Graphics.Rasterific.CubicBezier:cachedBezierAt from Rasterific-0.6.1

Percentage Accurate: 92.2% → 95.7%

Time: 18.0s

Alternatives: 15

Speedup: 1.2×

• 32.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (+ (+ (+ x (* y z)) (* t a)) (* (* a z) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return ((x + (y * z)) + (t * a)) + ((a * z) * b);
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = ((x + (y * z)) + (t * a)) + ((a * z) * b)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return ((x + (y * z)) + (t * a)) + ((a * z) * b);
}

Python

def code(x, y, z, t, a, b):
	return ((x + (y * z)) + (t * a)) + ((a * z) * b)

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(Float64(x + Float64(y * z)) + Float64(t * a)) + Float64(Float64(a * z) * b))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = ((x + (y * z)) + (t * a)) + ((a * z) * b);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision] + N[(N[(a * z), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]

Initial Program: 92.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (+ (+ (+ x (* y z)) (* t a)) (* (* a z) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return ((x + (y * z)) + (t * a)) + ((a * z) * b);
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = ((x + (y * z)) + (t * a)) + ((a * z) * b)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return ((x + (y * z)) + (t * a)) + ((a * z) * b);
}

Python

def code(x, y, z, t, a, b):
	return ((x + (y * z)) + (t * a)) + ((a * z) * b)

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(Float64(x + Float64(y * z)) + Float64(t * a)) + Float64(Float64(a * z) * b))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = ((x + (y * z)) + (t * a)) + ((a * z) * b);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision] + N[(N[(a * z), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]

Alternative 1: 95.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t \cdot a + \left(x + y \cdot z\right)\right) + \left(z \cdot a\right) \cdot b\\ \mathbf{if}\;t_1 \leq 2 \cdot 10^{+279}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y + a \cdot b\right) + \left(x + t \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ (* t a) (+ x (* y z))) (* (* z a) b))))
   (if (<= t_1 2e+279) t_1 (+ (* z (+ y (* a b))) (+ x (* t a))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((t * a) + (x + (y * z))) + ((z * a) * b);
	double tmp;
	if (t_1 <= 2e+279) {
		tmp = t_1;
	} else {
		tmp = (z * (y + (a * b))) + (x + (t * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((t * a) + (x + (y * z))) + ((z * a) * b)
    if (t_1 <= 2d+279) then
        tmp = t_1
    else
        tmp = (z * (y + (a * b))) + (x + (t * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((t * a) + (x + (y * z))) + ((z * a) * b);
	double tmp;
	if (t_1 <= 2e+279) {
		tmp = t_1;
	} else {
		tmp = (z * (y + (a * b))) + (x + (t * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((t * a) + (x + (y * z))) + ((z * a) * b)
	tmp = 0
	if t_1 <= 2e+279:
		tmp = t_1
	else:
		tmp = (z * (y + (a * b))) + (x + (t * a))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(t * a) + Float64(x + Float64(y * z))) + Float64(Float64(z * a) * b))
	tmp = 0.0
	if (t_1 <= 2e+279)
		tmp = t_1;
	else
		tmp = Float64(Float64(z * Float64(y + Float64(a * b))) + Float64(x + Float64(t * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((t * a) + (x + (y * z))) + ((z * a) * b);
	tmp = 0.0;
	if (t_1 <= 2e+279)
		tmp = t_1;
	else
		tmp = (z * (y + (a * b))) + (x + (t * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(t * a), $MachinePrecision] + N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(z * a), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 2e+279], t$95$1, N[(N[(z * N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (+.f64 (+.f64 x (*.f64 y z)) (*.f64 t a)) (*.f64 (*.f64 a z) b)) < 2.00000000000000012e279

   1. Initial program 98.9%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]

   if 2.00000000000000012e279 < (+.f64 (+.f64 (+.f64 x (*.f64 y z)) (*.f64 t a)) (*.f64 (*.f64 a z) b))

   1. Initial program 67.0%

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

      1. *-commutative 67.0%

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

      2. associate-*l* 77.3%

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

   3. Simplified 77.3%

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

   4. Taylor expanded in z around 0 95.5%

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

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(t \cdot a + \left(x + y \cdot z\right)\right) + \left(z \cdot a\right) \cdot b \leq 2 \cdot 10^{+279}:\\ \;\;\;\;\left(t \cdot a + \left(x + y \cdot z\right)\right) + \left(z \cdot a\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y + a \cdot b\right) + \left(x + t \cdot a\right)\\ \end{array} \]

Alternative 2: 36.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(z \cdot b\right)\\ \mathbf{if}\;z \leq -8.5 \cdot 10^{+113}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.3 \cdot 10^{+29}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-195}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-87}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-56}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+202} \lor \neg \left(z \leq 5.7 \cdot 10^{+256}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (* z b))))
   (if (<= z -8.5e+113)
     t_1
     (if (<= z -4.3e+29)
       (* t a)
       (if (<= z 2e-195)
         x
         (if (<= z 6.2e-87)
           (* t a)
           (if (<= z 4.4e-56)
             x
             (if (or (<= z 2.2e+202) (not (<= z 5.7e+256))) t_1 (* y z)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (z * b);
	double tmp;
	if (z <= -8.5e+113) {
		tmp = t_1;
	} else if (z <= -4.3e+29) {
		tmp = t * a;
	} else if (z <= 2e-195) {
		tmp = x;
	} else if (z <= 6.2e-87) {
		tmp = t * a;
	} else if (z <= 4.4e-56) {
		tmp = x;
	} else if ((z <= 2.2e+202) || !(z <= 5.7e+256)) {
		tmp = t_1;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (z * b)
    if (z <= (-8.5d+113)) then
        tmp = t_1
    else if (z <= (-4.3d+29)) then
        tmp = t * a
    else if (z <= 2d-195) then
        tmp = x
    else if (z <= 6.2d-87) then
        tmp = t * a
    else if (z <= 4.4d-56) then
        tmp = x
    else if ((z <= 2.2d+202) .or. (.not. (z <= 5.7d+256))) then
        tmp = t_1
    else
        tmp = y * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (z * b);
	double tmp;
	if (z <= -8.5e+113) {
		tmp = t_1;
	} else if (z <= -4.3e+29) {
		tmp = t * a;
	} else if (z <= 2e-195) {
		tmp = x;
	} else if (z <= 6.2e-87) {
		tmp = t * a;
	} else if (z <= 4.4e-56) {
		tmp = x;
	} else if ((z <= 2.2e+202) || !(z <= 5.7e+256)) {
		tmp = t_1;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (z * b)
	tmp = 0
	if z <= -8.5e+113:
		tmp = t_1
	elif z <= -4.3e+29:
		tmp = t * a
	elif z <= 2e-195:
		tmp = x
	elif z <= 6.2e-87:
		tmp = t * a
	elif z <= 4.4e-56:
		tmp = x
	elif (z <= 2.2e+202) or not (z <= 5.7e+256):
		tmp = t_1
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(z * b))
	tmp = 0.0
	if (z <= -8.5e+113)
		tmp = t_1;
	elseif (z <= -4.3e+29)
		tmp = Float64(t * a);
	elseif (z <= 2e-195)
		tmp = x;
	elseif (z <= 6.2e-87)
		tmp = Float64(t * a);
	elseif (z <= 4.4e-56)
		tmp = x;
	elseif ((z <= 2.2e+202) || !(z <= 5.7e+256))
		tmp = t_1;
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (z * b);
	tmp = 0.0;
	if (z <= -8.5e+113)
		tmp = t_1;
	elseif (z <= -4.3e+29)
		tmp = t * a;
	elseif (z <= 2e-195)
		tmp = x;
	elseif (z <= 6.2e-87)
		tmp = t * a;
	elseif (z <= 4.4e-56)
		tmp = x;
	elseif ((z <= 2.2e+202) || ~((z <= 5.7e+256)))
		tmp = t_1;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(z * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8.5e+113], t$95$1, If[LessEqual[z, -4.3e+29], N[(t * a), $MachinePrecision], If[LessEqual[z, 2e-195], x, If[LessEqual[z, 6.2e-87], N[(t * a), $MachinePrecision], If[LessEqual[z, 4.4e-56], x, If[Or[LessEqual[z, 2.2e+202], N[Not[LessEqual[z, 5.7e+256]], $MachinePrecision]], t$95$1, N[(y * z), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -8.5000000000000001e113 or 4.40000000000000008e-56 < z < 2.19999999999999978e202 or 5.6999999999999997e256 < z

