Development.Shake.Progress:decay from shake-0.15.5

Percentage Accurate: 65.8% → 88.0%

Time: 16.6s

Alternatives: 19

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: 65.8% 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: 88.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ \mathbf{if}\;z \leq -4.9 \cdot 10^{+64}:\\ \;\;\;\;\frac{y}{z} \cdot \frac{x}{b - y} + \left(\frac{t}{b - y} + \left(\frac{a - t}{\frac{z \cdot {\left(b - y\right)}^{2}}{y}} - \frac{a}{b - y}\right)\right)\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-14}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{t_1} + \frac{y}{\frac{t_1}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{a - t}{y - b} - \frac{\frac{y}{\frac{y - b}{x}} + \frac{t - a}{\frac{{\left(y - b\right)}^{2}}{y}}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y)))))
   (if (<= z -4.9e+64)
     (+
      (* (/ y z) (/ x (- b y)))
      (+
       (/ t (- b y))
       (- (/ (- a t) (/ (* z (pow (- b y) 2.0)) y)) (/ a (- b y)))))
     (if (<= z 1.5e-14)
       (+ (/ (* z (- t a)) t_1) (/ y (/ t_1 x)))
       (-
        (/ (- a t) (- y b))
        (/ (+ (/ y (/ (- y b) x)) (/ (- t a) (/ (pow (- y b) 2.0) y))) z))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double tmp;
	if (z <= -4.9e+64) {
		tmp = ((y / z) * (x / (b - y))) + ((t / (b - y)) + (((a - t) / ((z * pow((b - y), 2.0)) / y)) - (a / (b - y))));
	} else if (z <= 1.5e-14) {
		tmp = ((z * (t - a)) / t_1) + (y / (t_1 / x));
	} else {
		tmp = ((a - t) / (y - b)) - (((y / ((y - b) / x)) + ((t - a) / (pow((y - b), 2.0) / y))) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y + (z * (b - y))
    if (z <= (-4.9d+64)) then
        tmp = ((y / z) * (x / (b - y))) + ((t / (b - y)) + (((a - t) / ((z * ((b - y) ** 2.0d0)) / y)) - (a / (b - y))))
    else if (z <= 1.5d-14) then
        tmp = ((z * (t - a)) / t_1) + (y / (t_1 / x))
    else
        tmp = ((a - t) / (y - b)) - (((y / ((y - b) / x)) + ((t - a) / (((y - b) ** 2.0d0) / y))) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double tmp;
	if (z <= -4.9e+64) {
		tmp = ((y / z) * (x / (b - y))) + ((t / (b - y)) + (((a - t) / ((z * Math.pow((b - y), 2.0)) / y)) - (a / (b - y))));
	} else if (z <= 1.5e-14) {
		tmp = ((z * (t - a)) / t_1) + (y / (t_1 / x));
	} else {
		tmp = ((a - t) / (y - b)) - (((y / ((y - b) / x)) + ((t - a) / (Math.pow((y - b), 2.0) / y))) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z * (b - y))
	tmp = 0
	if z <= -4.9e+64:
		tmp = ((y / z) * (x / (b - y))) + ((t / (b - y)) + (((a - t) / ((z * math.pow((b - y), 2.0)) / y)) - (a / (b - y))))
	elif z <= 1.5e-14:
		tmp = ((z * (t - a)) / t_1) + (y / (t_1 / x))
	else:
		tmp = ((a - t) / (y - b)) - (((y / ((y - b) / x)) + ((t - a) / (math.pow((y - b), 2.0) / y))) / z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(z * Float64(b - y)))
	tmp = 0.0
	if (z <= -4.9e+64)
		tmp = Float64(Float64(Float64(y / z) * Float64(x / Float64(b - y))) + Float64(Float64(t / Float64(b - y)) + Float64(Float64(Float64(a - t) / Float64(Float64(z * (Float64(b - y) ^ 2.0)) / y)) - Float64(a / Float64(b - y)))));
	elseif (z <= 1.5e-14)
		tmp = Float64(Float64(Float64(z * Float64(t - a)) / t_1) + Float64(y / Float64(t_1 / x)));
	else
		tmp = Float64(Float64(Float64(a - t) / Float64(y - b)) - Float64(Float64(Float64(y / Float64(Float64(y - b) / x)) + Float64(Float64(t - a) / Float64((Float64(y - b) ^ 2.0) / y))) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (z * (b - y));
	tmp = 0.0;
	if (z <= -4.9e+64)
		tmp = ((y / z) * (x / (b - y))) + ((t / (b - y)) + (((a - t) / ((z * ((b - y) ^ 2.0)) / y)) - (a / (b - y))));
	elseif (z <= 1.5e-14)
		tmp = ((z * (t - a)) / t_1) + (y / (t_1 / x));
	else
		tmp = ((a - t) / (y - b)) - (((y / ((y - b) / x)) + ((t - a) / (((y - b) ^ 2.0) / y))) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.9e+64], N[(N[(N[(y / z), $MachinePrecision] * N[(x / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(a - t), $MachinePrecision] / N[(N[(z * N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] - N[(a / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.5e-14], N[(N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision] + N[(y / N[(t$95$1 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(a - t), $MachinePrecision] / N[(y - b), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(y / N[(N[(y - b), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] + N[(N[(t - a), $MachinePrecision] / N[(N[Power[N[(y - b), $MachinePrecision], 2.0], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.9000000000000003e64

   1. Initial program 44.5%

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

   2. Taylor expanded in z around inf 66.7%

      \[\leadsto \color{blue}{\left(\frac{y \cdot x}{z \cdot \left(b - y\right)} + \frac{t}{b - y}\right) - \left(\frac{\left(t - a\right) \cdot y}{z \cdot {\left(b - y\right)}^{2}} + \frac{a}{b - y}\right)} \]
   3. Step-by-step derivation

      1. associate--l+ 66.7%

         \[\leadsto \color{blue}{\frac{y \cdot x}{z \cdot \left(b - y\right)} + \left(\frac{t}{b - y} - \left(\frac{\left(t - a\right) \cdot y}{z \cdot {\left(b - y\right)}^{2}} + \frac{a}{b - y}\right)\right)} \]

      2. times-frac 76.8%

         \[\leadsto \color{blue}{\frac{y}{z} \cdot \frac{x}{b - y}} + \left(\frac{t}{b - y} - \left(\frac{\left(t - a\right) \cdot y}{z \cdot {\left(b - y\right)}^{2}} + \frac{a}{b - y}\right)\right) \]

      3. +-commutative 76.8%

         \[\leadsto \frac{y}{z} \cdot \frac{x}{b - y} + \left(\frac{t}{b - y} - \color{blue}{\left(\frac{a}{b - y} + \frac{\left(t - a\right) \cdot y}{z \cdot {\left(b - y\right)}^{2}}\right)}\right) \]

      4. associate-/l* 94.7%

         \[\leadsto \frac{y}{z} \cdot \frac{x}{b - y} + \left(\frac{t}{b - y} - \left(\frac{a}{b - y} + \color{blue}{\frac{t - a}{\frac{z \cdot {\left(b - y\right)}^{2}}{y}}}\right)\right) \]

   4. Simplified 94.7%

      \[\leadsto \color{blue}{\frac{y}{z} \cdot \frac{x}{b - y} + \left(\frac{t}{b - y} - \left(\frac{a}{b - y} + \frac{t - a}{\frac{z \cdot {\left(b - y\right)}^{2}}{y}}\right)\right)} \]

   if -4.9000000000000003e64 < z < 1.4999999999999999e-14

   1. Initial program 88.2%

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

   2. Taylor expanded in x around inf 88.2%

      \[\leadsto \color{blue}{\frac{\left(t - a\right) \cdot z}{y + \left(b - y\right) \cdot z} + \frac{y \cdot x}{y + \left(b - y\right) \cdot z}} \]
   3. Step-by-step derivation

      1. *-un-lft-identity 88.2%

         \[\leadsto \frac{\left(t - a\right) \cdot z}{y + \left(b - y\right) \cdot z} + \color{blue}{1 \cdot \frac{y \cdot x}{y + \left(b - y\right) \cdot z}} \]

      2. associate-/l* 90.3%

         \[\leadsto \frac{\left(t - a\right) \cdot z}{y + \left(b - y\right) \cdot z} + 1 \cdot \color{blue}{\frac{y}{\frac{y + \left(b - y\right) \cdot z}{x}}} \]

      3. *-commutative 90.3%

         \[\leadsto \frac{\left(t - a\right) \cdot z}{y + \left(b - y\right) \cdot z} + 1 \cdot \frac{y}{\frac{y + \color{blue}{z \cdot \left(b - y\right)}}{x}} \]

   4. Applied egg-rr 90.3%

      \[\leadsto \frac{\left(t - a\right) \cdot z}{y + \left(b - y\right) \cdot z} + \color{blue}{1 \cdot \frac{y}{\frac{y + z \cdot \left(b - y\right)}{x}}} \]

   if 1.4999999999999999e-14 < z

   1. Initial program 51.2%

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

      1. sub-neg 51.2%

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

      2. distribute-lft-in 51.3%

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

   3. Applied egg-rr 51.3%

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

   4. Taylor expanded in z around -inf 73.2%

      \[\leadsto \color{blue}{-1 \cdot \frac{t - a}{y + -1 \cdot b} + -1 \cdot \frac{\frac{y \cdot x}{y + -1 \cdot b} - -1 \cdot \frac{\left(t - a\right) \cdot y}{{\left(y + -1 \cdot b\right)}^{2}}}{z}} \]
   5. Step-by-step derivation

      1. mul-1-neg 73.2%

         \[\leadsto -1 \cdot \frac{t - a}{y + -1 \cdot b} + \color{blue}{\left(-\frac{\frac{y \cdot x}{y + -1 \cdot b} - -1 \cdot \frac{\left(t - a\right) \cdot y}{{\left(y + -1 \cdot b\right)}^{2}}}{z}\right)} \]

      2. unsub-neg 73.2%

         \[\leadsto \color{blue}{-1 \cdot \frac{t - a}{y + -1 \cdot b} - \frac{\frac{y \cdot x}{y + -1 \cdot b} - -1 \cdot \frac{\left(t - a\right) \cdot y}{{\left(y + -1 \cdot b\right)}^{2}}}{z}} \]

      3. associate-*r/ 73.2%

         \[\leadsto \color{blue}{\frac{-1 \cdot \left(t - a\right)}{y + -1 \cdot b}} - \frac{\frac{y \cdot x}{y + -1 \cdot b} - -1 \cdot \frac{\left(t - a\right) \cdot y}{{\left(y + -1 \cdot b\right)}^{2}}}{z} \]

      4. mul-1-neg 73.2%

         \[\leadsto \frac{\color{blue}{-\left(t - a\right)}}{y + -1 \cdot b} - \frac{\frac{y \cdot x}{y + -1 \cdot b} - -1 \cdot \frac{\left(t - a\right) \cdot y}{{\left(y + -1 \cdot b\right)}^{2}}}{z} \]

      5. mul-1-neg 73.2%

         \[\leadsto \frac{-\left(t - a\right)}{y + \color{blue}{\left(-b\right)}} - \frac{\frac{y \cdot x}{y + -1 \cdot b} - -1 \cdot \frac{\left(t - a\right) \cdot y}{{\left(y + -1 \cdot b\right)}^{2}}}{z} \]

      6. unsub-neg 73.2%

         \[\leadsto \frac{-\left(t - a\right)}{\color{blue}{y - b}} - \frac{\frac{y \cdot x}{y + -1 \cdot b} - -1 \cdot \frac{\left(t - a\right) \cdot y}{{\left(y + -1 \cdot b\right)}^{2}}}{z} \]

