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

Percentage Accurate: 99.6% → 99.7%

Time: 10.1s

Alternatives: 12

Speedup: 1.0×

• 20.3% 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: 99.6% 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: 99.7% accurate, 0.1× 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 99.7%

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

   1. +-commutative 99.7%

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

   2. associate-*l* 99.8%

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

   3. fma-define 99.8%

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

3. Simplified 99.8%

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

5. Final simplification 99.8%

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

Alternative 2: 61.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(y \cdot z\right)\\ t_1 := -6 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;z \leq -4.8 \cdot 10^{+125}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{+95}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3 \cdot 10^{+70}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -5.8:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.55 \cdot 10^{-6}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-69}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+23} \lor \neg \left(z \leq 1.1 \cdot 10^{+127}\right) \land z \leq 2.6 \cdot 10^{+188}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 6.0 (* y z))) (t_1 (* -6.0 (* x z))))
   (if (<= z -4.8e+125)
     t_0
     (if (<= z -1.35e+95)
       t_1
       (if (<= z -3e+70)
         t_0
         (if (<= z -5.8)
           t_1
           (if (<= z -2.55e-6)
             t_0
             (if (<= z 1.8e-69)
               x
               (if (or (<= z 6.2e+23)
                       (and (not (<= z 1.1e+127)) (<= z 2.6e+188)))
                 t_0
                 t_1)))))))))

C

double code(double x, double y, double z) {
	double t_0 = 6.0 * (y * z);
	double t_1 = -6.0 * (x * z);
	double tmp;
	if (z <= -4.8e+125) {
		tmp = t_0;
	} else if (z <= -1.35e+95) {
		tmp = t_1;
	} else if (z <= -3e+70) {
		tmp = t_0;
	} else if (z <= -5.8) {
		tmp = t_1;
	} else if (z <= -2.55e-6) {
		tmp = t_0;
	} else if (z <= 1.8e-69) {
		tmp = x;
	} else if ((z <= 6.2e+23) || (!(z <= 1.1e+127) && (z <= 2.6e+188))) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = 6.0d0 * (y * z)
    t_1 = (-6.0d0) * (x * z)
    if (z <= (-4.8d+125)) then
        tmp = t_0
    else if (z <= (-1.35d+95)) then
        tmp = t_1
    else if (z <= (-3d+70)) then
        tmp = t_0
    else if (z <= (-5.8d0)) then
        tmp = t_1
    else if (z <= (-2.55d-6)) then
        tmp = t_0
    else if (z <= 1.8d-69) then
        tmp = x
    else if ((z <= 6.2d+23) .or. (.not. (z <= 1.1d+127)) .and. (z <= 2.6d+188)) then
        tmp = t_0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 6.0 * (y * z);
	double t_1 = -6.0 * (x * z);
	double tmp;
	if (z <= -4.8e+125) {
		tmp = t_0;
	} else if (z <= -1.35e+95) {
		tmp = t_1;
	} else if (z <= -3e+70) {
		tmp = t_0;
	} else if (z <= -5.8) {
		tmp = t_1;
	} else if (z <= -2.55e-6) {
		tmp = t_0;
	} else if (z <= 1.8e-69) {
		tmp = x;
	} else if ((z <= 6.2e+23) || (!(z <= 1.1e+127) && (z <= 2.6e+188))) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 6.0 * (y * z)
	t_1 = -6.0 * (x * z)
	tmp = 0
	if z <= -4.8e+125:
		tmp = t_0
	elif z <= -1.35e+95:
		tmp = t_1
	elif z <= -3e+70:
		tmp = t_0
	elif z <= -5.8:
		tmp = t_1
	elif z <= -2.55e-6:
		tmp = t_0
	elif z <= 1.8e-69:
		tmp = x
	elif (z <= 6.2e+23) or (not (z <= 1.1e+127) and (z <= 2.6e+188)):
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(6.0 * Float64(y * z))
	t_1 = Float64(-6.0 * Float64(x * z))
	tmp = 0.0
	if (z <= -4.8e+125)
		tmp = t_0;
	elseif (z <= -1.35e+95)
		tmp = t_1;
	elseif (z <= -3e+70)
		tmp = t_0;
	elseif (z <= -5.8)
		tmp = t_1;
	elseif (z <= -2.55e-6)
		tmp = t_0;
	elseif (z <= 1.8e-69)
		tmp = x;
	elseif ((z <= 6.2e+23) || (!(z <= 1.1e+127) && (z <= 2.6e+188)))
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 6.0 * (y * z);
	t_1 = -6.0 * (x * z);
	tmp = 0.0;
	if (z <= -4.8e+125)
		tmp = t_0;
	elseif (z <= -1.35e+95)
		tmp = t_1;
	elseif (z <= -3e+70)
		tmp = t_0;
	elseif (z <= -5.8)
		tmp = t_1;
	elseif (z <= -2.55e-6)
		tmp = t_0;
	elseif (z <= 1.8e-69)
		tmp = x;
	elseif ((z <= 6.2e+23) || (~((z <= 1.1e+127)) && (z <= 2.6e+188)))
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.8e+125], t$95$0, If[LessEqual[z, -1.35e+95], t$95$1, If[LessEqual[z, -3e+70], t$95$0, If[LessEqual[z, -5.8], t$95$1, If[LessEqual[z, -2.55e-6], t$95$0, If[LessEqual[z, 1.8e-69], x, If[Or[LessEqual[z, 6.2e+23], And[N[Not[LessEqual[z, 1.1e+127]], $MachinePrecision], LessEqual[z, 2.6e+188]]], t$95$0, t$95$1]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.7999999999999999e125 or -1.35e95 < z < -2.99999999999999976e70 or -5.79999999999999982 < z < -2.5500000000000001e-6 or 1.80000000000000009e-69 < z < 6.19999999999999941e23 or 1.1000000000000001e127 < z < 2.59999999999999987e188