   1. Initial program 85.6%

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

      1. *-commutative 85.6%

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

      2. associate-*l* 90.9%

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

   3. Simplified 90.9%

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

   4. Taylor expanded in z around inf 82.8%

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

   5. Taylor expanded in y around 0 55.2%

      \[\leadsto \color{blue}{a \cdot \left(z \cdot b\right)} \]

   if -8.5000000000000001e113 < z < -4.3000000000000003e29 or 2.0000000000000002e-195 < z < 6.19999999999999995e-87

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

      2. associate-*l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t around inf 49.9%

      \[\leadsto \color{blue}{a \cdot t} \]

   if -4.3000000000000003e29 < z < 2.0000000000000002e-195 or 6.19999999999999995e-87 < z < 4.40000000000000008e-56

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. associate-*l* 91.2%

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

   3. Simplified 91.2%

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

   4. Taylor expanded in x around inf 49.7%

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

   if 2.19999999999999978e202 < z < 5.6999999999999997e256

   1. Initial program 44.4%

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

      1. *-commutative 44.4%

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

      2. associate-*l* 55.6%

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

   3. Simplified 55.6%

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

   4. Taylor expanded in y around inf 66.8%

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

      1. *-commutative 66.8%

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

   6. Simplified 66.8%

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

4. Final simplification 53.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+113}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;z \leq -4.3 \cdot 10^{+29}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-195}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-87}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-56}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+202} \lor \neg \left(z \leq 5.7 \cdot 10^{+256}\right):\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 3: 71.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot a + y \cdot z\\ t_2 := z \cdot \left(y + a \cdot b\right)\\ \mathbf{if}\;z \leq -6.2 \cdot 10^{+114}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -4.3 \cdot 10^{+30}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-46}:\\ \;\;\;\;x + a \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-86}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-137}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-58}:\\ \;\;\;\;x + t \cdot a\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (* t a) (* y z))) (t_2 (* z (+ y (* a b)))))
   (if (<= z -6.2e+114)
     t_2
     (if (<= z -4.3e+30)
       t_1
       (if (<= z -2.1e-46)
         (+ x (* a (* z b)))
         (if (<= z -3.5e-86)
           t_1
           (if (<= z -1.25e-137)
             (+ x (* y z))
             (if (<= z 1.35e-58) (+ x (* t a)) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t * a) + (y * z);
	double t_2 = z * (y + (a * b));
	double tmp;
	if (z <= -6.2e+114) {
		tmp = t_2;
	} else if (z <= -4.3e+30) {
		tmp = t_1;
	} else if (z <= -2.1e-46) {
		tmp = x + (a * (z * b));
	} else if (z <= -3.5e-86) {
		tmp = t_1;
	} else if (z <= -1.25e-137) {
		tmp = x + (y * z);
	} else if (z <= 1.35e-58) {
		tmp = x + (t * a);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (t * a) + (y * z)
    t_2 = z * (y + (a * b))
    if (z <= (-6.2d+114)) then
        tmp = t_2
    else if (z <= (-4.3d+30)) then
        tmp = t_1
    else if (z <= (-2.1d-46)) then
        tmp = x + (a * (z * b))
    else if (z <= (-3.5d-86)) then
        tmp = t_1
    else if (z <= (-1.25d-137)) then
        tmp = x + (y * z)
    else if (z <= 1.35d-58) then
        tmp = x + (t * a)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t * a) + (y * z);
	double t_2 = z * (y + (a * b));
	double tmp;
	if (z <= -6.2e+114) {
		tmp = t_2;
	} else if (z <= -4.3e+30) {
		tmp = t_1;
	} else if (z <= -2.1e-46) {
		tmp = x + (a * (z * b));
	} else if (z <= -3.5e-86) {
		tmp = t_1;
	} else if (z <= -1.25e-137) {
		tmp = x + (y * z);
	} else if (z <= 1.35e-58) {
		tmp = x + (t * a);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t * a) + (y * z)
	t_2 = z * (y + (a * b))
	tmp = 0
	if z <= -6.2e+114:
		tmp = t_2
	elif z <= -4.3e+30:
		tmp = t_1
	elif z <= -2.1e-46:
		tmp = x + (a * (z * b))
	elif z <= -3.5e-86:
		tmp = t_1
	elif z <= -1.25e-137:
		tmp = x + (y * z)
	elif z <= 1.35e-58:
		tmp = x + (t * a)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t * a) + Float64(y * z))
	t_2 = Float64(z * Float64(y + Float64(a * b)))
	tmp = 0.0
	if (z <= -6.2e+114)
		tmp = t_2;
	elseif (z <= -4.3e+30)
		tmp = t_1;
	elseif (z <= -2.1e-46)
		tmp = Float64(x + Float64(a * Float64(z * b)));
	elseif (z <= -3.5e-86)
		tmp = t_1;
	elseif (z <= -1.25e-137)
		tmp = Float64(x + Float64(y * z));
	elseif (z <= 1.35e-58)
		tmp = Float64(x + Float64(t * a));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t * a) + (y * z);
	t_2 = z * (y + (a * b));
	tmp = 0.0;
	if (z <= -6.2e+114)
		tmp = t_2;
	elseif (z <= -4.3e+30)
		tmp = t_1;
	elseif (z <= -2.1e-46)
		tmp = x + (a * (z * b));
	elseif (z <= -3.5e-86)
		tmp = t_1;
	elseif (z <= -1.25e-137)
		tmp = x + (y * z);
	elseif (z <= 1.35e-58)
		tmp = x + (t * a);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t * a), $MachinePrecision] + N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.2e+114], t$95$2, If[LessEqual[z, -4.3e+30], t$95$1, If[LessEqual[z, -2.1e-46], N[(x + N[(a * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.5e-86], t$95$1, If[LessEqual[z, -1.25e-137], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.35e-58], N[(x + N[(t * a), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -6.2000000000000001e114 or 1.3499999999999999e-58 < z

   1. Initial program 83.2%

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

      1. *-commutative 83.2%

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

      2. associate-*l* 88.7%

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

   3. Simplified 88.7%

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

   4. Taylor expanded in z around inf 81.3%

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

   if -6.2000000000000001e114 < z < -4.3e30 or -2.09999999999999987e-46 < z < -3.50000000000000021e-86

   1. Initial program 99.8%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]

   2. Taylor expanded in x around 0 87.3%

      \[\leadsto \color{blue}{\left(y \cdot z + a \cdot t\right)} + \left(a \cdot z\right) \cdot b \]
   3. Step-by-step derivation

      1. +-commutative 87.3%

         \[\leadsto \color{blue}{\left(a \cdot t + y \cdot z\right)} + \left(a \cdot z\right) \cdot b \]

      2. *-commutative 87.3%

         \[\leadsto \left(a \cdot t + \color{blue}{z \cdot y}\right) + \left(a \cdot z\right) \cdot b \]

      3. fma-def 87.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(a, t, z \cdot y\right)} + \left(a \cdot z\right) \cdot b \]

   4. Simplified 87.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, t, z \cdot y\right)} + \left(a \cdot z\right) \cdot b \]

   5. Taylor expanded in b around 0 77.3%

      \[\leadsto \color{blue}{y \cdot z + a \cdot t} \]

   if -4.3e30 < z < -2.09999999999999987e-46

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. *-commutative 100.0%

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

      3. associate-*l* 99.8%

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

      4. *-commutative 99.8%

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

      5. fma-def 99.8%

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

      6. *-commutative 99.8%

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

      7. +-commutative 99.8%

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

      8. fma-def 99.8%

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

      9. +-commutative 99.8%

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

      10. fma-def 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around 0 88.9%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot z\right) + \left(a \cdot t + x\right)} \]

   5. Taylor expanded in t around 0 86.1%

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

   if -3.50000000000000021e-86 < z < -1.25e-137

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. associate-*l* 82.9%

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

   3. Simplified 82.9%

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

   4. Taylor expanded in a around 0 73.7%

      \[\leadsto \color{blue}{y \cdot z + x} \]

   if -1.25e-137 < z < 1.3499999999999999e-58

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. associate-*l* 92.8%

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

   3. Simplified 92.8%

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

   4. Taylor expanded in z around 0 89.3%

      \[\leadsto \color{blue}{a \cdot t + x} \]
3. Recombined 5 regimes into one program.