   6. Simplified 93.5%

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

4. Final simplification 91.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.9 \cdot 10^{+64}:\\ \;\;\;\;\frac{y}{z} \cdot \frac{x}{b - y} + \left(\frac{t}{b - y} + \left(\frac{a - t}{\frac{z \cdot {\left(b - y\right)}^{2}}{y}} - \frac{a}{b - y}\right)\right)\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-14}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} + \frac{y}{\frac{y + z \cdot \left(b - y\right)}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{a - t}{y - b} - \frac{\frac{y}{\frac{y - b}{x}} + \frac{t - a}{\frac{{\left(y - b\right)}^{2}}{y}}}{z}\\ \end{array} \]

Alternative 2: 88.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ \mathbf{if}\;z \leq -5.1 \cdot 10^{+64} \lor \neg \left(z \leq 1.5 \cdot 10^{-14}\right):\\ \;\;\;\;\frac{a - t}{y - b} - \frac{\frac{y}{\frac{y - b}{x}} + \frac{t - a}{\frac{{\left(y - b\right)}^{2}}{y}}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{t_1} + \frac{y}{\frac{t_1}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y)))))
   (if (or (<= z -5.1e+64) (not (<= z 1.5e-14)))
     (-
      (/ (- a t) (- y b))
      (/ (+ (/ y (/ (- y b) x)) (/ (- t a) (/ (pow (- y b) 2.0) y))) z))
     (+ (/ (* z (- t a)) t_1) (/ y (/ t_1 x))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double tmp;
	if ((z <= -5.1e+64) || !(z <= 1.5e-14)) {
		tmp = ((a - t) / (y - b)) - (((y / ((y - b) / x)) + ((t - a) / (pow((y - b), 2.0) / y))) / z);
	} else {
		tmp = ((z * (t - a)) / t_1) + (y / (t_1 / 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 = y + (z * (b - y))
    if ((z <= (-5.1d+64)) .or. (.not. (z <= 1.5d-14))) then
        tmp = ((a - t) / (y - b)) - (((y / ((y - b) / x)) + ((t - a) / (((y - b) ** 2.0d0) / y))) / z)
    else
        tmp = ((z * (t - a)) / t_1) + (y / (t_1 / 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 = y + (z * (b - y));
	double tmp;
	if ((z <= -5.1e+64) || !(z <= 1.5e-14)) {
		tmp = ((a - t) / (y - b)) - (((y / ((y - b) / x)) + ((t - a) / (Math.pow((y - b), 2.0) / y))) / z);
	} else {
		tmp = ((z * (t - a)) / t_1) + (y / (t_1 / x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z * (b - y))
	tmp = 0
	if (z <= -5.1e+64) or not (z <= 1.5e-14):
		tmp = ((a - t) / (y - b)) - (((y / ((y - b) / x)) + ((t - a) / (math.pow((y - b), 2.0) / y))) / z)
	else:
		tmp = ((z * (t - a)) / t_1) + (y / (t_1 / x))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(z * Float64(b - y)))
	tmp = 0.0
	if ((z <= -5.1e+64) || !(z <= 1.5e-14))
		tmp = Float64(Float64(Float64(a - t) / Float64(y - b)) - Float64(Float64(Float64(y / Float64(Float64(y - b) / x)) + Float64(Float64(t - a) / Float64((Float64(y - b) ^ 2.0) / y))) / z));
	else
		tmp = Float64(Float64(Float64(z * Float64(t - a)) / t_1) + Float64(y / Float64(t_1 / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (z * (b - y));
	tmp = 0.0;
	if ((z <= -5.1e+64) || ~((z <= 1.5e-14)))
		tmp = ((a - t) / (y - b)) - (((y / ((y - b) / x)) + ((t - a) / (((y - b) ^ 2.0) / y))) / z);
	else
		tmp = ((z * (t - a)) / t_1) + (y / (t_1 / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[z, -5.1e+64], N[Not[LessEqual[z, 1.5e-14]], $MachinePrecision]], N[(N[(N[(a - t), $MachinePrecision] / N[(y - b), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(y / N[(N[(y - b), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] + N[(N[(t - a), $MachinePrecision] / N[(N[Power[N[(y - b), $MachinePrecision], 2.0], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision] + N[(y / N[(t$95$1 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.10000000000000024e64 or 1.4999999999999999e-14 < z

   1. Initial program 49.0%

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

      1. sub-neg 49.0%

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

      2. distribute-lft-in 48.9%

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

   3. Applied egg-rr 48.9%

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

   4. Taylor expanded in z around -inf 70.3%

      \[\leadsto \color{blue}{-1 \cdot \frac{t - a}{y + -1 \cdot b} + -1 \cdot \frac{\frac{y \cdot x}{y + -1 \cdot b} - -1 \cdot \frac{\left(t - a\right) \cdot y}{{\left(y + -1 \cdot b\right)}^{2}}}{z}} \]
   5. Step-by-step derivation

      1. mul-1-neg 70.3%

         \[\leadsto -1 \cdot \frac{t - a}{y + -1 \cdot b} + \color{blue}{\left(-\frac{\frac{y \cdot x}{y + -1 \cdot b} - -1 \cdot \frac{\left(t - a\right) \cdot y}{{\left(y + -1 \cdot b\right)}^{2}}}{z}\right)} \]

      2. unsub-neg 70.3%

         \[\leadsto \color{blue}{-1 \cdot \frac{t - a}{y + -1 \cdot b} - \frac{\frac{y \cdot x}{y + -1 \cdot b} - -1 \cdot \frac{\left(t - a\right) \cdot y}{{\left(y + -1 \cdot b\right)}^{2}}}{z}} \]

      3. associate-*r/ 70.3%

         \[\leadsto \color{blue}{\frac{-1 \cdot \left(t - a\right)}{y + -1 \cdot b}} - \frac{\frac{y \cdot x}{y + -1 \cdot b} - -1 \cdot \frac{\left(t - a\right) \cdot y}{{\left(y + -1 \cdot b\right)}^{2}}}{z} \]

      4. mul-1-neg 70.3%

         \[\leadsto \frac{\color{blue}{-\left(t - a\right)}}{y + -1 \cdot b} - \frac{\frac{y \cdot x}{y + -1 \cdot b} - -1 \cdot \frac{\left(t - a\right) \cdot y}{{\left(y + -1 \cdot b\right)}^{2}}}{z} \]

      5. mul-1-neg 70.3%

         \[\leadsto \frac{-\left(t - a\right)}{y + \color{blue}{\left(-b\right)}} - \frac{\frac{y \cdot x}{y + -1 \cdot b} - -1 \cdot \frac{\left(t - a\right) \cdot y}{{\left(y + -1 \cdot b\right)}^{2}}}{z} \]

      6. unsub-neg 70.3%

         \[\leadsto \frac{-\left(t - a\right)}{\color{blue}{y - b}} - \frac{\frac{y \cdot x}{y + -1 \cdot b} - -1 \cdot \frac{\left(t - a\right) \cdot y}{{\left(y + -1 \cdot b\right)}^{2}}}{z} \]

   6. Simplified 93.1%

      \[\leadsto \color{blue}{\frac{-\left(t - a\right)}{y - b} - \frac{\frac{y}{\frac{y - b}{x}} + \frac{t - a}{\frac{{\left(y - b\right)}^{2}}{y}}}{z}} \]

   if -5.10000000000000024e64 < z < 1.4999999999999999e-14

   1. Initial program 88.2%

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

   2. Taylor expanded in x around inf 88.2%

      \[\leadsto \color{blue}{\frac{\left(t - a\right) \cdot z}{y + \left(b - y\right) \cdot z} + \frac{y \cdot x}{y + \left(b - y\right) \cdot z}} \]
   3. Step-by-step derivation

      1. *-un-lft-identity 88.2%

         \[\leadsto \frac{\left(t - a\right) \cdot z}{y + \left(b - y\right) \cdot z} + \color{blue}{1 \cdot \frac{y \cdot x}{y + \left(b - y\right) \cdot z}} \]

      2. associate-/l* 90.3%

         \[\leadsto \frac{\left(t - a\right) \cdot z}{y + \left(b - y\right) \cdot z} + 1 \cdot \color{blue}{\frac{y}{\frac{y + \left(b - y\right) \cdot z}{x}}} \]

      3. *-commutative 90.3%

         \[\leadsto \frac{\left(t - a\right) \cdot z}{y + \left(b - y\right) \cdot z} + 1 \cdot \frac{y}{\frac{y + \color{blue}{z \cdot \left(b - y\right)}}{x}} \]

   4. Applied egg-rr 90.3%

      \[\leadsto \frac{\left(t - a\right) \cdot z}{y + \left(b - y\right) \cdot z} + \color{blue}{1 \cdot \frac{y}{\frac{y + z \cdot \left(b - y\right)}{x}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.1 \cdot 10^{+64} \lor \neg \left(z \leq 1.5 \cdot 10^{-14}\right):\\ \;\;\;\;\frac{a - t}{y - b} - \frac{\frac{y}{\frac{y - b}{x}} + \frac{t - a}{\frac{{\left(y - b\right)}^{2}}{y}}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} + \frac{y}{\frac{y + z \cdot \left(b - y\right)}{x}}\\ \end{array} \]

Alternative 3: 83.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := \frac{z \cdot \left(t - a\right)}{t_1}\\ t_3 := t_2 + \frac{y \cdot x}{t_1}\\ t_4 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -3.1 \cdot 10^{+84}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq -5.3 \cdot 10^{-236}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 10^{-103}:\\ \;\;\;\;x + t_2\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+44}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y))))
        (t_2 (/ (* z (- t a)) t_1))
        (t_3 (+ t_2 (/ (* y x) t_1)))
        (t_4 (/ (- t a) (- b y))))
   (if (<= z -3.1e+84)
     t_4
     (if (<= z -5.3e-236)
       t_3
       (if (<= z 1e-103) (+ x t_2) (if (<= z 8.5e+44) t_3 t_4))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double t_2 = (z * (t - a)) / t_1;
	double t_3 = t_2 + ((y * x) / t_1);
	double t_4 = (t - a) / (b - y);
	double tmp;
	if (z <= -3.1e+84) {
		tmp = t_4;
	} else if (z <= -5.3e-236) {
		tmp = t_3;
	} else if (z <= 1e-103) {
		tmp = x + t_2;
	} else if (z <= 8.5e+44) {
		tmp = t_3;
	} else {
		tmp = t_4;
	}
	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 = y + (z * (b - y))
    t_2 = (z * (t - a)) / t_1
    t_3 = t_2 + ((y * x) / t_1)
    t_4 = (t - a) / (b - y)
    if (z <= (-3.1d+84)) then
        tmp = t_4
    else if (z <= (-5.3d-236)) then
        tmp = t_3
    else if (z <= 1d-103) then
        tmp = x + t_2
    else if (z <= 8.5d+44) then
        tmp = t_3
    else
        tmp = t_4
    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 * (b - y));
	double t_2 = (z * (t - a)) / t_1;
	double t_3 = t_2 + ((y * x) / t_1);
	double t_4 = (t - a) / (b - y);
	double tmp;
	if (z <= -3.1e+84) {
		tmp = t_4;
	} else if (z <= -5.3e-236) {
		tmp = t_3;
	} else if (z <= 1e-103) {
		tmp = x + t_2;
	} else if (z <= 8.5e+44) {
		tmp = t_3;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z * (b - y))
	t_2 = (z * (t - a)) / t_1
	t_3 = t_2 + ((y * x) / t_1)
	t_4 = (t - a) / (b - y)
	tmp = 0
	if z <= -3.1e+84:
		tmp = t_4
	elif z <= -5.3e-236:
		tmp = t_3
	elif z <= 1e-103:
		tmp = x + t_2
	elif z <= 8.5e+44:
		tmp = t_3
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(z * Float64(b - y)))
	t_2 = Float64(Float64(z * Float64(t - a)) / t_1)
	t_3 = Float64(t_2 + Float64(Float64(y * x) / t_1))
	t_4 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -3.1e+84)
		tmp = t_4;
	elseif (z <= -5.3e-236)
		tmp = t_3;
	elseif (z <= 1e-103)
		tmp = Float64(x + t_2);
	elseif (z <= 8.5e+44)
		tmp = t_3;
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (z * (b - y));
	t_2 = (z * (t - a)) / t_1;
	t_3 = t_2 + ((y * x) / t_1);
	t_4 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -3.1e+84)
		tmp = t_4;
	elseif (z <= -5.3e-236)
		tmp = t_3;
	elseif (z <= 1e-103)
		tmp = x + t_2;
	elseif (z <= 8.5e+44)
		tmp = t_3;
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 + N[(N[(y * x), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.1e+84], t$95$4, If[LessEqual[z, -5.3e-236], t$95$3, If[LessEqual[z, 1e-103], N[(x + t$95$2), $MachinePrecision], If[LessEqual[z, 8.5e+44], t$95$3, t$95$4]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.10000000000000003e84 or 8.5e44 < z

