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

Percentage Accurate: 99.7% → 99.8%

Time: 7.2s

Alternatives: 10

Speedup: 1.1×

• 20.6% 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: 99.8% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

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

   2. +-commutative N/A

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

   3. lift-*.f64 N/A

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

   4. lift-*.f64 N/A

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

   5. associate-*l* N/A

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

   6. lower-fma.f64 N/A

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

   7. *-commutative N/A

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

   8. lower-*.f64 99.8

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

4. Applied rewrites 99.8%

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

5. Final simplification 99.8%

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

Alternative 2: 98.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(6 \cdot z\right) \cdot \left(y - x\right)\\ \mathbf{if}\;z \leq -52000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-7}:\\ \;\;\;\;\left(z \cdot y\right) \cdot 6 + x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (* 6.0 z) (- y x))))
   (if (<= z -52000000.0) t_0 (if (<= z 7.5e-7) (+ (* (* z y) 6.0) x) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (6.0 * z) * (y - x);
	double tmp;
	if (z <= -52000000.0) {
		tmp = t_0;
	} else if (z <= 7.5e-7) {
		tmp = ((z * y) * 6.0) + 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 - x)
    if (z <= (-52000000.0d0)) then
        tmp = t_0
    else if (z <= 7.5d-7) then
        tmp = ((z * y) * 6.0d0) + 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 - x);
	double tmp;
	if (z <= -52000000.0) {
		tmp = t_0;
	} else if (z <= 7.5e-7) {
		tmp = ((z * y) * 6.0) + x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (6.0 * z) * (y - x)
	tmp = 0
	if z <= -52000000.0:
		tmp = t_0
	elif z <= 7.5e-7:
		tmp = ((z * y) * 6.0) + x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(6.0 * z) * Float64(y - x))
	tmp = 0.0
	if (z <= -52000000.0)
		tmp = t_0;
	elseif (z <= 7.5e-7)
		tmp = Float64(Float64(Float64(z * y) * 6.0) + x);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (6.0 * z) * (y - x);
	tmp = 0.0;
	if (z <= -52000000.0)
		tmp = t_0;
	elseif (z <= 7.5e-7)
		tmp = ((z * y) * 6.0) + x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(6.0 * z), $MachinePrecision] * N[(y - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -52000000.0], t$95$0, If[LessEqual[z, 7.5e-7], N[(N[(N[(z * y), $MachinePrecision] * 6.0), $MachinePrecision] + x), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.2e7 or 7.5000000000000002e-7 < 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. *-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. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 99.6

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

   5. Applied rewrites 99.6%

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

   7. Applied rewrites 99.7%

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

   if -5.2e7 < z < 7.5000000000000002e-7

   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 inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 98.5

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

   5. Applied rewrites 98.5%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -52000000:\\ \;\;\;\;\left(6 \cdot z\right) \cdot \left(y - x\right)\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-7}:\\ \;\;\;\;\left(z \cdot y\right) \cdot 6 + x\\ \mathbf{else}:\\ \;\;\;\;\left(6 \cdot z\right) \cdot \left(y - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(6 \cdot z\right) \cdot \left(y - x\right)\\ \mathbf{if}\;z \leq -480000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-7}:\\ \;\;\;\;\mathsf{fma}\left(6 \cdot y, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (* 6.0 z) (- y x))))
   (if (<= z -480000.0) t_0 (if (<= z 7.5e-7) (fma (* 6.0 y) z x) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (6.0 * z) * (y - x);
	double tmp;
	if (z <= -480000.0) {
		tmp = t_0;
	} else if (z <= 7.5e-7) {
		tmp = fma((6.0 * y), z, x);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(6.0 * z) * Float64(y - x))
	tmp = 0.0
	if (z <= -480000.0)
		tmp = t_0;
	elseif (z <= 7.5e-7)
		tmp = fma(Float64(6.0 * y), z, x);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(6.0 * z), $MachinePrecision] * N[(y - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -480000.0], t$95$0, If[LessEqual[z, 7.5e-7], N[(N[(6.0 * y), $MachinePrecision] * z + x), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -4.8e5 or 7.5000000000000002e-7 < 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. *-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. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 99.6