   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* 99.8%

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

      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-define 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 76.0%

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

      1. *-commutative 76.0%

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

   7. Simplified 76.0%

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

   if -4.7999999999999999e125 < z < -1.35e95 or -2.99999999999999976e70 < z < -5.79999999999999982 or 6.19999999999999941e23 < z < 1.1000000000000001e127 or 2.59999999999999987e188 < z

   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* 99.7%

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

      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-define 99.6%

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

   4. Applied egg-rr 99.6%

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

   5. Taylor expanded in z around inf 97.7%

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

   6. Taylor expanded in y around 0 68.1%

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

   if -2.5500000000000001e-6 < z < 1.80000000000000009e-69

   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 69.2%

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

4. Final simplification 70.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+125}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{+95}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -3 \cdot 10^{+70}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -5.8:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -2.55 \cdot 10^{-6}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-69}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+23} \lor \neg \left(z \leq 1.1 \cdot 10^{+127}\right) \land z \leq 2.6 \cdot 10^{+188}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 61.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(y \cdot z\right)\\ t_1 := -6 \cdot \left(x \cdot z\right)\\ t_2 := x \cdot \left(z \cdot -6\right)\\ \mathbf{if}\;z \leq -5.5 \cdot 10^{+125}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{+96}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -3 \cdot 10^{+70}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -5.8:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.55 \cdot 10^{-6}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-69}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{+23}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{+132}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+189}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 6.0 (* y z))) (t_1 (* -6.0 (* x z))) (t_2 (* x (* z -6.0))))
   (if (<= z -5.5e+125)
     t_0
     (if (<= z -6.6e+96)
       t_2
       (if (<= z -3e+70)
         t_0
         (if (<= z -5.8)
           t_1
           (if (<= z -2.55e-6)
             t_0
             (if (<= z 6.5e-69)
               x
               (if (<= z 8.8e+23)
                 t_0
                 (if (<= z 4.1e+132) t_1 (if (<= z 3.7e+189) t_0 t_2)))))))))))

