Graphics.Rasterific.CubicBezier:cachedBezierAt from Rasterific-0.6.1

Percentage Accurate: 92.2% → 93.8%

Time: 10.9s

Alternatives: 14

Speedup: 0.5×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 92.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 93.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -7.6 \cdot 10^{+216}:\\ \;\;\;\;z \cdot \left(y + b \cdot a\right) + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, z, x\right) + a \cdot \left(t + b \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -7.6e+216)
   (+ (* z (+ y (* b a))) x)
   (+ (fma y z x) (* a (+ t (* b z))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -7.6e+216) {
		tmp = (z * (y + (b * a))) + x;
	} else {
		tmp = fma(y, z, x) + (a * (t + (b * z)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -7.6e+216)
		tmp = Float64(Float64(z * Float64(y + Float64(b * a))) + x);
	else
		tmp = Float64(fma(y, z, x) + Float64(a * Float64(t + Float64(b * z))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -7.6e+216], N[(N[(z * N[(y + N[(b * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(N[(y * z + x), $MachinePrecision] + N[(a * N[(t + N[(b * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 2: 95.4% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 3: 73.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(y + b \cdot a\right)\\ t_2 := x + a \cdot t\\ \mathbf{if}\;z \leq -2.55 \cdot 10^{+66}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-56}:\\ \;\;\;\;a \cdot t + z \cdot y\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-117}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 10^{-69}:\\ \;\;\;\;x + z \cdot y\\ \mathbf{elif}\;z \leq 10^{+27}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (+ y (* b a)))) (t_2 (+ x (* a t))))
   (if (<= z -2.55e+66)
     t_1
     (if (<= z -2.6e-56)
       (+ (* a t) (* z y))
       (if (<= z 1.45e-117)
         t_2
         (if (<= z 1e-69) (+ x (* z y)) (if (<= z 1e+27) t_2 t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (y + (b * a));
	double t_2 = x + (a * t);
	double tmp;
	if (z <= -2.55e+66) {
		tmp = t_1;
	} else if (z <= -2.6e-56) {
		tmp = (a * t) + (z * y);
	} else if (z <= 1.45e-117) {
		tmp = t_2;
	} else if (z <= 1e-69) {
		tmp = x + (z * y);
	} else if (z <= 1e+27) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = z * (y + (b * a))
    t_2 = x + (a * t)
    if (z <= (-2.55d+66)) then
        tmp = t_1
    else if (z <= (-2.6d-56)) then
        tmp = (a * t) + (z * y)
    else if (z <= 1.45d-117) then
        tmp = t_2
    else if (z <= 1d-69) then
        tmp = x + (z * y)
    else if (z <= 1d+27) then
        tmp = t_2
    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 * (y + (b * a));
	double t_2 = x + (a * t);
	double tmp;
	if (z <= -2.55e+66) {
		tmp = t_1;
	} else if (z <= -2.6e-56) {
		tmp = (a * t) + (z * y);
	} else if (z <= 1.45e-117) {
		tmp = t_2;
	} else if (z <= 1e-69) {
		tmp = x + (z * y);
	} else if (z <= 1e+27) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (y + (b * a))
	t_2 = x + (a * t)
	tmp = 0
	if z <= -2.55e+66:
		tmp = t_1
	elif z <= -2.6e-56:
		tmp = (a * t) + (z * y)
	elif z <= 1.45e-117:
		tmp = t_2
	elif z <= 1e-69:
		tmp = x + (z * y)
	elif z <= 1e+27:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(y + Float64(b * a)))
	t_2 = Float64(x + Float64(a * t))
	tmp = 0.0
	if (z <= -2.55e+66)
		tmp = t_1;
	elseif (z <= -2.6e-56)
		tmp = Float64(Float64(a * t) + Float64(z * y));
	elseif (z <= 1.45e-117)
		tmp = t_2;
	elseif (z <= 1e-69)
		tmp = Float64(x + Float64(z * y));
	elseif (z <= 1e+27)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (y + (b * a));
	t_2 = x + (a * t);
	tmp = 0.0;
	if (z <= -2.55e+66)
		tmp = t_1;
	elseif (z <= -2.6e-56)
		tmp = (a * t) + (z * y);
	elseif (z <= 1.45e-117)
		tmp = t_2;
	elseif (z <= 1e-69)
		tmp = x + (z * y);
