Graphics.Rasterific.CubicBezier:cachedBezierAt from Rasterific-0.6.1

Percentage Accurate: 92.1% → 96.4%

Time: 12.9s

Alternatives: 13

Speedup: 0.4×

• 33.1% 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: 92.1% 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: 96.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(z \cdot a\right) \cdot b\\ \mathbf{if}\;t\_1 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

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

C

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

Java

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

Python

def code(x, y, z, t, a, b):
	t_1 = ((x + (y * z)) + (t * a)) + ((z * a) * b)
	tmp = 0
	if t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = a * (t + (z * b))
	return tmp

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision] + N[(N[(z * a), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(a * N[(t + N[(z * b), $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)) < +inf.0

   1. Initial program 99.5%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
   2. Add Preprocessing

   if +inf.0 < (+.f64 (+.f64 (+.f64 x (*.f64 y z)) (*.f64 t a)) (*.f64 (*.f64 a z) b))

   1. Initial program 0.0%

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

      1. associate-+l+ 0.0%

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

      2. associate-*l* 10.5%

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

   3. Simplified 10.5%

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

   5. Taylor expanded in a around inf 68.4%

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

4. Final simplification 97.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(z \cdot a\right) \cdot b \leq \infty:\\ \;\;\;\;\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(z \cdot a\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 56.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot z\\ \mathbf{if}\;t \leq -5 \cdot 10^{+162}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-231}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.6 \cdot 10^{-261}:\\ \;\;\;\;\left(z \cdot a\right) \cdot b\\ \mathbf{elif}\;t \leq 5.7 \cdot 10^{-111}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.95 \cdot 10^{-52}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{+106}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* y z))))
   (if (<= t -5e+162)
     (* t a)
     (if (<= t -9e-231)
       t_1
       (if (<= t -1.6e-261)
         (* (* z a) b)
         (if (<= t 5.7e-111)
           t_1
           (if (<= t 2.95e-52)
             (* a (* z b))
             (if (<= t 4.6e+106) t_1 (* t a)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y * z);
	double tmp;
	if (t <= -5e+162) {
		tmp = t * a;
	} else if (t <= -9e-231) {
		tmp = t_1;
	} else if (t <= -1.6e-261) {
		tmp = (z * a) * b;
	} else if (t <= 5.7e-111) {
		tmp = t_1;
	} else if (t <= 2.95e-52) {
		tmp = a * (z * b);
	} else if (t <= 4.6e+106) {
		tmp = t_1;
	} else {
		tmp = 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 = x + (y * z)
    if (t <= (-5d+162)) then
        tmp = t * a
    else if (t <= (-9d-231)) then
        tmp = t_1
    else if (t <= (-1.6d-261)) then
        tmp = (z * a) * b
    else if (t <= 5.7d-111) then
        tmp = t_1
    else if (t <= 2.95d-52) then
        tmp = a * (z * b)
    else if (t <= 4.6d+106) then
        tmp = t_1
    else
        tmp = 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 = x + (y * z);
	double tmp;
	if (t <= -5e+162) {
		tmp = t * a;
	} else if (t <= -9e-231) {
		tmp = t_1;
	} else if (t <= -1.6e-261) {
		tmp = (z * a) * b;
	} else if (t <= 5.7e-111) {
		tmp = t_1;
	} else if (t <= 2.95e-52) {
		tmp = a * (z * b);
	} else if (t <= 4.6e+106) {
		tmp = t_1;
	} else {
		tmp = t * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (y * z)
	tmp = 0
	if t <= -5e+162:
		tmp = t * a
	elif t <= -9e-231:
		tmp = t_1
	elif t <= -1.6e-261:
		tmp = (z * a) * b
	elif t <= 5.7e-111:
		tmp = t_1
	elif t <= 2.95e-52:
		tmp = a * (z * b)
	elif t <= 4.6e+106:
		tmp = t_1
	else:
		tmp = t * a
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(y * z))
	tmp = 0.0
	if (t <= -5e+162)
		tmp = Float64(t * a);
	elseif (t <= -9e-231)
		tmp = t_1;
	elseif (t <= -1.6e-261)
		tmp = Float64(Float64(z * a) * b);
	elseif (t <= 5.7e-111)
		tmp = t_1;
	elseif (t <= 2.95e-52)
		tmp = Float64(a * Float64(z * b));
	elseif (t <= 4.6e+106)
		tmp = t_1;
	else
		tmp = Float64(t * a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (y * z);
	tmp = 0.0;
	if (t <= -5e+162)
		tmp = t * a;
	elseif (t <= -9e-231)
		tmp = t_1;
	elseif (t <= -1.6e-261)
		tmp = (z * a) * b;
	elseif (t <= 5.7e-111)
		tmp = t_1;
	elseif (t <= 2.95e-52)
		tmp = a * (z * b);
	elseif (t <= 4.6e+106)
		tmp = t_1;
	else
		tmp = t * a;
	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[t, -5e+162], N[(t * a), $MachinePrecision], If[LessEqual[t, -9e-231], t$95$1, If[LessEqual[t, -1.6e-261], N[(N[(z * a), $MachinePrecision] * b), $MachinePrecision], If[LessEqual[t, 5.7e-111], t$95$1, If[LessEqual[t, 2.95e-52], N[(a * N[(z * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.6e+106], t$95$1, N[(t * a), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -4.9999999999999997e162 or 4.6000000000000004e106 < t