   1. Initial program 40.7%

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

   2. Taylor expanded in z around inf 88.8%

      \[\leadsto \color{blue}{\frac{t - a}{b - y}} \]

   if -3.10000000000000003e84 < z < -5.3000000000000002e-236 or 9.99999999999999958e-104 < z < 8.5e44

   1. Initial program 90.0%

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

   2. Taylor expanded in x around inf 90.0%

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

   if -5.3000000000000002e-236 < z < 9.99999999999999958e-104

   1. Initial program 87.0%

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

   2. Taylor expanded in x around inf 87.0%

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

   3. Taylor expanded in z around 0 95.1%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+84}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -5.3 \cdot 10^{-236}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} + \frac{y \cdot x}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 10^{-103}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+44}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} + \frac{y \cdot x}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 4: 84.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ \mathbf{if}\;z \leq -8.2 \cdot 10^{+86} \lor \neg \left(z \leq 2.35 \cdot 10^{+48}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{t_1} + \frac{y}{\frac{t_1}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y)))))
   (if (or (<= z -8.2e+86) (not (<= z 2.35e+48)))
     (/ (- t a) (- b y))
     (+ (/ (* z (- t a)) t_1) (/ y (/ t_1 x))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double tmp;
	if ((z <= -8.2e+86) || !(z <= 2.35e+48)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((z * (t - a)) / t_1) + (y / (t_1 / 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 = y + (z * (b - y))
    if ((z <= (-8.2d+86)) .or. (.not. (z <= 2.35d+48))) then
        tmp = (t - a) / (b - y)
    else
        tmp = ((z * (t - a)) / t_1) + (y / (t_1 / 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 = y + (z * (b - y));
	double tmp;
	if ((z <= -8.2e+86) || !(z <= 2.35e+48)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((z * (t - a)) / t_1) + (y / (t_1 / x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z * (b - y))
	tmp = 0
	if (z <= -8.2e+86) or not (z <= 2.35e+48):
		tmp = (t - a) / (b - y)
	else:
		tmp = ((z * (t - a)) / t_1) + (y / (t_1 / x))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(z * Float64(b - y)))
	tmp = 0.0
	if ((z <= -8.2e+86) || !(z <= 2.35e+48))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(Float64(Float64(z * Float64(t - a)) / t_1) + Float64(y / Float64(t_1 / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (z * (b - y));
	tmp = 0.0;
	if ((z <= -8.2e+86) || ~((z <= 2.35e+48)))
		tmp = (t - a) / (b - y);
	else
		tmp = ((z * (t - a)) / t_1) + (y / (t_1 / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[z, -8.2e+86], N[Not[LessEqual[z, 2.35e+48]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision] + N[(y / N[(t$95$1 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -8.1999999999999998e86 or 2.35000000000000006e48 < z

   1. Initial program 40.7%

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

   2. Taylor expanded in z around inf 88.8%

      \[\leadsto \color{blue}{\frac{t - a}{b - y}} \]

   if -8.1999999999999998e86 < z < 2.35000000000000006e48

   1. Initial program 88.9%

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

   2. Taylor expanded in x around inf 88.9%

      \[\leadsto \color{blue}{\frac{\left(t - a\right) \cdot z}{y + \left(b - y\right) \cdot z} + \frac{y \cdot x}{y + \left(b - y\right) \cdot z}} \]
   3. Step-by-step derivation

      1. *-un-lft-identity 88.9%

         \[\leadsto \frac{\left(t - a\right) \cdot z}{y + \left(b - y\right) \cdot z} + \color{blue}{1 \cdot \frac{y \cdot x}{y + \left(b - y\right) \cdot z}} \]

      2. associate-/l* 89.5%

         \[\leadsto \frac{\left(t - a\right) \cdot z}{y + \left(b - y\right) \cdot z} + 1 \cdot \color{blue}{\frac{y}{\frac{y + \left(b - y\right) \cdot z}{x}}} \]

      3. *-commutative 89.5%

         \[\leadsto \frac{\left(t - a\right) \cdot z}{y + \left(b - y\right) \cdot z} + 1 \cdot \frac{y}{\frac{y + \color{blue}{z \cdot \left(b - y\right)}}{x}} \]

   4. Applied egg-rr 89.5%

      \[\leadsto \frac{\left(t - a\right) \cdot z}{y + \left(b - y\right) \cdot z} + \color{blue}{1 \cdot \frac{y}{\frac{y + z \cdot \left(b - y\right)}{x}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+86} \lor \neg \left(z \leq 2.35 \cdot 10^{+48}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} + \frac{y}{\frac{y + z \cdot \left(b - y\right)}{x}}\\ \end{array} \]

Alternative 5: 83.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(t - a\right)\\ t_2 := y + z \cdot \left(b - y\right)\\ t_3 := \frac{y \cdot x + t_1}{t_2}\\ t_4 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -2.9 \cdot 10^{+94}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq -5.6 \cdot 10^{-235}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-106}:\\ \;\;\;\;x + \frac{t_1}{t_2}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+49}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- t a)))
        (t_2 (+ y (* z (- b y))))
        (t_3 (/ (+ (* y x) t_1) t_2))
        (t_4 (/ (- t a) (- b y))))
   (if (<= z -2.9e+94)
     t_4
     (if (<= z -5.6e-235)
       t_3
       (if (<= z 4e-106) (+ x (/ t_1 t_2)) (if (<= z 6.2e+49) t_3 t_4))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (t - a);
	double t_2 = y + (z * (b - y));
	double t_3 = ((y * x) + t_1) / t_2;
	double t_4 = (t - a) / (b - y);
	double tmp;
	if (z <= -2.9e+94) {
		tmp = t_4;
	} else if (z <= -5.6e-235) {
		tmp = t_3;
	} else if (z <= 4e-106) {
		tmp = x + (t_1 / t_2);
	} else if (z <= 6.2e+49) {
		tmp = t_3;
	} else {
		tmp = t_4;
	}
	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 = z * (t - a)
    t_2 = y + (z * (b - y))
    t_3 = ((y * x) + t_1) / t_2
    t_4 = (t - a) / (b - y)
    if (z <= (-2.9d+94)) then
        tmp = t_4
    else if (z <= (-5.6d-235)) then
        tmp = t_3
    else if (z <= 4d-106) then
        tmp = x + (t_1 / t_2)
    else if (z <= 6.2d+49) then
        tmp = t_3
    else
        tmp = t_4
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (t - a);
	double t_2 = y + (z * (b - y));
	double t_3 = ((y * x) + t_1) / t_2;
	double t_4 = (t - a) / (b - y);
	double tmp;
	if (z <= -2.9e+94) {
		tmp = t_4;
	} else if (z <= -5.6e-235) {
		tmp = t_3;
	} else if (z <= 4e-106) {
		tmp = x + (t_1 / t_2);
	} else if (z <= 6.2e+49) {
		tmp = t_3;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (t - a)
	t_2 = y + (z * (b - y))
	t_3 = ((y * x) + t_1) / t_2
	t_4 = (t - a) / (b - y)
	tmp = 0
	if z <= -2.9e+94:
		tmp = t_4
	elif z <= -5.6e-235:
		tmp = t_3
	elif z <= 4e-106:
		tmp = x + (t_1 / t_2)
	elif z <= 6.2e+49:
		tmp = t_3
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(t - a))
	t_2 = Float64(y + Float64(z * Float64(b - y)))
	t_3 = Float64(Float64(Float64(y * x) + t_1) / t_2)
	t_4 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -2.9e+94)
		tmp = t_4;
	elseif (z <= -5.6e-235)
		tmp = t_3;
	elseif (z <= 4e-106)
		tmp = Float64(x + Float64(t_1 / t_2));
	elseif (z <= 6.2e+49)
		tmp = t_3;
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (t - a);
	t_2 = y + (z * (b - y));
	t_3 = ((y * x) + t_1) / t_2;
	t_4 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -2.9e+94)
		tmp = t_4;
	elseif (z <= -5.6e-235)
		tmp = t_3;
	elseif (z <= 4e-106)
		tmp = x + (t_1 / t_2);
	elseif (z <= 6.2e+49)
		tmp = t_3;
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(y * x), $MachinePrecision] + t$95$1), $MachinePrecision] / t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.9e+94], t$95$4, If[LessEqual[z, -5.6e-235], t$95$3, If[LessEqual[z, 4e-106], N[(x + N[(t$95$1 / t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.2e+49], t$95$3, t$95$4]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.8999999999999998e94 or 6.19999999999999985e49 < z

   1. Initial program 40.7%

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

   2. Taylor expanded in z around inf 88.8%

      \[\leadsto \color{blue}{\frac{t - a}{b - y}} \]

   if -2.8999999999999998e94 < z < -5.5999999999999999e-235 or 3.99999999999999976e-106 < z < 6.19999999999999985e49

   1. Initial program 90.0%

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

   if -5.5999999999999999e-235 < z < 3.99999999999999976e-106

   1. Initial program 87.0%

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

   2. Taylor expanded in x around inf 87.0%

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

   3. Taylor expanded in z around 0 95.1%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+94}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -5.6 \cdot 10^{-235}:\\ \;\;\;\;\frac{y \cdot x + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-106}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+49}:\\ \;\;\;\;\frac{y \cdot x + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 6: 80.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -3.2 \cdot 10^{+15}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 5.9 \cdot 10^{-52}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{t_1}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+41}:\\ \;\;\;\;\frac{y \cdot x + z \cdot t}{t_1}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y)))) (t_2 (/ (- t a) (- b y))))
   (if (<= z -3.2e+15)
     t_2
     (if (<= z 5.9e-52)
       (+ x (/ (* z (- t a)) t_1))
       (if (<= z 3.5e+41) (/ (+ (* y x) (* z t)) t_1) t_2)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -3.2e+15) {
		tmp = t_2;
	} else if (z <= 5.9e-52) {
		tmp = x + ((z * (t - a)) / t_1);
	} else if (z <= 3.5e+41) {
		tmp = ((y * x) + (z * t)) / 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 * (b - y))
    t_2 = (t - a) / (b - y)
    if (z <= (-3.2d+15)) then
        tmp = t_2
    else if (z <= 5.9d-52) then
        tmp = x + ((z * (t - a)) / t_1)
    else if (z <= 3.5d+41) then
        tmp = ((y * x) + (z * t)) / 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 * (b - y));
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -3.2e+15) {
		tmp = t_2;
	} else if (z <= 5.9e-52) {
		tmp = x + ((z * (t - a)) / t_1);
	} else if (z <= 3.5e+41) {
		tmp = ((y * x) + (z * t)) / t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z * (b - y))
	t_2 = (t - a) / (b - y)
	tmp = 0
	if z <= -3.2e+15:
		tmp = t_2
	elif z <= 5.9e-52:
		tmp = x + ((z * (t - a)) / t_1)
	elif z <= 3.5e+41:
		tmp = ((y * x) + (z * t)) / t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(z * Float64(b - y)))
	t_2 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -3.2e+15)
		tmp = t_2;
	elseif (z <= 5.9e-52)
		tmp = Float64(x + Float64(Float64(z * Float64(t - a)) / t_1));
	elseif (z <= 3.5e+41)
		tmp = Float64(Float64(Float64(y * x) + Float64(z * t)) / 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 * (b - y));
	t_2 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -3.2e+15)
		tmp = t_2;
	elseif (z <= 5.9e-52)
		tmp = x + ((z * (t - a)) / t_1);
	elseif (z <= 3.5e+41)
		tmp = ((y * x) + (z * t)) / 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[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.2e+15], t$95$2, If[LessEqual[z, 5.9e-52], N[(x + N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.5e+41], N[(N[(N[(y * x), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.2e15 or 3.4999999999999999e41 < z