	elseif (z <= 1e+27)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(y + N[(b * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(a * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.55e+66], t$95$1, If[LessEqual[z, -2.6e-56], N[(N[(a * t), $MachinePrecision] + N[(z * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.45e-117], t$95$2, If[LessEqual[z, 1e-69], N[(x + N[(z * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1e+27], t$95$2, t$95$1]]]]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 4: 40.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.2 \cdot 10^{+72}:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;a \leq -4.5 \cdot 10^{+26}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -6.2 \cdot 10^{-118}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;a \leq -3.9 \cdot 10^{-180}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{-230}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-23}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -3.2e+72)
   (* a t)
   (if (<= a -4.5e+26)
     x
     (if (<= a -6.2e-118)
       (* z y)
       (if (<= a -3.9e-180)
         x
         (if (<= a 3.8e-230) (* z y) (if (<= a 1.2e-23) x (* a t))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -3.2e+72) {
		tmp = a * t;
	} else if (a <= -4.5e+26) {
		tmp = x;
	} else if (a <= -6.2e-118) {
		tmp = z * y;
	} else if (a <= -3.9e-180) {
		tmp = x;
	} else if (a <= 3.8e-230) {
		tmp = z * y;
	} else if (a <= 1.2e-23) {
		tmp = x;
	} else {
		tmp = a * t;
	}
	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 <= (-3.2d+72)) then
        tmp = a * t
    else if (a <= (-4.5d+26)) then
        tmp = x
    else if (a <= (-6.2d-118)) then
        tmp = z * y
    else if (a <= (-3.9d-180)) then
        tmp = x
    else if (a <= 3.8d-230) then
        tmp = z * y
    else if (a <= 1.2d-23) then
        tmp = x
    else
        tmp = a * t
    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 <= -3.2e+72) {
		tmp = a * t;
	} else if (a <= -4.5e+26) {
		tmp = x;
	} else if (a <= -6.2e-118) {
		tmp = z * y;
	} else if (a <= -3.9e-180) {
		tmp = x;
	} else if (a <= 3.8e-230) {
		tmp = z * y;
	} else if (a <= 1.2e-23) {
		tmp = x;
	} else {
		tmp = a * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -3.2e+72:
		tmp = a * t
	elif a <= -4.5e+26:
		tmp = x
	elif a <= -6.2e-118:
		tmp = z * y
	elif a <= -3.9e-180:
		tmp = x
	elif a <= 3.8e-230:
		tmp = z * y
	elif a <= 1.2e-23:
		tmp = x
	else:
		tmp = a * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -3.2e+72)
		tmp = Float64(a * t);
	elseif (a <= -4.5e+26)
		tmp = x;
	elseif (a <= -6.2e-118)
		tmp = Float64(z * y);
	elseif (a <= -3.9e-180)
		tmp = x;
	elseif (a <= 3.8e-230)
		tmp = Float64(z * y);
	elseif (a <= 1.2e-23)
		tmp = x;
	else
		tmp = Float64(a * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -3.2e+72)
		tmp = a * t;
	elseif (a <= -4.5e+26)
		tmp = x;
	elseif (a <= -6.2e-118)
		tmp = z * y;
	elseif (a <= -3.9e-180)
		tmp = x;
	elseif (a <= 3.8e-230)
		tmp = z * y;
	elseif (a <= 1.2e-23)
		tmp = x;
	else
		tmp = a * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -3.2e+72], N[(a * t), $MachinePrecision], If[LessEqual[a, -4.5e+26], x, If[LessEqual[a, -6.2e-118], N[(z * y), $MachinePrecision], If[LessEqual[a, -3.9e-180], x, If[LessEqual[a, 3.8e-230], N[(z * y), $MachinePrecision], If[LessEqual[a, 1.2e-23], x, N[(a * t), $MachinePrecision]]]]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 5: 73.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + a \cdot t\\ t_2 := z \cdot \left(y + b \cdot a\right)\\ \mathbf{if}\;z \leq -2.4 \cdot 10^{+65}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-117}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-69}:\\ \;\;\;\;x + z \cdot y\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+26}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* a t))) (t_2 (* z (+ y (* b a)))))
   (if (<= z -2.4e+65)
     t_2
     (if (<= z 4.2e-117)
       t_1
       (if (<= z 1.4e-69) (+ x (* z y)) (if (<= z 3.6e+26) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (a * t);
	double t_2 = z * (y + (b * a));
	double tmp;
	if (z <= -2.4e+65) {
		tmp = t_2;
	} else if (z <= 4.2e-117) {
		tmp = t_1;
	} else if (z <= 1.4e-69) {
		tmp = x + (z * y);
	} else if (z <= 3.6e+26) {
		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 + (a * t)
    t_2 = z * (y + (b * a))
    if (z <= (-2.4d+65)) then
        tmp = t_2
    else if (z <= 4.2d-117) then
        tmp = t_1
    else if (z <= 1.4d-69) then