   1. Initial program 88.3%

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

      1. associate-+l+ 88.3%

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

      2. associate-*l* 86.0%

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

   3. Simplified 86.0%

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

   5. Taylor expanded in t around inf 64.4%

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

   if -4.9999999999999997e162 < t < -8.9999999999999996e-231 or -1.60000000000000002e-261 < t < 5.7e-111 or 2.9500000000000001e-52 < t < 4.6000000000000004e106

   1. Initial program 93.7%

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

      1. associate-+l+ 93.7%

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

      2. associate-*l* 89.7%

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

   3. Simplified 89.7%

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

   5. Taylor expanded in a around 0 67.9%

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

   if -8.9999999999999996e-231 < t < -1.60000000000000002e-261

   1. Initial program 90.0%

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

      1. associate-+l+ 90.0%

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

      2. associate-*l* 89.7%

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

   3. Simplified 89.7%

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

   5. Taylor expanded in z around inf 80.7%

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

   6. Taylor expanded in y around 0 76.6%

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

      1. associate-*r* 67.2%

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

      2. *-commutative 67.2%

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

      3. associate-*l* 76.8%

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

   8. Simplified 76.8%

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

   if 5.7e-111 < t < 2.9500000000000001e-52

   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. associate-+l+ 99.8%

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

      2. associate-*l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 88.8%

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

   6. Taylor expanded in y around 0 89.1%

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

      1. *-commutative 89.1%

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

   8. Simplified 89.1%

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

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+162}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-231}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{elif}\;t \leq -1.6 \cdot 10^{-261}:\\ \;\;\;\;\left(z \cdot a\right) \cdot b\\ \mathbf{elif}\;t \leq 5.7 \cdot 10^{-111}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{elif}\;t \leq 2.95 \cdot 10^{-52}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{+106}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 61.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot z\\ t_2 := x + t \cdot a\\ \mathbf{if}\;t \leq -2.1 \cdot 10^{+56}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -8.2 \cdot 10^{-231}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{-261}:\\ \;\;\;\;\left(z \cdot a\right) \cdot b\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-111}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-52}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;t \leq 2.95 \cdot 10^{+106}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* y z))) (t_2 (+ x (* t a))))
   (if (<= t -2.1e+56)
     t_2
     (if (<= t -8.2e-231)
       t_1
       (if (<= t -1.8e-261)
         (* (* z a) b)
         (if (<= t 2.4e-111)
           t_1
           (if (<= t 2.5e-52)
             (* a (* z b))
             (if (<= t 2.95e+106) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y * z);
	double t_2 = x + (t * a);
	double tmp;
	if (t <= -2.1e+56) {
		tmp = t_2;
	} else if (t <= -8.2e-231) {
		tmp = t_1;
	} else if (t <= -1.8e-261) {
		tmp = (z * a) * b;
	} else if (t <= 2.4e-111) {
		tmp = t_1;
	} else if (t <= 2.5e-52) {
		tmp = a * (z * b);
	} else if (t <= 2.95e+106) {
		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 + (y * z)
    t_2 = x + (t * a)
    if (t <= (-2.1d+56)) then
        tmp = t_2
    else if (t <= (-8.2d-231)) then
        tmp = t_1
    else if (t <= (-1.8d-261)) then
        tmp = (z * a) * b
    else if (t <= 2.4d-111) then
        tmp = t_1
    else if (t <= 2.5d-52) then
        tmp = a * (z * b)
    else if (t <= 2.95d+106) 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 + (y * z);
	double t_2 = x + (t * a);
	double tmp;
	if (t <= -2.1e+56) {
		tmp = t_2;
	} else if (t <= -8.2e-231) {
		tmp = t_1;
	} else if (t <= -1.8e-261) {
		tmp = (z * a) * b;
	} else if (t <= 2.4e-111) {
		tmp = t_1;
	} else if (t <= 2.5e-52) {
		tmp = a * (z * b);
	} else if (t <= 2.95e+106) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (y * z)
	t_2 = x + (t * a)
	tmp = 0
	if t <= -2.1e+56:
		tmp = t_2
	elif t <= -8.2e-231:
		tmp = t_1
	elif t <= -1.8e-261:
		tmp = (z * a) * b
	elif t <= 2.4e-111:
		tmp = t_1
	elif t <= 2.5e-52:
		tmp = a * (z * b)
	elif t <= 2.95e+106:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(y * z))
	t_2 = Float64(x + Float64(t * a))
	tmp = 0.0
	if (t <= -2.1e+56)
		tmp = t_2;
	elseif (t <= -8.2e-231)
		tmp = t_1;
	elseif (t <= -1.8e-261)
		tmp = Float64(Float64(z * a) * b);
	elseif (t <= 2.4e-111)
		tmp = t_1;
	elseif (t <= 2.5e-52)
		tmp = Float64(a * Float64(z * b));
	elseif (t <= 2.95e+106)
		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 + (y * z);
	t_2 = x + (t * a);
	tmp = 0.0;
	if (t <= -2.1e+56)
		tmp = t_2;
	elseif (t <= -8.2e-231)
		tmp = t_1;
	elseif (t <= -1.8e-261)
		tmp = (z * a) * b;
	elseif (t <= 2.4e-111)
		tmp = t_1;
	elseif (t <= 2.5e-52)
		tmp = a * (z * b);
	elseif (t <= 2.95e+106)
		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[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(t * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.1e+56], t$95$2, If[LessEqual[t, -8.2e-231], t$95$1, If[LessEqual[t, -1.8e-261], N[(N[(z * a), $MachinePrecision] * b), $MachinePrecision], If[LessEqual[t, 2.4e-111], t$95$1, If[LessEqual[t, 2.5e-52], N[(a * N[(z * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.95e+106], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.10000000000000017e56 or 2.95000000000000014e106 < t

