Graphics.Rasterific.CubicBezier:cachedBezierAt from Rasterific-0.6.1

Percentage Accurate: 92.6% → 97.0%

Time: 13.8s

Alternatives: 10

Speedup: 0.8×

• 32.0% 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: 92.6% 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: 97.0% accurate, 0.5× 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 99.2%

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

   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. *-commutative 0.0%

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

      3. associate-*l* 25.0%

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

   3. Simplified 25.0%

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

   4. Taylor expanded in a around inf 80.0%

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

4. Final simplification 97.7%

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

Alternative 2: 79.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot z\\ t_2 := x + \left(t \cdot a + a \cdot \left(z \cdot b\right)\right)\\ \mathbf{if}\;a \leq -7.6 \cdot 10^{-5}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{-129}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.08 \cdot 10^{-162}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -2.3 \cdot 10^{-177}:\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{elif}\;a \leq 3.7 \cdot 10^{-87}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* y z))) (t_2 (+ x (+ (* t a) (* a (* z b))))))
   (if (<= a -7.6e-5)
     t_2
     (if (<= a -4.2e-129)
       t_1
       (if (<= a -1.08e-162)
         t_2
         (if (<= a -2.3e-177)
           (* z (+ y (* a b)))
           (if (<= a 3.7e-87) 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) + (a * (z * b)));
	double tmp;
	if (a <= -7.6e-5) {
		tmp = t_2;
	} else if (a <= -4.2e-129) {
		tmp = t_1;
	} else if (a <= -1.08e-162) {
		tmp = t_2;
	} else if (a <= -2.3e-177) {
		tmp = z * (y + (a * b));
	} else if (a <= 3.7e-87) {
		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) + (a * (z * b)))
    if (a <= (-7.6d-5)) then
        tmp = t_2
    else if (a <= (-4.2d-129)) then
        tmp = t_1
    else if (a <= (-1.08d-162)) then
        tmp = t_2
    else if (a <= (-2.3d-177)) then
        tmp = z * (y + (a * b))
    else if (a <= 3.7d-87) 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) + (a * (z * b)));
	double tmp;
	if (a <= -7.6e-5) {
		tmp = t_2;
	} else if (a <= -4.2e-129) {
		tmp = t_1;
	} else if (a <= -1.08e-162) {
		tmp = t_2;
	} else if (a <= -2.3e-177) {
		tmp = z * (y + (a * b));
	} else if (a <= 3.7e-87) {
		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) + (a * (z * b)))
	tmp = 0
	if a <= -7.6e-5:
		tmp = t_2
	elif a <= -4.2e-129:
		tmp = t_1
	elif a <= -1.08e-162:
		tmp = t_2
	elif a <= -2.3e-177:
		tmp = z * (y + (a * b))
	elif a <= 3.7e-87:
		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(Float64(t * a) + Float64(a * Float64(z * b))))
	tmp = 0.0
	if (a <= -7.6e-5)
		tmp = t_2;
	elseif (a <= -4.2e-129)
		tmp = t_1;
	elseif (a <= -1.08e-162)
		tmp = t_2;
	elseif (a <= -2.3e-177)
		tmp = Float64(z * Float64(y + Float64(a * b)));
	elseif (a <= 3.7e-87)
		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) + (a * (z * b)));
	tmp = 0.0;
	if (a <= -7.6e-5)
		tmp = t_2;
	elseif (a <= -4.2e-129)
		tmp = t_1;
	elseif (a <= -1.08e-162)
		tmp = t_2;
	elseif (a <= -2.3e-177)
		tmp = z * (y + (a * b));
	elseif (a <= 3.7e-87)
		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[(N[(t * a), $MachinePrecision] + N[(a * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -7.6e-5], t$95$2, If[LessEqual[a, -4.2e-129], t$95$1, If[LessEqual[a, -1.08e-162], t$95$2, If[LessEqual[a, -2.3e-177], N[(z * N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.7e-87], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -7.6000000000000004e-5 or -4.2e-129 < a < -1.08000000000000006e-162 or 3.7000000000000002e-87 < a

