\right)\right)}}}\right)\right)\right) \]

      7. flip3-+ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(\frac{1}{4 + \color{blue}{z \cdot -6}}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{/.f64}\left(1, \color{blue}{\left(4 + z \cdot -6\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(4, \color{blue}{\left(z \cdot -6\right)}\right)\right)\right)\right) \]

      10. *-lowering-*.f64 99.6%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(4, \mathsf{*.f64}\left(z, \color{blue}{-6}\right)\right)\right)\right)\right) \]

   6. Applied egg-rr 99.6%

      \[\leadsto x + \color{blue}{\frac{y - x}{\frac{1}{4 + z \cdot -6}}} \]

   7. Taylor expanded in z around inf

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

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

         \[\leadsto \mathsf{*.f64}\left(-6, \color{blue}{\left(z \cdot \left(y - x\right)\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(-6, \mathsf{*.f64}\left(z, \color{blue}{\left(y - x\right)}\right)\right) \]

      3. --lowering--.f64 98.0%

         \[\leadsto \mathsf{*.f64}\left(-6, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(y, \color{blue}{x}\right)\right)\right) \]

   9. Simplified 98.0%

      \[\leadsto \color{blue}{-6 \cdot \left(z \cdot \left(y - x\right)\right)} \]

   10. Taylor expanded in y around 0

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

       1. *-commutative N/A

          \[\leadsto \left(x \cdot z\right) \cdot \color{blue}{6} \]

       2. associate-*r* N/A

          \[\leadsto x \cdot \color{blue}{\left(z \cdot 6\right)} \]

       3. *-commutative N/A

          \[\leadsto x \cdot \left(6 \cdot \color{blue}{z}\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(6 \cdot z\right)}\right) \]

       5. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(z \cdot \color{blue}{6}\right)\right) \]

       6. *-lowering-*.f64 60.5%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(z, \color{blue}{6}\right)\right) \]

   12. Simplified 60.5%

       \[\leadsto \color{blue}{x \cdot \left(z \cdot 6\right)} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 4: 73.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{if}\;z \leq -5.2 \cdot 10^{-16}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-288}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-149}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1320000:\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* (- y x) z))))
   (if (<= z -5.2e-16)
     t_0
     (if (<= z 1.9e-288)
       (* y 4.0)
       (if (<= z 3.7e-149)
         (* x -3.0)
         (if (<= z 1320000.0) (* 6.0 (* y (- 0.6666666666666666 z))) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * ((y - x) * z);
	double tmp;
	if (z <= -5.2e-16) {
		tmp = t_0;
	} else if (z <= 1.9e-288) {
		tmp = y * 4.0;
	} else if (z <= 3.7e-149) {
		tmp = x * -3.0;
	} else if (z <= 1320000.0) {
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	} 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 = (-6.0d0) * ((y - x) * z)
    if (z <= (-5.2d-16)) then
        tmp = t_0
    else if (z <= 1.9d-288) then
        tmp = y * 4.0d0
    else if (z <= 3.7d-149) then
        tmp = x * (-3.0d0)
    else if (z <= 1320000.0d0) then
        tmp = 6.0d0 * (y * (0.6666666666666666d0 - z))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -6.0 * ((y - x) * z);
	double tmp;
	if (z <= -5.2e-16) {
		tmp = t_0;
	} else if (z <= 1.9e-288) {
		tmp = y * 4.0;
	} else if (z <= 3.7e-149) {
		tmp = x * -3.0;
	} else if (z <= 1320000.0) {
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * ((y - x) * z)
	tmp = 0
	if z <= -5.2e-16:
		tmp = t_0
	elif z <= 1.9e-288:
		tmp = y * 4.0
	elif z <= 3.7e-149:
		tmp = x * -3.0
	elif z <= 1320000.0:
		tmp = 6.0 * (y * (0.6666666666666666 - z))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(Float64(y - x) * z))
	tmp = 0.0
	if (z <= -5.2e-16)
		tmp = t_0;
	elseif (z <= 1.9e-288)
		tmp = Float64(y * 4.0);
	elseif (z <= 3.7e-149)
		tmp = Float64(x * -3.0);
	elseif (z <= 1320000.0)
		tmp = Float64(6.0 * Float64(y * Float64(0.6666666666666666 - z)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * ((y - x) * z);
	tmp = 0.0;
	if (z <= -5.2e-16)
		tmp = t_0;
	elseif (z <= 1.9e-288)
		tmp = y * 4.0;
	elseif (z <= 3.7e-149)
		tmp = x * -3.0;
	elseif (z <= 1320000.0)
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.2e-16], t$95$0, If[LessEqual[z, 1.9e-288], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 3.7e-149], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 1320000.0], N[(6.0 * N[(y * N[(0.6666666666666666 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.1999999999999997e-16 or 1.32e6 < z

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)\right)}\right) \]

      2. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - x\right) \cdot \color{blue}{\left(6 \cdot \left(\frac{2}{3} - z\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(y - x\right), \color{blue}{\left(6 \cdot \left(\frac{2}{3} - z\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(\color{blue}{6} \cdot \left(\frac{2}{3} - z\right)\right)\right)\right) \]

      5. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(6 \cdot \left(\frac{2}{3} + \color{blue}{\left(\mathsf{neg}\left(z\right)\right)}\right)\right)\right)\right) \]

      6. distribute-lft-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(6 \cdot \frac{2}{3} + \color{blue}{6 \cdot \left(\mathsf{neg}\left(z\right)\right)}\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(6 \cdot \frac{2}{3} + \left(\mathsf{neg}\left(z\right)\right) \cdot \color{blue}{6}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(\left(6 \cdot \frac{2}{3}\right), \color{blue}{\left(\left(\mathsf{neg}\left(z\right)\right) \cdot 6\right)}\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(\left(6 \cdot \frac{2}{3}\right), \left(\left(\mathsf{neg}\left(z\right)\right) \cdot 6\right)\right)\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(\color{blue}{\left(\mathsf{neg}\left(z\right)\right)} \cdot 6\right)\right)\right)\right) \]

      11. distribute-lft-neg-out N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(\mathsf{neg}\left(z \cdot 6\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(z \cdot \color{blue}{\left(\mathsf{neg}\left(6\right)\right)}\right)\right)\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(z \cdot -6\right)\right)\right)\right) \]

      14. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(z \cdot \left(6 \cdot \color{blue}{-1}\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \mathsf{*.f64}\left(z, \color{blue}{\left(6 \cdot -1\right)}\right)\right)\right)\right) \]

      16. metadata-eval 99.8%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \mathsf{*.f64}\left(z, -6\right)\right)\right)\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x + \left(y - x\right) \cdot \left(4 + z \cdot -6\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. flip3-+ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - x\right) \cdot \frac{{4}^{3} + {\left(z \cdot -6\right)}^{3}}{\color{blue}{4 \cdot 4 + \left(\left(z \cdot -6\right) \cdot \left(z \cdot -6\right) - 4 \cdot \left(z \cdot -6\right)\right)}}\right)\right) \]

      2. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - x\right) \cdot \frac{1}{\color{blue}{\frac{4 \cdot 4 + \left(\left(z \cdot -6\right) \cdot \left(z \cdot -6\right) - 4 \cdot \left(z \cdot -6\right)\right)}{{4}^{3} + {\left(z \cdot -6\right)}^{3}}}}\right)\right) \]

      3. un-div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y - x}{\color{blue}{\frac{4 \cdot 4 + \left(\left(z \cdot -6\right) \cdot \left(z \cdot -6\right) - 4 \cdot \left(z \cdot -6\right)\right)}{{4}^{3} + {\left(z \cdot -6\right)}^{3}}}}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(y - x\right), \color{blue}{\left(\frac{4 \cdot 4 + \left(\left(z \cdot -6\right) \cdot \left(z \cdot -6\right) - 4 \cdot \left(z \cdot -6\right)\right)}{{4}^{3} + {\left(z \cdot -6\right)}^{3}}\right)}\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(\frac{\color{blue}{4 \cdot 4 + \left(\left(z \cdot -6\right) \cdot \left(z \cdot -6\right) - 4 \cdot \left(z \cdot -6\right)\right)}}{{4}^{3} + {\left(z \cdot -6\right)}^{3}}\right)\right)\right) \]

      6. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(\frac{1}{\color{blue}{\frac{{4}^{3} + {\left(z \cdot -6\right)}^{3}}{4 \cdot 4 + \left(\left(z \cdot -6\right) \cdot \left(z \cdot -6\right) - 4 \cdot \left(z \cdot -6\right)\right)}}}\right)\right)\right) \]

      7. flip3-+ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(\frac{1}{4 + \color{blue}{z \cdot -6}}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{/.f64}\left(1, \color{blue}{\left(4 + z \cdot -6\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(4, \color{blue}{\left(z \cdot -6\right)}\right)\right)\right)\right) \]

      10. *-lowering-*.f64 99.7%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(4, \mathsf{*.f64}\left(z, \color{blue}{-6}\right)\right)\right)\right)\right) \]

   6. Applied egg-rr 99.7%

      \[\leadsto x + \color{blue}{\frac{y - x}{\frac{1}{4 + z \cdot -6}}} \]

