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

Percentage Accurate: 99.7% → 98.5%

Time: 10.8s

Alternatives: 13

Speedup: 1.1×

• 21.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(\mathsf{fma}\left(z, -6, 1\right), x, \left(z \cdot 6\right) \cdot y\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (fma (fma z -6.0 1.0) x (* (* z 6.0) y)))

C

double code(double x, double y, double z) {
	return fma(fma(z, -6.0, 1.0), x, ((z * 6.0) * y));
}

Julia

function code(x, y, z)
	return fma(fma(z, -6.0, 1.0), x, Float64(Float64(z * 6.0) * y))
end

Wolfram

code[x_, y_, z_] := N[(N[(z * -6.0 + 1.0), $MachinePrecision] * x + N[(N[(z * 6.0), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.8%

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

   1. lift--.f64 N/A

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

   2. associate-*l* N/A

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

   3. *-commutative N/A

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

   4. lift--.f64 N/A

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

   5. sub-neg N/A

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

   6. +-commutative N/A

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

   7. distribute-lft-in N/A

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

   8. lower-fma.f64 N/A

      \[\leadsto x + \color{blue}{\mathsf{fma}\left(6 \cdot z, \mathsf{neg}\left(x\right), \left(6 \cdot z\right) \cdot y\right)} \]

   9. lower-*.f64 N/A

      \[\leadsto x + \mathsf{fma}\left(\color{blue}{6 \cdot z}, \mathsf{neg}\left(x\right), \left(6 \cdot z\right) \cdot y\right) \]

   10. lower-neg.f64 N/A

       \[\leadsto x + \mathsf{fma}\left(6 \cdot z, \color{blue}{\mathsf{neg}\left(x\right)}, \left(6 \cdot z\right) \cdot y\right) \]

   11. lower-*.f64 N/A

       \[\leadsto x + \mathsf{fma}\left(6 \cdot z, \mathsf{neg}\left(x\right), \color{blue}{\left(6 \cdot z\right) \cdot y}\right) \]

   12. lower-*.f64 99.8

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

4. Applied egg-rr 99.8%

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

   1. lift-*.f64 N/A

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

   2. lift-neg.f64 N/A

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

   3. lift-*.f64 N/A

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

   4. lift-*.f64 N/A

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

   5. associate-+r+ N/A

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

   6. lift-neg.f64 N/A

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

   7. distribute-rgt-neg-out N/A

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

   8. unsub-neg N/A

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

   9. lift-*.f64 N/A

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

   10. associate-*l* N/A

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

   11. *-commutative N/A

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

   12. cancel-sign-sub-inv N/A

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

   13. metadata-eval N/A

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

   14. *-commutative N/A

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

   15. associate-*l* N/A

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

   16. *-commutative N/A

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

   17. lift-*.f64 N/A

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

   18. distribute-rgt1-in N/A

       \[\leadsto \color{blue}{\left(z \cdot -6 + 1\right) \cdot x} + \left(6 \cdot z\right) \cdot y \]

   19. lower-fma.f64 N/A

       \[\leadsto \color{blue}{\mathsf{fma}\left(z \cdot -6 + 1, x, \left(6 \cdot z\right) \cdot y\right)} \]

6. Applied egg-rr 99.9%

   \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(z, -6, 1\right), x, \left(6 \cdot z\right) \cdot y\right)} \]

7. Final simplification 99.9%

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

Alternative 2: 60.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(z \cdot y\right)\\ \mathbf{if}\;z \leq -4.5 \cdot 10^{+190}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-5}:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq 2.75 \cdot 10^{-39}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+91}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+230}:\\ \;\;\;\;z \cdot \left(-6 \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot 6\right) \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 6.0 (* z y))))
   (if (<= z -4.5e+190)
     t_0
     (if (<= z -7e-5)
       (* x (* z -6.0))
       (if (<= z 2.75e-39)
         x
         (if (<= z 1.1e+91)
           t_0
           (if (<= z 3e+230) (* z (* -6.0 x)) (* (* z 6.0) y))))))))

C

double code(double x, double y, double z) {
	double t_0 = 6.0 * (z * y);
	double tmp;
	if (z <= -4.5e+190) {
		tmp = t_0;
	} else if (z <= -7e-5) {
		tmp = x * (z * -6.0);
	} else if (z <= 2.75e-39) {
		tmp = x;
	} else if (z <= 1.1e+91) {
		tmp = t_0;
	} else if (z <= 3e+230) {
		tmp = z * (-6.0 * x);
	} else {
		tmp = (z * 6.0) * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 6.0d0 * (z * y)
    if (z <= (-4.5d+190)) then
        tmp = t_0
    else if (z <= (-7d-5)) then
        tmp = x * (z * (-6.0d0))
    else if (z <= 2.75d-39) then
        tmp = x
    else if (z <= 1.1d+91) then
        tmp = t_0
    else if (z <= 3d+230) then
        tmp = z * ((-6.0d0) * x)
    else
        tmp = (z * 6.0d0) * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 6.0 * (z * y);
	double tmp;
	if (z <= -4.5e+190) {
		tmp = t_0;
	} else if (z <= -7e-5) {
		tmp = x * (z * -6.0);
	} else if (z <= 2.75e-39) {
		tmp = x;
	} else if (z <= 1.1e+91) {
		tmp = t_0;
	} else if (z <= 3e+230) {
		tmp = z * (-6.0 * x);
	} else {
		tmp = (z * 6.0) * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 6.0 * (z * y)
	tmp = 0
	if z <= -4.5e+190:
		tmp = t_0
	elif z <= -7e-5:
		tmp = x * (z * -6.0)
	elif z <= 2.75e-39:
		tmp = x
	elif z <= 1.1e+91:
		tmp = t_0
	elif z <= 3e+230:
		tmp = z * (-6.0 * x)
	else:
		tmp = (z * 6.0) * y
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(6.0 * Float64(z * y))
	tmp = 0.0
	if (z <= -4.5e+190)
		tmp = t_0;
	elseif (z <= -7e-5)
		tmp = Float64(x * Float64(z * -6.0));
	elseif (z <= 2.75e-39)
		tmp = x;
	elseif (z <= 1.1e+91)
		tmp = t_0;
	elseif (z <= 3e+230)
		tmp = Float64(z * Float64(-6.0 * x));
	else
		tmp = Float64(Float64(z * 6.0) * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 6.0 * (z * y);
	tmp = 0.0;
	if (z <= -4.5e+190)
		tmp = t_0;
	elseif (z <= -7e-5)
		tmp = x * (z * -6.0);
	elseif (z <= 2.75e-39)
		tmp = x;
	elseif (z <= 1.1e+91)
		tmp = t_0;
	elseif (z <= 3e+230)
		tmp = z * (-6.0 * x);
	else
		tmp = (z * 6.0) * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(6.0 * N[(z * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.5e+190], t$95$0, If[LessEqual[z, -7e-5], N[(x * N[(z * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.75e-39], x, If[LessEqual[z, 1.1e+91], t$95$0, If[LessEqual[z, 3e+230], N[(z * N[(-6.0 * x), $MachinePrecision]), $MachinePrecision], N[(N[(z * 6.0), $MachinePrecision] * y), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -4.4999999999999999e190 or 2.75000000000000009e-39 < z < 1.1e91

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 65.9

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

   5. Simplified 65.9%

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

   if -4.4999999999999999e190 < z < -6.9999999999999994e-5

   1. Initial program 99.6%

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

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

      2. distribute-lft-out-- N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. metadata-eval N/A

         \[\leadsto \color{blue}{\left(-1 \cdot -6\right)} \cdot \left(y \cdot z\right) - \left(6 \cdot z\right) \cdot x \]

      6. associate-*r* N/A

         \[\leadsto \color{blue}{-1 \cdot \left(-6 \cdot \left(y \cdot z\right)\right)} - \left(6 \cdot z\right) \cdot x \]

      7. *-commutative N/A

         \[\leadsto -1 \cdot \left(-6 \cdot \color{blue}{\left(z \cdot y\right)}\right) - \left(6 \cdot z\right) \cdot x \]

      8. associate-*r* N/A

         \[\leadsto -1 \cdot \color{blue}{\left(\left(-6 \cdot z\right) \cdot y\right)} - \left(6 \cdot z\right) \cdot x \]

      9. *-commutative N/A

         \[\leadsto -1 \cdot \color{blue}{\left(y \cdot \left(-6 \cdot z\right)\right)} - \left(6 \cdot z\right) \cdot x \]

      10. associate-*r* N/A

          \[\leadsto \color{blue}{\left(-1 \cdot y\right) \cdot \left(-6 \cdot z\right)} - \left(6 \cdot z\right) \cdot x \]

      11. *-commutative N/A

          \[\leadsto \left(-1 \cdot y\right) \cdot \left(-6 \cdot z\right) - \color{blue}{x \cdot \left(6 \cdot z\right)} \]

      12. metadata-eval N/A

          \[\leadsto \left(-1 \cdot y\right) \cdot \left(-6 \cdot z\right) - x \cdot \left(\color{blue}{\left(\mathsf{neg}\left(-6\right)\right)} \cdot z\right) \]

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

          \[\leadsto \left(-1 \cdot y\right) \cdot \left(-6 \cdot z\right) - x \cdot \color{blue}{\left(\mathsf{neg}\left(-6 \cdot z\right)\right)} \]

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

          \[\leadsto \left(-1 \cdot y\right) \cdot \left(-6 \cdot z\right) - \color{blue}{\left(\mathsf{neg}\left(x \cdot \left(-6 \cdot z\right)\right)\right)} \]