   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. associate-+l+ 87.5%

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

      2. associate-*l* 85.7%

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

   3. Simplified 85.7%

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

   5. Taylor expanded in z around 0 66.3%

      \[\leadsto \color{blue}{x + a \cdot t} \]
   6. Step-by-step derivation

      1. +-commutative 66.3%

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

   7. Simplified 66.3%

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

   if -2.10000000000000017e56 < t < -8.2000000000000003e-231 or -1.79999999999999999e-261 < t < 2.4000000000000001e-111 or 2.5e-52 < t < 2.95000000000000014e106

   1. Initial program 95.0%

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

      1. associate-+l+ 95.0%

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

      2. associate-*l* 90.4%

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

   3. Simplified 90.4%

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

   5. Taylor expanded in a around 0 72.0%

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

   if -8.2000000000000003e-231 < t < -1.79999999999999999e-261

   1. Initial program 90.0%

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

      1. associate-+l+ 90.0%

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

      2. associate-*l* 89.7%

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

   3. Simplified 89.7%

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

   5. Taylor expanded in z around inf 80.7%

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

   6. Taylor expanded in y around 0 76.6%

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

      1. associate-*r* 67.2%

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

      2. *-commutative 67.2%

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

      3. associate-*l* 76.8%

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

   8. Simplified 76.8%

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

   if 2.4000000000000001e-111 < t < 2.5e-52

   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. associate-+l+ 99.8%

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

      2. associate-*l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 88.8%

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

   6. Taylor expanded in y around 0 89.1%

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

      1. *-commutative 89.1%

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

   8. Simplified 89.1%

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

4. Final simplification 70.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{+56}:\\ \;\;\;\;x + t \cdot a\\ \mathbf{elif}\;t \leq -8.2 \cdot 10^{-231}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{-261}:\\ \;\;\;\;\left(z \cdot a\right) \cdot b\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-111}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-52}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;t \leq 2.95 \cdot 10^{+106}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 39.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{+56}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;t \leq -3.7 \cdot 10^{-87}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;t \leq -1.12 \cdot 10^{-184}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.08 \cdot 10^{-156}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{+54}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{+105}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -4e+56)
   (* t a)
   (if (<= t -3.7e-87)
     (* y z)
     (if (<= t -1.12e-184)
       x
       (if (<= t 1.08e-156)
         (* y z)
         (if (<= t 9.5e+54) x (if (<= t 6.5e+105) (* y z) (* t a))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -4e+56) {
		tmp = t * a;
	} else if (t <= -3.7e-87) {
		tmp = y * z;
	} else if (t <= -1.12e-184) {
		tmp = x;
	} else if (t <= 1.08e-156) {
		tmp = y * z;
	} else if (t <= 9.5e+54) {
		tmp = x;
	} else if (t <= 6.5e+105) {
		tmp = y * z;
	} else {
		tmp = 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) :: tmp
    if (t <= (-4d+56)) then
        tmp = t * a
    else if (t <= (-3.7d-87)) then
        tmp = y * z
    else if (t <= (-1.12d-184)) then
        tmp = x
    else if (t <= 1.08d-156) then
        tmp = y * z
    else if (t <= 9.5d+54) then
        tmp = x
    else if (t <= 6.5d+105) then
        tmp = y * z
    else
        tmp = 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 tmp;
	if (t <= -4e+56) {
		tmp = t * a;
	} else if (t <= -3.7e-87) {
		tmp = y * z;
	} else if (t <= -1.12e-184) {
		tmp = x;
	} else if (t <= 1.08e-156) {
		tmp = y * z;
	} else if (t <= 9.5e+54) {
		tmp = x;
	} else if (t <= 6.5e+105) {
		tmp = y * z;
	} else {
		tmp = t * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -4e+56:
		tmp = t * a
	elif t <= -3.7e-87:
		tmp = y * z
	elif t <= -1.12e-184:
		tmp = x
	elif t <= 1.08e-156:
		tmp = y * z
	elif t <= 9.5e+54:
		tmp = x
	elif t <= 6.5e+105:
		tmp = y * z
	else:
		tmp = t * a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -4e+56)
		tmp = Float64(t * a);
	elseif (t <= -3.7e-87)
		tmp = Float64(y * z);
	elseif (t <= -1.12e-184)
		tmp = x;
	elseif (t <= 1.08e-156)
		tmp = Float64(y * z);
	elseif (t <= 9.5e+54)
		tmp = x;
	elseif (t <= 6.5e+105)
		tmp = Float64(y * z);
	else
		tmp = Float64(t * a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -4e+56)
		tmp = t * a;
	elseif (t <= -3.7e-87)
		tmp = y * z;
	elseif (t <= -1.12e-184)
		tmp = x;
	elseif (t <= 1.08e-156)
		tmp = y * z;
	elseif (t <= 9.5e+54)
		tmp = x;
	elseif (t <= 6.5e+105)
		tmp = y * z;
	else
		tmp = t * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -4e+56], N[(t * a), $MachinePrecision], If[LessEqual[t, -3.7e-87], N[(y * z), $MachinePrecision], If[LessEqual[t, -1.12e-184], x, If[LessEqual[t, 1.08e-156], N[(y * z), $MachinePrecision], If[LessEqual[t, 9.5e+54], x, If[LessEqual[t, 6.5e+105], N[(y * z), $MachinePrecision], N[(t * a), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.00000000000000037e56 or 6.50000000000000049e105 < t

