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

Percentage Accurate: 99.5% → 99.8%

Time: 12.4s

Alternatives: 15

Speedup: 1.2×

• 21.4% 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: 99.8% 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: 50.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(z \cdot 6\right)\\ t_1 := y \cdot \left(z \cdot -6\right)\\ \mathbf{if}\;z \leq -3.8 \cdot 10^{+211}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -4200000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-62}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.6:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+170}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (* z 6.0))) (t_1 (* y (* z -6.0))))
   (if (<= z -3.8e+211)
     t_0
     (if (<= z -4200000000000.0)
       t_1
       (if (<= z -4.8e-62)
         (* x -3.0)
         (if (<= z 0.6) (* y 4.0) (if (<= z 6.2e+170) t_0 t_1)))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (z * 6.0);
	double t_1 = y * (z * -6.0);
	double tmp;
	if (z <= -3.8e+211) {
		tmp = t_0;
	} else if (z <= -4200000000000.0) {
		tmp = t_1;
	} else if (z <= -4.8e-62) {
		tmp = x * -3.0;
	} else if (z <= 0.6) {
		tmp = y * 4.0;
	} else if (z <= 6.2e+170) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	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) :: t_1
    real(8) :: tmp
    t_0 = x * (z * 6.0d0)
    t_1 = y * (z * (-6.0d0))
    if (z <= (-3.8d+211)) then
        tmp = t_0
    else if (z <= (-4200000000000.0d0)) then
        tmp = t_1
    else if (z <= (-4.8d-62)) then
        tmp = x * (-3.0d0)
    else if (z <= 0.6d0) then
        tmp = y * 4.0d0
    else if (z <= 6.2d+170) then
        tmp = t_0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (z * 6.0);
	double t_1 = y * (z * -6.0);
	double tmp;
	if (z <= -3.8e+211) {
		tmp = t_0;
	} else if (z <= -4200000000000.0) {
		tmp = t_1;
	} else if (z <= -4.8e-62) {
		tmp = x * -3.0;
	} else if (z <= 0.6) {
		tmp = y * 4.0;
	} else if (z <= 6.2e+170) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (z * 6.0)
	t_1 = y * (z * -6.0)
	tmp = 0
	if z <= -3.8e+211:
		tmp = t_0
	elif z <= -4200000000000.0:
		tmp = t_1
	elif z <= -4.8e-62:
		tmp = x * -3.0
	elif z <= 0.6:
		tmp = y * 4.0
	elif z <= 6.2e+170:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(z * 6.0))
	t_1 = Float64(y * Float64(z * -6.0))
	tmp = 0.0
	if (z <= -3.8e+211)
		tmp = t_0;
	elseif (z <= -4200000000000.0)
		tmp = t_1;
	elseif (z <= -4.8e-62)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.6)
		tmp = Float64(y * 4.0);
	elseif (z <= 6.2e+170)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (z * 6.0);
	t_1 = y * (z * -6.0);
	tmp = 0.0;
	if (z <= -3.8e+211)
		tmp = t_0;
	elseif (z <= -4200000000000.0)
		tmp = t_1;
	elseif (z <= -4.8e-62)
		tmp = x * -3.0;
	elseif (z <= 0.6)
		tmp = y * 4.0;
	elseif (z <= 6.2e+170)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(z * 6.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(y * N[(z * -6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.8e+211], t$95$0, If[LessEqual[z, -4200000000000.0], t$95$1, If[LessEqual[z, -4.8e-62], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.6], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 6.2e+170], t$95$0, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.80000000000000016e211 or 0.599999999999999978 < z < 6.2e170

   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 96.6%

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

   7. Simplified 96.6%

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

   8. Taylor expanded in y around 0

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

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

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 60.0%

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

   10. Simplified 60.0%

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

   11. Taylor expanded in z around inf

       \[\leadsto \color{blue}{6 \cdot \left(x \cdot z\right)} \]
   12. 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 60.1%

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

   13. Simplified 60.1%

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

   if -3.80000000000000016e211 < z < -4.2e12 or 6.2e170 < 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 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 65.4%

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

   5. Simplified 65.4%

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

   6. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

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

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 65.3%

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

   8. Simplified 65.3%

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

   if -4.2e12 < z < -4.79999999999999967e-62

   1. Initial program 98.9%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   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 77.8%

