Diagrams.Solve.Polynomial:cubForm from diagrams-solve-0.1, J

Percentage Accurate: 78.7% → 89.5%

Time: 24.4s

Alternatives: 21

Speedup: 0.8×

• 36.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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), intent (in) :: c
    code = ((((x * 9.0d0) * y) - (((z * 4.0d0) * t) * a)) + b) / (z * c)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
}

Python

def code(x, y, z, t, a, b, c):
	return ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c)

Julia

function code(x, y, z, t, a, b, c)
	return Float64(Float64(Float64(Float64(Float64(x * 9.0) * y) - Float64(Float64(Float64(z * 4.0) * t) * a)) + b) / Float64(z * c))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c)
	tmp = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(N[(N[(N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision] - N[(N[(N[(z * 4.0), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]

Initial Program: 78.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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), intent (in) :: c
    code = ((((x * 9.0d0) * y) - (((z * 4.0d0) * t) * a)) + b) / (z * c)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
}

Python

def code(x, y, z, t, a, b, c):
	return ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c)

Julia

function code(x, y, z, t, a, b, c)
	return Float64(Float64(Float64(Float64(Float64(x * 9.0) * y) - Float64(Float64(Float64(z * 4.0) * t) * a)) + b) / Float64(z * c))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c)
	tmp = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(N[(N[(N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision] - N[(N[(N[(z * 4.0), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]

Alternative 1: 89.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} c_m = \left|c\right| \\ c_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := \frac{b}{c_m \cdot z}\\ c_s \cdot \begin{array}{l} \mathbf{if}\;c_m \leq 6.8 \cdot 10^{-43}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, 9 \cdot y, z \cdot \left(\left(-4 \cdot t\right) \cdot a\right)\right) + b}{c_m \cdot z}\\ \mathbf{elif}\;c_m \leq 5.2 \cdot 10^{+224}:\\ \;\;\;\;\mathsf{fma}\left(-4, \frac{a}{\frac{c_m}{t}}, \mathsf{fma}\left(9, \frac{x}{c_m} \cdot \frac{y}{z}, t_1\right)\right)\\ \mathbf{elif}\;c_m \leq 2.7 \cdot 10^{+251}:\\ \;\;\;\;\frac{1}{z} \cdot \mathsf{fma}\left(-4, \frac{a}{\frac{c_m}{z \cdot t}}, \mathsf{fma}\left(9, \frac{x}{\frac{c_m}{y}}, \frac{b}{c_m}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t \cdot \frac{a}{c_m}, -4, \mathsf{fma}\left(9, y \cdot \frac{x}{c_m \cdot z}, t_1\right)\right)\\ \end{array} \end{array} \end{array} \]

FPCore

c_m = (fabs.f64 c)
c_s = (copysign.f64 1 c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (let* ((t_1 (/ b (* c_m z))))
   (*
    c_s
    (if (<= c_m 6.8e-43)
      (/ (+ (fma x (* 9.0 y) (* z (* (* -4.0 t) a))) b) (* c_m z))
      (if (<= c_m 5.2e+224)
        (fma -4.0 (/ a (/ c_m t)) (fma 9.0 (* (/ x c_m) (/ y z)) t_1))
        (if (<= c_m 2.7e+251)
          (*
           (/ 1.0 z)
           (fma
            -4.0
            (/ a (/ c_m (* z t)))
            (fma 9.0 (/ x (/ c_m y)) (/ b c_m))))
          (fma (* t (/ a c_m)) -4.0 (fma 9.0 (* y (/ x (* c_m z))) t_1))))))))

C

c_m = fabs(c);
c_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double t_1 = b / (c_m * z);
	double tmp;
	if (c_m <= 6.8e-43) {
		tmp = (fma(x, (9.0 * y), (z * ((-4.0 * t) * a))) + b) / (c_m * z);
	} else if (c_m <= 5.2e+224) {
		tmp = fma(-4.0, (a / (c_m / t)), fma(9.0, ((x / c_m) * (y / z)), t_1));
	} else if (c_m <= 2.7e+251) {
		tmp = (1.0 / z) * fma(-4.0, (a / (c_m / (z * t))), fma(9.0, (x / (c_m / y)), (b / c_m)));
	} else {
		tmp = fma((t * (a / c_m)), -4.0, fma(9.0, (y * (x / (c_m * z))), t_1));
	}
	return c_s * tmp;
}

Julia

c_m = abs(c)
c_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	t_1 = Float64(b / Float64(c_m * z))
	tmp = 0.0
	if (c_m <= 6.8e-43)
		tmp = Float64(Float64(fma(x, Float64(9.0 * y), Float64(z * Float64(Float64(-4.0 * t) * a))) + b) / Float64(c_m * z));
	elseif (c_m <= 5.2e+224)
		tmp = fma(-4.0, Float64(a / Float64(c_m / t)), fma(9.0, Float64(Float64(x / c_m) * Float64(y / z)), t_1));
	elseif (c_m <= 2.7e+251)
		tmp = Float64(Float64(1.0 / z) * fma(-4.0, Float64(a / Float64(c_m / Float64(z * t))), fma(9.0, Float64(x / Float64(c_m / y)), Float64(b / c_m))));
	else
		tmp = fma(Float64(t * Float64(a / c_m)), -4.0, fma(9.0, Float64(y * Float64(x / Float64(c_m * z))), t_1));
	end
	return Float64(c_s * tmp)
end

Wolfram

c_m = N[Abs[c], $MachinePrecision]
c_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := Block[{t$95$1 = N[(b / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]}, N[(c$95$s * If[LessEqual[c$95$m, 6.8e-43], N[(N[(N[(x * N[(9.0 * y), $MachinePrecision] + N[(z * N[(N[(-4.0 * t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[c$95$m, 5.2e+224], N[(-4.0 * N[(a / N[(c$95$m / t), $MachinePrecision]), $MachinePrecision] + N[(9.0 * N[(N[(x / c$95$m), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[c$95$m, 2.7e+251], N[(N[(1.0 / z), $MachinePrecision] * N[(-4.0 * N[(a / N[(c$95$m / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(9.0 * N[(x / N[(c$95$m / y), $MachinePrecision]), $MachinePrecision] + N[(b / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t * N[(a / c$95$m), $MachinePrecision]), $MachinePrecision] * -4.0 + N[(9.0 * N[(y * N[(x / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]]]]), $MachinePrecision]]

Derivation

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

Alternative 2: 89.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} c_m = \left|c\right| \\ c_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c_s \cdot \begin{array}{l} \mathbf{if}\;c_m \leq 1.75 \cdot 10^{-39}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, 9 \cdot y, z \cdot \left(\left(-4 \cdot t\right) \cdot a\right)\right) + b}{c_m \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-4, \frac{a}{\frac{c_m}{t}}, \mathsf{fma}\left(9, \frac{x}{c_m} \cdot \frac{y}{z}, \frac{b}{c_m \cdot z}\right)\right)\\ \end{array} \end{array} \]

FPCore

c_m = (fabs.f64 c)
c_s = (copysign.f64 1 c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (*
  c_s
  (if (<= c_m 1.75e-39)
    (/ (+ (fma x (* 9.0 y) (* z (* (* -4.0 t) a))) b) (* c_m z))
    (fma
     -4.0
     (/ a (/ c_m t))
     (fma 9.0 (* (/ x c_m) (/ y z)) (/ b (* c_m z)))))))

C

c_m = fabs(c);
c_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (c_m <= 1.75e-39) {
		tmp = (fma(x, (9.0 * y), (z * ((-4.0 * t) * a))) + b) / (c_m * z);
	} else {
		tmp = fma(-4.0, (a / (c_m / t)), fma(9.0, ((x / c_m) * (y / z)), (b / (c_m * z))));
	}
	return c_s * tmp;
}

Julia

c_m = abs(c)
c_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if (c_m <= 1.75e-39)
		tmp = Float64(Float64(fma(x, Float64(9.0 * y), Float64(z * Float64(Float64(-4.0 * t) * a))) + b) / Float64(c_m * z));
	else
		tmp = fma(-4.0, Float64(a / Float64(c_m / t)), fma(9.0, Float64(Float64(x / c_m) * Float64(y / z)), Float64(b / Float64(c_m * z))));
	end
	return Float64(c_s * tmp)
end

Wolfram

c_m = N[Abs[c], $MachinePrecision]
c_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[LessEqual[c$95$m, 1.75e-39], N[(N[(N[(x * N[(9.0 * y), $MachinePrecision] + N[(z * N[(N[(-4.0 * t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(a / N[(c$95$m / t), $MachinePrecision]), $MachinePrecision] + N[(9.0 * N[(N[(x / c$95$m), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision] + N[(b / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

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

Alternative 3: 87.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} c_m = \left|c\right| \\ c_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := \frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c_m \cdot z}\\ t_2 := \left(b + \mathsf{fma}\left(x, 9 \cdot y, \left(-4 \cdot t\right) \cdot \left(z \cdot a\right)\right)\right) \cdot \frac{-1}{c_m \cdot \left(-z\right)}\\ c_s \cdot \begin{array}{l} \mathbf{if}\;t_1 \leq -1 \cdot 10^{+121}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_1 \leq 10^{+71}:\\ \;\;\;\;\frac{1}{z} \cdot \frac{b + \mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(z \cdot \left(-4 \cdot t\right)\right)\right)}{c_m}\\ \mathbf{elif}\;t_1 \leq \infty:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-4 \cdot \frac{a}{c_m}\right)\\ \end{array} \end{array} \end{array} \]

FPCore

c_m = (fabs.f64 c)
c_s = (copysign.f64 1 c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (let* ((t_1 (/ (+ b (- (* y (* x 9.0)) (* a (* t (* z 4.0))))) (* c_m z)))
        (t_2
         (*
          (+ b (fma x (* 9.0 y) (* (* -4.0 t) (* z a))))
          (/ -1.0 (* c_m (- z))))))
   (*
    c_s
    (if (<= t_1 -1e+121)
      t_2
      (if (<= t_1 1e+71)
        (* (/ 1.0 z) (/ (+ b (fma x (* 9.0 y) (* a (* z (* -4.0 t))))) c_m))
        (if (<= t_1 INFINITY) t_2 (* t (* -4.0 (/ a c_m)))))))))

C

c_m = fabs(c);
c_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double t_1 = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (c_m * z);
	double t_2 = (b + fma(x, (9.0 * y), ((-4.0 * t) * (z * a)))) * (-1.0 / (c_m * -z));
	double tmp;
	if (t_1 <= -1e+121) {
		tmp = t_2;
	} else if (t_1 <= 1e+71) {
		tmp = (1.0 / z) * ((b + fma(x, (9.0 * y), (a * (z * (-4.0 * t))))) / c_m);
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = t_2;
	} else {
		tmp = t * (-4.0 * (a / c_m));
	}
	return c_s * tmp;
}

Julia

c_m = abs(c)
c_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	t_1 = Float64(Float64(b + Float64(Float64(y * Float64(x * 9.0)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(c_m * z))
	t_2 = Float64(Float64(b + fma(x, Float64(9.0 * y), Float64(Float64(-4.0 * t) * Float64(z * a)))) * Float64(-1.0 / Float64(c_m * Float64(-z))))
	tmp = 0.0
	if (t_1 <= -1e+121)
		tmp = t_2;
	elseif (t_1 <= 1e+71)
		tmp = Float64(Float64(1.0 / z) * Float64(Float64(b + fma(x, Float64(9.0 * y), Float64(a * Float64(z * Float64(-4.0 * t))))) / c_m));
	elseif (t_1 <= Inf)
		tmp = t_2;
	else
		tmp = Float64(t * Float64(-4.0 * Float64(a / c_m)));
	end
	return Float64(c_s * tmp)
end