C

double code(double x, double y, double z) {
	double t_0 = 6.0 * (y * z);
	double t_1 = -6.0 * (x * z);
	double t_2 = x * (z * -6.0);
	double tmp;
	if (z <= -5.5e+125) {
		tmp = t_0;
	} else if (z <= -6.6e+96) {
		tmp = t_2;
	} else if (z <= -3e+70) {
		tmp = t_0;
	} else if (z <= -5.8) {
		tmp = t_1;
	} else if (z <= -2.55e-6) {
		tmp = t_0;
	} else if (z <= 6.5e-69) {
		tmp = x;
	} else if (z <= 8.8e+23) {
		tmp = t_0;
	} else if (z <= 4.1e+132) {
		tmp = t_1;
	} else if (z <= 3.7e+189) {
		tmp = t_0;
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: tmp
    t_0 = 6.0d0 * (y * z)
    t_1 = (-6.0d0) * (x * z)
    t_2 = x * (z * (-6.0d0))
    if (z <= (-5.5d+125)) then
        tmp = t_0
    else if (z <= (-6.6d+96)) then
        tmp = t_2
    else if (z <= (-3d+70)) then
        tmp = t_0
    else if (z <= (-5.8d0)) then
        tmp = t_1
    else if (z <= (-2.55d-6)) then
        tmp = t_0
    else if (z <= 6.5d-69) then
        tmp = x
    else if (z <= 8.8d+23) then
        tmp = t_0
    else if (z <= 4.1d+132) then
        tmp = t_1
    else if (z <= 3.7d+189) then
        tmp = t_0
    else
        tmp = t_2
    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 t_1 = -6.0 * (x * z);
	double t_2 = x * (z * -6.0);
	double tmp;
	if (z <= -5.5e+125) {
		tmp = t_0;
	} else if (z <= -6.6e+96) {
		tmp = t_2;
	} else if (z <= -3e+70) {
		tmp = t_0;
	} else if (z <= -5.8) {
		tmp = t_1;
	} else if (z <= -2.55e-6) {
		tmp = t_0;
	} else if (z <= 6.5e-69) {
		tmp = x;
	} else if (z <= 8.8e+23) {
		tmp = t_0;
	} else if (z <= 4.1e+132) {
		tmp = t_1;
	} else if (z <= 3.7e+189) {
		tmp = t_0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 6.0 * (y * z)
	t_1 = -6.0 * (x * z)
	t_2 = x * (z * -6.0)
	tmp = 0
	if z <= -5.5e+125:
		tmp = t_0
	elif z <= -6.6e+96:
		tmp = t_2
	elif z <= -3e+70:
		tmp = t_0
	elif z <= -5.8:
		tmp = t_1
	elif z <= -2.55e-6:
		tmp = t_0
	elif z <= 6.5e-69:
		tmp = x
	elif z <= 8.8e+23:
		tmp = t_0
	elif z <= 4.1e+132:
		tmp = t_1
	elif z <= 3.7e+189:
		tmp = t_0
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(6.0 * Float64(y * z))
	t_1 = Float64(-6.0 * Float64(x * z))
	t_2 = Float64(x * Float64(z * -6.0))
	tmp = 0.0
	if (z <= -5.5e+125)
		tmp = t_0;
	elseif (z <= -6.6e+96)
		tmp = t_2;
	elseif (z <= -3e+70)
		tmp = t_0;
	elseif (z <= -5.8)
		tmp = t_1;
	elseif (z <= -2.55e-6)
		tmp = t_0;
	elseif (z <= 6.5e-69)
		tmp = x;
	elseif (z <= 8.8e+23)
		tmp = t_0;
	elseif (z <= 4.1e+132)
		tmp = t_1;
	elseif (z <= 3.7e+189)
		tmp = t_0;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 6.0 * (y * z);
	t_1 = -6.0 * (x * z);
	t_2 = x * (z * -6.0);
	tmp = 0.0;
	if (z <= -5.5e+125)
		tmp = t_0;
	elseif (z <= -6.6e+96)
		tmp = t_2;
	elseif (z <= -3e+70)
		tmp = t_0;
	elseif (z <= -5.8)
		tmp = t_1;
	elseif (z <= -2.55e-6)
		tmp = t_0;
	elseif (z <= 6.5e-69)
		tmp = x;
	elseif (z <= 8.8e+23)
		tmp = t_0;
	elseif (z <= 4.1e+132)
		tmp = t_1;
	elseif (z <= 3.7e+189)
		tmp = t_0;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(z * -6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.5e+125], t$95$0, If[LessEqual[z, -6.6e+96], t$95$2, If[LessEqual[z, -3e+70], t$95$0, If[LessEqual[z, -5.8], t$95$1, If[LessEqual[z, -2.55e-6], t$95$0, If[LessEqual[z, 6.5e-69], x, If[LessEqual[z, 8.8e+23], t$95$0, If[LessEqual[z, 4.1e+132], t$95$1, If[LessEqual[z, 3.7e+189], t$95$0, t$95$2]]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.49999999999999996e125 or -6.59999999999999969e96 < z < -2.99999999999999976e70 or -5.79999999999999982 < z < -2.5500000000000001e-6 or 6.49999999999999951e-69 < z < 8.80000000000000034e23 or 4.09999999999999992e132 < z < 3.70000000000000021e189

