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

Percentage Accurate: 99.5% → 99.8%

Time: 10.8s

Alternatives: 13

Speedup: 1.9×

• 20.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(\mathsf{fma}\left(-6, z, 4\right), y - x, x\right) \end{array} \]

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.6%

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

   1. lift-+.f64 N/A

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

   2. +-commutative N/A

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

   3. lift-*.f64 N/A

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

   4. lift-*.f64 N/A

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

   5. associate-*l* N/A

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

   6. *-commutative N/A

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

   7. lower-fma.f64 N/A

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

   8. lift--.f64 N/A

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

   9. sub-neg N/A

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

   10. +-commutative N/A

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

   11. distribute-lft-in N/A

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

   12. neg-mul-1 N/A

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

   13. associate-*r* N/A

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

   14. metadata-eval N/A

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

   15. metadata-eval N/A

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

   16. lower-fma.f64 N/A

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

   17. metadata-eval N/A

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

   18. lift-/.f64 N/A

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

   19. metadata-eval N/A

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

   20. metadata-eval 99.8

       \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(-6, z, \color{blue}{4}\right), y - x, x\right) \]

4. Applied rewrites 99.8%

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

Alternative 2: 97.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{2}{3} - z\\ t_1 := \left(z \cdot -6\right) \cdot \left(y - x\right)\\ \mathbf{if}\;t\_0 \leq -2:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq 1:\\ \;\;\;\;\mathsf{fma}\left(-3, x, y \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (/ 2.0 3.0) z)) (t_1 (* (* z -6.0) (- y x))))
   (if (<= t_0 -2.0) t_1 (if (<= t_0 1.0) (fma -3.0 x (* y 4.0)) t_1))))

C

double code(double x, double y, double z) {
	double t_0 = (2.0 / 3.0) - z;
	double t_1 = (z * -6.0) * (y - x);
	double tmp;
	if (t_0 <= -2.0) {
		tmp = t_1;
	} else if (t_0 <= 1.0) {
		tmp = fma(-3.0, x, (y * 4.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(2.0 / 3.0) - z)
	t_1 = Float64(Float64(z * -6.0) * Float64(y - x))
	tmp = 0.0
	if (t_0 <= -2.0)
		tmp = t_1;
	elseif (t_0 <= 1.0)
		tmp = fma(-3.0, x, Float64(y * 4.0));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(2.0 / 3.0), $MachinePrecision] - z), $MachinePrecision]}, Block[{t$95$1 = N[(N[(z * -6.0), $MachinePrecision] * N[(y - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -2.0], t$95$1, If[LessEqual[t$95$0, 1.0], N[(-3.0 * x + N[(y * 4.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (/.f64 #s(literal 2 binary64) #s(literal 3 binary64)) z) < -2 or 1 < (-.f64 (/.f64 #s(literal 2 binary64) #s(literal 3 binary64)) z)

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 97.4

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

   5. Applied rewrites 97.4%

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

   7. Applied rewrites 97.4%

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

   if -2 < (-.f64 (/.f64 #s(literal 2 binary64) #s(literal 3 binary64)) z) < 1

   1. Initial program 99.4%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift--.f64 N/A

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

      4. sub-neg N/A

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

      5. distribute-rgt-in N/A

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

      6. lower-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. neg-mul-1 N/A

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

      9. associate-*r* N/A

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

      10. metadata-eval N/A

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

      11. metadata-eval N/A

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

      12. lower-*.f64 N/A

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

      13. metadata-eval 99.5

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

   4. Applied rewrites 99.5%

      \[\leadsto x + \color{blue}{\mathsf{fma}\left(y, 6, -6 \cdot x\right)} \cdot \left(\frac{2}{3} - z\right) \]
   5. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. lower-fma.f64 N/A

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

      6. lift-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. metadata-eval 99.4

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

   6. Applied rewrites 99.4%

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

   7. Taylor expanded in z around 0

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

      1. distribute-rgt-in N/A

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

      2. associate-+r+ N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. metadata-eval N/A

         \[\leadsto \left(x + \color{blue}{-4} \cdot x\right) + \left(6 \cdot y\right) \cdot \frac{2}{3} \]