Wolfram

c_m = N[Abs[c], $MachinePrecision]
c_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := Block[{t$95$1 = N[(N[(b + N[(N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b + N[(x * N[(9.0 * y), $MachinePrecision] + N[(N[(-4.0 * t), $MachinePrecision] * N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(-1.0 / N[(c$95$m * (-z)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(c$95$s * If[LessEqual[t$95$1, -1e+121], t$95$2, If[LessEqual[t$95$1, 1e+71], N[(N[(1.0 / z), $MachinePrecision] * N[(N[(b + N[(x * N[(9.0 * y), $MachinePrecision] + N[(a * N[(z * N[(-4.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, Infinity], t$95$2, N[(t * N[(-4.0 * N[(a / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]), $MachinePrecision]]]

Derivation

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

Alternative 4: 86.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} c_m = \left|c\right| \\ c_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := \frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c_m \cdot z}\\ c_s \cdot \begin{array}{l} \mathbf{if}\;t_1 \leq -2 \cdot 10^{-245}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+247}:\\ \;\;\;\;\frac{1}{z} \cdot \frac{b + \mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(z \cdot \left(-4 \cdot t\right)\right)\right)}{c_m}\\ \mathbf{elif}\;t_1 \leq \infty:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, 9 \cdot y, z \cdot \left(\left(-4 \cdot t\right) \cdot a\right)\right) + b}{c_m \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-4 \cdot \frac{a}{c_m}\right)\\ \end{array} \end{array} \end{array} \]

FPCore

c_m = (fabs.f64 c)
c_s = (copysign.f64 1 c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (let* ((t_1 (/ (+ b (- (* y (* x 9.0)) (* a (* t (* z 4.0))))) (* c_m z))))
   (*
    c_s
    (if (<= t_1 -2e-245)
      t_1
      (if (<= t_1 5e+247)
        (* (/ 1.0 z) (/ (+ b (fma x (* 9.0 y) (* a (* z (* -4.0 t))))) c_m))
        (if (<= t_1 INFINITY)
          (/ (+ (fma x (* 9.0 y) (* z (* (* -4.0 t) a))) b) (* c_m z))
          (* t (* -4.0 (/ a c_m)))))))))

C

c_m = fabs(c);
c_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double t_1 = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (c_m * z);
	double tmp;
	if (t_1 <= -2e-245) {
		tmp = t_1;
	} else if (t_1 <= 5e+247) {
		tmp = (1.0 / z) * ((b + fma(x, (9.0 * y), (a * (z * (-4.0 * t))))) / c_m);
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = (fma(x, (9.0 * y), (z * ((-4.0 * t) * a))) + b) / (c_m * z);
	} else {
		tmp = t * (-4.0 * (a / c_m));
	}
	return c_s * tmp;
}

Julia

c_m = abs(c)
c_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	t_1 = Float64(Float64(b + Float64(Float64(y * Float64(x * 9.0)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(c_m * z))
	tmp = 0.0
	if (t_1 <= -2e-245)
		tmp = t_1;
	elseif (t_1 <= 5e+247)
		tmp = Float64(Float64(1.0 / z) * Float64(Float64(b + fma(x, Float64(9.0 * y), Float64(a * Float64(z * Float64(-4.0 * t))))) / c_m));
	elseif (t_1 <= Inf)
		tmp = Float64(Float64(fma(x, Float64(9.0 * y), Float64(z * Float64(Float64(-4.0 * t) * a))) + b) / Float64(c_m * z));
	else
		tmp = Float64(t * Float64(-4.0 * Float64(a / c_m)));
	end
	return Float64(c_s * tmp)
end

Wolfram

c_m = N[Abs[c], $MachinePrecision]
c_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := Block[{t$95$1 = N[(N[(b + N[(N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]}, N[(c$95$s * If[LessEqual[t$95$1, -2e-245], t$95$1, If[LessEqual[t$95$1, 5e+247], N[(N[(1.0 / z), $MachinePrecision] * N[(N[(b + N[(x * N[(9.0 * y), $MachinePrecision] + N[(a * N[(z * N[(-4.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, Infinity], N[(N[(N[(x * N[(9.0 * y), $MachinePrecision] + N[(z * N[(N[(-4.0 * t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision], N[(t * N[(-4.0 * N[(a / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]), $MachinePrecision]]

Derivation

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

Alternative 5: 86.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} c_m = \left|c\right| \\ c_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+114}:\\ \;\;\;\;\left(\frac{b}{c_m \cdot z} + 9 \cdot \frac{x \cdot y}{c_m \cdot z}\right) - 4 \cdot \frac{t \cdot a}{c_m}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+111}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c_m \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{a}{\frac{c_m}{t}}, -4, 9 \cdot \frac{x}{\frac{z}{\frac{y}{c_m}}}\right)\\ \end{array} \end{array} \]

FPCore

c_m = (fabs.f64 c)
c_s = (copysign.f64 1 c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (*
  c_s
  (if (<= z -6.8e+114)
    (-
     (+ (/ b (* c_m z)) (* 9.0 (/ (* x y) (* c_m z))))
     (* 4.0 (/ (* t a) c_m)))
    (if (<= z 1.35e+111)
      (/ (+ b (- (* y (* x 9.0)) (* a (* t (* z 4.0))))) (* c_m z))
      (fma (/ a (/ c_m t)) -4.0 (* 9.0 (/ x (/ z (/ y c_m)))))))))

C

c_m = fabs(c);
c_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (z <= -6.8e+114) {
		tmp = ((b / (c_m * z)) + (9.0 * ((x * y) / (c_m * z)))) - (4.0 * ((t * a) / c_m));
	} else if (z <= 1.35e+111) {
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (c_m * z);
	} else {
		tmp = fma((a / (c_m / t)), -4.0, (9.0 * (x / (z / (y / c_m)))));
	}
	return c_s * tmp;
}

Julia

c_m = abs(c)
c_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if (z <= -6.8e+114)
		tmp = Float64(Float64(Float64(b / Float64(c_m * z)) + Float64(9.0 * Float64(Float64(x * y) / Float64(c_m * z)))) - Float64(4.0 * Float64(Float64(t * a) / c_m)));
	elseif (z <= 1.35e+111)
		tmp = Float64(Float64(b + Float64(Float64(y * Float64(x * 9.0)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(c_m * z));
	else
		tmp = fma(Float64(a / Float64(c_m / t)), -4.0, Float64(9.0 * Float64(x / Float64(z / Float64(y / c_m)))));
	end
	return Float64(c_s * tmp)
end

Wolfram

c_m = N[Abs[c], $MachinePrecision]
c_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[LessEqual[z, -6.8e+114], N[(N[(N[(b / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision] + N[(9.0 * N[(N[(x * y), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(N[(t * a), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.35e+111], N[(N[(b + N[(N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision], N[(N[(a / N[(c$95$m / t), $MachinePrecision]), $MachinePrecision] * -4.0 + N[(9.0 * N[(x / N[(z / N[(y / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

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

Alternative 6: 86.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} c_m = \left|c\right| \\ c_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := \frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c_m \cdot z}\\ c_s \cdot \begin{array}{l} \mathbf{if}\;t_1 \leq -2 \cdot 10^{-245}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;\frac{1}{z} \cdot \frac{b + 9 \cdot \left(x \cdot y\right)}{c_m}\\ \mathbf{elif}\;t_1 \leq \infty:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right)}{c_m \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-4 \cdot \frac{a}{c_m}\right)\\ \end{array} \end{array} \end{array} \]

FPCore

c_m = (fabs.f64 c)
c_s = (copysign.f64 1 c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (let* ((t_1 (/ (+ b (- (* y (* x 9.0)) (* a (* t (* z 4.0))))) (* c_m z))))
   (*
    c_s
    (if (<= t_1 -2e-245)
      t_1
      (if (<= t_1 0.0)
        (* (/ 1.0 z) (/ (+ b (* 9.0 (* x y))) c_m))
        (if (<= t_1 INFINITY)
          (/ (+ b (- (* x (* 9.0 y)) (* (* z 4.0) (* t a)))) (* c_m z))
          (* t (* -4.0 (/ a c_m)))))))))

C

c_m = fabs(c);
c_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double t_1 = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (c_m * z);
	double tmp;
	if (t_1 <= -2e-245) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = (1.0 / z) * ((b + (9.0 * (x * y))) / c_m);
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = (b + ((x * (9.0 * y)) - ((z * 4.0) * (t * a)))) / (c_m * z);
	} else {
		tmp = t * (-4.0 * (a / c_m));
	}
	return c_s * tmp;
}

Java

c_m = Math.abs(c);
c_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double t_1 = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (c_m * z);
	double tmp;
	if (t_1 <= -2e-245) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = (1.0 / z) * ((b + (9.0 * (x * y))) / c_m);
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = (b + ((x * (9.0 * y)) - ((z * 4.0) * (t * a)))) / (c_m * z);
	} else {
		tmp = t * (-4.0 * (a / c_m));
	}
	return c_s * tmp;
}

Python

c_m = math.fabs(c)
c_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	t_1 = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (c_m * z)
	tmp = 0
	if t_1 <= -2e-245:
		tmp = t_1
	elif t_1 <= 0.0:
		tmp = (1.0 / z) * ((b + (9.0 * (x * y))) / c_m)
	elif t_1 <= math.inf:
		tmp = (b + ((x * (9.0 * y)) - ((z * 4.0) * (t * a)))) / (c_m * z)
	else:
		tmp = t * (-4.0 * (a / c_m))
	return c_s * tmp

Julia

c_m = abs(c)
c_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	t_1 = Float64(Float64(b + Float64(Float64(y * Float64(x * 9.0)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(c_m * z))
	tmp = 0.0
	if (t_1 <= -2e-245)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(1.0 / z) * Float64(Float64(b + Float64(9.0 * Float64(x * y))) / c_m));
	elseif (t_1 <= Inf)
		tmp = Float64(Float64(b + Float64(Float64(x * Float64(9.0 * y)) - Float64(Float64(z * 4.0) * Float64(t * a)))) / Float64(c_m * z));
	else
		tmp = Float64(t * Float64(-4.0 * Float64(a / c_m)));
	end
	return Float64(c_s * tmp)
end

MATLAB

c_m = abs(c);
c_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	t_1 = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (c_m * z);
	tmp = 0.0;
	if (t_1 <= -2e-245)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = (1.0 / z) * ((b + (9.0 * (x * y))) / c_m);
	elseif (t_1 <= Inf)
		tmp = (b + ((x * (9.0 * y)) - ((z * 4.0) * (t * a)))) / (c_m * z);
	else
		tmp = t * (-4.0 * (a / c_m));
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c_m = N[Abs[c], $MachinePrecision]
c_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := Block[{t$95$1 = N[(N[(b + N[(N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]}, N[(c$95$s * If[LessEqual[t$95$1, -2e-245], t$95$1, If[LessEqual[t$95$1, 0.0], N[(N[(1.0 / z), $MachinePrecision] * N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, Infinity], N[(N[(b + N[(N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision] - N[(N[(z * 4.0), $MachinePrecision] * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision], N[(t * N[(-4.0 * N[(a / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]), $MachinePrecision]]

Derivation

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

Alternative 7: 72.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} c_m = \left|c\right| \\ c_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := 9 \cdot \left(y \cdot \frac{x}{c_m \cdot z}\right) - 4 \cdot \left(t \cdot \frac{a}{c_m}\right)\\ c_s \cdot \begin{array}{l} \mathbf{if}\;t \leq -165000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -4.7 \cdot 10^{-11}:\\ \;\;\;\;\frac{b - 4 \cdot \left(a \cdot \left(z \cdot t\right)\right)}{c_m \cdot z}\\ \mathbf{elif}\;t \leq -7.1 \cdot 10^{-99} \lor \neg \left(t \leq 8 \cdot 10^{-73}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{z} \cdot \frac{b + 9 \cdot \left(x \cdot y\right)}{c_m}\\ \end{array} \end{array} \end{array} \]