   7. Taylor expanded in z around inf

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

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

         \[\leadsto \mathsf{*.f64}\left(-6, \color{blue}{\left(z \cdot \left(y - x\right)\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(-6, \mathsf{*.f64}\left(z, \color{blue}{\left(y - x\right)}\right)\right) \]

      3. --lowering--.f64 97.3%

         \[\leadsto \mathsf{*.f64}\left(-6, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(y, \color{blue}{x}\right)\right)\right) \]

   9. Simplified 97.3%

      \[\leadsto \color{blue}{-6 \cdot \left(z \cdot \left(y - x\right)\right)} \]

   if -5.1999999999999997e-16 < z < 1.8999999999999999e-288

   1. Initial program 99.4%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{6 \cdot \left(y \cdot \left(\frac{2}{3} - z\right)\right)} \]
   4. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(6, \color{blue}{\left(y \cdot \left(\frac{2}{3} - z\right)\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{2}{3} - z\right)}\right)\right) \]

      3. --lowering--.f64 60.5%

         \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\frac{2}{3}, \color{blue}{z}\right)\right)\right) \]

   5. Simplified 60.5%

      \[\leadsto \color{blue}{6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)} \]

   6. Taylor expanded in z around 0

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

      1. *-commutative N/A

         \[\leadsto y \cdot \color{blue}{4} \]

      2. *-lowering-*.f64 60.7%

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{4}\right) \]

   8. Simplified 60.7%

      \[\leadsto \color{blue}{y \cdot 4} \]

   if 1.8999999999999999e-288 < z < 3.6999999999999999e-149

   1. Initial program 99.4%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)\right)}\right) \]

      2. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - x\right) \cdot \color{blue}{\left(6 \cdot \left(\frac{2}{3} - z\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(y - x\right), \color{blue}{\left(6 \cdot \left(\frac{2}{3} - z\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(\color{blue}{6} \cdot \left(\frac{2}{3} - z\right)\right)\right)\right) \]

      5. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(6 \cdot \left(\frac{2}{3} + \color{blue}{\left(\mathsf{neg}\left(z\right)\right)}\right)\right)\right)\right) \]

      6. distribute-lft-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(6 \cdot \frac{2}{3} + \color{blue}{6 \cdot \left(\mathsf{neg}\left(z\right)\right)}\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(6 \cdot \frac{2}{3} + \left(\mathsf{neg}\left(z\right)\right) \cdot \color{blue}{6}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(\left(6 \cdot \frac{2}{3}\right), \color{blue}{\left(\left(\mathsf{neg}\left(z\right)\right) \cdot 6\right)}\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(\left(6 \cdot \frac{2}{3}\right), \left(\left(\mathsf{neg}\left(z\right)\right) \cdot 6\right)\right)\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(\color{blue}{\left(\mathsf{neg}\left(z\right)\right)} \cdot 6\right)\right)\right)\right) \]

      11. distribute-lft-neg-out N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(\mathsf{neg}\left(z \cdot 6\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(z \cdot \color{blue}{\left(\mathsf{neg}\left(6\right)\right)}\right)\right)\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(z \cdot -6\right)\right)\right)\right) \]

      14. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(z \cdot \left(6 \cdot \color{blue}{-1}\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \mathsf{*.f64}\left(z, \color{blue}{\left(6 \cdot -1\right)}\right)\right)\right)\right) \]

      16. metadata-eval 99.6%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \mathsf{*.f64}\left(z, -6\right)\right)\right)\right) \]

   3. Simplified 99.6%

      \[\leadsto \color{blue}{x + \left(y - x\right) \cdot \left(4 + z \cdot -6\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0

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

   7. Simplified 99.6%

      \[\leadsto x + \left(y - x\right) \cdot \color{blue}{4} \]

   8. Taylor expanded in x around inf

      \[\leadsto \color{blue}{-3 \cdot x} \]
   9. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto x \cdot \color{blue}{-3} \]

      2. *-lowering-*.f64 63.0%

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{-3}\right) \]

   10. Simplified 63.0%

       \[\leadsto \color{blue}{x \cdot -3} \]

   if 3.6999999999999999e-149 < z < 1.32e6

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{6 \cdot \left(y \cdot \left(\frac{2}{3} - z\right)\right)} \]
   4. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(6, \color{blue}{\left(y \cdot \left(\frac{2}{3} - z\right)\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{2}{3} - z\right)}\right)\right) \]

      3. --lowering--.f64 69.1%

         \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\frac{2}{3}, \color{blue}{z}\right)\right)\right) \]

   5. Simplified 69.1%

      \[\leadsto \color{blue}{6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 81.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{-16}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-288}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-149}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1320000:\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{if}\;z \leq -5.2 \cdot 10^{-16}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{-289}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{-147}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.62:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* (- y x) z))))
   (if (<= z -5.2e-16)
     t_0
     (if (<= z 5.3e-289)
       (* y 4.0)
       (if (<= z 9.8e-147) (* x -3.0) (if (<= z 0.62) (* y 4.0) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * ((y - x) * z);
	double tmp;
	if (z <= -5.2e-16) {
		tmp = t_0;
	} else if (z <= 5.3e-289) {
		tmp = y * 4.0;
	} else if (z <= 9.8e-147) {
		tmp = x * -3.0;
	} else if (z <= 0.62) {
		tmp = y * 4.0;
	} 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 = (-6.0d0) * ((y - x) * z)
    if (z <= (-5.2d-16)) then
        tmp = t_0
    else if (z <= 5.3d-289) then
        tmp = y * 4.0d0
    else if (z <= 9.8d-147) then
        tmp = x * (-3.0d0)
    else if (z <= 0.62d0) then
        tmp = y * 4.0d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -6.0 * ((y - x) * z);
	double tmp;
	if (z <= -5.2e-16) {
		tmp = t_0;
	} else if (z <= 5.3e-289) {
		tmp = y * 4.0;
	} else if (z <= 9.8e-147) {
		tmp = x * -3.0;
	} else if (z <= 0.62) {
		tmp = y * 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * ((y - x) * z)
	tmp = 0
	if z <= -5.2e-16:
		tmp = t_0
	elif z <= 5.3e-289:
		tmp = y * 4.0
	elif z <= 9.8e-147:
		tmp = x * -3.0
	elif z <= 0.62:
		tmp = y * 4.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(Float64(y - x) * z))
	tmp = 0.0
	if (z <= -5.2e-16)
		tmp = t_0;
	elseif (z <= 5.3e-289)
		tmp = Float64(y * 4.0);
	elseif (z <= 9.8e-147)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.62)
		tmp = Float64(y * 4.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * ((y - x) * z);
	tmp = 0.0;
	if (z <= -5.2e-16)
		tmp = t_0;
	elseif (z <= 5.3e-289)
		tmp = y * 4.0;
	elseif (z <= 9.8e-147)
		tmp = x * -3.0;
	elseif (z <= 0.62)
		tmp = y * 4.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.2e-16], t$95$0, If[LessEqual[z, 5.3e-289], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 9.8e-147], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.62], N[(y * 4.0), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.1999999999999997e-16 or 0.619999999999999996 < z

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)\right)}\right) \]

      2. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - x\right) \cdot \color{blue}{\left(6 \cdot \left(\frac{2}{3} - z\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(y - x\right), \color{blue}{\left(6 \cdot \left(\frac{2}{3} - z\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(\color{blue}{6} \cdot \left(\frac{2}{3} - z\right)\right)\right)\right) \]

      5. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(6 \cdot \left(\frac{2}{3} + \color{blue}{\left(\mathsf{neg}\left(z\right)\right)}\right)\right)\right)\right) \]

      6. distribute-lft-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(6 \cdot \frac{2}{3} + \color{blue}{6 \cdot \left(\mathsf{neg}\left(z\right)\right)}\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(6 \cdot \frac{2}{3} + \left(\mathsf{neg}\left(z\right)\right) \cdot \color{blue}{6}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(\left(6 \cdot \frac{2}{3}\right), \color{blue}{\left(\left(\mathsf{neg}\left(z\right)\right) \cdot 6\right)}\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(\left(6 \cdot \frac{2}{3}\right), \left(\left(\mathsf{neg}\left(z\right)\right) \cdot 6\right)\right)\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(\color{blue}{\left(\mathsf{neg}\left(z\right)\right)} \cdot 6\right)\right)\right)\right) \]

      11. distribute-lft-neg-out N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(\mathsf{neg}\left(z \cdot 6\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(z \cdot \color{blue}{\left(\mathsf{neg}\left(6\right)\right)}\right)\right)\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(z \cdot -6\right)\right)\right)\right) \]

      14. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(z \cdot \left(6 \cdot \color{blue}{-1}\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \mathsf{*.f64}\left(z, \color{blue}{\left(6 \cdot -1\right)}\right)\right)\right)\right) \]

      16. metadata-eval 99.8%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \mathsf{*.f64}\left(z, -6\right)\right)\right)\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x + \left(y - x\right) \cdot \left(4 + z \cdot -6\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. flip3-+ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - x\right) \cdot \frac{{4}^{3} + {\left(z \cdot -6\right)}^{3}}{\color{blue}{4 \cdot 4 + \left(\left(z \cdot -6\right) \cdot \left(z \cdot -6\right) - 4 \cdot \left(z \cdot -6\right)\right)}}\right)\right) \]