   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* 99.8%

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

      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-define 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 76.0%

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

      1. *-commutative 76.0%

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

   7. Simplified 76.0%

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

   if -5.49999999999999996e125 < z < -6.59999999999999969e96 or 3.70000000000000021e189 < z

   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* 99.6%

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

      5. fma-define 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 z around inf 99.6%

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

   6. Taylor expanded in y around 0 70.4%

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

      1. *-commutative 70.4%

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

      2. associate-*l* 70.5%

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

   8. Simplified 70.5%

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

   if -2.99999999999999976e70 < z < -5.79999999999999982 or 8.80000000000000034e23 < z < 4.09999999999999992e132

   1. Initial program 99.3%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   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-define 99.4%

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

   4. Applied egg-rr 99.4%

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

   5. Taylor expanded in z around inf 94.8%

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

   6. Taylor expanded in y around 0 64.6%

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

   if -2.5500000000000001e-6 < z < 6.49999999999999951e-69

   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 69.2%

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

4. Final simplification 70.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+125}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{+96}:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -3 \cdot 10^{+70}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -5.8:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -2.55 \cdot 10^{-6}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-69}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{+23}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{+132}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+189}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 61.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(6 \cdot z\right)\\ t_1 := 6 \cdot \left(y \cdot z\right)\\ t_2 := -6 \cdot \left(x \cdot z\right)\\ t_3 := x \cdot \left(z \cdot -6\right)\\ \mathbf{if}\;z \leq -4.8 \cdot 10^{+125}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{+95}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq -3 \cdot 10^{+70}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -5.8:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-6}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-69}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+20}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+126}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+189}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (* 6.0 z)))
        (t_1 (* 6.0 (* y z)))
        (t_2 (* -6.0 (* x z)))
        (t_3 (* x (* z -6.0))))
   (if (<= z -4.8e+125)
     t_1
     (if (<= z -3.8e+95)
       t_3
       (if (<= z -3e+70)
         t_1
         (if (<= z -5.8)
           t_2
           (if (<= z -6.2e-6)
             t_1
             (if (<= z 5e-69)
               x
               (if (<= z 4.8e+20)
                 t_0
                 (if (<= z 3.4e+126)
                   t_2