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

   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 65.8%

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

   10. Simplified 65.8%

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

   if -4.79999999999999967e-62 < z < 0.599999999999999978

   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 58.9%

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

   5. Simplified 58.9%

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

   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 59.2%

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

   8. Simplified 59.2%

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

Alternative 3: 74.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(y - x\right) \cdot \left(z \cdot -6\right)\\ \mathbf{if}\;z \leq -4200000000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-63}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{elif}\;z \leq 28000:\\ \;\;\;\;y \cdot \left(\left(0.6666666666666666 - z\right) \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (- y x) (* z -6.0))))
   (if (<= z -4200000000000.0)
     t_0
     (if (<= z -4.2e-63)
       (* x (+ -3.0 (* z 6.0)))
       (if (<= z 28000.0) (* y (* (- 0.6666666666666666 z) 6.0)) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = (y - x) * (z * -6.0);
	double tmp;
	if (z <= -4200000000000.0) {
		tmp = t_0;
	} else if (z <= -4.2e-63) {
		tmp = x * (-3.0 + (z * 6.0));
	} else if (z <= 28000.0) {
		tmp = y * ((0.6666666666666666 - 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 - x) * (z * (-6.0d0))
    if (z <= (-4200000000000.0d0)) then
        tmp = t_0
    else if (z <= (-4.2d-63)) then
        tmp = x * ((-3.0d0) + (z * 6.0d0))
    else if (z <= 28000.0d0) then
        tmp = y * ((0.6666666666666666d0 - 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 - x) * (z * -6.0);
	double tmp;
	if (z <= -4200000000000.0) {
		tmp = t_0;
	} else if (z <= -4.2e-63) {
		tmp = x * (-3.0 + (z * 6.0));
	} else if (z <= 28000.0) {
		tmp = y * ((0.6666666666666666 - z) * 6.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (y - x) * (z * -6.0)
	tmp = 0
	if z <= -4200000000000.0:
		tmp = t_0
	elif z <= -4.2e-63:
		tmp = x * (-3.0 + (z * 6.0))
	elif z <= 28000.0:
		tmp = y * ((0.6666666666666666 - z) * 6.0)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(y - x) * Float64(z * -6.0))
	tmp = 0.0
	if (z <= -4200000000000.0)
		tmp = t_0;
	elseif (z <= -4.2e-63)
		tmp = Float64(x * Float64(-3.0 + Float64(z * 6.0)));
	elseif (z <= 28000.0)
		tmp = Float64(y * Float64(Float64(0.6666666666666666 - z) * 6.0));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (y - x) * (z * -6.0);
	tmp = 0.0;
	if (z <= -4200000000000.0)
		tmp = t_0;
	elseif (z <= -4.2e-63)
		tmp = x * (-3.0 + (z * 6.0));
	elseif (z <= 28000.0)
		tmp = y * ((0.6666666666666666 - z) * 6.0);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(y - x), $MachinePrecision] * N[(z * -6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4200000000000.0], t$95$0, If[LessEqual[z, -4.2e-63], N[(x * N[(-3.0 + N[(z * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 28000.0], N[(y * N[(N[(0.6666666666666666 - z), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.2e12 or 28000 < 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

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

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

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

      2. associate-+r+ N/A

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

      3. +-commutative N/A

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

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

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

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

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

      6. *-commutative N/A

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

      7. associate-*r/ N/A

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

      8. *-commutative N/A

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

      9. associate-/l* N/A

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

      10. metadata-eval N/A

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

      11. associate-*r/ N/A

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

      12. distribute-lft-out N/A

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

      13. +-commutative N/A

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

      14. metadata-eval N/A

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

      15. sub-neg N/A

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

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

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

      17. --lowering--.f64 N/A

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

      18. sub-neg N/A

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

      19. metadata-eval N/A

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

      20. +-commutative N/A

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

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

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

      22. associate-*r/ N/A

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

      23. metadata-eval N/A

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

   5. Simplified 99.8%

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

   6. Taylor expanded in z around inf

      \[\leadsto \color{blue}{-6 \cdot \left(z \cdot \left(y - x\right)\right)} \]
   7. 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

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

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

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

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

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

      5. *-lowering-*.f64 99.2%

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

   8. Simplified 99.2%

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

   if -4.2e12 < z < -4.2e-63

   1. Initial program 98.9%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   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. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(1 + -6 \cdot \left(\frac{2}{3} + \color{blue}{\left(\mathsf{neg}\left(z\right)\right)}\right)\right)\right) \]

      3. neg-mul-1 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(1 + -6 \cdot \left(\frac{2}{3} + -1 \cdot \color{blue}{z}\right)\right)\right) \]

      4. distribute-lft-in N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(1 + \left(-6 \cdot \frac{2}{3} + \color{blue}{-6 \cdot \left(-1 \cdot z\right)}\right)\right)\right) \]

      5. metadata-eval N/A

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

      6. *-commutative N/A

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

      7. associate-*l* N/A

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

      8. associate-+r+ N/A

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

      9. *-commutative N/A

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

      10. +-commutative N/A

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

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

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

      12. associate-*r* N/A

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

      13. metadata-eval N/A

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

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

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

      15. metadata-eval 82.0%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(6, z\right), -3\right)\right) \]