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+114}:\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{elif}\;z \leq -4.3 \cdot 10^{+30}:\\ \;\;\;\;t \cdot a + y \cdot z\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-46}:\\ \;\;\;\;x + a \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-86}:\\ \;\;\;\;t \cdot a + y \cdot z\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-137}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-58}:\\ \;\;\;\;x + t \cdot a\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \end{array} \]

Alternative 4: 36.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(z \cdot b\right)\\ \mathbf{if}\;a \leq -2.8 \cdot 10^{+246}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.5 \cdot 10^{+214}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;a \leq -2.5 \cdot 10^{-85}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.85 \cdot 10^{-104}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;a \leq 1.95 \cdot 10^{-270}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-149}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot a\right) \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (* z b))))
   (if (<= a -2.8e+246)
     t_1
     (if (<= a -1.5e+214)
       (* t a)
       (if (<= a -2.5e-85)
         t_1
         (if (<= a -1.85e-104)
           (* t a)
           (if (<= a 1.95e-270)
             x
             (if (<= a 5e-149) (* y z) (* (* z a) b)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (z * b);
	double tmp;
	if (a <= -2.8e+246) {
		tmp = t_1;
	} else if (a <= -1.5e+214) {
		tmp = t * a;
	} else if (a <= -2.5e-85) {
		tmp = t_1;
	} else if (a <= -1.85e-104) {
		tmp = t * a;
	} else if (a <= 1.95e-270) {
		tmp = x;
	} else if (a <= 5e-149) {
		tmp = y * z;
	} else {
		tmp = (z * a) * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (z * b)
    if (a <= (-2.8d+246)) then
        tmp = t_1
    else if (a <= (-1.5d+214)) then
        tmp = t * a
    else if (a <= (-2.5d-85)) then
        tmp = t_1
    else if (a <= (-1.85d-104)) then
        tmp = t * a
    else if (a <= 1.95d-270) then
        tmp = x
    else if (a <= 5d-149) then
        tmp = y * z
    else
        tmp = (z * a) * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (z * b);
	double tmp;
	if (a <= -2.8e+246) {
		tmp = t_1;
	} else if (a <= -1.5e+214) {
		tmp = t * a;
	} else if (a <= -2.5e-85) {
		tmp = t_1;
	} else if (a <= -1.85e-104) {
		tmp = t * a;
	} else if (a <= 1.95e-270) {
		tmp = x;
	} else if (a <= 5e-149) {
		tmp = y * z;
	} else {
		tmp = (z * a) * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (z * b)
	tmp = 0
	if a <= -2.8e+246:
		tmp = t_1
	elif a <= -1.5e+214:
		tmp = t * a
	elif a <= -2.5e-85:
		tmp = t_1
	elif a <= -1.85e-104:
		tmp = t * a
	elif a <= 1.95e-270:
		tmp = x
	elif a <= 5e-149:
		tmp = y * z
	else:
		tmp = (z * a) * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(z * b))
	tmp = 0.0
	if (a <= -2.8e+246)
		tmp = t_1;
	elseif (a <= -1.5e+214)
		tmp = Float64(t * a);
	elseif (a <= -2.5e-85)
		tmp = t_1;
	elseif (a <= -1.85e-104)
		tmp = Float64(t * a);
	elseif (a <= 1.95e-270)
		tmp = x;
	elseif (a <= 5e-149)
		tmp = Float64(y * z);
	else
		tmp = Float64(Float64(z * a) * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (z * b);
	tmp = 0.0;
	if (a <= -2.8e+246)
		tmp = t_1;
	elseif (a <= -1.5e+214)
		tmp = t * a;
	elseif (a <= -2.5e-85)
		tmp = t_1;
	elseif (a <= -1.85e-104)
		tmp = t * a;
	elseif (a <= 1.95e-270)
		tmp = x;
	elseif (a <= 5e-149)
		tmp = y * z;
	else
		tmp = (z * a) * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(z * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.8e+246], t$95$1, If[LessEqual[a, -1.5e+214], N[(t * a), $MachinePrecision], If[LessEqual[a, -2.5e-85], t$95$1, If[LessEqual[a, -1.85e-104], N[(t * a), $MachinePrecision], If[LessEqual[a, 1.95e-270], x, If[LessEqual[a, 5e-149], N[(y * z), $MachinePrecision], N[(N[(z * a), $MachinePrecision] * b), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -2.79999999999999988e246 or -1.5000000000000001e214 < a < -2.5000000000000001e-85

   1. Initial program 85.1%

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

      1. *-commutative 85.1%

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

      2. associate-*l* 87.8%

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

   3. Simplified 87.8%

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

   4. Taylor expanded in z around inf 65.8%

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

   5. Taylor expanded in y around 0 54.5%

      \[\leadsto \color{blue}{a \cdot \left(z \cdot b\right)} \]

   if -2.79999999999999988e246 < a < -1.5000000000000001e214 or -2.5000000000000001e-85 < a < -1.85e-104

   1. Initial program 92.2%

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

      1. *-commutative 92.2%

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

      2. associate-*l* 92.5%

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

   3. Simplified 92.5%

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

   4. Taylor expanded in t around inf 73.1%

      \[\leadsto \color{blue}{a \cdot t} \]

   if -1.85e-104 < a < 1.94999999999999993e-270

   1. Initial program 98.1%

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

      1. *-commutative 98.1%

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

      2. associate-*l* 98.2%

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

   3. Simplified 98.2%

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

   4. Taylor expanded in x around inf 49.1%

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

   if 1.94999999999999993e-270 < a < 4.99999999999999968e-149

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. associate-*l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 59.5%

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

      1. *-commutative 59.5%

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

   6. Simplified 59.5%

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

   if 4.99999999999999968e-149 < a

   1. Initial program 88.0%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]

   2. Taylor expanded in x around 0 71.0%

      \[\leadsto \color{blue}{\left(y \cdot z + a \cdot t\right)} + \left(a \cdot z\right) \cdot b \]
   3. Step-by-step derivation

      1. +-commutative 71.0%

         \[\leadsto \color{blue}{\left(a \cdot t + y \cdot z\right)} + \left(a \cdot z\right) \cdot b \]

      2. *-commutative 71.0%

         \[\leadsto \left(a \cdot t + \color{blue}{z \cdot y}\right) + \left(a \cdot z\right) \cdot b \]

      3. fma-def 71.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(a, t, z \cdot y\right)} + \left(a \cdot z\right) \cdot b \]

   4. Simplified 71.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, t, z \cdot y\right)} + \left(a \cdot z\right) \cdot b \]

   5. Taylor expanded in z around 0 77.1%

      \[\leadsto \color{blue}{z \cdot \left(a \cdot b + y\right) + a \cdot t} \]

   6. Taylor expanded in b around inf 43.0%

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

      1. associate-*r* 44.1%

         \[\leadsto \color{blue}{\left(a \cdot b\right) \cdot z} \]

      2. *-commutative 44.1%

         \[\leadsto \color{blue}{\left(b \cdot a\right)} \cdot z \]

      3. associate-*r* 45.3%

         \[\leadsto \color{blue}{b \cdot \left(a \cdot z\right)} \]

   8. Simplified 45.3%

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

4. Final simplification 51.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.8 \cdot 10^{+246}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;a \leq -1.5 \cdot 10^{+214}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;a \leq -2.5 \cdot 10^{-85}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;a \leq -1.85 \cdot 10^{-104}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;a \leq 1.95 \cdot 10^{-270}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-149}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot a\right) \cdot b\\ \end{array} \]