      2. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - x\right) \cdot \frac{1}{\color{blue}{\frac{4 \cdot 4 + \left(\left(z \cdot -6\right) \cdot \left(z \cdot -6\right) - 4 \cdot \left(z \cdot -6\right)\right)}{{4}^{3} + {\left(z \cdot -6\right)}^{3}}}}\right)\right) \]

      3. un-div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y - x}{\color{blue}{\frac{4 \cdot 4 + \left(\left(z \cdot -6\right) \cdot \left(z \cdot -6\right) - 4 \cdot \left(z \cdot -6\right)\right)}{{4}^{3} + {\left(z \cdot -6\right)}^{3}}}}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(y - x\right), \color{blue}{\left(\frac{4 \cdot 4 + \left(\left(z \cdot -6\right) \cdot \left(z \cdot -6\right) - 4 \cdot \left(z \cdot -6\right)\right)}{{4}^{3} + {\left(z \cdot -6\right)}^{3}}\right)}\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(\frac{\color{blue}{4 \cdot 4 + \left(\left(z \cdot -6\right) \cdot \left(z \cdot -6\right) - 4 \cdot \left(z \cdot -6\right)\right)}}{{4}^{3} + {\left(z \cdot -6\right)}^{3}}\right)\right)\right) \]

      6. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(\frac{1}{\color{blue}{\frac{{4}^{3} + {\left(z \cdot -6\right)}^{3}}{4 \cdot 4 + \left(\left(z \cdot -6\right) \cdot \left(z \cdot -6\right) - 4 \cdot \left(z \cdot -6\right)\right)}}}\right)\right)\right) \]

      7. flip3-+ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(\frac{1}{4 + \color{blue}{z \cdot -6}}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{/.f64}\left(1, \color{blue}{\left(4 + z \cdot -6\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(4, \color{blue}{\left(z \cdot -6\right)}\right)\right)\right)\right) \]

      10. *-lowering-*.f64 99.7%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(4, \mathsf{*.f64}\left(z, \color{blue}{-6}\right)\right)\right)\right)\right) \]

   6. Applied egg-rr 99.7%

      \[\leadsto x + \color{blue}{\frac{y - x}{\frac{1}{4 + z \cdot -6}}} \]

   7. Taylor expanded in z around inf

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

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

         \[\leadsto \mathsf{*.f64}\left(-6, \color{blue}{\left(z \cdot \left(y - x\right)\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(-6, \mathsf{*.f64}\left(z, \color{blue}{\left(y - x\right)}\right)\right) \]

      3. --lowering--.f64 97.3%

         \[\leadsto \mathsf{*.f64}\left(-6, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(y, \color{blue}{x}\right)\right)\right) \]

   9. Simplified 97.3%

      \[\leadsto \color{blue}{-6 \cdot \left(z \cdot \left(y - x\right)\right)} \]

   if -5.1999999999999997e-16 < z < 5.3e-289 or 9.8000000000000001e-147 < z < 0.619999999999999996

   1. Initial program 99.5%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{6 \cdot \left(y \cdot \left(\frac{2}{3} - z\right)\right)} \]
   4. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(6, \color{blue}{\left(y \cdot \left(\frac{2}{3} - z\right)\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{2}{3} - z\right)}\right)\right) \]

      3. --lowering--.f64 62.9%

         \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\frac{2}{3}, \color{blue}{z}\right)\right)\right) \]

   5. Simplified 62.9%

      \[\leadsto \color{blue}{6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)} \]

   6. Taylor expanded in z around 0

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

      1. *-commutative N/A

         \[\leadsto y \cdot \color{blue}{4} \]

      2. *-lowering-*.f64 62.7%

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{4}\right) \]

   8. Simplified 62.7%

      \[\leadsto \color{blue}{y \cdot 4} \]

   if 5.3e-289 < z < 9.8000000000000001e-147

   1. Initial program 99.4%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)\right)}\right) \]

      2. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - x\right) \cdot \color{blue}{\left(6 \cdot \left(\frac{2}{3} - z\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(y - x\right), \color{blue}{\left(6 \cdot \left(\frac{2}{3} - z\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(\color{blue}{6} \cdot \left(\frac{2}{3} - z\right)\right)\right)\right) \]

      5. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(6 \cdot \left(\frac{2}{3} + \color{blue}{\left(\mathsf{neg}\left(z\right)\right)}\right)\right)\right)\right) \]

      6. distribute-lft-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(6 \cdot \frac{2}{3} + \color{blue}{6 \cdot \left(\mathsf{neg}\left(z\right)\right)}\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(6 \cdot \frac{2}{3} + \left(\mathsf{neg}\left(z\right)\right) \cdot \color{blue}{6}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(\left(6 \cdot \frac{2}{3}\right), \color{blue}{\left(\left(\mathsf{neg}\left(z\right)\right) \cdot 6\right)}\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(\left(6 \cdot \frac{2}{3}\right), \left(\left(\mathsf{neg}\left(z\right)\right) \cdot 6\right)\right)\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(\color{blue}{\left(\mathsf{neg}\left(z\right)\right)} \cdot 6\right)\right)\right)\right) \]

      11. distribute-lft-neg-out N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(\mathsf{neg}\left(z \cdot 6\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(z \cdot \color{blue}{\left(\mathsf{neg}\left(6\right)\right)}\right)\right)\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(z \cdot -6\right)\right)\right)\right) \]

      14. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(z \cdot \left(6 \cdot \color{blue}{-1}\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \mathsf{*.f64}\left(z, \color{blue}{\left(6 \cdot -1\right)}\right)\right)\right)\right) \]

      16. metadata-eval 99.6%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \mathsf{*.f64}\left(z, -6\right)\right)\right)\right) \]

   3. Simplified 99.6%

      \[\leadsto \color{blue}{x + \left(y - x\right) \cdot \left(4 + z \cdot -6\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0

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

   7. Simplified 99.6%

      \[\leadsto x + \left(y - x\right) \cdot \color{blue}{4} \]

   8. Taylor expanded in x around inf

      \[\leadsto \color{blue}{-3 \cdot x} \]
   9. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto x \cdot \color{blue}{-3} \]

      2. *-lowering-*.f64 63.0%

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{-3}\right) \]

   10. Simplified 63.0%

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

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{-16}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{-289}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{-147}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.62:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 50.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -5.2 \cdot 10^{-16}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-284}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-148}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.68:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* y z))))
   (if (<= z -5.2e-16)
     t_0
     (if (<= z 7.5e-284)
       (* y 4.0)
       (if (<= z 1.25e-148) (* x -3.0) (if (<= z 0.68) (* y 4.0) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double tmp;
	if (z <= -5.2e-16) {
		tmp = t_0;
	} else if (z <= 7.5e-284) {
		tmp = y * 4.0;
	} else if (z <= 1.25e-148) {
		tmp = x * -3.0;
	} else if (z <= 0.68) {
		tmp = y * 4.0;
	} 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 = (-6.0d0) * (y * z)
    if (z <= (-5.2d-16)) then
        tmp = t_0
    else if (z <= 7.5d-284) then
        tmp = y * 4.0d0
    else if (z <= 1.25d-148) then
        tmp = x * (-3.0d0)
    else if (z <= 0.68d0) then
        tmp = y * 4.0d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double tmp;
	if (z <= -5.2e-16) {
		tmp = t_0;
	} else if (z <= 7.5e-284) {
		tmp = y * 4.0;
	} else if (z <= 1.25e-148) {
		tmp = x * -3.0;
	} else if (z <= 0.68) {
		tmp = y * 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (y * z)
	tmp = 0
	if z <= -5.2e-16:
		tmp = t_0
	elif z <= 7.5e-284:
		tmp = y * 4.0
	elif z <= 1.25e-148:
		tmp = x * -3.0
	elif z <= 0.68:
		tmp = y * 4.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(y * z))
	tmp = 0.0
	if (z <= -5.2e-16)
		tmp = t_0;
	elseif (z <= 7.5e-284)
		tmp = Float64(y * 4.0);
	elseif (z <= 1.25e-148)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.68)
		tmp = Float64(y * 4.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (y * z);
	tmp = 0.0;
	if (z <= -5.2e-16)
		tmp = t_0;
	elseif (z <= 7.5e-284)
		tmp = y * 4.0;
	elseif (z <= 1.25e-148)
		tmp = x * -3.0;
	elseif (z <= 0.68)
		tmp = y * 4.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.2e-16], t$95$0, If[LessEqual[z, 7.5e-284], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 1.25e-148], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.68], N[(y * 4.0), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.1999999999999997e-16 or 0.680000000000000049 < z

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{6 \cdot \left(y \cdot \left(\frac{2}{3} - z\right)\right)} \]
   4. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(6, \color{blue}{\left(y \cdot \left(\frac{2}{3} - z\right)\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{2}{3} - z\right)}\right)\right) \]

