Development.Shake.Progress:decay from shake-0.15.5

Percentage Accurate: 66.3% → 91.1%

Time: 23.8s

Alternatives: 21

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 66.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 91.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y - z \cdot \left(y - b\right)\\ t_2 := \left(\frac{y}{z} \cdot \frac{x}{b - y} + \frac{t - a}{b - y}\right) + \frac{\frac{a - t}{\frac{z}{y}}}{{\left(b - y\right)}^{2}}\\ t_3 := \frac{x}{z + -1}\\ t_4 := z \cdot \left(t - a\right)\\ t_5 := \frac{x \cdot y + t_4}{t_1}\\ \mathbf{if}\;t_5 \leq -\infty:\\ \;\;\;\;\frac{a - t}{y} - t_3\\ \mathbf{elif}\;t_5 \leq -2 \cdot 10^{-293}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, t_4\right)}{t_1}\\ \mathbf{elif}\;t_5 \leq 0:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_5 \leq 10^{+266}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;t_5 \leq \infty:\\ \;\;\;\;\frac{z}{y} \cdot \frac{a - t}{z + -1} - t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- y (* z (- y b))))
        (t_2
         (+
          (+ (* (/ y z) (/ x (- b y))) (/ (- t a) (- b y)))
          (/ (/ (- a t) (/ z y)) (pow (- b y) 2.0))))
        (t_3 (/ x (+ z -1.0)))
        (t_4 (* z (- t a)))
        (t_5 (/ (+ (* x y) t_4) t_1)))
   (if (<= t_5 (- INFINITY))
     (- (/ (- a t) y) t_3)
     (if (<= t_5 -2e-293)
       (/ (fma x y t_4) t_1)
       (if (<= t_5 0.0)
         t_2
         (if (<= t_5 1e+266)
           t_5
           (if (<= t_5 INFINITY)
             (- (* (/ z y) (/ (- a t) (+ z -1.0))) t_3)
             t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y - (z * (y - b));
	double t_2 = (((y / z) * (x / (b - y))) + ((t - a) / (b - y))) + (((a - t) / (z / y)) / pow((b - y), 2.0));
	double t_3 = x / (z + -1.0);
	double t_4 = z * (t - a);
	double t_5 = ((x * y) + t_4) / t_1;
	double tmp;
	if (t_5 <= -((double) INFINITY)) {
		tmp = ((a - t) / y) - t_3;
	} else if (t_5 <= -2e-293) {
		tmp = fma(x, y, t_4) / t_1;
	} else if (t_5 <= 0.0) {
		tmp = t_2;
	} else if (t_5 <= 1e+266) {
		tmp = t_5;
	} else if (t_5 <= ((double) INFINITY)) {
		tmp = ((z / y) * ((a - t) / (z + -1.0))) - t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y - Float64(z * Float64(y - b)))
	t_2 = Float64(Float64(Float64(Float64(y / z) * Float64(x / Float64(b - y))) + Float64(Float64(t - a) / Float64(b - y))) + Float64(Float64(Float64(a - t) / Float64(z / y)) / (Float64(b - y) ^ 2.0)))
	t_3 = Float64(x / Float64(z + -1.0))
	t_4 = Float64(z * Float64(t - a))
	t_5 = Float64(Float64(Float64(x * y) + t_4) / t_1)
	tmp = 0.0
	if (t_5 <= Float64(-Inf))
		tmp = Float64(Float64(Float64(a - t) / y) - t_3);
	elseif (t_5 <= -2e-293)
		tmp = Float64(fma(x, y, t_4) / t_1);
	elseif (t_5 <= 0.0)
		tmp = t_2;
	elseif (t_5 <= 1e+266)
		tmp = t_5;
	elseif (t_5 <= Inf)
		tmp = Float64(Float64(Float64(z / y) * Float64(Float64(a - t) / Float64(z + -1.0))) - t_3);
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y - N[(z * N[(y - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(y / z), $MachinePrecision] * N[(x / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(a - t), $MachinePrecision] / N[(z / y), $MachinePrecision]), $MachinePrecision] / N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(N[(x * y), $MachinePrecision] + t$95$4), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[t$95$5, (-Infinity)], N[(N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision] - t$95$3), $MachinePrecision], If[LessEqual[t$95$5, -2e-293], N[(N[(x * y + t$95$4), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[t$95$5, 0.0], t$95$2, If[LessEqual[t$95$5, 1e+266], t$95$5, If[LessEqual[t$95$5, Infinity], N[(N[(N[(z / y), $MachinePrecision] * N[(N[(a - t), $MachinePrecision] / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$3), $MachinePrecision], t$95$2]]]]]]]]]]

Derivation

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

Alternative 2: 83.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y - z \cdot \left(y - b\right)\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -7.8 \cdot 10^{+28}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-252}:\\ \;\;\;\;\left(\frac{z \cdot t}{t_1} + \frac{x \cdot y}{t_1}\right) - \frac{z \cdot a}{t_1}\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{-203}:\\ \;\;\;\;\frac{z}{y} \cdot \frac{a - t}{z + -1} - \frac{x}{z + -1}\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{+39}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, z \cdot \left(t - a\right)\right)}{t_1}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- y (* z (- y b)))) (t_2 (/ (- t a) (- b y))))
   (if (<= z -7.8e+28)
     t_2
     (if (<= z -3.4e-252)
       (- (+ (/ (* z t) t_1) (/ (* x y) t_1)) (/ (* z a) t_1))
       (if (<= z 7.4e-203)
         (- (* (/ z y) (/ (- a t) (+ z -1.0))) (/ x (+ z -1.0)))
         (if (<= z 5.4e+39) (/ (fma x y (* z (- t a))) t_1) t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y - (z * (y - b));
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -7.8e+28) {
		tmp = t_2;
	} else if (z <= -3.4e-252) {
		tmp = (((z * t) / t_1) + ((x * y) / t_1)) - ((z * a) / t_1);
	} else if (z <= 7.4e-203) {
		tmp = ((z / y) * ((a - t) / (z + -1.0))) - (x / (z + -1.0));
	} else if (z <= 5.4e+39) {
		tmp = fma(x, y, (z * (t - a))) / t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y - Float64(z * Float64(y - b)))
	t_2 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -7.8e+28)
		tmp = t_2;
	elseif (z <= -3.4e-252)
		tmp = Float64(Float64(Float64(Float64(z * t) / t_1) + Float64(Float64(x * y) / t_1)) - Float64(Float64(z * a) / t_1));
	elseif (z <= 7.4e-203)
		tmp = Float64(Float64(Float64(z / y) * Float64(Float64(a - t) / Float64(z + -1.0))) - Float64(x / Float64(z + -1.0)));
	elseif (z <= 5.4e+39)
		tmp = Float64(fma(x, y, Float64(z * Float64(t - a))) / t_1);
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y - N[(z * N[(y - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.8e+28], t$95$2, If[LessEqual[z, -3.4e-252], N[(N[(N[(N[(z * t), $MachinePrecision] / t$95$1), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] - N[(N[(z * a), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.4e-203], N[(N[(N[(z / y), $MachinePrecision] * N[(N[(a - t), $MachinePrecision] / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.4e+39], N[(N[(x * y + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], t$95$2]]]]]]