   1. Initial program 87.1%

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

      1. associate-+l+ 87.1%

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

      2. *-commutative 87.1%

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

      3. associate-*l* 84.1%

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

   3. Simplified 84.1%

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

   4. Taylor expanded in y around 0 88.3%

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

   if -7.6000000000000004e-5 < a < -4.2e-129 or -2.30000000000000022e-177 < a < 3.7000000000000002e-87

   1. Initial program 97.9%

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

      1. associate-+l+ 97.9%

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

      2. *-commutative 97.9%

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

      3. associate-*l* 97.9%

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

   3. Simplified 97.9%

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

   4. Taylor expanded in a around 0 89.2%

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

   if -1.08000000000000006e-162 < a < -2.30000000000000022e-177

   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. *-commutative 100.0%

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

      3. associate-*l* 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in z around inf 99.5%

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

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.6 \cdot 10^{-5}:\\ \;\;\;\;x + \left(t \cdot a + a \cdot \left(z \cdot b\right)\right)\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{-129}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{elif}\;a \leq -1.08 \cdot 10^{-162}:\\ \;\;\;\;x + \left(t \cdot a + a \cdot \left(z \cdot b\right)\right)\\ \mathbf{elif}\;a \leq -2.3 \cdot 10^{-177}:\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{elif}\;a \leq 3.7 \cdot 10^{-87}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \left(t \cdot a + a \cdot \left(z \cdot b\right)\right)\\ \end{array} \]

Alternative 3: 79.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot z\\ t_2 := x + \left(t \cdot a + a \cdot \left(z \cdot b\right)\right)\\ \mathbf{if}\;a \leq -8.6 \cdot 10^{-8}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.25 \cdot 10^{-134}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.45 \cdot 10^{-179}:\\ \;\;\;\;\left(z \cdot a\right) \cdot b + \left(y \cdot z + t \cdot a\right)\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-94}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* y z))) (t_2 (+ x (+ (* t a) (* a (* z b))))))
   (if (<= a -8.6e-8)
     t_2
     (if (<= a -1.25e-134)
       t_1
       (if (<= a -1.45e-179)
         (+ (* (* z a) b) (+ (* y z) (* t a)))
         (if (<= a 5e-94) 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) + (a * (z * b)));
	double tmp;
	if (a <= -8.6e-8) {
		tmp = t_2;
	} else if (a <= -1.25e-134) {
		tmp = t_1;
	} else if (a <= -1.45e-179) {
		tmp = ((z * a) * b) + ((y * z) + (t * a));
	} else if (a <= 5e-94) {
		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) + (a * (z * b)))
    if (a <= (-8.6d-8)) then
        tmp = t_2
    else if (a <= (-1.25d-134)) then
        tmp = t_1
    else if (a <= (-1.45d-179)) then
        tmp = ((z * a) * b) + ((y * z) + (t * a))
    else if (a <= 5d-94) 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) + (a * (z * b)));
	double tmp;
	if (a <= -8.6e-8) {
		tmp = t_2;
	} else if (a <= -1.25e-134) {
		tmp = t_1;
	} else if (a <= -1.45e-179) {
		tmp = ((z * a) * b) + ((y * z) + (t * a));
	} else if (a <= 5e-94) {
		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) + (a * (z * b)))
	tmp = 0
	if a <= -8.6e-8:
		tmp = t_2
	elif a <= -1.25e-134:
		tmp = t_1
	elif a <= -1.45e-179:
		tmp = ((z * a) * b) + ((y * z) + (t * a))
	elif a <= 5e-94:
		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(Float64(t * a) + Float64(a * Float64(z * b))))
	tmp = 0.0
	if (a <= -8.6e-8)
		tmp = t_2;
	elseif (a <= -1.25e-134)
		tmp = t_1;
	elseif (a <= -1.45e-179)
		tmp = Float64(Float64(Float64(z * a) * b) + Float64(Float64(y * z) + Float64(t * a)));
	elseif (a <= 5e-94)
		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) + (a * (z * b)));
	tmp = 0.0;
	if (a <= -8.6e-8)
		tmp = t_2;
	elseif (a <= -1.25e-134)
		tmp = t_1;
	elseif (a <= -1.45e-179)
		tmp = ((z * a) * b) + ((y * z) + (t * a));
	elseif (a <= 5e-94)
		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[(N[(t * a), $MachinePrecision] + N[(a * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -8.6e-8], t$95$2, If[LessEqual[a, -1.25e-134], t$95$1, If[LessEqual[a, -1.45e-179], N[(N[(N[(z * a), $MachinePrecision] * b), $MachinePrecision] + N[(N[(y * z), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5e-94], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -8.6000000000000002e-8 or 4.9999999999999995e-94 < a