   5. Simplified 82.0%

      \[\leadsto \color{blue}{x \cdot \left(6 \cdot z + -3\right)} \]

   if -4.2e-63 < z < 28000

   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 58.8%

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

   5. Simplified 58.8%

      \[\leadsto \color{blue}{6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

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

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

      4. *-commutative N/A

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

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

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

      6. --lowering--.f64 59.0%

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

   7. Applied egg-rr 59.0%

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

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4200000000000:\\ \;\;\;\;\left(y - x\right) \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-63}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{elif}\;z \leq 28000:\\ \;\;\;\;y \cdot \left(\left(0.6666666666666666 - z\right) \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot \left(z \cdot -6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \mathbf{if}\;z \leq -4200000000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-64}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{elif}\;z \leq 6500:\\ \;\;\;\;y \cdot \left(\left(0.6666666666666666 - z\right) \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (* (- y x) -6.0))))
   (if (<= z -4200000000000.0)
     t_0
     (if (<= z -9e-64)
       (* x (+ -3.0 (* z 6.0)))
       (if (<= z 6500.0) (* y (* (- 0.6666666666666666 z) 6.0)) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = z * ((y - x) * -6.0);
	double tmp;
	if (z <= -4200000000000.0) {
		tmp = t_0;
	} else if (z <= -9e-64) {
		tmp = x * (-3.0 + (z * 6.0));
	} else if (z <= 6500.0) {
		tmp = y * ((0.6666666666666666 - 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 = z * ((y - x) * (-6.0d0))
    if (z <= (-4200000000000.0d0)) then
        tmp = t_0
    else if (z <= (-9d-64)) then
        tmp = x * ((-3.0d0) + (z * 6.0d0))
    else if (z <= 6500.0d0) then
        tmp = y * ((0.6666666666666666d0 - 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 = z * ((y - x) * -6.0);
	double tmp;
	if (z <= -4200000000000.0) {
		tmp = t_0;
	} else if (z <= -9e-64) {
		tmp = x * (-3.0 + (z * 6.0));
	} else if (z <= 6500.0) {
		tmp = y * ((0.6666666666666666 - z) * 6.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * ((y - x) * -6.0)
	tmp = 0
	if z <= -4200000000000.0:
		tmp = t_0
	elif z <= -9e-64:
		tmp = x * (-3.0 + (z * 6.0))
	elif z <= 6500.0:
		tmp = y * ((0.6666666666666666 - z) * 6.0)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(Float64(y - x) * -6.0))
	tmp = 0.0
	if (z <= -4200000000000.0)
		tmp = t_0;
	elseif (z <= -9e-64)
		tmp = Float64(x * Float64(-3.0 + Float64(z * 6.0)));
	elseif (z <= 6500.0)
		tmp = Float64(y * Float64(Float64(0.6666666666666666 - z) * 6.0));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * ((y - x) * -6.0);
	tmp = 0.0;
	if (z <= -4200000000000.0)
		tmp = t_0;
	elseif (z <= -9e-64)
		tmp = x * (-3.0 + (z * 6.0));
	elseif (z <= 6500.0)
		tmp = y * ((0.6666666666666666 - z) * 6.0);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(N[(y - x), $MachinePrecision] * -6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4200000000000.0], t$95$0, If[LessEqual[z, -9e-64], N[(x * N[(-3.0 + N[(z * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6500.0], N[(y * N[(N[(0.6666666666666666 - z), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.2e12 or 6500 < 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 99.1%

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

   5. Simplified 99.1%

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

   if -4.2e12 < z < -9.00000000000000019e-64

   1. Initial program 98.9%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   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. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(1 + -6 \cdot \left(\frac{2}{3} + \color{blue}{\left(\mathsf{neg}\left(z\right)\right)}\right)\right)\right) \]

      3. neg-mul-1 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(1 + -6 \cdot \left(\frac{2}{3} + -1 \cdot \color{blue}{z}\right)\right)\right) \]

      4. distribute-lft-in N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(1 + \left(-6 \cdot \frac{2}{3} + \color{blue}{-6 \cdot \left(-1 \cdot z\right)}\right)\right)\right) \]

      5. metadata-eval N/A

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

      6. *-commutative N/A

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

      7. associate-*l* N/A

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

      8. associate-+r+ N/A

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

      9. *-commutative N/A

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

      10. +-commutative N/A

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

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

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

      12. associate-*r* N/A

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

      13. metadata-eval N/A

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

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

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

      15. metadata-eval 82.0%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(6, z\right), -3\right)\right) \]