   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. associate-+l+ 87.5%

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

      2. associate-*l* 85.7%

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

   3. Simplified 85.7%

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

   5. Taylor expanded in t around inf 58.8%

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

   if -4.00000000000000037e56 < t < -3.7000000000000002e-87 or -1.11999999999999997e-184 < t < 1.08e-156 or 9.4999999999999999e54 < t < 6.50000000000000049e105

   1. Initial program 92.5%

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

      1. associate-+l+ 92.5%

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

      2. associate-*l* 88.3%

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

   3. Simplified 88.3%

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

   5. Taylor expanded in y around inf 42.9%

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

      1. *-commutative 42.9%

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

   7. Simplified 42.9%

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

   if -3.7000000000000002e-87 < t < -1.11999999999999997e-184 or 1.08e-156 < t < 9.4999999999999999e54

   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. associate-+l+ 100.0%

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

      2. associate-*l* 96.2%

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

   3. Simplified 96.2%

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

   5. Taylor expanded in x around inf 46.8%

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

4. Final simplification 49.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{+56}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;t \leq -3.7 \cdot 10^{-87}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;t \leq -1.12 \cdot 10^{-184}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.08 \cdot 10^{-156}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{+54}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{+105}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 80.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(t \cdot a + y \cdot z\right)\\ t_2 := z \cdot \left(y + a \cdot b\right)\\ \mathbf{if}\;z \leq -500000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-71}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-48}:\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \mathbf{elif}\;z \leq 46000000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (+ (* t a) (* y z)))) (t_2 (* z (+ y (* a b)))))
   (if (<= z -500000000.0)
     t_2
     (if (<= z 3.3e-71)
       t_1
       (if (<= z 3e-48) (* a (+ t (* z b))) (if (<= z 46000000.0) 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) + (y * z));
	double t_2 = z * (y + (a * b));
	double tmp;
	if (z <= -500000000.0) {
		tmp = t_2;
	} else if (z <= 3.3e-71) {
		tmp = t_1;
	} else if (z <= 3e-48) {
		tmp = a * (t + (z * b));
	} else if (z <= 46000000.0) {
		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) + (y * z))
    t_2 = z * (y + (a * b))
    if (z <= (-500000000.0d0)) then
        tmp = t_2
    else if (z <= 3.3d-71) then
        tmp = t_1
    else if (z <= 3d-48) then
        tmp = a * (t + (z * b))
    else if (z <= 46000000.0d0) 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) + (y * z));
	double t_2 = z * (y + (a * b));
	double tmp;
	if (z <= -500000000.0) {
		tmp = t_2;
	} else if (z <= 3.3e-71) {
		tmp = t_1;
	} else if (z <= 3e-48) {
		tmp = a * (t + (z * b));
	} else if (z <= 46000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + ((t * a) + (y * z))
	t_2 = z * (y + (a * b))
	tmp = 0
	if z <= -500000000.0:
		tmp = t_2
	elif z <= 3.3e-71:
		tmp = t_1
	elif z <= 3e-48:
		tmp = a * (t + (z * b))
	elif z <= 46000000.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(Float64(t * a) + Float64(y * z)))
	t_2 = Float64(z * Float64(y + Float64(a * b)))
	tmp = 0.0
	if (z <= -500000000.0)
		tmp = t_2;
	elseif (z <= 3.3e-71)
		tmp = t_1;
	elseif (z <= 3e-48)
		tmp = Float64(a * Float64(t + Float64(z * b)));
	elseif (z <= 46000000.0)
		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) + (y * z));
	t_2 = z * (y + (a * b));
	tmp = 0.0;
	if (z <= -500000000.0)
		tmp = t_2;
	elseif (z <= 3.3e-71)
		tmp = t_1;
	elseif (z <= 3e-48)
		tmp = a * (t + (z * b));
	elseif (z <= 46000000.0)
		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[(N[(t * a), $MachinePrecision] + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -500000000.0], t$95$2, If[LessEqual[z, 3.3e-71], t$95$1, If[LessEqual[z, 3e-48], N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 46000000.0], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5e8 or 4.6e7 < z