   1. Initial program 45.6%

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

   2. Taylor expanded in z around inf 84.5%

      \[\leadsto \color{blue}{\frac{t - a}{b - y}} \]

   if -3.2e15 < z < 5.90000000000000019e-52

   1. Initial program 88.5%

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

   2. Taylor expanded in x around inf 88.5%

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

   3. Taylor expanded in z around 0 88.1%

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

   if 5.90000000000000019e-52 < z < 3.4999999999999999e41

   1. Initial program 99.7%

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

      1. fma-def 99.7%

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

      2. +-commutative 99.7%

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

      3. fma-def 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in a around 0 87.5%

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

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+15}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq 5.9 \cdot 10^{-52}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+41}:\\ \;\;\;\;\frac{y \cdot x + z \cdot t}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 7: 36.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-a}{b}\\ \mathbf{if}\;z \leq -3.5 \cdot 10^{+157}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{+100}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq -8 \cdot 10^{+71}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{+18}:\\ \;\;\;\;\frac{-t}{y}\\ \mathbf{elif}\;z \leq -29:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 1.62 \cdot 10^{-38}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{+49}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 1.36 \cdot 10^{+188}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- a) b)))
   (if (<= z -3.5e+157)
     t_1
     (if (<= z -2.4e+100)
       (/ t b)
       (if (<= z -8e+71)
         t_1
         (if (<= z -6.5e+18)
           (/ (- t) y)
           (if (<= z -29.0)
             (/ t b)
             (if (<= z 1.62e-38)
               x
               (if (<= z 7.6e+49)
                 (/ t b)
                 (if (<= z 1.36e+188) t_1 (/ t b)))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -a / b;
	double tmp;
	if (z <= -3.5e+157) {
		tmp = t_1;
	} else if (z <= -2.4e+100) {
		tmp = t / b;
	} else if (z <= -8e+71) {
		tmp = t_1;
	} else if (z <= -6.5e+18) {
		tmp = -t / y;
	} else if (z <= -29.0) {
		tmp = t / b;
	} else if (z <= 1.62e-38) {
		tmp = x;
	} else if (z <= 7.6e+49) {
		tmp = t / b;
	} else if (z <= 1.36e+188) {
		tmp = t_1;
	} else {
		tmp = t / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = -a / b
    if (z <= (-3.5d+157)) then
        tmp = t_1
    else if (z <= (-2.4d+100)) then
        tmp = t / b
    else if (z <= (-8d+71)) then
        tmp = t_1
    else if (z <= (-6.5d+18)) then
        tmp = -t / y
    else if (z <= (-29.0d0)) then
        tmp = t / b
    else if (z <= 1.62d-38) then
        tmp = x
    else if (z <= 7.6d+49) then
        tmp = t / b
    else if (z <= 1.36d+188) then
        tmp = t_1
    else
        tmp = t / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -a / b;
	double tmp;
	if (z <= -3.5e+157) {
		tmp = t_1;
	} else if (z <= -2.4e+100) {
		tmp = t / b;
	} else if (z <= -8e+71) {
		tmp = t_1;
	} else if (z <= -6.5e+18) {
		tmp = -t / y;
	} else if (z <= -29.0) {
		tmp = t / b;
	} else if (z <= 1.62e-38) {
		tmp = x;
	} else if (z <= 7.6e+49) {
		tmp = t / b;
	} else if (z <= 1.36e+188) {
		tmp = t_1;
	} else {
		tmp = t / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = -a / b
	tmp = 0
	if z <= -3.5e+157:
		tmp = t_1
	elif z <= -2.4e+100:
		tmp = t / b
	elif z <= -8e+71:
		tmp = t_1
	elif z <= -6.5e+18:
		tmp = -t / y
	elif z <= -29.0:
		tmp = t / b
	elif z <= 1.62e-38:
		tmp = x
	elif z <= 7.6e+49:
		tmp = t / b
	elif z <= 1.36e+188:
		tmp = t_1
	else:
		tmp = t / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(-a) / b)
	tmp = 0.0
	if (z <= -3.5e+157)
		tmp = t_1;
	elseif (z <= -2.4e+100)
		tmp = Float64(t / b);
	elseif (z <= -8e+71)
		tmp = t_1;
	elseif (z <= -6.5e+18)
		tmp = Float64(Float64(-t) / y);
	elseif (z <= -29.0)
		tmp = Float64(t / b);
	elseif (z <= 1.62e-38)
		tmp = x;
	elseif (z <= 7.6e+49)
		tmp = Float64(t / b);
	elseif (z <= 1.36e+188)
		tmp = t_1;
	else
		tmp = Float64(t / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = -a / b;
	tmp = 0.0;
	if (z <= -3.5e+157)
		tmp = t_1;
	elseif (z <= -2.4e+100)
		tmp = t / b;
	elseif (z <= -8e+71)
		tmp = t_1;
	elseif (z <= -6.5e+18)
		tmp = -t / y;
	elseif (z <= -29.0)
		tmp = t / b;
	elseif (z <= 1.62e-38)
		tmp = x;
	elseif (z <= 7.6e+49)
		tmp = t / b;
	elseif (z <= 1.36e+188)
		tmp = t_1;
	else
		tmp = t / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[((-a) / b), $MachinePrecision]}, If[LessEqual[z, -3.5e+157], t$95$1, If[LessEqual[z, -2.4e+100], N[(t / b), $MachinePrecision], If[LessEqual[z, -8e+71], t$95$1, If[LessEqual[z, -6.5e+18], N[((-t) / y), $MachinePrecision], If[LessEqual[z, -29.0], N[(t / b), $MachinePrecision], If[LessEqual[z, 1.62e-38], x, If[LessEqual[z, 7.6e+49], N[(t / b), $MachinePrecision], If[LessEqual[z, 1.36e+188], t$95$1, N[(t / b), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.50000000000000002e157 or -2.40000000000000012e100 < z < -8.0000000000000003e71 or 7.5999999999999997e49 < z < 1.36e188

   1. Initial program 50.1%

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

   2. Taylor expanded in a around inf 36.2%

      \[\leadsto \frac{\color{blue}{-1 \cdot \left(a \cdot z\right)}}{y + z \cdot \left(b - y\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 36.2%

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

      2. distribute-lft-neg-out 36.2%

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

      3. *-commutative 36.2%

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

   4. Simplified 36.2%

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

   5. Taylor expanded in y around 0 52.5%

      \[\leadsto \color{blue}{-1 \cdot \frac{a}{b}} \]
   6. Step-by-step derivation

      1. mul-1-neg 52.5%

         \[\leadsto \color{blue}{-\frac{a}{b}} \]

   7. Simplified 52.5%

      \[\leadsto \color{blue}{-\frac{a}{b}} \]

   if -3.50000000000000002e157 < z < -2.40000000000000012e100 or -6.5e18 < z < -29 or 1.62e-38 < z < 7.5999999999999997e49 or 1.36e188 < z

   1. Initial program 52.7%

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

   2. Taylor expanded in x around inf 52.7%

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

   3. Taylor expanded in b around inf 60.6%

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

   4. Taylor expanded in t around inf 47.3%

      \[\leadsto \color{blue}{\frac{t}{b}} \]

   if -8.0000000000000003e71 < z < -6.5e18

   1. Initial program 76.1%

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

   2. Taylor expanded in y around -inf 75.1%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{z - 1} + -1 \cdot \frac{\frac{\left(t - a\right) \cdot z}{z - 1} - -1 \cdot \frac{z \cdot \left(b \cdot x\right)}{{\left(z - 1\right)}^{2}}}{y}} \]
   3. Step-by-step derivation

      1. mul-1-neg 75.1%

         \[\leadsto -1 \cdot \frac{x}{z - 1} + \color{blue}{\left(-\frac{\frac{\left(t - a\right) \cdot z}{z - 1} - -1 \cdot \frac{z \cdot \left(b \cdot x\right)}{{\left(z - 1\right)}^{2}}}{y}\right)} \]

      2. unsub-neg 75.1%

         \[\leadsto \color{blue}{-1 \cdot \frac{x}{z - 1} - \frac{\frac{\left(t - a\right) \cdot z}{z - 1} - -1 \cdot \frac{z \cdot \left(b \cdot x\right)}{{\left(z - 1\right)}^{2}}}{y}} \]

      3. mul-1-neg 75.1%

         \[\leadsto \color{blue}{\left(-\frac{x}{z - 1}\right)} - \frac{\frac{\left(t - a\right) \cdot z}{z - 1} - -1 \cdot \frac{z \cdot \left(b \cdot x\right)}{{\left(z - 1\right)}^{2}}}{y} \]

      4. distribute-neg-frac 75.1%

         \[\leadsto \color{blue}{\frac{-x}{z - 1}} - \frac{\frac{\left(t - a\right) \cdot z}{z - 1} - -1 \cdot \frac{z \cdot \left(b \cdot x\right)}{{\left(z - 1\right)}^{2}}}{y} \]

      5. cancel-sign-sub-inv 75.1%

         \[\leadsto \frac{-x}{z - 1} - \frac{\color{blue}{\frac{\left(t - a\right) \cdot z}{z - 1} + \left(--1\right) \cdot \frac{z \cdot \left(b \cdot x\right)}{{\left(z - 1\right)}^{2}}}}{y} \]

      6. associate-/l* 75.1%

         \[\leadsto \frac{-x}{z - 1} - \frac{\color{blue}{\frac{t - a}{\frac{z - 1}{z}}} + \left(--1\right) \cdot \frac{z \cdot \left(b \cdot x\right)}{{\left(z - 1\right)}^{2}}}{y} \]

      7. metadata-eval 75.1%

         \[\leadsto \frac{-x}{z - 1} - \frac{\frac{t - a}{\frac{z - 1}{z}} + \color{blue}{1} \cdot \frac{z \cdot \left(b \cdot x\right)}{{\left(z - 1\right)}^{2}}}{y} \]

      8. *-lft-identity 75.1%

         \[\leadsto \frac{-x}{z - 1} - \frac{\frac{t - a}{\frac{z - 1}{z}} + \color{blue}{\frac{z \cdot \left(b \cdot x\right)}{{\left(z - 1\right)}^{2}}}}{y} \]

      9. associate-/l* 75.1%

         \[\leadsto \frac{-x}{z - 1} - \frac{\frac{t - a}{\frac{z - 1}{z}} + \color{blue}{\frac{z}{\frac{{\left(z - 1\right)}^{2}}{b \cdot x}}}}{y} \]