      3. --lowering--.f64 52.6%

         \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\frac{2}{3}, \color{blue}{z}\right)\right)\right) \]

   5. Simplified 52.6%

      \[\leadsto \color{blue}{6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)} \]

   6. Taylor expanded in z around inf

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

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

         \[\leadsto \mathsf{*.f64}\left(-6, \color{blue}{\left(y \cdot z\right)}\right) \]

      2. *-lowering-*.f64 52.2%

         \[\leadsto \mathsf{*.f64}\left(-6, \mathsf{*.f64}\left(y, \color{blue}{z}\right)\right) \]

   8. Simplified 52.2%

      \[\leadsto \color{blue}{-6 \cdot \left(y \cdot z\right)} \]

   if -5.1999999999999997e-16 < z < 7.4999999999999999e-284 or 1.25e-148 < z < 0.680000000000000049

   1. Initial program 99.5%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{6 \cdot \left(y \cdot \left(\frac{2}{3} - z\right)\right)} \]
   4. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(6, \color{blue}{\left(y \cdot \left(\frac{2}{3} - z\right)\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{2}{3} - z\right)}\right)\right) \]

      3. --lowering--.f64 62.9%

         \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\frac{2}{3}, \color{blue}{z}\right)\right)\right) \]

   5. Simplified 62.9%

      \[\leadsto \color{blue}{6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)} \]

   6. Taylor expanded in z around 0

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

      1. *-commutative N/A

         \[\leadsto y \cdot \color{blue}{4} \]

      2. *-lowering-*.f64 62.7%

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{4}\right) \]

   8. Simplified 62.7%

      \[\leadsto \color{blue}{y \cdot 4} \]

   if 7.4999999999999999e-284 < z < 1.25e-148

   1. Initial program 99.4%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)\right)}\right) \]

      2. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - x\right) \cdot \color{blue}{\left(6 \cdot \left(\frac{2}{3} - z\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(y - x\right), \color{blue}{\left(6 \cdot \left(\frac{2}{3} - z\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(\color{blue}{6} \cdot \left(\frac{2}{3} - z\right)\right)\right)\right) \]

      5. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(6 \cdot \left(\frac{2}{3} + \color{blue}{\left(\mathsf{neg}\left(z\right)\right)}\right)\right)\right)\right) \]

      6. distribute-lft-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(6 \cdot \frac{2}{3} + \color{blue}{6 \cdot \left(\mathsf{neg}\left(z\right)\right)}\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(6 \cdot \frac{2}{3} + \left(\mathsf{neg}\left(z\right)\right) \cdot \color{blue}{6}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(\left(6 \cdot \frac{2}{3}\right), \color{blue}{\left(\left(\mathsf{neg}\left(z\right)\right) \cdot 6\right)}\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(\left(6 \cdot \frac{2}{3}\right), \left(\left(\mathsf{neg}\left(z\right)\right) \cdot 6\right)\right)\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(\color{blue}{\left(\mathsf{neg}\left(z\right)\right)} \cdot 6\right)\right)\right)\right) \]

      11. distribute-lft-neg-out N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(\mathsf{neg}\left(z \cdot 6\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(z \cdot \color{blue}{\left(\mathsf{neg}\left(6\right)\right)}\right)\right)\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(z \cdot -6\right)\right)\right)\right) \]

      14. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(z \cdot \left(6 \cdot \color{blue}{-1}\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \mathsf{*.f64}\left(z, \color{blue}{\left(6 \cdot -1\right)}\right)\right)\right)\right) \]

      16. metadata-eval 99.6%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \mathsf{*.f64}\left(z, -6\right)\right)\right)\right) \]

   3. Simplified 99.6%

      \[\leadsto \color{blue}{x + \left(y - x\right) \cdot \left(4 + z \cdot -6\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0

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

   7. Simplified 99.6%

      \[\leadsto x + \left(y - x\right) \cdot \color{blue}{4} \]

   8. Taylor expanded in x around inf

      \[\leadsto \color{blue}{-3 \cdot x} \]
   9. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto x \cdot \color{blue}{-3} \]

      2. *-lowering-*.f64 63.0%

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{-3}\right) \]

   10. Simplified 63.0%

       \[\leadsto \color{blue}{x \cdot -3} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 7: 97.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + \left(y - x\right) \cdot \left(z \cdot -6\right)\\ \mathbf{if}\;z \leq -0.66:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 0.65:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ x (* (- y x) (* z -6.0)))))
   (if (<= z -0.66) t_0 (if (<= z 0.65) (+ x (* (- y x) 4.0)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x + ((y - x) * (z * -6.0));
	double tmp;
	if (z <= -0.66) {
		tmp = t_0;
	} else if (z <= 0.65) {
		tmp = x + ((y - x) * 4.0);
	} 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 = x + ((y - x) * (z * (-6.0d0)))
    if (z <= (-0.66d0)) then
        tmp = t_0
    else if (z <= 0.65d0) then
        tmp = x + ((y - x) * 4.0d0)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x + ((y - x) * (z * -6.0));
	double tmp;
	if (z <= -0.66) {
		tmp = t_0;
	} else if (z <= 0.65) {
		tmp = x + ((y - x) * 4.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x + ((y - x) * (z * -6.0))
	tmp = 0
	if z <= -0.66:
		tmp = t_0
	elif z <= 0.65:
		tmp = x + ((y - x) * 4.0)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x + Float64(Float64(y - x) * Float64(z * -6.0)))
	tmp = 0.0
	if (z <= -0.66)
		tmp = t_0;
	elseif (z <= 0.65)
		tmp = Float64(x + Float64(Float64(y - x) * 4.0));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x + ((y - x) * (z * -6.0));
	tmp = 0.0;
	if (z <= -0.66)
		tmp = t_0;
	elseif (z <= 0.65)
		tmp = x + ((y - x) * 4.0);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x + N[(N[(y - x), $MachinePrecision] * N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.66], t$95$0, If[LessEqual[z, 0.65], N[(x + N[(N[(y - x), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -0.660000000000000031 or 0.650000000000000022 < z

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)\right)}\right) \]

      2. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - x\right) \cdot \color{blue}{\left(6 \cdot \left(\frac{2}{3} - z\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(y - x\right), \color{blue}{\left(6 \cdot \left(\frac{2}{3} - z\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(\color{blue}{6} \cdot \left(\frac{2}{3} - z\right)\right)\right)\right) \]

      5. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(6 \cdot \left(\frac{2}{3} + \color{blue}{\left(\mathsf{neg}\left(z\right)\right)}\right)\right)\right)\right) \]

      6. distribute-lft-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(6 \cdot \frac{2}{3} + \color{blue}{6 \cdot \left(\mathsf{neg}\left(z\right)\right)}\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(6 \cdot \frac{2}{3} + \left(\mathsf{neg}\left(z\right)\right) \cdot \color{blue}{6}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(\left(6 \cdot \frac{2}{3}\right), \color{blue}{\left(\left(\mathsf{neg}\left(z\right)\right) \cdot 6\right)}\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(\left(6 \cdot \frac{2}{3}\right), \left(\left(\mathsf{neg}\left(z\right)\right) \cdot 6\right)\right)\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(\color{blue}{\left(\mathsf{neg}\left(z\right)\right)} \cdot 6\right)\right)\right)\right) \]

      11. distribute-lft-neg-out N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(\mathsf{neg}\left(z \cdot 6\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(z \cdot \color{blue}{\left(\mathsf{neg}\left(6\right)\right)}\right)\right)\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(z \cdot -6\right)\right)\right)\right) \]

      14. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(z \cdot \left(6 \cdot \color{blue}{-1}\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \mathsf{*.f64}\left(z, \color{blue}{\left(6 \cdot -1\right)}\right)\right)\right)\right) \]

      16. metadata-eval 99.8%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \mathsf{*.f64}\left(z, -6\right)\right)\right)\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x + \left(y - x\right) \cdot \left(4 + z \cdot -6\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \color{blue}{\left(-6 \cdot z\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(z \cdot \color{blue}{-6}\right)\right)\right) \]

      2. *-lowering-*.f64 98.6%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{*.f64}\left(z, \color{blue}{-6}\right)\right)\right) \]

   7. Simplified 98.6%

      \[\leadsto x + \left(y - x\right) \cdot \color{blue}{\left(z \cdot -6\right)} \]

   if -0.660000000000000031 < z < 0.650000000000000022

   1. Initial program 99.5%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)\right)}\right) \]

      2. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - x\right) \cdot \color{blue}{\left(6 \cdot \left(\frac{2}{3} - z\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(y - x\right), \color{blue}{\left(6 \cdot \left(\frac{2}{3} - z\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(\color{blue}{6} \cdot \left(\frac{2}{3} - z\right)\right)\right)\right) \]

      5. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(6 \cdot \left(\frac{2}{3} + \color{blue}{\left(\mathsf{neg}\left(z\right)\right)}\right)\right)\right)\right) \]