   5. Simplified 82.0%

      \[\leadsto \color{blue}{x \cdot \left(6 \cdot z + -3\right)} \]

   if -9.00000000000000019e-64 < z < 6500

   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 58.8%

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

   5. Simplified 58.8%

      \[\leadsto \color{blue}{6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

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

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

      4. *-commutative N/A

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

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

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

      6. --lowering--.f64 59.0%

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

   7. Applied egg-rr 59.0%

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

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4200000000000:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-64}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{elif}\;z \leq 6500:\\ \;\;\;\;y \cdot \left(\left(0.6666666666666666 - z\right) \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \mathbf{if}\;z \leq -4200000000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-65}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{elif}\;z \leq 215000:\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (* (- y x) -6.0))))
   (if (<= z -4200000000000.0)
     t_0
     (if (<= z -1.6e-65)
       (* x (+ -3.0 (* z 6.0)))
       (if (<= z 215000.0) (* 6.0 (* y (- 0.6666666666666666 z))) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = z * ((y - x) * -6.0);
	double tmp;
	if (z <= -4200000000000.0) {
		tmp = t_0;
	} else if (z <= -1.6e-65) {
		tmp = x * (-3.0 + (z * 6.0));
	} else if (z <= 215000.0) {
		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 = z * ((y - x) * (-6.0d0))
    if (z <= (-4200000000000.0d0)) then
        tmp = t_0
    else if (z <= (-1.6d-65)) then
        tmp = x * ((-3.0d0) + (z * 6.0d0))
    else if (z <= 215000.0d0) 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 = z * ((y - x) * -6.0);
	double tmp;
	if (z <= -4200000000000.0) {
		tmp = t_0;
	} else if (z <= -1.6e-65) {
		tmp = x * (-3.0 + (z * 6.0));
	} else if (z <= 215000.0) {
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * ((y - x) * -6.0)
	tmp = 0
	if z <= -4200000000000.0:
		tmp = t_0
	elif z <= -1.6e-65:
		tmp = x * (-3.0 + (z * 6.0))
	elif z <= 215000.0:
		tmp = 6.0 * (y * (0.6666666666666666 - z))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(Float64(y - x) * -6.0))
	tmp = 0.0
	if (z <= -4200000000000.0)
		tmp = t_0;
	elseif (z <= -1.6e-65)
		tmp = Float64(x * Float64(-3.0 + Float64(z * 6.0)));
	elseif (z <= 215000.0)
		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 = z * ((y - x) * -6.0);
	tmp = 0.0;
	if (z <= -4200000000000.0)
		tmp = t_0;
	elseif (z <= -1.6e-65)
		tmp = x * (-3.0 + (z * 6.0));
	elseif (z <= 215000.0)
		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[(z * N[(N[(y - x), $MachinePrecision] * -6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4200000000000.0], t$95$0, If[LessEqual[z, -1.6e-65], N[(x * N[(-3.0 + N[(z * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 215000.0], N[(6.0 * N[(y * N[(0.6666666666666666 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.2e12 or 215000 < 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 99.1%

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

   5. Simplified 99.1%

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

   if -4.2e12 < z < -1.6e-65

   1. Initial program 98.9%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   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. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(1 + -6 \cdot \left(\frac{2}{3} + \color{blue}{\left(\mathsf{neg}\left(z\right)\right)}\right)\right)\right) \]

      3. neg-mul-1 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(1 + -6 \cdot \left(\frac{2}{3} + -1 \cdot \color{blue}{z}\right)\right)\right) \]

      4. distribute-lft-in N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(1 + \left(-6 \cdot \frac{2}{3} + \color{blue}{-6 \cdot \left(-1 \cdot z\right)}\right)\right)\right) \]

      5. metadata-eval N/A

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

      6. *-commutative N/A

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

      7. associate-*l* N/A

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

      8. associate-+r+ N/A

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

      9. *-commutative N/A

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

      10. +-commutative N/A

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

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

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

      12. associate-*r* N/A

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

      13. metadata-eval N/A

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

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

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

      15. metadata-eval 82.0%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(6, z\right), -3\right)\right) \]

   5. Simplified 82.0%

      \[\leadsto \color{blue}{x \cdot \left(6 \cdot z + -3\right)} \]

