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

Percentage Accurate: 99.7% → 99.8%

Time: 9.5s

Alternatives: 13

Speedup: 1.0×

• 21.1% 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, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. associate-*r* 99.8%

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

   2. +-commutative 99.8%

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

   3. *-commutative 99.8%

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

   4. associate-*r* 99.8%

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

   5. fma-def 99.8%

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

4. Applied egg-rr 99.8%

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

5. Final simplification 99.8%

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

Alternative 2: 99.7% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. +-commutative 99.8%

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

   2. *-commutative 99.8%

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

   3. fma-def 99.8%

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

   4. remove-double-neg 99.8%

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

   5. distribute-lft-neg-in 99.8%

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

   6. distribute-rgt-neg-in 99.8%

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

   7. sub-neg 99.8%

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

   8. distribute-neg-in 99.8%

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

   9. remove-double-neg 99.8%

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

   10. +-commutative 99.8%

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

   11. sub-neg 99.8%

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

   12. metadata-eval 99.8%

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

3. Simplified 99.8%

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

5. Final simplification 99.8%

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

Alternative 3: 60.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(x \cdot z\right)\\ t_1 := 6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -180000000000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{-36}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-60}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+143} \lor \neg \left(z \leq 7.5 \cdot 10^{+181}\right) \land z \leq 8.1 \cdot 10^{+245}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* x z))) (t_1 (* 6.0 (* y z))))
   (if (<= z -180000000000.0)
     t_0
     (if (<= z -6.8e-36)
       t_1
       (if (<= z 1.4e-60)
         x
         (if (or (<= z 1.1e+143) (and (not (<= z 7.5e+181)) (<= z 8.1e+245)))
           t_1
           t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (x * z);
	double t_1 = 6.0 * (y * z);
	double tmp;
	if (z <= -180000000000.0) {
		tmp = t_0;
	} else if (z <= -6.8e-36) {
		tmp = t_1;
	} else if (z <= 1.4e-60) {
		tmp = x;
	} else if ((z <= 1.1e+143) || (!(z <= 7.5e+181) && (z <= 8.1e+245))) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (-6.0d0) * (x * z)
    t_1 = 6.0d0 * (y * z)
    if (z <= (-180000000000.0d0)) then
        tmp = t_0
    else if (z <= (-6.8d-36)) then
        tmp = t_1
    else if (z <= 1.4d-60) then
        tmp = x
    else if ((z <= 1.1d+143) .or. (.not. (z <= 7.5d+181)) .and. (z <= 8.1d+245)) then
        tmp = t_1
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -6.0 * (x * z);
	double t_1 = 6.0 * (y * z);
	double tmp;
	if (z <= -180000000000.0) {
		tmp = t_0;
	} else if (z <= -6.8e-36) {
		tmp = t_1;
	} else if (z <= 1.4e-60) {
		tmp = x;
	} else if ((z <= 1.1e+143) || (!(z <= 7.5e+181) && (z <= 8.1e+245))) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (x * z)
	t_1 = 6.0 * (y * z)
	tmp = 0
	if z <= -180000000000.0:
		tmp = t_0
	elif z <= -6.8e-36:
		tmp = t_1
	elif z <= 1.4e-60:
		tmp = x
	elif (z <= 1.1e+143) or (not (z <= 7.5e+181) and (z <= 8.1e+245)):
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(x * z))
	t_1 = Float64(6.0 * Float64(y * z))
	tmp = 0.0
	if (z <= -180000000000.0)
		tmp = t_0;
	elseif (z <= -6.8e-36)
		tmp = t_1;
	elseif (z <= 1.4e-60)
		tmp = x;
	elseif ((z <= 1.1e+143) || (!(z <= 7.5e+181) && (z <= 8.1e+245)))
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (x * z);
	t_1 = 6.0 * (y * z);
	tmp = 0.0;
	if (z <= -180000000000.0)
		tmp = t_0;
	elseif (z <= -6.8e-36)
		tmp = t_1;
	elseif (z <= 1.4e-60)
		tmp = x;
	elseif ((z <= 1.1e+143) || (~((z <= 7.5e+181)) && (z <= 8.1e+245)))
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -180000000000.0], t$95$0, If[LessEqual[z, -6.8e-36], t$95$1, If[LessEqual[z, 1.4e-60], x, If[Or[LessEqual[z, 1.1e+143], And[N[Not[LessEqual[z, 7.5e+181]], $MachinePrecision], LessEqual[z, 8.1e+245]]], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.8e11 or 1.10000000000000007e143 < z < 7.5000000000000005e181 or 8.10000000000000023e245 < z