      6. distribute-rgt1-in N/A

         \[\leadsto \color{blue}{\left(-4 + 1\right) \cdot x} + \left(6 \cdot y\right) \cdot \frac{2}{3} \]

      7. metadata-eval N/A

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

      8. *-commutative N/A

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

      9. associate-*r* N/A

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

      10. metadata-eval N/A

          \[\leadsto -3 \cdot x + \color{blue}{4} \cdot y \]

      11. lower-fma.f64 N/A

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

      12. lower-*.f64 97.6

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

   9. Applied rewrites 97.6%

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

4. Final simplification 97.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{2}{3} - z \leq -2:\\ \;\;\;\;\left(z \cdot -6\right) \cdot \left(y - x\right)\\ \mathbf{elif}\;\frac{2}{3} - z \leq 1:\\ \;\;\;\;\mathsf{fma}\left(-3, x, y \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot -6\right) \cdot \left(y - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 97.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{2}{3} - z\\ t_1 := \left(\left(y - x\right) \cdot z\right) \cdot -6\\ \mathbf{if}\;t\_0 \leq -2:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq 1:\\ \;\;\;\;\mathsf{fma}\left(-3, x, y \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (/ 2.0 3.0) z)) (t_1 (* (* (- y x) z) -6.0)))
   (if (<= t_0 -2.0) t_1 (if (<= t_0 1.0) (fma -3.0 x (* y 4.0)) t_1))))

C

double code(double x, double y, double z) {
	double t_0 = (2.0 / 3.0) - z;
	double t_1 = ((y - x) * z) * -6.0;
	double tmp;
	if (t_0 <= -2.0) {
		tmp = t_1;
	} else if (t_0 <= 1.0) {
		tmp = fma(-3.0, x, (y * 4.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(2.0 / 3.0) - z)
	t_1 = Float64(Float64(Float64(y - x) * z) * -6.0)
	tmp = 0.0
	if (t_0 <= -2.0)
		tmp = t_1;
	elseif (t_0 <= 1.0)
		tmp = fma(-3.0, x, Float64(y * 4.0));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(2.0 / 3.0), $MachinePrecision] - z), $MachinePrecision]}, Block[{t$95$1 = N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] * -6.0), $MachinePrecision]}, If[LessEqual[t$95$0, -2.0], t$95$1, If[LessEqual[t$95$0, 1.0], N[(-3.0 * x + N[(y * 4.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (/.f64 #s(literal 2 binary64) #s(literal 3 binary64)) z) < -2 or 1 < (-.f64 (/.f64 #s(literal 2 binary64) #s(literal 3 binary64)) z)

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 97.4

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

   5. Applied rewrites 97.4%

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

   if -2 < (-.f64 (/.f64 #s(literal 2 binary64) #s(literal 3 binary64)) z) < 1

   1. Initial program 99.4%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift--.f64 N/A

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

      4. sub-neg N/A

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

      5. distribute-rgt-in N/A

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

      6. lower-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. neg-mul-1 N/A

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

      9. associate-*r* N/A

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

      10. metadata-eval N/A

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

      11. metadata-eval N/A

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

      12. lower-*.f64 N/A

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

      13. metadata-eval 99.5

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

   4. Applied rewrites 99.5%

      \[\leadsto x + \color{blue}{\mathsf{fma}\left(y, 6, -6 \cdot x\right)} \cdot \left(\frac{2}{3} - z\right) \]
   5. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. lower-fma.f64 N/A

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

      6. lift-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. metadata-eval 99.4

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

   6. Applied rewrites 99.4%

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

   7. Taylor expanded in z around 0

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

      1. distribute-rgt-in N/A

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

      2. associate-+r+ N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. metadata-eval N/A

         \[\leadsto \left(x + \color{blue}{-4} \cdot x\right) + \left(6 \cdot y\right) \cdot \frac{2}{3} \]

      6. distribute-rgt1-in N/A

         \[\leadsto \color{blue}{\left(-4 + 1\right) \cdot x} + \left(6 \cdot y\right) \cdot \frac{2}{3} \]