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

   5. Applied rewrites 99.6%

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

   7. Applied rewrites 99.7%

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

   if -4.8e5 < z < 7.5000000000000002e-7

   1. Initial program 99.9%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift--.f64 N/A

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

      4. sub-neg N/A

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

      5. distribute-rgt-in N/A

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

      6. lower-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. neg-mul-1 N/A

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

      9. associate-*r* N/A

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

      10. metadata-eval N/A

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

      11. metadata-eval N/A

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

      12. lower-*.f64 N/A

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

      13. metadata-eval 99.8

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

   4. Applied rewrites 99.8%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 99.8

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

      5. lift-fma.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 99.8

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

   6. Applied rewrites 99.8%

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

   7. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 98.5

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

   9. Applied rewrites 98.5%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -480000:\\ \;\;\;\;\left(6 \cdot z\right) \cdot \left(y - x\right)\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-7}:\\ \;\;\;\;\mathsf{fma}\left(6 \cdot y, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(6 \cdot z\right) \cdot \left(y - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 98.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(z \cdot \left(y - x\right)\right) \cdot 6\\ \mathbf{if}\;z \leq -480000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-7}:\\ \;\;\;\;\mathsf{fma}\left(6 \cdot y, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (* z (- y x)) 6.0)))
   (if (<= z -480000.0) t_0 (if (<= z 7.5e-7) (fma (* 6.0 y) z x) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (z * (y - x)) * 6.0;
	double tmp;
	if (z <= -480000.0) {
		tmp = t_0;
	} else if (z <= 7.5e-7) {
		tmp = fma((6.0 * y), z, x);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(z * Float64(y - x)) * 6.0)
	tmp = 0.0
	if (z <= -480000.0)
		tmp = t_0;
	elseif (z <= 7.5e-7)
		tmp = fma(Float64(6.0 * y), z, x);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(z * N[(y - x), $MachinePrecision]), $MachinePrecision] * 6.0), $MachinePrecision]}, If[LessEqual[z, -480000.0], t$95$0, If[LessEqual[z, 7.5e-7], N[(N[(6.0 * y), $MachinePrecision] * z + x), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -4.8e5 or 7.5000000000000002e-7 < 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. *-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. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 99.6

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

   5. Applied rewrites 99.6%

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

   if -4.8e5 < z < 7.5000000000000002e-7

   1. Initial program 99.9%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift--.f64 N/A

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

      4. sub-neg N/A

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

      5. distribute-rgt-in N/A

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

      6. lower-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. neg-mul-1 N/A

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

      9. associate-*r* N/A

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

      10. metadata-eval N/A

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

      11. metadata-eval N/A

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

      12. lower-*.f64 N/A

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

      13. metadata-eval 99.8

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

   4. Applied rewrites 99.8%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 99.8

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

      5. lift-fma.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 99.8

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

   6. Applied rewrites 99.8%

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

   7. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 98.5

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

   9. Applied rewrites 98.5%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -480000:\\ \;\;\;\;\left(z \cdot \left(y - x\right)\right) \cdot 6\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-7}:\\ \;\;\;\;\mathsf{fma}\left(6 \cdot y, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot \left(y - x\right)\right) \cdot 6\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 86.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(6 \cdot y, z, x\right)\\ \mathbf{if}\;y \leq -2.3 \cdot 10^{-101}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-56}:\\ \;\;\;\;\mathsf{fma}\left(z \cdot x, -6, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (fma (* 6.0 y) z x)))
   (if (<= y -2.3e-101) t_0 (if (<= y 4.6e-56) (fma (* z x) -6.0 x) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = fma((6.0 * y), z, x);
	double tmp;
	if (y <= -2.3e-101) {
		tmp = t_0;
	} else if (y <= 4.6e-56) {
		tmp = fma((z * x), -6.0, x);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = fma(Float64(6.0 * y), z, x)
	tmp = 0.0
	if (y <= -2.3e-101)
		tmp = t_0;
	elseif (y <= 4.6e-56)
		tmp = fma(Float64(z * x), -6.0, x);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(6.0 * y), $MachinePrecision] * z + x), $MachinePrecision]}, If[LessEqual[y, -2.3e-101], t$95$0, If[LessEqual[y, 4.6e-56], N[(N[(z * x), $MachinePrecision] * -6.0 + x), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.2999999999999999e-101 or 4.60000000000000005e-56 < y