      6. distribute-lft-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(6 \cdot \frac{2}{3} + \color{blue}{6 \cdot \left(\mathsf{neg}\left(z\right)\right)}\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(6 \cdot \frac{2}{3} + \left(\mathsf{neg}\left(z\right)\right) \cdot \color{blue}{6}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(\left(6 \cdot \frac{2}{3}\right), \color{blue}{\left(\left(\mathsf{neg}\left(z\right)\right) \cdot 6\right)}\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(\left(6 \cdot \frac{2}{3}\right), \left(\left(\mathsf{neg}\left(z\right)\right) \cdot 6\right)\right)\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(\color{blue}{\left(\mathsf{neg}\left(z\right)\right)} \cdot 6\right)\right)\right)\right) \]

      11. distribute-lft-neg-out N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(\mathsf{neg}\left(z \cdot 6\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(z \cdot \color{blue}{\left(\mathsf{neg}\left(6\right)\right)}\right)\right)\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(z \cdot -6\right)\right)\right)\right) \]

      14. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(z \cdot \left(6 \cdot \color{blue}{-1}\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \mathsf{*.f64}\left(z, \color{blue}{\left(6 \cdot -1\right)}\right)\right)\right)\right) \]

      16. metadata-eval 99.8%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \mathsf{*.f64}\left(z, -6\right)\right)\right)\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x + \left(y - x\right) \cdot \left(4 + z \cdot -6\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0

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

   7. Simplified 99.1%

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

Alternative 8: 97.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.55:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq 0.58:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.55)
   (* -6.0 (* (- y x) z))
   (if (<= z 0.58) (+ x (* (- y x) 4.0)) (* z (* (- y x) -6.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.55) {
		tmp = -6.0 * ((y - x) * z);
	} else if (z <= 0.58) {
		tmp = x + ((y - x) * 4.0);
	} else {
		tmp = z * ((y - x) * -6.0);
	}
	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) :: tmp
    if (z <= (-0.55d0)) then
        tmp = (-6.0d0) * ((y - x) * z)
    else if (z <= 0.58d0) then
        tmp = x + ((y - x) * 4.0d0)
    else
        tmp = z * ((y - x) * (-6.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.55) {
		tmp = -6.0 * ((y - x) * z);
	} else if (z <= 0.58) {
		tmp = x + ((y - x) * 4.0);
	} else {
		tmp = z * ((y - x) * -6.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.55:
		tmp = -6.0 * ((y - x) * z)
	elif z <= 0.58:
		tmp = x + ((y - x) * 4.0)
	else:
		tmp = z * ((y - x) * -6.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.55)
		tmp = Float64(-6.0 * Float64(Float64(y - x) * z));
	elseif (z <= 0.58)
		tmp = Float64(x + Float64(Float64(y - x) * 4.0));
	else
		tmp = Float64(z * Float64(Float64(y - x) * -6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.55)
		tmp = -6.0 * ((y - x) * z);
	elseif (z <= 0.58)
		tmp = x + ((y - x) * 4.0);
	else
		tmp = z * ((y - x) * -6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.55], N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.58], N[(x + N[(N[(y - x), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(y - x), $MachinePrecision] * -6.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.55000000000000004

   1. Initial program 99.6%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)\right)}\right) \]

      2. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - x\right) \cdot \color{blue}{\left(6 \cdot \left(\frac{2}{3} - z\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(y - x\right), \color{blue}{\left(6 \cdot \left(\frac{2}{3} - z\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(\color{blue}{6} \cdot \left(\frac{2}{3} - z\right)\right)\right)\right) \]

      5. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(6 \cdot \left(\frac{2}{3} + \color{blue}{\left(\mathsf{neg}\left(z\right)\right)}\right)\right)\right)\right) \]

      6. distribute-lft-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(6 \cdot \frac{2}{3} + \color{blue}{6 \cdot \left(\mathsf{neg}\left(z\right)\right)}\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(6 \cdot \frac{2}{3} + \left(\mathsf{neg}\left(z\right)\right) \cdot \color{blue}{6}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(\left(6 \cdot \frac{2}{3}\right), \color{blue}{\left(\left(\mathsf{neg}\left(z\right)\right) \cdot 6\right)}\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(\left(6 \cdot \frac{2}{3}\right), \left(\left(\mathsf{neg}\left(z\right)\right) \cdot 6\right)\right)\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(\color{blue}{\left(\mathsf{neg}\left(z\right)\right)} \cdot 6\right)\right)\right)\right) \]

      11. distribute-lft-neg-out N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(\mathsf{neg}\left(z \cdot 6\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(z \cdot \color{blue}{\left(\mathsf{neg}\left(6\right)\right)}\right)\right)\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(z \cdot -6\right)\right)\right)\right) \]

      14. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(z \cdot \left(6 \cdot \color{blue}{-1}\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \mathsf{*.f64}\left(z, \color{blue}{\left(6 \cdot -1\right)}\right)\right)\right)\right) \]

      16. metadata-eval 99.8%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \mathsf{*.f64}\left(z, -6\right)\right)\right)\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x + \left(y - x\right) \cdot \left(4 + z \cdot -6\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. flip3-+ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - x\right) \cdot \frac{{4}^{3} + {\left(z \cdot -6\right)}^{3}}{\color{blue}{4 \cdot 4 + \left(\left(z \cdot -6\right) \cdot \left(z \cdot -6\right) - 4 \cdot \left(z \cdot -6\right)\right)}}\right)\right) \]

      2. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - x\right) \cdot \frac{1}{\color{blue}{\frac{4 \cdot 4 + \left(\left(z \cdot -6\right) \cdot \left(z \cdot -6\right) - 4 \cdot \left(z \cdot -6\right)\right)}{{4}^{3} + {\left(z \cdot -6\right)}^{3}}}}\right)\right) \]

      3. un-div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y - x}{\color{blue}{\frac{4 \cdot 4 + \left(\left(z \cdot -6\right) \cdot \left(z \cdot -6\right) - 4 \cdot \left(z \cdot -6\right)\right)}{{4}^{3} + {\left(z \cdot -6\right)}^{3}}}}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(y - x\right), \color{blue}{\left(\frac{4 \cdot 4 + \left(\left(z \cdot -6\right) \cdot \left(z \cdot -6\right) - 4 \cdot \left(z \cdot -6\right)\right)}{{4}^{3} + {\left(z \cdot -6\right)}^{3}}\right)}\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(\frac{\color{blue}{4 \cdot 4 + \left(\left(z \cdot -6\right) \cdot \left(z \cdot -6\right) - 4 \cdot \left(z \cdot -6\right)\right)}}{{4}^{3} + {\left(z \cdot -6\right)}^{3}}\right)\right)\right) \]

      6. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(\frac{1}{\color{blue}{\frac{{4}^{3} + {\left(z \cdot -6\right)}^{3}}{4 \cdot 4 + \left(\left(z \cdot -6\right) \cdot \left(z \cdot -6\right) - 4 \cdot \left(z \cdot -6\right)\right)}}}\right)\right)\right) \]

      7. flip3-+ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(\frac{1}{4 + \color{blue}{z \cdot -6}}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{/.f64}\left(1, \color{blue}{\left(4 + z \cdot -6\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(4, \color{blue}{\left(z \cdot -6\right)}\right)\right)\right)\right) \]

      10. *-lowering-*.f64 99.7%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(4, \mathsf{*.f64}\left(z, \color{blue}{-6}\right)\right)\right)\right)\right) \]

   6. Applied egg-rr 99.7%

      \[\leadsto x + \color{blue}{\frac{y - x}{\frac{1}{4 + z \cdot -6}}} \]

   7. Taylor expanded in z around inf

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

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

         \[\leadsto \mathsf{*.f64}\left(-6, \color{blue}{\left(z \cdot \left(y - x\right)\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(-6, \mathsf{*.f64}\left(z, \color{blue}{\left(y - x\right)}\right)\right) \]

      3. --lowering--.f64 98.3%

         \[\leadsto \mathsf{*.f64}\left(-6, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(y, \color{blue}{x}\right)\right)\right) \]

   9. Simplified 98.3%

      \[\leadsto \color{blue}{-6 \cdot \left(z \cdot \left(y - x\right)\right)} \]

   if -0.55000000000000004 < z < 0.57999999999999996

   1. Initial program 99.5%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)\right)}\right) \]

      2. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - x\right) \cdot \color{blue}{\left(6 \cdot \left(\frac{2}{3} - z\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(y - x\right), \color{blue}{\left(6 \cdot \left(\frac{2}{3} - z\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(\color{blue}{6} \cdot \left(\frac{2}{3} - z\right)\right)\right)\right) \]

      5. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(6 \cdot \left(\frac{2}{3} + \color{blue}{\left(\mathsf{neg}\left(z\right)\right)}\right)\right)\right)\right) \]

      6. distribute-lft-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(6 \cdot \frac{2}{3} + \color{blue}{6 \cdot \left(\mathsf{neg}\left(z\right)\right)}\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(6 \cdot \frac{2}{3} + \left(\mathsf{neg}\left(z\right)\right) \cdot \color{blue}{6}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(\left(6 \cdot \frac{2}{3}\right), \color{blue}{\left(\left(\mathsf{neg}\left(z\right)\right) \cdot 6\right)}\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(\left(6 \cdot \frac{2}{3}\right), \left(\left(\mathsf{neg}\left(z\right)\right) \cdot 6\right)\right)\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(\color{blue}{\left(\mathsf{neg}\left(z\right)\right)} \cdot 6\right)\right)\right)\right) \]