Derivation

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

Alternative 3: 87.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot y + z \cdot \left(t - a\right)}{y - z \cdot \left(y - b\right)}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z + -1}\\ \mathbf{elif}\;t_1 \leq -2 \cdot 10^{-293} \lor \neg \left(t_1 \leq 0\right) \land t_1 \leq 10^{+305}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ (* x y) (* z (- t a))) (- y (* z (- y b))))))
   (if (<= t_1 (- INFINITY))
     (- (/ (- a t) y) (/ x (+ z -1.0)))
     (if (or (<= t_1 -2e-293) (and (not (<= t_1 0.0)) (<= t_1 1e+305)))
       t_1
       (/ (- t a) (- b y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x * y) + (z * (t - a))) / (y - (z * (y - b)));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = ((a - t) / y) - (x / (z + -1.0));
	} else if ((t_1 <= -2e-293) || (!(t_1 <= 0.0) && (t_1 <= 1e+305))) {
		tmp = t_1;
	} else {
		tmp = (t - a) / (b - y);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x * y) + (z * (t - a))) / (y - (z * (y - b)));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = ((a - t) / y) - (x / (z + -1.0));
	} else if ((t_1 <= -2e-293) || (!(t_1 <= 0.0) && (t_1 <= 1e+305))) {
		tmp = t_1;
	} else {
		tmp = (t - a) / (b - y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((x * y) + (z * (t - a))) / (y - (z * (y - b)))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = ((a - t) / y) - (x / (z + -1.0))
	elif (t_1 <= -2e-293) or (not (t_1 <= 0.0) and (t_1 <= 1e+305)):
		tmp = t_1
	else:
		tmp = (t - a) / (b - y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(x * y) + Float64(z * Float64(t - a))) / Float64(y - Float64(z * Float64(y - b))))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(Float64(a - t) / y) - Float64(x / Float64(z + -1.0)));
	elseif ((t_1 <= -2e-293) || (!(t_1 <= 0.0) && (t_1 <= 1e+305)))
		tmp = t_1;
	else
		tmp = Float64(Float64(t - a) / Float64(b - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((x * y) + (z * (t - a))) / (y - (z * (y - b)));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = ((a - t) / y) - (x / (z + -1.0));
	elseif ((t_1 <= -2e-293) || (~((t_1 <= 0.0)) && (t_1 <= 1e+305)))
		tmp = t_1;
	else
		tmp = (t - a) / (b - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(x * y), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y - N[(z * N[(y - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision] - N[(x / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t$95$1, -2e-293], And[N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision], LessEqual[t$95$1, 1e+305]]], t$95$1, N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

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

Alternative 4: 83.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y - z \cdot \left(y - b\right)\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -1.46 \cdot 10^{+32}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{-252}:\\ \;\;\;\;\left(\frac{z \cdot t}{t_1} + \frac{x \cdot y}{t_1}\right) - \frac{z \cdot a}{t_1}\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{-203}:\\ \;\;\;\;\frac{z}{y} \cdot \frac{a - t}{z + -1} - \frac{x}{z + -1}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+40}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{t_1}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- y (* z (- y b)))) (t_2 (/ (- t a) (- b y))))
   (if (<= z -1.46e+32)
     t_2
     (if (<= z -4.4e-252)
       (- (+ (/ (* z t) t_1) (/ (* x y) t_1)) (/ (* z a) t_1))
       (if (<= z 7.4e-203)
         (- (* (/ z y) (/ (- a t) (+ z -1.0))) (/ x (+ z -1.0)))
         (if (<= z 1.3e+40) (/ (+ (* x y) (* z (- t a))) t_1) t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y - (z * (y - b));
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -1.46e+32) {
		tmp = t_2;
	} else if (z <= -4.4e-252) {
		tmp = (((z * t) / t_1) + ((x * y) / t_1)) - ((z * a) / t_1);
	} else if (z <= 7.4e-203) {
		tmp = ((z / y) * ((a - t) / (z + -1.0))) - (x / (z + -1.0));
	} else if (z <= 1.3e+40) {
		tmp = ((x * y) + (z * (t - a))) / t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y - (z * (y - b))
    t_2 = (t - a) / (b - y)
    if (z <= (-1.46d+32)) then
        tmp = t_2
    else if (z <= (-4.4d-252)) then
        tmp = (((z * t) / t_1) + ((x * y) / t_1)) - ((z * a) / t_1)
    else if (z <= 7.4d-203) then
        tmp = ((z / y) * ((a - t) / (z + (-1.0d0)))) - (x / (z + (-1.0d0)))
    else if (z <= 1.3d+40) then
        tmp = ((x * y) + (z * (t - a))) / t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y - (z * (y - b));
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -1.46e+32) {
		tmp = t_2;
	} else if (z <= -4.4e-252) {
		tmp = (((z * t) / t_1) + ((x * y) / t_1)) - ((z * a) / t_1);
	} else if (z <= 7.4e-203) {
		tmp = ((z / y) * ((a - t) / (z + -1.0))) - (x / (z + -1.0));
	} else if (z <= 1.3e+40) {
		tmp = ((x * y) + (z * (t - a))) / t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y - (z * (y - b))
	t_2 = (t - a) / (b - y)
	tmp = 0
	if z <= -1.46e+32:
		tmp = t_2
	elif z <= -4.4e-252:
		tmp = (((z * t) / t_1) + ((x * y) / t_1)) - ((z * a) / t_1)
	elif z <= 7.4e-203:
		tmp = ((z / y) * ((a - t) / (z + -1.0))) - (x / (z + -1.0))
	elif z <= 1.3e+40:
		tmp = ((x * y) + (z * (t - a))) / t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y - Float64(z * Float64(y - b)))
	t_2 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -1.46e+32)
		tmp = t_2;
	elseif (z <= -4.4e-252)
		tmp = Float64(Float64(Float64(Float64(z * t) / t_1) + Float64(Float64(x * y) / t_1)) - Float64(Float64(z * a) / t_1));
	elseif (z <= 7.4e-203)
		tmp = Float64(Float64(Float64(z / y) * Float64(Float64(a - t) / Float64(z + -1.0))) - Float64(x / Float64(z + -1.0)));
	elseif (z <= 1.3e+40)
		tmp = Float64(Float64(Float64(x * y) + Float64(z * Float64(t - a))) / t_1);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y - (z * (y - b));
	t_2 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -1.46e+32)
		tmp = t_2;
	elseif (z <= -4.4e-252)
		tmp = (((z * t) / t_1) + ((x * y) / t_1)) - ((z * a) / t_1);
	elseif (z <= 7.4e-203)
		tmp = ((z / y) * ((a - t) / (z + -1.0))) - (x / (z + -1.0));
	elseif (z <= 1.3e+40)
		tmp = ((x * y) + (z * (t - a))) / t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y - N[(z * N[(y - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.46e+32], t$95$2, If[LessEqual[z, -4.4e-252], N[(N[(N[(N[(z * t), $MachinePrecision] / t$95$1), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] - N[(N[(z * a), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.4e-203], N[(N[(N[(z / y), $MachinePrecision] * N[(N[(a - t), $MachinePrecision] / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.3e+40], N[(N[(N[(x * y), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], t$95$2]]]]]]