                   (if (<= z 1.25e+189) t_0 t_3)))))))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (6.0 * z);
	double t_1 = 6.0 * (y * z);
	double t_2 = -6.0 * (x * z);
	double t_3 = x * (z * -6.0);
	double tmp;
	if (z <= -4.8e+125) {
		tmp = t_1;
	} else if (z <= -3.8e+95) {
		tmp = t_3;
	} else if (z <= -3e+70) {
		tmp = t_1;
	} else if (z <= -5.8) {
		tmp = t_2;
	} else if (z <= -6.2e-6) {
		tmp = t_1;
	} else if (z <= 5e-69) {
		tmp = x;
	} else if (z <= 4.8e+20) {
		tmp = t_0;
	} else if (z <= 3.4e+126) {
		tmp = t_2;
	} else if (z <= 1.25e+189) {
		tmp = t_0;
	} else {
		tmp = t_3;
	}
	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) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_0 = y * (6.0d0 * z)
    t_1 = 6.0d0 * (y * z)
    t_2 = (-6.0d0) * (x * z)
    t_3 = x * (z * (-6.0d0))
    if (z <= (-4.8d+125)) then
        tmp = t_1
    else if (z <= (-3.8d+95)) then
        tmp = t_3
    else if (z <= (-3d+70)) then
        tmp = t_1
    else if (z <= (-5.8d0)) then
        tmp = t_2
    else if (z <= (-6.2d-6)) then
        tmp = t_1
    else if (z <= 5d-69) then
        tmp = x
    else if (z <= 4.8d+20) then
        tmp = t_0
    else if (z <= 3.4d+126) then
        tmp = t_2
    else if (z <= 1.25d+189) then
        tmp = t_0
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * (6.0 * z);
	double t_1 = 6.0 * (y * z);
	double t_2 = -6.0 * (x * z);
	double t_3 = x * (z * -6.0);
	double tmp;
	if (z <= -4.8e+125) {
		tmp = t_1;
	} else if (z <= -3.8e+95) {
		tmp = t_3;
	} else if (z <= -3e+70) {
		tmp = t_1;
	} else if (z <= -5.8) {
		tmp = t_2;
	} else if (z <= -6.2e-6) {
		tmp = t_1;
	} else if (z <= 5e-69) {
		tmp = x;
	} else if (z <= 4.8e+20) {
		tmp = t_0;
	} else if (z <= 3.4e+126) {
		tmp = t_2;
	} else if (z <= 1.25e+189) {
		tmp = t_0;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (6.0 * z)
	t_1 = 6.0 * (y * z)
	t_2 = -6.0 * (x * z)
	t_3 = x * (z * -6.0)
	tmp = 0
	if z <= -4.8e+125:
		tmp = t_1
	elif z <= -3.8e+95:
		tmp = t_3
	elif z <= -3e+70:
		tmp = t_1
	elif z <= -5.8:
		tmp = t_2
	elif z <= -6.2e-6:
		tmp = t_1
	elif z <= 5e-69:
		tmp = x
	elif z <= 4.8e+20:
		tmp = t_0
	elif z <= 3.4e+126:
		tmp = t_2
	elif z <= 1.25e+189:
		tmp = t_0
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(6.0 * z))
	t_1 = Float64(6.0 * Float64(y * z))
	t_2 = Float64(-6.0 * Float64(x * z))
	t_3 = Float64(x * Float64(z * -6.0))
	tmp = 0.0
	if (z <= -4.8e+125)
		tmp = t_1;
	elseif (z <= -3.8e+95)
		tmp = t_3;
	elseif (z <= -3e+70)
		tmp = t_1;
	elseif (z <= -5.8)
		tmp = t_2;
	elseif (z <= -6.2e-6)
		tmp = t_1;
	elseif (z <= 5e-69)
		tmp = x;
	elseif (z <= 4.8e+20)
		tmp = t_0;
	elseif (z <= 3.4e+126)
		tmp = t_2;
	elseif (z <= 1.25e+189)
		tmp = t_0;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (6.0 * z);
	t_1 = 6.0 * (y * z);
	t_2 = -6.0 * (x * z);
	t_3 = x * (z * -6.0);
	tmp = 0.0;
	if (z <= -4.8e+125)
		tmp = t_1;
	elseif (z <= -3.8e+95)
		tmp = t_3;
	elseif (z <= -3e+70)
		tmp = t_1;
	elseif (z <= -5.8)
		tmp = t_2;
	elseif (z <= -6.2e-6)
		tmp = t_1;
	elseif (z <= 5e-69)
		tmp = x;
	elseif (z <= 4.8e+20)
		tmp = t_0;
	elseif (z <= 3.4e+126)
		tmp = t_2;
	elseif (z <= 1.25e+189)
		tmp = t_0;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(6.0 * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(z * -6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.8e+125], t$95$1, If[LessEqual[z, -3.8e+95], t$95$3, If[LessEqual[z, -3e+70], t$95$1, If[LessEqual[z, -5.8], t$95$2, If[LessEqual[z, -6.2e-6], t$95$1, If[LessEqual[z, 5e-69], x, If[LessEqual[z, 4.8e+20], t$95$0, If[LessEqual[z, 3.4e+126], t$95$2, If[LessEqual[z, 1.25e+189], t$95$0, t$95$3]]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -4.7999999999999999e125 or -3.7999999999999999e95 < z < -2.99999999999999976e70 or -5.79999999999999982 < z < -6.1999999999999999e-6