   4. Simplified 75.1%

      \[\leadsto \color{blue}{\frac{-x}{z - 1} - \frac{\frac{t - a}{\frac{z - 1}{z}} + \frac{z}{\frac{{\left(z - 1\right)}^{2}}{b \cdot x}}}{y}} \]

   5. Taylor expanded in t around inf 66.8%

      \[\leadsto \frac{-x}{z - 1} - \color{blue}{\frac{t \cdot z}{\left(z - 1\right) \cdot y}} \]
   6. Step-by-step derivation

      1. times-frac 66.7%

         \[\leadsto \frac{-x}{z - 1} - \color{blue}{\frac{t}{z - 1} \cdot \frac{z}{y}} \]

      2. sub-neg 66.7%

         \[\leadsto \frac{-x}{z - 1} - \frac{t}{\color{blue}{z + \left(-1\right)}} \cdot \frac{z}{y} \]

      3. metadata-eval 66.7%

         \[\leadsto \frac{-x}{z - 1} - \frac{t}{z + \color{blue}{-1}} \cdot \frac{z}{y} \]

      4. +-commutative 66.7%

         \[\leadsto \frac{-x}{z - 1} - \frac{t}{\color{blue}{-1 + z}} \cdot \frac{z}{y} \]

   7. Simplified 66.7%

      \[\leadsto \frac{-x}{z - 1} - \color{blue}{\frac{t}{-1 + z} \cdot \frac{z}{y}} \]

   8. Taylor expanded in z around inf 51.8%

      \[\leadsto \color{blue}{-1 \cdot \frac{t}{y}} \]
   9. Step-by-step derivation

      1. associate-*r/ 51.8%

         \[\leadsto \color{blue}{\frac{-1 \cdot t}{y}} \]

      2. mul-1-neg 51.8%

         \[\leadsto \frac{\color{blue}{-t}}{y} \]

   10. Simplified 51.8%

       \[\leadsto \color{blue}{\frac{-t}{y}} \]

   if -29 < z < 1.62e-38

   1. Initial program 88.9%

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

   2. Taylor expanded in z around 0 51.6%

      \[\leadsto \color{blue}{x} \]
3. Recombined 4 regimes into one program.

4. Final simplification 50.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+157}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{+100}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq -8 \cdot 10^{+71}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{+18}:\\ \;\;\;\;\frac{-t}{y}\\ \mathbf{elif}\;z \leq -29:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 1.62 \cdot 10^{-38}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{+49}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 1.36 \cdot 10^{+188}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \]

Alternative 8: 80.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7400000000000 \lor \neg \left(z \leq 7.2 \cdot 10^{-15}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -7400000000000.0) (not (<= z 7.2e-15)))
   (/ (- t a) (- b y))
   (+ x (/ (* z (- t a)) (+ y (* z (- b y)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -7400000000000.0) || !(z <= 7.2e-15)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x + ((z * (t - a)) / (y + (z * (b - 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 <= (-7400000000000.0d0)) .or. (.not. (z <= 7.2d-15))) then
        tmp = (t - a) / (b - y)
    else
        tmp = x + ((z * (t - a)) / (y + (z * (b - 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 <= -7400000000000.0) || !(z <= 7.2e-15)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x + ((z * (t - a)) / (y + (z * (b - y))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -7400000000000.0) or not (z <= 7.2e-15):
		tmp = (t - a) / (b - y)
	else:
		tmp = x + ((z * (t - a)) / (y + (z * (b - y))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -7400000000000.0) || !(z <= 7.2e-15))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(x + Float64(Float64(z * Float64(t - a)) / Float64(y + Float64(z * Float64(b - y)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -7400000000000.0) || ~((z <= 7.2e-15)))
		tmp = (t - a) / (b - y);
	else
		tmp = x + ((z * (t - a)) / (y + (z * (b - y))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -7400000000000.0], N[Not[LessEqual[z, 7.2e-15]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.4e12 or 7.2000000000000002e-15 < z

   1. Initial program 51.5%

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

   2. Taylor expanded in z around inf 82.7%

      \[\leadsto \color{blue}{\frac{t - a}{b - y}} \]

   if -7.4e12 < z < 7.2000000000000002e-15

   1. Initial program 89.4%

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

   2. Taylor expanded in x around inf 89.4%

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

   3. Taylor expanded in z around 0 86.9%

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

4. Final simplification 84.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7400000000000 \lor \neg \left(z \leq 7.2 \cdot 10^{-15}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \end{array} \]

Alternative 9: 36.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-a}{b}\\ \mathbf{if}\;z \leq -2.6 \cdot 10^{+143}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{+99}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{+72}:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;z \leq -25500000000000:\\ \;\;\;\;\frac{-t}{y}\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{-38}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+50}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+188}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- a) b)))
   (if (<= z -2.6e+143)
     t_1
     (if (<= z -5.5e+99)
       (/ t b)
       (if (<= z -1.7e+72)
         (/ (- x) z)
         (if (<= z -25500000000000.0)
           (/ (- t) y)
           (if (<= z 2.05e-38)
             x
             (if (<= z 1.35e+50)
               (/ t b)
               (if (<= z 7.5e+188) t_1 (/ t b))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -a / b;
	double tmp;
	if (z <= -2.6e+143) {
		tmp = t_1;
	} else if (z <= -5.5e+99) {
		tmp = t / b;
	} else if (z <= -1.7e+72) {
		tmp = -x / z;
	} else if (z <= -25500000000000.0) {
		tmp = -t / y;
	} else if (z <= 2.05e-38) {
		tmp = x;
	} else if (z <= 1.35e+50) {
		tmp = t / b;
	} else if (z <= 7.5e+188) {
		tmp = t_1;
	} else {
		tmp = t / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = -a / b
    if (z <= (-2.6d+143)) then
        tmp = t_1
    else if (z <= (-5.5d+99)) then
        tmp = t / b
    else if (z <= (-1.7d+72)) then
        tmp = -x / z
    else if (z <= (-25500000000000.0d0)) then
        tmp = -t / y
    else if (z <= 2.05d-38) then
        tmp = x
    else if (z <= 1.35d+50) then
        tmp = t / b
    else if (z <= 7.5d+188) then
        tmp = t_1
    else
        tmp = t / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -a / b;
	double tmp;
	if (z <= -2.6e+143) {
		tmp = t_1;
	} else if (z <= -5.5e+99) {
		tmp = t / b;
	} else if (z <= -1.7e+72) {
		tmp = -x / z;
	} else if (z <= -25500000000000.0) {
		tmp = -t / y;
	} else if (z <= 2.05e-38) {
		tmp = x;
	} else if (z <= 1.35e+50) {
		tmp = t / b;
	} else if (z <= 7.5e+188) {
		tmp = t_1;
	} else {
		tmp = t / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = -a / b
	tmp = 0
	if z <= -2.6e+143:
		tmp = t_1
	elif z <= -5.5e+99:
		tmp = t / b
	elif z <= -1.7e+72:
		tmp = -x / z
	elif z <= -25500000000000.0:
		tmp = -t / y
	elif z <= 2.05e-38:
		tmp = x
	elif z <= 1.35e+50:
		tmp = t / b
	elif z <= 7.5e+188:
		tmp = t_1
	else:
		tmp = t / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(-a) / b)
	tmp = 0.0
	if (z <= -2.6e+143)
		tmp = t_1;
	elseif (z <= -5.5e+99)
		tmp = Float64(t / b);
	elseif (z <= -1.7e+72)
		tmp = Float64(Float64(-x) / z);
	elseif (z <= -25500000000000.0)
		tmp = Float64(Float64(-t) / y);
	elseif (z <= 2.05e-38)
		tmp = x;
	elseif (z <= 1.35e+50)
		tmp = Float64(t / b);
	elseif (z <= 7.5e+188)
		tmp = t_1;
	else
		tmp = Float64(t / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = -a / b;
	tmp = 0.0;
	if (z <= -2.6e+143)
		tmp = t_1;
	elseif (z <= -5.5e+99)
		tmp = t / b;
	elseif (z <= -1.7e+72)
		tmp = -x / z;
	elseif (z <= -25500000000000.0)
		tmp = -t / y;
	elseif (z <= 2.05e-38)
		tmp = x;
	elseif (z <= 1.35e+50)
		tmp = t / b;
	elseif (z <= 7.5e+188)
		tmp = t_1;
	else
		tmp = t / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[((-a) / b), $MachinePrecision]}, If[LessEqual[z, -2.6e+143], t$95$1, If[LessEqual[z, -5.5e+99], N[(t / b), $MachinePrecision], If[LessEqual[z, -1.7e+72], N[((-x) / z), $MachinePrecision], If[LessEqual[z, -25500000000000.0], N[((-t) / y), $MachinePrecision], If[LessEqual[z, 2.05e-38], x, If[LessEqual[z, 1.35e+50], N[(t / b), $MachinePrecision], If[LessEqual[z, 7.5e+188], t$95$1, N[(t / b), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.5999999999999999e143 or 1.35e50 < z < 7.4999999999999996e188

   1. Initial program 49.3%

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

   2. Taylor expanded in a around inf 36.1%

      \[\leadsto \frac{\color{blue}{-1 \cdot \left(a \cdot z\right)}}{y + z \cdot \left(b - y\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 36.1%

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

      2. distribute-lft-neg-out 36.1%

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

      3. *-commutative 36.1%

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

   4. Simplified 36.1%

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

   5. Taylor expanded in y around 0 53.4%

      \[\leadsto \color{blue}{-1 \cdot \frac{a}{b}} \]
   6. Step-by-step derivation

      1. mul-1-neg 53.4%

         \[\leadsto \color{blue}{-\frac{a}{b}} \]

   7. Simplified 53.4%

      \[\leadsto \color{blue}{-\frac{a}{b}} \]

   if -2.5999999999999999e143 < z < -5.5000000000000002e99 or 2.0499999999999999e-38 < z < 1.35e50 or 7.4999999999999996e188 < z

   1. Initial program 51.2%

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

   2. Taylor expanded in x around inf 51.2%

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

   3. Taylor expanded in b around inf 59.4%

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

   4. Taylor expanded in t around inf 45.6%

      \[\leadsto \color{blue}{\frac{t}{b}} \]

   if -5.5000000000000002e99 < z < -1.6999999999999999e72

   1. Initial program 65.6%

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

   2. Taylor expanded in y around inf 53.5%

      \[\leadsto \color{blue}{\frac{x}{-1 \cdot z + 1}} \]
   3. Step-by-step derivation

      1. +-commutative 53.5%

         \[\leadsto \frac{x}{\color{blue}{1 + -1 \cdot z}} \]

      2. mul-1-neg 53.5%

         \[\leadsto \frac{x}{1 + \color{blue}{\left(-z\right)}} \]

      3. unsub-neg 53.5%

         \[\leadsto \frac{x}{\color{blue}{1 - z}} \]

   4. Simplified 53.5%

      \[\leadsto \color{blue}{\frac{x}{1 - z}} \]

   5. Taylor expanded in z around inf 53.5%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{z}} \]
   6. Step-by-step derivation

      1. associate-*r/ 53.5%

         \[\leadsto \color{blue}{\frac{-1 \cdot x}{z}} \]

      2. mul-1-neg 53.5%

         \[\leadsto \frac{\color{blue}{-x}}{z} \]

   7. Simplified 53.5%

      \[\leadsto \color{blue}{\frac{-x}{z}} \]

   if -1.6999999999999999e72 < z < -2.55e13

   1. Initial program 77.8%

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

   2. Taylor expanded in y around -inf 69.7%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{z - 1} + -1 \cdot \frac{\frac{\left(t - a\right) \cdot z}{z - 1} - -1 \cdot \frac{z \cdot \left(b \cdot x\right)}{{\left(z - 1\right)}^{2}}}{y}} \]
   3. Step-by-step derivation