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

          \[\leadsto \left(-1 \cdot y\right) \cdot \left(-6 \cdot z\right) - \color{blue}{\left(\mathsf{neg}\left(x\right)\right) \cdot \left(-6 \cdot z\right)} \]

      16. mul-1-neg N/A

          \[\leadsto \left(-1 \cdot y\right) \cdot \left(-6 \cdot z\right) - \color{blue}{\left(-1 \cdot x\right)} \cdot \left(-6 \cdot z\right) \]

      17. distribute-rgt-out-- N/A

          \[\leadsto \color{blue}{\left(-6 \cdot z\right) \cdot \left(-1 \cdot y - -1 \cdot x\right)} \]

      18. distribute-lft-out-- N/A

          \[\leadsto \left(-6 \cdot z\right) \cdot \color{blue}{\left(-1 \cdot \left(y - x\right)\right)} \]

      19. neg-mul-1 N/A

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

      20. neg-sub0 N/A

          \[\leadsto \left(-6 \cdot z\right) \cdot \color{blue}{\left(0 - \left(y - x\right)\right)} \]

      21. associate-+l- N/A

          \[\leadsto \left(-6 \cdot z\right) \cdot \color{blue}{\left(\left(0 - y\right) + x\right)} \]

      22. neg-sub0 N/A

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

      23. mul-1-neg N/A

          \[\leadsto \left(-6 \cdot z\right) \cdot \left(\color{blue}{-1 \cdot y} + x\right) \]

      24. *-lft-identity N/A

          \[\leadsto \left(-6 \cdot z\right) \cdot \left(\color{blue}{1 \cdot \left(-1 \cdot y\right)} + x\right) \]

      25. *-inverses N/A

          \[\leadsto \left(-6 \cdot z\right) \cdot \left(\color{blue}{\frac{x}{x}} \cdot \left(-1 \cdot y\right) + x\right) \]

      26. associate-*l/ N/A

          \[\leadsto \left(-6 \cdot z\right) \cdot \left(\color{blue}{\frac{x \cdot \left(-1 \cdot y\right)}{x}} + x\right) \]

      27. associate-*r/ N/A

          \[\leadsto \left(-6 \cdot z\right) \cdot \left(\color{blue}{x \cdot \frac{-1 \cdot y}{x}} + x\right) \]

      28. associate-*r/ N/A

          \[\leadsto \left(-6 \cdot z\right) \cdot \left(x \cdot \color{blue}{\left(-1 \cdot \frac{y}{x}\right)} + x\right) \]

      29. *-rgt-identity N/A

          \[\leadsto \left(-6 \cdot z\right) \cdot \left(x \cdot \left(-1 \cdot \frac{y}{x}\right) + \color{blue}{x \cdot 1}\right) \]

   5. Simplified 96.2%

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

   6. Taylor expanded in x around inf

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

      1. metadata-eval N/A

         \[\leadsto \color{blue}{\left(-1 \cdot 6\right)} \cdot \left(x \cdot z\right) \]

      2. associate-*r* N/A

         \[\leadsto \color{blue}{-1 \cdot \left(6 \cdot \left(x \cdot z\right)\right)} \]

      3. associate-*r* N/A

         \[\leadsto -1 \cdot \color{blue}{\left(\left(6 \cdot x\right) \cdot z\right)} \]

      4. associate-*r* N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(6 \cdot x\right)\right) \cdot z} \]

      5. *-commutative N/A

         \[\leadsto \left(-1 \cdot \color{blue}{\left(x \cdot 6\right)}\right) \cdot z \]

      6. associate-*l* N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot x\right) \cdot 6\right)} \cdot z \]

      7. *-commutative N/A

         \[\leadsto \color{blue}{z \cdot \left(\left(-1 \cdot x\right) \cdot 6\right)} \]

      8. lower-*.f64 N/A

         \[\leadsto \color{blue}{z \cdot \left(\left(-1 \cdot x\right) \cdot 6\right)} \]

      9. *-commutative N/A

         \[\leadsto z \cdot \color{blue}{\left(6 \cdot \left(-1 \cdot x\right)\right)} \]

      10. associate-*r* N/A

          \[\leadsto z \cdot \color{blue}{\left(\left(6 \cdot -1\right) \cdot x\right)} \]

      11. metadata-eval N/A

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

      12. lower-*.f64 53.8

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

   8. Simplified 53.8%

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 53.8

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

   10. Applied egg-rr 53.8%

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

   if -6.9999999999999994e-5 < z < 2.75000000000000009e-39

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 75.5

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

   5. Simplified 75.5%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. distribute-rgt1-in N/A

         \[\leadsto \color{blue}{\left(z \cdot -6 + 1\right) \cdot x} \]

      4. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(z \cdot -6 + 1\right) \cdot x} \]

      5. lift-*.f64 N/A

         \[\leadsto \left(\color{blue}{z \cdot -6} + 1\right) \cdot x \]

      6. lower-fma.f64 75.5

         \[\leadsto \color{blue}{\mathsf{fma}\left(z, -6, 1\right)} \cdot x \]

   7. Applied egg-rr 75.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z, -6, 1\right) \cdot x} \]

   8. Taylor expanded in z around 0

      \[\leadsto \color{blue}{1} \cdot x \]
   9. Step-by-step derivation

   10. Simplified 75.2%

       \[\leadsto \color{blue}{1} \cdot x \]
   11. Step-by-step derivation

       1. *-lft-identity 75.2

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

   12. Applied egg-rr 75.2%

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

   if 1.1e91 < z < 3.00000000000000008e230

   1. Initial program 99.8%

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

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

      2. distribute-lft-out-- N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. metadata-eval N/A

         \[\leadsto \color{blue}{\left(-1 \cdot -6\right)} \cdot \left(y \cdot z\right) - \left(6 \cdot z\right) \cdot x \]

      6. associate-*r* N/A

         \[\leadsto \color{blue}{-1 \cdot \left(-6 \cdot \left(y \cdot z\right)\right)} - \left(6 \cdot z\right) \cdot x \]

      7. *-commutative N/A

         \[\leadsto -1 \cdot \left(-6 \cdot \color{blue}{\left(z \cdot y\right)}\right) - \left(6 \cdot z\right) \cdot x \]

      8. associate-*r* N/A

         \[\leadsto -1 \cdot \color{blue}{\left(\left(-6 \cdot z\right) \cdot y\right)} - \left(6 \cdot z\right) \cdot x \]

      9. *-commutative N/A

         \[\leadsto -1 \cdot \color{blue}{\left(y \cdot \left(-6 \cdot z\right)\right)} - \left(6 \cdot z\right) \cdot x \]

      10. associate-*r* N/A

          \[\leadsto \color{blue}{\left(-1 \cdot y\right) \cdot \left(-6 \cdot z\right)} - \left(6 \cdot z\right) \cdot x \]

      11. *-commutative N/A

          \[\leadsto \left(-1 \cdot y\right) \cdot \left(-6 \cdot z\right) - \color{blue}{x \cdot \left(6 \cdot z\right)} \]

      12. metadata-eval N/A

          \[\leadsto \left(-1 \cdot y\right) \cdot \left(-6 \cdot z\right) - x \cdot \left(\color{blue}{\left(\mathsf{neg}\left(-6\right)\right)} \cdot z\right) \]

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

          \[\leadsto \left(-1 \cdot y\right) \cdot \left(-6 \cdot z\right) - x \cdot \color{blue}{\left(\mathsf{neg}\left(-6 \cdot z\right)\right)} \]

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

          \[\leadsto \left(-1 \cdot y\right) \cdot \left(-6 \cdot z\right) - \color{blue}{\left(\mathsf{neg}\left(x \cdot \left(-6 \cdot z\right)\right)\right)} \]

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

          \[\leadsto \left(-1 \cdot y\right) \cdot \left(-6 \cdot z\right) - \color{blue}{\left(\mathsf{neg}\left(x\right)\right) \cdot \left(-6 \cdot z\right)} \]

      16. mul-1-neg N/A

          \[\leadsto \left(-1 \cdot y\right) \cdot \left(-6 \cdot z\right) - \color{blue}{\left(-1 \cdot x\right)} \cdot \left(-6 \cdot z\right) \]

      17. distribute-rgt-out-- N/A

          \[\leadsto \color{blue}{\left(-6 \cdot z\right) \cdot \left(-1 \cdot y - -1 \cdot x\right)} \]

      18. distribute-lft-out-- N/A

          \[\leadsto \left(-6 \cdot z\right) \cdot \color{blue}{\left(-1 \cdot \left(y - x\right)\right)} \]

      19. neg-mul-1 N/A

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

      20. neg-sub0 N/A

          \[\leadsto \left(-6 \cdot z\right) \cdot \color{blue}{\left(0 - \left(y - x\right)\right)} \]

      21. associate-+l- N/A

          \[\leadsto \left(-6 \cdot z\right) \cdot \color{blue}{\left(\left(0 - y\right) + x\right)} \]

      22. neg-sub0 N/A

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

      23. mul-1-neg N/A

          \[\leadsto \left(-6 \cdot z\right) \cdot \left(\color{blue}{-1 \cdot y} + x\right) \]

      24. *-lft-identity N/A

          \[\leadsto \left(-6 \cdot z\right) \cdot \left(\color{blue}{1 \cdot \left(-1 \cdot y\right)} + x\right) \]

      25. *-inverses N/A

          \[\leadsto \left(-6 \cdot z\right) \cdot \left(\color{blue}{\frac{x}{x}} \cdot \left(-1 \cdot y\right) + x\right) \]

      26. associate-*l/ N/A

          \[\leadsto \left(-6 \cdot z\right) \cdot \left(\color{blue}{\frac{x \cdot \left(-1 \cdot y\right)}{x}} + x\right) \]