      11. distribute-lft-neg-out N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(\mathsf{neg}\left(z \cdot 6\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(z \cdot \color{blue}{\left(\mathsf{neg}\left(6\right)\right)}\right)\right)\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(z \cdot -6\right)\right)\right)\right) \]

      14. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(z \cdot \left(6 \cdot \color{blue}{-1}\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \mathsf{*.f64}\left(z, \color{blue}{\left(6 \cdot -1\right)}\right)\right)\right)\right) \]

      16. metadata-eval 99.8%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \mathsf{*.f64}\left(z, -6\right)\right)\right)\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x + \left(y - x\right) \cdot \left(4 + z \cdot -6\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0

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

   7. Simplified 99.1%

      \[\leadsto x + \left(y - x\right) \cdot \color{blue}{4} \]

   if 0.57999999999999996 < z

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. associate-*r* N/A

         \[\leadsto \left(-6 \cdot z\right) \cdot \color{blue}{\left(y - x\right)} \]

      2. *-commutative N/A

         \[\leadsto \left(z \cdot -6\right) \cdot \left(\color{blue}{y} - x\right) \]

      3. associate-*r* N/A

         \[\leadsto z \cdot \color{blue}{\left(-6 \cdot \left(y - x\right)\right)} \]

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

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(-6 \cdot \left(y - x\right)\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(-6, \color{blue}{\left(y - x\right)}\right)\right) \]

      6. --lowering--.f64 98.8%

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(-6, \mathsf{\_.f64}\left(y, \color{blue}{x}\right)\right)\right) \]

   5. Simplified 98.8%

      \[\leadsto \color{blue}{z \cdot \left(-6 \cdot \left(y - x\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.55:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq 0.58:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 75.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(4 + z \cdot -6\right)\\ \mathbf{if}\;y \leq -5.2 \cdot 10^{+15}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+57}:\\ \;\;\;\;x \cdot \left(z \cdot 6 + -3\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (+ 4.0 (* z -6.0)))))
   (if (<= y -5.2e+15) t_0 (if (<= y 5.5e+57) (* x (+ (* z 6.0) -3.0)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = y * (4.0 + (z * -6.0));
	double tmp;
	if (y <= -5.2e+15) {
		tmp = t_0;
	} else if (y <= 5.5e+57) {
		tmp = x * ((z * 6.0) + -3.0);
	} 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 = y * (4.0d0 + (z * (-6.0d0)))
    if (y <= (-5.2d+15)) then
        tmp = t_0
    else if (y <= 5.5d+57) then
        tmp = x * ((z * 6.0d0) + (-3.0d0))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * (4.0 + (z * -6.0));
	double tmp;
	if (y <= -5.2e+15) {
		tmp = t_0;
	} else if (y <= 5.5e+57) {
		tmp = x * ((z * 6.0) + -3.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (4.0 + (z * -6.0))
	tmp = 0
	if y <= -5.2e+15:
		tmp = t_0
	elif y <= 5.5e+57:
		tmp = x * ((z * 6.0) + -3.0)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(4.0 + Float64(z * -6.0)))
	tmp = 0.0
	if (y <= -5.2e+15)
		tmp = t_0;
	elseif (y <= 5.5e+57)
		tmp = Float64(x * Float64(Float64(z * 6.0) + -3.0));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (4.0 + (z * -6.0));
	tmp = 0.0;
	if (y <= -5.2e+15)
		tmp = t_0;
	elseif (y <= 5.5e+57)
		tmp = x * ((z * 6.0) + -3.0);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(4.0 + N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.2e+15], t$95$0, If[LessEqual[y, 5.5e+57], N[(x * N[(N[(z * 6.0), $MachinePrecision] + -3.0), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -5.2e15 or 5.5000000000000002e57 < y

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)\right)}\right) \]

      2. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - x\right) \cdot \color{blue}{\left(6 \cdot \left(\frac{2}{3} - z\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(y - x\right), \color{blue}{\left(6 \cdot \left(\frac{2}{3} - z\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(\color{blue}{6} \cdot \left(\frac{2}{3} - z\right)\right)\right)\right) \]

      5. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(6 \cdot \left(\frac{2}{3} + \color{blue}{\left(\mathsf{neg}\left(z\right)\right)}\right)\right)\right)\right) \]

      6. distribute-lft-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(6 \cdot \frac{2}{3} + \color{blue}{6 \cdot \left(\mathsf{neg}\left(z\right)\right)}\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(6 \cdot \frac{2}{3} + \left(\mathsf{neg}\left(z\right)\right) \cdot \color{blue}{6}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(\left(6 \cdot \frac{2}{3}\right), \color{blue}{\left(\left(\mathsf{neg}\left(z\right)\right) \cdot 6\right)}\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(\left(6 \cdot \frac{2}{3}\right), \left(\left(\mathsf{neg}\left(z\right)\right) \cdot 6\right)\right)\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(\color{blue}{\left(\mathsf{neg}\left(z\right)\right)} \cdot 6\right)\right)\right)\right) \]

      11. distribute-lft-neg-out N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(\mathsf{neg}\left(z \cdot 6\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(z \cdot \color{blue}{\left(\mathsf{neg}\left(6\right)\right)}\right)\right)\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(z \cdot -6\right)\right)\right)\right) \]

      14. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(z \cdot \left(6 \cdot \color{blue}{-1}\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \mathsf{*.f64}\left(z, \color{blue}{\left(6 \cdot -1\right)}\right)\right)\right)\right) \]

      16. metadata-eval 99.9%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \mathsf{*.f64}\left(z, -6\right)\right)\right)\right) \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x + \left(y - x\right) \cdot \left(4 + z \cdot -6\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. flip3-+ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - x\right) \cdot \frac{{4}^{3} + {\left(z \cdot -6\right)}^{3}}{\color{blue}{4 \cdot 4 + \left(\left(z \cdot -6\right) \cdot \left(z \cdot -6\right) - 4 \cdot \left(z \cdot -6\right)\right)}}\right)\right) \]

      2. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - x\right) \cdot \frac{1}{\color{blue}{\frac{4 \cdot 4 + \left(\left(z \cdot -6\right) \cdot \left(z \cdot -6\right) - 4 \cdot \left(z \cdot -6\right)\right)}{{4}^{3} + {\left(z \cdot -6\right)}^{3}}}}\right)\right) \]

      3. un-div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y - x}{\color{blue}{\frac{4 \cdot 4 + \left(\left(z \cdot -6\right) \cdot \left(z \cdot -6\right) - 4 \cdot \left(z \cdot -6\right)\right)}{{4}^{3} + {\left(z \cdot -6\right)}^{3}}}}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(y - x\right), \color{blue}{\left(\frac{4 \cdot 4 + \left(\left(z \cdot -6\right) \cdot \left(z \cdot -6\right) - 4 \cdot \left(z \cdot -6\right)\right)}{{4}^{3} + {\left(z \cdot -6\right)}^{3}}\right)}\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(\frac{\color{blue}{4 \cdot 4 + \left(\left(z \cdot -6\right) \cdot \left(z \cdot -6\right) - 4 \cdot \left(z \cdot -6\right)\right)}}{{4}^{3} + {\left(z \cdot -6\right)}^{3}}\right)\right)\right) \]

      6. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(\frac{1}{\color{blue}{\frac{{4}^{3} + {\left(z \cdot -6\right)}^{3}}{4 \cdot 4 + \left(\left(z \cdot -6\right) \cdot \left(z \cdot -6\right) - 4 \cdot \left(z \cdot -6\right)\right)}}}\right)\right)\right) \]

      7. flip3-+ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(\frac{1}{4 + \color{blue}{z \cdot -6}}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{/.f64}\left(1, \color{blue}{\left(4 + z \cdot -6\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(4, \color{blue}{\left(z \cdot -6\right)}\right)\right)\right)\right) \]

      10. *-lowering-*.f64 99.8%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(4, \mathsf{*.f64}\left(z, \color{blue}{-6}\right)\right)\right)\right)\right) \]

   6. Applied egg-rr 99.8%

      \[\leadsto x + \color{blue}{\frac{y - x}{\frac{1}{4 + z \cdot -6}}} \]

   7. Taylor expanded in x around 0

      \[\leadsto \color{blue}{y \cdot \left(4 + -6 \cdot z\right)} \]
   8. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(4 + -6 \cdot z\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(4, \color{blue}{\left(-6 \cdot z\right)}\right)\right) \]

      3. *-lowering-*.f64 89.4%

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(4, \mathsf{*.f64}\left(-6, \color{blue}{z}\right)\right)\right) \]

   9. Simplified 89.4%

      \[\leadsto \color{blue}{y \cdot \left(4 + -6 \cdot z\right)} \]

   if -5.2e15 < y < 5.5000000000000002e57

   1. Initial program 99.5%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot \left(\frac{2}{3} - z\right)\right)} \]
   4. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 + -6 \cdot \left(\frac{2}{3} - z\right)\right)}\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(-6 \cdot \left(\frac{2}{3} - z\right) + \color{blue}{1}\right)\right) \]