      1. mul-1-neg 69.7%

         \[\leadsto -1 \cdot \frac{x}{z - 1} + \color{blue}{\left(-\frac{\frac{\left(t - a\right) \cdot z}{z - 1} - -1 \cdot \frac{z \cdot \left(b \cdot x\right)}{{\left(z - 1\right)}^{2}}}{y}\right)} \]

      2. unsub-neg 69.7%

         \[\leadsto \color{blue}{-1 \cdot \frac{x}{z - 1} - \frac{\frac{\left(t - a\right) \cdot z}{z - 1} - -1 \cdot \frac{z \cdot \left(b \cdot x\right)}{{\left(z - 1\right)}^{2}}}{y}} \]

      3. mul-1-neg 69.7%

         \[\leadsto \color{blue}{\left(-\frac{x}{z - 1}\right)} - \frac{\frac{\left(t - a\right) \cdot z}{z - 1} - -1 \cdot \frac{z \cdot \left(b \cdot x\right)}{{\left(z - 1\right)}^{2}}}{y} \]

      4. distribute-neg-frac 69.7%

         \[\leadsto \color{blue}{\frac{-x}{z - 1}} - \frac{\frac{\left(t - a\right) \cdot z}{z - 1} - -1 \cdot \frac{z \cdot \left(b \cdot x\right)}{{\left(z - 1\right)}^{2}}}{y} \]

      5. cancel-sign-sub-inv 69.7%

         \[\leadsto \frac{-x}{z - 1} - \frac{\color{blue}{\frac{\left(t - a\right) \cdot z}{z - 1} + \left(--1\right) \cdot \frac{z \cdot \left(b \cdot x\right)}{{\left(z - 1\right)}^{2}}}}{y} \]

      6. associate-/l* 69.7%

         \[\leadsto \frac{-x}{z - 1} - \frac{\color{blue}{\frac{t - a}{\frac{z - 1}{z}}} + \left(--1\right) \cdot \frac{z \cdot \left(b \cdot x\right)}{{\left(z - 1\right)}^{2}}}{y} \]

      7. metadata-eval 69.7%

         \[\leadsto \frac{-x}{z - 1} - \frac{\frac{t - a}{\frac{z - 1}{z}} + \color{blue}{1} \cdot \frac{z \cdot \left(b \cdot x\right)}{{\left(z - 1\right)}^{2}}}{y} \]

      8. *-lft-identity 69.7%

         \[\leadsto \frac{-x}{z - 1} - \frac{\frac{t - a}{\frac{z - 1}{z}} + \color{blue}{\frac{z \cdot \left(b \cdot x\right)}{{\left(z - 1\right)}^{2}}}}{y} \]

      9. associate-/l* 69.7%

         \[\leadsto \frac{-x}{z - 1} - \frac{\frac{t - a}{\frac{z - 1}{z}} + \color{blue}{\frac{z}{\frac{{\left(z - 1\right)}^{2}}{b \cdot x}}}}{y} \]

   4. Simplified 69.7%

      \[\leadsto \color{blue}{\frac{-x}{z - 1} - \frac{\frac{t - a}{\frac{z - 1}{z}} + \frac{z}{\frac{{\left(z - 1\right)}^{2}}{b \cdot x}}}{y}} \]

   5. Taylor expanded in t around inf 62.1%

      \[\leadsto \frac{-x}{z - 1} - \color{blue}{\frac{t \cdot z}{\left(z - 1\right) \cdot y}} \]
   6. Step-by-step derivation

      1. times-frac 61.9%

         \[\leadsto \frac{-x}{z - 1} - \color{blue}{\frac{t}{z - 1} \cdot \frac{z}{y}} \]

      2. sub-neg 61.9%

         \[\leadsto \frac{-x}{z - 1} - \frac{t}{\color{blue}{z + \left(-1\right)}} \cdot \frac{z}{y} \]

      3. metadata-eval 61.9%

         \[\leadsto \frac{-x}{z - 1} - \frac{t}{z + \color{blue}{-1}} \cdot \frac{z}{y} \]

      4. +-commutative 61.9%

         \[\leadsto \frac{-x}{z - 1} - \frac{t}{\color{blue}{-1 + z}} \cdot \frac{z}{y} \]

   7. Simplified 61.9%

      \[\leadsto \frac{-x}{z - 1} - \color{blue}{\frac{t}{-1 + z} \cdot \frac{z}{y}} \]

   8. Taylor expanded in z around inf 48.2%

      \[\leadsto \color{blue}{-1 \cdot \frac{t}{y}} \]
   9. Step-by-step derivation

      1. associate-*r/ 48.2%

         \[\leadsto \color{blue}{\frac{-1 \cdot t}{y}} \]

      2. mul-1-neg 48.2%

         \[\leadsto \frac{\color{blue}{-t}}{y} \]

   10. Simplified 48.2%

       \[\leadsto \color{blue}{\frac{-t}{y}} \]

   if -2.55e13 < z < 2.0499999999999999e-38

   1. Initial program 89.0%

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

   2. Taylor expanded in z around 0 51.2%

      \[\leadsto \color{blue}{x} \]
3. Recombined 5 regimes into one program.

4. Final simplification 50.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+143}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{+99}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{+72}:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;z \leq -25500000000000:\\ \;\;\;\;\frac{-t}{y}\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{-38}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+50}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+188}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \]

Alternative 10: 66.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \left(x + \frac{t}{y}\right)\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -3.5 \cdot 10^{-9}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-127}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.55 \cdot 10^{-61}:\\ \;\;\;\;\frac{z \cdot \left(-a\right)}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-14}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* z (+ x (/ t y))))) (t_2 (/ (- t a) (- b y))))
   (if (<= z -3.5e-9)
     t_2
     (if (<= z 1.5e-127)
       t_1
       (if (<= z 2.55e-61)
         (/ (* z (- a)) (+ y (* z b)))
         (if (<= z 1.5e-14) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z * (x + (t / y)));
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -3.5e-9) {
		tmp = t_2;
	} else if (z <= 1.5e-127) {
		tmp = t_1;
	} else if (z <= 2.55e-61) {
		tmp = (z * -a) / (y + (z * b));
	} else if (z <= 1.5e-14) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (z * (x + (t / y)))
    t_2 = (t - a) / (b - y)
    if (z <= (-3.5d-9)) then
        tmp = t_2
    else if (z <= 1.5d-127) then
        tmp = t_1
    else if (z <= 2.55d-61) then
        tmp = (z * -a) / (y + (z * b))
    else if (z <= 1.5d-14) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z * (x + (t / y)));
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -3.5e-9) {
		tmp = t_2;
	} else if (z <= 1.5e-127) {
		tmp = t_1;
	} else if (z <= 2.55e-61) {
		tmp = (z * -a) / (y + (z * b));
	} else if (z <= 1.5e-14) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (z * (x + (t / y)))
	t_2 = (t - a) / (b - y)
	tmp = 0
	if z <= -3.5e-9:
		tmp = t_2
	elif z <= 1.5e-127:
		tmp = t_1
	elif z <= 2.55e-61:
		tmp = (z * -a) / (y + (z * b))
	elif z <= 1.5e-14:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(z * Float64(x + Float64(t / y))))
	t_2 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -3.5e-9)
		tmp = t_2;
	elseif (z <= 1.5e-127)
		tmp = t_1;
	elseif (z <= 2.55e-61)
		tmp = Float64(Float64(z * Float64(-a)) / Float64(y + Float64(z * b)));
	elseif (z <= 1.5e-14)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (z * (x + (t / y)));
	t_2 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -3.5e-9)
		tmp = t_2;
	elseif (z <= 1.5e-127)
		tmp = t_1;
	elseif (z <= 2.55e-61)
		tmp = (z * -a) / (y + (z * b));
	elseif (z <= 1.5e-14)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(z * N[(x + N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.5e-9], t$95$2, If[LessEqual[z, 1.5e-127], t$95$1, If[LessEqual[z, 2.55e-61], N[(N[(z * (-a)), $MachinePrecision] / N[(y + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.5e-14], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.4999999999999999e-9 or 1.4999999999999999e-14 < z

   1. Initial program 52.9%

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

   2. Taylor expanded in z around inf 81.7%

      \[\leadsto \color{blue}{\frac{t - a}{b - y}} \]

   if -3.4999999999999999e-9 < z < 1.50000000000000004e-127 or 2.54999999999999984e-61 < z < 1.4999999999999999e-14

   1. Initial program 88.6%

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

   2. Taylor expanded in y around -inf 78.0%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{z - 1} + -1 \cdot \frac{\frac{\left(t - a\right) \cdot z}{z - 1} - -1 \cdot \frac{z \cdot \left(b \cdot x\right)}{{\left(z - 1\right)}^{2}}}{y}} \]
   3. Step-by-step derivation

      1. mul-1-neg 78.0%

         \[\leadsto -1 \cdot \frac{x}{z - 1} + \color{blue}{\left(-\frac{\frac{\left(t - a\right) \cdot z}{z - 1} - -1 \cdot \frac{z \cdot \left(b \cdot x\right)}{{\left(z - 1\right)}^{2}}}{y}\right)} \]

      2. unsub-neg 78.0%

         \[\leadsto \color{blue}{-1 \cdot \frac{x}{z - 1} - \frac{\frac{\left(t - a\right) \cdot z}{z - 1} - -1 \cdot \frac{z \cdot \left(b \cdot x\right)}{{\left(z - 1\right)}^{2}}}{y}} \]

      3. mul-1-neg 78.0%

         \[\leadsto \color{blue}{\left(-\frac{x}{z - 1}\right)} - \frac{\frac{\left(t - a\right) \cdot z}{z - 1} - -1 \cdot \frac{z \cdot \left(b \cdot x\right)}{{\left(z - 1\right)}^{2}}}{y} \]

      4. distribute-neg-frac 78.0%

         \[\leadsto \color{blue}{\frac{-x}{z - 1}} - \frac{\frac{\left(t - a\right) \cdot z}{z - 1} - -1 \cdot \frac{z \cdot \left(b \cdot x\right)}{{\left(z - 1\right)}^{2}}}{y} \]

      5. cancel-sign-sub-inv 78.0%

         \[\leadsto \frac{-x}{z - 1} - \frac{\color{blue}{\frac{\left(t - a\right) \cdot z}{z - 1} + \left(--1\right) \cdot \frac{z \cdot \left(b \cdot x\right)}{{\left(z - 1\right)}^{2}}}}{y} \]

      6. associate-/l* 77.9%

         \[\leadsto \frac{-x}{z - 1} - \frac{\color{blue}{\frac{t - a}{\frac{z - 1}{z}}} + \left(--1\right) \cdot \frac{z \cdot \left(b \cdot x\right)}{{\left(z - 1\right)}^{2}}}{y} \]

      7. metadata-eval 77.9%

         \[\leadsto \frac{-x}{z - 1} - \frac{\frac{t - a}{\frac{z - 1}{z}} + \color{blue}{1} \cdot \frac{z \cdot \left(b \cdot x\right)}{{\left(z - 1\right)}^{2}}}{y} \]

      8. *-lft-identity 77.9%

         \[\leadsto \frac{-x}{z - 1} - \frac{\frac{t - a}{\frac{z - 1}{z}} + \color{blue}{\frac{z \cdot \left(b \cdot x\right)}{{\left(z - 1\right)}^{2}}}}{y} \]