Alternative 5: 39.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+129}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{+63}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;y \leq -230000000:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.38 \cdot 10^{-105}:\\ \;\;\;\;\left(z \cdot a\right) \cdot b\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{-257}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{+105}:\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -2.6e+129)
   (* y z)
   (if (<= y -8.5e+63)
     (* t a)
     (if (<= y -230000000.0)
       x
       (if (<= y -1.38e-105)
         (* (* z a) b)
         (if (<= y -1.1e-257)
           x
           (if (<= y 5.6e+105) (* z (* a b)) (* y z))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.6e+129) {
		tmp = y * z;
	} else if (y <= -8.5e+63) {
		tmp = t * a;
	} else if (y <= -230000000.0) {
		tmp = x;
	} else if (y <= -1.38e-105) {
		tmp = (z * a) * b;
	} else if (y <= -1.1e-257) {
		tmp = x;
	} else if (y <= 5.6e+105) {
		tmp = z * (a * b);
	} else {
		tmp = y * z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-2.6d+129)) then
        tmp = y * z
    else if (y <= (-8.5d+63)) then
        tmp = t * a
    else if (y <= (-230000000.0d0)) then
        tmp = x
    else if (y <= (-1.38d-105)) then
        tmp = (z * a) * b
    else if (y <= (-1.1d-257)) then
        tmp = x
    else if (y <= 5.6d+105) then
        tmp = z * (a * b)
    else
        tmp = y * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.6e+129) {
		tmp = y * z;
	} else if (y <= -8.5e+63) {
		tmp = t * a;
	} else if (y <= -230000000.0) {
		tmp = x;
	} else if (y <= -1.38e-105) {
		tmp = (z * a) * b;
	} else if (y <= -1.1e-257) {
		tmp = x;
	} else if (y <= 5.6e+105) {
		tmp = z * (a * b);
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -2.6e+129:
		tmp = y * z
	elif y <= -8.5e+63:
		tmp = t * a
	elif y <= -230000000.0:
		tmp = x
	elif y <= -1.38e-105:
		tmp = (z * a) * b
	elif y <= -1.1e-257:
		tmp = x
	elif y <= 5.6e+105:
		tmp = z * (a * b)
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -2.6e+129)
		tmp = Float64(y * z);
	elseif (y <= -8.5e+63)
		tmp = Float64(t * a);
	elseif (y <= -230000000.0)
		tmp = x;
	elseif (y <= -1.38e-105)
		tmp = Float64(Float64(z * a) * b);
	elseif (y <= -1.1e-257)
		tmp = x;
	elseif (y <= 5.6e+105)
		tmp = Float64(z * Float64(a * b));
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -2.6e+129)
		tmp = y * z;
	elseif (y <= -8.5e+63)
		tmp = t * a;
	elseif (y <= -230000000.0)
		tmp = x;
	elseif (y <= -1.38e-105)
		tmp = (z * a) * b;
	elseif (y <= -1.1e-257)
		tmp = x;
	elseif (y <= 5.6e+105)
		tmp = z * (a * b);
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -2.6e+129], N[(y * z), $MachinePrecision], If[LessEqual[y, -8.5e+63], N[(t * a), $MachinePrecision], If[LessEqual[y, -230000000.0], x, If[LessEqual[y, -1.38e-105], N[(N[(z * a), $MachinePrecision] * b), $MachinePrecision], If[LessEqual[y, -1.1e-257], x, If[LessEqual[y, 5.6e+105], N[(z * N[(a * b), $MachinePrecision]), $MachinePrecision], N[(y * z), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -2.60000000000000012e129 or 5.6000000000000003e105 < y

   1. Initial program 90.3%

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

      1. *-commutative 90.3%

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

      2. associate-*l* 85.8%

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

   3. Simplified 85.8%

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

   4. Taylor expanded in y around inf 63.6%

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

      1. *-commutative 63.6%

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

   6. Simplified 63.6%

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

   if -2.60000000000000012e129 < y < -8.5000000000000004e63

   1. Initial program 75.0%

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

      1. *-commutative 75.0%

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

      2. associate-*l* 75.0%

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

   3. Simplified 75.0%

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

   4. Taylor expanded in t around inf 75.3%

      \[\leadsto \color{blue}{a \cdot t} \]

   if -8.5000000000000004e63 < y < -2.3e8 or -1.3800000000000001e-105 < y < -1.09999999999999994e-257

   1. Initial program 93.6%

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

      1. *-commutative 93.6%

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

      2. associate-*l* 95.8%

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

   3. Simplified 95.8%

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

   4. Taylor expanded in x around inf 46.7%

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

   if -2.3e8 < y < -1.3800000000000001e-105

   1. Initial program 95.5%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]

   2. Taylor expanded in x around 0 80.1%

      \[\leadsto \color{blue}{\left(y \cdot z + a \cdot t\right)} + \left(a \cdot z\right) \cdot b \]
   3. Step-by-step derivation

      1. +-commutative 80.1%

         \[\leadsto \color{blue}{\left(a \cdot t + y \cdot z\right)} + \left(a \cdot z\right) \cdot b \]

      2. *-commutative 80.1%

         \[\leadsto \left(a \cdot t + \color{blue}{z \cdot y}\right) + \left(a \cdot z\right) \cdot b \]

      3. fma-def 80.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(a, t, z \cdot y\right)} + \left(a \cdot z\right) \cdot b \]

   4. Simplified 80.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, t, z \cdot y\right)} + \left(a \cdot z\right) \cdot b \]

   5. Taylor expanded in z around 0 80.4%

      \[\leadsto \color{blue}{z \cdot \left(a \cdot b + y\right) + a \cdot t} \]

   6. Taylor expanded in b around inf 42.1%

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

      1. associate-*r* 38.0%

         \[\leadsto \color{blue}{\left(a \cdot b\right) \cdot z} \]

      2. *-commutative 38.0%

         \[\leadsto \color{blue}{\left(b \cdot a\right)} \cdot z \]

      3. associate-*r* 42.2%

         \[\leadsto \color{blue}{b \cdot \left(a \cdot z\right)} \]

   8. Simplified 42.2%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot z\right)} \]

   if -1.09999999999999994e-257 < y < 5.6000000000000003e105

   1. Initial program 89.8%

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

      1. *-commutative 89.8%

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

      2. associate-*l* 93.9%

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

   3. Simplified 93.9%

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

   4. Taylor expanded in z around inf 52.1%

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

   5. Taylor expanded in a around inf 42.0%

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

      1. associate-*r* 45.8%

         \[\leadsto \color{blue}{\left(a \cdot b\right) \cdot z} \]

      2. *-commutative 45.8%

         \[\leadsto \color{blue}{z \cdot \left(a \cdot b\right)} \]