   if -1.6e-65 < z < 215000

   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 58.8%

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

   5. Simplified 58.8%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4200000000000:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-65}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{elif}\;z \leq 215000:\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 59.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \mathbf{if}\;y \leq -1.7 \cdot 10^{-99}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-300}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-147}:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 6.0 (* y (- 0.6666666666666666 z)))))
   (if (<= y -1.7e-99)
     t_0
     (if (<= y 2.3e-300)
       (* x (* z 6.0))
       (if (<= y 8.2e-147) (* x -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 <= -1.7e-99) {
		tmp = t_0;
	} else if (y <= 2.3e-300) {
		tmp = x * (z * 6.0);
	} else if (y <= 8.2e-147) {
		tmp = x * -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 <= (-1.7d-99)) then
        tmp = t_0
    else if (y <= 2.3d-300) then
        tmp = x * (z * 6.0d0)
    else if (y <= 8.2d-147) then
        tmp = x * (-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 <= -1.7e-99) {
		tmp = t_0;
	} else if (y <= 2.3e-300) {
		tmp = x * (z * 6.0);
	} else if (y <= 8.2e-147) {
		tmp = x * -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 <= -1.7e-99:
		tmp = t_0
	elif y <= 2.3e-300:
		tmp = x * (z * 6.0)
	elif y <= 8.2e-147:
		tmp = x * -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 <= -1.7e-99)
		tmp = t_0;
	elseif (y <= 2.3e-300)
		tmp = Float64(x * Float64(z * 6.0));
	elseif (y <= 8.2e-147)
		tmp = Float64(x * -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 <= -1.7e-99)
		tmp = t_0;
	elseif (y <= 2.3e-300)
		tmp = x * (z * 6.0);
	elseif (y <= 8.2e-147)
		tmp = x * -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, -1.7e-99], t$95$0, If[LessEqual[y, 2.3e-300], N[(x * N[(z * 6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.2e-147], N[(x * -3.0), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.70000000000000003e-99 or 8.1999999999999999e-147 < y

   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. 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 67.8%

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

   5. Simplified 67.8%

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

   if -1.70000000000000003e-99 < y < 2.30000000000000001e-300

   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 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 71.5%

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

   7. Simplified 71.5%

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

   8. Taylor expanded in y around 0

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

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

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 59.3%

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

   10. Simplified 59.3%

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

   11. Taylor expanded in z around inf

       \[\leadsto \color{blue}{6 \cdot \left(x \cdot z\right)} \]
   12. 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 60.0%

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

   13. Simplified 60.0%

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

   if 2.30000000000000001e-300 < y < 8.1999999999999999e-147

   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 66.4%

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

   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 57.4%

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

   10. Simplified 57.4%

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

Alternative 7: 50.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(z \cdot 6\right)\\ \mathbf{if}\;z \leq -0.5:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-61}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.68:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (* z 6.0))))
   (if (<= z -0.5)
     t_0
     (if (<= z -1.1e-61) (* x -3.0) (if (<= z 0.68) (* y 4.0) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = x * (z * 6.0);
	double tmp;
	if (z <= -0.5) {
		tmp = t_0;
	} else if (z <= -1.1e-61) {
		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 = x * (z * 6.0d0)
    if (z <= (-0.5d0)) then
        tmp = t_0
    else if (z <= (-1.1d-61)) 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 = x * (z * 6.0);
	double tmp;
	if (z <= -0.5) {
		tmp = t_0;
	} else if (z <= -1.1e-61) {
		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 = x * (z * 6.0)
	tmp = 0
	if z <= -0.5:
		tmp = t_0
	elif z <= -1.1e-61:
		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(x * Float64(z * 6.0))
	tmp = 0.0
	if (z <= -0.5)
		tmp = t_0;
	elseif (z <= -1.1e-61)
		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 = x * (z * 6.0);
	tmp = 0.0;
	if (z <= -0.5)
		tmp = t_0;
	elseif (z <= -1.1e-61)
		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[(x * N[(z * 6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.5], t$95$0, If[LessEqual[z, -1.1e-61], 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 < -0.5 or 0.680000000000000049 < z

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   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 97.8%

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

   7. Simplified 97.8%

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

   8. Taylor expanded in y around 0

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

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

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 49.8%

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

   10. Simplified 49.8%

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

   11. Taylor expanded in z around inf

       \[\leadsto \color{blue}{6 \cdot \left(x \cdot z\right)} \]
   12. 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 50.6%

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

   13. Simplified 50.6%

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

   if -0.5 < z < -1.10000000000000004e-61

   1. Initial program 99.0%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   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 92.6%

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

   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 78.0%

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

   10. Simplified 78.0%

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

   if -1.10000000000000004e-61 < 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 58.9%

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

   5. Simplified 58.9%

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

   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 59.2%

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

   8. Simplified 59.2%

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

Alternative 8: 97.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(y - x\right) \cdot \left(z \cdot -6\right)\\ \mathbf{if}\;z \leq -0.6:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 0.62:\\ \;\;\;\;y \cdot 4 + x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (- y x) (* z -6.0))))
   (if (<= z -0.6) t_0 (if (<= z 0.62) (+ (* y 4.0) (* x -3.0)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (y - x) * (z * -6.0);
	double tmp;
	if (z <= -0.6) {
		tmp = t_0;
	} else if (z <= 0.62) {
		tmp = (y * 4.0) + (x * -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 - x) * (z * (-6.0d0))
    if (z <= (-0.6d0)) then
        tmp = t_0
    else if (z <= 0.62d0) then
        tmp = (y * 4.0d0) + (x * (-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 - x) * (z * -6.0);
	double tmp;
	if (z <= -0.6) {
		tmp = t_0;
	} else if (z <= 0.62) {
		tmp = (y * 4.0) + (x * -3.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (y - x) * (z * -6.0)
	tmp = 0
	if z <= -0.6:
		tmp = t_0
	elif z <= 0.62:
		tmp = (y * 4.0) + (x * -3.0)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(y - x) * Float64(z * -6.0))
	tmp = 0.0
	if (z <= -0.6)
		tmp = t_0;
	elseif (z <= 0.62)
		tmp = Float64(Float64(y * 4.0) + Float64(x * -3.0));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (y - x) * (z * -6.0);
	tmp = 0.0;
	if (z <= -0.6)
		tmp = t_0;
	elseif (z <= 0.62)
		tmp = (y * 4.0) + (x * -3.0);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(y - x), $MachinePrecision] * N[(z * -6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.6], t$95$0, If[LessEqual[z, 0.62], N[(N[(y * 4.0), $MachinePrecision] + N[(x * -3.0), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -0.599999999999999978 or 0.619999999999999996 < 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