Derivation

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

Alternative 5: 71.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ t_2 := z \cdot \left(t - a\right)\\ t_3 := y - z \cdot \left(y - b\right)\\ t_4 := \frac{x \cdot y + z \cdot t}{t_3}\\ \mathbf{if}\;z \leq -2 \cdot 10^{+17}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-7}:\\ \;\;\;\;\frac{x}{1 + \frac{z}{\frac{y}{b - y}}}\\ \mathbf{elif}\;z \leq -7.1 \cdot 10^{-115}:\\ \;\;\;\;\frac{t_2}{y + z \cdot b}\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-293}:\\ \;\;\;\;x + \frac{z}{\frac{y}{t - a}}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-268}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-177}:\\ \;\;\;\;\frac{x}{1 + \frac{z}{\frac{y}{b}}}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-115}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq 580000:\\ \;\;\;\;\frac{t_2}{t_3}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y)))
        (t_2 (* z (- t a)))
        (t_3 (- y (* z (- y b))))
        (t_4 (/ (+ (* x y) (* z t)) t_3)))
   (if (<= z -2e+17)
     t_1
     (if (<= z -2.2e-7)
       (/ x (+ 1.0 (/ z (/ y (- b y)))))
       (if (<= z -7.1e-115)
         (/ t_2 (+ y (* z b)))
         (if (<= z -5.8e-293)
           (+ x (/ z (/ y (- t a))))
           (if (<= z 1.2e-268)
             t_4
             (if (<= z 4.2e-177)
               (/ x (+ 1.0 (/ z (/ y b))))
               (if (<= z 4.5e-115)
                 t_4
                 (if (<= z 580000.0) (/ t_2 t_3) t_1))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double t_2 = z * (t - a);
	double t_3 = y - (z * (y - b));
	double t_4 = ((x * y) + (z * t)) / t_3;
	double tmp;
	if (z <= -2e+17) {
		tmp = t_1;
	} else if (z <= -2.2e-7) {
		tmp = x / (1.0 + (z / (y / (b - y))));
	} else if (z <= -7.1e-115) {
		tmp = t_2 / (y + (z * b));
	} else if (z <= -5.8e-293) {
		tmp = x + (z / (y / (t - a)));
	} else if (z <= 1.2e-268) {
		tmp = t_4;
	} else if (z <= 4.2e-177) {
		tmp = x / (1.0 + (z / (y / b)));
	} else if (z <= 4.5e-115) {
		tmp = t_4;
	} else if (z <= 580000.0) {
		tmp = t_2 / t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    t_2 = z * (t - a)
    t_3 = y - (z * (y - b))
    t_4 = ((x * y) + (z * t)) / t_3
    if (z <= (-2d+17)) then
        tmp = t_1
    else if (z <= (-2.2d-7)) then
        tmp = x / (1.0d0 + (z / (y / (b - y))))
    else if (z <= (-7.1d-115)) then
        tmp = t_2 / (y + (z * b))
    else if (z <= (-5.8d-293)) then
        tmp = x + (z / (y / (t - a)))
    else if (z <= 1.2d-268) then
        tmp = t_4
    else if (z <= 4.2d-177) then
        tmp = x / (1.0d0 + (z / (y / b)))
    else if (z <= 4.5d-115) then
        tmp = t_4
    else if (z <= 580000.0d0) then
        tmp = t_2 / t_3
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double t_2 = z * (t - a);
	double t_3 = y - (z * (y - b));
	double t_4 = ((x * y) + (z * t)) / t_3;
	double tmp;
	if (z <= -2e+17) {
		tmp = t_1;
	} else if (z <= -2.2e-7) {
		tmp = x / (1.0 + (z / (y / (b - y))));
	} else if (z <= -7.1e-115) {
		tmp = t_2 / (y + (z * b));
	} else if (z <= -5.8e-293) {
		tmp = x + (z / (y / (t - a)));
	} else if (z <= 1.2e-268) {
		tmp = t_4;
	} else if (z <= 4.2e-177) {
		tmp = x / (1.0 + (z / (y / b)));
	} else if (z <= 4.5e-115) {
		tmp = t_4;
	} else if (z <= 580000.0) {
		tmp = t_2 / t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	t_2 = z * (t - a)
	t_3 = y - (z * (y - b))
	t_4 = ((x * y) + (z * t)) / t_3
	tmp = 0
	if z <= -2e+17:
		tmp = t_1
	elif z <= -2.2e-7:
		tmp = x / (1.0 + (z / (y / (b - y))))
	elif z <= -7.1e-115:
		tmp = t_2 / (y + (z * b))
	elif z <= -5.8e-293:
		tmp = x + (z / (y / (t - a)))
	elif z <= 1.2e-268:
		tmp = t_4
	elif z <= 4.2e-177:
		tmp = x / (1.0 + (z / (y / b)))
	elif z <= 4.5e-115:
		tmp = t_4
	elif z <= 580000.0:
		tmp = t_2 / t_3
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	t_2 = Float64(z * Float64(t - a))
	t_3 = Float64(y - Float64(z * Float64(y - b)))
	t_4 = Float64(Float64(Float64(x * y) + Float64(z * t)) / t_3)
	tmp = 0.0
	if (z <= -2e+17)
		tmp = t_1;
	elseif (z <= -2.2e-7)
		tmp = Float64(x / Float64(1.0 + Float64(z / Float64(y / Float64(b - y)))));
	elseif (z <= -7.1e-115)
		tmp = Float64(t_2 / Float64(y + Float64(z * b)));
	elseif (z <= -5.8e-293)
		tmp = Float64(x + Float64(z / Float64(y / Float64(t - a))));
	elseif (z <= 1.2e-268)
		tmp = t_4;
	elseif (z <= 4.2e-177)
		tmp = Float64(x / Float64(1.0 + Float64(z / Float64(y / b))));
	elseif (z <= 4.5e-115)
		tmp = t_4;
	elseif (z <= 580000.0)
		tmp = Float64(t_2 / t_3);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	t_2 = z * (t - a);
	t_3 = y - (z * (y - b));
	t_4 = ((x * y) + (z * t)) / t_3;
	tmp = 0.0;
	if (z <= -2e+17)
		tmp = t_1;
	elseif (z <= -2.2e-7)
		tmp = x / (1.0 + (z / (y / (b - y))));
	elseif (z <= -7.1e-115)
		tmp = t_2 / (y + (z * b));
	elseif (z <= -5.8e-293)
		tmp = x + (z / (y / (t - a)));
	elseif (z <= 1.2e-268)
		tmp = t_4;
	elseif (z <= 4.2e-177)
		tmp = x / (1.0 + (z / (y / b)));
	elseif (z <= 4.5e-115)
		tmp = t_4;
	elseif (z <= 580000.0)
		tmp = t_2 / t_3;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y - N[(z * N[(y - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] / t$95$3), $MachinePrecision]}, If[LessEqual[z, -2e+17], t$95$1, If[LessEqual[z, -2.2e-7], N[(x / N[(1.0 + N[(z / N[(y / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -7.1e-115], N[(t$95$2 / N[(y + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -5.8e-293], N[(x + N[(z / N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.2e-268], t$95$4, If[LessEqual[z, 4.2e-177], N[(x / N[(1.0 + N[(z / N[(y / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.5e-115], t$95$4, If[LessEqual[z, 580000.0], N[(t$95$2 / t$95$3), $MachinePrecision], t$95$1]]]]]]]]]]]]