FPCore

c_m = (fabs.f64 c)
c_s = (copysign.f64 1 c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (let* ((t_1 (- (* 9.0 (* y (/ x (* c_m z)))) (* 4.0 (* t (/ a c_m))))))
   (*
    c_s
    (if (<= t -165000000.0)
      t_1
      (if (<= t -4.7e-11)
        (/ (- b (* 4.0 (* a (* z t)))) (* c_m z))
        (if (or (<= t -7.1e-99) (not (<= t 8e-73)))
          t_1
          (* (/ 1.0 z) (/ (+ b (* 9.0 (* x y))) c_m))))))))

C

c_m = fabs(c);
c_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double t_1 = (9.0 * (y * (x / (c_m * z)))) - (4.0 * (t * (a / c_m)));
	double tmp;
	if (t <= -165000000.0) {
		tmp = t_1;
	} else if (t <= -4.7e-11) {
		tmp = (b - (4.0 * (a * (z * t)))) / (c_m * z);
	} else if ((t <= -7.1e-99) || !(t <= 8e-73)) {
		tmp = t_1;
	} else {
		tmp = (1.0 / z) * ((b + (9.0 * (x * y))) / c_m);
	}
	return c_s * tmp;
}

Fortran

c_m = abs(c)
c_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    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), intent (in) :: c_m
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (9.0d0 * (y * (x / (c_m * z)))) - (4.0d0 * (t * (a / c_m)))
    if (t <= (-165000000.0d0)) then
        tmp = t_1
    else if (t <= (-4.7d-11)) then
        tmp = (b - (4.0d0 * (a * (z * t)))) / (c_m * z)
    else if ((t <= (-7.1d-99)) .or. (.not. (t <= 8d-73))) then
        tmp = t_1
    else
        tmp = (1.0d0 / z) * ((b + (9.0d0 * (x * y))) / c_m)
    end if
    code = c_s * tmp
end function

Java

c_m = Math.abs(c);
c_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double t_1 = (9.0 * (y * (x / (c_m * z)))) - (4.0 * (t * (a / c_m)));
	double tmp;
	if (t <= -165000000.0) {
		tmp = t_1;
	} else if (t <= -4.7e-11) {
		tmp = (b - (4.0 * (a * (z * t)))) / (c_m * z);
	} else if ((t <= -7.1e-99) || !(t <= 8e-73)) {
		tmp = t_1;
	} else {
		tmp = (1.0 / z) * ((b + (9.0 * (x * y))) / c_m);
	}
	return c_s * tmp;
}

Python

c_m = math.fabs(c)
c_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	t_1 = (9.0 * (y * (x / (c_m * z)))) - (4.0 * (t * (a / c_m)))
	tmp = 0
	if t <= -165000000.0:
		tmp = t_1
	elif t <= -4.7e-11:
		tmp = (b - (4.0 * (a * (z * t)))) / (c_m * z)
	elif (t <= -7.1e-99) or not (t <= 8e-73):
		tmp = t_1
	else:
		tmp = (1.0 / z) * ((b + (9.0 * (x * y))) / c_m)
	return c_s * tmp

Julia

c_m = abs(c)
c_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	t_1 = Float64(Float64(9.0 * Float64(y * Float64(x / Float64(c_m * z)))) - Float64(4.0 * Float64(t * Float64(a / c_m))))
	tmp = 0.0
	if (t <= -165000000.0)
		tmp = t_1;
	elseif (t <= -4.7e-11)
		tmp = Float64(Float64(b - Float64(4.0 * Float64(a * Float64(z * t)))) / Float64(c_m * z));
	elseif ((t <= -7.1e-99) || !(t <= 8e-73))
		tmp = t_1;
	else
		tmp = Float64(Float64(1.0 / z) * Float64(Float64(b + Float64(9.0 * Float64(x * y))) / c_m));
	end
	return Float64(c_s * tmp)
end

MATLAB

c_m = abs(c);
c_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	t_1 = (9.0 * (y * (x / (c_m * z)))) - (4.0 * (t * (a / c_m)));
	tmp = 0.0;
	if (t <= -165000000.0)
		tmp = t_1;
	elseif (t <= -4.7e-11)
		tmp = (b - (4.0 * (a * (z * t)))) / (c_m * z);
	elseif ((t <= -7.1e-99) || ~((t <= 8e-73)))
		tmp = t_1;
	else
		tmp = (1.0 / z) * ((b + (9.0 * (x * y))) / c_m);
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c_m = N[Abs[c], $MachinePrecision]
c_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := Block[{t$95$1 = N[(N[(9.0 * N[(y * N[(x / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(t * N[(a / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(c$95$s * If[LessEqual[t, -165000000.0], t$95$1, If[LessEqual[t, -4.7e-11], N[(N[(b - N[(4.0 * N[(a * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, -7.1e-99], N[Not[LessEqual[t, 8e-73]], $MachinePrecision]], t$95$1, N[(N[(1.0 / z), $MachinePrecision] * N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision]]]]), $MachinePrecision]]

Derivation

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

Alternative 8: 86.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} c_m = \left|c\right| \\ c_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+116}:\\ \;\;\;\;\left(\frac{b}{c_m \cdot z} + 9 \cdot \frac{x \cdot y}{c_m \cdot z}\right) - 4 \cdot \frac{t \cdot a}{c_m}\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{+112}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c_m \cdot z}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(y \cdot \frac{x}{c_m \cdot z}\right) - 4 \cdot \left(t \cdot \frac{a}{c_m}\right)\\ \end{array} \end{array} \]

FPCore

c_m = (fabs.f64 c)
c_s = (copysign.f64 1 c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (*
  c_s
  (if (<= z -2e+116)
    (-
     (+ (/ b (* c_m z)) (* 9.0 (/ (* x y) (* c_m z))))
     (* 4.0 (/ (* t a) c_m)))
    (if (<= z 7.6e+112)
      (/ (+ b (- (* y (* x 9.0)) (* a (* t (* z 4.0))))) (* c_m z))
      (- (* 9.0 (* y (/ x (* c_m z)))) (* 4.0 (* t (/ a c_m))))))))

C

c_m = fabs(c);
c_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (z <= -2e+116) {
		tmp = ((b / (c_m * z)) + (9.0 * ((x * y) / (c_m * z)))) - (4.0 * ((t * a) / c_m));
	} else if (z <= 7.6e+112) {
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (c_m * z);
	} else {
		tmp = (9.0 * (y * (x / (c_m * z)))) - (4.0 * (t * (a / c_m)));
	}
	return c_s * tmp;
}

Fortran

c_m = abs(c)
c_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    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), intent (in) :: c_m
    real(8) :: tmp
    if (z <= (-2d+116)) then
        tmp = ((b / (c_m * z)) + (9.0d0 * ((x * y) / (c_m * z)))) - (4.0d0 * ((t * a) / c_m))
    else if (z <= 7.6d+112) then
        tmp = (b + ((y * (x * 9.0d0)) - (a * (t * (z * 4.0d0))))) / (c_m * z)
    else
        tmp = (9.0d0 * (y * (x / (c_m * z)))) - (4.0d0 * (t * (a / c_m)))
    end if
    code = c_s * tmp
end function

Java

c_m = Math.abs(c);
c_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (z <= -2e+116) {
		tmp = ((b / (c_m * z)) + (9.0 * ((x * y) / (c_m * z)))) - (4.0 * ((t * a) / c_m));
	} else if (z <= 7.6e+112) {
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (c_m * z);
	} else {
		tmp = (9.0 * (y * (x / (c_m * z)))) - (4.0 * (t * (a / c_m)));
	}
	return c_s * tmp;
}

Python

c_m = math.fabs(c)
c_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	tmp = 0
	if z <= -2e+116:
		tmp = ((b / (c_m * z)) + (9.0 * ((x * y) / (c_m * z)))) - (4.0 * ((t * a) / c_m))
	elif z <= 7.6e+112:
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (c_m * z)
	else:
		tmp = (9.0 * (y * (x / (c_m * z)))) - (4.0 * (t * (a / c_m)))
	return c_s * tmp

Julia

c_m = abs(c)
c_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if (z <= -2e+116)
		tmp = Float64(Float64(Float64(b / Float64(c_m * z)) + Float64(9.0 * Float64(Float64(x * y) / Float64(c_m * z)))) - Float64(4.0 * Float64(Float64(t * a) / c_m)));
	elseif (z <= 7.6e+112)
		tmp = Float64(Float64(b + Float64(Float64(y * Float64(x * 9.0)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(c_m * z));
	else
		tmp = Float64(Float64(9.0 * Float64(y * Float64(x / Float64(c_m * z)))) - Float64(4.0 * Float64(t * Float64(a / c_m))));
	end
	return Float64(c_s * tmp)
end

MATLAB

c_m = abs(c);
c_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0;
	if (z <= -2e+116)
		tmp = ((b / (c_m * z)) + (9.0 * ((x * y) / (c_m * z)))) - (4.0 * ((t * a) / c_m));
	elseif (z <= 7.6e+112)
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (c_m * z);
	else
		tmp = (9.0 * (y * (x / (c_m * z)))) - (4.0 * (t * (a / c_m)));
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c_m = N[Abs[c], $MachinePrecision]
c_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[LessEqual[z, -2e+116], N[(N[(N[(b / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision] + N[(9.0 * N[(N[(x * y), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(N[(t * a), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.6e+112], N[(N[(b + N[(N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision], N[(N[(9.0 * N[(y * N[(x / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(t * N[(a / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

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

Alternative 9: 63.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} c_m = \left|c\right| \\ c_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := \frac{b + 9 \cdot \left(x \cdot y\right)}{c_m \cdot z}\\ t_2 := t \cdot \left(-4 \cdot \frac{a}{c_m}\right)\\ c_s \cdot \begin{array}{l} \mathbf{if}\;a \leq -1 \cdot 10^{-77}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 0.36:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 26000000000000:\\ \;\;\;\;\frac{-4 \cdot t}{\frac{c_m}{a}}\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{+104}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{+223}:\\ \;\;\;\;\frac{-4 \cdot a}{\frac{c_m}{t}}\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{+264}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \end{array} \]

FPCore

c_m = (fabs.f64 c)
c_s = (copysign.f64 1 c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (let* ((t_1 (/ (+ b (* 9.0 (* x y))) (* c_m z)))
        (t_2 (* t (* -4.0 (/ a c_m)))))
   (*
    c_s
    (if (<= a -1e-77)
      t_2
      (if (<= a 0.36)
        t_1
        (if (<= a 26000000000000.0)
          (/ (* -4.0 t) (/ c_m a))
          (if (<= a 3.2e+104)
            t_1
            (if (<= a 6.5e+223)
              (/ (* -4.0 a) (/ c_m t))
              (if (<= a 2.4e+264) t_1 t_2)))))))))

C

c_m = fabs(c);
c_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double t_1 = (b + (9.0 * (x * y))) / (c_m * z);
	double t_2 = t * (-4.0 * (a / c_m));
	double tmp;
	if (a <= -1e-77) {
		tmp = t_2;
	} else if (a <= 0.36) {
		tmp = t_1;
	} else if (a <= 26000000000000.0) {
		tmp = (-4.0 * t) / (c_m / a);
	} else if (a <= 3.2e+104) {
		tmp = t_1;
	} else if (a <= 6.5e+223) {
		tmp = (-4.0 * a) / (c_m / t);
	} else if (a <= 2.4e+264) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return c_s * tmp;
}

Fortran

c_m = abs(c)
c_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    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), intent (in) :: c_m
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (b + (9.0d0 * (x * y))) / (c_m * z)
    t_2 = t * ((-4.0d0) * (a / c_m))
    if (a <= (-1d-77)) then
        tmp = t_2
    else if (a <= 0.36d0) then
        tmp = t_1
    else if (a <= 26000000000000.0d0) then
        tmp = ((-4.0d0) * t) / (c_m / a)
    else if (a <= 3.2d+104) then
        tmp = t_1
    else if (a <= 6.5d+223) then
        tmp = ((-4.0d0) * a) / (c_m / t)
    else if (a <= 2.4d+264) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = c_s * tmp
end function