      7. metadata-eval N/A

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

      8. *-commutative N/A

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

      9. associate-*r* N/A

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

      10. metadata-eval N/A

          \[\leadsto -3 \cdot x + \color{blue}{4} \cdot y \]

      11. lower-fma.f64 N/A

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

      12. lower-*.f64 97.6

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

   9. Applied rewrites 97.6%

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

4. Final simplification 97.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{2}{3} - z \leq -2:\\ \;\;\;\;\left(\left(y - x\right) \cdot z\right) \cdot -6\\ \mathbf{elif}\;\frac{2}{3} - z \leq 1:\\ \;\;\;\;\mathsf{fma}\left(-3, x, y \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y - x\right) \cdot z\right) \cdot -6\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -19:\\ \;\;\;\;\left(y \cdot -6\right) \cdot z\\ \mathbf{elif}\;z \leq 0.65:\\ \;\;\;\;\mathsf{fma}\left(y - x, 4, x\right)\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+209}:\\ \;\;\;\;\left(z \cdot -6\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot z\right) \cdot 6\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -19.0)
   (* (* y -6.0) z)
   (if (<= z 0.65)
     (fma (- y x) 4.0 x)
     (if (<= z 5.5e+209) (* (* z -6.0) y) (* (* x z) 6.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -19.0) {
		tmp = (y * -6.0) * z;
	} else if (z <= 0.65) {
		tmp = fma((y - x), 4.0, x);
	} else if (z <= 5.5e+209) {
		tmp = (z * -6.0) * y;
	} else {
		tmp = (x * z) * 6.0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -19.0)
		tmp = Float64(Float64(y * -6.0) * z);
	elseif (z <= 0.65)
		tmp = fma(Float64(y - x), 4.0, x);
	elseif (z <= 5.5e+209)
		tmp = Float64(Float64(z * -6.0) * y);
	else
		tmp = Float64(Float64(x * z) * 6.0);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -19.0], N[(N[(y * -6.0), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[z, 0.65], N[(N[(y - x), $MachinePrecision] * 4.0 + x), $MachinePrecision], If[LessEqual[z, 5.5e+209], N[(N[(z * -6.0), $MachinePrecision] * y), $MachinePrecision], N[(N[(x * z), $MachinePrecision] * 6.0), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -19

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 97.9

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

   5. Applied rewrites 97.9%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 55.9%

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

   if -19 < z < 0.650000000000000022

   1. Initial program 99.4%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 4, x\right)} \]

      4. lower--.f64 97.5

         \[\leadsto \mathsf{fma}\left(\color{blue}{y - x}, 4, x\right) \]

   5. Applied rewrites 97.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 4, x\right)} \]

   if 0.650000000000000022 < z < 5.49999999999999967e209

   1. Initial program 99.7%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lift--.f64 N/A

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

      6. flip-- N/A

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

      7. associate-*l/ N/A

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

      8. flip-+ N/A

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

      9. lift--.f64 N/A

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

      10. associate-/r/ N/A

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

      11. lower-fma.f64 N/A

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

   4. Applied rewrites 69.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{\left(\mathsf{fma}\left(-z, z, 0.4444444444444444\right) \cdot 6\right) \cdot \left(y - x\right)}{\mathsf{fma}\left(-z, z, 0.4444444444444444\right)}, 0.6666666666666666 - z, x\right)} \]

   5. Taylor expanded in y around inf

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

      1. metadata-eval N/A

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

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

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. sub-neg N/A

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

      6. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(\left(-6 \cdot \left(\frac{2}{3} + \color{blue}{-1 \cdot z}\right)\right) \cdot y\right) \]

      7. distribute-lft-in N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\left(-6 \cdot \frac{2}{3} + -6 \cdot \left(-1 \cdot z\right)\right)} \cdot y\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{neg}\left(\left(\color{blue}{-4} + -6 \cdot \left(-1 \cdot z\right)\right) \cdot y\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{neg}\left(\left(\color{blue}{4 \cdot -1} + -6 \cdot \left(-1 \cdot z\right)\right) \cdot y\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{neg}\left(\left(4 \cdot -1 + -6 \cdot \color{blue}{\left(z \cdot -1\right)}\right) \cdot y\right) \]