      27. associate-*r/ N/A

          \[\leadsto \left(-6 \cdot z\right) \cdot \left(\color{blue}{x \cdot \frac{-1 \cdot y}{x}} + x\right) \]

      28. associate-*r/ N/A

          \[\leadsto \left(-6 \cdot z\right) \cdot \left(x \cdot \color{blue}{\left(-1 \cdot \frac{y}{x}\right)} + x\right) \]

      29. *-rgt-identity N/A

          \[\leadsto \left(-6 \cdot z\right) \cdot \left(x \cdot \left(-1 \cdot \frac{y}{x}\right) + \color{blue}{x \cdot 1}\right) \]

   5. Simplified 99.8%

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

   6. Taylor expanded in x around inf

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

      1. metadata-eval N/A

         \[\leadsto \color{blue}{\left(-1 \cdot 6\right)} \cdot \left(x \cdot z\right) \]

      2. associate-*r* N/A

         \[\leadsto \color{blue}{-1 \cdot \left(6 \cdot \left(x \cdot z\right)\right)} \]

      3. associate-*r* N/A

         \[\leadsto -1 \cdot \color{blue}{\left(\left(6 \cdot x\right) \cdot z\right)} \]

      4. associate-*r* N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(6 \cdot x\right)\right) \cdot z} \]

      5. *-commutative N/A

         \[\leadsto \left(-1 \cdot \color{blue}{\left(x \cdot 6\right)}\right) \cdot z \]

      6. associate-*l* N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot x\right) \cdot 6\right)} \cdot z \]

      7. *-commutative N/A

         \[\leadsto \color{blue}{z \cdot \left(\left(-1 \cdot x\right) \cdot 6\right)} \]

      8. lower-*.f64 N/A

         \[\leadsto \color{blue}{z \cdot \left(\left(-1 \cdot x\right) \cdot 6\right)} \]

      9. *-commutative N/A

         \[\leadsto z \cdot \color{blue}{\left(6 \cdot \left(-1 \cdot x\right)\right)} \]

      10. associate-*r* N/A

          \[\leadsto z \cdot \color{blue}{\left(\left(6 \cdot -1\right) \cdot x\right)} \]

      11. metadata-eval N/A

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

      12. lower-*.f64 72.1

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

   8. Simplified 72.1%

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

   if 3.00000000000000008e230 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 81.4

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

   5. Simplified 81.4%

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

      1. *-commutative N/A

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

      2. associate-*l* N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 81.5

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

   7. Applied egg-rr 81.5%

      \[\leadsto \color{blue}{\left(6 \cdot z\right) \cdot y} \]
3. Recombined 5 regimes into one program.

4. Final simplification 69.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+190}:\\ \;\;\;\;6 \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-5}:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq 2.75 \cdot 10^{-39}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+91}:\\ \;\;\;\;6 \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+230}:\\ \;\;\;\;z \cdot \left(-6 \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot 6\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 60.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(z \cdot y\right)\\ t_1 := z \cdot \left(-6 \cdot x\right)\\ \mathbf{if}\;z \leq -3.2 \cdot 10^{+188}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-5}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-39}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+91}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+230}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot 6\right) \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 6.0 (* z y))) (t_1 (* z (* -6.0 x))))
   (if (<= z -3.2e+188)
     t_0
     (if (<= z -7e-5)
       t_1
       (if (<= z 2e-39)
         x
         (if (<= z 1.5e+91) t_0 (if (<= z 8.2e+230) t_1 (* (* z 6.0) y))))))))

C

double code(double x, double y, double z) {
	double t_0 = 6.0 * (z * y);
	double t_1 = z * (-6.0 * x);
	double tmp;
	if (z <= -3.2e+188) {
		tmp = t_0;
	} else if (z <= -7e-5) {
		tmp = t_1;
	} else if (z <= 2e-39) {
		tmp = x;
	} else if (z <= 1.5e+91) {
		tmp = t_0;
	} else if (z <= 8.2e+230) {
		tmp = t_1;
	} else {
		tmp = (z * 6.0) * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = 6.0d0 * (z * y)
    t_1 = z * ((-6.0d0) * x)
    if (z <= (-3.2d+188)) then
        tmp = t_0
    else if (z <= (-7d-5)) then
        tmp = t_1
    else if (z <= 2d-39) then
        tmp = x
    else if (z <= 1.5d+91) then
        tmp = t_0
    else if (z <= 8.2d+230) then
        tmp = t_1
    else
        tmp = (z * 6.0d0) * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 6.0 * (z * y);
	double t_1 = z * (-6.0 * x);
	double tmp;
	if (z <= -3.2e+188) {
		tmp = t_0;
	} else if (z <= -7e-5) {
		tmp = t_1;
	} else if (z <= 2e-39) {
		tmp = x;
	} else if (z <= 1.5e+91) {
		tmp = t_0;
	} else if (z <= 8.2e+230) {
		tmp = t_1;
	} else {
		tmp = (z * 6.0) * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 6.0 * (z * y)
	t_1 = z * (-6.0 * x)
	tmp = 0
	if z <= -3.2e+188:
		tmp = t_0
	elif z <= -7e-5:
		tmp = t_1
	elif z <= 2e-39:
		tmp = x
	elif z <= 1.5e+91:
		tmp = t_0
	elif z <= 8.2e+230:
		tmp = t_1
	else:
		tmp = (z * 6.0) * y
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(6.0 * Float64(z * y))
	t_1 = Float64(z * Float64(-6.0 * x))
	tmp = 0.0
	if (z <= -3.2e+188)
		tmp = t_0;
	elseif (z <= -7e-5)
		tmp = t_1;
	elseif (z <= 2e-39)
		tmp = x;
	elseif (z <= 1.5e+91)
		tmp = t_0;
	elseif (z <= 8.2e+230)
		tmp = t_1;
	else
		tmp = Float64(Float64(z * 6.0) * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 6.0 * (z * y);
	t_1 = z * (-6.0 * x);
	tmp = 0.0;
	if (z <= -3.2e+188)
		tmp = t_0;
	elseif (z <= -7e-5)
		tmp = t_1;
	elseif (z <= 2e-39)
		tmp = x;
	elseif (z <= 1.5e+91)
		tmp = t_0;
	elseif (z <= 8.2e+230)
		tmp = t_1;
	else
		tmp = (z * 6.0) * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(6.0 * N[(z * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(z * N[(-6.0 * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.2e+188], t$95$0, If[LessEqual[z, -7e-5], t$95$1, If[LessEqual[z, 2e-39], x, If[LessEqual[z, 1.5e+91], t$95$0, If[LessEqual[z, 8.2e+230], t$95$1, N[(N[(z * 6.0), $MachinePrecision] * y), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.1999999999999997e188 or 1.99999999999999986e-39 < z < 1.50000000000000003e91

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 65.9

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

   5. Simplified 65.9%

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

   if -3.1999999999999997e188 < z < -6.9999999999999994e-5 or 1.50000000000000003e91 < z < 8.20000000000000026e230

   1. Initial program 99.7%

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

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

      2. distribute-lft-out-- N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. metadata-eval N/A

         \[\leadsto \color{blue}{\left(-1 \cdot -6\right)} \cdot \left(y \cdot z\right) - \left(6 \cdot z\right) \cdot x \]

      6. associate-*r* N/A

         \[\leadsto \color{blue}{-1 \cdot \left(-6 \cdot \left(y \cdot z\right)\right)} - \left(6 \cdot z\right) \cdot x \]

      7. *-commutative N/A

         \[\leadsto -1 \cdot \left(-6 \cdot \color{blue}{\left(z \cdot y\right)}\right) - \left(6 \cdot z\right) \cdot x \]

      8. associate-*r* N/A

         \[\leadsto -1 \cdot \color{blue}{\left(\left(-6 \cdot z\right) \cdot y\right)} - \left(6 \cdot z\right) \cdot x \]

      9. *-commutative N/A

         \[\leadsto -1 \cdot \color{blue}{\left(y \cdot \left(-6 \cdot z\right)\right)} - \left(6 \cdot z\right) \cdot x \]

      10. associate-*r* N/A

          \[\leadsto \color{blue}{\left(-1 \cdot y\right) \cdot \left(-6 \cdot z\right)} - \left(6 \cdot z\right) \cdot x \]

      11. *-commutative N/A

          \[\leadsto \left(-1 \cdot y\right) \cdot \left(-6 \cdot z\right) - \color{blue}{x \cdot \left(6 \cdot z\right)} \]

      12. metadata-eval N/A

          \[\leadsto \left(-1 \cdot y\right) \cdot \left(-6 \cdot z\right) - x \cdot \left(\color{blue}{\left(\mathsf{neg}\left(-6\right)\right)} \cdot z\right) \]

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

          \[\leadsto \left(-1 \cdot y\right) \cdot \left(-6 \cdot z\right) - x \cdot \color{blue}{\left(\mathsf{neg}\left(-6 \cdot z\right)\right)} \]

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

          \[\leadsto \left(-1 \cdot y\right) \cdot \left(-6 \cdot z\right) - \color{blue}{\left(\mathsf{neg}\left(x \cdot \left(-6 \cdot z\right)\right)\right)} \]

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

          \[\leadsto \left(-1 \cdot y\right) \cdot \left(-6 \cdot z\right) - \color{blue}{\left(\mathsf{neg}\left(x\right)\right) \cdot \left(-6 \cdot z\right)} \]

      16. mul-1-neg N/A

          \[\leadsto \left(-1 \cdot y\right) \cdot \left(-6 \cdot z\right) - \color{blue}{\left(-1 \cdot x\right)} \cdot \left(-6 \cdot z\right) \]