   1. Initial program 99.7%

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

      1. +-commutative 99.7%

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

      2. *-commutative 99.7%

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

      3. fma-def 99.7%

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

      4. remove-double-neg 99.7%

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

      5. distribute-lft-neg-in 99.7%

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

      6. distribute-rgt-neg-in 99.7%

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

      7. sub-neg 99.7%

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

      8. distribute-neg-in 99.7%

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

      9. remove-double-neg 99.7%

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

      10. +-commutative 99.7%

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

      11. sub-neg 99.7%

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

      12. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around inf 99.4%

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

   6. Taylor expanded in x around inf 62.6%

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

   if -1.8e11 < z < -6.8000000000000005e-36 or 1.4000000000000001e-60 < z < 1.10000000000000007e143 or 7.5000000000000005e181 < z < 8.10000000000000023e245

   1. Initial program 99.7%

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

      1. associate-*r* 99.7%

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

      2. +-commutative 99.7%

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

      3. *-commutative 99.7%

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

      4. associate-*r* 99.6%

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

      5. fma-def 99.8%

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in y around inf 75.4%

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

      1. *-commutative 75.4%

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

   7. Simplified 75.4%

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

   if -6.8000000000000005e-36 < z < 1.4000000000000001e-60

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 71.1%

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

4. Final simplification 69.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -180000000000:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{-36}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-60}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+143} \lor \neg \left(z \leq 7.5 \cdot 10^{+181}\right) \land z \leq 8.1 \cdot 10^{+245}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 60.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(z \cdot -6\right)\\ t_1 := 6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -260000000000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-39}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-53}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+142}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+181}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 5.9 \cdot 10^{+245}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (* z -6.0))) (t_1 (* 6.0 (* y z))))
   (if (<= z -260000000000.0)
     t_0
     (if (<= z -2.2e-39)
       t_1
       (if (<= z 1.8e-53)
         x
         (if (<= z 3.2e+142)
           t_1
           (if (<= z 1.7e+181)
             (* -6.0 (* x z))
             (if (<= z 5.9e+245) t_1 t_0))))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (z * -6.0);
	double t_1 = 6.0 * (y * z);
	double tmp;
	if (z <= -260000000000.0) {
		tmp = t_0;
	} else if (z <= -2.2e-39) {
		tmp = t_1;
	} else if (z <= 1.8e-53) {
		tmp = x;
	} else if (z <= 3.2e+142) {
		tmp = t_1;
	} else if (z <= 1.7e+181) {
		tmp = -6.0 * (x * z);
	} else if (z <= 5.9e+245) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x * (z * (-6.0d0))
    t_1 = 6.0d0 * (y * z)
    if (z <= (-260000000000.0d0)) then
        tmp = t_0
    else if (z <= (-2.2d-39)) then
        tmp = t_1
    else if (z <= 1.8d-53) then
        tmp = x
    else if (z <= 3.2d+142) then
        tmp = t_1
    else if (z <= 1.7d+181) then
        tmp = (-6.0d0) * (x * z)
    else if (z <= 5.9d+245) then
        tmp = t_1
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (z * -6.0);
	double t_1 = 6.0 * (y * z);
	double tmp;
	if (z <= -260000000000.0) {
		tmp = t_0;
	} else if (z <= -2.2e-39) {
		tmp = t_1;
	} else if (z <= 1.8e-53) {
		tmp = x;
	} else if (z <= 3.2e+142) {
		tmp = t_1;
	} else if (z <= 1.7e+181) {
		tmp = -6.0 * (x * z);
	} else if (z <= 5.9e+245) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (z * -6.0)
	t_1 = 6.0 * (y * z)
	tmp = 0
	if z <= -260000000000.0:
		tmp = t_0
	elif z <= -2.2e-39:
		tmp = t_1
	elif z <= 1.8e-53:
		tmp = x
	elif z <= 3.2e+142:
		tmp = t_1
	elif z <= 1.7e+181:
		tmp = -6.0 * (x * z)
	elif z <= 5.9e+245:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(z * -6.0))
	t_1 = Float64(6.0 * Float64(y * z))
	tmp = 0.0
	if (z <= -260000000000.0)
		tmp = t_0;
	elseif (z <= -2.2e-39)
		tmp = t_1;
	elseif (z <= 1.8e-53)
		tmp = x;
	elseif (z <= 3.2e+142)
		tmp = t_1;
	elseif (z <= 1.7e+181)
		tmp = Float64(-6.0 * Float64(x * z));
	elseif (z <= 5.9e+245)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (z * -6.0);
	t_1 = 6.0 * (y * z);
	tmp = 0.0;
	if (z <= -260000000000.0)
		tmp = t_0;
	elseif (z <= -2.2e-39)
		tmp = t_1;
	elseif (z <= 1.8e-53)
		tmp = x;
	elseif (z <= 3.2e+142)
		tmp = t_1;
	elseif (z <= 1.7e+181)
		tmp = -6.0 * (x * z);
	elseif (z <= 5.9e+245)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(z * -6.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -260000000000.0], t$95$0, If[LessEqual[z, -2.2e-39], t$95$1, If[LessEqual[z, 1.8e-53], x, If[LessEqual[z, 3.2e+142], t$95$1, If[LessEqual[z, 1.7e+181], N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.9e+245], t$95$1, t$95$0]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.6e11 or 5.9000000000000002e245 < z