Java

c_m = Math.abs(c);
c_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double t_1 = (b + (9.0 * (x * y))) / (c_m * z);
	double t_2 = t * (-4.0 * (a / c_m));
	double tmp;
	if (a <= -1e-77) {
		tmp = t_2;
	} else if (a <= 0.36) {
		tmp = t_1;
	} else if (a <= 26000000000000.0) {
		tmp = (-4.0 * t) / (c_m / a);
	} else if (a <= 3.2e+104) {
		tmp = t_1;
	} else if (a <= 6.5e+223) {
		tmp = (-4.0 * a) / (c_m / t);
	} else if (a <= 2.4e+264) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return c_s * tmp;
}

Python

c_m = math.fabs(c)
c_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	t_1 = (b + (9.0 * (x * y))) / (c_m * z)
	t_2 = t * (-4.0 * (a / c_m))
	tmp = 0
	if a <= -1e-77:
		tmp = t_2
	elif a <= 0.36:
		tmp = t_1
	elif a <= 26000000000000.0:
		tmp = (-4.0 * t) / (c_m / a)
	elif a <= 3.2e+104:
		tmp = t_1
	elif a <= 6.5e+223:
		tmp = (-4.0 * a) / (c_m / t)
	elif a <= 2.4e+264:
		tmp = t_1
	else:
		tmp = t_2
	return c_s * tmp

Julia

c_m = abs(c)
c_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	t_1 = Float64(Float64(b + Float64(9.0 * Float64(x * y))) / Float64(c_m * z))
	t_2 = Float64(t * Float64(-4.0 * Float64(a / c_m)))
	tmp = 0.0
	if (a <= -1e-77)
		tmp = t_2;
	elseif (a <= 0.36)
		tmp = t_1;
	elseif (a <= 26000000000000.0)
		tmp = Float64(Float64(-4.0 * t) / Float64(c_m / a));
	elseif (a <= 3.2e+104)
		tmp = t_1;
	elseif (a <= 6.5e+223)
		tmp = Float64(Float64(-4.0 * a) / Float64(c_m / t));
	elseif (a <= 2.4e+264)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return Float64(c_s * tmp)
end

MATLAB

c_m = abs(c);
c_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	t_1 = (b + (9.0 * (x * y))) / (c_m * z);
	t_2 = t * (-4.0 * (a / c_m));
	tmp = 0.0;
	if (a <= -1e-77)
		tmp = t_2;
	elseif (a <= 0.36)
		tmp = t_1;
	elseif (a <= 26000000000000.0)
		tmp = (-4.0 * t) / (c_m / a);
	elseif (a <= 3.2e+104)
		tmp = t_1;
	elseif (a <= 6.5e+223)
		tmp = (-4.0 * a) / (c_m / t);
	elseif (a <= 2.4e+264)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c_m = N[Abs[c], $MachinePrecision]
c_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := Block[{t$95$1 = N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(-4.0 * N[(a / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(c$95$s * If[LessEqual[a, -1e-77], t$95$2, If[LessEqual[a, 0.36], t$95$1, If[LessEqual[a, 26000000000000.0], N[(N[(-4.0 * t), $MachinePrecision] / N[(c$95$m / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.2e+104], t$95$1, If[LessEqual[a, 6.5e+223], N[(N[(-4.0 * a), $MachinePrecision] / N[(c$95$m / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.4e+264], t$95$1, t$95$2]]]]]]), $MachinePrecision]]]

Derivation

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

Alternative 10: 84.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} c_m = \left|c\right| \\ c_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+132} \lor \neg \left(z \leq 1.8 \cdot 10^{+117}\right):\\ \;\;\;\;9 \cdot \left(y \cdot \frac{x}{c_m \cdot z}\right) - 4 \cdot \left(t \cdot \frac{a}{c_m}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right)}{c_m \cdot z}\\ \end{array} \end{array} \]

FPCore

c_m = (fabs.f64 c)
c_s = (copysign.f64 1 c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (*
  c_s
  (if (or (<= z -8.5e+132) (not (<= z 1.8e+117)))
    (- (* 9.0 (* y (/ x (* c_m z)))) (* 4.0 (* t (/ a c_m))))
    (/ (+ b (- (* x (* 9.0 y)) (* (* z 4.0) (* t a)))) (* c_m z)))))

C

c_m = fabs(c);
c_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if ((z <= -8.5e+132) || !(z <= 1.8e+117)) {
		tmp = (9.0 * (y * (x / (c_m * z)))) - (4.0 * (t * (a / c_m)));
	} else {
		tmp = (b + ((x * (9.0 * y)) - ((z * 4.0) * (t * a)))) / (c_m * z);
	}
	return c_s * tmp;
}

Fortran

c_m = abs(c)
c_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    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), intent (in) :: c_m
    real(8) :: tmp
    if ((z <= (-8.5d+132)) .or. (.not. (z <= 1.8d+117))) then
        tmp = (9.0d0 * (y * (x / (c_m * z)))) - (4.0d0 * (t * (a / c_m)))
    else
        tmp = (b + ((x * (9.0d0 * y)) - ((z * 4.0d0) * (t * a)))) / (c_m * z)
    end if
    code = c_s * tmp
end function

Java

c_m = Math.abs(c);
c_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if ((z <= -8.5e+132) || !(z <= 1.8e+117)) {
		tmp = (9.0 * (y * (x / (c_m * z)))) - (4.0 * (t * (a / c_m)));
	} else {
		tmp = (b + ((x * (9.0 * y)) - ((z * 4.0) * (t * a)))) / (c_m * z);
	}
	return c_s * tmp;
}

Python

c_m = math.fabs(c)
c_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	tmp = 0
	if (z <= -8.5e+132) or not (z <= 1.8e+117):
		tmp = (9.0 * (y * (x / (c_m * z)))) - (4.0 * (t * (a / c_m)))
	else:
		tmp = (b + ((x * (9.0 * y)) - ((z * 4.0) * (t * a)))) / (c_m * z)
	return c_s * tmp

Julia

c_m = abs(c)
c_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if ((z <= -8.5e+132) || !(z <= 1.8e+117))
		tmp = Float64(Float64(9.0 * Float64(y * Float64(x / Float64(c_m * z)))) - Float64(4.0 * Float64(t * Float64(a / c_m))));
	else
		tmp = Float64(Float64(b + Float64(Float64(x * Float64(9.0 * y)) - Float64(Float64(z * 4.0) * Float64(t * a)))) / Float64(c_m * z));
	end
	return Float64(c_s * tmp)
end

MATLAB

c_m = abs(c);
c_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0;
	if ((z <= -8.5e+132) || ~((z <= 1.8e+117)))
		tmp = (9.0 * (y * (x / (c_m * z)))) - (4.0 * (t * (a / c_m)));
	else
		tmp = (b + ((x * (9.0 * y)) - ((z * 4.0) * (t * a)))) / (c_m * z);
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c_m = N[Abs[c], $MachinePrecision]
c_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[Or[LessEqual[z, -8.5e+132], N[Not[LessEqual[z, 1.8e+117]], $MachinePrecision]], N[(N[(9.0 * N[(y * N[(x / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(t * N[(a / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b + N[(N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision] - N[(N[(z * 4.0), $MachinePrecision] * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

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

Alternative 11: 49.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} c_m = \left|c\right| \\ c_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := 9 \cdot \left(y \cdot \frac{x}{c_m \cdot z}\right)\\ t_2 := t \cdot \left(-4 \cdot \frac{a}{c_m}\right)\\ c_s \cdot \begin{array}{l} \mathbf{if}\;a \leq -1.85 \cdot 10^{-79}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{-157}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{-91}:\\ \;\;\;\;\frac{\frac{b}{c_m}}{z}\\ \mathbf{elif}\;a \leq 108:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.42 \cdot 10^{+49}:\\ \;\;\;\;b \cdot \frac{1}{c_m \cdot z}\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{+51}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \end{array} \]

FPCore

c_m = (fabs.f64 c)
c_s = (copysign.f64 1 c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (let* ((t_1 (* 9.0 (* y (/ x (* c_m z))))) (t_2 (* t (* -4.0 (/ a c_m)))))
   (*
    c_s
    (if (<= a -1.85e-79)
      t_2
      (if (<= a 6.2e-157)
        t_1
        (if (<= a 7.5e-91)
          (/ (/ b c_m) z)
          (if (<= a 108.0)
            t_1
            (if (<= a 1.42e+49)
              (* b (/ 1.0 (* c_m z)))
              (if (<= a 4.8e+51) t_1 t_2)))))))))

C

c_m = fabs(c);
c_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double t_1 = 9.0 * (y * (x / (c_m * z)));
	double t_2 = t * (-4.0 * (a / c_m));
	double tmp;
	if (a <= -1.85e-79) {
		tmp = t_2;
	} else if (a <= 6.2e-157) {
		tmp = t_1;
	} else if (a <= 7.5e-91) {
		tmp = (b / c_m) / z;
	} else if (a <= 108.0) {
		tmp = t_1;
	} else if (a <= 1.42e+49) {
		tmp = b * (1.0 / (c_m * z));
	} else if (a <= 4.8e+51) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return c_s * tmp;
}

Fortran

c_m = abs(c)
c_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    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), intent (in) :: c_m
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 9.0d0 * (y * (x / (c_m * z)))
    t_2 = t * ((-4.0d0) * (a / c_m))
    if (a <= (-1.85d-79)) then
        tmp = t_2
    else if (a <= 6.2d-157) then
        tmp = t_1
    else if (a <= 7.5d-91) then
        tmp = (b / c_m) / z
    else if (a <= 108.0d0) then
        tmp = t_1
    else if (a <= 1.42d+49) then
        tmp = b * (1.0d0 / (c_m * z))
    else if (a <= 4.8d+51) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = c_s * tmp
end function

Java

c_m = Math.abs(c);
c_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double t_1 = 9.0 * (y * (x / (c_m * z)));
	double t_2 = t * (-4.0 * (a / c_m));
	double tmp;
	if (a <= -1.85e-79) {
		tmp = t_2;
	} else if (a <= 6.2e-157) {
		tmp = t_1;
	} else if (a <= 7.5e-91) {
		tmp = (b / c_m) / z;
	} else if (a <= 108.0) {
		tmp = t_1;
	} else if (a <= 1.42e+49) {
		tmp = b * (1.0 / (c_m * z));
	} else if (a <= 4.8e+51) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return c_s * tmp;
}

Python

c_m = math.fabs(c)
c_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	t_1 = 9.0 * (y * (x / (c_m * z)))
	t_2 = t * (-4.0 * (a / c_m))
	tmp = 0
	if a <= -1.85e-79:
		tmp = t_2
	elif a <= 6.2e-157:
		tmp = t_1
	elif a <= 7.5e-91:
		tmp = (b / c_m) / z
	elif a <= 108.0:
		tmp = t_1
	elif a <= 1.42e+49:
		tmp = b * (1.0 / (c_m * z))
	elif a <= 4.8e+51:
		tmp = t_1
	else:
		tmp = t_2
	return c_s * tmp

Julia

c_m = abs(c)
c_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	t_1 = Float64(9.0 * Float64(y * Float64(x / Float64(c_m * z))))
	t_2 = Float64(t * Float64(-4.0 * Float64(a / c_m)))
	tmp = 0.0
	if (a <= -1.85e-79)
		tmp = t_2;
	elseif (a <= 6.2e-157)
		tmp = t_1;
	elseif (a <= 7.5e-91)
		tmp = Float64(Float64(b / c_m) / z);
	elseif (a <= 108.0)
		tmp = t_1;
	elseif (a <= 1.42e+49)
		tmp = Float64(b * Float64(1.0 / Float64(c_m * z)));
	elseif (a <= 4.8e+51)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return Float64(c_s * tmp)
end