      3. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(-6 \cdot \left(\frac{2}{3} + \left(\mathsf{neg}\left(z\right)\right)\right) + 1\right)\right) \]

      4. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(-6 \cdot \left(\frac{2}{3} + -1 \cdot z\right) + 1\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(-6 \cdot \left(-1 \cdot z + \frac{2}{3}\right) + 1\right)\right) \]

      6. distribute-lft-in N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\left(-6 \cdot \left(-1 \cdot z\right) + -6 \cdot \frac{2}{3}\right) + 1\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\left(-6 \cdot \left(z \cdot -1\right) + -6 \cdot \frac{2}{3}\right) + 1\right)\right) \]

      8. associate-*l* N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\left(\left(-6 \cdot z\right) \cdot -1 + -6 \cdot \frac{2}{3}\right) + 1\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\left(\left(-6 \cdot z\right) \cdot -1 + -4\right) + 1\right)\right) \]

      10. associate-+l+ N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\left(-6 \cdot z\right) \cdot -1 + \color{blue}{\left(-4 + 1\right)}\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\left(-6 \cdot z\right) \cdot -1 + -3\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\left(-6 \cdot z\right) \cdot -1 + \left(1 + \color{blue}{-4}\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(-6 \cdot z\right) \cdot -1\right), \color{blue}{\left(1 + -4\right)}\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(-1 \cdot \left(-6 \cdot z\right)\right), \left(\color{blue}{1} + -4\right)\right)\right) \]

      15. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(-1 \cdot -6\right) \cdot z\right), \left(\color{blue}{1} + -4\right)\right)\right) \]

      16. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(6 \cdot z\right), \left(1 + -4\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(6, z\right), \left(\color{blue}{1} + -4\right)\right)\right) \]

      18. metadata-eval 75.6%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(6, z\right), -3\right)\right) \]

   5. Simplified 75.6%

      \[\leadsto \color{blue}{x \cdot \left(6 \cdot z + -3\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{+15}:\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+57}:\\ \;\;\;\;x \cdot \left(z \cdot 6 + -3\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 74.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \mathbf{if}\;y \leq -6.5 \cdot 10^{+17}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+59}:\\ \;\;\;\;x \cdot \left(z \cdot 6 + -3\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 6.0 (* y (- 0.6666666666666666 z)))))
   (if (<= y -6.5e+17) t_0 (if (<= y 1.6e+59) (* x (+ (* z 6.0) -3.0)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = 6.0 * (y * (0.6666666666666666 - z));
	double tmp;
	if (y <= -6.5e+17) {
		tmp = t_0;
	} else if (y <= 1.6e+59) {
		tmp = x * ((z * 6.0) + -3.0);
	} 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 = 6.0d0 * (y * (0.6666666666666666d0 - z))
    if (y <= (-6.5d+17)) then
        tmp = t_0
    else if (y <= 1.6d+59) then
        tmp = x * ((z * 6.0d0) + (-3.0d0))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 6.0 * (y * (0.6666666666666666 - z));
	double tmp;
	if (y <= -6.5e+17) {
		tmp = t_0;
	} else if (y <= 1.6e+59) {
		tmp = x * ((z * 6.0) + -3.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 6.0 * (y * (0.6666666666666666 - z))
	tmp = 0
	if y <= -6.5e+17:
		tmp = t_0
	elif y <= 1.6e+59:
		tmp = x * ((z * 6.0) + -3.0)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(6.0 * Float64(y * Float64(0.6666666666666666 - z)))
	tmp = 0.0
	if (y <= -6.5e+17)
		tmp = t_0;
	elseif (y <= 1.6e+59)
		tmp = Float64(x * Float64(Float64(z * 6.0) + -3.0));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 6.0 * (y * (0.6666666666666666 - z));
	tmp = 0.0;
	if (y <= -6.5e+17)
		tmp = t_0;
	elseif (y <= 1.6e+59)
		tmp = x * ((z * 6.0) + -3.0);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(6.0 * N[(y * N[(0.6666666666666666 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.5e+17], t$95$0, If[LessEqual[y, 1.6e+59], N[(x * N[(N[(z * 6.0), $MachinePrecision] + -3.0), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -6.5e17 or 1.59999999999999991e59 < y

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{6 \cdot \left(y \cdot \left(\frac{2}{3} - z\right)\right)} \]
   4. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(6, \color{blue}{\left(y \cdot \left(\frac{2}{3} - z\right)\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{2}{3} - z\right)}\right)\right) \]

      3. --lowering--.f64 89.2%

         \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\frac{2}{3}, \color{blue}{z}\right)\right)\right) \]

   5. Simplified 89.2%

      \[\leadsto \color{blue}{6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)} \]

   if -6.5e17 < y < 1.59999999999999991e59

   1. Initial program 99.5%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot \left(\frac{2}{3} - z\right)\right)} \]
   4. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 + -6 \cdot \left(\frac{2}{3} - z\right)\right)}\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(-6 \cdot \left(\frac{2}{3} - z\right) + \color{blue}{1}\right)\right) \]

      3. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(-6 \cdot \left(\frac{2}{3} + \left(\mathsf{neg}\left(z\right)\right)\right) + 1\right)\right) \]

      4. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(-6 \cdot \left(\frac{2}{3} + -1 \cdot z\right) + 1\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(-6 \cdot \left(-1 \cdot z + \frac{2}{3}\right) + 1\right)\right) \]

      6. distribute-lft-in N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\left(-6 \cdot \left(-1 \cdot z\right) + -6 \cdot \frac{2}{3}\right) + 1\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\left(-6 \cdot \left(z \cdot -1\right) + -6 \cdot \frac{2}{3}\right) + 1\right)\right) \]

      8. associate-*l* N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\left(\left(-6 \cdot z\right) \cdot -1 + -6 \cdot \frac{2}{3}\right) + 1\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\left(\left(-6 \cdot z\right) \cdot -1 + -4\right) + 1\right)\right) \]

      10. associate-+l+ N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\left(-6 \cdot z\right) \cdot -1 + \color{blue}{\left(-4 + 1\right)}\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\left(-6 \cdot z\right) \cdot -1 + -3\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\left(-6 \cdot z\right) \cdot -1 + \left(1 + \color{blue}{-4}\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(-6 \cdot z\right) \cdot -1\right), \color{blue}{\left(1 + -4\right)}\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(-1 \cdot \left(-6 \cdot z\right)\right), \left(\color{blue}{1} + -4\right)\right)\right) \]

      15. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(-1 \cdot -6\right) \cdot z\right), \left(\color{blue}{1} + -4\right)\right)\right) \]

      16. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(6 \cdot z\right), \left(1 + -4\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(6, z\right), \left(\color{blue}{1} + -4\right)\right)\right) \]

      18. metadata-eval 75.6%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(6, z\right), -3\right)\right) \]

   5. Simplified 75.6%

      \[\leadsto \color{blue}{x \cdot \left(6 \cdot z + -3\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 81.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+17}:\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+59}:\\ \;\;\;\;x \cdot \left(z \cdot 6 + -3\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 37.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+31}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+142}:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;y \cdot 4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.2e+31) (* y 4.0) (if (<= y 1.3e+142) (* x -3.0) (* y 4.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.2e+31) {
		tmp = y * 4.0;
	} else if (y <= 1.3e+142) {
		tmp = x * -3.0;
	} else {
		tmp = y * 4.0;
	}
	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) :: tmp
    if (y <= (-1.2d+31)) then
        tmp = y * 4.0d0
    else if (y <= 1.3d+142) then
        tmp = x * (-3.0d0)
    else
        tmp = y * 4.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.2e+31) {
		tmp = y * 4.0;
	} else if (y <= 1.3e+142) {
		tmp = x * -3.0;
	} else {
		tmp = y * 4.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.2e+31:
		tmp = y * 4.0
	elif y <= 1.3e+142:
		tmp = x * -3.0
	else:
		tmp = y * 4.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.2e+31)
		tmp = Float64(y * 4.0);
	elseif (y <= 1.3e+142)
		tmp = Float64(x * -3.0);
	else
		tmp = Float64(y * 4.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.2e+31)
		tmp = y * 4.0;
	elseif (y <= 1.3e+142)
		tmp = x * -3.0;
	else
		tmp = y * 4.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.2e+31], N[(y * 4.0), $MachinePrecision], If[LessEqual[y, 1.3e+142], N[(x * -3.0), $MachinePrecision], N[(y * 4.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.19999999999999991e31 or 1.30000000000000011e142 < y

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{6 \cdot \left(y \cdot \left(\frac{2}{3} - z\right)\right)} \]
   4. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(6, \color{blue}{\left(y \cdot \left(\frac{2}{3} - z\right)\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{2}{3} - z\right)}\right)\right) \]

      3. --lowering--.f64 93.1%

         \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\frac{2}{3}, \color{blue}{z}\right)\right)\right) \]

   5. Simplified 93.1%

      \[\leadsto \color{blue}{6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)} \]

   6. Taylor expanded in z around 0

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

      1. *-commutative N/A

         \[\leadsto y \cdot \color{blue}{4} \]