      11. associate-*l* N/A

          \[\leadsto \mathsf{neg}\left(\left(4 \cdot -1 + \color{blue}{\left(-6 \cdot z\right) \cdot -1}\right) \cdot y\right) \]

      12. distribute-rgt-in N/A

          \[\leadsto \mathsf{neg}\left(\color{blue}{\left(-1 \cdot \left(4 + -6 \cdot z\right)\right)} \cdot y\right) \]

      13. mul-1-neg N/A

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

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

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

      15. *-commutative N/A

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

      16. remove-double-neg N/A

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

      17. *-commutative N/A

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

      18. lower-*.f64 N/A

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

      19. +-commutative N/A

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

      20. *-commutative N/A

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

      21. lower-fma.f64 65.8

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

   7. Applied rewrites 65.8%

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

   8. Taylor expanded in z around inf

      \[\leadsto \left(-6 \cdot z\right) \cdot y \]
   9. Step-by-step derivation

   10. Applied rewrites 61.6%

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

   if 5.49999999999999967e209 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 99.9

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

   5. Applied rewrites 99.9%

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

   7. Applied rewrites 99.8%

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

   8. Taylor expanded in y around 0

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

   10. Applied rewrites 75.1%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -19:\\ \;\;\;\;\left(y \cdot -6\right) \cdot z\\ \mathbf{elif}\;z \leq 0.65:\\ \;\;\;\;\mathsf{fma}\left(y - x, 4, x\right)\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+209}:\\ \;\;\;\;\left(z \cdot -6\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot z\right) \cdot 6\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -19:\\ \;\;\;\;\left(y \cdot -6\right) \cdot z\\ \mathbf{elif}\;z \leq 0.65:\\ \;\;\;\;\mathsf{fma}\left(y - x, 4, x\right)\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+209}:\\ \;\;\;\;\left(y \cdot z\right) \cdot -6\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot z\right) \cdot 6\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -19.0)
   (* (* y -6.0) z)
   (if (<= z 0.65)
     (fma (- y x) 4.0 x)
     (if (<= z 5.5e+209) (* (* y z) -6.0) (* (* x z) 6.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -19.0) {
		tmp = (y * -6.0) * z;
	} else if (z <= 0.65) {
		tmp = fma((y - x), 4.0, x);
	} else if (z <= 5.5e+209) {
		tmp = (y * z) * -6.0;
	} else {
		tmp = (x * z) * 6.0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -19.0)
		tmp = Float64(Float64(y * -6.0) * z);
	elseif (z <= 0.65)
		tmp = fma(Float64(y - x), 4.0, x);
	elseif (z <= 5.5e+209)
		tmp = Float64(Float64(y * z) * -6.0);
	else
		tmp = Float64(Float64(x * z) * 6.0);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -19.0], N[(N[(y * -6.0), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[z, 0.65], N[(N[(y - x), $MachinePrecision] * 4.0 + x), $MachinePrecision], If[LessEqual[z, 5.5e+209], N[(N[(y * z), $MachinePrecision] * -6.0), $MachinePrecision], N[(N[(x * z), $MachinePrecision] * 6.0), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -19

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 97.9

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

   5. Applied rewrites 97.9%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 55.9%

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

   if -19 < z < 0.650000000000000022

   1. Initial program 99.4%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 4, x\right)} \]

      4. lower--.f64 97.5

         \[\leadsto \mathsf{fma}\left(\color{blue}{y - x}, 4, x\right) \]

   5. Applied rewrites 97.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 4, x\right)} \]

   if 0.650000000000000022 < z < 5.49999999999999967e209

   1. Initial program 99.7%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 95.5

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

   5. Applied rewrites 95.5%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 61.5%

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

   if 5.49999999999999967e209 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 99.9