   1. Initial program 85.5%

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

      1. associate-+l+ 85.5%

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

      2. associate-*l* 78.9%

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

   3. Simplified 78.9%

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

   5. Taylor expanded in z around inf 84.2%

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

   if -5e8 < z < 3.3000000000000002e-71 or 2.9999999999999999e-48 < z < 4.6e7

   1. Initial program 98.3%

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

      1. associate-+l+ 98.3%

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

      2. associate-*l* 98.3%

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

   3. Simplified 98.3%

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

   5. Taylor expanded in b around 0 89.8%

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

   if 3.3000000000000002e-71 < z < 2.9999999999999999e-48

   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. associate-+l+ 99.8%

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

      2. associate-*l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in a around inf 87.6%

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

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -500000000:\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-71}:\\ \;\;\;\;x + \left(t \cdot a + y \cdot z\right)\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-48}:\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \mathbf{elif}\;z \leq 46000000:\\ \;\;\;\;x + \left(t \cdot a + y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 73.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + t \cdot a\\ t_2 := z \cdot \left(y + a \cdot b\right)\\ \mathbf{if}\;z \leq -2.2 \cdot 10^{-60}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-68}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{-48}:\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \mathbf{elif}\;z \leq 2600000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* t a))) (t_2 (* z (+ y (* a b)))))
   (if (<= z -2.2e-60)
     t_2
     (if (<= z 2.3e-68)
       t_1
       (if (<= z 7.8e-48)
         (* a (+ t (* z b)))
         (if (<= z 2600000.0) 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 <= -2.2e-60) {
		tmp = t_2;
	} else if (z <= 2.3e-68) {
		tmp = t_1;
	} else if (z <= 7.8e-48) {
		tmp = a * (t + (z * b));
	} else if (z <= 2600000.0) {
		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 <= (-2.2d-60)) then
        tmp = t_2
    else if (z <= 2.3d-68) then
        tmp = t_1
    else if (z <= 7.8d-48) then
        tmp = a * (t + (z * b))
    else if (z <= 2600000.0d0) 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 <= -2.2e-60) {
		tmp = t_2;
	} else if (z <= 2.3e-68) {
		tmp = t_1;
	} else if (z <= 7.8e-48) {
		tmp = a * (t + (z * b));
	} else if (z <= 2600000.0) {
		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 <= -2.2e-60:
		tmp = t_2
	elif z <= 2.3e-68:
		tmp = t_1
	elif z <= 7.8e-48:
		tmp = a * (t + (z * b))
	elif z <= 2600000.0:
		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 <= -2.2e-60)
		tmp = t_2;
	elseif (z <= 2.3e-68)
		tmp = t_1;
	elseif (z <= 7.8e-48)
		tmp = Float64(a * Float64(t + Float64(z * b)));
	elseif (z <= 2600000.0)
		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 <= -2.2e-60)
		tmp = t_2;
	elseif (z <= 2.3e-68)
		tmp = t_1;
	elseif (z <= 7.8e-48)
		tmp = a * (t + (z * b));
	elseif (z <= 2600000.0)
		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, -2.2e-60], t$95$2, If[LessEqual[z, 2.3e-68], t$95$1, If[LessEqual[z, 7.8e-48], N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2600000.0], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.1999999999999999e-60 or 2.6e6 < z

   1. Initial program 86.8%

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

      1. associate-+l+ 86.8%

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

      2. associate-*l* 80.9%

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

   3. Simplified 80.9%

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

   5. Taylor expanded in z around inf 81.4%

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

   if -2.1999999999999999e-60 < z < 2.29999999999999997e-68 or 7.800000000000001e-48 < z < 2.6e6