   7. Simplified 45.8%

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

4. Final simplification 52.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+129}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{+63}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;y \leq -230000000:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.38 \cdot 10^{-105}:\\ \;\;\;\;\left(z \cdot a\right) \cdot b\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{-257}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{+105}:\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 6: 71.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + t \cdot a\\ t_2 := z \cdot \left(y + a \cdot b\right)\\ \mathbf{if}\;z \leq -1.6 \cdot 10^{+76}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -220:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{-22}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-137}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-63}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* t a))) (t_2 (* z (+ y (* a b)))))
   (if (<= z -1.6e+76)
     t_2
     (if (<= z -220.0)
       t_1
       (if (<= z -4.1e-22)
         t_2
         (if (<= z -1.25e-137) (+ x (* y z)) (if (<= z 3.6e-63) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (t * a);
	double t_2 = z * (y + (a * b));
	double tmp;
	if (z <= -1.6e+76) {
		tmp = t_2;
	} else if (z <= -220.0) {
		tmp = t_1;
	} else if (z <= -4.1e-22) {
		tmp = t_2;
	} else if (z <= -1.25e-137) {
		tmp = x + (y * z);
	} else if (z <= 3.6e-63) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (t * a)
    t_2 = z * (y + (a * b))
    if (z <= (-1.6d+76)) then
        tmp = t_2
    else if (z <= (-220.0d0)) then
        tmp = t_1
    else if (z <= (-4.1d-22)) then
        tmp = t_2
    else if (z <= (-1.25d-137)) then
        tmp = x + (y * z)
    else if (z <= 3.6d-63) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (t * a);
	double t_2 = z * (y + (a * b));
	double tmp;
	if (z <= -1.6e+76) {
		tmp = t_2;
	} else if (z <= -220.0) {
		tmp = t_1;
	} else if (z <= -4.1e-22) {
		tmp = t_2;
	} else if (z <= -1.25e-137) {
		tmp = x + (y * z);
	} else if (z <= 3.6e-63) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (t * a)
	t_2 = z * (y + (a * b))
	tmp = 0
	if z <= -1.6e+76:
		tmp = t_2
	elif z <= -220.0:
		tmp = t_1
	elif z <= -4.1e-22:
		tmp = t_2
	elif z <= -1.25e-137:
		tmp = x + (y * z)
	elif z <= 3.6e-63:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(t * a))
	t_2 = Float64(z * Float64(y + Float64(a * b)))
	tmp = 0.0
	if (z <= -1.6e+76)
		tmp = t_2;
	elseif (z <= -220.0)
		tmp = t_1;
	elseif (z <= -4.1e-22)
		tmp = t_2;
	elseif (z <= -1.25e-137)
		tmp = Float64(x + Float64(y * z));
	elseif (z <= 3.6e-63)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (t * a);
	t_2 = z * (y + (a * b));
	tmp = 0.0;
	if (z <= -1.6e+76)
		tmp = t_2;
	elseif (z <= -220.0)
		tmp = t_1;
	elseif (z <= -4.1e-22)
		tmp = t_2;
	elseif (z <= -1.25e-137)
		tmp = x + (y * z);
	elseif (z <= 3.6e-63)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(t * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.6e+76], t$95$2, If[LessEqual[z, -220.0], t$95$1, If[LessEqual[z, -4.1e-22], t$95$2, If[LessEqual[z, -1.25e-137], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.6e-63], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.59999999999999988e76 or -220 < z < -4.0999999999999999e-22 or 3.60000000000000008e-63 < z

   1. Initial program 84.9%

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

      1. *-commutative 84.9%

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

      2. associate-*l* 89.9%

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

   3. Simplified 89.9%

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

   4. Taylor expanded in z around inf 80.2%

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

   if -1.59999999999999988e76 < z < -220 or -1.25e-137 < z < 3.60000000000000008e-63

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. associate-*l* 94.0%

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

   3. Simplified 94.0%

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

   4. Taylor expanded in z around 0 86.3%

      \[\leadsto \color{blue}{a \cdot t + x} \]

   if -4.0999999999999999e-22 < z < -1.25e-137

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

      2. associate-*l* 89.5%

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

   3. Simplified 89.5%

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

   4. Taylor expanded in a around 0 67.5%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+76}:\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{elif}\;z \leq -220:\\ \;\;\;\;x + t \cdot a\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{-22}:\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-137}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-63}:\\ \;\;\;\;x + t \cdot a\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \end{array} \]

Alternative 7: 60.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot z\\ \mathbf{if}\;z \leq -2.2 \cdot 10^{+213}:\\ \;\;\;\;\left(z \cdot a\right) \cdot b\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{+60}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-22}:\\ \;\;\;\;x + t \cdot a\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+116} \lor \neg \left(z \leq 5.7 \cdot 10^{+256}\right):\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* y z))))
   (if (<= z -2.2e+213)
     (* (* z a) b)
     (if (<= z -1.4e+60)
       t_1
       (if (<= z 2.3e-22)
         (+ x (* t a))
         (if (or (<= z 3.4e+116) (not (<= z 5.7e+256))) (* z (* a b)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y * z);
	double tmp;
	if (z <= -2.2e+213) {
		tmp = (z * a) * b;
	} else if (z <= -1.4e+60) {
		tmp = t_1;
	} else if (z <= 2.3e-22) {
		tmp = x + (t * a);
	} else if ((z <= 3.4e+116) || !(z <= 5.7e+256)) {
		tmp = z * (a * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y * z)
    if (z <= (-2.2d+213)) then
        tmp = (z * a) * b
    else if (z <= (-1.4d+60)) then
        tmp = t_1
    else if (z <= 2.3d-22) then
        tmp = x + (t * a)
    else if ((z <= 3.4d+116) .or. (.not. (z <= 5.7d+256))) then
        tmp = z * (a * b)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y * z);
	double tmp;
	if (z <= -2.2e+213) {
		tmp = (z * a) * b;
	} else if (z <= -1.4e+60) {
		tmp = t_1;
	} else if (z <= 2.3e-22) {
		tmp = x + (t * a);
	} else if ((z <= 3.4e+116) || !(z <= 5.7e+256)) {
		tmp = z * (a * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (y * z)
	tmp = 0
	if z <= -2.2e+213:
		tmp = (z * a) * b
	elif z <= -1.4e+60:
		tmp = t_1
	elif z <= 2.3e-22:
		tmp = x + (t * a)
	elif (z <= 3.4e+116) or not (z <= 5.7e+256):
		tmp = z * (a * b)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(y * z))
	tmp = 0.0
	if (z <= -2.2e+213)
		tmp = Float64(Float64(z * a) * b);
	elseif (z <= -1.4e+60)
		tmp = t_1;
	elseif (z <= 2.3e-22)
		tmp = Float64(x + Float64(t * a));
	elseif ((z <= 3.4e+116) || !(z <= 5.7e+256))
		tmp = Float64(z * Float64(a * b));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (y * z);
	tmp = 0.0;
	if (z <= -2.2e+213)
		tmp = (z * a) * b;
	elseif (z <= -1.4e+60)
		tmp = t_1;
	elseif (z <= 2.3e-22)
		tmp = x + (t * a);
	elseif ((z <= 3.4e+116) || ~((z <= 5.7e+256)))
		tmp = z * (a * b);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.2e+213], N[(N[(z * a), $MachinePrecision] * b), $MachinePrecision], If[LessEqual[z, -1.4e+60], t$95$1, If[LessEqual[z, 2.3e-22], N[(x + N[(t * a), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 3.4e+116], N[Not[LessEqual[z, 5.7e+256]], $MachinePrecision]], N[(z * N[(a * b), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.1999999999999999e213

   1. Initial program 73.1%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]

   2. Taylor expanded in x around 0 69.4%

      \[\leadsto \color{blue}{\left(y \cdot z + a \cdot t\right)} + \left(a \cdot z\right) \cdot b \]
   3. Step-by-step derivation

      1. +-commutative 69.4%

         \[\leadsto \color{blue}{\left(a \cdot t + y \cdot z\right)} + \left(a \cdot z\right) \cdot b \]

      2. *-commutative 69.4%

         \[\leadsto \left(a \cdot t + \color{blue}{z \cdot y}\right) + \left(a \cdot z\right) \cdot b \]

      3. fma-def 69.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(a, t, z \cdot y\right)} + \left(a \cdot z\right) \cdot b \]

   4. Simplified 69.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, t, z \cdot y\right)} + \left(a \cdot z\right) \cdot b \]

   5. Taylor expanded in z around 0 96.4%

      \[\leadsto \color{blue}{z \cdot \left(a \cdot b + y\right) + a \cdot t} \]

   6. Taylor expanded in b around inf 70.0%

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

      1. associate-*r* 73.5%

         \[\leadsto \color{blue}{\left(a \cdot b\right) \cdot z} \]

      2. *-commutative 73.5%

         \[\leadsto \color{blue}{\left(b \cdot a\right)} \cdot z \]

      3. associate-*r* 73.6%

         \[\leadsto \color{blue}{b \cdot \left(a \cdot z\right)} \]

   8. Simplified 73.6%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot z\right)} \]

   if -2.1999999999999999e213 < z < -1.4e60 or 3.40000000000000023e116 < z < 5.6999999999999997e256