   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

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

      2. *-commutative N/A

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

      3. lift--.f64 N/A

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

      4. sub-neg N/A

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

      5. distribute-rgt-in N/A

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

      6. lower-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. neg-mul-1 N/A

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

      9. associate-*r* N/A

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

      10. metadata-eval N/A

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

      11. metadata-eval N/A

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

      12. lower-*.f64 N/A

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

      13. metadata-eval 99.8

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

   4. Applied rewrites 99.8%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 99.8

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

      5. lift-fma.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 99.8

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

   6. Applied rewrites 99.8%

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

   7. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 90.9

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

   9. Applied rewrites 90.9%

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

   if -2.2999999999999999e-101 < y < 4.60000000000000005e-56

   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

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 91.5

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

   5. Applied rewrites 91.5%

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

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{-101}:\\ \;\;\;\;\mathsf{fma}\left(6 \cdot y, z, x\right)\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-56}:\\ \;\;\;\;\mathsf{fma}\left(z \cdot x, -6, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(6 \cdot y, z, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 75.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(6 \cdot z\right) \cdot y\\ \mathbf{if}\;y \leq -1.7 \cdot 10^{+77}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+45}:\\ \;\;\;\;\mathsf{fma}\left(z \cdot x, -6, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (* 6.0 z) y)))
   (if (<= y -1.7e+77) t_0 (if (<= y 5.2e+45) (fma (* z x) -6.0 x) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (6.0 * z) * y;
	double tmp;
	if (y <= -1.7e+77) {
		tmp = t_0;
	} else if (y <= 5.2e+45) {
		tmp = fma((z * x), -6.0, x);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(6.0 * z) * y)
	tmp = 0.0
	if (y <= -1.7e+77)
		tmp = t_0;
	elseif (y <= 5.2e+45)
		tmp = fma(Float64(z * x), -6.0, x);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(6.0 * z), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -1.7e+77], t$95$0, If[LessEqual[y, 5.2e+45], N[(N[(z * x), $MachinePrecision] * -6.0 + x), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.69999999999999998e77 or 5.20000000000000014e45 < y

   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 inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 76.1

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

   5. Applied rewrites 76.1%

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

   7. Applied rewrites 76.2%

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

   if -1.69999999999999998e77 < y < 5.20000000000000014e45

   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

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 82.3

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

   5. Applied rewrites 82.3%

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

Alternative 7: 50.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(6 \cdot z\right) \cdot y\\ \mathbf{if}\;y \leq -1.25 \cdot 10^{-7}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-56}:\\ \;\;\;\;\left(z \cdot x\right) \cdot -6\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (* 6.0 z) y)))
   (if (<= y -1.25e-7) t_0 (if (<= y 4.6e-56) (* (* z x) -6.0) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (6.0 * z) * y;
	double tmp;
	if (y <= -1.25e-7) {
		tmp = t_0;
	} else if (y <= 4.6e-56) {
		tmp = (z * x) * -6.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (6.0d0 * z) * y
    if (y <= (-1.25d-7)) then
        tmp = t_0
    else if (y <= 4.6d-56) then
        tmp = (z * x) * (-6.0d0)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (6.0 * z) * y;
	double tmp;
	if (y <= -1.25e-7) {
		tmp = t_0;
	} else if (y <= 4.6e-56) {
		tmp = (z * x) * -6.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (6.0 * z) * y
	tmp = 0
	if y <= -1.25e-7:
		tmp = t_0
	elif y <= 4.6e-56:
		tmp = (z * x) * -6.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(6.0 * z) * y)
	tmp = 0.0
	if (y <= -1.25e-7)
		tmp = t_0;
	elseif (y <= 4.6e-56)
		tmp = Float64(Float64(z * x) * -6.0);
	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 (y <= -1.25e-7)
		tmp = t_0;
	elseif (y <= 4.6e-56)
		tmp = (z * x) * -6.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(6.0 * z), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -1.25e-7], t$95$0, If[LessEqual[y, 4.6e-56], N[(N[(z * x), $MachinePrecision] * -6.0), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.24999999999999994e-7 or 4.60000000000000005e-56 < y