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 62.2%

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

   4. Taylor expanded in z around inf 61.6%

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

      1. *-commutative 61.6%

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

      2. associate-*r* 61.7%

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

   6. Simplified 61.7%

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

   if -2.6e11 < z < -2.20000000000000001e-39 or 1.7999999999999999e-53 < z < 3.20000000000000005e142 or 1.70000000000000015e181 < z < 5.9000000000000002e245

   1. Initial program 99.7%

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

      1. associate-*r* 99.7%

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

      2. +-commutative 99.7%

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

      3. *-commutative 99.7%

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

      4. associate-*r* 99.6%

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

      5. fma-def 99.8%

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in y around inf 75.4%

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

      1. *-commutative 75.4%

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

   7. Simplified 75.4%

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

   if -2.20000000000000001e-39 < z < 1.7999999999999999e-53

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 71.1%

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

   if 3.20000000000000005e142 < z < 1.70000000000000015e181

   1. Initial program 99.7%

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

      1. +-commutative 99.7%

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

      2. *-commutative 99.7%

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

      3. fma-def 99.7%

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

      4. remove-double-neg 99.7%

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

      5. distribute-lft-neg-in 99.7%

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

      6. distribute-rgt-neg-in 99.7%

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

      7. sub-neg 99.7%

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

      8. distribute-neg-in 99.7%

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

      9. remove-double-neg 99.7%

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

      10. +-commutative 99.7%

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

      11. sub-neg 99.7%

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

      12. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around inf 99.7%

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

   6. Taylor expanded in x around inf 67.6%

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

4. Final simplification 69.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -260000000000:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-39}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-53}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+142}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+181}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 5.9 \cdot 10^{+245}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 60.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(z \cdot -6\right)\\ t_1 := 6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -470000000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-42}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-55}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+142}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+182}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{+245}:\\ \;\;\;\;y \cdot \left(z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (* z -6.0))) (t_1 (* 6.0 (* y z))))