        tmp = x + (z * y)
    else if (z <= 3.6d+26) 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 + (a * t);
	double t_2 = z * (y + (b * a));
	double tmp;
	if (z <= -2.4e+65) {
		tmp = t_2;
	} else if (z <= 4.2e-117) {
		tmp = t_1;
	} else if (z <= 1.4e-69) {
		tmp = x + (z * y);
	} else if (z <= 3.6e+26) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (a * t)
	t_2 = z * (y + (b * a))
	tmp = 0
	if z <= -2.4e+65:
		tmp = t_2
	elif z <= 4.2e-117:
		tmp = t_1
	elif z <= 1.4e-69:
		tmp = x + (z * y)
	elif z <= 3.6e+26:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(a * t))
	t_2 = Float64(z * Float64(y + Float64(b * a)))
	tmp = 0.0
	if (z <= -2.4e+65)
		tmp = t_2;
	elseif (z <= 4.2e-117)
		tmp = t_1;
	elseif (z <= 1.4e-69)
		tmp = Float64(x + Float64(z * y));
	elseif (z <= 3.6e+26)
		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 + (a * t);
	t_2 = z * (y + (b * a));
	tmp = 0.0;
	if (z <= -2.4e+65)
		tmp = t_2;
	elseif (z <= 4.2e-117)
		tmp = t_1;
	elseif (z <= 1.4e-69)
		tmp = x + (z * y);
	elseif (z <= 3.6e+26)
		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[(a * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(y + N[(b * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.4e+65], t$95$2, If[LessEqual[z, 4.2e-117], t$95$1, If[LessEqual[z, 1.4e-69], N[(x + N[(z * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.6e+26], t$95$1, t$95$2]]]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 6: 74.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(t + b \cdot z\right)\\ \mathbf{if}\;a \leq -7 \cdot 10^{+75}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -5.2 \cdot 10^{+26}:\\ \;\;\;\;x + b \cdot \left(z \cdot a\right)\\ \mathbf{elif}\;a \leq -3.7 \cdot 10^{-58}:\\ \;\;\;\;z \cdot \left(y + b \cdot a\right)\\ \mathbf{elif}\;a \leq 8.6 \cdot 10^{-25}:\\ \;\;\;\;x + z \cdot y\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (+ t (* b z)))))
   (if (<= a -7e+75)
     t_1
     (if (<= a -5.2e+26)
       (+ x (* b (* z a)))
       (if (<= a -3.7e-58)
         (* z (+ y (* b a)))
         (if (<= a 8.6e-25) (+ x (* z y)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (t + (b * z));
	double tmp;
	if (a <= -7e+75) {
		tmp = t_1;
	} else if (a <= -5.2e+26) {
		tmp = x + (b * (z * a));
	} else if (a <= -3.7e-58) {
		tmp = z * (y + (b * a));
	} else if (a <= 8.6e-25) {
		tmp = x + (z * y);
	} 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 * (t + (b * z))
    if (a <= (-7d+75)) then
        tmp = t_1
    else if (a <= (-5.2d+26)) then
        tmp = x + (b * (z * a))
    else if (a <= (-3.7d-58)) then
        tmp = z * (y + (b * a))
    else if (a <= 8.6d-25) then
        tmp = x + (z * y)
    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 * (t + (b * z));
	double tmp;
	if (a <= -7e+75) {
		tmp = t_1;
	} else if (a <= -5.2e+26) {
		tmp = x + (b * (z * a));
	} else if (a <= -3.7e-58) {
		tmp = z * (y + (b * a));
	} else if (a <= 8.6e-25) {
		tmp = x + (z * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (t + (b * z))
	tmp = 0
	if a <= -7e+75:
		tmp = t_1
	elif a <= -5.2e+26:
		tmp = x + (b * (z * a))
	elif a <= -3.7e-58:
		tmp = z * (y + (b * a))
	elif a <= 8.6e-25:
		tmp = x + (z * y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(t + Float64(b * z)))
	tmp = 0.0
	if (a <= -7e+75)
		tmp = t_1;
	elseif (a <= -5.2e+26)
		tmp = Float64(x + Float64(b * Float64(z * a)));
	elseif (a <= -3.7e-58)
		tmp = Float64(z * Float64(y + Float64(b * a)));
	elseif (a <= 8.6e-25)
		tmp = Float64(x + Float64(z * y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (t + (b * z));
	tmp = 0.0;
	if (a <= -7e+75)
		tmp = t_1;
	elseif (a <= -5.2e+26)
		tmp = x + (b * (z * a));
	elseif (a <= -3.7e-58)
		tmp = z * (y + (b * a));
	elseif (a <= 8.6e-25)
		tmp = x + (z * y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(t + N[(b * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -7e+75], t$95$1, If[LessEqual[a, -5.2e+26], N[(x + N[(b * N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -3.7e-58], N[(z * N[(y + N[(b * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8.6e-25], N[(x + N[(z * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 7: 62.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot y\\ t_2 := x + a \cdot t\\ \mathbf{if}\;t \leq -2.9 \cdot 10^{+72}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.2 \cdot 10^{-207}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.1 \cdot 10^{-281}:\\ \;\;\;\;a \cdot \left(b \cdot z\right)\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{-5}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* z y))) (t_2 (+ x (* a t))))