   1. Initial program 86.5%

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

      1. associate-+l+ 86.5%

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

      2. *-commutative 86.5%

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

      3. associate-*l* 83.3%

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

   3. Simplified 83.3%

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

   4. Taylor expanded in y around 0 88.4%

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

   if -8.6000000000000002e-8 < a < -1.2500000000000001e-134 or -1.4499999999999999e-179 < a < 4.9999999999999995e-94

   1. Initial program 98.0%

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

      1. associate-+l+ 98.0%

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

      2. *-commutative 98.0%

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

      3. associate-*l* 98.0%

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

   3. Simplified 98.0%

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

   4. Taylor expanded in a around 0 89.3%

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

   if -1.2500000000000001e-134 < a < -1.4499999999999999e-179

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 85.1%

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

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.6 \cdot 10^{-8}:\\ \;\;\;\;x + \left(t \cdot a + a \cdot \left(z \cdot b\right)\right)\\ \mathbf{elif}\;a \leq -1.25 \cdot 10^{-134}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{elif}\;a \leq -1.45 \cdot 10^{-179}:\\ \;\;\;\;\left(z \cdot a\right) \cdot b + \left(y \cdot z + t \cdot a\right)\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-94}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \left(t \cdot a + a \cdot \left(z \cdot b\right)\right)\\ \end{array} \]

Alternative 4: 93.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -8 \cdot 10^{+244}:\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \mathbf{elif}\;a \leq 1.16 \cdot 10^{+70}:\\ \;\;\;\;\left(x + y \cdot z\right) + \left(z \cdot \left(a \cdot b\right) + t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(t \cdot a + a \cdot \left(z \cdot b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -8e+244)
   (* a (+ t (* z b)))
   (if (<= a 1.16e+70)
     (+ (+ x (* y z)) (+ (* z (* a b)) (* t a)))
     (+ x (+ (* t a) (* a (* z b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -8e+244) {
		tmp = a * (t + (z * b));
	} else if (a <= 1.16e+70) {
		tmp = (x + (y * z)) + ((z * (a * b)) + (t * a));
	} else {
		tmp = x + ((t * a) + (a * (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 <= (-8d+244)) then
        tmp = a * (t + (z * b))
    else if (a <= 1.16d+70) then
        tmp = (x + (y * z)) + ((z * (a * b)) + (t * a))
    else
        tmp = x + ((t * a) + (a * (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 <= -8e+244) {
		tmp = a * (t + (z * b));
	} else if (a <= 1.16e+70) {
		tmp = (x + (y * z)) + ((z * (a * b)) + (t * a));
	} else {
		tmp = x + ((t * a) + (a * (z * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -8e+244:
		tmp = a * (t + (z * b))
	elif a <= 1.16e+70:
		tmp = (x + (y * z)) + ((z * (a * b)) + (t * a))
	else:
		tmp = x + ((t * a) + (a * (z * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -8e+244)
		tmp = Float64(a * Float64(t + Float64(z * b)));
	elseif (a <= 1.16e+70)
		tmp = Float64(Float64(x + Float64(y * z)) + Float64(Float64(z * Float64(a * b)) + Float64(t * a)));
	else
		tmp = Float64(x + Float64(Float64(t * a) + Float64(a * Float64(z * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -8e+244)
		tmp = a * (t + (z * b));
	elseif (a <= 1.16e+70)
		tmp = (x + (y * z)) + ((z * (a * b)) + (t * a));
	else
		tmp = x + ((t * a) + (a * (z * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -8e+244], N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.16e+70], N[(N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(N[(z * N[(a * b), $MachinePrecision]), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t * a), $MachinePrecision] + N[(a * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -8.0000000000000006e244