   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* 100.0%

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

      5. fma-define 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in y around inf 73.6%

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

      1. *-commutative 73.6%

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

   7. Simplified 73.6%

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

   if -4.7999999999999999e125 < z < -3.7999999999999999e95 or 1.2500000000000001e189 < z

   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* 99.6%

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

      5. fma-define 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 z around inf 99.6%

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

   6. Taylor expanded in y around 0 70.4%

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

      1. *-commutative 70.4%

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

      2. associate-*l* 70.5%

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

   8. Simplified 70.5%

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

   if -2.99999999999999976e70 < z < -5.79999999999999982 or 4.8e20 < z < 3.39999999999999989e126

   1. Initial program 99.3%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   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-define 99.4%

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

   4. Applied egg-rr 99.4%

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

   5. Taylor expanded in z around inf 94.8%

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

   6. Taylor expanded in y around 0 64.6%

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

   if -6.1999999999999999e-6 < z < 5.00000000000000033e-69

   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 69.2%

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

   if 5.00000000000000033e-69 < z < 4.8e20 or 3.39999999999999989e126 < z < 1.2500000000000001e189

   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* 99.8%

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

      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* 99.5%

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

      5. fma-define 99.5%

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

   4. Applied egg-rr 99.5%

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

   5. Taylor expanded in y around inf 83.2%

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

      1. *-commutative 83.2%

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

   7. Simplified 83.2%

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

   8. Taylor expanded in z around inf 79.3%

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

      1. associate-*r* 79.3%

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

      2. *-commutative 79.3%

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

      3. associate-*r* 79.6%

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

   10. Simplified 79.6%

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

4. Final simplification 70.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+125}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{+95}:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -3 \cdot 10^{+70}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -5.8:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-6}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-69}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+20}:\\ \;\;\;\;y \cdot \left(6 \cdot z\right)\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+126}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+189}:\\ \;\;\;\;y \cdot \left(6 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.55 \cdot 10^{-6} \lor \neg \left(z \leq 6.5 \cdot 10^{-69}\right):\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.55e-6) (not (<= z 6.5e-69))) (* 6.0 (* (- y x) z)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.55e-6) || !(z <= 6.5e-69)) {
		tmp = 6.0 * ((y - 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 <= (-2.55d-6)) .or. (.not. (z <= 6.5d-69))) then
        tmp = 6.0d0 * ((y - 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 <= -2.55e-6) || !(z <= 6.5e-69)) {
		tmp = 6.0 * ((y - x) * z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2.55e-6) or not (z <= 6.5e-69):
		tmp = 6.0 * ((y - x) * z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -2.55e-6) || !(z <= 6.5e-69))
		tmp = Float64(6.0 * Float64(Float64(y - x) * z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -2.55e-6) || ~((z <= 6.5e-69)))
		tmp = 6.0 * ((y - x) * z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2.55e-6], N[Not[LessEqual[z, 6.5e-69]], $MachinePrecision]], N[(6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -2.5500000000000001e-6 or 6.49999999999999951e-69 < z

   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* 99.8%

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

      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* 99.7%

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

      5. fma-define 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 z around inf 97.5%