   1. Initial program 98.2%

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

      1. associate-+l+ 98.2%

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

      2. associate-*l* 98.2%

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

   3. Simplified 98.2%

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

   5. Taylor expanded in z around 0 77.0%

      \[\leadsto \color{blue}{x + a \cdot t} \]
   6. Step-by-step derivation

      1. +-commutative 77.0%

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

   7. Simplified 77.0%

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

   if 2.29999999999999997e-68 < z < 7.800000000000001e-48

   1. Initial program 99.7%

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

      1. associate-+l+ 99.7%

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

      2. associate-*l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in a around inf 100.0%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{-60}:\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-68}:\\ \;\;\;\;x + t \cdot a\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{-48}:\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \mathbf{elif}\;z \leq 2600000:\\ \;\;\;\;x + t \cdot a\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 38.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(z \cdot b\right)\\ \mathbf{if}\;b \leq -4.1 \cdot 10^{+52}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{-125}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;b \leq 1.1 \cdot 10^{-39}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;b \leq 1.52 \cdot 10^{+128}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (* z b))))
   (if (<= b -4.1e+52)
     t_1
     (if (<= b 1.5e-125)
       (* y z)
       (if (<= b 1.1e-39) (* t a) (if (<= b 1.52e+128) (* y z) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (z * b);
	double tmp;
	if (b <= -4.1e+52) {
		tmp = t_1;
	} else if (b <= 1.5e-125) {
		tmp = y * z;
	} else if (b <= 1.1e-39) {
		tmp = t * a;
	} else if (b <= 1.52e+128) {
		tmp = y * z;
	} 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 = a * (z * b)
    if (b <= (-4.1d+52)) then
        tmp = t_1
    else if (b <= 1.5d-125) then
        tmp = y * z
    else if (b <= 1.1d-39) then
        tmp = t * a
    else if (b <= 1.52d+128) then
        tmp = y * z
    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 = a * (z * b);
	double tmp;
	if (b <= -4.1e+52) {
		tmp = t_1;
	} else if (b <= 1.5e-125) {
		tmp = y * z;
	} else if (b <= 1.1e-39) {
		tmp = t * a;
	} else if (b <= 1.52e+128) {
		tmp = y * z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (z * b)
	tmp = 0
	if b <= -4.1e+52:
		tmp = t_1
	elif b <= 1.5e-125:
		tmp = y * z
	elif b <= 1.1e-39:
		tmp = t * a
	elif b <= 1.52e+128:
		tmp = y * z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(z * b))
	tmp = 0.0
	if (b <= -4.1e+52)
		tmp = t_1;
	elseif (b <= 1.5e-125)
		tmp = Float64(y * z);
	elseif (b <= 1.1e-39)
		tmp = Float64(t * a);
	elseif (b <= 1.52e+128)
		tmp = Float64(y * z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (z * b);
	tmp = 0.0;
	if (b <= -4.1e+52)
		tmp = t_1;
	elseif (b <= 1.5e-125)
		tmp = y * z;
	elseif (b <= 1.1e-39)
		tmp = t * a;
	elseif (b <= 1.52e+128)
		tmp = y * z;
	else
		tmp = t_1;
	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[b, -4.1e+52], t$95$1, If[LessEqual[b, 1.5e-125], N[(y * z), $MachinePrecision], If[LessEqual[b, 1.1e-39], N[(t * a), $MachinePrecision], If[LessEqual[b, 1.52e+128], N[(y * z), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -4.1e52 or 1.51999999999999992e128 < b

   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. associate-+l+ 89.8%

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

      2. associate-*l* 79.6%

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

   3. Simplified 79.6%

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

   5. Taylor expanded in z around inf 64.5%

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

   6. Taylor expanded in y around 0 50.1%

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

      1. *-commutative 50.1%

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

   8. Simplified 50.1%

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

   if -4.1e52 < b < 1.49999999999999995e-125 or 1.1e-39 < b < 1.51999999999999992e128

   1. Initial program 94.8%

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

      1. associate-+l+ 94.8%

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

      2. associate-*l* 96.2%

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

   3. Simplified 96.2%

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

   5. Taylor expanded in y around inf 42.2%

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

      1. *-commutative 42.2%

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

   7. Simplified 42.2%

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

   if 1.49999999999999995e-125 < b < 1.1e-39

   1. Initial program 85.7%

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

      1. associate-+l+ 85.7%

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

      2. associate-*l* 92.7%

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

   3. Simplified 92.7%

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

   5. Taylor expanded in t around inf 59.0%

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

4. Final simplification 46.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.1 \cdot 10^{+52}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{-125}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;b \leq 1.1 \cdot 10^{-39}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;b \leq 1.52 \cdot 10^{+128}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 38.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z \cdot a\right) \cdot b\\ \mathbf{if}\;b \leq -8.5 \cdot 10^{+51}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 6 \cdot 10^{-129}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;b \leq 3.4 \cdot 10^{-37}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;b \leq 4 \cdot 10^{+131}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* z a) b)))
   (if (<= b -8.5e+51)
     t_1
     (if (<= b 6e-129)
       (* y z)
       (if (<= b 3.4e-37) (* t a) (if (<= b 4e+131) (* y z) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z * a) * b;
	double tmp;
	if (b <= -8.5e+51) {
		tmp = t_1;
	} else if (b <= 6e-129) {
		tmp = y * z;
	} else if (b <= 3.4e-37) {
		tmp = t * a;
	} else if (b <= 4e+131) {
		tmp = y * z;
	} 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 * a) * b
    if (b <= (-8.5d+51)) then
        tmp = t_1
    else if (b <= 6d-129) then
        tmp = y * z
    else if (b <= 3.4d-37) then
        tmp = t * a
    else if (b <= 4d+131) then
        tmp = y * z
    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 * a) * b;
	double tmp;
	if (b <= -8.5e+51) {
		tmp = t_1;
	} else if (b <= 6e-129) {
		tmp = y * z;
	} else if (b <= 3.4e-37) {
		tmp = t * a;
	} else if (b <= 4e+131) {
		tmp = y * z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z * a) * b
	tmp = 0
	if b <= -8.5e+51:
		tmp = t_1
	elif b <= 6e-129:
		tmp = y * z
	elif b <= 3.4e-37:
		tmp = t * a
	elif b <= 4e+131:
		tmp = y * z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z * a) * b)
	tmp = 0.0
	if (b <= -8.5e+51)
		tmp = t_1;
	elseif (b <= 6e-129)
		tmp = Float64(y * z);
	elseif (b <= 3.4e-37)
		tmp = Float64(t * a);
	elseif (b <= 4e+131)
		tmp = Float64(y * z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z * a) * b;
	tmp = 0.0;
	if (b <= -8.5e+51)
		tmp = t_1;
	elseif (b <= 6e-129)
		tmp = y * z;
	elseif (b <= 3.4e-37)
		tmp = t * a;
	elseif (b <= 4e+131)
		tmp = y * z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z * a), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -8.5e+51], t$95$1, If[LessEqual[b, 6e-129], N[(y * z), $MachinePrecision], If[LessEqual[b, 3.4e-37], N[(t * a), $MachinePrecision], If[LessEqual[b, 4e+131], N[(y * z), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -8.4999999999999999e51 or 3.9999999999999996e131 < b