      17. distribute-rgt-out-- N/A

          \[\leadsto \color{blue}{\left(-6 \cdot z\right) \cdot \left(-1 \cdot y - -1 \cdot x\right)} \]

      18. distribute-lft-out-- N/A

          \[\leadsto \left(-6 \cdot z\right) \cdot \color{blue}{\left(-1 \cdot \left(y - x\right)\right)} \]

      19. neg-mul-1 N/A

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

      20. neg-sub0 N/A

          \[\leadsto \left(-6 \cdot z\right) \cdot \color{blue}{\left(0 - \left(y - x\right)\right)} \]

      21. associate-+l- N/A

          \[\leadsto \left(-6 \cdot z\right) \cdot \color{blue}{\left(\left(0 - y\right) + x\right)} \]

      22. neg-sub0 N/A

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

      23. mul-1-neg N/A

          \[\leadsto \left(-6 \cdot z\right) \cdot \left(\color{blue}{-1 \cdot y} + x\right) \]

      24. *-lft-identity N/A

          \[\leadsto \left(-6 \cdot z\right) \cdot \left(\color{blue}{1 \cdot \left(-1 \cdot y\right)} + x\right) \]

      25. *-inverses N/A

          \[\leadsto \left(-6 \cdot z\right) \cdot \left(\color{blue}{\frac{x}{x}} \cdot \left(-1 \cdot y\right) + x\right) \]

      26. associate-*l/ N/A

          \[\leadsto \left(-6 \cdot z\right) \cdot \left(\color{blue}{\frac{x \cdot \left(-1 \cdot y\right)}{x}} + x\right) \]

      27. associate-*r/ N/A

          \[\leadsto \left(-6 \cdot z\right) \cdot \left(\color{blue}{x \cdot \frac{-1 \cdot y}{x}} + x\right) \]

      28. associate-*r/ N/A

          \[\leadsto \left(-6 \cdot z\right) \cdot \left(x \cdot \color{blue}{\left(-1 \cdot \frac{y}{x}\right)} + x\right) \]

      29. *-rgt-identity N/A

          \[\leadsto \left(-6 \cdot z\right) \cdot \left(x \cdot \left(-1 \cdot \frac{y}{x}\right) + \color{blue}{x \cdot 1}\right) \]

   5. Simplified 97.6%

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

   6. Taylor expanded in x around inf

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

      1. metadata-eval N/A

         \[\leadsto \color{blue}{\left(-1 \cdot 6\right)} \cdot \left(x \cdot z\right) \]

      2. associate-*r* N/A

         \[\leadsto \color{blue}{-1 \cdot \left(6 \cdot \left(x \cdot z\right)\right)} \]

      3. associate-*r* N/A

         \[\leadsto -1 \cdot \color{blue}{\left(\left(6 \cdot x\right) \cdot z\right)} \]

      4. associate-*r* N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(6 \cdot x\right)\right) \cdot z} \]

      5. *-commutative N/A

         \[\leadsto \left(-1 \cdot \color{blue}{\left(x \cdot 6\right)}\right) \cdot z \]

      6. associate-*l* N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot x\right) \cdot 6\right)} \cdot z \]

      7. *-commutative N/A

         \[\leadsto \color{blue}{z \cdot \left(\left(-1 \cdot x\right) \cdot 6\right)} \]

      8. lower-*.f64 N/A

         \[\leadsto \color{blue}{z \cdot \left(\left(-1 \cdot x\right) \cdot 6\right)} \]

      9. *-commutative N/A

         \[\leadsto z \cdot \color{blue}{\left(6 \cdot \left(-1 \cdot x\right)\right)} \]

      10. associate-*r* N/A

          \[\leadsto z \cdot \color{blue}{\left(\left(6 \cdot -1\right) \cdot x\right)} \]

      11. metadata-eval N/A

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

      12. lower-*.f64 61.0

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

   8. Simplified 61.0%

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

   if -6.9999999999999994e-5 < z < 1.99999999999999986e-39

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 75.5

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

   5. Simplified 75.5%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. distribute-rgt1-in N/A

         \[\leadsto \color{blue}{\left(z \cdot -6 + 1\right) \cdot x} \]

      4. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(z \cdot -6 + 1\right) \cdot x} \]

      5. lift-*.f64 N/A

         \[\leadsto \left(\color{blue}{z \cdot -6} + 1\right) \cdot x \]

      6. lower-fma.f64 75.5

         \[\leadsto \color{blue}{\mathsf{fma}\left(z, -6, 1\right)} \cdot x \]

   7. Applied egg-rr 75.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z, -6, 1\right) \cdot x} \]

   8. Taylor expanded in z around 0

      \[\leadsto \color{blue}{1} \cdot x \]
   9. Step-by-step derivation

   10. Simplified 75.2%

       \[\leadsto \color{blue}{1} \cdot x \]
   11. Step-by-step derivation

       1. *-lft-identity 75.2

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

   12. Applied egg-rr 75.2%

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

   if 8.20000000000000026e230 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 81.4

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

   5. Simplified 81.4%

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

      1. *-commutative N/A

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

      2. associate-*l* N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 81.5

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

   7. Applied egg-rr 81.5%

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

4. Final simplification 69.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+188}:\\ \;\;\;\;6 \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-5}:\\ \;\;\;\;z \cdot \left(-6 \cdot x\right)\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-39}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+91}:\\ \;\;\;\;6 \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+230}:\\ \;\;\;\;z \cdot \left(-6 \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot 6\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 60.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(z \cdot y\right)\\ t_1 := z \cdot \left(-6 \cdot x\right)\\ \mathbf{if}\;z \leq -9.6 \cdot 10^{+185}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-5}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-39}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.55 \cdot 10^{+92}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1.08 \cdot 10^{+230}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 6.0 (* z y))) (t_1 (* z (* -6.0 x))))
   (if (<= z -9.6e+185)
     t_0
     (if (<= z -7e-5)
       t_1
       (if (<= z 1.9e-39)
         x
         (if (<= z 2.55e+92) t_0 (if (<= z 1.08e+230) t_1 t_0)))))))

C

double code(double x, double y, double z) {
	double t_0 = 6.0 * (z * y);
	double t_1 = z * (-6.0 * x);
	double tmp;
	if (z <= -9.6e+185) {
		tmp = t_0;
	} else if (z <= -7e-5) {
		tmp = t_1;
	} else if (z <= 1.9e-39) {
		tmp = x;
	} else if (z <= 2.55e+92) {
		tmp = t_0;
	} else if (z <= 1.08e+230) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_0 = 6.0d0 * (z * y)
    t_1 = z * ((-6.0d0) * x)
    if (z <= (-9.6d+185)) then
        tmp = t_0
    else if (z <= (-7d-5)) then
        tmp = t_1
    else if (z <= 1.9d-39) then
        tmp = x
    else if (z <= 2.55d+92) then
        tmp = t_0
    else if (z <= 1.08d+230) then
        tmp = t_1
    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 * (z * y);
	double t_1 = z * (-6.0 * x);
	double tmp;
	if (z <= -9.6e+185) {
		tmp = t_0;
	} else if (z <= -7e-5) {
		tmp = t_1;
	} else if (z <= 1.9e-39) {
		tmp = x;
	} else if (z <= 2.55e+92) {
		tmp = t_0;
	} else if (z <= 1.08e+230) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 6.0 * (z * y)
	t_1 = z * (-6.0 * x)
	tmp = 0
	if z <= -9.6e+185:
		tmp = t_0
	elif z <= -7e-5:
		tmp = t_1
	elif z <= 1.9e-39:
		tmp = x
	elif z <= 2.55e+92:
		tmp = t_0
	elif z <= 1.08e+230:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(6.0 * Float64(z * y))
	t_1 = Float64(z * Float64(-6.0 * x))
	tmp = 0.0
	if (z <= -9.6e+185)
		tmp = t_0;
	elseif (z <= -7e-5)
		tmp = t_1;
	elseif (z <= 1.9e-39)
		tmp = x;
	elseif (z <= 2.55e+92)
		tmp = t_0;
	elseif (z <= 1.08e+230)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 6.0 * (z * y);
	t_1 = z * (-6.0 * x);
	tmp = 0.0;
	if (z <= -9.6e+185)
		tmp = t_0;
	elseif (z <= -7e-5)
		tmp = t_1;
	elseif (z <= 1.9e-39)
		tmp = x;
	elseif (z <= 2.55e+92)
		tmp = t_0;
	elseif (z <= 1.08e+230)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(6.0 * N[(z * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(z * N[(-6.0 * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9.6e+185], t$95$0, If[LessEqual[z, -7e-5], t$95$1, If[LessEqual[z, 1.9e-39], x, If[LessEqual[z, 2.55e+92], t$95$0, If[LessEqual[z, 1.08e+230], t$95$1, t$95$0]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.59999999999999956e185 or 1.9000000000000001e-39 < z < 2.5500000000000001e92 or 1.08e230 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 70.3

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

   5. Simplified 70.3%

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

   if -9.59999999999999956e185 < z < -6.9999999999999994e-5 or 2.5500000000000001e92 < z < 1.08e230

   1. Initial program 99.7%

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

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

      2. distribute-lft-out-- N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. metadata-eval N/A

         \[\leadsto \color{blue}{\left(-1 \cdot -6\right)} \cdot \left(y \cdot z\right) - \left(6 \cdot z\right) \cdot x \]

      6. associate-*r* N/A

         \[\leadsto \color{blue}{-1 \cdot \left(-6 \cdot \left(y \cdot z\right)\right)} - \left(6 \cdot z\right) \cdot x \]