   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 inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 68.5

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

   5. Applied rewrites 68.5%

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

   7. Applied rewrites 68.6%

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

   if -1.24999999999999994e-7 < y < 4.60000000000000005e-56

   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. *-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. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 65.3

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

   5. Applied rewrites 65.3%

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

   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 52.9%

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

Alternative 8: 50.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(6 \cdot y\right) \cdot z\\ \mathbf{if}\;y \leq -1.25 \cdot 10^{-7}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-56}:\\ \;\;\;\;\left(z \cdot x\right) \cdot -6\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (* 6.0 y) z)))
   (if (<= y -1.25e-7) t_0 (if (<= y 4.6e-56) (* (* z x) -6.0) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (6.0 * y) * z;
	double tmp;
	if (y <= -1.25e-7) {
		tmp = t_0;
	} else if (y <= 4.6e-56) {
		tmp = (z * x) * -6.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (6.0d0 * y) * z
    if (y <= (-1.25d-7)) then
        tmp = t_0
    else if (y <= 4.6d-56) then
        tmp = (z * x) * (-6.0d0)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (6.0 * y) * z;
	double tmp;
	if (y <= -1.25e-7) {
		tmp = t_0;
	} else if (y <= 4.6e-56) {
		tmp = (z * x) * -6.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (6.0 * y) * z
	tmp = 0
	if y <= -1.25e-7:
		tmp = t_0
	elif y <= 4.6e-56:
		tmp = (z * x) * -6.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(6.0 * y) * z)
	tmp = 0.0
	if (y <= -1.25e-7)
		tmp = t_0;
	elseif (y <= 4.6e-56)
		tmp = Float64(Float64(z * x) * -6.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (6.0 * y) * z;
	tmp = 0.0;
	if (y <= -1.25e-7)
		tmp = t_0;
	elseif (y <= 4.6e-56)
		tmp = (z * x) * -6.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(6.0 * y), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[y, -1.25e-7], t$95$0, If[LessEqual[y, 4.6e-56], N[(N[(z * x), $MachinePrecision] * -6.0), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.24999999999999994e-7 or 4.60000000000000005e-56 < y

   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 inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 68.5

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

   5. Applied rewrites 68.5%

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

   7. Applied rewrites 68.6%

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

   if -1.24999999999999994e-7 < y < 4.60000000000000005e-56

   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. *-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. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 65.3

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

   5. Applied rewrites 65.3%

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

   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 52.9%

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

Alternative 9: 27.7% accurate, 1.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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. *-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. *-commutative N/A

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

   4. lower-*.f64 N/A

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

   5. lower--.f64 70.2

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

5. Applied rewrites 70.2%

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

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 28.8%

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

Alternative 10: 27.7% accurate, 1.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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. *-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. *-commutative N/A

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

   4. lower-*.f64 N/A

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

   5. lower--.f64 70.2

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

5. Applied rewrites 70.2%

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

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 28.8%

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

10. Applied rewrites 28.8%

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

11. Final simplification 28.8%

    \[\leadsto \left(-6 \cdot x\right) \cdot z \]
12. 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 2024268 
(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)))