MATLAB

c_m = abs(c);
c_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	t_1 = 9.0 * (y * (x / (c_m * z)));
	t_2 = t * (-4.0 * (a / c_m));
	tmp = 0.0;
	if (a <= -1.85e-79)
		tmp = t_2;
	elseif (a <= 6.2e-157)
		tmp = t_1;
	elseif (a <= 7.5e-91)
		tmp = (b / c_m) / z;
	elseif (a <= 108.0)
		tmp = t_1;
	elseif (a <= 1.42e+49)
		tmp = b * (1.0 / (c_m * z));
	elseif (a <= 4.8e+51)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c_m = N[Abs[c], $MachinePrecision]
c_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := Block[{t$95$1 = N[(9.0 * N[(y * N[(x / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(-4.0 * N[(a / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(c$95$s * If[LessEqual[a, -1.85e-79], t$95$2, If[LessEqual[a, 6.2e-157], t$95$1, If[LessEqual[a, 7.5e-91], N[(N[(b / c$95$m), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[a, 108.0], t$95$1, If[LessEqual[a, 1.42e+49], N[(b * N[(1.0 / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.8e+51], t$95$1, t$95$2]]]]]]), $MachinePrecision]]]

Derivation

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

Alternative 12: 71.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} c_m = \left|c\right| \\ c_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c_s \cdot \begin{array}{l} \mathbf{if}\;b \leq -7.5 \cdot 10^{-80} \lor \neg \left(b \leq 5 \cdot 10^{+61}\right):\\ \;\;\;\;\frac{b - 4 \cdot \left(a \cdot \left(z \cdot t\right)\right)}{c_m \cdot z}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \frac{x \cdot y}{c_m \cdot z} + -4 \cdot \frac{t \cdot a}{c_m}\\ \end{array} \end{array} \]

FPCore

c_m = (fabs.f64 c)
c_s = (copysign.f64 1 c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (*
  c_s
  (if (or (<= b -7.5e-80) (not (<= b 5e+61)))
    (/ (- b (* 4.0 (* a (* z t)))) (* c_m z))
    (+ (* 9.0 (/ (* x y) (* c_m z))) (* -4.0 (/ (* t a) c_m))))))

C

c_m = fabs(c);
c_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if ((b <= -7.5e-80) || !(b <= 5e+61)) {
		tmp = (b - (4.0 * (a * (z * t)))) / (c_m * z);
	} else {
		tmp = (9.0 * ((x * y) / (c_m * z))) + (-4.0 * ((t * a) / c_m));
	}
	return c_s * tmp;
}

Fortran

c_m = abs(c)
c_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    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), intent (in) :: c_m
    real(8) :: tmp
    if ((b <= (-7.5d-80)) .or. (.not. (b <= 5d+61))) then
        tmp = (b - (4.0d0 * (a * (z * t)))) / (c_m * z)
    else
        tmp = (9.0d0 * ((x * y) / (c_m * z))) + ((-4.0d0) * ((t * a) / c_m))
    end if
    code = c_s * tmp
end function

Java

c_m = Math.abs(c);
c_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if ((b <= -7.5e-80) || !(b <= 5e+61)) {
		tmp = (b - (4.0 * (a * (z * t)))) / (c_m * z);
	} else {
		tmp = (9.0 * ((x * y) / (c_m * z))) + (-4.0 * ((t * a) / c_m));
	}
	return c_s * tmp;
}

Python

c_m = math.fabs(c)
c_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	tmp = 0
	if (b <= -7.5e-80) or not (b <= 5e+61):
		tmp = (b - (4.0 * (a * (z * t)))) / (c_m * z)
	else:
		tmp = (9.0 * ((x * y) / (c_m * z))) + (-4.0 * ((t * a) / c_m))
	return c_s * tmp

Julia

c_m = abs(c)
c_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if ((b <= -7.5e-80) || !(b <= 5e+61))
		tmp = Float64(Float64(b - Float64(4.0 * Float64(a * Float64(z * t)))) / Float64(c_m * z));
	else
		tmp = Float64(Float64(9.0 * Float64(Float64(x * y) / Float64(c_m * z))) + Float64(-4.0 * Float64(Float64(t * a) / c_m)));
	end
	return Float64(c_s * tmp)
end

MATLAB

c_m = abs(c);
c_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0;
	if ((b <= -7.5e-80) || ~((b <= 5e+61)))
		tmp = (b - (4.0 * (a * (z * t)))) / (c_m * z);
	else
		tmp = (9.0 * ((x * y) / (c_m * z))) + (-4.0 * ((t * a) / c_m));
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c_m = N[Abs[c], $MachinePrecision]
c_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[Or[LessEqual[b, -7.5e-80], N[Not[LessEqual[b, 5e+61]], $MachinePrecision]], N[(N[(b - N[(4.0 * N[(a * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision], N[(N[(9.0 * N[(N[(x * y), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * N[(N[(t * a), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

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

Alternative 13: 48.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} c_m = \left|c\right| \\ c_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -1.14 \cdot 10^{+30}:\\ \;\;\;\;9 \cdot \left(\frac{y}{c_m} \cdot \frac{x}{z}\right)\\ \mathbf{elif}\;y \leq -9.8 \cdot 10^{-262}:\\ \;\;\;\;\frac{-4 \cdot t}{\frac{c_m}{a}}\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-252}:\\ \;\;\;\;\frac{\frac{b}{z}}{c_m}\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{-16}:\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c_m}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(y \cdot \frac{x}{c_m \cdot z}\right)\\ \end{array} \end{array} \]

FPCore

c_m = (fabs.f64 c)
c_s = (copysign.f64 1 c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (*
  c_s
  (if (<= y -1.14e+30)
    (* 9.0 (* (/ y c_m) (/ x z)))
    (if (<= y -9.8e-262)
      (/ (* -4.0 t) (/ c_m a))
      (if (<= y 6.5e-252)
        (/ (/ b z) c_m)
        (if (<= y 3.3e-16)
          (* -4.0 (/ (* t a) c_m))
          (* 9.0 (* y (/ x (* c_m z))))))))))

C

c_m = fabs(c);
c_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (y <= -1.14e+30) {
		tmp = 9.0 * ((y / c_m) * (x / z));
	} else if (y <= -9.8e-262) {
		tmp = (-4.0 * t) / (c_m / a);
	} else if (y <= 6.5e-252) {
		tmp = (b / z) / c_m;
	} else if (y <= 3.3e-16) {
		tmp = -4.0 * ((t * a) / c_m);
	} else {
		tmp = 9.0 * (y * (x / (c_m * z)));
	}
	return c_s * tmp;
}

Fortran

c_m = abs(c)
c_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    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), intent (in) :: c_m
    real(8) :: tmp
    if (y <= (-1.14d+30)) then
        tmp = 9.0d0 * ((y / c_m) * (x / z))
    else if (y <= (-9.8d-262)) then
        tmp = ((-4.0d0) * t) / (c_m / a)
    else if (y <= 6.5d-252) then
        tmp = (b / z) / c_m
    else if (y <= 3.3d-16) then
        tmp = (-4.0d0) * ((t * a) / c_m)
    else
        tmp = 9.0d0 * (y * (x / (c_m * z)))
    end if
    code = c_s * tmp
end function

Java

c_m = Math.abs(c);
c_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (y <= -1.14e+30) {
		tmp = 9.0 * ((y / c_m) * (x / z));
	} else if (y <= -9.8e-262) {
		tmp = (-4.0 * t) / (c_m / a);
	} else if (y <= 6.5e-252) {
		tmp = (b / z) / c_m;
	} else if (y <= 3.3e-16) {
		tmp = -4.0 * ((t * a) / c_m);
	} else {
		tmp = 9.0 * (y * (x / (c_m * z)));
	}
	return c_s * tmp;
}

Python

c_m = math.fabs(c)
c_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	tmp = 0
	if y <= -1.14e+30:
		tmp = 9.0 * ((y / c_m) * (x / z))
	elif y <= -9.8e-262:
		tmp = (-4.0 * t) / (c_m / a)
	elif y <= 6.5e-252:
		tmp = (b / z) / c_m
	elif y <= 3.3e-16:
		tmp = -4.0 * ((t * a) / c_m)
	else:
		tmp = 9.0 * (y * (x / (c_m * z)))
	return c_s * tmp

Julia

c_m = abs(c)
c_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if (y <= -1.14e+30)
		tmp = Float64(9.0 * Float64(Float64(y / c_m) * Float64(x / z)));
	elseif (y <= -9.8e-262)
		tmp = Float64(Float64(-4.0 * t) / Float64(c_m / a));
	elseif (y <= 6.5e-252)
		tmp = Float64(Float64(b / z) / c_m);
	elseif (y <= 3.3e-16)
		tmp = Float64(-4.0 * Float64(Float64(t * a) / c_m));
	else
		tmp = Float64(9.0 * Float64(y * Float64(x / Float64(c_m * z))));
	end
	return Float64(c_s * tmp)
end

MATLAB

c_m = abs(c);
c_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0;
	if (y <= -1.14e+30)
		tmp = 9.0 * ((y / c_m) * (x / z));
	elseif (y <= -9.8e-262)
		tmp = (-4.0 * t) / (c_m / a);
	elseif (y <= 6.5e-252)
		tmp = (b / z) / c_m;
	elseif (y <= 3.3e-16)
		tmp = -4.0 * ((t * a) / c_m);
	else
		tmp = 9.0 * (y * (x / (c_m * z)));
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c_m = N[Abs[c], $MachinePrecision]
c_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[LessEqual[y, -1.14e+30], N[(9.0 * N[(N[(y / c$95$m), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -9.8e-262], N[(N[(-4.0 * t), $MachinePrecision] / N[(c$95$m / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.5e-252], N[(N[(b / z), $MachinePrecision] / c$95$m), $MachinePrecision], If[LessEqual[y, 3.3e-16], N[(-4.0 * N[(N[(t * a), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision], N[(9.0 * N[(y * N[(x / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]), $MachinePrecision]

Derivation

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

Alternative 14: 50.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} c_m = \left|c\right| \\ c_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := 9 \cdot \left(\frac{x}{c_m} \cdot \frac{y}{z}\right)\\ t_2 := t \cdot \left(-4 \cdot \frac{a}{c_m}\right)\\ c_s \cdot \begin{array}{l} \mathbf{if}\;a \leq -1.05 \cdot 10^{-79}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -4 \cdot 10^{-219}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{-270}:\\ \;\;\;\;\frac{b}{c_m \cdot z}\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{+51}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \end{array} \]

FPCore

c_m = (fabs.f64 c)
c_s = (copysign.f64 1 c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (let* ((t_1 (* 9.0 (* (/ x c_m) (/ y z)))) (t_2 (* t (* -4.0 (/ a c_m)))))
   (*
    c_s
    (if (<= a -1.05e-79)
      t_2
      (if (<= a -4e-219)
        t_1
        (if (<= a 1.55e-270) (/ b (* c_m z)) (if (<= a 3.2e+51) t_1 t_2)))))))

C

c_m = fabs(c);
c_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double t_1 = 9.0 * ((x / c_m) * (y / z));
	double t_2 = t * (-4.0 * (a / c_m));
	double tmp;
	if (a <= -1.05e-79) {
		tmp = t_2;
	} else if (a <= -4e-219) {
		tmp = t_1;
	} else if (a <= 1.55e-270) {
		tmp = b / (c_m * z);
	} else if (a <= 3.2e+51) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return c_s * tmp;
}

Fortran

c_m = abs(c)
c_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    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), intent (in) :: c_m
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 9.0d0 * ((x / c_m) * (y / z))
    t_2 = t * ((-4.0d0) * (a / c_m))
    if (a <= (-1.05d-79)) then
        tmp = t_2
    else if (a <= (-4d-219)) then
        tmp = t_1
    else if (a <= 1.55d-270) then
        tmp = b / (c_m * z)
    else if (a <= 3.2d+51) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = c_s * tmp
end function