      7. *-commutative N/A

         \[\leadsto -1 \cdot \left(-6 \cdot \color{blue}{\left(z \cdot y\right)}\right) - \left(6 \cdot z\right) \cdot x \]

      8. associate-*r* N/A

         \[\leadsto -1 \cdot \color{blue}{\left(\left(-6 \cdot z\right) \cdot y\right)} - \left(6 \cdot z\right) \cdot x \]

      9. *-commutative N/A

         \[\leadsto -1 \cdot \color{blue}{\left(y \cdot \left(-6 \cdot z\right)\right)} - \left(6 \cdot z\right) \cdot x \]

      10. associate-*r* N/A

          \[\leadsto \color{blue}{\left(-1 \cdot y\right) \cdot \left(-6 \cdot z\right)} - \left(6 \cdot z\right) \cdot x \]

      11. *-commutative N/A

          \[\leadsto \left(-1 \cdot y\right) \cdot \left(-6 \cdot z\right) - \color{blue}{x \cdot \left(6 \cdot z\right)} \]

      12. metadata-eval N/A

          \[\leadsto \left(-1 \cdot y\right) \cdot \left(-6 \cdot z\right) - x \cdot \left(\color{blue}{\left(\mathsf{neg}\left(-6\right)\right)} \cdot z\right) \]

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

          \[\leadsto \left(-1 \cdot y\right) \cdot \left(-6 \cdot z\right) - x \cdot \color{blue}{\left(\mathsf{neg}\left(-6 \cdot z\right)\right)} \]

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

          \[\leadsto \left(-1 \cdot y\right) \cdot \left(-6 \cdot z\right) - \color{blue}{\left(\mathsf{neg}\left(x \cdot \left(-6 \cdot z\right)\right)\right)} \]

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

          \[\leadsto \left(-1 \cdot y\right) \cdot \left(-6 \cdot z\right) - \color{blue}{\left(\mathsf{neg}\left(x\right)\right) \cdot \left(-6 \cdot z\right)} \]

      16. mul-1-neg N/A

          \[\leadsto \left(-1 \cdot y\right) \cdot \left(-6 \cdot z\right) - \color{blue}{\left(-1 \cdot x\right)} \cdot \left(-6 \cdot z\right) \]

      17. distribute-rgt-out-- N/A

          \[\leadsto \color{blue}{\left(-6 \cdot z\right) \cdot \left(-1 \cdot y - -1 \cdot x\right)} \]

      18. distribute-lft-out-- N/A

          \[\leadsto \left(-6 \cdot z\right) \cdot \color{blue}{\left(-1 \cdot \left(y - x\right)\right)} \]

      19. neg-mul-1 N/A

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

      20. neg-sub0 N/A

          \[\leadsto \left(-6 \cdot z\right) \cdot \color{blue}{\left(0 - \left(y - x\right)\right)} \]

      21. associate-+l- N/A

          \[\leadsto \left(-6 \cdot z\right) \cdot \color{blue}{\left(\left(0 - y\right) + x\right)} \]

      22. neg-sub0 N/A

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

      23. mul-1-neg N/A

          \[\leadsto \left(-6 \cdot z\right) \cdot \left(\color{blue}{-1 \cdot y} + x\right) \]

      24. *-lft-identity N/A

          \[\leadsto \left(-6 \cdot z\right) \cdot \left(\color{blue}{1 \cdot \left(-1 \cdot y\right)} + x\right) \]

      25. *-inverses N/A

          \[\leadsto \left(-6 \cdot z\right) \cdot \left(\color{blue}{\frac{x}{x}} \cdot \left(-1 \cdot y\right) + x\right) \]

      26. associate-*l/ N/A

          \[\leadsto \left(-6 \cdot z\right) \cdot \left(\color{blue}{\frac{x \cdot \left(-1 \cdot y\right)}{x}} + x\right) \]

      27. associate-*r/ N/A

          \[\leadsto \left(-6 \cdot z\right) \cdot \left(\color{blue}{x \cdot \frac{-1 \cdot y}{x}} + x\right) \]

      28. associate-*r/ N/A

          \[\leadsto \left(-6 \cdot z\right) \cdot \left(x \cdot \color{blue}{\left(-1 \cdot \frac{y}{x}\right)} + x\right) \]

      29. *-rgt-identity N/A

          \[\leadsto \left(-6 \cdot z\right) \cdot \left(x \cdot \left(-1 \cdot \frac{y}{x}\right) + \color{blue}{x \cdot 1}\right) \]

   5. Simplified 97.6%

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

   6. Taylor expanded in x around inf

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

      1. metadata-eval N/A

         \[\leadsto \color{blue}{\left(-1 \cdot 6\right)} \cdot \left(x \cdot z\right) \]

      2. associate-*r* N/A

         \[\leadsto \color{blue}{-1 \cdot \left(6 \cdot \left(x \cdot z\right)\right)} \]

      3. associate-*r* N/A

         \[\leadsto -1 \cdot \color{blue}{\left(\left(6 \cdot x\right) \cdot z\right)} \]

      4. associate-*r* N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(6 \cdot x\right)\right) \cdot z} \]

      5. *-commutative N/A

         \[\leadsto \left(-1 \cdot \color{blue}{\left(x \cdot 6\right)}\right) \cdot z \]

      6. associate-*l* N/A

         \[\leadsto \color{blue}{\left(\left(-1 \cdot x\right) \cdot 6\right)} \cdot z \]

      7. *-commutative N/A

         \[\leadsto \color{blue}{z \cdot \left(\left(-1 \cdot x\right) \cdot 6\right)} \]

      8. lower-*.f64 N/A

         \[\leadsto \color{blue}{z \cdot \left(\left(-1 \cdot x\right) \cdot 6\right)} \]

      9. *-commutative N/A

         \[\leadsto z \cdot \color{blue}{\left(6 \cdot \left(-1 \cdot x\right)\right)} \]

      10. associate-*r* N/A

          \[\leadsto z \cdot \color{blue}{\left(\left(6 \cdot -1\right) \cdot x\right)} \]

      11. metadata-eval N/A

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

      12. lower-*.f64 61.0

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

   8. Simplified 61.0%

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

   if -6.9999999999999994e-5 < z < 1.9000000000000001e-39

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 75.5

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

   5. Simplified 75.5%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. distribute-rgt1-in N/A

         \[\leadsto \color{blue}{\left(z \cdot -6 + 1\right) \cdot x} \]

      4. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(z \cdot -6 + 1\right) \cdot x} \]

      5. lift-*.f64 N/A

         \[\leadsto \left(\color{blue}{z \cdot -6} + 1\right) \cdot x \]

      6. lower-fma.f64 75.5

         \[\leadsto \color{blue}{\mathsf{fma}\left(z, -6, 1\right)} \cdot x \]

   7. Applied egg-rr 75.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z, -6, 1\right) \cdot x} \]

   8. Taylor expanded in z around 0

      \[\leadsto \color{blue}{1} \cdot x \]
   9. Step-by-step derivation

   10. Simplified 75.2%

       \[\leadsto \color{blue}{1} \cdot x \]
   11. Step-by-step derivation

       1. *-lft-identity 75.2

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

   12. Applied egg-rr 75.2%

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

4. Final simplification 69.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.6 \cdot 10^{+185}:\\ \;\;\;\;6 \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-5}:\\ \;\;\;\;z \cdot \left(-6 \cdot x\right)\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-39}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.55 \cdot 10^{+92}:\\ \;\;\;\;6 \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq 1.08 \cdot 10^{+230}:\\ \;\;\;\;z \cdot \left(-6 \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(z \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 98.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.17:\\ \;\;\;\;\left(z \cdot -6\right) \cdot \left(x - y\right)\\ \mathbf{elif}\;z \leq 0.17:\\ \;\;\;\;\mathsf{fma}\left(z \cdot 6, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-6 \cdot \left(x - y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.17)
   (* (* z -6.0) (- x y))
   (if (<= z 0.17) (fma (* z 6.0) y x) (* z (* -6.0 (- x y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.17) {
		tmp = (z * -6.0) * (x - y);
	} else if (z <= 0.17) {
		tmp = fma((z * 6.0), y, x);
	} else {
		tmp = z * (-6.0 * (x - y));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.17)
		tmp = Float64(Float64(z * -6.0) * Float64(x - y));
	elseif (z <= 0.17)
		tmp = fma(Float64(z * 6.0), y, x);
	else
		tmp = Float64(z * Float64(-6.0 * Float64(x - y)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.17], N[(N[(z * -6.0), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.17], N[(N[(z * 6.0), $MachinePrecision] * y + x), $MachinePrecision], N[(z * N[(-6.0 * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.170000000000000012

   1. Initial program 99.7%

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

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

      2. distribute-lft-out-- N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. metadata-eval N/A

         \[\leadsto \color{blue}{\left(-1 \cdot -6\right)} \cdot \left(y \cdot z\right) - \left(6 \cdot z\right) \cdot x \]

      6. associate-*r* N/A

         \[\leadsto \color{blue}{-1 \cdot \left(-6 \cdot \left(y \cdot z\right)\right)} - \left(6 \cdot z\right) \cdot x \]

      7. *-commutative N/A

         \[\leadsto -1 \cdot \left(-6 \cdot \color{blue}{\left(z \cdot y\right)}\right) - \left(6 \cdot z\right) \cdot x \]

      8. associate-*r* N/A

         \[\leadsto -1 \cdot \color{blue}{\left(\left(-6 \cdot z\right) \cdot y\right)} - \left(6 \cdot z\right) \cdot x \]