   1. Initial program 68.7%

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

      1. associate-+l+ 68.7%

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

      2. *-commutative 68.7%

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

      3. associate-*l* 68.3%

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

   3. Simplified 68.3%

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

   4. Taylor expanded in a around inf 100.0%

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

   if -8.0000000000000006e244 < a < 1.1599999999999999e70

   1. Initial program 96.3%

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

      1. associate-+l+ 96.3%

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

      2. *-commutative 96.3%

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

      3. associate-*l* 94.2%

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

   3. Simplified 94.2%

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

   if 1.1599999999999999e70 < a

   1. Initial program 82.0%

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

      1. associate-+l+ 82.0%

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

      2. *-commutative 82.0%

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

      3. associate-*l* 80.2%

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

   3. Simplified 80.2%

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

   4. Taylor expanded in y around 0 92.0%

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

4. Final simplification 94.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8 \cdot 10^{+244}:\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \mathbf{elif}\;a \leq 1.16 \cdot 10^{+70}:\\ \;\;\;\;\left(x + y \cdot z\right) + \left(z \cdot \left(a \cdot b\right) + t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(t \cdot a + a \cdot \left(z \cdot b\right)\right)\\ \end{array} \]

Alternative 5: 39.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.6 \cdot 10^{+16}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{-273}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{-221}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{-87}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;a \leq 2.16 \cdot 10^{+15}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -1.6e+16)
   (* t a)
   (if (<= a 3.4e-273)
     (* y z)
     (if (<= a 3.4e-221)
       x
       (if (<= a 1.4e-87) (* y z) (if (<= a 2.16e+15) x (* t a)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -1.6e+16) {
		tmp = t * a;
	} else if (a <= 3.4e-273) {
		tmp = y * z;
	} else if (a <= 3.4e-221) {
		tmp = x;
	} else if (a <= 1.4e-87) {
		tmp = y * z;
	} else if (a <= 2.16e+15) {
		tmp = x;
	} 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 (a <= (-1.6d+16)) then
        tmp = t * a
    else if (a <= 3.4d-273) then
        tmp = y * z
    else if (a <= 3.4d-221) then
        tmp = x
    else if (a <= 1.4d-87) then
        tmp = y * z
    else if (a <= 2.16d+15) then
        tmp = x
    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 (a <= -1.6e+16) {
		tmp = t * a;
	} else if (a <= 3.4e-273) {
		tmp = y * z;
	} else if (a <= 3.4e-221) {
		tmp = x;
	} else if (a <= 1.4e-87) {
		tmp = y * z;
	} else if (a <= 2.16e+15) {
		tmp = x;
	} else {
		tmp = t * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -1.6e+16:
		tmp = t * a
	elif a <= 3.4e-273:
		tmp = y * z
	elif a <= 3.4e-221:
		tmp = x
	elif a <= 1.4e-87:
		tmp = y * z
	elif a <= 2.16e+15:
		tmp = x
	else:
		tmp = t * a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -1.6e+16)
		tmp = Float64(t * a);
	elseif (a <= 3.4e-273)
		tmp = Float64(y * z);
	elseif (a <= 3.4e-221)
		tmp = x;
	elseif (a <= 1.4e-87)
		tmp = Float64(y * z);
	elseif (a <= 2.16e+15)
		tmp = x;
	else
		tmp = Float64(t * a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -1.6e+16)
		tmp = t * a;
	elseif (a <= 3.4e-273)
		tmp = y * z;
	elseif (a <= 3.4e-221)
		tmp = x;
	elseif (a <= 1.4e-87)
		tmp = y * z;
	elseif (a <= 2.16e+15)
		tmp = x;
	else
		tmp = t * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -1.6e+16], N[(t * a), $MachinePrecision], If[LessEqual[a, 3.4e-273], N[(y * z), $MachinePrecision], If[LessEqual[a, 3.4e-221], x, If[LessEqual[a, 1.4e-87], N[(y * z), $MachinePrecision], If[LessEqual[a, 2.16e+15], x, N[(t * a), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.6e16 or 2.16e15 < a