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

   if -2.5500000000000001e-6 < z < 6.49999999999999951e-69

   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 69.2%

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

4. Final simplification 84.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.55 \cdot 10^{-6} \lor \neg \left(z \leq 6.5 \cdot 10^{-69}\right):\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 84.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.55 \cdot 10^{-6}:\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-69}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot \left(6 \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -2.55e-6)
   (* 6.0 (* (- y x) z))
   (if (<= z 5.2e-69) x (* (- y x) (* 6.0 z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.55e-6) {
		tmp = 6.0 * ((y - x) * z);
	} else if (z <= 5.2e-69) {
		tmp = x;
	} else {
		tmp = (y - x) * (6.0 * 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 <= (-2.55d-6)) then
        tmp = 6.0d0 * ((y - x) * z)
    else if (z <= 5.2d-69) then
        tmp = x
    else
        tmp = (y - x) * (6.0d0 * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.55e-6) {
		tmp = 6.0 * ((y - x) * z);
	} else if (z <= 5.2e-69) {
		tmp = x;
	} else {
		tmp = (y - x) * (6.0 * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -2.55e-6:
		tmp = 6.0 * ((y - x) * z)
	elif z <= 5.2e-69:
		tmp = x
	else:
		tmp = (y - x) * (6.0 * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -2.55e-6)
		tmp = Float64(6.0 * Float64(Float64(y - x) * z));
	elseif (z <= 5.2e-69)
		tmp = x;
	else
		tmp = Float64(Float64(y - x) * Float64(6.0 * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -2.55e-6)
		tmp = 6.0 * ((y - x) * z);
	elseif (z <= 5.2e-69)
		tmp = x;
	else
		tmp = (y - x) * (6.0 * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -2.55e-6], N[(6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.2e-69], x, N[(N[(y - x), $MachinePrecision] * N[(6.0 * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.5500000000000001e-6

   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* 99.8%

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

      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-define 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 z around inf 97.5%

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

   if -2.5500000000000001e-6 < z < 5.2000000000000004e-69

   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 69.2%

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

   if 5.2000000000000004e-69 < z

   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* 99.7%

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

      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-define 99.6%

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

   4. Applied egg-rr 99.6%

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

   5. Taylor expanded in z around inf 97.5%

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

      1. *-commutative 97.5%

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

      2. *-commutative 97.5%

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

      3. associate-*r* 97.6%

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

   7. Simplified 97.6%

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

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.55 \cdot 10^{-6}:\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-69}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot \left(6 \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 83.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+20}:\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-69}:\\ \;\;\;\;x + -6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot \left(6 \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -5.2e+20)
   (* 6.0 (* (- y x) z))
   (if (<= z 1.8e-69) (+ x (* -6.0 (* x z))) (* (- y x) (* 6.0 z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -5.2e+20) {
		tmp = 6.0 * ((y - x) * z);
	} else if (z <= 1.8e-69) {
		tmp = x + (-6.0 * (x * z));
	} else {
		tmp = (y - x) * (6.0 * 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 <= (-5.2d+20)) then
        tmp = 6.0d0 * ((y - x) * z)
    else if (z <= 1.8d-69) then
        tmp = x + ((-6.0d0) * (x * z))
    else
        tmp = (y - x) * (6.0d0 * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -5.2e+20) {
		tmp = 6.0 * ((y - x) * z);
	} else if (z <= 1.8e-69) {
		tmp = x + (-6.0 * (x * z));
	} else {
		tmp = (y - x) * (6.0 * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -5.2e+20:
		tmp = 6.0 * ((y - x) * z)
	elif z <= 1.8e-69:
		tmp = x + (-6.0 * (x * z))
	else:
		tmp = (y - x) * (6.0 * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -5.2e+20)
		tmp = Float64(6.0 * Float64(Float64(y - x) * z));
	elseif (z <= 1.8e-69)
		tmp = Float64(x + Float64(-6.0 * Float64(x * z)));
	else
		tmp = Float64(Float64(y - x) * Float64(6.0 * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -5.2e+20)
		tmp = 6.0 * ((y - x) * z);
	elseif (z <= 1.8e-69)
		tmp = x + (-6.0 * (x * z));
	else
		tmp = (y - x) * (6.0 * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -5.2e+20], N[(6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.8e-69], N[(x + N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y - x), $MachinePrecision] * N[(6.0 * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.2e20

   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* 99.8%

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

      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* 99.9%

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

      5. fma-define 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 z around inf 99.9%