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

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

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

      2. associate-+r+ N/A

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

      3. +-commutative N/A

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

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

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

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

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

      6. *-commutative N/A

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

      7. associate-*r/ N/A

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

      8. *-commutative N/A

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

      9. associate-/l* N/A

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

      10. metadata-eval N/A

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

      11. associate-*r/ N/A

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

      12. distribute-lft-out N/A

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

      13. +-commutative N/A

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

      14. metadata-eval N/A

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

      15. sub-neg N/A

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

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

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

      17. --lowering--.f64 N/A

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

      18. sub-neg N/A

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

      19. metadata-eval N/A

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

      20. +-commutative N/A

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

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

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

      22. associate-*r/ N/A

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

      23. metadata-eval N/A

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

   5. Simplified 99.8%

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

   6. Taylor expanded in z around inf

      \[\leadsto \color{blue}{-6 \cdot \left(z \cdot \left(y - x\right)\right)} \]
   7. 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

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

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

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

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

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

      5. *-lowering-*.f64 97.8%

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

   8. Simplified 97.8%

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

   if -0.599999999999999978 < z < 0.619999999999999996

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

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

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

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

      4. metadata-eval N/A

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

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

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

      6. --lowering--.f64 99.4%

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

   4. Applied egg-rr 99.4%

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

   5. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. sub-neg N/A

         \[\leadsto 4 \cdot \left(y + \left(\mathsf{neg}\left(x\right)\right)\right) + x \]

      3. mul-1-neg N/A

         \[\leadsto 4 \cdot \left(y + -1 \cdot x\right) + x \]

      4. distribute-lft-in N/A

         \[\leadsto \left(4 \cdot y + 4 \cdot \left(-1 \cdot x\right)\right) + x \]

      5. mul-1-neg N/A

         \[\leadsto \left(4 \cdot y + 4 \cdot \left(\mathsf{neg}\left(x\right)\right)\right) + x \]

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

         \[\leadsto \left(4 \cdot y + \left(\mathsf{neg}\left(4 \cdot x\right)\right)\right) + x \]

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

         \[\leadsto \left(4 \cdot y + \left(\mathsf{neg}\left(4\right)\right) \cdot x\right) + x \]

      8. metadata-eval N/A

         \[\leadsto \left(4 \cdot y + -4 \cdot x\right) + x \]

      9. associate-+r+ N/A

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

      10. +-commutative N/A

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

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

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

      12. *-commutative N/A

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

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

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

      14. distribute-rgt1-in N/A

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

      15. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(-3 \cdot x\right)\right) \]

      16. *-commutative N/A

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

      17. *-lowering-*.f64 98.9%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \mathsf{*.f64}\left(x, \color{blue}{-3}\right)\right) \]

   7. Simplified 98.9%

      \[\leadsto \color{blue}{y \cdot 4 + x \cdot -3} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.6:\\ \;\;\;\;\left(y - x\right) \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq 0.62:\\ \;\;\;\;y \cdot 4 + x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot \left(z \cdot -6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 97.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(y - x\right) \cdot \left(z \cdot -6\right)\\ \mathbf{if}\;z \leq -0.6:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 0.6:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (- y x) (* z -6.0))))
   (if (<= z -0.6) t_0 (if (<= z 0.6) (+ x (* (- y x) 4.0)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (y - x) * (z * -6.0);
	double tmp;
	if (z <= -0.6) {
		tmp = t_0;
	} else if (z <= 0.6) {
		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 = (y - x) * (z * (-6.0d0))
    if (z <= (-0.6d0)) then
        tmp = t_0
    else if (z <= 0.6d0) 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 = (y - x) * (z * -6.0);
	double tmp;
	if (z <= -0.6) {
		tmp = t_0;
	} else if (z <= 0.6) {
		tmp = x + ((y - x) * 4.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (y - x) * (z * -6.0)
	tmp = 0
	if z <= -0.6:
		tmp = t_0
	elif z <= 0.6:
		tmp = x + ((y - x) * 4.0)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(y - x) * Float64(z * -6.0))
	tmp = 0.0
	if (z <= -0.6)
		tmp = t_0;
	elseif (z <= 0.6)
		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 = (y - x) * (z * -6.0);
	tmp = 0.0;
	if (z <= -0.6)
		tmp = t_0;
	elseif (z <= 0.6)
		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[(N[(y - x), $MachinePrecision] * N[(z * -6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.6], t$95$0, If[LessEqual[z, 0.6], N[(x + N[(N[(y - x), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -0.599999999999999978 or 0.599999999999999978 < 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