   (if (<= t -2.9e+72)
     t_2
     (if (<= t -1.2e-207)
       t_1
       (if (<= t -1.1e-281) (* a (* b z)) (if (<= t 3.4e-5) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z * y);
	double t_2 = x + (a * t);
	double tmp;
	if (t <= -2.9e+72) {
		tmp = t_2;
	} else if (t <= -1.2e-207) {
		tmp = t_1;
	} else if (t <= -1.1e-281) {
		tmp = a * (b * z);
	} else if (t <= 3.4e-5) {
		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 + (z * y)
    t_2 = x + (a * t)
    if (t <= (-2.9d+72)) then
        tmp = t_2
    else if (t <= (-1.2d-207)) then
        tmp = t_1
    else if (t <= (-1.1d-281)) then
        tmp = a * (b * z)
    else if (t <= 3.4d-5) 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 + (z * y);
	double t_2 = x + (a * t);
	double tmp;
	if (t <= -2.9e+72) {
		tmp = t_2;
	} else if (t <= -1.2e-207) {
		tmp = t_1;
	} else if (t <= -1.1e-281) {
		tmp = a * (b * z);
	} else if (t <= 3.4e-5) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (z * y)
	t_2 = x + (a * t)
	tmp = 0
	if t <= -2.9e+72:
		tmp = t_2
	elif t <= -1.2e-207:
		tmp = t_1
	elif t <= -1.1e-281:
		tmp = a * (b * z)
	elif t <= 3.4e-5:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(z * y))
	t_2 = Float64(x + Float64(a * t))
	tmp = 0.0
	if (t <= -2.9e+72)
		tmp = t_2;
	elseif (t <= -1.2e-207)
		tmp = t_1;
	elseif (t <= -1.1e-281)
		tmp = Float64(a * Float64(b * z));
	elseif (t <= 3.4e-5)
		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 + (z * y);
	t_2 = x + (a * t);
	tmp = 0.0;
	if (t <= -2.9e+72)
		tmp = t_2;
	elseif (t <= -1.2e-207)
		tmp = t_1;
	elseif (t <= -1.1e-281)
		tmp = a * (b * z);
	elseif (t <= 3.4e-5)
		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[(z * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(a * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.9e+72], t$95$2, If[LessEqual[t, -1.2e-207], t$95$1, If[LessEqual[t, -1.1e-281], N[(a * N[(b * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.4e-5], t$95$1, t$95$2]]]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 8: 86.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{+72} \lor \neg \left(t \leq 13600\right):\\ \;\;\;\;x + \left(a \cdot t + z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y + b \cdot a\right) + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -4e+72) (not (<= t 13600.0)))
   (+ x (+ (* a t) (* z y)))
   (+ (* z (+ y (* b a))) x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -4e+72) || !(t <= 13600.0)) {
		tmp = x + ((a * t) + (z * y));
	} else {
		tmp = (z * (y + (b * a))) + 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 <= (-4d+72)) .or. (.not. (t <= 13600.0d0))) then
        tmp = x + ((a * t) + (z * y))
    else
        tmp = (z * (y + (b * a))) + 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 <= -4e+72) || !(t <= 13600.0)) {
		tmp = x + ((a * t) + (z * y));
	} else {
		tmp = (z * (y + (b * a))) + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -4e+72) or not (t <= 13600.0):
		tmp = x + ((a * t) + (z * y))
	else:
		tmp = (z * (y + (b * a))) + x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -4e+72) || !(t <= 13600.0))
		tmp = Float64(x + Float64(Float64(a * t) + Float64(z * y)));
	else
		tmp = Float64(Float64(z * Float64(y + Float64(b * a))) + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -4e+72) || ~((t <= 13600.0)))
		tmp = x + ((a * t) + (z * y));
	else
		tmp = (z * (y + (b * a))) + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -4e+72], N[Not[LessEqual[t, 13600.0]], $MachinePrecision]], N[(x + N[(N[(a * t), $MachinePrecision] + N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z * N[(y + N[(b * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 9: 81.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.6 \cdot 10^{+167}:\\ \;\;\;\;z \cdot \left(y + b \cdot a\right)\\ \mathbf{elif}\;b \leq 5.2 \cdot 10^{+63}:\\ \;\;\;\;x + \left(a \cdot t + z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot \left(z \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.6e+167)