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

   5. Applied rewrites 99.9%

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

   7. Applied rewrites 99.8%

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

   8. Taylor expanded in y around 0

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

   10. Applied rewrites 75.1%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -19:\\ \;\;\;\;\left(y \cdot -6\right) \cdot z\\ \mathbf{elif}\;z \leq 0.65:\\ \;\;\;\;\mathsf{fma}\left(y - x, 4, x\right)\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+209}:\\ \;\;\;\;\left(y \cdot z\right) \cdot -6\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot z\right) \cdot 6\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 74.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(y \cdot -6\right) \cdot z\\ \mathbf{if}\;z \leq -19:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 0.65:\\ \;\;\;\;\mathsf{fma}\left(y - x, 4, x\right)\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+209}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot z\right) \cdot 6\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (* y -6.0) z)))
   (if (<= z -19.0)
     t_0
     (if (<= z 0.65)
       (fma (- y x) 4.0 x)
       (if (<= z 5.5e+209) t_0 (* (* x z) 6.0))))))

C

double code(double x, double y, double z) {
	double t_0 = (y * -6.0) * z;
	double tmp;
	if (z <= -19.0) {
		tmp = t_0;
	} else if (z <= 0.65) {
		tmp = fma((y - x), 4.0, x);
	} else if (z <= 5.5e+209) {
		tmp = t_0;
	} else {
		tmp = (x * z) * 6.0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(y * -6.0) * z)
	tmp = 0.0
	if (z <= -19.0)
		tmp = t_0;
	elseif (z <= 0.65)
		tmp = fma(Float64(y - x), 4.0, x);
	elseif (z <= 5.5e+209)
		tmp = t_0;
	else
		tmp = Float64(Float64(x * z) * 6.0);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(y * -6.0), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[z, -19.0], t$95$0, If[LessEqual[z, 0.65], N[(N[(y - x), $MachinePrecision] * 4.0 + x), $MachinePrecision], If[LessEqual[z, 5.5e+209], t$95$0, N[(N[(x * z), $MachinePrecision] * 6.0), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -19 or 0.650000000000000022 < z < 5.49999999999999967e209

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 96.9

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

   5. Applied rewrites 96.9%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 58.4%

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

   if -19 < z < 0.650000000000000022

   1. Initial program 99.4%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 4, x\right)} \]

      4. lower--.f64 97.5

         \[\leadsto \mathsf{fma}\left(\color{blue}{y - x}, 4, x\right) \]

   5. Applied rewrites 97.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 4, x\right)} \]

   if 5.49999999999999967e209 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 99.9

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

   5. Applied rewrites 99.9%

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

   7. Applied rewrites 99.8%

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

   8. Taylor expanded in y around 0

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

   10. Applied rewrites 75.1%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -19:\\ \;\;\;\;\left(y \cdot -6\right) \cdot z\\ \mathbf{elif}\;z \leq 0.65:\\ \;\;\;\;\mathsf{fma}\left(y - x, 4, x\right)\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+209}:\\ \;\;\;\;\left(y \cdot -6\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot z\right) \cdot 6\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 74.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(y \cdot -6\right) \cdot z\\ \mathbf{if}\;z \leq -19:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 0.65:\\ \;\;\;\;\mathsf{fma}\left(y - x, 4, x\right)\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+209}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\left(6 \cdot z\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (* y -6.0) z)))
   (if (<= z -19.0)
     t_0
     (if (<= z 0.65)
       (fma (- y x) 4.0 x)
       (if (<= z 5.5e+209) t_0 (* (* 6.0 z) x))))))

C

double code(double x, double y, double z) {
	double t_0 = (y * -6.0) * z;
	double tmp;
	if (z <= -19.0) {
		tmp = t_0;
	} else if (z <= 0.65) {
		tmp = fma((y - x), 4.0, x);
	} else if (z <= 5.5e+209) {
		tmp = t_0;
	} else {
		tmp = (6.0 * z) * x;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(y * -6.0) * z)
	tmp = 0.0
	if (z <= -19.0)
		tmp = t_0;
	elseif (z <= 0.65)
		tmp = fma(Float64(y - x), 4.0, x);
	elseif (z <= 5.5e+209)
		tmp = t_0;
	else
		tmp = Float64(Float64(6.0 * z) * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(y * -6.0), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[z, -19.0], t$95$0, If[LessEqual[z, 0.65], N[(N[(y - x), $MachinePrecision] * 4.0 + x), $MachinePrecision], If[LessEqual[z, 5.5e+209], t$95$0, N[(N[(6.0 * z), $MachinePrecision] * x), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -19 or 0.650000000000000022 < z < 5.49999999999999967e209