Derivation

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

Alternative 6: 72.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y - z \cdot \left(y - b\right)\\ t_2 := \frac{x \cdot y - z \cdot a}{t_1}\\ t_3 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -2.15 \cdot 10^{+17}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-131}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-288}:\\ \;\;\;\;x + \frac{z}{\frac{y}{t - a}}\\ \mathbf{elif}\;z \leq 1.08 \cdot 10^{-268}:\\ \;\;\;\;\frac{x \cdot y + z \cdot t}{t_1}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-176}:\\ \;\;\;\;\frac{x}{1 + \frac{z}{\frac{y}{b}}}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-129}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 370000000000:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{t_1}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+34}:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- y (* z (- y b))))
        (t_2 (/ (- (* x y) (* z a)) t_1))
        (t_3 (/ (- t a) (- b y))))
   (if (<= z -2.15e+17)
     t_3
     (if (<= z -3.6e-131)
       t_2
       (if (<= z -2.7e-288)
         (+ x (/ z (/ y (- t a))))
         (if (<= z 1.08e-268)
           (/ (+ (* x y) (* z t)) t_1)
           (if (<= z 1.8e-176)
             (/ x (+ 1.0 (/ z (/ y b))))
             (if (<= z 1.5e-129)
               t_2
               (if (<= z 370000000000.0)
                 (/ (* z (- t a)) t_1)
                 (if (<= z 2.6e+34)
                   (- (/ (- a t) y) (/ x (+ z -1.0)))
                   t_3))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y - (z * (y - b));
	double t_2 = ((x * y) - (z * a)) / t_1;
	double t_3 = (t - a) / (b - y);
	double tmp;
	if (z <= -2.15e+17) {
		tmp = t_3;
	} else if (z <= -3.6e-131) {
		tmp = t_2;
	} else if (z <= -2.7e-288) {
		tmp = x + (z / (y / (t - a)));
	} else if (z <= 1.08e-268) {
		tmp = ((x * y) + (z * t)) / t_1;
	} else if (z <= 1.8e-176) {
		tmp = x / (1.0 + (z / (y / b)));
	} else if (z <= 1.5e-129) {
		tmp = t_2;
	} else if (z <= 370000000000.0) {
		tmp = (z * (t - a)) / t_1;
	} else if (z <= 2.6e+34) {
		tmp = ((a - t) / y) - (x / (z + -1.0));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = y - (z * (y - b))
    t_2 = ((x * y) - (z * a)) / t_1
    t_3 = (t - a) / (b - y)
    if (z <= (-2.15d+17)) then
        tmp = t_3
    else if (z <= (-3.6d-131)) then
        tmp = t_2
    else if (z <= (-2.7d-288)) then
        tmp = x + (z / (y / (t - a)))
    else if (z <= 1.08d-268) then
        tmp = ((x * y) + (z * t)) / t_1
    else if (z <= 1.8d-176) then
        tmp = x / (1.0d0 + (z / (y / b)))
    else if (z <= 1.5d-129) then
        tmp = t_2
    else if (z <= 370000000000.0d0) then
        tmp = (z * (t - a)) / t_1
    else if (z <= 2.6d+34) then
        tmp = ((a - t) / y) - (x / (z + (-1.0d0)))
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y - (z * (y - b));
	double t_2 = ((x * y) - (z * a)) / t_1;
	double t_3 = (t - a) / (b - y);
	double tmp;
	if (z <= -2.15e+17) {
		tmp = t_3;
	} else if (z <= -3.6e-131) {
		tmp = t_2;
	} else if (z <= -2.7e-288) {
		tmp = x + (z / (y / (t - a)));
	} else if (z <= 1.08e-268) {
		tmp = ((x * y) + (z * t)) / t_1;
	} else if (z <= 1.8e-176) {
		tmp = x / (1.0 + (z / (y / b)));
	} else if (z <= 1.5e-129) {
		tmp = t_2;
	} else if (z <= 370000000000.0) {
		tmp = (z * (t - a)) / t_1;
	} else if (z <= 2.6e+34) {
		tmp = ((a - t) / y) - (x / (z + -1.0));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y - (z * (y - b))
	t_2 = ((x * y) - (z * a)) / t_1
	t_3 = (t - a) / (b - y)
	tmp = 0
	if z <= -2.15e+17:
		tmp = t_3
	elif z <= -3.6e-131:
		tmp = t_2
	elif z <= -2.7e-288:
		tmp = x + (z / (y / (t - a)))
	elif z <= 1.08e-268:
		tmp = ((x * y) + (z * t)) / t_1
	elif z <= 1.8e-176:
		tmp = x / (1.0 + (z / (y / b)))
	elif z <= 1.5e-129:
		tmp = t_2
	elif z <= 370000000000.0:
		tmp = (z * (t - a)) / t_1
	elif z <= 2.6e+34:
		tmp = ((a - t) / y) - (x / (z + -1.0))
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y - Float64(z * Float64(y - b)))
	t_2 = Float64(Float64(Float64(x * y) - Float64(z * a)) / t_1)
	t_3 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -2.15e+17)
		tmp = t_3;
	elseif (z <= -3.6e-131)
		tmp = t_2;
	elseif (z <= -2.7e-288)
		tmp = Float64(x + Float64(z / Float64(y / Float64(t - a))));
	elseif (z <= 1.08e-268)
		tmp = Float64(Float64(Float64(x * y) + Float64(z * t)) / t_1);
	elseif (z <= 1.8e-176)
		tmp = Float64(x / Float64(1.0 + Float64(z / Float64(y / b))));
	elseif (z <= 1.5e-129)
		tmp = t_2;
	elseif (z <= 370000000000.0)
		tmp = Float64(Float64(z * Float64(t - a)) / t_1);
	elseif (z <= 2.6e+34)
		tmp = Float64(Float64(Float64(a - t) / y) - Float64(x / Float64(z + -1.0)));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y - (z * (y - b));
	t_2 = ((x * y) - (z * a)) / t_1;
	t_3 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -2.15e+17)
		tmp = t_3;
	elseif (z <= -3.6e-131)
		tmp = t_2;
	elseif (z <= -2.7e-288)
		tmp = x + (z / (y / (t - a)));
	elseif (z <= 1.08e-268)
		tmp = ((x * y) + (z * t)) / t_1;
	elseif (z <= 1.8e-176)
		tmp = x / (1.0 + (z / (y / b)));
	elseif (z <= 1.5e-129)
		tmp = t_2;
	elseif (z <= 370000000000.0)
		tmp = (z * (t - a)) / t_1;
	elseif (z <= 2.6e+34)
		tmp = ((a - t) / y) - (x / (z + -1.0));
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y - N[(z * N[(y - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x * y), $MachinePrecision] - N[(z * a), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.15e+17], t$95$3, If[LessEqual[z, -3.6e-131], t$95$2, If[LessEqual[z, -2.7e-288], N[(x + N[(z / N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.08e-268], N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[z, 1.8e-176], N[(x / N[(1.0 + N[(z / N[(y / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.5e-129], t$95$2, If[LessEqual[z, 370000000000.0], N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[z, 2.6e+34], N[(N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision] - N[(x / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]]]

Derivation

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

Alternative 7: 83.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot y + z \cdot \left(t - a\right)}{y - z \cdot \left(y - b\right)}\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -2.9 \cdot 10^{+32}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-252}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 8.1 \cdot 10^{-203}:\\ \;\;\;\;\frac{z}{y} \cdot \frac{a - t}{z + -1} - \frac{x}{z + -1}\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{+40}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ (* x y) (* z (- t a))) (- y (* z (- y b)))))
        (t_2 (/ (- t a) (- b y))))
   (if (<= z -2.9e+32)
     t_2
     (if (<= z -4.5e-252)
       t_1
       (if (<= z 8.1e-203)
         (- (* (/ z y) (/ (- a t) (+ z -1.0))) (/ x (+ z -1.0)))
         (if (<= z 4.1e+40) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x * y) + (z * (t - a))) / (y - (z * (y - b)));
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -2.9e+32) {
		tmp = t_2;
	} else if (z <= -4.5e-252) {
		tmp = t_1;
	} else if (z <= 8.1e-203) {
		tmp = ((z / y) * ((a - t) / (z + -1.0))) - (x / (z + -1.0));
	} else if (z <= 4.1e+40) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((x * y) + (z * (t - a))) / (y - (z * (y - b)))
    t_2 = (t - a) / (b - y)
    if (z <= (-2.9d+32)) then
        tmp = t_2
    else if (z <= (-4.5d-252)) then
        tmp = t_1
    else if (z <= 8.1d-203) then
        tmp = ((z / y) * ((a - t) / (z + (-1.0d0)))) - (x / (z + (-1.0d0)))
    else if (z <= 4.1d+40) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x * y) + (z * (t - a))) / (y - (z * (y - b)));
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -2.9e+32) {
		tmp = t_2;
	} else if (z <= -4.5e-252) {
		tmp = t_1;
	} else if (z <= 8.1e-203) {
		tmp = ((z / y) * ((a - t) / (z + -1.0))) - (x / (z + -1.0));
	} else if (z <= 4.1e+40) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((x * y) + (z * (t - a))) / (y - (z * (y - b)))
	t_2 = (t - a) / (b - y)
	tmp = 0
	if z <= -2.9e+32:
		tmp = t_2
	elif z <= -4.5e-252:
		tmp = t_1
	elif z <= 8.1e-203:
		tmp = ((z / y) * ((a - t) / (z + -1.0))) - (x / (z + -1.0))
	elif z <= 4.1e+40:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(x * y) + Float64(z * Float64(t - a))) / Float64(y - Float64(z * Float64(y - b))))
	t_2 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -2.9e+32)
		tmp = t_2;
	elseif (z <= -4.5e-252)
		tmp = t_1;
	elseif (z <= 8.1e-203)
		tmp = Float64(Float64(Float64(z / y) * Float64(Float64(a - t) / Float64(z + -1.0))) - Float64(x / Float64(z + -1.0)));
	elseif (z <= 4.1e+40)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((x * y) + (z * (t - a))) / (y - (z * (y - b)));
	t_2 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -2.9e+32)
		tmp = t_2;
	elseif (z <= -4.5e-252)
		tmp = t_1;
	elseif (z <= 8.1e-203)
		tmp = ((z / y) * ((a - t) / (z + -1.0))) - (x / (z + -1.0));
	elseif (z <= 4.1e+40)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(x * y), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y - N[(z * N[(y - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.9e+32], t$95$2, If[LessEqual[z, -4.5e-252], t$95$1, If[LessEqual[z, 8.1e-203], N[(N[(N[(z / y), $MachinePrecision] * N[(N[(a - t), $MachinePrecision] / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.1e+40], t$95$1, t$95$2]]]]]]