   1. Initial program 82.3%

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

      1. *-commutative 82.3%

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

      2. associate-*l* 90.4%

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

   3. Simplified 90.4%

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

   4. Taylor expanded in a around 0 60.2%

      \[\leadsto \color{blue}{y \cdot z + x} \]

   if -1.4e60 < z < 2.2999999999999998e-22

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. associate-*l* 92.9%

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

   3. Simplified 92.9%

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

   4. Taylor expanded in z around 0 75.5%

      \[\leadsto \color{blue}{a \cdot t + x} \]

   if 2.2999999999999998e-22 < z < 3.40000000000000023e116 or 5.6999999999999997e256 < z

   1. Initial program 92.2%

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

      1. *-commutative 92.2%

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

      2. associate-*l* 96.0%

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

   3. Simplified 96.0%

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

   4. Taylor expanded in z around inf 82.3%

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

   5. Taylor expanded in a around inf 59.9%

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

      1. associate-*r* 61.8%

         \[\leadsto \color{blue}{\left(a \cdot b\right) \cdot z} \]

      2. *-commutative 61.8%

         \[\leadsto \color{blue}{z \cdot \left(a \cdot b\right)} \]

   7. Simplified 61.8%

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

4. Final simplification 68.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+213}:\\ \;\;\;\;\left(z \cdot a\right) \cdot b\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{+60}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-22}:\\ \;\;\;\;x + t \cdot a\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+116} \lor \neg \left(z \leq 5.7 \cdot 10^{+256}\right):\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]

Alternative 8: 40.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+131}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -7.8 \cdot 10^{+64}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;y \leq -360000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{-69}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-29}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -3.2e+131)
   (* y z)
   (if (<= y -7.8e+64)
     (* t a)
     (if (<= y -360000000000.0)
       x
       (if (<= y -3.8e-69) (* t a) (if (<= y 6e-29) x (* y z)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -3.2e+131) {
		tmp = y * z;
	} else if (y <= -7.8e+64) {
		tmp = t * a;
	} else if (y <= -360000000000.0) {
		tmp = x;
	} else if (y <= -3.8e-69) {
		tmp = t * a;
	} else if (y <= 6e-29) {
		tmp = x;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-3.2d+131)) then
        tmp = y * z
    else if (y <= (-7.8d+64)) then
        tmp = t * a
    else if (y <= (-360000000000.0d0)) then
        tmp = x
    else if (y <= (-3.8d-69)) then
        tmp = t * a
    else if (y <= 6d-29) then
        tmp = x
    else
        tmp = y * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -3.2e+131) {
		tmp = y * z;
	} else if (y <= -7.8e+64) {
		tmp = t * a;
	} else if (y <= -360000000000.0) {
		tmp = x;
	} else if (y <= -3.8e-69) {
		tmp = t * a;
	} else if (y <= 6e-29) {
		tmp = x;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -3.2e+131:
		tmp = y * z
	elif y <= -7.8e+64:
		tmp = t * a
	elif y <= -360000000000.0:
		tmp = x
	elif y <= -3.8e-69:
		tmp = t * a
	elif y <= 6e-29:
		tmp = x
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -3.2e+131)
		tmp = Float64(y * z);
	elseif (y <= -7.8e+64)
		tmp = Float64(t * a);
	elseif (y <= -360000000000.0)
		tmp = x;
	elseif (y <= -3.8e-69)
		tmp = Float64(t * a);
	elseif (y <= 6e-29)
		tmp = x;
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -3.2e+131)
		tmp = y * z;
	elseif (y <= -7.8e+64)
		tmp = t * a;
	elseif (y <= -360000000000.0)
		tmp = x;
	elseif (y <= -3.8e-69)
		tmp = t * a;
	elseif (y <= 6e-29)
		tmp = x;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -3.2e+131], N[(y * z), $MachinePrecision], If[LessEqual[y, -7.8e+64], N[(t * a), $MachinePrecision], If[LessEqual[y, -360000000000.0], x, If[LessEqual[y, -3.8e-69], N[(t * a), $MachinePrecision], If[LessEqual[y, 6e-29], x, N[(y * z), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.2000000000000002e131 or 6.0000000000000005e-29 < y

   1. Initial program 86.9%

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

      1. *-commutative 86.9%

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

      2. associate-*l* 85.2%

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

   3. Simplified 85.2%

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

   4. Taylor expanded in y around inf 55.2%

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

      1. *-commutative 55.2%

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

   6. Simplified 55.2%

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

   if -3.2000000000000002e131 < y < -7.7999999999999996e64 or -3.6e11 < y < -3.7999999999999998e-69

   1. Initial program 87.5%

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

      1. *-commutative 87.5%

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

      2. associate-*l* 87.9%

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

   3. Simplified 87.9%

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

   4. Taylor expanded in t around inf 52.8%

      \[\leadsto \color{blue}{a \cdot t} \]

   if -7.7999999999999996e64 < y < -3.6e11 or -3.7999999999999998e-69 < y < 6.0000000000000005e-29

   1. Initial program 94.4%

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

      1. *-commutative 94.4%

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

      2. associate-*l* 96.9%

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

   3. Simplified 96.9%

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

   4. Taylor expanded in x around inf 38.3%

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

4. Final simplification 46.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+131}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -7.8 \cdot 10^{+64}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;y \leq -360000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{-69}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-29}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 9: 56.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(a \cdot b\right)\\ \mathbf{if}\;z \leq -1.2 \cdot 10^{+128}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-22}:\\ \;\;\;\;x + t \cdot a\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+198} \lor \neg \left(z \leq 2.1 \cdot 10^{+255}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (* a b))))
   (if (<= z -1.2e+128)
     t_1
     (if (<= z 4.4e-22)
       (+ x (* t a))
       (if (or (<= z 3e+198) (not (<= z 2.1e+255))) t_1 (* y z))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (a * b);
	double tmp;
	if (z <= -1.2e+128) {
		tmp = t_1;
	} else if (z <= 4.4e-22) {
		tmp = x + (t * a);
	} else if ((z <= 3e+198) || !(z <= 2.1e+255)) {
		tmp = t_1;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * (a * b)
    if (z <= (-1.2d+128)) then
        tmp = t_1
    else if (z <= 4.4d-22) then
        tmp = x + (t * a)
    else if ((z <= 3d+198) .or. (.not. (z <= 2.1d+255))) then
        tmp = t_1
    else
        tmp = y * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (a * b);
	double tmp;
	if (z <= -1.2e+128) {
		tmp = t_1;
	} else if (z <= 4.4e-22) {
		tmp = x + (t * a);
	} else if ((z <= 3e+198) || !(z <= 2.1e+255)) {
		tmp = t_1;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (a * b)
	tmp = 0
	if z <= -1.2e+128:
		tmp = t_1
	elif z <= 4.4e-22:
		tmp = x + (t * a)
	elif (z <= 3e+198) or not (z <= 2.1e+255):
		tmp = t_1
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(a * b))
	tmp = 0.0
	if (z <= -1.2e+128)
		tmp = t_1;
	elseif (z <= 4.4e-22)
		tmp = Float64(x + Float64(t * a));
	elseif ((z <= 3e+198) || !(z <= 2.1e+255))
		tmp = t_1;
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (a * b);
	tmp = 0.0;
	if (z <= -1.2e+128)
		tmp = t_1;
	elseif (z <= 4.4e-22)
		tmp = x + (t * a);
	elseif ((z <= 3e+198) || ~((z <= 2.1e+255)))
		tmp = t_1;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(a * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.2e+128], t$95$1, If[LessEqual[z, 4.4e-22], N[(x + N[(t * a), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 3e+198], N[Not[LessEqual[z, 2.1e+255]], $MachinePrecision]], t$95$1, N[(y * z), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.2000000000000001e128 or 4.4000000000000001e-22 < z < 3.00000000000000019e198 or 2.1e255 < z

   1. Initial program 85.4%

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

      1. *-commutative 85.4%

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

      2. associate-*l* 91.0%

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

   3. Simplified 91.0%

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

   4. Taylor expanded in z around inf 84.8%

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

   5. Taylor expanded in a around inf 56.3%

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

      1. associate-*r* 57.8%

         \[\leadsto \color{blue}{\left(a \cdot b\right) \cdot z} \]

      2. *-commutative 57.8%

         \[\leadsto \color{blue}{z \cdot \left(a \cdot b\right)} \]

   7. Simplified 57.8%

      \[\leadsto \color{blue}{z \cdot \left(a \cdot b\right)} \]

   if -1.2000000000000001e128 < z < 4.4000000000000001e-22

   1. Initial program 99.2%

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

      1. *-commutative 99.2%

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

      2. associate-*l* 93.9%

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

   3. Simplified 93.9%

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

   4. Taylor expanded in z around 0 71.2%

      \[\leadsto \color{blue}{a \cdot t + x} \]

   if 3.00000000000000019e198 < z < 2.1e255

   1. Initial program 44.4%

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

      1. *-commutative 44.4%

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

      2. associate-*l* 55.6%

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

   3. Simplified 55.6%

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

   4. Taylor expanded in y around inf 66.8%

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

      1. *-commutative 66.8%

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

   6. Simplified 66.8%

      \[\leadsto \color{blue}{z \cdot y} \]
3. Recombined 3 regimes into one program.