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 96.9

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

   5. Applied rewrites 96.9%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 58.4%

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

   if -19 < z < 0.650000000000000022

   1. Initial program 99.4%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 4, x\right)} \]

      4. lower--.f64 97.5

         \[\leadsto \mathsf{fma}\left(\color{blue}{y - x}, 4, x\right) \]

   5. Applied rewrites 97.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 4, x\right)} \]

   if 5.49999999999999967e209 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 99.9

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

   5. Applied rewrites 99.9%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 75.0%

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

   10. Applied rewrites 75.0%

       \[\leadsto \left(z \cdot 6\right) \cdot x \]
3. Recombined 3 regimes into one program.

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -19:\\ \;\;\;\;\left(y \cdot -6\right) \cdot z\\ \mathbf{elif}\;z \leq 0.65:\\ \;\;\;\;\mathsf{fma}\left(y - x, 4, x\right)\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+209}:\\ \;\;\;\;\left(y \cdot -6\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(6 \cdot z\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 74.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(y \cdot -6\right) \cdot z\\ \mathbf{if}\;z \leq -19:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 0.65:\\ \;\;\;\;\mathsf{fma}\left(y - x, 4, x\right)\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+209}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\left(6 \cdot x\right) \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (* y -6.0) z)))
   (if (<= z -19.0)
     t_0
     (if (<= z 0.65)
       (fma (- y x) 4.0 x)
       (if (<= z 5.5e+209) t_0 (* (* 6.0 x) z))))))

C

double code(double x, double y, double z) {
	double t_0 = (y * -6.0) * z;
	double tmp;
	if (z <= -19.0) {
		tmp = t_0;
	} else if (z <= 0.65) {
		tmp = fma((y - x), 4.0, x);
	} else if (z <= 5.5e+209) {
		tmp = t_0;
	} else {
		tmp = (6.0 * x) * z;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(y * -6.0) * z)
	tmp = 0.0
	if (z <= -19.0)
		tmp = t_0;
	elseif (z <= 0.65)
		tmp = fma(Float64(y - x), 4.0, x);
	elseif (z <= 5.5e+209)
		tmp = t_0;
	else
		tmp = Float64(Float64(6.0 * x) * z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(y * -6.0), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[z, -19.0], t$95$0, If[LessEqual[z, 0.65], N[(N[(y - x), $MachinePrecision] * 4.0 + x), $MachinePrecision], If[LessEqual[z, 5.5e+209], t$95$0, N[(N[(6.0 * x), $MachinePrecision] * z), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -19 or 0.650000000000000022 < z < 5.49999999999999967e209

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 96.9

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

   5. Applied rewrites 96.9%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 58.4%

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

   if -19 < z < 0.650000000000000022

   1. Initial program 99.4%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 4, x\right)} \]

      4. lower--.f64 97.5

         \[\leadsto \mathsf{fma}\left(\color{blue}{y - x}, 4, x\right) \]

   5. Applied rewrites 97.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 4, x\right)} \]

   if 5.49999999999999967e209 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 99.9

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

   5. Applied rewrites 99.9%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 75.0%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -19:\\ \;\;\;\;\left(y \cdot -6\right) \cdot z\\ \mathbf{elif}\;z \leq 0.65:\\ \;\;\;\;\mathsf{fma}\left(y - x, 4, x\right)\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+209}:\\ \;\;\;\;\left(y \cdot -6\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(6 \cdot x\right) \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 74.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(z, -6, 4\right) \cdot y\\ \mathbf{if}\;y \leq -1.65 \cdot 10^{+20}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-76}:\\ \;\;\;\;\mathsf{fma}\left(6, z, -3\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (fma z -6.0 4.0) y)))
   (if (<= y -1.65e+20) t_0 (if (<= y 3.5e-76) (* (fma 6.0 z -3.0) x) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = fma(z, -6.0, 4.0) * y;
	double tmp;
	if (y <= -1.65e+20) {
		tmp = t_0;
	} else if (y <= 3.5e-76) {
		tmp = fma(6.0, z, -3.0) * x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(fma(z, -6.0, 4.0) * y)
	tmp = 0.0
	if (y <= -1.65e+20)
		tmp = t_0;
	elseif (y <= 3.5e-76)
		tmp = Float64(fma(6.0, z, -3.0) * x);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(z * -6.0 + 4.0), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -1.65e+20], t$95$0, If[LessEqual[y, 3.5e-76], N[(N[(6.0 * z + -3.0), $MachinePrecision] * x), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.65e20 or 3.49999999999999997e-76 < y