      9. *-commutative N/A

         \[\leadsto -1 \cdot \color{blue}{\left(y \cdot \left(-6 \cdot z\right)\right)} - \left(6 \cdot z\right) \cdot x \]

      10. associate-*r* N/A

          \[\leadsto \color{blue}{\left(-1 \cdot y\right) \cdot \left(-6 \cdot z\right)} - \left(6 \cdot z\right) \cdot x \]

      11. *-commutative N/A

          \[\leadsto \left(-1 \cdot y\right) \cdot \left(-6 \cdot z\right) - \color{blue}{x \cdot \left(6 \cdot z\right)} \]

      12. metadata-eval N/A

          \[\leadsto \left(-1 \cdot y\right) \cdot \left(-6 \cdot z\right) - x \cdot \left(\color{blue}{\left(\mathsf{neg}\left(-6\right)\right)} \cdot z\right) \]

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

          \[\leadsto \left(-1 \cdot y\right) \cdot \left(-6 \cdot z\right) - x \cdot \color{blue}{\left(\mathsf{neg}\left(-6 \cdot z\right)\right)} \]

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

          \[\leadsto \left(-1 \cdot y\right) \cdot \left(-6 \cdot z\right) - \color{blue}{\left(\mathsf{neg}\left(x \cdot \left(-6 \cdot z\right)\right)\right)} \]

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

          \[\leadsto \left(-1 \cdot y\right) \cdot \left(-6 \cdot z\right) - \color{blue}{\left(\mathsf{neg}\left(x\right)\right) \cdot \left(-6 \cdot z\right)} \]

      16. mul-1-neg N/A

          \[\leadsto \left(-1 \cdot y\right) \cdot \left(-6 \cdot z\right) - \color{blue}{\left(-1 \cdot x\right)} \cdot \left(-6 \cdot z\right) \]

      17. distribute-rgt-out-- N/A

          \[\leadsto \color{blue}{\left(-6 \cdot z\right) \cdot \left(-1 \cdot y - -1 \cdot x\right)} \]

      18. distribute-lft-out-- N/A

          \[\leadsto \left(-6 \cdot z\right) \cdot \color{blue}{\left(-1 \cdot \left(y - x\right)\right)} \]

      19. neg-mul-1 N/A

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

      20. neg-sub0 N/A

          \[\leadsto \left(-6 \cdot z\right) \cdot \color{blue}{\left(0 - \left(y - x\right)\right)} \]

      21. associate-+l- N/A

          \[\leadsto \left(-6 \cdot z\right) \cdot \color{blue}{\left(\left(0 - y\right) + x\right)} \]

      22. neg-sub0 N/A

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

      23. mul-1-neg N/A

          \[\leadsto \left(-6 \cdot z\right) \cdot \left(\color{blue}{-1 \cdot y} + x\right) \]

      24. *-lft-identity N/A

          \[\leadsto \left(-6 \cdot z\right) \cdot \left(\color{blue}{1 \cdot \left(-1 \cdot y\right)} + x\right) \]

      25. *-inverses N/A

          \[\leadsto \left(-6 \cdot z\right) \cdot \left(\color{blue}{\frac{x}{x}} \cdot \left(-1 \cdot y\right) + x\right) \]

      26. associate-*l/ N/A

          \[\leadsto \left(-6 \cdot z\right) \cdot \left(\color{blue}{\frac{x \cdot \left(-1 \cdot y\right)}{x}} + x\right) \]

      27. associate-*r/ N/A

          \[\leadsto \left(-6 \cdot z\right) \cdot \left(\color{blue}{x \cdot \frac{-1 \cdot y}{x}} + x\right) \]

      28. associate-*r/ N/A

          \[\leadsto \left(-6 \cdot z\right) \cdot \left(x \cdot \color{blue}{\left(-1 \cdot \frac{y}{x}\right)} + x\right) \]

      29. *-rgt-identity N/A

          \[\leadsto \left(-6 \cdot z\right) \cdot \left(x \cdot \left(-1 \cdot \frac{y}{x}\right) + \color{blue}{x \cdot 1}\right) \]

   5. Simplified 97.7%

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

   if -0.170000000000000012 < z < 0.170000000000000012

   1. Initial program 99.8%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. +-commutative N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. associate-*l* N/A

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

      8. *-commutative N/A

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

      9. associate-*r* N/A

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

      10. lower-fma.f64 N/A

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

      11. lower-*.f64 99.9

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 98.3

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

   7. Simplified 98.3%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. associate-*l* N/A

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

      5. lift-*.f64 N/A

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

      6. lower-fma.f64 98.4

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 98.4

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

   9. Applied egg-rr 98.4%

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

   if 0.170000000000000012 < z

   1. Initial program 99.8%

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

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

      2. distribute-lft-out-- N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. metadata-eval N/A

         \[\leadsto \color{blue}{\left(-1 \cdot -6\right)} \cdot \left(y \cdot z\right) - \left(6 \cdot z\right) \cdot x \]

      6. associate-*r* N/A

         \[\leadsto \color{blue}{-1 \cdot \left(-6 \cdot \left(y \cdot z\right)\right)} - \left(6 \cdot z\right) \cdot x \]

      7. *-commutative N/A

         \[\leadsto -1 \cdot \left(-6 \cdot \color{blue}{\left(z \cdot y\right)}\right) - \left(6 \cdot z\right) \cdot x \]

      8. associate-*r* N/A

         \[\leadsto -1 \cdot \color{blue}{\left(\left(-6 \cdot z\right) \cdot y\right)} - \left(6 \cdot z\right) \cdot x \]

      9. *-commutative N/A

         \[\leadsto -1 \cdot \color{blue}{\left(y \cdot \left(-6 \cdot z\right)\right)} - \left(6 \cdot z\right) \cdot x \]

      10. associate-*r* N/A

          \[\leadsto \color{blue}{\left(-1 \cdot y\right) \cdot \left(-6 \cdot z\right)} - \left(6 \cdot z\right) \cdot x \]

      11. *-commutative N/A

          \[\leadsto \left(-1 \cdot y\right) \cdot \left(-6 \cdot z\right) - \color{blue}{x \cdot \left(6 \cdot z\right)} \]

      12. metadata-eval N/A

          \[\leadsto \left(-1 \cdot y\right) \cdot \left(-6 \cdot z\right) - x \cdot \left(\color{blue}{\left(\mathsf{neg}\left(-6\right)\right)} \cdot z\right) \]

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

          \[\leadsto \left(-1 \cdot y\right) \cdot \left(-6 \cdot z\right) - x \cdot \color{blue}{\left(\mathsf{neg}\left(-6 \cdot z\right)\right)} \]

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

          \[\leadsto \left(-1 \cdot y\right) \cdot \left(-6 \cdot z\right) - \color{blue}{\left(\mathsf{neg}\left(x \cdot \left(-6 \cdot z\right)\right)\right)} \]

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

          \[\leadsto \left(-1 \cdot y\right) \cdot \left(-6 \cdot z\right) - \color{blue}{\left(\mathsf{neg}\left(x\right)\right) \cdot \left(-6 \cdot z\right)} \]

      16. mul-1-neg N/A

          \[\leadsto \left(-1 \cdot y\right) \cdot \left(-6 \cdot z\right) - \color{blue}{\left(-1 \cdot x\right)} \cdot \left(-6 \cdot z\right) \]

      17. distribute-rgt-out-- N/A

          \[\leadsto \color{blue}{\left(-6 \cdot z\right) \cdot \left(-1 \cdot y - -1 \cdot x\right)} \]

      18. distribute-lft-out-- N/A

          \[\leadsto \left(-6 \cdot z\right) \cdot \color{blue}{\left(-1 \cdot \left(y - x\right)\right)} \]

      19. neg-mul-1 N/A

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

      20. neg-sub0 N/A

          \[\leadsto \left(-6 \cdot z\right) \cdot \color{blue}{\left(0 - \left(y - x\right)\right)} \]

      21. associate-+l- N/A

          \[\leadsto \left(-6 \cdot z\right) \cdot \color{blue}{\left(\left(0 - y\right) + x\right)} \]

      22. neg-sub0 N/A

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

      23. mul-1-neg N/A

          \[\leadsto \left(-6 \cdot z\right) \cdot \left(\color{blue}{-1 \cdot y} + x\right) \]

      24. *-lft-identity N/A

          \[\leadsto \left(-6 \cdot z\right) \cdot \left(\color{blue}{1 \cdot \left(-1 \cdot y\right)} + x\right) \]

      25. *-inverses N/A

          \[\leadsto \left(-6 \cdot z\right) \cdot \left(\color{blue}{\frac{x}{x}} \cdot \left(-1 \cdot y\right) + x\right) \]

      26. associate-*l/ N/A

          \[\leadsto \left(-6 \cdot z\right) \cdot \left(\color{blue}{\frac{x \cdot \left(-1 \cdot y\right)}{x}} + x\right) \]

      27. associate-*r/ N/A

          \[\leadsto \left(-6 \cdot z\right) \cdot \left(\color{blue}{x \cdot \frac{-1 \cdot y}{x}} + x\right) \]

      28. associate-*r/ N/A

          \[\leadsto \left(-6 \cdot z\right) \cdot \left(x \cdot \color{blue}{\left(-1 \cdot \frac{y}{x}\right)} + x\right) \]

      29. *-rgt-identity N/A

          \[\leadsto \left(-6 \cdot z\right) \cdot \left(x \cdot \left(-1 \cdot \frac{y}{x}\right) + \color{blue}{x \cdot 1}\right) \]