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

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

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

      2. associate-+r+ N/A

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

      3. +-commutative N/A

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

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

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

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

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

      6. *-commutative N/A

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

      7. associate-*r/ N/A

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

      8. *-commutative N/A

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

      9. associate-/l* N/A

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

      10. metadata-eval N/A

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

      11. associate-*r/ N/A

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

      12. distribute-lft-out N/A

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

      13. +-commutative N/A

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

      14. metadata-eval N/A

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

      15. sub-neg N/A

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

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

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

      17. --lowering--.f64 N/A

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

      18. sub-neg N/A

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

      19. metadata-eval N/A

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

      20. +-commutative N/A

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

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

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

      22. associate-*r/ N/A

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

      23. metadata-eval N/A

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

   5. Simplified 99.8%

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

   6. Taylor expanded in z around inf

      \[\leadsto \color{blue}{-6 \cdot \left(z \cdot \left(y - x\right)\right)} \]
   7. 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

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

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

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

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

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

      5. *-lowering-*.f64 97.8%

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

   8. Simplified 97.8%

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

   if -0.599999999999999978 < z < 0.599999999999999978

   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 99.8%

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

   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 98.8%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.6:\\ \;\;\;\;\left(y - x\right) \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq 0.6:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot \left(z \cdot -6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 76.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{if}\;x \leq -2.5 \cdot 10^{-45}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 175000:\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ -3.0 (* z 6.0)))))
   (if (<= x -2.5e-45)
     t_0
     (if (<= x 175000.0) (* 6.0 (* y (- 0.6666666666666666 z))) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x * (-3.0 + (z * 6.0));
	double tmp;
	if (x <= -2.5e-45) {
		tmp = t_0;
	} else if (x <= 175000.0) {
		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 = x * ((-3.0d0) + (z * 6.0d0))
    if (x <= (-2.5d-45)) then
        tmp = t_0
    else if (x <= 175000.0d0) 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 = x * (-3.0 + (z * 6.0));
	double tmp;
	if (x <= -2.5e-45) {
		tmp = t_0;
	} else if (x <= 175000.0) {
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (-3.0 + (z * 6.0))
	tmp = 0
	if x <= -2.5e-45:
		tmp = t_0
	elif x <= 175000.0:
		tmp = 6.0 * (y * (0.6666666666666666 - z))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(-3.0 + Float64(z * 6.0)))
	tmp = 0.0
	if (x <= -2.5e-45)
		tmp = t_0;
	elseif (x <= 175000.0)
		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 = x * (-3.0 + (z * 6.0));
	tmp = 0.0;
	if (x <= -2.5e-45)
		tmp = t_0;
	elseif (x <= 175000.0)
		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[(x * N[(-3.0 + N[(z * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.5e-45], t$95$0, If[LessEqual[x, 175000.0], N[(6.0 * N[(y * N[(0.6666666666666666 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.49999999999999988e-45 or 175000 < x

   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. 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. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(1 + -6 \cdot \left(\frac{2}{3} + \color{blue}{\left(\mathsf{neg}\left(z\right)\right)}\right)\right)\right) \]

      3. neg-mul-1 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(1 + -6 \cdot \left(\frac{2}{3} + -1 \cdot \color{blue}{z}\right)\right)\right) \]

      4. distribute-lft-in N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(1 + \left(-6 \cdot \frac{2}{3} + \color{blue}{-6 \cdot \left(-1 \cdot z\right)}\right)\right)\right) \]

      5. metadata-eval N/A

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

      6. *-commutative N/A

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

      7. associate-*l* N/A

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

      8. associate-+r+ N/A

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

      9. *-commutative N/A

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

      10. +-commutative N/A

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

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

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

      12. associate-*r* N/A

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

      13. metadata-eval N/A

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

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

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

      15. metadata-eval 76.0%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(6, z\right), -3\right)\right) \]