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

   if -5.2e20 < z < 1.80000000000000009e-69

   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 70.8%

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

   if 1.80000000000000009e-69 < z

   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* 99.7%

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

      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-define 99.6%

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

   4. Applied egg-rr 99.6%

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

   5. Taylor expanded in z around inf 97.5%

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

      1. *-commutative 97.5%

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

      2. *-commutative 97.5%

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

      3. associate-*r* 97.6%

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

   7. Simplified 97.6%

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

4. Final simplification 84.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+20}:\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-69}:\\ \;\;\;\;x + -6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot \left(6 \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 98.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.17:\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-9}:\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot \left(6 \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.17)
   (* 6.0 (* (- y x) z))
   (if (<= z 5.5e-9) (+ x (* 6.0 (* y z))) (* (- y x) (* 6.0 z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.17) {
		tmp = 6.0 * ((y - x) * z);
	} else if (z <= 5.5e-9) {
		tmp = x + (6.0 * (y * z));
	} else {
		tmp = (y - x) * (6.0 * 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 <= (-0.17d0)) then
        tmp = 6.0d0 * ((y - x) * z)
    else if (z <= 5.5d-9) then
        tmp = x + (6.0d0 * (y * z))
    else
        tmp = (y - x) * (6.0d0 * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.17) {
		tmp = 6.0 * ((y - x) * z);
	} else if (z <= 5.5e-9) {
		tmp = x + (6.0 * (y * z));
	} else {
		tmp = (y - x) * (6.0 * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.17:
		tmp = 6.0 * ((y - x) * z)
	elif z <= 5.5e-9:
		tmp = x + (6.0 * (y * z))
	else:
		tmp = (y - x) * (6.0 * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.17)
		tmp = Float64(6.0 * Float64(Float64(y - x) * z));
	elseif (z <= 5.5e-9)
		tmp = Float64(x + Float64(6.0 * Float64(y * z)));
	else
		tmp = Float64(Float64(y - x) * Float64(6.0 * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.17)
		tmp = 6.0 * ((y - x) * z);
	elseif (z <= 5.5e-9)
		tmp = x + (6.0 * (y * z));
	else
		tmp = (y - x) * (6.0 * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.17], N[(6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.5e-9], N[(x + N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y - x), $MachinePrecision] * N[(6.0 * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.170000000000000012

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Add Preprocessing
   3. 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-define 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 z around inf 97.5%

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

   if -0.170000000000000012 < z < 5.4999999999999996e-9

   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 98.6%

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

      1. *-commutative 98.6%

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

   5. Simplified 98.6%

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

   if 5.4999999999999996e-9 < z

   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-define 99.6%

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

   4. Applied egg-rr 99.6%

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

   5. Taylor expanded in z around inf 99.6%

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

      1. *-commutative 99.6%

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

      2. *-commutative 99.6%

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

      3. associate-*r* 99.7%

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

   7. Simplified 99.7%

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

4. Final simplification 98.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.17:\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-9}:\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot \left(6 \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 61.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.17 \lor \neg \left(z \leq 5.5 \cdot 10^{-9}\right):\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.17) (not (<= z 5.5e-9))) (* -6.0 (* x z)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.17) || !(z <= 5.5e-9)) {
		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 <= (-0.17d0)) .or. (.not. (z <= 5.5d-9))) 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 <= -0.17) || !(z <= 5.5e-9)) {
		tmp = -6.0 * (x * z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.17) or not (z <= 5.5e-9):
		tmp = -6.0 * (x * z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.17) || !(z <= 5.5e-9))
		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 <= -0.17) || ~((z <= 5.5e-9)))
		tmp = -6.0 * (x * z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.17], N[Not[LessEqual[z, 5.5e-9]], $MachinePrecision]], N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -0.170000000000000012 or 5.4999999999999996e-9 < z

   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* 99.8%

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

      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* 99.7%

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

      5. fma-define 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 z around inf 98.7%

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

   6. Taylor expanded in y around 0 53.3%

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

   if -0.170000000000000012 < z < 5.4999999999999996e-9

   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 65.1%

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

4. Final simplification 59.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.17 \lor \neg \left(z \leq 5.5 \cdot 10^{-9}\right):\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 99.6% 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 99.7%

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

3. Final simplification 99.7%

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

Alternative 11: 99.7% accurate, 1.0× speedup

Math

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

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(y - x) * Float64(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[(y - x), $MachinePrecision] * N[(6.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.7%

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

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

Alternative 12: 36.9% 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 99.7%

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

3. Taylor expanded in z around 0 34.5%

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

4. Final simplification 34.5%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 99.7% 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 2024043 
(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)))