   1. Initial program 99.6%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. sub-neg N/A

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

      5. mul-1-neg N/A

         \[\leadsto \left(6 \cdot \left(\frac{2}{3} + \color{blue}{-1 \cdot z}\right)\right) \cdot y \]

      6. +-commutative N/A

         \[\leadsto \left(6 \cdot \color{blue}{\left(-1 \cdot z + \frac{2}{3}\right)}\right) \cdot y \]

      7. distribute-lft-in N/A

         \[\leadsto \color{blue}{\left(6 \cdot \left(-1 \cdot z\right) + 6 \cdot \frac{2}{3}\right)} \cdot y \]

      8. metadata-eval N/A

         \[\leadsto \left(6 \cdot \left(-1 \cdot z\right) + \color{blue}{4}\right) \cdot y \]

      9. associate-*r* N/A

         \[\leadsto \left(\color{blue}{\left(6 \cdot -1\right) \cdot z} + 4\right) \cdot y \]

      10. metadata-eval N/A

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

      11. *-commutative N/A

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

      12. lower-fma.f64 83.0

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

   5. Applied rewrites 83.0%

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

   if -1.65e20 < y < 3.49999999999999997e-76

   1. Initial program 99.6%

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

   3. Taylor expanded in y around 0

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

      1. metadata-eval N/A

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

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

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. sub-neg N/A

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

      6. *-lft-identity N/A

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

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

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

      8. neg-mul-1 N/A

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

      9. associate-*r* N/A

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

      10. distribute-rgt-in N/A

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

      11. metadata-eval N/A

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

      12. distribute-rgt-in N/A

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

      13. +-commutative N/A

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

      14. metadata-eval N/A

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

      15. sub-neg N/A

          \[\leadsto x \cdot \left(-1 \cdot \color{blue}{\left(6 \cdot \left(\frac{2}{3} - z\right) - 1\right)}\right) \]

      16. neg-mul-1 N/A

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

      17. *-commutative N/A

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

      18. lower-*.f64 N/A

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

   5. Applied rewrites 80.8%

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

Alternative 10: 74.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(y \cdot -6\right) \cdot z\\ \mathbf{if}\;z \leq -19:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 0.65:\\ \;\;\;\;\mathsf{fma}\left(y - x, 4, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (* y -6.0) z)))
   (if (<= z -19.0) t_0 (if (<= z 0.65) (fma (- y x) 4.0 x) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (y * -6.0) * z;
	double tmp;
	if (z <= -19.0) {
		tmp = t_0;
	} else if (z <= 0.65) {
		tmp = fma((y - x), 4.0, x);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(y * -6.0) * z)
	tmp = 0.0
	if (z <= -19.0)
		tmp = t_0;
	elseif (z <= 0.65)
		tmp = fma(Float64(y - x), 4.0, x);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(y * -6.0), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[z, -19.0], t$95$0, If[LessEqual[z, 0.65], N[(N[(y - x), $MachinePrecision] * 4.0 + x), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -19 or 0.650000000000000022 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 97.4

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

   5. Applied rewrites 97.4%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 54.8%

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

   if -19 < z < 0.650000000000000022

   1. Initial program 99.4%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 4, x\right)} \]

      4. lower--.f64 97.5

         \[\leadsto \mathsf{fma}\left(\color{blue}{y - x}, 4, x\right) \]