   (* z (+ y (* b a)))
   (if (<= b 5.2e+63) (+ x (+ (* a t) (* z y))) (+ x (* b (* z a))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.6e+167) {
		tmp = z * (y + (b * a));
	} else if (b <= 5.2e+63) {
		tmp = x + ((a * t) + (z * y));
	} else {
		tmp = x + (b * (z * 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 (b <= (-1.6d+167)) then
        tmp = z * (y + (b * a))
    else if (b <= 5.2d+63) then
        tmp = x + ((a * t) + (z * y))
    else
        tmp = x + (b * (z * 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 (b <= -1.6e+167) {
		tmp = z * (y + (b * a));
	} else if (b <= 5.2e+63) {
		tmp = x + ((a * t) + (z * y));
	} else {
		tmp = x + (b * (z * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.6e+167:
		tmp = z * (y + (b * a))
	elif b <= 5.2e+63:
		tmp = x + ((a * t) + (z * y))
	else:
		tmp = x + (b * (z * a))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.6e+167)
		tmp = Float64(z * Float64(y + Float64(b * a)));
	elseif (b <= 5.2e+63)
		tmp = Float64(x + Float64(Float64(a * t) + Float64(z * y)));
	else
		tmp = Float64(x + Float64(b * Float64(z * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.6e+167)
		tmp = z * (y + (b * a));
	elseif (b <= 5.2e+63)
		tmp = x + ((a * t) + (z * y));
	else
		tmp = x + (b * (z * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.6e+167], N[(z * N[(y + N[(b * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.2e+63], N[(x + N[(N[(a * t), $MachinePrecision] + N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(b * N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 10: 40.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.6 \cdot 10^{+63}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;y \leq -1.85 \cdot 10^{-193}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-149}:\\ \;\;\;\;a \cdot \left(b \cdot z\right)\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+65}:\\ \;\;\;\;a \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -8.6e+63)
   (* z y)
   (if (<= y -1.85e-193)
     x
     (if (<= y 2.1e-149) (* a (* b z)) (if (<= y 1.45e+65) (* a t) (* z y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -8.6e+63) {
		tmp = z * y;
	} else if (y <= -1.85e-193) {
		tmp = x;
	} else if (y <= 2.1e-149) {
		tmp = a * (b * z);
	} else if (y <= 1.45e+65) {
		tmp = a * t;
	} else {
		tmp = z * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-8.6d+63)) then
        tmp = z * y
    else if (y <= (-1.85d-193)) then
        tmp = x
    else if (y <= 2.1d-149) then
        tmp = a * (b * z)
    else if (y <= 1.45d+65) then
        tmp = a * t
    else
        tmp = z * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -8.6e+63) {
		tmp = z * y;
	} else if (y <= -1.85e-193) {
		tmp = x;
	} else if (y <= 2.1e-149) {
		tmp = a * (b * z);
	} else if (y <= 1.45e+65) {
		tmp = a * t;
	} else {
		tmp = z * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -8.6e+63:
		tmp = z * y
	elif y <= -1.85e-193:
		tmp = x
	elif y <= 2.1e-149:
		tmp = a * (b * z)
	elif y <= 1.45e+65:
		tmp = a * t
	else:
		tmp = z * y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -8.6e+63)
		tmp = Float64(z * y);
	elseif (y <= -1.85e-193)
		tmp = x;
	elseif (y <= 2.1e-149)
		tmp = Float64(a * Float64(b * z));
	elseif (y <= 1.45e+65)
		tmp = Float64(a * t);
	else
		tmp = Float64(z * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -8.6e+63)
		tmp = z * y;
	elseif (y <= -1.85e-193)
		tmp = x;
	elseif (y <= 2.1e-149)
		tmp = a * (b * z);
	elseif (y <= 1.45e+65)
		tmp = a * t;
	else
		tmp = z * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -8.6e+63], N[(z * y), $MachinePrecision], If[LessEqual[y, -1.85e-193], x, If[LessEqual[y, 2.1e-149], N[(a * N[(b * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.45e+65], N[(a * t), $MachinePrecision], N[(z * y), $MachinePrecision]]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 11: 73.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.3 \cdot 10^{+97} \lor \neg \left(a \leq 1.6 \cdot 10^{-24}\right):\\ \;\;\;\;a \cdot \left(t + b \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -2.3e+97) (not (<= a 1.6e-24)))