   (if (<= z -470000000.0)
     t_0
     (if (<= z -2e-42)
       t_1
       (if (<= z 1.5e-55)
         x
         (if (<= z 4.4e+142)
           t_1
           (if (<= z 2.6e+182)
             (* -6.0 (* x z))
             (if (<= z 1.65e+245) (* y (* z 6.0)) t_0))))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (z * -6.0);
	double t_1 = 6.0 * (y * z);
	double tmp;
	if (z <= -470000000.0) {
		tmp = t_0;
	} else if (z <= -2e-42) {
		tmp = t_1;
	} else if (z <= 1.5e-55) {
		tmp = x;
	} else if (z <= 4.4e+142) {
		tmp = t_1;
	} else if (z <= 2.6e+182) {
		tmp = -6.0 * (x * z);
	} else if (z <= 1.65e+245) {
		tmp = y * (z * 6.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x * (z * (-6.0d0))
    t_1 = 6.0d0 * (y * z)
    if (z <= (-470000000.0d0)) then
        tmp = t_0
    else if (z <= (-2d-42)) then
        tmp = t_1
    else if (z <= 1.5d-55) then
        tmp = x
    else if (z <= 4.4d+142) then
        tmp = t_1
    else if (z <= 2.6d+182) then
        tmp = (-6.0d0) * (x * z)
    else if (z <= 1.65d+245) then
        tmp = y * (z * 6.0d0)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (z * -6.0);
	double t_1 = 6.0 * (y * z);
	double tmp;
	if (z <= -470000000.0) {
		tmp = t_0;
	} else if (z <= -2e-42) {
		tmp = t_1;
	} else if (z <= 1.5e-55) {
		tmp = x;
	} else if (z <= 4.4e+142) {
		tmp = t_1;
	} else if (z <= 2.6e+182) {
		tmp = -6.0 * (x * z);
	} else if (z <= 1.65e+245) {
		tmp = y * (z * 6.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (z * -6.0)
	t_1 = 6.0 * (y * z)
	tmp = 0
	if z <= -470000000.0:
		tmp = t_0
	elif z <= -2e-42:
		tmp = t_1
	elif z <= 1.5e-55:
		tmp = x
	elif z <= 4.4e+142:
		tmp = t_1
	elif z <= 2.6e+182:
		tmp = -6.0 * (x * z)
	elif z <= 1.65e+245:
		tmp = y * (z * 6.0)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(z * -6.0))
	t_1 = Float64(6.0 * Float64(y * z))
	tmp = 0.0
	if (z <= -470000000.0)
		tmp = t_0;
	elseif (z <= -2e-42)
		tmp = t_1;
	elseif (z <= 1.5e-55)
		tmp = x;
	elseif (z <= 4.4e+142)
		tmp = t_1;
	elseif (z <= 2.6e+182)
		tmp = Float64(-6.0 * Float64(x * z));
	elseif (z <= 1.65e+245)
		tmp = Float64(y * Float64(z * 6.0));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (z * -6.0);
	t_1 = 6.0 * (y * z);
	tmp = 0.0;
	if (z <= -470000000.0)
		tmp = t_0;
	elseif (z <= -2e-42)
		tmp = t_1;
	elseif (z <= 1.5e-55)
		tmp = x;
	elseif (z <= 4.4e+142)
		tmp = t_1;
	elseif (z <= 2.6e+182)
		tmp = -6.0 * (x * z);
	elseif (z <= 1.65e+245)
		tmp = y * (z * 6.0);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(z * -6.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -470000000.0], t$95$0, If[LessEqual[z, -2e-42], t$95$1, If[LessEqual[z, 1.5e-55], x, If[LessEqual[z, 4.4e+142], t$95$1, If[LessEqual[z, 2.6e+182], N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.65e+245], N[(y * N[(z * 6.0), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -4.7e8 or 1.65000000000000005e245 < z

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 62.2%

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

   4. Taylor expanded in z around inf 61.6%

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

      1. *-commutative 61.6%

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

      2. associate-*r* 61.7%

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

   6. Simplified 61.7%

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

   if -4.7e8 < z < -2.00000000000000008e-42 or 1.50000000000000008e-55 < z < 4.39999999999999974e142