Java

c_m = Math.abs(c);
c_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double t_1 = 9.0 * ((x / c_m) * (y / z));
	double t_2 = t * (-4.0 * (a / c_m));
	double tmp;
	if (a <= -1.05e-79) {
		tmp = t_2;
	} else if (a <= -4e-219) {
		tmp = t_1;
	} else if (a <= 1.55e-270) {
		tmp = b / (c_m * z);
	} else if (a <= 3.2e+51) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return c_s * tmp;
}

Python

c_m = math.fabs(c)
c_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	t_1 = 9.0 * ((x / c_m) * (y / z))
	t_2 = t * (-4.0 * (a / c_m))
	tmp = 0
	if a <= -1.05e-79:
		tmp = t_2
	elif a <= -4e-219:
		tmp = t_1
	elif a <= 1.55e-270:
		tmp = b / (c_m * z)
	elif a <= 3.2e+51:
		tmp = t_1
	else:
		tmp = t_2
	return c_s * tmp

Julia

c_m = abs(c)
c_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	t_1 = Float64(9.0 * Float64(Float64(x / c_m) * Float64(y / z)))
	t_2 = Float64(t * Float64(-4.0 * Float64(a / c_m)))
	tmp = 0.0
	if (a <= -1.05e-79)
		tmp = t_2;
	elseif (a <= -4e-219)
		tmp = t_1;
	elseif (a <= 1.55e-270)
		tmp = Float64(b / Float64(c_m * z));
	elseif (a <= 3.2e+51)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return Float64(c_s * tmp)
end

MATLAB

c_m = abs(c);
c_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	t_1 = 9.0 * ((x / c_m) * (y / z));
	t_2 = t * (-4.0 * (a / c_m));
	tmp = 0.0;
	if (a <= -1.05e-79)
		tmp = t_2;
	elseif (a <= -4e-219)
		tmp = t_1;
	elseif (a <= 1.55e-270)
		tmp = b / (c_m * z);
	elseif (a <= 3.2e+51)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c_m = N[Abs[c], $MachinePrecision]
c_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := Block[{t$95$1 = N[(9.0 * N[(N[(x / c$95$m), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(-4.0 * N[(a / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(c$95$s * If[LessEqual[a, -1.05e-79], t$95$2, If[LessEqual[a, -4e-219], t$95$1, If[LessEqual[a, 1.55e-270], N[(b / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.2e+51], t$95$1, t$95$2]]]]), $MachinePrecision]]]

Derivation

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

Alternative 15: 50.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} c_m = \left|c\right| \\ c_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := t \cdot \left(-4 \cdot \frac{a}{c_m}\right)\\ c_s \cdot \begin{array}{l} \mathbf{if}\;a \leq -1.3 \cdot 10^{-78}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -4.1 \cdot 10^{-219}:\\ \;\;\;\;\frac{1}{\frac{\frac{c_m}{x}}{y} \cdot \frac{z}{9}}\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{-270}:\\ \;\;\;\;\frac{b}{c_m \cdot z}\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{+51}:\\ \;\;\;\;9 \cdot \left(\frac{x}{c_m} \cdot \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \end{array} \]

FPCore

c_m = (fabs.f64 c)
c_s = (copysign.f64 1 c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (let* ((t_1 (* t (* -4.0 (/ a c_m)))))
   (*
    c_s
    (if (<= a -1.3e-78)
      t_1
      (if (<= a -4.1e-219)
        (/ 1.0 (* (/ (/ c_m x) y) (/ z 9.0)))
        (if (<= a 1.6e-270)
          (/ b (* c_m z))
          (if (<= a 3.2e+51) (* 9.0 (* (/ x c_m) (/ y z))) t_1)))))))

C

c_m = fabs(c);
c_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double t_1 = t * (-4.0 * (a / c_m));
	double tmp;
	if (a <= -1.3e-78) {
		tmp = t_1;
	} else if (a <= -4.1e-219) {
		tmp = 1.0 / (((c_m / x) / y) * (z / 9.0));
	} else if (a <= 1.6e-270) {
		tmp = b / (c_m * z);
	} else if (a <= 3.2e+51) {
		tmp = 9.0 * ((x / c_m) * (y / z));
	} else {
		tmp = t_1;
	}
	return c_s * tmp;
}

Fortran

c_m = abs(c)
c_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    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), intent (in) :: c_m
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((-4.0d0) * (a / c_m))
    if (a <= (-1.3d-78)) then
        tmp = t_1
    else if (a <= (-4.1d-219)) then
        tmp = 1.0d0 / (((c_m / x) / y) * (z / 9.0d0))
    else if (a <= 1.6d-270) then
        tmp = b / (c_m * z)
    else if (a <= 3.2d+51) then
        tmp = 9.0d0 * ((x / c_m) * (y / z))
    else
        tmp = t_1
    end if
    code = c_s * tmp
end function

Java

c_m = Math.abs(c);
c_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double t_1 = t * (-4.0 * (a / c_m));
	double tmp;
	if (a <= -1.3e-78) {
		tmp = t_1;
	} else if (a <= -4.1e-219) {
		tmp = 1.0 / (((c_m / x) / y) * (z / 9.0));
	} else if (a <= 1.6e-270) {
		tmp = b / (c_m * z);
	} else if (a <= 3.2e+51) {
		tmp = 9.0 * ((x / c_m) * (y / z));
	} else {
		tmp = t_1;
	}
	return c_s * tmp;
}

Python

c_m = math.fabs(c)
c_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	t_1 = t * (-4.0 * (a / c_m))
	tmp = 0
	if a <= -1.3e-78:
		tmp = t_1
	elif a <= -4.1e-219:
		tmp = 1.0 / (((c_m / x) / y) * (z / 9.0))
	elif a <= 1.6e-270:
		tmp = b / (c_m * z)
	elif a <= 3.2e+51:
		tmp = 9.0 * ((x / c_m) * (y / z))
	else:
		tmp = t_1
	return c_s * tmp

Julia

c_m = abs(c)
c_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	t_1 = Float64(t * Float64(-4.0 * Float64(a / c_m)))
	tmp = 0.0
	if (a <= -1.3e-78)
		tmp = t_1;
	elseif (a <= -4.1e-219)
		tmp = Float64(1.0 / Float64(Float64(Float64(c_m / x) / y) * Float64(z / 9.0)));
	elseif (a <= 1.6e-270)
		tmp = Float64(b / Float64(c_m * z));
	elseif (a <= 3.2e+51)
		tmp = Float64(9.0 * Float64(Float64(x / c_m) * Float64(y / z)));
	else
		tmp = t_1;
	end
	return Float64(c_s * tmp)
end

MATLAB

c_m = abs(c);
c_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	t_1 = t * (-4.0 * (a / c_m));
	tmp = 0.0;
	if (a <= -1.3e-78)
		tmp = t_1;
	elseif (a <= -4.1e-219)
		tmp = 1.0 / (((c_m / x) / y) * (z / 9.0));
	elseif (a <= 1.6e-270)
		tmp = b / (c_m * z);
	elseif (a <= 3.2e+51)
		tmp = 9.0 * ((x / c_m) * (y / z));
	else
		tmp = t_1;
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c_m = N[Abs[c], $MachinePrecision]
c_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := Block[{t$95$1 = N[(t * N[(-4.0 * N[(a / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(c$95$s * If[LessEqual[a, -1.3e-78], t$95$1, If[LessEqual[a, -4.1e-219], N[(1.0 / N[(N[(N[(c$95$m / x), $MachinePrecision] / y), $MachinePrecision] * N[(z / 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.6e-270], N[(b / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.2e+51], N[(9.0 * N[(N[(x / c$95$m), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]), $MachinePrecision]]

Derivation

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

Alternative 16: 64.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} c_m = \left|c\right| \\ c_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c_s \cdot \begin{array}{l} \mathbf{if}\;a \leq -1 \cdot 10^{-77} \lor \neg \left(a \leq 5.2 \cdot 10^{+104}\right):\\ \;\;\;\;t \cdot \left(-4 \cdot \frac{a}{c_m}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{z} \cdot \frac{b + 9 \cdot \left(x \cdot y\right)}{c_m}\\ \end{array} \end{array} \]

FPCore

c_m = (fabs.f64 c)
c_s = (copysign.f64 1 c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (*
  c_s
  (if (or (<= a -1e-77) (not (<= a 5.2e+104)))
    (* t (* -4.0 (/ a c_m)))
    (* (/ 1.0 z) (/ (+ b (* 9.0 (* x y))) c_m)))))

C

c_m = fabs(c);
c_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if ((a <= -1e-77) || !(a <= 5.2e+104)) {
		tmp = t * (-4.0 * (a / c_m));
	} else {
		tmp = (1.0 / z) * ((b + (9.0 * (x * y))) / c_m);
	}
	return c_s * tmp;
}

Fortran

c_m = abs(c)
c_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    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), intent (in) :: c_m
    real(8) :: tmp
    if ((a <= (-1d-77)) .or. (.not. (a <= 5.2d+104))) then
        tmp = t * ((-4.0d0) * (a / c_m))
    else
        tmp = (1.0d0 / z) * ((b + (9.0d0 * (x * y))) / c_m)
    end if
    code = c_s * tmp
end function

Java

c_m = Math.abs(c);
c_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if ((a <= -1e-77) || !(a <= 5.2e+104)) {
		tmp = t * (-4.0 * (a / c_m));
	} else {
		tmp = (1.0 / z) * ((b + (9.0 * (x * y))) / c_m);
	}
	return c_s * tmp;
}

Python

c_m = math.fabs(c)
c_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	tmp = 0
	if (a <= -1e-77) or not (a <= 5.2e+104):
		tmp = t * (-4.0 * (a / c_m))
	else:
		tmp = (1.0 / z) * ((b + (9.0 * (x * y))) / c_m)
	return c_s * tmp

Julia

c_m = abs(c)
c_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if ((a <= -1e-77) || !(a <= 5.2e+104))
		tmp = Float64(t * Float64(-4.0 * Float64(a / c_m)));
	else
		tmp = Float64(Float64(1.0 / z) * Float64(Float64(b + Float64(9.0 * Float64(x * y))) / c_m));
	end
	return Float64(c_s * tmp)
end

MATLAB

c_m = abs(c);
c_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0;
	if ((a <= -1e-77) || ~((a <= 5.2e+104)))
		tmp = t * (-4.0 * (a / c_m));
	else
		tmp = (1.0 / z) * ((b + (9.0 * (x * y))) / c_m);
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c_m = N[Abs[c], $MachinePrecision]
c_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[Or[LessEqual[a, -1e-77], N[Not[LessEqual[a, 5.2e+104]], $MachinePrecision]], N[(t * N[(-4.0 * N[(a / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 / z), $MachinePrecision] * N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

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

Alternative 17: 50.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} c_m = \left|c\right| \\ c_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := t \cdot \left(-4 \cdot \frac{a}{c_m}\right)\\ c_s \cdot \begin{array}{l} \mathbf{if}\;a \leq -8.3 \cdot 10^{-78}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 5.9 \cdot 10^{-49}:\\ \;\;\;\;b \cdot \frac{1}{c_m \cdot z}\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{+22}:\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c_m}\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{+51}:\\ \;\;\;\;\frac{\frac{b}{z}}{c_m}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \end{array} \]

FPCore

c_m = (fabs.f64 c)
c_s = (copysign.f64 1 c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (let* ((t_1 (* t (* -4.0 (/ a c_m)))))
   (*
    c_s
    (if (<= a -8.3e-78)
      t_1
      (if (<= a 5.9e-49)
        (* b (/ 1.0 (* c_m z)))
        (if (<= a 1.1e+22)
          (* -4.0 (/ (* t a) c_m))
          (if (<= a 6.8e+51) (/ (/ b z) c_m) t_1)))))))