   5. Simplified 99.3%

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

      1. lift--.f64 N/A

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

      2. associate-*l* N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 99.3

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

   7. Applied egg-rr 99.3%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.17:\\ \;\;\;\;\left(z \cdot -6\right) \cdot \left(x - y\right)\\ \mathbf{elif}\;z \leq 0.17:\\ \;\;\;\;\mathsf{fma}\left(z \cdot 6, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-6 \cdot \left(x - y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 98.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(-6 \cdot \left(x - y\right)\right)\\ \mathbf{if}\;z \leq -0.155:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 0.17:\\ \;\;\;\;\mathsf{fma}\left(z \cdot 6, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (* -6.0 (- x y)))))
   (if (<= z -0.155) t_0 (if (<= z 0.17) (fma (* z 6.0) y x) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = z * (-6.0 * (x - y));
	double tmp;
	if (z <= -0.155) {
		tmp = t_0;
	} else if (z <= 0.17) {
		tmp = fma((z * 6.0), y, x);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(-6.0 * Float64(x - y)))
	tmp = 0.0
	if (z <= -0.155)
		tmp = t_0;
	elseif (z <= 0.17)
		tmp = fma(Float64(z * 6.0), y, x);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(-6.0 * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.155], t$95$0, If[LessEqual[z, 0.17], N[(N[(z * 6.0), $MachinePrecision] * y + x), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -0.154999999999999999 or 0.170000000000000012 < z

   1. Initial program 99.7%

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

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

      2. distribute-lft-out-- N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. metadata-eval N/A

         \[\leadsto \color{blue}{\left(-1 \cdot -6\right)} \cdot \left(y \cdot z\right) - \left(6 \cdot z\right) \cdot x \]

      6. associate-*r* N/A

         \[\leadsto \color{blue}{-1 \cdot \left(-6 \cdot \left(y \cdot z\right)\right)} - \left(6 \cdot z\right) \cdot x \]

      7. *-commutative N/A

         \[\leadsto -1 \cdot \left(-6 \cdot \color{blue}{\left(z \cdot y\right)}\right) - \left(6 \cdot z\right) \cdot x \]

      8. associate-*r* N/A

         \[\leadsto -1 \cdot \color{blue}{\left(\left(-6 \cdot z\right) \cdot y\right)} - \left(6 \cdot z\right) \cdot x \]

      9. *-commutative N/A

         \[\leadsto -1 \cdot \color{blue}{\left(y \cdot \left(-6 \cdot z\right)\right)} - \left(6 \cdot z\right) \cdot x \]

      10. associate-*r* N/A

          \[\leadsto \color{blue}{\left(-1 \cdot y\right) \cdot \left(-6 \cdot z\right)} - \left(6 \cdot z\right) \cdot x \]

      11. *-commutative N/A

          \[\leadsto \left(-1 \cdot y\right) \cdot \left(-6 \cdot z\right) - \color{blue}{x \cdot \left(6 \cdot z\right)} \]

      12. metadata-eval N/A

          \[\leadsto \left(-1 \cdot y\right) \cdot \left(-6 \cdot z\right) - x \cdot \left(\color{blue}{\left(\mathsf{neg}\left(-6\right)\right)} \cdot z\right) \]

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

          \[\leadsto \left(-1 \cdot y\right) \cdot \left(-6 \cdot z\right) - x \cdot \color{blue}{\left(\mathsf{neg}\left(-6 \cdot z\right)\right)} \]

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

          \[\leadsto \left(-1 \cdot y\right) \cdot \left(-6 \cdot z\right) - \color{blue}{\left(\mathsf{neg}\left(x \cdot \left(-6 \cdot z\right)\right)\right)} \]

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

          \[\leadsto \left(-1 \cdot y\right) \cdot \left(-6 \cdot z\right) - \color{blue}{\left(\mathsf{neg}\left(x\right)\right) \cdot \left(-6 \cdot z\right)} \]

      16. mul-1-neg N/A

          \[\leadsto \left(-1 \cdot y\right) \cdot \left(-6 \cdot z\right) - \color{blue}{\left(-1 \cdot x\right)} \cdot \left(-6 \cdot z\right) \]

      17. distribute-rgt-out-- N/A

          \[\leadsto \color{blue}{\left(-6 \cdot z\right) \cdot \left(-1 \cdot y - -1 \cdot x\right)} \]

      18. distribute-lft-out-- N/A

          \[\leadsto \left(-6 \cdot z\right) \cdot \color{blue}{\left(-1 \cdot \left(y - x\right)\right)} \]

      19. neg-mul-1 N/A

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

      20. neg-sub0 N/A

          \[\leadsto \left(-6 \cdot z\right) \cdot \color{blue}{\left(0 - \left(y - x\right)\right)} \]

      21. associate-+l- N/A

          \[\leadsto \left(-6 \cdot z\right) \cdot \color{blue}{\left(\left(0 - y\right) + x\right)} \]

      22. neg-sub0 N/A

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

      23. mul-1-neg N/A

          \[\leadsto \left(-6 \cdot z\right) \cdot \left(\color{blue}{-1 \cdot y} + x\right) \]

      24. *-lft-identity N/A

          \[\leadsto \left(-6 \cdot z\right) \cdot \left(\color{blue}{1 \cdot \left(-1 \cdot y\right)} + x\right) \]

      25. *-inverses N/A

          \[\leadsto \left(-6 \cdot z\right) \cdot \left(\color{blue}{\frac{x}{x}} \cdot \left(-1 \cdot y\right) + x\right) \]

      26. associate-*l/ N/A

          \[\leadsto \left(-6 \cdot z\right) \cdot \left(\color{blue}{\frac{x \cdot \left(-1 \cdot y\right)}{x}} + x\right) \]

      27. associate-*r/ N/A

          \[\leadsto \left(-6 \cdot z\right) \cdot \left(\color{blue}{x \cdot \frac{-1 \cdot y}{x}} + x\right) \]

      28. associate-*r/ N/A

          \[\leadsto \left(-6 \cdot z\right) \cdot \left(x \cdot \color{blue}{\left(-1 \cdot \frac{y}{x}\right)} + x\right) \]

      29. *-rgt-identity N/A

          \[\leadsto \left(-6 \cdot z\right) \cdot \left(x \cdot \left(-1 \cdot \frac{y}{x}\right) + \color{blue}{x \cdot 1}\right) \]

   5. Simplified 98.4%

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

      1. lift--.f64 N/A

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

      2. associate-*l* N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 98.4

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

   7. Applied egg-rr 98.4%

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

   if -0.154999999999999999 < z < 0.170000000000000012

   1. Initial program 99.8%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. +-commutative N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. associate-*l* N/A

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

      8. *-commutative N/A

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

      9. associate-*r* N/A

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

      10. lower-fma.f64 N/A

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

      11. lower-*.f64 99.9

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 98.3

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

   7. Simplified 98.3%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. associate-*l* N/A

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

      5. lift-*.f64 N/A

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

      6. lower-fma.f64 98.4

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 98.4

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

   9. Applied egg-rr 98.4%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.155:\\ \;\;\;\;z \cdot \left(-6 \cdot \left(x - y\right)\right)\\ \mathbf{elif}\;z \leq 0.17:\\ \;\;\;\;\mathsf{fma}\left(z \cdot 6, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-6 \cdot \left(x - y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 86.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(z \cdot x, -6, x\right)\\ \mathbf{if}\;x \leq -5.6 \cdot 10^{+42}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{+74}:\\ \;\;\;\;\mathsf{fma}\left(z \cdot 6, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (fma (* z x) -6.0 x)))
   (if (<= x -5.6e+42) t_0 (if (<= x 3.1e+74) (fma (* z 6.0) y x) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = fma((z * x), -6.0, x);
	double tmp;
	if (x <= -5.6e+42) {
		tmp = t_0;
	} else if (x <= 3.1e+74) {
		tmp = fma((z * 6.0), y, x);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = fma(Float64(z * x), -6.0, x)
	tmp = 0.0
	if (x <= -5.6e+42)
		tmp = t_0;
	elseif (x <= 3.1e+74)
		tmp = fma(Float64(z * 6.0), y, x);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(z * x), $MachinePrecision] * -6.0 + x), $MachinePrecision]}, If[LessEqual[x, -5.6e+42], t$95$0, If[LessEqual[x, 3.1e+74], N[(N[(z * 6.0), $MachinePrecision] * y + x), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -5.5999999999999999e42 or 3.10000000000000021e74 < x

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 93.4

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

   5. Simplified 93.4%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. associate-*r* N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 93.4

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

   7. Applied egg-rr 93.4%

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

   if -5.5999999999999999e42 < x < 3.10000000000000021e74

   1. Initial program 99.7%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. +-commutative N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. associate-*l* N/A

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

      8. *-commutative N/A

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

      9. associate-*r* N/A

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

      10. lower-fma.f64 N/A

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

      11. lower-*.f64 99.7

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

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 85.4

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

   7. Simplified 85.4%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. associate-*l* N/A

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

      5. lift-*.f64 N/A

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

      6. lower-fma.f64 85.5

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 85.5

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

   9. Applied egg-rr 85.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z \cdot 6, y, x\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 8: 86.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(z, -6, 1\right) \cdot x\\ \mathbf{if}\;x \leq -8 \cdot 10^{+40}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 5.4 \cdot 10^{+82}:\\ \;\;\;\;\mathsf{fma}\left(z \cdot 6, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (fma z -6.0 1.0) x)))
   (if (<= x -8e+40) t_0 (if (<= x 5.4e+82) (fma (* z 6.0) y x) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = fma(z, -6.0, 1.0) * x;
	double tmp;
	if (x <= -8e+40) {
		tmp = t_0;
	} else if (x <= 5.4e+82) {
		tmp = fma((z * 6.0), y, x);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(fma(z, -6.0, 1.0) * x)
	tmp = 0.0
	if (x <= -8e+40)
		tmp = t_0;
	elseif (x <= 5.4e+82)
		tmp = fma(Float64(z * 6.0), y, x);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(z * -6.0 + 1.0), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[x, -8e+40], t$95$0, If[LessEqual[x, 5.4e+82], N[(N[(z * 6.0), $MachinePrecision] * y + x), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -8.00000000000000024e40 or 5.3999999999999999e82 < x