      9. associate-/l* 77.9%

         \[\leadsto \frac{-x}{z - 1} - \frac{\frac{t - a}{\frac{z - 1}{z}} + \color{blue}{\frac{z}{\frac{{\left(z - 1\right)}^{2}}{b \cdot x}}}}{y} \]

   4. Simplified 77.9%

      \[\leadsto \color{blue}{\frac{-x}{z - 1} - \frac{\frac{t - a}{\frac{z - 1}{z}} + \frac{z}{\frac{{\left(z - 1\right)}^{2}}{b \cdot x}}}{y}} \]

   5. Taylor expanded in t around inf 70.9%

      \[\leadsto \frac{-x}{z - 1} - \color{blue}{\frac{t \cdot z}{\left(z - 1\right) \cdot y}} \]
   6. Step-by-step derivation

      1. times-frac 69.2%

         \[\leadsto \frac{-x}{z - 1} - \color{blue}{\frac{t}{z - 1} \cdot \frac{z}{y}} \]

      2. sub-neg 69.2%

         \[\leadsto \frac{-x}{z - 1} - \frac{t}{\color{blue}{z + \left(-1\right)}} \cdot \frac{z}{y} \]

      3. metadata-eval 69.2%

         \[\leadsto \frac{-x}{z - 1} - \frac{t}{z + \color{blue}{-1}} \cdot \frac{z}{y} \]

      4. +-commutative 69.2%

         \[\leadsto \frac{-x}{z - 1} - \frac{t}{\color{blue}{-1 + z}} \cdot \frac{z}{y} \]

   7. Simplified 69.2%

      \[\leadsto \frac{-x}{z - 1} - \color{blue}{\frac{t}{-1 + z} \cdot \frac{z}{y}} \]

   8. Taylor expanded in z around 0 70.3%

      \[\leadsto \color{blue}{\left(x - -1 \cdot \frac{t}{y}\right) \cdot z + x} \]

   if 1.50000000000000004e-127 < z < 2.54999999999999984e-61

   1. Initial program 92.7%

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

   2. Taylor expanded in a around inf 65.4%

      \[\leadsto \frac{\color{blue}{-1 \cdot \left(a \cdot z\right)}}{y + z \cdot \left(b - y\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 65.4%

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

      2. distribute-lft-neg-out 65.4%

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

      3. *-commutative 65.4%

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

   4. Simplified 65.4%

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

   5. Taylor expanded in b around inf 65.4%

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

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{-9}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-127}:\\ \;\;\;\;x + z \cdot \left(x + \frac{t}{y}\right)\\ \mathbf{elif}\;z \leq 2.55 \cdot 10^{-61}:\\ \;\;\;\;\frac{z \cdot \left(-a\right)}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-14}:\\ \;\;\;\;x + z \cdot \left(x + \frac{t}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 11: 62.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -4.8:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{-146}:\\ \;\;\;\;x \cdot \frac{1}{1 - z}\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-47}:\\ \;\;\;\;\frac{z \cdot \left(-a\right)}{y + z \cdot b}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -4.8)
     t_1
     (if (<= z 2.35e-146)
       (* x (/ 1.0 (- 1.0 z)))
       (if (<= z 1.05e-47) (/ (* z (- a)) (+ y (* z 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 tmp;
	if (z <= -4.8) {
		tmp = t_1;
	} else if (z <= 2.35e-146) {
		tmp = x * (1.0 / (1.0 - z));
	} else if (z <= 1.05e-47) {
		tmp = (z * -a) / (y + (z * 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 = (t - a) / (b - y)
    if (z <= (-4.8d0)) then
        tmp = t_1
    else if (z <= 2.35d-146) then
        tmp = x * (1.0d0 / (1.0d0 - z))
    else if (z <= 1.05d-47) then
        tmp = (z * -a) / (y + (z * 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 tmp;
	if (z <= -4.8) {
		tmp = t_1;
	} else if (z <= 2.35e-146) {
		tmp = x * (1.0 / (1.0 - z));
	} else if (z <= 1.05e-47) {
		tmp = (z * -a) / (y + (z * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	tmp = 0
	if z <= -4.8:
		tmp = t_1
	elif z <= 2.35e-146:
		tmp = x * (1.0 / (1.0 - z))
	elif z <= 1.05e-47:
		tmp = (z * -a) / (y + (z * 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))
	tmp = 0.0
	if (z <= -4.8)
		tmp = t_1;
	elseif (z <= 2.35e-146)
		tmp = Float64(x * Float64(1.0 / Float64(1.0 - z)));
	elseif (z <= 1.05e-47)
		tmp = Float64(Float64(z * Float64(-a)) / Float64(y + Float64(z * 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);
	tmp = 0.0;
	if (z <= -4.8)
		tmp = t_1;
	elseif (z <= 2.35e-146)
		tmp = x * (1.0 / (1.0 - z));
	elseif (z <= 1.05e-47)
		tmp = (z * -a) / (y + (z * 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]}, If[LessEqual[z, -4.8], t$95$1, If[LessEqual[z, 2.35e-146], N[(x * N[(1.0 / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.05e-47], N[(N[(z * (-a)), $MachinePrecision] / N[(y + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.79999999999999982 or 1.05e-47 < z

   1. Initial program 54.7%

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

   2. Taylor expanded in z around inf 81.0%

      \[\leadsto \color{blue}{\frac{t - a}{b - y}} \]

   if -4.79999999999999982 < z < 2.35e-146

   1. Initial program 87.9%

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

   2. Taylor expanded in y around inf 62.3%

      \[\leadsto \color{blue}{\frac{x}{-1 \cdot z + 1}} \]
   3. Step-by-step derivation

      1. +-commutative 62.3%

         \[\leadsto \frac{x}{\color{blue}{1 + -1 \cdot z}} \]

      2. mul-1-neg 62.3%

         \[\leadsto \frac{x}{1 + \color{blue}{\left(-z\right)}} \]

      3. unsub-neg 62.3%

         \[\leadsto \frac{x}{\color{blue}{1 - z}} \]

   4. Simplified 62.3%

      \[\leadsto \color{blue}{\frac{x}{1 - z}} \]
   5. Step-by-step derivation

      1. div-inv 62.3%

         \[\leadsto \color{blue}{x \cdot \frac{1}{1 - z}} \]

   6. Applied egg-rr 62.3%

      \[\leadsto \color{blue}{x \cdot \frac{1}{1 - z}} \]

   if 2.35e-146 < z < 1.05e-47

   1. Initial program 91.5%

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

   2. Taylor expanded in a around inf 49.8%

      \[\leadsto \frac{\color{blue}{-1 \cdot \left(a \cdot z\right)}}{y + z \cdot \left(b - y\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 49.8%

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

      2. distribute-lft-neg-out 49.8%

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

      3. *-commutative 49.8%

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

   4. Simplified 49.8%

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

   5. Taylor expanded in b around inf 49.8%

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

4. Final simplification 71.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{-146}:\\ \;\;\;\;x \cdot \frac{1}{1 - z}\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-47}:\\ \;\;\;\;\frac{z \cdot \left(-a\right)}{y + z \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 12: 40.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{b - y}\\ t_2 := \frac{-a}{b}\\ \mathbf{if}\;z \leq -4.7 \cdot 10^{+175}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-62}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-38}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+50} \lor \neg \left(z \leq 1.3 \cdot 10^{+188}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ t (- b y))) (t_2 (/ (- a) b)))
   (if (<= z -4.7e+175)
     t_2
     (if (<= z -2.7e-62)
       t_1
       (if (<= z 2e-38)
         x
         (if (or (<= z 3.3e+50) (not (<= z 1.3e+188))) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t / (b - y);
	double t_2 = -a / b;
	double tmp;
	if (z <= -4.7e+175) {
		tmp = t_2;
	} else if (z <= -2.7e-62) {
		tmp = t_1;
	} else if (z <= 2e-38) {
		tmp = x;
	} else if ((z <= 3.3e+50) || !(z <= 1.3e+188)) {
		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 = t / (b - y)
    t_2 = -a / b
    if (z <= (-4.7d+175)) then
        tmp = t_2
    else if (z <= (-2.7d-62)) then
        tmp = t_1
    else if (z <= 2d-38) then
        tmp = x
    else if ((z <= 3.3d+50) .or. (.not. (z <= 1.3d+188))) 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 = t / (b - y);
	double t_2 = -a / b;
	double tmp;
	if (z <= -4.7e+175) {
		tmp = t_2;
	} else if (z <= -2.7e-62) {
		tmp = t_1;
	} else if (z <= 2e-38) {
		tmp = x;
	} else if ((z <= 3.3e+50) || !(z <= 1.3e+188)) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t / (b - y)
	t_2 = -a / b
	tmp = 0
	if z <= -4.7e+175:
		tmp = t_2
	elif z <= -2.7e-62:
		tmp = t_1
	elif z <= 2e-38:
		tmp = x
	elif (z <= 3.3e+50) or not (z <= 1.3e+188):
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t / Float64(b - y))
	t_2 = Float64(Float64(-a) / b)
	tmp = 0.0
	if (z <= -4.7e+175)
		tmp = t_2;
	elseif (z <= -2.7e-62)
		tmp = t_1;
	elseif (z <= 2e-38)
		tmp = x;
	elseif ((z <= 3.3e+50) || !(z <= 1.3e+188))
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t / (b - y);
	t_2 = -a / b;
	tmp = 0.0;
	if (z <= -4.7e+175)
		tmp = t_2;
	elseif (z <= -2.7e-62)
		tmp = t_1;
	elseif (z <= 2e-38)
		tmp = x;
	elseif ((z <= 3.3e+50) || ~((z <= 1.3e+188)))
		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[(t / N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[((-a) / b), $MachinePrecision]}, If[LessEqual[z, -4.7e+175], t$95$2, If[LessEqual[z, -2.7e-62], t$95$1, If[LessEqual[z, 2e-38], x, If[Or[LessEqual[z, 3.3e+50], N[Not[LessEqual[z, 1.3e+188]], $MachinePrecision]], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.69999999999999995e175 or 3.3e50 < z < 1.29999999999999994e188

   1. Initial program 48.2%

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

   2. Taylor expanded in a around inf 35.5%

      \[\leadsto \frac{\color{blue}{-1 \cdot \left(a \cdot z\right)}}{y + z \cdot \left(b - y\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 35.5%

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

      2. distribute-lft-neg-out 35.5%

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

      3. *-commutative 35.5%

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

   4. Simplified 35.5%

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

   5. Taylor expanded in y around 0 54.4%

      \[\leadsto \color{blue}{-1 \cdot \frac{a}{b}} \]
   6. Step-by-step derivation

      1. mul-1-neg 54.4%

         \[\leadsto \color{blue}{-\frac{a}{b}} \]

   7. Simplified 54.4%

      \[\leadsto \color{blue}{-\frac{a}{b}} \]

   if -4.69999999999999995e175 < z < -2.70000000000000019e-62 or 1.9999999999999999e-38 < z < 3.3e50 or 1.29999999999999994e188 < z

   1. Initial program 61.1%

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

   2. Taylor expanded in z around inf 71.2%

      \[\leadsto \color{blue}{\frac{t - a}{b - y}} \]

   3. Taylor expanded in t around inf 52.5%

      \[\leadsto \color{blue}{\frac{t}{b - y}} \]

   if -2.70000000000000019e-62 < z < 1.9999999999999999e-38

   1. Initial program 88.0%

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

   2. Taylor expanded in z around 0 54.2%

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

4. Final simplification 53.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.7 \cdot 10^{+175}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-62}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-38}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+50} \lor \neg \left(z \leq 1.3 \cdot 10^{+188}\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{-a}{b}\\ \end{array} \]