   1. Initial program 84.1%

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

      1. associate-+l+ 84.1%

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

      2. *-commutative 84.1%

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

      3. associate-*l* 80.3%

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

   3. Simplified 80.3%

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

   4. Taylor expanded in t around inf 47.2%

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

   if -1.6e16 < a < 3.39999999999999991e-273 or 3.4000000000000001e-221 < a < 1.4e-87

   1. Initial program 98.0%

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

      1. associate-+l+ 98.0%

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

      2. *-commutative 98.0%

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

      3. associate-*l* 98.0%

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

   3. Simplified 98.0%

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

   4. Taylor expanded in y around inf 55.4%

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

      1. *-commutative 55.4%

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

   6. Simplified 55.4%

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

   if 3.39999999999999991e-273 < a < 3.4000000000000001e-221 or 1.4e-87 < a < 2.16e15

   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. associate-+l+ 99.9%

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

      2. *-commutative 99.9%

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

      3. associate-*l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 58.1%

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

4. Final simplification 51.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.6 \cdot 10^{+16}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{-273}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{-221}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{-87}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;a \leq 2.16 \cdot 10^{+15}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot a\\ \end{array} \]

Alternative 6: 59.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+145}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+148}:\\ \;\;\;\;x + t \cdot a\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{+238}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot a\right) \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -3.6e+145)
   (* a (* z b))
   (if (<= z 1.05e+148)
     (+ x (* t a))
     (if (<= z 2.05e+238) (* y z) (* (* z a) b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -3.6e+145) {
		tmp = a * (z * b);
	} else if (z <= 1.05e+148) {
		tmp = x + (t * a);
	} else if (z <= 2.05e+238) {
		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) :: tmp
    if (z <= (-3.6d+145)) then
        tmp = a * (z * b)
    else if (z <= 1.05d+148) then
        tmp = x + (t * a)
    else if (z <= 2.05d+238) 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 tmp;
	if (z <= -3.6e+145) {
		tmp = a * (z * b);
	} else if (z <= 1.05e+148) {
		tmp = x + (t * a);
	} else if (z <= 2.05e+238) {
		tmp = y * z;
	} else {
		tmp = (z * a) * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -3.6e+145:
		tmp = a * (z * b)
	elif z <= 1.05e+148:
		tmp = x + (t * a)
	elif z <= 2.05e+238:
		tmp = y * z
	else:
		tmp = (z * a) * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -3.6e+145)
		tmp = Float64(a * Float64(z * b));
	elseif (z <= 1.05e+148)
		tmp = Float64(x + Float64(t * a));
	elseif (z <= 2.05e+238)
		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)
	tmp = 0.0;
	if (z <= -3.6e+145)
		tmp = a * (z * b);
	elseif (z <= 1.05e+148)
		tmp = x + (t * a);
	elseif (z <= 2.05e+238)
		tmp = y * z;
	else
		tmp = (z * a) * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -3.6e+145], N[(a * N[(z * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.05e+148], N[(x + N[(t * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.05e+238], N[(y * z), $MachinePrecision], N[(N[(z * a), $MachinePrecision] * b), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.59999999999999974e145