4. Final simplification 64.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+128}:\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-22}:\\ \;\;\;\;x + t \cdot a\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+198} \lor \neg \left(z \leq 2.1 \cdot 10^{+255}\right):\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 10: 85.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -8200000000000 \lor \neg \left(a \leq 4.2 \cdot 10^{-149}\right):\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + t \cdot a\right) + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -8200000000000.0) (not (<= a 4.2e-149)))
   (+ x (* a (+ t (* z b))))
   (+ (+ x (* t a)) (* y z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -8200000000000.0) || !(a <= 4.2e-149)) {
		tmp = x + (a * (t + (z * b)));
	} else {
		tmp = (x + (t * a)) + (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((a <= (-8200000000000.0d0)) .or. (.not. (a <= 4.2d-149))) then
        tmp = x + (a * (t + (z * b)))
    else
        tmp = (x + (t * a)) + (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -8200000000000.0) || !(a <= 4.2e-149)) {
		tmp = x + (a * (t + (z * b)));
	} else {
		tmp = (x + (t * a)) + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -8200000000000.0) or not (a <= 4.2e-149):
		tmp = x + (a * (t + (z * b)))
	else:
		tmp = (x + (t * a)) + (y * z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -8200000000000.0) || !(a <= 4.2e-149))
		tmp = Float64(x + Float64(a * Float64(t + Float64(z * b))));
	else
		tmp = Float64(Float64(x + Float64(t * a)) + Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -8200000000000.0) || ~((a <= 4.2e-149)))
		tmp = x + (a * (t + (z * b)));
	else
		tmp = (x + (t * a)) + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -8200000000000.0], N[Not[LessEqual[a, 4.2e-149]], $MachinePrecision]], N[(x + N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(t * a), $MachinePrecision]), $MachinePrecision] + N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -8.2e12 or 4.20000000000000022e-149 < a

   1. Initial program 84.2%

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

      1. associate-+l+ 84.2%

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

      2. +-commutative 84.2%

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

      3. *-commutative 84.2%

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

      4. *-commutative 84.2%

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

      5. associate-*l* 89.6%

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

      6. distribute-rgt-out 90.3%

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

      7. fma-def 91.7%

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

      8. *-commutative 91.7%

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

      9. +-commutative 91.7%

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

      10. fma-def 91.7%

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

   3. Simplified 91.7%

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

   4. Taylor expanded in y around 0 87.7%

      \[\leadsto \color{blue}{x + a \cdot \left(z \cdot b + t\right)} \]

   if -8.2e12 < a < 4.20000000000000022e-149

   1. Initial program 99.0%

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

      1. *-commutative 99.0%

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

      2. associate-*l* 99.0%

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

   3. Simplified 99.0%

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

   4. Taylor expanded in b around 0 85.2%

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

4. Final simplification 86.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8200000000000 \lor \neg \left(a \leq 4.2 \cdot 10^{-149}\right):\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + t \cdot a\right) + y \cdot z\\ \end{array} \]

Alternative 11: 85.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.5 \cdot 10^{-47} \lor \neg \left(b \leq 0.66\right):\\ \;\;\;\;x + z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + t \cdot a\right) + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -2.5e-47) (not (<= b 0.66)))
   (+ x (* z (+ y (* a b))))
   (+ (+ x (* t a)) (* y z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -2.5e-47) || !(b <= 0.66)) {
		tmp = x + (z * (y + (a * b)));
	} else {
		tmp = (x + (t * a)) + (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-2.5d-47)) .or. (.not. (b <= 0.66d0))) then
        tmp = x + (z * (y + (a * b)))
    else
        tmp = (x + (t * a)) + (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -2.5e-47) || !(b <= 0.66)) {
		tmp = x + (z * (y + (a * b)));
	} else {
		tmp = (x + (t * a)) + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -2.5e-47) or not (b <= 0.66):
		tmp = x + (z * (y + (a * b)))
	else:
		tmp = (x + (t * a)) + (y * z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -2.5e-47) || !(b <= 0.66))
		tmp = Float64(x + Float64(z * Float64(y + Float64(a * b))));
	else
		tmp = Float64(Float64(x + Float64(t * a)) + Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -2.5e-47) || ~((b <= 0.66)))
		tmp = x + (z * (y + (a * b)));
	else
		tmp = (x + (t * a)) + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -2.5e-47], N[Not[LessEqual[b, 0.66]], $MachinePrecision]], N[(x + N[(z * N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(t * a), $MachinePrecision]), $MachinePrecision] + N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -2.50000000000000006e-47 or 0.660000000000000031 < b

   1. Initial program 92.6%

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

      1. *-commutative 92.6%

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

      2. associate-*l* 87.7%

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

   3. Simplified 87.7%

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

   4. Taylor expanded in z around 0 94.4%

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

   5. Taylor expanded in t around 0 90.4%

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

   if -2.50000000000000006e-47 < b < 0.660000000000000031

   1. Initial program 88.5%

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

      1. *-commutative 88.5%

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

      2. associate-*l* 95.0%

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

   3. Simplified 95.0%

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

   4. Taylor expanded in b around 0 88.5%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.5 \cdot 10^{-47} \lor \neg \left(b \leq 0.66\right):\\ \;\;\;\;x + z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + t \cdot a\right) + y \cdot z\\ \end{array} \]

Alternative 12: 80.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{+143}:\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+138}:\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot a + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -3.7e+143)
   (* z (+ y (* a b)))
   (if (<= y 6.5e+138) (+ x (* a (+ t (* z b)))) (+ (* t a) (* y z)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -3.7e+143) {
		tmp = z * (y + (a * b));
	} else if (y <= 6.5e+138) {
		tmp = x + (a * (t + (z * b)));
	} else {
		tmp = (t * a) + (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-3.7d+143)) then
        tmp = z * (y + (a * b))
    else if (y <= 6.5d+138) then
        tmp = x + (a * (t + (z * b)))
    else
        tmp = (t * a) + (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -3.7e+143) {
		tmp = z * (y + (a * b));
	} else if (y <= 6.5e+138) {
		tmp = x + (a * (t + (z * b)));
	} else {
		tmp = (t * a) + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -3.7e+143:
		tmp = z * (y + (a * b))
	elif y <= 6.5e+138:
		tmp = x + (a * (t + (z * b)))
	else:
		tmp = (t * a) + (y * z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -3.7e+143)
		tmp = Float64(z * Float64(y + Float64(a * b)));
	elseif (y <= 6.5e+138)
		tmp = Float64(x + Float64(a * Float64(t + Float64(z * b))));
	else
		tmp = Float64(Float64(t * a) + Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -3.7e+143)
		tmp = z * (y + (a * b));
	elseif (y <= 6.5e+138)
		tmp = x + (a * (t + (z * b)));
	else
		tmp = (t * a) + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -3.7e+143], N[(z * N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.5e+138], N[(x + N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t * a), $MachinePrecision] + N[(y * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.7000000000000002e143