Derivation

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

Alternative 8: 72.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ t_2 := z \cdot \left(t - a\right)\\ \mathbf{if}\;z \leq -5.1 \cdot 10^{+17}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -5.4 \cdot 10^{-8}:\\ \;\;\;\;\frac{x}{1 + \frac{z}{\frac{y}{b - y}}}\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-112}:\\ \;\;\;\;\frac{t_2}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-129}:\\ \;\;\;\;x + \frac{z}{\frac{y}{t - a}}\\ \mathbf{elif}\;z \leq 2650000:\\ \;\;\;\;\frac{t_2}{y - z \cdot \left(y - b\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))) (t_2 (* z (- t a))))
   (if (<= z -5.1e+17)
     t_1
     (if (<= z -5.4e-8)
       (/ x (+ 1.0 (/ z (/ y (- b y)))))
       (if (<= z -7.5e-112)
         (/ t_2 (+ y (* z b)))
         (if (<= z 1.5e-129)
           (+ x (/ z (/ y (- t a))))
           (if (<= z 2650000.0) (/ t_2 (- y (* z (- y b)))) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double t_2 = z * (t - a);
	double tmp;
	if (z <= -5.1e+17) {
		tmp = t_1;
	} else if (z <= -5.4e-8) {
		tmp = x / (1.0 + (z / (y / (b - y))));
	} else if (z <= -7.5e-112) {
		tmp = t_2 / (y + (z * b));
	} else if (z <= 1.5e-129) {
		tmp = x + (z / (y / (t - a)));
	} else if (z <= 2650000.0) {
		tmp = t_2 / (y - (z * (y - b)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    t_2 = z * (t - a)
    if (z <= (-5.1d+17)) then
        tmp = t_1
    else if (z <= (-5.4d-8)) then
        tmp = x / (1.0d0 + (z / (y / (b - y))))
    else if (z <= (-7.5d-112)) then
        tmp = t_2 / (y + (z * b))
    else if (z <= 1.5d-129) then
        tmp = x + (z / (y / (t - a)))
    else if (z <= 2650000.0d0) then
        tmp = t_2 / (y - (z * (y - b)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double t_2 = z * (t - a);
	double tmp;
	if (z <= -5.1e+17) {
		tmp = t_1;
	} else if (z <= -5.4e-8) {
		tmp = x / (1.0 + (z / (y / (b - y))));
	} else if (z <= -7.5e-112) {
		tmp = t_2 / (y + (z * b));
	} else if (z <= 1.5e-129) {
		tmp = x + (z / (y / (t - a)));
	} else if (z <= 2650000.0) {
		tmp = t_2 / (y - (z * (y - b)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	t_2 = z * (t - a)
	tmp = 0
	if z <= -5.1e+17:
		tmp = t_1
	elif z <= -5.4e-8:
		tmp = x / (1.0 + (z / (y / (b - y))))
	elif z <= -7.5e-112:
		tmp = t_2 / (y + (z * b))
	elif z <= 1.5e-129:
		tmp = x + (z / (y / (t - a)))
	elif z <= 2650000.0:
		tmp = t_2 / (y - (z * (y - b)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	t_2 = Float64(z * Float64(t - a))
	tmp = 0.0
	if (z <= -5.1e+17)
		tmp = t_1;
	elseif (z <= -5.4e-8)
		tmp = Float64(x / Float64(1.0 + Float64(z / Float64(y / Float64(b - y)))));
	elseif (z <= -7.5e-112)
		tmp = Float64(t_2 / Float64(y + Float64(z * b)));
	elseif (z <= 1.5e-129)
		tmp = Float64(x + Float64(z / Float64(y / Float64(t - a))));
	elseif (z <= 2650000.0)
		tmp = Float64(t_2 / Float64(y - Float64(z * Float64(y - b))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	t_2 = z * (t - a);
	tmp = 0.0;
	if (z <= -5.1e+17)
		tmp = t_1;
	elseif (z <= -5.4e-8)
		tmp = x / (1.0 + (z / (y / (b - y))));
	elseif (z <= -7.5e-112)
		tmp = t_2 / (y + (z * b));
	elseif (z <= 1.5e-129)
		tmp = x + (z / (y / (t - a)));
	elseif (z <= 2650000.0)
		tmp = t_2 / (y - (z * (y - b)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.1e+17], t$95$1, If[LessEqual[z, -5.4e-8], N[(x / N[(1.0 + N[(z / N[(y / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -7.5e-112], N[(t$95$2 / N[(y + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.5e-129], N[(x + N[(z / N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2650000.0], N[(t$95$2 / N[(y - N[(z * N[(y - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

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

Alternative 9: 72.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ t_2 := \frac{z \cdot \left(t - a\right)}{y + z \cdot b}\\ \mathbf{if}\;z \leq -4.8 \cdot 10^{+17}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-8}:\\ \;\;\;\;\frac{x}{1 + \frac{z}{\frac{y}{b - y}}}\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-109}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-129}:\\ \;\;\;\;x + \frac{z}{\frac{y}{t - a}}\\ \mathbf{elif}\;z \leq 0.2:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))) (t_2 (/ (* z (- t a)) (+ y (* z b)))))
   (if (<= z -4.8e+17)
     t_1
     (if (<= z -2.9e-8)
       (/ x (+ 1.0 (/ z (/ y (- b y)))))
       (if (<= z -1.15e-109)
         t_2
         (if (<= z 1.5e-129)
           (+ x (/ z (/ y (- t a))))
           (if (<= z 0.2) t_2 t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double t_2 = (z * (t - a)) / (y + (z * b));
	double tmp;
	if (z <= -4.8e+17) {
		tmp = t_1;
	} else if (z <= -2.9e-8) {
		tmp = x / (1.0 + (z / (y / (b - y))));
	} else if (z <= -1.15e-109) {
		tmp = t_2;
	} else if (z <= 1.5e-129) {
		tmp = x + (z / (y / (t - a)));
	} else if (z <= 0.2) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    t_2 = (z * (t - a)) / (y + (z * b))
    if (z <= (-4.8d+17)) then
        tmp = t_1
    else if (z <= (-2.9d-8)) then
        tmp = x / (1.0d0 + (z / (y / (b - y))))
    else if (z <= (-1.15d-109)) then
        tmp = t_2
    else if (z <= 1.5d-129) then
        tmp = x + (z / (y / (t - a)))
    else if (z <= 0.2d0) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double t_2 = (z * (t - a)) / (y + (z * b));
	double tmp;
	if (z <= -4.8e+17) {
		tmp = t_1;
	} else if (z <= -2.9e-8) {
		tmp = x / (1.0 + (z / (y / (b - y))));
	} else if (z <= -1.15e-109) {
		tmp = t_2;
	} else if (z <= 1.5e-129) {
		tmp = x + (z / (y / (t - a)));
	} else if (z <= 0.2) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	t_2 = (z * (t - a)) / (y + (z * b))
	tmp = 0
	if z <= -4.8e+17:
		tmp = t_1
	elif z <= -2.9e-8:
		tmp = x / (1.0 + (z / (y / (b - y))))
	elif z <= -1.15e-109:
		tmp = t_2
	elif z <= 1.5e-129:
		tmp = x + (z / (y / (t - a)))
	elif z <= 0.2:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	t_2 = Float64(Float64(z * Float64(t - a)) / Float64(y + Float64(z * b)))
	tmp = 0.0
	if (z <= -4.8e+17)
		tmp = t_1;
	elseif (z <= -2.9e-8)
		tmp = Float64(x / Float64(1.0 + Float64(z / Float64(y / Float64(b - y)))));
	elseif (z <= -1.15e-109)
		tmp = t_2;
	elseif (z <= 1.5e-129)
		tmp = Float64(x + Float64(z / Float64(y / Float64(t - a))));
	elseif (z <= 0.2)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	t_2 = (z * (t - a)) / (y + (z * b));
	tmp = 0.0;
	if (z <= -4.8e+17)
		tmp = t_1;
	elseif (z <= -2.9e-8)
		tmp = x / (1.0 + (z / (y / (b - y))));
	elseif (z <= -1.15e-109)
		tmp = t_2;
	elseif (z <= 1.5e-129)
		tmp = x + (z / (y / (t - a)));
	elseif (z <= 0.2)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.8e+17], t$95$1, If[LessEqual[z, -2.9e-8], N[(x / N[(1.0 + N[(z / N[(y / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.15e-109], t$95$2, If[LessEqual[z, 1.5e-129], N[(x + N[(z / N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.2], t$95$2, t$95$1]]]]]]]