   1. Initial program 77.5%

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

      1. +-commutative 77.5%

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

      2. *-commutative 77.5%

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

      3. associate-*l* 83.9%

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

      4. *-commutative 83.9%

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

      5. fma-def 90.8%

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

      6. *-commutative 90.8%

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

      7. +-commutative 90.8%

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

      8. fma-def 90.8%

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

      9. +-commutative 90.8%

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

      10. fma-def 90.8%

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

   3. Simplified 90.8%

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

      1. fma-udef 90.8%

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

      2. fma-udef 90.8%

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

      3. +-commutative 90.8%

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

      4. +-commutative 90.8%

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

      5. +-commutative 90.8%

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

      6. *-commutative 90.8%

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

      7. fma-def 90.8%

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

      8. *-commutative 90.8%

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

   5. Applied egg-rr 90.8%

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

   6. Taylor expanded in b around inf 48.2%

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

      1. *-commutative 48.2%

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

   8. Simplified 48.2%

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

   if -3.59999999999999974e145 < z < 1.04999999999999999e148

   1. Initial program 98.8%

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

      1. associate-+l+ 98.8%

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

      2. *-commutative 98.8%

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

      3. associate-*l* 92.3%

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

   3. Simplified 92.3%

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

   4. Taylor expanded in z around 0 65.5%

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

   if 1.04999999999999999e148 < z < 2.0499999999999999e238

   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. associate-+l+ 82.3%

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

      2. *-commutative 82.3%

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

      3. associate-*l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 59.9%

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

      1. *-commutative 59.9%

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

   6. Simplified 59.9%

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

   if 2.0499999999999999e238 < z

   1. Initial program 63.2%

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

      1. +-commutative 63.2%

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

      2. *-commutative 63.2%

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

      3. associate-*l* 68.4%

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

      4. *-commutative 68.4%

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

      5. fma-def 78.9%

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

      6. *-commutative 78.9%

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

      7. +-commutative 78.9%

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

      8. fma-def 78.9%

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

      9. +-commutative 78.9%

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

      10. fma-def 78.9%

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

   3. Simplified 78.9%

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

      1. fma-udef 78.9%

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

      2. fma-udef 78.9%

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

      3. +-commutative 78.9%

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

      4. +-commutative 78.9%

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

      5. +-commutative 78.9%

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

      6. *-commutative 78.9%

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

      7. fma-def 78.9%

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

      8. *-commutative 78.9%

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

   5. Applied egg-rr 78.9%

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

   6. Taylor expanded in x around 0 78.9%

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

   7. Taylor expanded in b around inf 61.4%

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

      1. *-commutative 61.4%

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

      2. associate-*r* 66.4%

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

   9. Simplified 66.4%

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

4. Final simplification 62.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+145}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+148}:\\ \;\;\;\;x + t \cdot a\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{+238}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot a\right) \cdot b\\ \end{array} \]

Alternative 7: 74.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.15 \cdot 10^{+31} \lor \neg \left(a \leq 70000\right):\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -1.15e+31) (not (<= a 70000.0)))
   (* 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 <= -1.15e+31) || !(a <= 70000.0)) {
		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 <= (-1.15d+31)) .or. (.not. (a <= 70000.0d0))) 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 <= -1.15e+31) || !(a <= 70000.0)) {
		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 <= -1.15e+31) or not (a <= 70000.0):
		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 <= -1.15e+31) || !(a <= 70000.0))
		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 <= -1.15e+31) || ~((a <= 70000.0)))
		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, -1.15e+31], N[Not[LessEqual[a, 70000.0]], $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 < -1.15e31 or 7e4 < 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%

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

      3. associate-*l* 81.1%

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

   3. Simplified 81.1%

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

   4. Taylor expanded in a around inf 81.9%

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

   if -1.15e31 < a < 7e4

   1. Initial program 97.8%

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

      1. associate-+l+ 97.8%

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

      2. *-commutative 97.8%

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

      3. associate-*l* 97.0%

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

   3. Simplified 97.0%

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

   4. Taylor expanded in a around 0 80.2%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.15 \cdot 10^{+31} \lor \neg \left(a \leq 70000\right):\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]