   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. associate-+l+ 89.8%

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

      2. associate-*l* 79.6%

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

   3. Simplified 79.6%

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

   5. Taylor expanded in z around inf 64.5%

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

   6. Taylor expanded in y around 0 50.1%

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

      1. associate-*r* 52.6%

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

      2. *-commutative 52.6%

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

      3. associate-*l* 55.9%

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

   8. Simplified 55.9%

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

   if -8.4999999999999999e51 < b < 5.9999999999999996e-129 or 3.40000000000000018e-37 < b < 3.9999999999999996e131

   1. Initial program 94.8%

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

      1. associate-+l+ 94.8%

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

      2. associate-*l* 96.2%

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

   3. Simplified 96.2%

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

   5. Taylor expanded in y around inf 42.2%

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

      1. *-commutative 42.2%

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

   7. Simplified 42.2%

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

   if 5.9999999999999996e-129 < b < 3.40000000000000018e-37

   1. Initial program 85.7%

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

      1. associate-+l+ 85.7%

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

      2. associate-*l* 92.7%

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

   3. Simplified 92.7%

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

   5. Taylor expanded in t around inf 59.0%

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

4. Final simplification 49.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8.5 \cdot 10^{+51}:\\ \;\;\;\;\left(z \cdot a\right) \cdot b\\ \mathbf{elif}\;b \leq 6 \cdot 10^{-129}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;b \leq 3.4 \cdot 10^{-37}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;b \leq 4 \cdot 10^{+131}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot a\right) \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 82.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot a + y \cdot z\\ \mathbf{if}\;x \leq -3 \cdot 10^{-53} \lor \neg \left(x \leq 9.2 \cdot 10^{+36}\right):\\ \;\;\;\;x + t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot a\right) \cdot b + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (* t a) (* y z))))
   (if (or (<= x -3e-53) (not (<= x 9.2e+36)))
     (+ x t_1)
     (+ (* (* z a) b) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t * a) + (y * z);
	double tmp;
	if ((x <= -3e-53) || !(x <= 9.2e+36)) {
		tmp = x + t_1;
	} else {
		tmp = ((z * a) * b) + 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 = (t * a) + (y * z)
    if ((x <= (-3d-53)) .or. (.not. (x <= 9.2d+36))) then
        tmp = x + t_1
    else
        tmp = ((z * a) * b) + 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 = (t * a) + (y * z);
	double tmp;
	if ((x <= -3e-53) || !(x <= 9.2e+36)) {
		tmp = x + t_1;
	} else {
		tmp = ((z * a) * b) + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t * a) + (y * z)
	tmp = 0
	if (x <= -3e-53) or not (x <= 9.2e+36):
		tmp = x + t_1
	else:
		tmp = ((z * a) * b) + t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t * a) + Float64(y * z))
	tmp = 0.0
	if ((x <= -3e-53) || !(x <= 9.2e+36))
		tmp = Float64(x + t_1);
	else
		tmp = Float64(Float64(Float64(z * a) * b) + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t * a) + (y * z);
	tmp = 0.0;
	if ((x <= -3e-53) || ~((x <= 9.2e+36)))
		tmp = x + t_1;
	else
		tmp = ((z * a) * b) + t_1;
	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]}, If[Or[LessEqual[x, -3e-53], N[Not[LessEqual[x, 9.2e+36]], $MachinePrecision]], N[(x + t$95$1), $MachinePrecision], N[(N[(N[(z * a), $MachinePrecision] * b), $MachinePrecision] + t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -3.0000000000000002e-53 or 9.19999999999999986e36 < x