   (* a (+ t (* b z)))
   (+ x (* z y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -2.3e+97) || !(a <= 1.6e-24)) {
		tmp = a * (t + (b * z));
	} else {
		tmp = x + (z * y);
	}
	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 <= (-2.3d+97)) .or. (.not. (a <= 1.6d-24))) then
        tmp = a * (t + (b * z))
    else
        tmp = x + (z * y)
    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 <= -2.3e+97) || !(a <= 1.6e-24)) {
		tmp = a * (t + (b * z));
	} else {
		tmp = x + (z * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -2.3e+97) or not (a <= 1.6e-24):
		tmp = a * (t + (b * z))
	else:
		tmp = x + (z * y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -2.3e+97) || !(a <= 1.6e-24))
		tmp = Float64(a * Float64(t + Float64(b * z)));
	else
		tmp = Float64(x + Float64(z * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -2.3e+97) || ~((a <= 1.6e-24)))
		tmp = a * (t + (b * z));
	else
		tmp = x + (z * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -2.3e+97], N[Not[LessEqual[a, 1.6e-24]], $MachinePrecision]], N[(a * N[(t + N[(b * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * y), $MachinePrecision]), $MachinePrecision]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 12: 59.4% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -8 \cdot 10^{+99}:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{+17}:\\ \;\;\;\;x + z \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -8e+99) (* a t) (if (<= a 1.1e+17) (+ x (* z y)) (* a (* b z)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -8e+99) {
		tmp = a * t;
	} else if (a <= 1.1e+17) {
		tmp = x + (z * y);
	} else {
		tmp = a * (b * 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 <= (-8d+99)) then
        tmp = a * t
    else if (a <= 1.1d+17) then
        tmp = x + (z * y)
    else
        tmp = a * (b * 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 <= -8e+99) {
		tmp = a * t;
	} else if (a <= 1.1e+17) {
		tmp = x + (z * y);
	} else {
		tmp = a * (b * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -8e+99:
		tmp = a * t
	elif a <= 1.1e+17:
		tmp = x + (z * y)
	else:
		tmp = a * (b * z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -8e+99)
		tmp = Float64(a * t);
	elseif (a <= 1.1e+17)
		tmp = Float64(x + Float64(z * y));
	else
		tmp = Float64(a * Float64(b * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -8e+99)
		tmp = a * t;
	elseif (a <= 1.1e+17)
		tmp = x + (z * y);
	else
		tmp = a * (b * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -8e+99], N[(a * t), $MachinePrecision], If[LessEqual[a, 1.1e+17], N[(x + N[(z * y), $MachinePrecision]), $MachinePrecision], N[(a * N[(b * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 13: 40.7% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.95 \cdot 10^{+73} \lor \neg \left(t \leq 6 \cdot 10^{+59}\right):\\ \;\;\;\;a \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -1.95e+73) (not (<= t 6e+59))) (* a t) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.95e+73) || !(t <= 6e+59)) {
		tmp = a * t;
	} 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 <= (-1.95d+73)) .or. (.not. (t <= 6d+59))) then
        tmp = a * t
    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 <= -1.95e+73) || !(t <= 6e+59)) {
		tmp = a * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -1.95e+73) or not (t <= 6e+59):
		tmp = a * t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -1.95e+73) || !(t <= 6e+59))
		tmp = Float64(a * t);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -1.95e+73) || ~((t <= 6e+59)))
		tmp = a * t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -1.95e+73], N[Not[LessEqual[t, 6e+59]], $MachinePrecision]], N[(a * t), $MachinePrecision], x]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 14: 27.1% 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

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

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 2024003 
(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)))