Derivation

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

Alternative 10: 69.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -95000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-8}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;z \leq -8.1 \cdot 10^{-109} \lor \neg \left(z \leq 1.55 \cdot 10^{-79}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{y}{t - a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -95000000000.0)
     t_1
     (if (<= z -1.7e-8)
       (/ x (- 1.0 z))
       (if (or (<= z -8.1e-109) (not (<= z 1.55e-79)))
         t_1
         (+ x (/ z (/ y (- t a)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -95000000000.0) {
		tmp = t_1;
	} else if (z <= -1.7e-8) {
		tmp = x / (1.0 - z);
	} else if ((z <= -8.1e-109) || !(z <= 1.55e-79)) {
		tmp = t_1;
	} else {
		tmp = x + (z / (y / (t - a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    if (z <= (-95000000000.0d0)) then
        tmp = t_1
    else if (z <= (-1.7d-8)) then
        tmp = x / (1.0d0 - z)
    else if ((z <= (-8.1d-109)) .or. (.not. (z <= 1.55d-79))) then
        tmp = t_1
    else
        tmp = x + (z / (y / (t - a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -95000000000.0) {
		tmp = t_1;
	} else if (z <= -1.7e-8) {
		tmp = x / (1.0 - z);
	} else if ((z <= -8.1e-109) || !(z <= 1.55e-79)) {
		tmp = t_1;
	} else {
		tmp = x + (z / (y / (t - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	tmp = 0
	if z <= -95000000000.0:
		tmp = t_1
	elif z <= -1.7e-8:
		tmp = x / (1.0 - z)
	elif (z <= -8.1e-109) or not (z <= 1.55e-79):
		tmp = t_1
	else:
		tmp = x + (z / (y / (t - a)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -95000000000.0)
		tmp = t_1;
	elseif (z <= -1.7e-8)
		tmp = Float64(x / Float64(1.0 - z));
	elseif ((z <= -8.1e-109) || !(z <= 1.55e-79))
		tmp = t_1;
	else
		tmp = Float64(x + Float64(z / Float64(y / Float64(t - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -95000000000.0)
		tmp = t_1;
	elseif (z <= -1.7e-8)
		tmp = x / (1.0 - z);
	elseif ((z <= -8.1e-109) || ~((z <= 1.55e-79)))
		tmp = t_1;
	else
		tmp = x + (z / (y / (t - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -95000000000.0], t$95$1, If[LessEqual[z, -1.7e-8], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -8.1e-109], N[Not[LessEqual[z, 1.55e-79]], $MachinePrecision]], t$95$1, N[(x + N[(z / N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

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

Alternative 11: 69.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -1.4 \cdot 10^{+35}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-7}:\\ \;\;\;\;\frac{-x}{z + -1} - \frac{t}{y}\\ \mathbf{elif}\;z \leq -8.1 \cdot 10^{-109} \lor \neg \left(z \leq 6.6 \cdot 10^{-80}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{y}{t - a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -1.4e+35)
     t_1
     (if (<= z -5.8e-7)
       (- (/ (- x) (+ z -1.0)) (/ t y))
       (if (or (<= z -8.1e-109) (not (<= z 6.6e-80)))
         t_1
         (+ x (/ z (/ y (- t a)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -1.4e+35) {
		tmp = t_1;
	} else if (z <= -5.8e-7) {
		tmp = (-x / (z + -1.0)) - (t / y);
	} else if ((z <= -8.1e-109) || !(z <= 6.6e-80)) {
		tmp = t_1;
	} else {
		tmp = x + (z / (y / (t - a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    if (z <= (-1.4d+35)) then
        tmp = t_1
    else if (z <= (-5.8d-7)) then
        tmp = (-x / (z + (-1.0d0))) - (t / y)
    else if ((z <= (-8.1d-109)) .or. (.not. (z <= 6.6d-80))) then
        tmp = t_1
    else
        tmp = x + (z / (y / (t - a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -1.4e+35) {
		tmp = t_1;
	} else if (z <= -5.8e-7) {
		tmp = (-x / (z + -1.0)) - (t / y);
	} else if ((z <= -8.1e-109) || !(z <= 6.6e-80)) {
		tmp = t_1;
	} else {
		tmp = x + (z / (y / (t - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	tmp = 0
	if z <= -1.4e+35:
		tmp = t_1
	elif z <= -5.8e-7:
		tmp = (-x / (z + -1.0)) - (t / y)
	elif (z <= -8.1e-109) or not (z <= 6.6e-80):
		tmp = t_1
	else:
		tmp = x + (z / (y / (t - a)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -1.4e+35)
		tmp = t_1;
	elseif (z <= -5.8e-7)
		tmp = Float64(Float64(Float64(-x) / Float64(z + -1.0)) - Float64(t / y));
	elseif ((z <= -8.1e-109) || !(z <= 6.6e-80))
		tmp = t_1;
	else
		tmp = Float64(x + Float64(z / Float64(y / Float64(t - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -1.4e+35)
		tmp = t_1;
	elseif (z <= -5.8e-7)
		tmp = (-x / (z + -1.0)) - (t / y);
	elseif ((z <= -8.1e-109) || ~((z <= 6.6e-80)))
		tmp = t_1;
	else
		tmp = x + (z / (y / (t - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.4e+35], t$95$1, If[LessEqual[z, -5.8e-7], N[(N[((-x) / N[(z + -1.0), $MachinePrecision]), $MachinePrecision] - N[(t / y), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -8.1e-109], N[Not[LessEqual[z, 6.6e-80]], $MachinePrecision]], t$95$1, N[(x + N[(z / N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

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

Alternative 12: 69.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -2 \cdot 10^{+17}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-7}:\\ \;\;\;\;\frac{x}{1 + \frac{z}{\frac{y}{b - y}}}\\ \mathbf{elif}\;z \leq -8.1 \cdot 10^{-109} \lor \neg \left(z \leq 1.55 \cdot 10^{-79}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{y}{t - a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -2e+17)
     t_1
     (if (<= z -1.6e-7)
       (/ x (+ 1.0 (/ z (/ y (- b y)))))
       (if (or (<= z -8.1e-109) (not (<= z 1.55e-79)))
         t_1
         (+ x (/ z (/ y (- t a)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -2e+17) {
		tmp = t_1;
	} else if (z <= -1.6e-7) {
		tmp = x / (1.0 + (z / (y / (b - y))));
	} else if ((z <= -8.1e-109) || !(z <= 1.55e-79)) {
		tmp = t_1;
	} else {
		tmp = x + (z / (y / (t - a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    if (z <= (-2d+17)) then
        tmp = t_1
    else if (z <= (-1.6d-7)) then
        tmp = x / (1.0d0 + (z / (y / (b - y))))
    else if ((z <= (-8.1d-109)) .or. (.not. (z <= 1.55d-79))) then
        tmp = t_1
    else
        tmp = x + (z / (y / (t - a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -2e+17) {
		tmp = t_1;
	} else if (z <= -1.6e-7) {
		tmp = x / (1.0 + (z / (y / (b - y))));
	} else if ((z <= -8.1e-109) || !(z <= 1.55e-79)) {
		tmp = t_1;
	} else {
		tmp = x + (z / (y / (t - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	tmp = 0
	if z <= -2e+17:
		tmp = t_1
	elif z <= -1.6e-7:
		tmp = x / (1.0 + (z / (y / (b - y))))
	elif (z <= -8.1e-109) or not (z <= 1.55e-79):
		tmp = t_1
	else:
		tmp = x + (z / (y / (t - a)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -2e+17)
		tmp = t_1;
	elseif (z <= -1.6e-7)
		tmp = Float64(x / Float64(1.0 + Float64(z / Float64(y / Float64(b - y)))));
	elseif ((z <= -8.1e-109) || !(z <= 1.55e-79))
		tmp = t_1;
	else
		tmp = Float64(x + Float64(z / Float64(y / Float64(t - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -2e+17)
		tmp = t_1;
	elseif (z <= -1.6e-7)
		tmp = x / (1.0 + (z / (y / (b - y))));
	elseif ((z <= -8.1e-109) || ~((z <= 1.55e-79)))
		tmp = t_1;
	else
		tmp = x + (z / (y / (t - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2e+17], t$95$1, If[LessEqual[z, -1.6e-7], N[(x / N[(1.0 + N[(z / N[(y / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -8.1e-109], N[Not[LessEqual[z, 1.55e-79]], $MachinePrecision]], t$95$1, N[(x + N[(z / N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