   1. Initial program 99.6%

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

      1. associate-*r* 99.6%

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

      2. +-commutative 99.6%

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

      3. *-commutative 99.6%

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

      4. associate-*r* 99.6%

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

      5. fma-def 99.8%

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in y around inf 68.5%

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

      1. *-commutative 68.5%

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

   7. Simplified 68.5%

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

   if -2.00000000000000008e-42 < z < 1.50000000000000008e-55

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 71.1%

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

   if 4.39999999999999974e142 < z < 2.6e182

   1. Initial program 99.7%

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

      1. +-commutative 99.7%

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

      2. *-commutative 99.7%

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

      3. fma-def 99.7%

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

      4. remove-double-neg 99.7%

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

      5. distribute-lft-neg-in 99.7%

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

      6. distribute-rgt-neg-in 99.7%

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

      7. sub-neg 99.7%

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

      8. distribute-neg-in 99.7%

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

      9. remove-double-neg 99.7%

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

      10. +-commutative 99.7%

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

      11. sub-neg 99.7%

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

      12. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around inf 99.7%

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

   6. Taylor expanded in x around inf 67.6%

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

   if 2.6e182 < z < 1.65000000000000005e245

   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. associate-*r* 100.0%

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

      2. +-commutative 100.0%

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

      3. *-commutative 100.0%

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

      4. associate-*r* 99.7%

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

      5. fma-def 99.7%

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

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in y around inf 92.4%

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

      1. *-commutative 92.4%

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

   7. Simplified 92.4%

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

   8. Taylor expanded in z around inf 92.4%

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

      1. associate-*r* 92.5%

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

      2. *-commutative 92.5%

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

      3. associate-*r* 92.7%

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

   10. Simplified 92.7%

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

4. Final simplification 69.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -470000000:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-42}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-55}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+142}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+182}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{+245}:\\ \;\;\;\;y \cdot \left(z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 60.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(z \cdot -6\right)\\ t_1 := 6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -49000000000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-36}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-56}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+143}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+181}:\\ \;\;\;\;z \cdot \left(x \cdot -6\right)\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+245}:\\ \;\;\;\;y \cdot \left(z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (* z -6.0))) (t_1 (* 6.0 (* y z))))
   (if (<= z -49000000000.0)
     t_0
     (if (<= z -7e-36)
       t_1
       (if (<= z 6.8e-56)
         x
         (if (<= z 1.2e+143)
           t_1
           (if (<= z 1.35e+181)
             (* z (* x -6.0))
             (if (<= z 4e+245) (* y (* z 6.0)) t_0))))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (z * -6.0);
	double t_1 = 6.0 * (y * z);
	double tmp;
	if (z <= -49000000000.0) {
		tmp = t_0;
	} else if (z <= -7e-36) {
		tmp = t_1;
	} else if (z <= 6.8e-56) {
		tmp = x;
	} else if (z <= 1.2e+143) {
		tmp = t_1;
	} else if (z <= 1.35e+181) {
		tmp = z * (x * -6.0);
	} else if (z <= 4e+245) {
		tmp = y * (z * 6.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x * (z * (-6.0d0))
    t_1 = 6.0d0 * (y * z)
    if (z <= (-49000000000.0d0)) then
        tmp = t_0
    else if (z <= (-7d-36)) then
        tmp = t_1
    else if (z <= 6.8d-56) then
        tmp = x
    else if (z <= 1.2d+143) then
        tmp = t_1
    else if (z <= 1.35d+181) then
        tmp = z * (x * (-6.0d0))
    else if (z <= 4d+245) then
        tmp = y * (z * 6.0d0)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (z * -6.0);
	double t_1 = 6.0 * (y * z);
	double tmp;
	if (z <= -49000000000.0) {
		tmp = t_0;
	} else if (z <= -7e-36) {
		tmp = t_1;
	} else if (z <= 6.8e-56) {
		tmp = x;
	} else if (z <= 1.2e+143) {
		tmp = t_1;
	} else if (z <= 1.35e+181) {
		tmp = z * (x * -6.0);
	} else if (z <= 4e+245) {
		tmp = y * (z * 6.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (z * -6.0)
	t_1 = 6.0 * (y * z)
	tmp = 0
	if z <= -49000000000.0:
		tmp = t_0
	elif z <= -7e-36:
		tmp = t_1
	elif z <= 6.8e-56:
		tmp = x
	elif z <= 1.2e+143:
		tmp = t_1
	elif z <= 1.35e+181:
		tmp = z * (x * -6.0)
	elif z <= 4e+245:
		tmp = y * (z * 6.0)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(z * -6.0))
	t_1 = Float64(6.0 * Float64(y * z))
	tmp = 0.0
	if (z <= -49000000000.0)
		tmp = t_0;
	elseif (z <= -7e-36)
		tmp = t_1;
	elseif (z <= 6.8e-56)
		tmp = x;
	elseif (z <= 1.2e+143)
		tmp = t_1;
	elseif (z <= 1.35e+181)
		tmp = Float64(z * Float64(x * -6.0));
	elseif (z <= 4e+245)
		tmp = Float64(y * Float64(z * 6.0));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (z * -6.0);
	t_1 = 6.0 * (y * z);
	tmp = 0.0;
	if (z <= -49000000000.0)
		tmp = t_0;
	elseif (z <= -7e-36)
		tmp = t_1;
	elseif (z <= 6.8e-56)
		tmp = x;
	elseif (z <= 1.2e+143)
		tmp = t_1;
	elseif (z <= 1.35e+181)
		tmp = z * (x * -6.0);
	elseif (z <= 4e+245)
		tmp = y * (z * 6.0);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(z * -6.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -49000000000.0], t$95$0, If[LessEqual[z, -7e-36], t$95$1, If[LessEqual[z, 6.8e-56], x, If[LessEqual[z, 1.2e+143], t$95$1, If[LessEqual[z, 1.35e+181], N[(z * N[(x * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4e+245], N[(y * N[(z * 6.0), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -4.9e10 or 4.00000000000000018e245 < z