   5. Applied rewrites 97.5%

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

4. Final simplification 74.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -19:\\ \;\;\;\;\left(y \cdot -6\right) \cdot z\\ \mathbf{elif}\;z \leq 0.65:\\ \;\;\;\;\mathsf{fma}\left(y - x, 4, x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot -6\right) \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 38.2% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{+57}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-103}:\\ \;\;\;\;-3 \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot 4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3.5e+57) (* y 4.0) (if (<= y 3.6e-103) (* -3.0 x) (* y 4.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.5e+57) {
		tmp = y * 4.0;
	} else if (y <= 3.6e-103) {
		tmp = -3.0 * x;
	} else {
		tmp = y * 4.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-3.5d+57)) then
        tmp = y * 4.0d0
    else if (y <= 3.6d-103) then
        tmp = (-3.0d0) * x
    else
        tmp = y * 4.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.5e+57) {
		tmp = y * 4.0;
	} else if (y <= 3.6e-103) {
		tmp = -3.0 * x;
	} else {
		tmp = y * 4.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -3.5e+57:
		tmp = y * 4.0
	elif y <= 3.6e-103:
		tmp = -3.0 * x
	else:
		tmp = y * 4.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3.5e+57)
		tmp = Float64(y * 4.0);
	elseif (y <= 3.6e-103)
		tmp = Float64(-3.0 * x);
	else
		tmp = Float64(y * 4.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -3.5e+57)
		tmp = y * 4.0;
	elseif (y <= 3.6e-103)
		tmp = -3.0 * x;
	else
		tmp = y * 4.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3.5e+57], N[(y * 4.0), $MachinePrecision], If[LessEqual[y, 3.6e-103], N[(-3.0 * x), $MachinePrecision], N[(y * 4.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.4999999999999997e57 or 3.5999999999999998e-103 < y

   1. Initial program 99.6%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 4, x\right)} \]

      4. lower--.f64 47.7

         \[\leadsto \mathsf{fma}\left(\color{blue}{y - x}, 4, x\right) \]

   5. Applied rewrites 47.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 4, x\right)} \]

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 38.5%

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

   if -3.4999999999999997e57 < y < 3.5999999999999998e-103

   1. Initial program 99.6%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 4, x\right)} \]

      4. lower--.f64 42.8

         \[\leadsto \mathsf{fma}\left(\color{blue}{y - x}, 4, x\right) \]

   5. Applied rewrites 42.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 4, x\right)} \]

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 34.9%

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

Alternative 12: 51.6% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(y - x, 4, x\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (fma (- y x) 4.0 x))

C

double code(double x, double y, double z) {
	return fma((y - x), 4.0, x);
}

Julia

function code(x, y, z)
	return fma(Float64(y - x), 4.0, x)
end

Wolfram

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

Derivation

1. Initial program 99.6%

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

3. Taylor expanded in z around 0

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

   1. +-commutative N/A

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

   2. *-commutative N/A

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

   3. lower-fma.f64 N/A

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 4, x\right)} \]

   4. lower--.f64 45.7

      \[\leadsto \mathsf{fma}\left(\color{blue}{y - x}, 4, x\right) \]

5. Applied rewrites 45.7%

   \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 4, x\right)} \]
6. Add Preprocessing

Alternative 13: 27.3% accurate, 5.2× speedup

Math

\[\begin{array}{l} \\ -3 \cdot x \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* -3.0 x))

C

double code(double x, double y, double z) {
	return -3.0 * 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 = (-3.0d0) * x
end function

Java

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

Python

def code(x, y, z):
	return -3.0 * x

Julia

function code(x, y, z)
	return Float64(-3.0 * x)
end

MATLAB

function tmp = code(x, y, z)
	tmp = -3.0 * x;
end

Wolfram

code[x_, y_, z_] := N[(-3.0 * x), $MachinePrecision]

Derivation

1. Initial program 99.6%

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

3. Taylor expanded in z around 0

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

   1. +-commutative N/A

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

   2. *-commutative N/A

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

   3. lower-fma.f64 N/A

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 4, x\right)} \]

   4. lower--.f64 45.7

      \[\leadsto \mathsf{fma}\left(\color{blue}{y - x}, 4, x\right) \]

5. Applied rewrites 45.7%

   \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 4, x\right)} \]

6. Taylor expanded in y around 0

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

8. Applied rewrites 20.9%

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

Reproduce

herbie shell --seed 2024268 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, D"
  :precision binary64
  (+ x (* (* (- y x) 6.0) (- (/ 2.0 3.0) z))))