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

Alternative 13: 64.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -95000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-7}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;z \leq -1.38 \cdot 10^{-120} \lor \neg \left(z \leq 6.6 \cdot 10^{-80}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -95000000000.0)
     t_1
     (if (<= z -1.6e-7)
       (/ x (- 1.0 z))
       (if (or (<= z -1.38e-120) (not (<= z 6.6e-80))) t_1 x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -95000000000.0) {
		tmp = t_1;
	} else if (z <= -1.6e-7) {
		tmp = x / (1.0 - z);
	} else if ((z <= -1.38e-120) || !(z <= 6.6e-80)) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    if (z <= (-95000000000.0d0)) then
        tmp = t_1
    else if (z <= (-1.6d-7)) then
        tmp = x / (1.0d0 - z)
    else if ((z <= (-1.38d-120)) .or. (.not. (z <= 6.6d-80))) then
        tmp = t_1
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -95000000000.0) {
		tmp = t_1;
	} else if (z <= -1.6e-7) {
		tmp = x / (1.0 - z);
	} else if ((z <= -1.38e-120) || !(z <= 6.6e-80)) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	tmp = 0
	if z <= -95000000000.0:
		tmp = t_1
	elif z <= -1.6e-7:
		tmp = x / (1.0 - z)
	elif (z <= -1.38e-120) or not (z <= 6.6e-80):
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -95000000000.0)
		tmp = t_1;
	elseif (z <= -1.6e-7)
		tmp = Float64(x / Float64(1.0 - z));
	elseif ((z <= -1.38e-120) || !(z <= 6.6e-80))
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -95000000000.0)
		tmp = t_1;
	elseif (z <= -1.6e-7)
		tmp = x / (1.0 - z);
	elseif ((z <= -1.38e-120) || ~((z <= 6.6e-80)))
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -95000000000.0], t$95$1, If[LessEqual[z, -1.6e-7], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -1.38e-120], N[Not[LessEqual[z, 6.6e-80]], $MachinePrecision]], t$95$1, x]]]]

Derivation

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

Alternative 14: 43.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a - t}{y}\\ \mathbf{if}\;z \leq -4 \cdot 10^{+15}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-79}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+111}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+123}:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- a t) y)))
   (if (<= z -4e+15)
     t_1
     (if (<= z 1.55e-79)
       (/ x (- 1.0 z))
       (if (<= z 1.55e+111)
         (/ t (- b y))
         (if (<= z 3.8e+123) (/ (- x) z) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a - t) / y;
	double tmp;
	if (z <= -4e+15) {
		tmp = t_1;
	} else if (z <= 1.55e-79) {
		tmp = x / (1.0 - z);
	} else if (z <= 1.55e+111) {
		tmp = t / (b - y);
	} else if (z <= 3.8e+123) {
		tmp = -x / z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a - t) / y
    if (z <= (-4d+15)) then
        tmp = t_1
    else if (z <= 1.55d-79) then
        tmp = x / (1.0d0 - z)
    else if (z <= 1.55d+111) then
        tmp = t / (b - y)
    else if (z <= 3.8d+123) then
        tmp = -x / z
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a - t) / y;
	double tmp;
	if (z <= -4e+15) {
		tmp = t_1;
	} else if (z <= 1.55e-79) {
		tmp = x / (1.0 - z);
	} else if (z <= 1.55e+111) {
		tmp = t / (b - y);
	} else if (z <= 3.8e+123) {
		tmp = -x / z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a - t) / y
	tmp = 0
	if z <= -4e+15:
		tmp = t_1
	elif z <= 1.55e-79:
		tmp = x / (1.0 - z)
	elif z <= 1.55e+111:
		tmp = t / (b - y)
	elif z <= 3.8e+123:
		tmp = -x / z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a - t) / y)
	tmp = 0.0
	if (z <= -4e+15)
		tmp = t_1;
	elseif (z <= 1.55e-79)
		tmp = Float64(x / Float64(1.0 - z));
	elseif (z <= 1.55e+111)
		tmp = Float64(t / Float64(b - y));
	elseif (z <= 3.8e+123)
		tmp = Float64(Float64(-x) / z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a - t) / y;
	tmp = 0.0;
	if (z <= -4e+15)
		tmp = t_1;
	elseif (z <= 1.55e-79)
		tmp = x / (1.0 - z);
	elseif (z <= 1.55e+111)
		tmp = t / (b - y);
	elseif (z <= 3.8e+123)
		tmp = -x / z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[z, -4e+15], t$95$1, If[LessEqual[z, 1.55e-79], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.55e+111], N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.8e+123], N[((-x) / z), $MachinePrecision], t$95$1]]]]]

Derivation

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

Alternative 15: 51.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -4.3 \cdot 10^{+181}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.95 \cdot 10^{+102}:\\ \;\;\;\;\frac{a - t}{y}\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{+92}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.95 \cdot 10^{-87}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (- 1.0 z))))
   (if (<= y -4.3e+181)
     t_1
     (if (<= y -1.95e+102)
       (/ (- a t) y)
       (if (<= y -1.6e+92) x (if (<= y 2.95e-87) (/ (- t a) b) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 - z);
	double tmp;
	if (y <= -4.3e+181) {
		tmp = t_1;
	} else if (y <= -1.95e+102) {
		tmp = (a - t) / y;
	} else if (y <= -1.6e+92) {
		tmp = x;
	} else if (y <= 2.95e-87) {
		tmp = (t - a) / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (1.0d0 - z)
    if (y <= (-4.3d+181)) then
        tmp = t_1
    else if (y <= (-1.95d+102)) then
        tmp = (a - t) / y
    else if (y <= (-1.6d+92)) then
        tmp = x
    else if (y <= 2.95d-87) then
        tmp = (t - a) / b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 - z);
	double tmp;
	if (y <= -4.3e+181) {
		tmp = t_1;
	} else if (y <= -1.95e+102) {
		tmp = (a - t) / y;
	} else if (y <= -1.6e+92) {
		tmp = x;
	} else if (y <= 2.95e-87) {
		tmp = (t - a) / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (1.0 - z)
	tmp = 0
	if y <= -4.3e+181:
		tmp = t_1
	elif y <= -1.95e+102:
		tmp = (a - t) / y
	elif y <= -1.6e+92:
		tmp = x
	elif y <= 2.95e-87:
		tmp = (t - a) / b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(1.0 - z))
	tmp = 0.0
	if (y <= -4.3e+181)
		tmp = t_1;
	elseif (y <= -1.95e+102)
		tmp = Float64(Float64(a - t) / y);
	elseif (y <= -1.6e+92)
		tmp = x;
	elseif (y <= 2.95e-87)
		tmp = Float64(Float64(t - a) / b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (1.0 - z);
	tmp = 0.0;
	if (y <= -4.3e+181)
		tmp = t_1;
	elseif (y <= -1.95e+102)
		tmp = (a - t) / y;
	elseif (y <= -1.6e+92)
		tmp = x;
	elseif (y <= 2.95e-87)
		tmp = (t - a) / b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.3e+181], t$95$1, If[LessEqual[y, -1.95e+102], N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, -1.6e+92], x, If[LessEqual[y, 2.95e-87], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision], t$95$1]]]]]