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 62.2%

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

   4. Taylor expanded in z around inf 61.6%

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

      1. *-commutative 61.6%

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

      2. associate-*r* 61.7%

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

   6. Simplified 61.7%

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

   if -4.9e10 < z < -6.9999999999999999e-36 or 6.79999999999999964e-56 < z < 1.1999999999999999e143

   1. Initial program 99.6%

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

      1. associate-*r* 99.6%

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

      2. +-commutative 99.6%

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

      3. *-commutative 99.6%

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

      4. associate-*r* 99.6%

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

      5. fma-def 99.8%

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in y around inf 68.5%

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

      1. *-commutative 68.5%

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

   7. Simplified 68.5%

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

   if -6.9999999999999999e-36 < z < 6.79999999999999964e-56

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 71.1%

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

   if 1.1999999999999999e143 < z < 1.35000000000000004e181

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 67.5%

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

   4. Taylor expanded in z around inf 67.6%

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

      1. associate-*r* 67.6%

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

      2. *-commutative 67.6%

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

   6. Simplified 67.6%

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

   if 1.35000000000000004e181 < z < 4.00000000000000018e245

   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. associate-*r* 100.0%

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

      2. +-commutative 100.0%

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

      3. *-commutative 100.0%

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

      4. associate-*r* 99.7%

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

      5. fma-def 99.7%

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

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in y around inf 92.4%

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

      1. *-commutative 92.4%

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

   7. Simplified 92.4%

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

   8. Taylor expanded in z around inf 92.4%

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

      1. associate-*r* 92.5%

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

      2. *-commutative 92.5%

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

      3. associate-*r* 92.7%

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

   10. Simplified 92.7%

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

4. Final simplification 69.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -49000000000:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-36}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-56}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+143}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+181}:\\ \;\;\;\;z \cdot \left(x \cdot -6\right)\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+245}:\\ \;\;\;\;y \cdot \left(z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 84.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{-44} \lor \neg \left(z \leq 1.85 \cdot 10^{-60}\right):\\ \;\;\;\;-6 \cdot \left(z \cdot \left(x - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -4.4e-44) (not (<= z 1.85e-60))) (* -6.0 (* z (- x y))) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4.4e-44) || !(z <= 1.85e-60)) {
		tmp = -6.0 * (z * (x - y));
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-4.4d-44)) .or. (.not. (z <= 1.85d-60))) then
        tmp = (-6.0d0) * (z * (x - y))
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4.4e-44) || !(z <= 1.85e-60)) {
		tmp = -6.0 * (z * (x - y));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -4.4e-44) or not (z <= 1.85e-60):
		tmp = -6.0 * (z * (x - y))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -4.4e-44) || !(z <= 1.85e-60))
		tmp = Float64(-6.0 * Float64(z * Float64(x - y)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -4.4e-44) || ~((z <= 1.85e-60)))
		tmp = -6.0 * (z * (x - y));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -4.4e-44], N[Not[LessEqual[z, 1.85e-60]], $MachinePrecision]], N[(-6.0 * N[(z * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -4.40000000000000024e-44 or 1.85000000000000012e-60 < z