C

c_m = fabs(c);
c_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double t_1 = t * (-4.0 * (a / c_m));
	double tmp;
	if (a <= -8.3e-78) {
		tmp = t_1;
	} else if (a <= 5.9e-49) {
		tmp = b * (1.0 / (c_m * z));
	} else if (a <= 1.1e+22) {
		tmp = -4.0 * ((t * a) / c_m);
	} else if (a <= 6.8e+51) {
		tmp = (b / z) / c_m;
	} else {
		tmp = t_1;
	}
	return c_s * tmp;
}

Fortran

c_m = abs(c)
c_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    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), intent (in) :: c_m
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((-4.0d0) * (a / c_m))
    if (a <= (-8.3d-78)) then
        tmp = t_1
    else if (a <= 5.9d-49) then
        tmp = b * (1.0d0 / (c_m * z))
    else if (a <= 1.1d+22) then
        tmp = (-4.0d0) * ((t * a) / c_m)
    else if (a <= 6.8d+51) then
        tmp = (b / z) / c_m
    else
        tmp = t_1
    end if
    code = c_s * tmp
end function

Java

c_m = Math.abs(c);
c_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double t_1 = t * (-4.0 * (a / c_m));
	double tmp;
	if (a <= -8.3e-78) {
		tmp = t_1;
	} else if (a <= 5.9e-49) {
		tmp = b * (1.0 / (c_m * z));
	} else if (a <= 1.1e+22) {
		tmp = -4.0 * ((t * a) / c_m);
	} else if (a <= 6.8e+51) {
		tmp = (b / z) / c_m;
	} else {
		tmp = t_1;
	}
	return c_s * tmp;
}

Python

c_m = math.fabs(c)
c_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	t_1 = t * (-4.0 * (a / c_m))
	tmp = 0
	if a <= -8.3e-78:
		tmp = t_1
	elif a <= 5.9e-49:
		tmp = b * (1.0 / (c_m * z))
	elif a <= 1.1e+22:
		tmp = -4.0 * ((t * a) / c_m)
	elif a <= 6.8e+51:
		tmp = (b / z) / c_m
	else:
		tmp = t_1
	return c_s * tmp

Julia

c_m = abs(c)
c_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	t_1 = Float64(t * Float64(-4.0 * Float64(a / c_m)))
	tmp = 0.0
	if (a <= -8.3e-78)
		tmp = t_1;
	elseif (a <= 5.9e-49)
		tmp = Float64(b * Float64(1.0 / Float64(c_m * z)));
	elseif (a <= 1.1e+22)
		tmp = Float64(-4.0 * Float64(Float64(t * a) / c_m));
	elseif (a <= 6.8e+51)
		tmp = Float64(Float64(b / z) / c_m);
	else
		tmp = t_1;
	end
	return Float64(c_s * tmp)
end

MATLAB

c_m = abs(c);
c_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	t_1 = t * (-4.0 * (a / c_m));
	tmp = 0.0;
	if (a <= -8.3e-78)
		tmp = t_1;
	elseif (a <= 5.9e-49)
		tmp = b * (1.0 / (c_m * z));
	elseif (a <= 1.1e+22)
		tmp = -4.0 * ((t * a) / c_m);
	elseif (a <= 6.8e+51)
		tmp = (b / z) / c_m;
	else
		tmp = t_1;
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c_m = N[Abs[c], $MachinePrecision]
c_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := Block[{t$95$1 = N[(t * N[(-4.0 * N[(a / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(c$95$s * If[LessEqual[a, -8.3e-78], t$95$1, If[LessEqual[a, 5.9e-49], N[(b * N[(1.0 / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.1e+22], N[(-4.0 * N[(N[(t * a), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.8e+51], N[(N[(b / z), $MachinePrecision] / c$95$m), $MachinePrecision], t$95$1]]]]), $MachinePrecision]]

Derivation

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

Alternative 18: 50.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} c_m = \left|c\right| \\ c_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := t \cdot \left(-4 \cdot \frac{a}{c_m}\right)\\ c_s \cdot \begin{array}{l} \mathbf{if}\;a \leq -1.02 \cdot 10^{-80}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 5.9 \cdot 10^{-49}:\\ \;\;\;\;b \cdot \frac{1}{c_m \cdot z}\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{+21}:\\ \;\;\;\;\frac{-4 \cdot a}{\frac{c_m}{t}}\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{+51}:\\ \;\;\;\;\frac{\frac{b}{z}}{c_m}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \end{array} \]

FPCore

c_m = (fabs.f64 c)
c_s = (copysign.f64 1 c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (let* ((t_1 (* t (* -4.0 (/ a c_m)))))
   (*
    c_s
    (if (<= a -1.02e-80)
      t_1
      (if (<= a 5.9e-49)
        (* b (/ 1.0 (* c_m z)))
        (if (<= a 8.5e+21)
          (/ (* -4.0 a) (/ c_m t))
          (if (<= a 3.1e+51) (/ (/ b z) c_m) t_1)))))))

C

c_m = fabs(c);
c_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double t_1 = t * (-4.0 * (a / c_m));
	double tmp;
	if (a <= -1.02e-80) {
		tmp = t_1;
	} else if (a <= 5.9e-49) {
		tmp = b * (1.0 / (c_m * z));
	} else if (a <= 8.5e+21) {
		tmp = (-4.0 * a) / (c_m / t);
	} else if (a <= 3.1e+51) {
		tmp = (b / z) / c_m;
	} else {
		tmp = t_1;
	}
	return c_s * tmp;
}

Fortran

c_m = abs(c)
c_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    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), intent (in) :: c_m
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((-4.0d0) * (a / c_m))
    if (a <= (-1.02d-80)) then
        tmp = t_1
    else if (a <= 5.9d-49) then
        tmp = b * (1.0d0 / (c_m * z))
    else if (a <= 8.5d+21) then
        tmp = ((-4.0d0) * a) / (c_m / t)
    else if (a <= 3.1d+51) then
        tmp = (b / z) / c_m
    else
        tmp = t_1
    end if
    code = c_s * tmp
end function

Java

c_m = Math.abs(c);
c_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double t_1 = t * (-4.0 * (a / c_m));
	double tmp;
	if (a <= -1.02e-80) {
		tmp = t_1;
	} else if (a <= 5.9e-49) {
		tmp = b * (1.0 / (c_m * z));
	} else if (a <= 8.5e+21) {
		tmp = (-4.0 * a) / (c_m / t);
	} else if (a <= 3.1e+51) {
		tmp = (b / z) / c_m;
	} else {
		tmp = t_1;
	}
	return c_s * tmp;
}

Python

c_m = math.fabs(c)
c_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	t_1 = t * (-4.0 * (a / c_m))
	tmp = 0
	if a <= -1.02e-80:
		tmp = t_1
	elif a <= 5.9e-49:
		tmp = b * (1.0 / (c_m * z))
	elif a <= 8.5e+21:
		tmp = (-4.0 * a) / (c_m / t)
	elif a <= 3.1e+51:
		tmp = (b / z) / c_m
	else:
		tmp = t_1
	return c_s * tmp

Julia

c_m = abs(c)
c_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	t_1 = Float64(t * Float64(-4.0 * Float64(a / c_m)))
	tmp = 0.0
	if (a <= -1.02e-80)
		tmp = t_1;
	elseif (a <= 5.9e-49)
		tmp = Float64(b * Float64(1.0 / Float64(c_m * z)));
	elseif (a <= 8.5e+21)
		tmp = Float64(Float64(-4.0 * a) / Float64(c_m / t));
	elseif (a <= 3.1e+51)
		tmp = Float64(Float64(b / z) / c_m);
	else
		tmp = t_1;
	end
	return Float64(c_s * tmp)
end

MATLAB

c_m = abs(c);
c_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	t_1 = t * (-4.0 * (a / c_m));
	tmp = 0.0;
	if (a <= -1.02e-80)
		tmp = t_1;
	elseif (a <= 5.9e-49)
		tmp = b * (1.0 / (c_m * z));
	elseif (a <= 8.5e+21)
		tmp = (-4.0 * a) / (c_m / t);
	elseif (a <= 3.1e+51)
		tmp = (b / z) / c_m;
	else
		tmp = t_1;
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c_m = N[Abs[c], $MachinePrecision]
c_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := Block[{t$95$1 = N[(t * N[(-4.0 * N[(a / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(c$95$s * If[LessEqual[a, -1.02e-80], t$95$1, If[LessEqual[a, 5.9e-49], N[(b * N[(1.0 / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8.5e+21], N[(N[(-4.0 * a), $MachinePrecision] / N[(c$95$m / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.1e+51], N[(N[(b / z), $MachinePrecision] / c$95$m), $MachinePrecision], t$95$1]]]]), $MachinePrecision]]

Derivation

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

Alternative 19: 50.4% accurate, 1.7× speedup

Math

\[\begin{array}{l} c_m = \left|c\right| \\ c_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{-90} \lor \neg \left(z \leq 2 \cdot 10^{-100}\right):\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c_m}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{c_m \cdot z}\\ \end{array} \end{array} \]

FPCore

c_m = (fabs.f64 c)
c_s = (copysign.f64 1 c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (*
  c_s
  (if (or (<= z -2.2e-90) (not (<= z 2e-100)))
    (* -4.0 (/ (* t a) c_m))
    (/ b (* c_m z)))))

C

c_m = fabs(c);
c_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if ((z <= -2.2e-90) || !(z <= 2e-100)) {
		tmp = -4.0 * ((t * a) / c_m);
	} else {
		tmp = b / (c_m * z);
	}
	return c_s * tmp;
}

Fortran

c_m = abs(c)
c_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    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), intent (in) :: c_m
    real(8) :: tmp
    if ((z <= (-2.2d-90)) .or. (.not. (z <= 2d-100))) then
        tmp = (-4.0d0) * ((t * a) / c_m)
    else
        tmp = b / (c_m * z)
    end if
    code = c_s * tmp
end function

Java

c_m = Math.abs(c);
c_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if ((z <= -2.2e-90) || !(z <= 2e-100)) {
		tmp = -4.0 * ((t * a) / c_m);
	} else {
		tmp = b / (c_m * z);
	}
	return c_s * tmp;
}

Python

c_m = math.fabs(c)
c_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	tmp = 0
	if (z <= -2.2e-90) or not (z <= 2e-100):
		tmp = -4.0 * ((t * a) / c_m)
	else:
		tmp = b / (c_m * z)
	return c_s * tmp

Julia

c_m = abs(c)
c_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if ((z <= -2.2e-90) || !(z <= 2e-100))
		tmp = Float64(-4.0 * Float64(Float64(t * a) / c_m));
	else
		tmp = Float64(b / Float64(c_m * z));
	end
	return Float64(c_s * tmp)
end

MATLAB

c_m = abs(c);
c_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0;
	if ((z <= -2.2e-90) || ~((z <= 2e-100)))
		tmp = -4.0 * ((t * a) / c_m);
	else
		tmp = b / (c_m * z);
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c_m = N[Abs[c], $MachinePrecision]
c_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[Or[LessEqual[z, -2.2e-90], N[Not[LessEqual[z, 2e-100]], $MachinePrecision]], N[(-4.0 * N[(N[(t * a), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision], N[(b / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

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

Alternative 20: 50.6% accurate, 1.7× speedup

Math

\[\begin{array}{l} c_m = \left|c\right| \\ c_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{-89} \lor \neg \left(z \leq 1.4 \cdot 10^{-99}\right):\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c_m}\\ \mathbf{else}:\\ \;\;\;\;b \cdot \frac{1}{c_m \cdot z}\\ \end{array} \end{array} \]

FPCore

c_m = (fabs.f64 c)
c_s = (copysign.f64 1 c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (*
  c_s
  (if (or (<= z -1.55e-89) (not (<= z 1.4e-99)))
    (* -4.0 (/ (* t a) c_m))
    (* b (/ 1.0 (* c_m z))))))