Derivation

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

Alternative 16: 33.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{-89}:\\ \;\;\;\;\frac{a}{y}\\ \mathbf{elif}\;z \leq 0.98:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+137} \lor \neg \left(z \leq 6.5 \cdot 10^{+241}\right):\\ \;\;\;\;\frac{-t}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -4.6e-89)
   (/ a y)
   (if (<= z 0.98)
     x
     (if (or (<= z 2e+137) (not (<= z 6.5e+241))) (/ (- t) y) (/ a y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -4.6e-89) {
		tmp = a / y;
	} else if (z <= 0.98) {
		tmp = x;
	} else if ((z <= 2e+137) || !(z <= 6.5e+241)) {
		tmp = -t / y;
	} else {
		tmp = a / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-4.6d-89)) then
        tmp = a / y
    else if (z <= 0.98d0) then
        tmp = x
    else if ((z <= 2d+137) .or. (.not. (z <= 6.5d+241))) then
        tmp = -t / y
    else
        tmp = a / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -4.6e-89) {
		tmp = a / y;
	} else if (z <= 0.98) {
		tmp = x;
	} else if ((z <= 2e+137) || !(z <= 6.5e+241)) {
		tmp = -t / y;
	} else {
		tmp = a / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -4.6e-89:
		tmp = a / y
	elif z <= 0.98:
		tmp = x
	elif (z <= 2e+137) or not (z <= 6.5e+241):
		tmp = -t / y
	else:
		tmp = a / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -4.6e-89)
		tmp = Float64(a / y);
	elseif (z <= 0.98)
		tmp = x;
	elseif ((z <= 2e+137) || !(z <= 6.5e+241))
		tmp = Float64(Float64(-t) / y);
	else
		tmp = Float64(a / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -4.6e-89)
		tmp = a / y;
	elseif (z <= 0.98)
		tmp = x;
	elseif ((z <= 2e+137) || ~((z <= 6.5e+241)))
		tmp = -t / y;
	else
		tmp = a / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -4.6e-89], N[(a / y), $MachinePrecision], If[LessEqual[z, 0.98], x, If[Or[LessEqual[z, 2e+137], N[Not[LessEqual[z, 6.5e+241]], $MachinePrecision]], N[((-t) / y), $MachinePrecision], N[(a / y), $MachinePrecision]]]]

Derivation

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

Alternative 17: 33.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{-89}:\\ \;\;\;\;\frac{a}{y}\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-5}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+137} \lor \neg \left(z \leq 5.4 \cdot 10^{+244}\right):\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -4.6e-89)
   (/ a y)
   (if (<= z 1.55e-5)
     x
     (if (or (<= z 2.4e+137) (not (<= z 5.4e+244))) (/ (- x) z) (/ a y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -4.6e-89) {
		tmp = a / y;
	} else if (z <= 1.55e-5) {
		tmp = x;
	} else if ((z <= 2.4e+137) || !(z <= 5.4e+244)) {
		tmp = -x / z;
	} else {
		tmp = a / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-4.6d-89)) then
        tmp = a / y
    else if (z <= 1.55d-5) then
        tmp = x
    else if ((z <= 2.4d+137) .or. (.not. (z <= 5.4d+244))) then
        tmp = -x / z
    else
        tmp = a / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -4.6e-89) {
		tmp = a / y;
	} else if (z <= 1.55e-5) {
		tmp = x;
	} else if ((z <= 2.4e+137) || !(z <= 5.4e+244)) {
		tmp = -x / z;
	} else {
		tmp = a / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -4.6e-89:
		tmp = a / y
	elif z <= 1.55e-5:
		tmp = x
	elif (z <= 2.4e+137) or not (z <= 5.4e+244):
		tmp = -x / z
	else:
		tmp = a / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -4.6e-89)
		tmp = Float64(a / y);
	elseif (z <= 1.55e-5)
		tmp = x;
	elseif ((z <= 2.4e+137) || !(z <= 5.4e+244))
		tmp = Float64(Float64(-x) / z);
	else
		tmp = Float64(a / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -4.6e-89)
		tmp = a / y;
	elseif (z <= 1.55e-5)
		tmp = x;
	elseif ((z <= 2.4e+137) || ~((z <= 5.4e+244)))
		tmp = -x / z;
	else
		tmp = a / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -4.6e-89], N[(a / y), $MachinePrecision], If[LessEqual[z, 1.55e-5], x, If[Or[LessEqual[z, 2.4e+137], N[Not[LessEqual[z, 5.4e+244]], $MachinePrecision]], N[((-x) / z), $MachinePrecision], N[(a / y), $MachinePrecision]]]]

Derivation

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

Alternative 18: 44.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-89} \lor \neg \left(z \leq 3.1 \cdot 10^{-80}\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -2e-89) (not (<= z 3.1e-80))) (/ t (- b y)) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2e-89) || !(z <= 3.1e-80)) {
		tmp = t / (b - y);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-2d-89)) .or. (.not. (z <= 3.1d-80))) then
        tmp = t / (b - y)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2e-89) || !(z <= 3.1e-80)) {
		tmp = t / (b - y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -2e-89) or not (z <= 3.1e-80):
		tmp = t / (b - y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -2e-89) || !(z <= 3.1e-80))
		tmp = Float64(t / Float64(b - y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -2e-89) || ~((z <= 3.1e-80)))
		tmp = t / (b - y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -2e-89], N[Not[LessEqual[z, 3.1e-80]], $MachinePrecision]], N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision], x]

Derivation

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

Alternative 19: 44.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+16} \lor \neg \left(z \leq 1.55 \cdot 10^{-79}\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -2.9e+16) (not (<= z 1.55e-79))) (/ t (- b y)) (/ x (- 1.0 z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.9e+16) || !(z <= 1.55e-79)) {
		tmp = t / (b - y);
	} else {
		tmp = x / (1.0 - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-2.9d+16)) .or. (.not. (z <= 1.55d-79))) then
        tmp = t / (b - y)
    else
        tmp = x / (1.0d0 - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.9e+16) || !(z <= 1.55e-79)) {
		tmp = t / (b - y);
	} else {
		tmp = x / (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -2.9e+16) or not (z <= 1.55e-79):
		tmp = t / (b - y)
	else:
		tmp = x / (1.0 - z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -2.9e+16) || !(z <= 1.55e-79))
		tmp = Float64(t / Float64(b - y));
	else
		tmp = Float64(x / Float64(1.0 - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -2.9e+16) || ~((z <= 1.55e-79)))
		tmp = t / (b - y);
	else
		tmp = x / (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -2.9e+16], N[Not[LessEqual[z, 1.55e-79]], $MachinePrecision]], N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 20: 33.2% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{-89} \lor \neg \left(z \leq 0.00175\right):\\ \;\;\;\;\frac{a}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -4.6e-89) (not (<= z 0.00175))) (/ a y) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -4.6e-89) || !(z <= 0.00175)) {
		tmp = a / y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-4.6d-89)) .or. (.not. (z <= 0.00175d0))) then
        tmp = a / y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -4.6e-89) || !(z <= 0.00175)) {
		tmp = a / y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -4.6e-89) or not (z <= 0.00175):
		tmp = a / y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -4.6e-89) || !(z <= 0.00175))
		tmp = Float64(a / y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -4.6e-89) || ~((z <= 0.00175)))
		tmp = a / y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -4.6e-89], N[Not[LessEqual[z, 0.00175]], $MachinePrecision]], N[(a / y), $MachinePrecision], x]

Derivation

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

Alternative 21: 25.6% accurate, 17.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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

Developer target: 73.5% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024008 
(FPCore (x y z t a b)
  :name "Development.Shake.Progress:decay from shake-0.15.5"
  :precision binary64

  :herbie-target
  (- (/ (+ (* z t) (* y x)) (+ y (* z (- b y)))) (/ a (+ (- b y) (/ y z))))

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