   1. Initial program 99.7%

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

      1. +-commutative 99.7%

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

      2. *-commutative 99.7%

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

      3. fma-def 99.7%

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

      4. remove-double-neg 99.7%

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

      5. distribute-lft-neg-in 99.7%

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

      6. distribute-rgt-neg-in 99.7%

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

      7. sub-neg 99.7%

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

      8. distribute-neg-in 99.7%

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

      9. remove-double-neg 99.7%

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

      10. +-commutative 99.7%

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

      11. sub-neg 99.7%

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

      12. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around inf 95.1%

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

   if -4.40000000000000024e-44 < z < 1.85000000000000012e-60

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 71.1%

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

4. Final simplification 85.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{-44} \lor \neg \left(z \leq 1.85 \cdot 10^{-60}\right):\\ \;\;\;\;-6 \cdot \left(z \cdot \left(x - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 84.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{-43} \lor \neg \left(z \leq 3.9 \cdot 10^{-59}\right):\\ \;\;\;\;-6 \cdot \left(z \cdot \left(x - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + -6 \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.05e-43) (not (<= z 3.9e-59)))
   (* -6.0 (* z (- x y)))
   (+ x (* -6.0 (* x z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.05e-43) || !(z <= 3.9e-59)) {
		tmp = -6.0 * (z * (x - y));
	} else {
		tmp = x + (-6.0 * (x * z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-1.05d-43)) .or. (.not. (z <= 3.9d-59))) then
        tmp = (-6.0d0) * (z * (x - y))
    else
        tmp = x + ((-6.0d0) * (x * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.05e-43) || !(z <= 3.9e-59)) {
		tmp = -6.0 * (z * (x - y));
	} else {
		tmp = x + (-6.0 * (x * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.05e-43) or not (z <= 3.9e-59):
		tmp = -6.0 * (z * (x - y))
	else:
		tmp = x + (-6.0 * (x * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.05e-43) || !(z <= 3.9e-59))
		tmp = Float64(-6.0 * Float64(z * Float64(x - y)));
	else
		tmp = Float64(x + Float64(-6.0 * Float64(x * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.05e-43) || ~((z <= 3.9e-59)))
		tmp = -6.0 * (z * (x - y));
	else
		tmp = x + (-6.0 * (x * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.05e-43], N[Not[LessEqual[z, 3.9e-59]], $MachinePrecision]], N[(-6.0 * N[(z * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.05e-43 or 3.90000000000000019e-59 < z