      2. *-lowering-*.f64 49.5%

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{4}\right) \]

   8. Simplified 49.5%

      \[\leadsto \color{blue}{y \cdot 4} \]

   if -1.19999999999999991e31 < y < 1.30000000000000011e142

   1. Initial program 99.5%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)\right)}\right) \]

      2. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - x\right) \cdot \color{blue}{\left(6 \cdot \left(\frac{2}{3} - z\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(y - x\right), \color{blue}{\left(6 \cdot \left(\frac{2}{3} - z\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(\color{blue}{6} \cdot \left(\frac{2}{3} - z\right)\right)\right)\right) \]

      5. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(6 \cdot \left(\frac{2}{3} + \color{blue}{\left(\mathsf{neg}\left(z\right)\right)}\right)\right)\right)\right) \]

      6. distribute-lft-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(6 \cdot \frac{2}{3} + \color{blue}{6 \cdot \left(\mathsf{neg}\left(z\right)\right)}\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(6 \cdot \frac{2}{3} + \left(\mathsf{neg}\left(z\right)\right) \cdot \color{blue}{6}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(\left(6 \cdot \frac{2}{3}\right), \color{blue}{\left(\left(\mathsf{neg}\left(z\right)\right) \cdot 6\right)}\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(\left(6 \cdot \frac{2}{3}\right), \left(\left(\mathsf{neg}\left(z\right)\right) \cdot 6\right)\right)\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(\color{blue}{\left(\mathsf{neg}\left(z\right)\right)} \cdot 6\right)\right)\right)\right) \]

      11. distribute-lft-neg-out N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(\mathsf{neg}\left(z \cdot 6\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(z \cdot \color{blue}{\left(\mathsf{neg}\left(6\right)\right)}\right)\right)\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(z \cdot -6\right)\right)\right)\right) \]

      14. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(z \cdot \left(6 \cdot \color{blue}{-1}\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \mathsf{*.f64}\left(z, \color{blue}{\left(6 \cdot -1\right)}\right)\right)\right)\right) \]

      16. metadata-eval 99.7%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \mathsf{*.f64}\left(z, -6\right)\right)\right)\right) \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{x + \left(y - x\right) \cdot \left(4 + z \cdot -6\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0

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

   7. Simplified 43.3%

      \[\leadsto x + \left(y - x\right) \cdot \color{blue}{4} \]

   8. Taylor expanded in x around inf

      \[\leadsto \color{blue}{-3 \cdot x} \]
   9. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto x \cdot \color{blue}{-3} \]

      2. *-lowering-*.f64 32.8%

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{-3}\right) \]

   10. Simplified 32.8%

       \[\leadsto \color{blue}{x \cdot -3} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 12: 99.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ x + \left(\left(y - x\right) \cdot \left(0.6666666666666666 - z\right)\right) \cdot 6 \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ x (* (* (- y x) (- 0.6666666666666666 z)) 6.0)))

C

double code(double x, double y, double z) {
	return x + (((y - x) * (0.6666666666666666 - z)) * 6.0);
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + (((y - x) * (0.6666666666666666d0 - z)) * 6.0d0)
end function

Java

public static double code(double x, double y, double z) {
	return x + (((y - x) * (0.6666666666666666 - z)) * 6.0);
}

Python

def code(x, y, z):
	return x + (((y - x) * (0.6666666666666666 - z)) * 6.0)

Julia

function code(x, y, z)
	return Float64(x + Float64(Float64(Float64(y - x) * Float64(0.6666666666666666 - z)) * 6.0))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + (((y - x) * (0.6666666666666666 - z)) * 6.0);
end

Wolfram

code[x_, y_, z_] := N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(0.6666666666666666 - z), $MachinePrecision]), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.6%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
2. Add Preprocessing
3. Step-by-step derivation

   1. *-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\frac{2}{3} - z\right) \cdot \color{blue}{\left(\left(y - x\right) \cdot 6\right)}\right)\right) \]

   2. associate-*r* N/A

      \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\left(\frac{2}{3} - z\right) \cdot \left(y - x\right)\right) \cdot \color{blue}{6}\right)\right) \]

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

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\left(\frac{2}{3} - z\right) \cdot \left(y - x\right)\right), \color{blue}{6}\right)\right) \]

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

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(\frac{2}{3} - z\right), \left(y - x\right)\right), 6\right)\right) \]

   5. --lowering--.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\left(\frac{2}{3}\right), z\right), \left(y - x\right)\right), 6\right)\right) \]

   6. metadata-eval N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\frac{2}{3}, z\right), \left(y - x\right)\right), 6\right)\right) \]

   7. --lowering--.f64 99.6%

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\frac{2}{3}, z\right), \mathsf{\_.f64}\left(y, x\right)\right), 6\right)\right) \]

4. Applied egg-rr 99.6%

   \[\leadsto x + \color{blue}{\left(\left(0.6666666666666666 - z\right) \cdot \left(y - x\right)\right) \cdot 6} \]

5. Final simplification 99.6%

   \[\leadsto x + \left(\left(y - x\right) \cdot \left(0.6666666666666666 - z\right)\right) \cdot 6 \]
6. Add Preprocessing

Alternative 13: 26.4% accurate, 4.3× speedup

Math

\[\begin{array}{l} \\ x \cdot -3 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* x -3.0))

C

double code(double x, double y, double z) {
	return x * -3.0;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x * (-3.0d0)
end function

Java

public static double code(double x, double y, double z) {
	return x * -3.0;
}

Python

def code(x, y, z):
	return x * -3.0

Julia

function code(x, y, z)
	return Float64(x * -3.0)
end

MATLAB

function tmp = code(x, y, z)
	tmp = x * -3.0;
end

Wolfram

code[x_, y_, z_] := N[(x * -3.0), $MachinePrecision]

Derivation

1. Initial program 99.6%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
2. Step-by-step derivation

   1. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)\right)}\right) \]

   2. associate-*l* N/A

      \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - x\right) \cdot \color{blue}{\left(6 \cdot \left(\frac{2}{3} - z\right)\right)}\right)\right) \]

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

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(y - x\right), \color{blue}{\left(6 \cdot \left(\frac{2}{3} - z\right)\right)}\right)\right) \]

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

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(\color{blue}{6} \cdot \left(\frac{2}{3} - z\right)\right)\right)\right) \]

   5. sub-neg N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(6 \cdot \left(\frac{2}{3} + \color{blue}{\left(\mathsf{neg}\left(z\right)\right)}\right)\right)\right)\right) \]

   6. distribute-lft-in N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(6 \cdot \frac{2}{3} + \color{blue}{6 \cdot \left(\mathsf{neg}\left(z\right)\right)}\right)\right)\right) \]

   7. *-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(6 \cdot \frac{2}{3} + \left(\mathsf{neg}\left(z\right)\right) \cdot \color{blue}{6}\right)\right)\right) \]

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

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(\left(6 \cdot \frac{2}{3}\right), \color{blue}{\left(\left(\mathsf{neg}\left(z\right)\right) \cdot 6\right)}\right)\right)\right) \]

   9. metadata-eval N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(\left(6 \cdot \frac{2}{3}\right), \left(\left(\mathsf{neg}\left(z\right)\right) \cdot 6\right)\right)\right)\right) \]

   10. metadata-eval N/A

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(\color{blue}{\left(\mathsf{neg}\left(z\right)\right)} \cdot 6\right)\right)\right)\right) \]

   11. distribute-lft-neg-out N/A

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(\mathsf{neg}\left(z \cdot 6\right)\right)\right)\right)\right) \]

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

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(z \cdot \color{blue}{\left(\mathsf{neg}\left(6\right)\right)}\right)\right)\right)\right) \]

   13. metadata-eval N/A

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(z \cdot -6\right)\right)\right)\right) \]

   14. metadata-eval N/A

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(z \cdot \left(6 \cdot \color{blue}{-1}\right)\right)\right)\right)\right) \]

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

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \mathsf{*.f64}\left(z, \color{blue}{\left(6 \cdot -1\right)}\right)\right)\right)\right) \]

   16. metadata-eval 99.8%

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \mathsf{*.f64}\left(z, -6\right)\right)\right)\right) \]

3. Simplified 99.8%

   \[\leadsto \color{blue}{x + \left(y - x\right) \cdot \left(4 + z \cdot -6\right)} \]
4. Add Preprocessing

5. Taylor expanded in z around 0

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

7. Simplified 47.2%

   \[\leadsto x + \left(y - x\right) \cdot \color{blue}{4} \]

8. Taylor expanded in x around inf

   \[\leadsto \color{blue}{-3 \cdot x} \]
9. Step-by-step derivation

   1. *-commutative N/A

      \[\leadsto x \cdot \color{blue}{-3} \]

   2. *-lowering-*.f64 23.0%

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{-3}\right) \]

10. Simplified 23.0%

    \[\leadsto \color{blue}{x \cdot -3} \]
11. Add Preprocessing

Reproduce

herbie shell --seed 2024155 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, D"
  :precision binary64
  (+ x (* (* (- y x) 6.0) (- (/ 2.0 3.0) z))))