   1. Initial program 90.1%

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

      1. associate-+l+ 90.1%

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

      2. associate-*l* 90.2%

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

   3. Simplified 90.2%

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

   5. Taylor expanded in b around 0 79.5%

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

   if -3.0000000000000002e-53 < x < 9.19999999999999986e36

   1. Initial program 94.0%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 89.7%

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

4. Final simplification 84.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{-53} \lor \neg \left(x \leq 9.2 \cdot 10^{+36}\right):\\ \;\;\;\;x + \left(t \cdot a + y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot a\right) \cdot b + \left(t \cdot a + y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 92.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 4 \cdot 10^{+157}:\\ \;\;\;\;\left(x + y \cdot z\right) + \left(a \cdot \left(z \cdot b\right) + t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a 4e+157)
   (+ (+ x (* y z)) (+ (* a (* z b)) (* t a)))
   (* a (+ t (* z b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= 4e+157) {
		tmp = (x + (y * z)) + ((a * (z * b)) + (t * a));
	} else {
		tmp = a * (t + (z * 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) :: tmp
    if (a <= 4d+157) then
        tmp = (x + (y * z)) + ((a * (z * b)) + (t * a))
    else
        tmp = a * (t + (z * 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 tmp;
	if (a <= 4e+157) {
		tmp = (x + (y * z)) + ((a * (z * b)) + (t * a));
	} else {
		tmp = a * (t + (z * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= 4e+157:
		tmp = (x + (y * z)) + ((a * (z * b)) + (t * a))
	else:
		tmp = a * (t + (z * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= 4e+157)
		tmp = Float64(Float64(x + Float64(y * z)) + Float64(Float64(a * Float64(z * b)) + Float64(t * a)));
	else
		tmp = Float64(a * Float64(t + Float64(z * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= 4e+157)
		tmp = (x + (y * z)) + ((a * (z * b)) + (t * a));
	else
		tmp = a * (t + (z * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, 4e+157], N[(N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(N[(a * N[(z * b), $MachinePrecision]), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 3.99999999999999993e157

   1. Initial program 93.4%

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

      1. associate-+l+ 93.4%

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

      2. associate-*l* 89.8%

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

   3. Simplified 89.8%

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

   if 3.99999999999999993e157 < a

   1. Initial program 82.1%

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

      1. associate-+l+ 82.1%

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

      2. associate-*l* 82.1%

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

   3. Simplified 82.1%

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

   5. Taylor expanded in a around inf 96.4%

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

4. Final simplification 90.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 4 \cdot 10^{+157}:\\ \;\;\;\;\left(x + y \cdot z\right) + \left(a \cdot \left(z \cdot b\right) + t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 75.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.1 \cdot 10^{-48} \lor \neg \left(a \leq 85000000000\right):\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -4.1e-48) (not (<= a 85000000000.0)))
   (* a (+ t (* z b)))
   (+ x (* y z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -4.1e-48) || !(a <= 85000000000.0)) {
		tmp = a * (t + (z * b));
	} else {
		tmp = x + (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 <= (-4.1d-48)) .or. (.not. (a <= 85000000000.0d0))) then
        tmp = a * (t + (z * b))
    else
        tmp = x + (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 <= -4.1e-48) || !(a <= 85000000000.0)) {
		tmp = a * (t + (z * b));
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -4.1e-48) or not (a <= 85000000000.0):
		tmp = a * (t + (z * b))
	else:
		tmp = x + (y * z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -4.1e-48) || !(a <= 85000000000.0))
		tmp = Float64(a * Float64(t + Float64(z * b)));
	else
		tmp = Float64(x + Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -4.1e-48) || ~((a <= 85000000000.0)))
		tmp = a * (t + (z * b));
	else
		tmp = x + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -4.1e-48], N[Not[LessEqual[a, 85000000000.0]], $MachinePrecision]], N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -4.10000000000000014e-48 or 8.5e10 < a

   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. associate-+l+ 86.4%

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

      2. associate-*l* 87.9%

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

   3. Simplified 87.9%

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

   5. Taylor expanded in a around inf 74.1%

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

   if -4.10000000000000014e-48 < a < 8.5e10

   1. Initial program 98.3%

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

      1. associate-+l+ 98.3%

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

      2. associate-*l* 90.1%

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

   3. Simplified 90.1%

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

   5. Taylor expanded in a around 0 72.1%

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

4. Final simplification 73.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.1 \cdot 10^{-48} \lor \neg \left(a \leq 85000000000\right):\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 39.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.6 \cdot 10^{+50} \lor \neg \left(t \leq 8 \cdot 10^{+63}\right):\\ \;\;\;\;t \cdot a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -4.6e+50) (not (<= t 8e+63))) (* t a) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -4.6e+50) || !(t <= 8e+63)) {
		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 ((t <= (-4.6d+50)) .or. (.not. (t <= 8d+63))) 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 ((t <= -4.6e+50) || !(t <= 8e+63)) {
		tmp = t * a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -4.6e+50) or not (t <= 8e+63):
		tmp = t * a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -4.6e+50) || !(t <= 8e+63))
		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 ((t <= -4.6e+50) || ~((t <= 8e+63)))
		tmp = t * a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -4.6e+50], N[Not[LessEqual[t, 8e+63]], $MachinePrecision]], N[(t * a), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if t < -4.59999999999999994e50 or 8.00000000000000046e63 < t

   1. Initial program 88.2%

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

      1. associate-+l+ 88.2%

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

      2. associate-*l* 86.5%

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

   3. Simplified 86.5%

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

   5. Taylor expanded in t around inf 56.9%

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

   if -4.59999999999999994e50 < t < 8.00000000000000046e63

   1. Initial program 94.8%

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

      1. associate-+l+ 94.8%

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

      2. associate-*l* 90.6%

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

   3. Simplified 90.6%

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

   5. Taylor expanded in x around inf 33.9%

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

4. Final simplification 43.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.6 \cdot 10^{+50} \lor \neg \left(t \leq 8 \cdot 10^{+63}\right):\\ \;\;\;\;t \cdot a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 26.0% 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 92.1%

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

   1. associate-+l+ 92.1%

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

   2. associate-*l* 88.9%

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

3. Simplified 88.9%

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

5. Taylor expanded in x around inf 23.9%

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

6. Final simplification 23.9%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 97.3% accurate, 0.7× 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 2024034 
(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)))