   1. Initial program 86.4%

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

      1. *-commutative 86.4%

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

      2. associate-*l* 76.3%

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

   3. Simplified 76.3%

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

   4. Taylor expanded in z around inf 74.3%

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

   if -3.7000000000000002e143 < y < 6.50000000000000054e138

   1. Initial program 91.2%

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

      1. associate-+l+ 91.2%

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

      2. +-commutative 91.2%

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

      3. *-commutative 91.2%

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

      4. *-commutative 91.2%

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

      5. associate-*l* 93.5%

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

      6. distribute-rgt-out 94.0%

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

      7. fma-def 94.0%

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

      8. *-commutative 94.0%

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

      9. +-commutative 94.0%

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

      10. fma-def 94.0%

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

   3. Simplified 94.0%

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

   4. Taylor expanded in y around 0 88.7%

      \[\leadsto \color{blue}{x + a \cdot \left(z \cdot b + t\right)} \]

   if 6.50000000000000054e138 < y

   1. Initial program 92.0%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]

   2. Taylor expanded in x around 0 84.6%

      \[\leadsto \color{blue}{\left(y \cdot z + a \cdot t\right)} + \left(a \cdot z\right) \cdot b \]
   3. Step-by-step derivation

      1. +-commutative 84.6%

         \[\leadsto \color{blue}{\left(a \cdot t + y \cdot z\right)} + \left(a \cdot z\right) \cdot b \]

      2. *-commutative 84.6%

         \[\leadsto \left(a \cdot t + \color{blue}{z \cdot y}\right) + \left(a \cdot z\right) \cdot b \]

      3. fma-def 84.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(a, t, z \cdot y\right)} + \left(a \cdot z\right) \cdot b \]

   4. Simplified 84.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, t, z \cdot y\right)} + \left(a \cdot z\right) \cdot b \]

   5. Taylor expanded in b around 0 82.3%

      \[\leadsto \color{blue}{y \cdot z + a \cdot t} \]
3. Recombined 3 regimes into one program.

4. Final simplification 85.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{+143}:\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+138}:\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot a + y \cdot z\\ \end{array} \]

Alternative 13: 93.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ z \cdot \left(y + a \cdot b\right) + \left(x + t \cdot a\right) \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (+ (* z (+ y (* a b))) (+ x (* t a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	return (z * (y + (a * b))) + (x + (t * a));
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = (z * (y + (a * b))) + (x + (t * a))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return (z * (y + (a * b))) + (x + (t * a));
}

Python

def code(x, y, z, t, a, b):
	return (z * (y + (a * b))) + (x + (t * a))

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(z * Float64(y + Float64(a * b))) + Float64(x + Float64(t * a)))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = (z * (y + (a * b))) + (x + (t * a));
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(z * N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 90.6%

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

   1. *-commutative 90.6%

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

   2. associate-*l* 91.2%

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

3. Simplified 91.2%

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

4. Taylor expanded in z around 0 95.8%

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

5. Final simplification 95.8%

   \[\leadsto z \cdot \left(y + a \cdot b\right) + \left(x + t \cdot a\right) \]

Alternative 14: 38.6% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{-74}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{+124}:\\ \;\;\;\;t \cdot a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -1.05e-74) x (if (<= x 2.2e+124) (* t a) x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.05e-74) {
		tmp = x;
	} else if (x <= 2.2e+124) {
		tmp = t * a;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-1.05d-74)) then
        tmp = x
    else if (x <= 2.2d+124) then
        tmp = t * a
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.05e-74) {
		tmp = x;
	} else if (x <= 2.2e+124) {
		tmp = t * a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -1.05e-74:
		tmp = x
	elif x <= 2.2e+124:
		tmp = t * a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -1.05e-74)
		tmp = x;
	elseif (x <= 2.2e+124)
		tmp = Float64(t * a);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -1.05e-74)
		tmp = x;
	elseif (x <= 2.2e+124)
		tmp = t * a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -1.05e-74], x, If[LessEqual[x, 2.2e+124], N[(t * a), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -1.05e-74 or 2.2000000000000001e124 < x

   1. Initial program 90.7%

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

      1. *-commutative 90.7%

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

      2. associate-*l* 91.8%

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

   3. Simplified 91.8%

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

   4. Taylor expanded in x around inf 46.2%

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

   if -1.05e-74 < x < 2.2000000000000001e124

   1. Initial program 90.6%

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

      1. *-commutative 90.6%

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

      2. associate-*l* 90.7%

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

   3. Simplified 90.7%

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

   4. Taylor expanded in t around inf 31.3%

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

4. Final simplification 37.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{-74}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{+124}:\\ \;\;\;\;t \cdot a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 15: 26.6% accurate, 15.0× speedup

Math

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

FPCore

(FPCore (x y z t a b) :precision binary64 x)

C

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

Fortran

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

Java

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

Python

def code(x, y, z, t, a, b):
	return x

Julia

function code(x, y, z, t, a, b)
	return x
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := x

Derivation

1. Initial program 90.6%

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

   1. *-commutative 90.6%

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

   2. associate-*l* 91.2%

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

3. Simplified 91.2%

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

4. Taylor expanded in x around inf 24.7%

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

5. Final simplification 24.7%

   \[\leadsto x \]

Developer target: 97.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(b \cdot a + y\right) + \left(x + t \cdot a\right)\\ \mathbf{if}\;z < -11820553527347888000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z < 4.7589743188364287 \cdot 10^{-122}:\\ \;\;\;\;\left(b \cdot z + t\right) \cdot a + \left(z \cdot y + x\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (* z (+ (* b a) y)) (+ x (* t a)))))
   (if (< z -11820553527347888000.0)
     t_1
     (if (< z 4.7589743188364287e-122)
       (+ (* (+ (* b z) t) a) (+ (* z y) x))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z * ((b * a) + y)) + (x + (t * a));
	double tmp;
	if (z < -11820553527347888000.0) {
		tmp = t_1;
	} else if (z < 4.7589743188364287e-122) {
		tmp = (((b * z) + t) * a) + ((z * y) + x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z * ((b * a) + y)) + (x + (t * a))
    if (z < (-11820553527347888000.0d0)) then
        tmp = t_1
    else if (z < 4.7589743188364287d-122) then
        tmp = (((b * z) + t) * a) + ((z * y) + x)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z * ((b * a) + y)) + (x + (t * a));
	double tmp;
	if (z < -11820553527347888000.0) {
		tmp = t_1;
	} else if (z < 4.7589743188364287e-122) {
		tmp = (((b * z) + t) * a) + ((z * y) + x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z * ((b * a) + y)) + (x + (t * a))
	tmp = 0
	if z < -11820553527347888000.0:
		tmp = t_1
	elif z < 4.7589743188364287e-122:
		tmp = (((b * z) + t) * a) + ((z * y) + x)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z * Float64(Float64(b * a) + y)) + Float64(x + Float64(t * a)))
	tmp = 0.0
	if (z < -11820553527347888000.0)
		tmp = t_1;
	elseif (z < 4.7589743188364287e-122)
		tmp = Float64(Float64(Float64(Float64(b * z) + t) * a) + Float64(Float64(z * y) + x));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z * ((b * a) + y)) + (x + (t * a));
	tmp = 0.0;
	if (z < -11820553527347888000.0)
		tmp = t_1;
	elseif (z < 4.7589743188364287e-122)
		tmp = (((b * z) + t) * a) + ((z * y) + x);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z * N[(N[(b * a), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision] + N[(x + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[z, -11820553527347888000.0], t$95$1, If[Less[z, 4.7589743188364287e-122], N[(N[(N[(N[(b * z), $MachinePrecision] + t), $MachinePrecision] * a), $MachinePrecision] + N[(N[(z * y), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2023274 
(FPCore (x y z t a b)
  :name "Graphics.Rasterific.CubicBezier:cachedBezierAt from Rasterific-0.6.1"
  :precision binary64

  :herbie-target
  (if (< z -11820553527347888000.0) (+ (* z (+ (* b a) y)) (+ x (* t a))) (if (< z 4.7589743188364287e-122) (+ (* (+ (* b z) t) a) (+ (* z y) x)) (+ (* z (+ (* b a) y)) (+ x (* t a)))))

  (+ (+ (+ x (* y z)) (* t a)) (* (* a z) b)))