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 93.4

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

   5. Simplified 93.4%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. distribute-rgt1-in N/A

         \[\leadsto \color{blue}{\left(z \cdot -6 + 1\right) \cdot x} \]

      4. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(z \cdot -6 + 1\right) \cdot x} \]

      5. lift-*.f64 N/A

         \[\leadsto \left(\color{blue}{z \cdot -6} + 1\right) \cdot x \]

      6. lower-fma.f64 93.4

         \[\leadsto \color{blue}{\mathsf{fma}\left(z, -6, 1\right)} \cdot x \]

   7. Applied egg-rr 93.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z, -6, 1\right) \cdot x} \]

   if -8.00000000000000024e40 < x < 5.3999999999999999e82

   1. Initial program 99.7%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. +-commutative N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. associate-*l* N/A

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

      8. *-commutative N/A

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

      9. associate-*r* N/A

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

      10. lower-fma.f64 N/A

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

      11. lower-*.f64 99.7

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

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 85.4

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

   7. Simplified 85.4%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. associate-*l* N/A

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

      5. lift-*.f64 N/A

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

      6. lower-fma.f64 85.5

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 85.5

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

   9. Applied egg-rr 85.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z \cdot 6, y, x\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 9: 74.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{+60}:\\ \;\;\;\;\left(z \cdot 6\right) \cdot y\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+83}:\\ \;\;\;\;\mathsf{fma}\left(z, -6, 1\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(z \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3.5e+60)
   (* (* z 6.0) y)
   (if (<= y 9.5e+83) (* (fma z -6.0 1.0) x) (* 6.0 (* z y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.5e+60) {
		tmp = (z * 6.0) * y;
	} else if (y <= 9.5e+83) {
		tmp = fma(z, -6.0, 1.0) * x;
	} else {
		tmp = 6.0 * (z * y);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3.5e+60)
		tmp = Float64(Float64(z * 6.0) * y);
	elseif (y <= 9.5e+83)
		tmp = Float64(fma(z, -6.0, 1.0) * x);
	else
		tmp = Float64(6.0 * Float64(z * y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3.5e+60], N[(N[(z * 6.0), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[y, 9.5e+83], N[(N[(z * -6.0 + 1.0), $MachinePrecision] * x), $MachinePrecision], N[(6.0 * N[(z * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.5000000000000002e60

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 82.6

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

   5. Simplified 82.6%

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

      1. *-commutative N/A

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

      2. associate-*l* N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 82.8

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

   7. Applied egg-rr 82.8%

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

   if -3.5000000000000002e60 < y < 9.5000000000000002e83

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 79.5

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

   5. Simplified 79.5%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. distribute-rgt1-in N/A

         \[\leadsto \color{blue}{\left(z \cdot -6 + 1\right) \cdot x} \]

      4. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(z \cdot -6 + 1\right) \cdot x} \]

      5. lift-*.f64 N/A

         \[\leadsto \left(\color{blue}{z \cdot -6} + 1\right) \cdot x \]

      6. lower-fma.f64 79.5

         \[\leadsto \color{blue}{\mathsf{fma}\left(z, -6, 1\right)} \cdot x \]

   7. Applied egg-rr 79.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z, -6, 1\right) \cdot x} \]

   if 9.5000000000000002e83 < y

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 76.6

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

   5. Simplified 76.6%

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

4. Final simplification 79.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{+60}:\\ \;\;\;\;\left(z \cdot 6\right) \cdot y\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+83}:\\ \;\;\;\;\mathsf{fma}\left(z, -6, 1\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(z \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 61.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(z \cdot y\right)\\ \mathbf{if}\;z \leq -5.5 \cdot 10^{-7}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-39}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 6.0 (* z y))))
   (if (<= z -5.5e-7) t_0 (if (<= z 2.2e-39) x t_0))))

C

double code(double x, double y, double z) {
	double t_0 = 6.0 * (z * y);
	double tmp;
	if (z <= -5.5e-7) {
		tmp = t_0;
	} else if (z <= 2.2e-39) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 6.0d0 * (z * y)
    if (z <= (-5.5d-7)) then
        tmp = t_0
    else if (z <= 2.2d-39) then
        tmp = x
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 6.0 * (z * y);
	double tmp;
	if (z <= -5.5e-7) {
		tmp = t_0;
	} else if (z <= 2.2e-39) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 6.0 * (z * y)
	tmp = 0
	if z <= -5.5e-7:
		tmp = t_0
	elif z <= 2.2e-39:
		tmp = x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(6.0 * Float64(z * y))
	tmp = 0.0
	if (z <= -5.5e-7)
		tmp = t_0;
	elseif (z <= 2.2e-39)
		tmp = x;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 6.0 * (z * y);
	tmp = 0.0;
	if (z <= -5.5e-7)
		tmp = t_0;
	elseif (z <= 2.2e-39)
		tmp = x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(6.0 * N[(z * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.5e-7], t$95$0, If[LessEqual[z, 2.2e-39], x, t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.5000000000000003e-7 or 2.20000000000000001e-39 < z

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 54.5

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

   5. Simplified 54.5%

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

   if -5.5000000000000003e-7 < z < 2.20000000000000001e-39

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 75.5

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

   5. Simplified 75.5%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. distribute-rgt1-in N/A

         \[\leadsto \color{blue}{\left(z \cdot -6 + 1\right) \cdot x} \]

      4. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(z \cdot -6 + 1\right) \cdot x} \]

      5. lift-*.f64 N/A

         \[\leadsto \left(\color{blue}{z \cdot -6} + 1\right) \cdot x \]

      6. lower-fma.f64 75.5

         \[\leadsto \color{blue}{\mathsf{fma}\left(z, -6, 1\right)} \cdot x \]

   7. Applied egg-rr 75.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z, -6, 1\right) \cdot x} \]

   8. Taylor expanded in z around 0

      \[\leadsto \color{blue}{1} \cdot x \]
   9. Step-by-step derivation

   10. Simplified 75.2%

       \[\leadsto \color{blue}{1} \cdot x \]
   11. Step-by-step derivation

       1. *-lft-identity 75.2

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

   12. Applied egg-rr 75.2%

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

4. Final simplification 63.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{-7}:\\ \;\;\;\;6 \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-39}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(z \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 99.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(z \cdot \left(y - x\right), 6, x\right) \end{array} \]

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. lift--.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. lift-*.f64 N/A

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

   4. +-commutative N/A

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

   5. lift-*.f64 N/A

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

   6. lift-*.f64 N/A

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

   7. associate-*l* N/A

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

   8. *-commutative N/A

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

   9. associate-*r* N/A

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

   10. lower-fma.f64 N/A

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

   11. lower-*.f64 99.8

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

4. Applied egg-rr 99.8%

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

5. Final simplification 99.8%

   \[\leadsto \mathsf{fma}\left(z \cdot \left(y - x\right), 6, x\right) \]
6. Add Preprocessing

Alternative 12: 99.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(6 \cdot \left(y - x\right), z, x\right) \end{array} \]

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. lift--.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. lift-*.f64 N/A

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

   4. +-commutative N/A

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

   5. lift-*.f64 N/A

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

   6. lower-fma.f64 99.8

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

4. Applied egg-rr 99.8%

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

5. Final simplification 99.8%

   \[\leadsto \mathsf{fma}\left(6 \cdot \left(y - x\right), z, x\right) \]
6. Add Preprocessing

Alternative 13: 35.8% accurate, 17.0× 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 99.8%

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

3. Taylor expanded in y around 0

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

   1. *-commutative N/A

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

   2. associate-*r* N/A

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

   3. *-commutative N/A

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

   4. lower-*.f64 N/A

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

   5. *-commutative N/A

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

   6. lower-*.f64 62.5

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

5. Simplified 62.5%

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

   1. lift-*.f64 N/A

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

   2. *-commutative N/A

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

   3. distribute-rgt1-in N/A

      \[\leadsto \color{blue}{\left(z \cdot -6 + 1\right) \cdot x} \]

   4. lower-*.f64 N/A

      \[\leadsto \color{blue}{\left(z \cdot -6 + 1\right) \cdot x} \]

   5. lift-*.f64 N/A

      \[\leadsto \left(\color{blue}{z \cdot -6} + 1\right) \cdot x \]

   6. lower-fma.f64 62.5

      \[\leadsto \color{blue}{\mathsf{fma}\left(z, -6, 1\right)} \cdot x \]

7. Applied egg-rr 62.5%

   \[\leadsto \color{blue}{\mathsf{fma}\left(z, -6, 1\right) \cdot x} \]

8. Taylor expanded in z around 0

   \[\leadsto \color{blue}{1} \cdot x \]
9. Step-by-step derivation

10. Simplified 34.5%

    \[\leadsto \color{blue}{1} \cdot x \]
11. Step-by-step derivation

    1. *-lft-identity 34.5

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

12. Applied egg-rr 34.5%

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

Developer Target 1: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024207 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, E"
  :precision binary64

  :alt
  (! :herbie-platform default (- x (* (* 6 z) (- x y))))

  (+ x (* (* (- y x) 6.0) z)))