   5. Simplified 76.0%

      \[\leadsto \color{blue}{x \cdot \left(6 \cdot z + -3\right)} \]

   if -2.49999999999999988e-45 < x < 175000

   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 78.8%

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

   5. Simplified 78.8%

      \[\leadsto \color{blue}{6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{-45}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{elif}\;x \leq 175000:\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 37.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{-66}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-37}:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;y \cdot 4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -8.5e-66) (* y 4.0) (if (<= y 1.5e-37) (* x -3.0) (* y 4.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -8.5e-66) {
		tmp = y * 4.0;
	} else if (y <= 1.5e-37) {
		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 <= (-8.5d-66)) then
        tmp = y * 4.0d0
    else if (y <= 1.5d-37) 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 <= -8.5e-66) {
		tmp = y * 4.0;
	} else if (y <= 1.5e-37) {
		tmp = x * -3.0;
	} else {
		tmp = y * 4.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -8.5e-66:
		tmp = y * 4.0
	elif y <= 1.5e-37:
		tmp = x * -3.0
	else:
		tmp = y * 4.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -8.5e-66)
		tmp = Float64(y * 4.0);
	elseif (y <= 1.5e-37)
		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 <= -8.5e-66)
		tmp = y * 4.0;
	elseif (y <= 1.5e-37)
		tmp = x * -3.0;
	else
		tmp = y * 4.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -8.5e-66], N[(y * 4.0), $MachinePrecision], If[LessEqual[y, 1.5e-37], N[(x * -3.0), $MachinePrecision], N[(y * 4.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -8.49999999999999966e-66 or 1.5e-37 < y

   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. 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 73.2%

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

   5. Simplified 73.2%

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

   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 36.3%

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

   8. Simplified 36.3%

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

   if -8.49999999999999966e-66 < y < 1.5e-37

   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 44.5%

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

   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 35.7%

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

   10. Simplified 35.7%

       \[\leadsto \color{blue}{x \cdot -3} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 12: 99.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ x + \left(0.6666666666666666 - z\right) \cdot \left(\left(y - x\right) \cdot 6\right) \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ x (* (- 0.6666666666666666 z) (* (- y x) 6.0))))

C

double code(double x, double y, double z) {
	return x + ((0.6666666666666666 - z) * ((y - x) * 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 + ((0.6666666666666666d0 - z) * ((y - x) * 6.0d0))
end function

Java

public static double code(double x, double y, double z) {
	return x + ((0.6666666666666666 - z) * ((y - x) * 6.0));
}

Python

def code(x, y, z):
	return x + ((0.6666666666666666 - z) * ((y - x) * 6.0))

Julia

function code(x, y, z)
	return Float64(x + Float64(Float64(0.6666666666666666 - z) * Float64(Float64(y - x) * 6.0)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + ((0.6666666666666666 - z) * ((y - x) * 6.0));
end

Wolfram

code[x_, y_, z_] := N[(x + N[(N[(0.6666666666666666 - z), $MachinePrecision] * N[(N[(y - x), $MachinePrecision] * 6.0), $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. 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. *-lowering-*.f64 N/A

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

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

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

   4. metadata-eval N/A

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

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

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

   6. --lowering--.f64 99.6%

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

4. Applied egg-rr 99.6%

   \[\leadsto x + \color{blue}{\left(0.6666666666666666 - z\right) \cdot \left(\left(y - x\right) \cdot 6\right)} \]
5. Add Preprocessing

Alternative 13: 99.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ x + 6 \cdot \left(\left(y - x\right) \cdot \left(0.6666666666666666 - z\right)\right) \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ x (* 6.0 (* (- y x) (- 0.6666666666666666 z)))))

C

double code(double x, double y, double z) {
	return x + (6.0 * ((y - x) * (0.6666666666666666 - 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 + (6.0d0 * ((y - x) * (0.6666666666666666d0 - z)))
end function

Java

public static double code(double x, double y, double z) {
	return x + (6.0 * ((y - x) * (0.6666666666666666 - z)));
}

Python

def code(x, y, z):
	return x + (6.0 * ((y - x) * (0.6666666666666666 - z)))

Julia

function code(x, y, z)
	return Float64(x + Float64(6.0 * Float64(Float64(y - x) * Float64(0.6666666666666666 - z))))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + (6.0 * ((y - x) * (0.6666666666666666 - z)));
end

Wolfram

code[x_, y_, z_] := N[(x + N[(6.0 * N[(N[(y - x), $MachinePrecision] * N[(0.6666666666666666 - z), $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. 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%

   \[\leadsto x + 6 \cdot \left(\left(y - x\right) \cdot \left(0.6666666666666666 - z\right)\right) \]
6. Add Preprocessing

Alternative 14: 25.4% 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 45.9%

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

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 21.3%

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

10. Simplified 21.3%

    \[\leadsto \color{blue}{x \cdot -3} \]
11. Add Preprocessing

Alternative 15: 2.6% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 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 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 55.8%

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

7. Simplified 55.8%

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

8. Taylor expanded in z around 0

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

10. Simplified 2.9%

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

Reproduce

herbie shell --seed 2024161 
(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))))