C

c_m = fabs(c);
c_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if ((z <= -1.55e-89) || !(z <= 1.4e-99)) {
		tmp = -4.0 * ((t * a) / c_m);
	} else {
		tmp = b * (1.0 / (c_m * z));
	}
	return c_s * tmp;
}

Fortran

c_m = abs(c)
c_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    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), intent (in) :: c_m
    real(8) :: tmp
    if ((z <= (-1.55d-89)) .or. (.not. (z <= 1.4d-99))) then
        tmp = (-4.0d0) * ((t * a) / c_m)
    else
        tmp = b * (1.0d0 / (c_m * z))
    end if
    code = c_s * tmp
end function

Java

c_m = Math.abs(c);
c_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if ((z <= -1.55e-89) || !(z <= 1.4e-99)) {
		tmp = -4.0 * ((t * a) / c_m);
	} else {
		tmp = b * (1.0 / (c_m * z));
	}
	return c_s * tmp;
}

Python

c_m = math.fabs(c)
c_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	tmp = 0
	if (z <= -1.55e-89) or not (z <= 1.4e-99):
		tmp = -4.0 * ((t * a) / c_m)
	else:
		tmp = b * (1.0 / (c_m * z))
	return c_s * tmp

Julia

c_m = abs(c)
c_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if ((z <= -1.55e-89) || !(z <= 1.4e-99))
		tmp = Float64(-4.0 * Float64(Float64(t * a) / c_m));
	else
		tmp = Float64(b * Float64(1.0 / Float64(c_m * z)));
	end
	return Float64(c_s * tmp)
end

MATLAB

c_m = abs(c);
c_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0;
	if ((z <= -1.55e-89) || ~((z <= 1.4e-99)))
		tmp = -4.0 * ((t * a) / c_m);
	else
		tmp = b * (1.0 / (c_m * z));
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c_m = N[Abs[c], $MachinePrecision]
c_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[Or[LessEqual[z, -1.55e-89], N[Not[LessEqual[z, 1.4e-99]], $MachinePrecision]], N[(-4.0 * N[(N[(t * a), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision], N[(b * N[(1.0 / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

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

Alternative 21: 35.7% accurate, 3.8× speedup

Math

\[\begin{array}{l} c_m = \left|c\right| \\ c_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c_s \cdot \frac{b}{c_m \cdot z} \end{array} \]

FPCore

c_m = (fabs.f64 c)
c_s = (copysign.f64 1 c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m) :precision binary64 (* c_s (/ b (* c_m z))))

C

c_m = fabs(c);
c_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	return c_s * (b / (c_m * z));
}

Fortran

c_m = abs(c)
c_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    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), intent (in) :: c_m
    code = c_s * (b / (c_m * z))
end function

Java

c_m = Math.abs(c);
c_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	return c_s * (b / (c_m * z));
}

Python

c_m = math.fabs(c)
c_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	return c_s * (b / (c_m * z))

Julia

c_m = abs(c)
c_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	return Float64(c_s * Float64(b / Float64(c_m * z)))
end

MATLAB

c_m = abs(c);
c_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp = code(c_s, x, y, z, t, a, b, c_m)
	tmp = c_s * (b / (c_m * z));
end

Wolfram

c_m = N[Abs[c], $MachinePrecision]
c_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * N[(b / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

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

Developer target: 80.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{b}{c \cdot z}\\ t_2 := 4 \cdot \frac{a \cdot t}{c}\\ t_3 := \left(x \cdot 9\right) \cdot y\\ t_4 := \left(t_3 - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b\\ t_5 := \frac{t_4}{z \cdot c}\\ t_6 := \frac{\left(t_3 - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}\\ \mathbf{if}\;t_5 < -1.100156740804105 \cdot 10^{-171}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;t_5 < 0:\\ \;\;\;\;\frac{\frac{t_4}{z}}{c}\\ \mathbf{elif}\;t_5 < 1.1708877911747488 \cdot 10^{-53}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;t_5 < 2.876823679546137 \cdot 10^{+130}:\\ \;\;\;\;\left(\left(9 \cdot \frac{y}{c}\right) \cdot \frac{x}{z} + t_1\right) - t_2\\ \mathbf{elif}\;t_5 < 1.3838515042456319 \cdot 10^{+158}:\\ \;\;\;\;t_6\\ \mathbf{else}:\\ \;\;\;\;\left(9 \cdot \left(\frac{y}{c \cdot z} \cdot x\right) + t_1\right) - t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ b (* c z)))
        (t_2 (* 4.0 (/ (* a t) c)))
        (t_3 (* (* x 9.0) y))
        (t_4 (+ (- t_3 (* (* (* z 4.0) t) a)) b))
        (t_5 (/ t_4 (* z c)))
        (t_6 (/ (+ (- t_3 (* (* z 4.0) (* t a))) b) (* z c))))
   (if (< t_5 -1.100156740804105e-171)
     t_6
     (if (< t_5 0.0)
       (/ (/ t_4 z) c)
       (if (< t_5 1.1708877911747488e-53)
         t_6
         (if (< t_5 2.876823679546137e+130)
           (- (+ (* (* 9.0 (/ y c)) (/ x z)) t_1) t_2)
           (if (< t_5 1.3838515042456319e+158)
             t_6
             (- (+ (* 9.0 (* (/ y (* c z)) x)) t_1) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b / (c * z);
	double t_2 = 4.0 * ((a * t) / c);
	double t_3 = (x * 9.0) * y;
	double t_4 = (t_3 - (((z * 4.0) * t) * a)) + b;
	double t_5 = t_4 / (z * c);
	double t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c);
	double tmp;
	if (t_5 < -1.100156740804105e-171) {
		tmp = t_6;
	} else if (t_5 < 0.0) {
		tmp = (t_4 / z) / c;
	} else if (t_5 < 1.1708877911747488e-53) {
		tmp = t_6;
	} else if (t_5 < 2.876823679546137e+130) {
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2;
	} else if (t_5 < 1.3838515042456319e+158) {
		tmp = t_6;
	} else {
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: tmp
    t_1 = b / (c * z)
    t_2 = 4.0d0 * ((a * t) / c)
    t_3 = (x * 9.0d0) * y
    t_4 = (t_3 - (((z * 4.0d0) * t) * a)) + b
    t_5 = t_4 / (z * c)
    t_6 = ((t_3 - ((z * 4.0d0) * (t * a))) + b) / (z * c)
    if (t_5 < (-1.100156740804105d-171)) then
        tmp = t_6
    else if (t_5 < 0.0d0) then
        tmp = (t_4 / z) / c
    else if (t_5 < 1.1708877911747488d-53) then
        tmp = t_6
    else if (t_5 < 2.876823679546137d+130) then
        tmp = (((9.0d0 * (y / c)) * (x / z)) + t_1) - t_2
    else if (t_5 < 1.3838515042456319d+158) then
        tmp = t_6
    else
        tmp = ((9.0d0 * ((y / (c * z)) * x)) + t_1) - 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 c) {
	double t_1 = b / (c * z);
	double t_2 = 4.0 * ((a * t) / c);
	double t_3 = (x * 9.0) * y;
	double t_4 = (t_3 - (((z * 4.0) * t) * a)) + b;
	double t_5 = t_4 / (z * c);
	double t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c);
	double tmp;
	if (t_5 < -1.100156740804105e-171) {
		tmp = t_6;
	} else if (t_5 < 0.0) {
		tmp = (t_4 / z) / c;
	} else if (t_5 < 1.1708877911747488e-53) {
		tmp = t_6;
	} else if (t_5 < 2.876823679546137e+130) {
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2;
	} else if (t_5 < 1.3838515042456319e+158) {
		tmp = t_6;
	} else {
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = b / (c * z)
	t_2 = 4.0 * ((a * t) / c)
	t_3 = (x * 9.0) * y
	t_4 = (t_3 - (((z * 4.0) * t) * a)) + b
	t_5 = t_4 / (z * c)
	t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c)
	tmp = 0
	if t_5 < -1.100156740804105e-171:
		tmp = t_6
	elif t_5 < 0.0:
		tmp = (t_4 / z) / c
	elif t_5 < 1.1708877911747488e-53:
		tmp = t_6
	elif t_5 < 2.876823679546137e+130:
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2
	elif t_5 < 1.3838515042456319e+158:
		tmp = t_6
	else:
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(b / Float64(c * z))
	t_2 = Float64(4.0 * Float64(Float64(a * t) / c))
	t_3 = Float64(Float64(x * 9.0) * y)
	t_4 = Float64(Float64(t_3 - Float64(Float64(Float64(z * 4.0) * t) * a)) + b)
	t_5 = Float64(t_4 / Float64(z * c))
	t_6 = Float64(Float64(Float64(t_3 - Float64(Float64(z * 4.0) * Float64(t * a))) + b) / Float64(z * c))
	tmp = 0.0
	if (t_5 < -1.100156740804105e-171)
		tmp = t_6;
	elseif (t_5 < 0.0)
		tmp = Float64(Float64(t_4 / z) / c);
	elseif (t_5 < 1.1708877911747488e-53)
		tmp = t_6;
	elseif (t_5 < 2.876823679546137e+130)
		tmp = Float64(Float64(Float64(Float64(9.0 * Float64(y / c)) * Float64(x / z)) + t_1) - t_2);
	elseif (t_5 < 1.3838515042456319e+158)
		tmp = t_6;
	else
		tmp = Float64(Float64(Float64(9.0 * Float64(Float64(y / Float64(c * z)) * x)) + t_1) - t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = b / (c * z);
	t_2 = 4.0 * ((a * t) / c);
	t_3 = (x * 9.0) * y;
	t_4 = (t_3 - (((z * 4.0) * t) * a)) + b;
	t_5 = t_4 / (z * c);
	t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c);
	tmp = 0.0;
	if (t_5 < -1.100156740804105e-171)
		tmp = t_6;
	elseif (t_5 < 0.0)
		tmp = (t_4 / z) / c;
	elseif (t_5 < 1.1708877911747488e-53)
		tmp = t_6;
	elseif (t_5 < 2.876823679546137e+130)
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2;
	elseif (t_5 < 1.3838515042456319e+158)
		tmp = t_6;
	else
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$4 = N[(N[(t$95$3 - N[(N[(N[(z * 4.0), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]}, Block[{t$95$5 = N[(t$95$4 / N[(z * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(N[(t$95$3 - N[(N[(z * 4.0), $MachinePrecision] * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[Less[t$95$5, -1.100156740804105e-171], t$95$6, If[Less[t$95$5, 0.0], N[(N[(t$95$4 / z), $MachinePrecision] / c), $MachinePrecision], If[Less[t$95$5, 1.1708877911747488e-53], t$95$6, If[Less[t$95$5, 2.876823679546137e+130], N[(N[(N[(N[(9.0 * N[(y / c), $MachinePrecision]), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision], If[Less[t$95$5, 1.3838515042456319e+158], t$95$6, N[(N[(N[(9.0 * N[(N[(y / N[(c * z), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision]]]]]]]]]]]]

Reproduce

herbie shell --seed 2023350 
(FPCore (x y z t a b c)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, J"
  :precision binary64

  :herbie-target
  (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) -1.100156740804105e-171) (/ (+ (- (* (* x 9.0) y) (* (* z 4.0) (* t a))) b) (* z c)) (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) 0.0) (/ (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) z) c) (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) 1.1708877911747488e-53) (/ (+ (- (* (* x 9.0) y) (* (* z 4.0) (* t a))) b) (* z c)) (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) 2.876823679546137e+130) (- (+ (* (* 9.0 (/ y c)) (/ x z)) (/ b (* c z))) (* 4.0 (/ (* a t) c))) (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) 1.3838515042456319e+158) (/ (+ (- (* (* x 9.0) y) (* (* z 4.0) (* t a))) b) (* z c)) (- (+ (* 9.0 (* (/ y (* c z)) x)) (/ b (* c z))) (* 4.0 (/ (* a t) c))))))))

  (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)))