   1. Initial program 99.7%

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

      1. +-commutative 99.7%

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

      2. *-commutative 99.7%

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

      3. fma-def 99.7%

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

      4. remove-double-neg 99.7%

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

      5. distribute-lft-neg-in 99.7%

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

      6. distribute-rgt-neg-in 99.7%

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

      7. sub-neg 99.7%

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

      8. distribute-neg-in 99.7%

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

      9. remove-double-neg 99.7%

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

      10. +-commutative 99.7%

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

      11. sub-neg 99.7%

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

      12. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around inf 95.1%

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

   if -1.05e-43 < z < 3.90000000000000019e-59

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 71.1%

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

4. Final simplification 85.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{-43} \lor \neg \left(z \leq 3.9 \cdot 10^{-59}\right):\\ \;\;\;\;-6 \cdot \left(z \cdot \left(x - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + -6 \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 98.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.16 \lor \neg \left(z \leq 165000\right):\\ \;\;\;\;-6 \cdot \left(z \cdot \left(x - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(y \cdot 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.16) (not (<= z 165000.0)))
   (* -6.0 (* z (- x y)))
   (+ x (* z (* y 6.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.16) || !(z <= 165000.0)) {
		tmp = -6.0 * (z * (x - y));
	} else {
		tmp = x + (z * (y * 6.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-0.16d0)) .or. (.not. (z <= 165000.0d0))) then
        tmp = (-6.0d0) * (z * (x - y))
    else
        tmp = x + (z * (y * 6.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.16) || !(z <= 165000.0)) {
		tmp = -6.0 * (z * (x - y));
	} else {
		tmp = x + (z * (y * 6.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.16) or not (z <= 165000.0):
		tmp = -6.0 * (z * (x - y))
	else:
		tmp = x + (z * (y * 6.0))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.16) || !(z <= 165000.0))
		tmp = Float64(-6.0 * Float64(z * Float64(x - y)));
	else
		tmp = Float64(x + Float64(z * Float64(y * 6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -0.16) || ~((z <= 165000.0)))
		tmp = -6.0 * (z * (x - y));
	else
		tmp = x + (z * (y * 6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.16], N[Not[LessEqual[z, 165000.0]], $MachinePrecision]], N[(-6.0 * N[(z * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(y * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.160000000000000003 or 165000 < z

   1. Initial program 99.7%

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

      1. +-commutative 99.7%

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

      2. *-commutative 99.7%

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

      3. fma-def 99.7%

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

      4. remove-double-neg 99.7%

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

      5. distribute-lft-neg-in 99.7%

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

      6. distribute-rgt-neg-in 99.7%

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

      7. sub-neg 99.7%

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

      8. distribute-neg-in 99.7%

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

      9. remove-double-neg 99.7%

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

      10. +-commutative 99.7%

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

      11. sub-neg 99.7%

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

      12. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around inf 99.0%

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

   if -0.160000000000000003 < z < 165000

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 98.3%

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

4. Final simplification 98.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.16 \lor \neg \left(z \leq 165000\right):\\ \;\;\;\;-6 \cdot \left(z \cdot \left(x - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(y \cdot 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 59.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.165 \lor \neg \left(z \leq 470\right):\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.165) (not (<= z 470.0))) (* -6.0 (* x z)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.165) || !(z <= 470.0)) {
		tmp = -6.0 * (x * z);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-0.165d0)) .or. (.not. (z <= 470.0d0))) then
        tmp = (-6.0d0) * (x * z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.165) || !(z <= 470.0)) {
		tmp = -6.0 * (x * z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.165) or not (z <= 470.0):
		tmp = -6.0 * (x * z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.165) || !(z <= 470.0))
		tmp = Float64(-6.0 * Float64(x * z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -0.165) || ~((z <= 470.0)))
		tmp = -6.0 * (x * z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.165], N[Not[LessEqual[z, 470.0]], $MachinePrecision]], N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -0.165000000000000008 or 470 < z

   1. Initial program 99.7%

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

      1. +-commutative 99.7%

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

      2. *-commutative 99.7%

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

      3. fma-def 99.7%

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

      4. remove-double-neg 99.7%

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

      5. distribute-lft-neg-in 99.7%

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

      6. distribute-rgt-neg-in 99.7%

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

      7. sub-neg 99.7%

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

      8. distribute-neg-in 99.7%

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

      9. remove-double-neg 99.7%

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

      10. +-commutative 99.7%

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

      11. sub-neg 99.7%

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

      12. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around inf 99.0%

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

   6. Taylor expanded in x around inf 52.4%

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

   if -0.165000000000000008 < z < 470

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 61.1%

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

4. Final simplification 56.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.165 \lor \neg \left(z \leq 470\right):\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 99.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

3. Final simplification 99.8%

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

Alternative 12: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. associate-*l* 99.8%

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

3. Simplified 99.8%

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

5. Final simplification 99.8%

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

Alternative 13: 35.7% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 99.8%

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

3. Taylor expanded in z around 0 33.1%

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

4. Final simplification 33.1%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 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 2024010 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, E"
  :precision binary64

  :herbie-target
  (- x (* (* 6.0 z) (- x y)))

  (+ x (* (* (- y x) 6.0) z)))