Alternative 8: 63.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.2 \cdot 10^{+16} \lor \neg \left(a \leq 1.3 \cdot 10^{-93}\right):\\ \;\;\;\;x + t \cdot a\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -5.2e+16) (not (<= a 1.3e-93))) (+ x (* t a)) (+ x (* y z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -5.2e+16) || !(a <= 1.3e-93)) {
		tmp = x + (t * a);
	} 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 <= (-5.2d+16)) .or. (.not. (a <= 1.3d-93))) then
        tmp = x + (t * a)
    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 <= -5.2e+16) || !(a <= 1.3e-93)) {
		tmp = x + (t * a);
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -5.2e+16) or not (a <= 1.3e-93):
		tmp = x + (t * a)
	else:
		tmp = x + (y * z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -5.2e+16) || !(a <= 1.3e-93))
		tmp = Float64(x + Float64(t * a));
	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 <= -5.2e+16) || ~((a <= 1.3e-93)))
		tmp = x + (t * a);
	else
		tmp = x + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -5.2e+16], N[Not[LessEqual[a, 1.3e-93]], $MachinePrecision]], N[(x + N[(t * a), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -5.2e16 or 1.2999999999999999e-93 < a

   1. Initial program 86.2%

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

      1. associate-+l+ 86.2%

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

      2. *-commutative 86.2%

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

      3. associate-*l* 82.9%

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

   3. Simplified 82.9%

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

   4. Taylor expanded in z around 0 59.1%

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

   if -5.2e16 < a < 1.2999999999999999e-93

   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. *-commutative 98.2%

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

      3. associate-*l* 98.2%

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

   3. Simplified 98.2%

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

   4. Taylor expanded in a around 0 83.7%

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

4. Final simplification 69.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.2 \cdot 10^{+16} \lor \neg \left(a \leq 1.3 \cdot 10^{-93}\right):\\ \;\;\;\;x + t \cdot a\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]

Alternative 9: 39.9% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.95 \cdot 10^{+28}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{+15}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -1.95e+28) (* t a) (if (<= a 2.1e+15) x (* t a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -1.95e+28) {
		tmp = t * a;
	} else if (a <= 2.1e+15) {
		tmp = x;
	} 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 (a <= (-1.95d+28)) then
        tmp = t * a
    else if (a <= 2.1d+15) then
        tmp = x
    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 (a <= -1.95e+28) {
		tmp = t * a;
	} else if (a <= 2.1e+15) {
		tmp = x;
	} else {
		tmp = t * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -1.95e+28:
		tmp = t * a
	elif a <= 2.1e+15:
		tmp = x
	else:
		tmp = t * a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -1.95e+28)
		tmp = Float64(t * a);
	elseif (a <= 2.1e+15)
		tmp = x;
	else
		tmp = Float64(t * a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -1.95e+28)
		tmp = t * a;
	elseif (a <= 2.1e+15)
		tmp = x;
	else
		tmp = t * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -1.95e+28], N[(t * a), $MachinePrecision], If[LessEqual[a, 2.1e+15], x, N[(t * a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.9499999999999999e28 or 2.1e15 < a

   1. Initial program 84.1%

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

      1. associate-+l+ 84.1%

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

      2. *-commutative 84.1%

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

      3. associate-*l* 81.0%

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

   3. Simplified 81.0%

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

   4. Taylor expanded in t around inf 48.7%

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

   if -1.9499999999999999e28 < a < 2.1e15

   1. Initial program 97.8%

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

      1. associate-+l+ 97.8%

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

      2. *-commutative 97.8%

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

      3. associate-*l* 97.0%

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

   3. Simplified 97.0%

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

   4. Taylor expanded in x around inf 39.9%

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

4. Final simplification 44.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.95 \cdot 10^{+28}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{+15}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot a\\ \end{array} \]

Alternative 10: 27.3% 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 91.4%

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

   1. associate-+l+ 91.4%

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

   2. *-commutative 91.4%

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

   3. associate-*l* 89.6%

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

3. Simplified 89.6%

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

4. Taylor expanded in x around inf 26.2%

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

5. Final simplification 26.2%

   \[\leadsto x \]

Developer target: 97.3% 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 2023297 
(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)))