Alternative 13: 41.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{b - y}\\ t_2 := \frac{-a}{b}\\ \mathbf{if}\;z \leq -1.05 \cdot 10^{+175}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -100:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-38}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;z \leq 1.48 \cdot 10^{+51} \lor \neg \left(z \leq 10^{+188}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ t (- b y))) (t_2 (/ (- a) b)))
   (if (<= z -1.05e+175)
     t_2
     (if (<= z -100.0)
       t_1
       (if (<= z 1.9e-38)
         (/ x (- 1.0 z))
         (if (or (<= z 1.48e+51) (not (<= z 1e+188))) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t / (b - y);
	double t_2 = -a / b;
	double tmp;
	if (z <= -1.05e+175) {
		tmp = t_2;
	} else if (z <= -100.0) {
		tmp = t_1;
	} else if (z <= 1.9e-38) {
		tmp = x / (1.0 - z);
	} else if ((z <= 1.48e+51) || !(z <= 1e+188)) {
		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 = t / (b - y)
    t_2 = -a / b
    if (z <= (-1.05d+175)) then
        tmp = t_2
    else if (z <= (-100.0d0)) then
        tmp = t_1
    else if (z <= 1.9d-38) then
        tmp = x / (1.0d0 - z)
    else if ((z <= 1.48d+51) .or. (.not. (z <= 1d+188))) 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 = t / (b - y);
	double t_2 = -a / b;
	double tmp;
	if (z <= -1.05e+175) {
		tmp = t_2;
	} else if (z <= -100.0) {
		tmp = t_1;
	} else if (z <= 1.9e-38) {
		tmp = x / (1.0 - z);
	} else if ((z <= 1.48e+51) || !(z <= 1e+188)) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t / (b - y)
	t_2 = -a / b
	tmp = 0
	if z <= -1.05e+175:
		tmp = t_2
	elif z <= -100.0:
		tmp = t_1
	elif z <= 1.9e-38:
		tmp = x / (1.0 - z)
	elif (z <= 1.48e+51) or not (z <= 1e+188):
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t / Float64(b - y))
	t_2 = Float64(Float64(-a) / b)
	tmp = 0.0
	if (z <= -1.05e+175)
		tmp = t_2;
	elseif (z <= -100.0)
		tmp = t_1;
	elseif (z <= 1.9e-38)
		tmp = Float64(x / Float64(1.0 - z));
	elseif ((z <= 1.48e+51) || !(z <= 1e+188))
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t / (b - y);
	t_2 = -a / b;
	tmp = 0.0;
	if (z <= -1.05e+175)
		tmp = t_2;
	elseif (z <= -100.0)
		tmp = t_1;
	elseif (z <= 1.9e-38)
		tmp = x / (1.0 - z);
	elseif ((z <= 1.48e+51) || ~((z <= 1e+188)))
		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[(t / N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[((-a) / b), $MachinePrecision]}, If[LessEqual[z, -1.05e+175], t$95$2, If[LessEqual[z, -100.0], t$95$1, If[LessEqual[z, 1.9e-38], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 1.48e+51], N[Not[LessEqual[z, 1e+188]], $MachinePrecision]], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.05e175 or 1.48e51 < z < 1e188

   1. Initial program 48.2%

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

   2. Taylor expanded in a around inf 35.5%

      \[\leadsto \frac{\color{blue}{-1 \cdot \left(a \cdot z\right)}}{y + z \cdot \left(b - y\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 35.5%

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

      2. distribute-lft-neg-out 35.5%

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

      3. *-commutative 35.5%

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

   4. Simplified 35.5%

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

   5. Taylor expanded in y around 0 54.4%

      \[\leadsto \color{blue}{-1 \cdot \frac{a}{b}} \]
   6. Step-by-step derivation

      1. mul-1-neg 54.4%

         \[\leadsto \color{blue}{-\frac{a}{b}} \]

   7. Simplified 54.4%

      \[\leadsto \color{blue}{-\frac{a}{b}} \]

   if -1.05e175 < z < -100 or 1.9e-38 < z < 1.48e51 or 1e188 < z

   1. Initial program 57.0%

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

   2. Taylor expanded in z around inf 74.9%

      \[\leadsto \color{blue}{\frac{t - a}{b - y}} \]

   3. Taylor expanded in t around inf 55.5%

      \[\leadsto \color{blue}{\frac{t}{b - y}} \]

   if -100 < z < 1.9e-38

   1. Initial program 88.9%

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

   2. Taylor expanded in y around inf 52.9%

      \[\leadsto \color{blue}{\frac{x}{-1 \cdot z + 1}} \]
   3. Step-by-step derivation

      1. +-commutative 52.9%

         \[\leadsto \frac{x}{\color{blue}{1 + -1 \cdot z}} \]

      2. mul-1-neg 52.9%

         \[\leadsto \frac{x}{1 + \color{blue}{\left(-z\right)}} \]

      3. unsub-neg 52.9%

         \[\leadsto \frac{x}{\color{blue}{1 - z}} \]

   4. Simplified 52.9%

      \[\leadsto \color{blue}{\frac{x}{1 - z}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 54.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+175}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;z \leq -100:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-38}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;z \leq 1.48 \cdot 10^{+51} \lor \neg \left(z \leq 10^{+188}\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{-a}{b}\\ \end{array} \]

Alternative 14: 36.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-a}{b}\\ \mathbf{if}\;z \leq -2.2 \cdot 10^{+141}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -0.74:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-38}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.16 \cdot 10^{+51}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{+189}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- a) b)))
   (if (<= z -2.2e+141)
     t_1
     (if (<= z -0.74)
       (/ t b)
       (if (<= z 1.95e-38)
         x
         (if (<= z 1.16e+51) (/ t b) (if (<= z 1.06e+189) t_1 (/ t b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -a / b;
	double tmp;
	if (z <= -2.2e+141) {
		tmp = t_1;
	} else if (z <= -0.74) {
		tmp = t / b;
	} else if (z <= 1.95e-38) {
		tmp = x;
	} else if (z <= 1.16e+51) {
		tmp = t / b;
	} else if (z <= 1.06e+189) {
		tmp = t_1;
	} else {
		tmp = t / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = -a / b
    if (z <= (-2.2d+141)) then
        tmp = t_1
    else if (z <= (-0.74d0)) then
        tmp = t / b
    else if (z <= 1.95d-38) then
        tmp = x
    else if (z <= 1.16d+51) then
        tmp = t / b
    else if (z <= 1.06d+189) then
        tmp = t_1
    else
        tmp = t / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -a / b;
	double tmp;
	if (z <= -2.2e+141) {
		tmp = t_1;
	} else if (z <= -0.74) {
		tmp = t / b;
	} else if (z <= 1.95e-38) {
		tmp = x;
	} else if (z <= 1.16e+51) {
		tmp = t / b;
	} else if (z <= 1.06e+189) {
		tmp = t_1;
	} else {
		tmp = t / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = -a / b
	tmp = 0
	if z <= -2.2e+141:
		tmp = t_1
	elif z <= -0.74:
		tmp = t / b
	elif z <= 1.95e-38:
		tmp = x
	elif z <= 1.16e+51:
		tmp = t / b
	elif z <= 1.06e+189:
		tmp = t_1
	else:
		tmp = t / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(-a) / b)
	tmp = 0.0
	if (z <= -2.2e+141)
		tmp = t_1;
	elseif (z <= -0.74)
		tmp = Float64(t / b);
	elseif (z <= 1.95e-38)
		tmp = x;
	elseif (z <= 1.16e+51)
		tmp = Float64(t / b);
	elseif (z <= 1.06e+189)
		tmp = t_1;
	else
		tmp = Float64(t / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = -a / b;
	tmp = 0.0;
	if (z <= -2.2e+141)
		tmp = t_1;
	elseif (z <= -0.74)
		tmp = t / b;
	elseif (z <= 1.95e-38)
		tmp = x;
	elseif (z <= 1.16e+51)
		tmp = t / b;
	elseif (z <= 1.06e+189)
		tmp = t_1;
	else
		tmp = t / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[((-a) / b), $MachinePrecision]}, If[LessEqual[z, -2.2e+141], t$95$1, If[LessEqual[z, -0.74], N[(t / b), $MachinePrecision], If[LessEqual[z, 1.95e-38], x, If[LessEqual[z, 1.16e+51], N[(t / b), $MachinePrecision], If[LessEqual[z, 1.06e+189], t$95$1, N[(t / b), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.2e141 or 1.16e51 < z < 1.05999999999999998e189

   1. Initial program 49.3%

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

   2. Taylor expanded in a around inf 36.1%

      \[\leadsto \frac{\color{blue}{-1 \cdot \left(a \cdot z\right)}}{y + z \cdot \left(b - y\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 36.1%

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

      2. distribute-lft-neg-out 36.1%

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

      3. *-commutative 36.1%

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

   4. Simplified 36.1%

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

   5. Taylor expanded in y around 0 53.4%

      \[\leadsto \color{blue}{-1 \cdot \frac{a}{b}} \]
   6. Step-by-step derivation

      1. mul-1-neg 53.4%

         \[\leadsto \color{blue}{-\frac{a}{b}} \]

   7. Simplified 53.4%

      \[\leadsto \color{blue}{-\frac{a}{b}} \]

   if -2.2e141 < z < -0.73999999999999999 or 1.95e-38 < z < 1.16e51 or 1.05999999999999998e189 < z

   1. Initial program 56.8%

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

   2. Taylor expanded in x around inf 56.9%

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

   3. Taylor expanded in b around inf 54.5%

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

   4. Taylor expanded in t around inf 40.1%

      \[\leadsto \color{blue}{\frac{t}{b}} \]

   if -0.73999999999999999 < z < 1.95e-38

   1. Initial program 88.9%

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

   2. Taylor expanded in z around 0 51.6%

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

4. Final simplification 48.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+141}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;z \leq -0.74:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-38}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.16 \cdot 10^{+51}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{+189}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \]

Alternative 15: 35.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.74:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-38}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+50}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+180}:\\ \;\;\;\;\frac{a}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -0.74)
   (/ t b)
   (if (<= z 1.9e-38)
     x
     (if (<= z 4.8e+50) (/ t b) (if (<= z 3.6e+180) (/ a y) (/ t b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -0.74) {
		tmp = t / b;
	} else if (z <= 1.9e-38) {
		tmp = x;
	} else if (z <= 4.8e+50) {
		tmp = t / b;
	} else if (z <= 3.6e+180) {
		tmp = a / y;
	} else {
		tmp = t / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-0.74d0)) then
        tmp = t / b
    else if (z <= 1.9d-38) then
        tmp = x
    else if (z <= 4.8d+50) then
        tmp = t / b
    else if (z <= 3.6d+180) then
        tmp = a / y
    else
        tmp = t / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -0.74) {
		tmp = t / b;
	} else if (z <= 1.9e-38) {
		tmp = x;
	} else if (z <= 4.8e+50) {
		tmp = t / b;
	} else if (z <= 3.6e+180) {
		tmp = a / y;
	} else {
		tmp = t / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -0.74:
		tmp = t / b
	elif z <= 1.9e-38:
		tmp = x
	elif z <= 4.8e+50:
		tmp = t / b
	elif z <= 3.6e+180:
		tmp = a / y
	else:
		tmp = t / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -0.74)
		tmp = Float64(t / b);
	elseif (z <= 1.9e-38)
		tmp = x;
	elseif (z <= 4.8e+50)
		tmp = Float64(t / b);
	elseif (z <= 3.6e+180)
		tmp = Float64(a / y);
	else
		tmp = Float64(t / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -0.74)
		tmp = t / b;
	elseif (z <= 1.9e-38)
		tmp = x;
	elseif (z <= 4.8e+50)
		tmp = t / b;
	elseif (z <= 3.6e+180)
		tmp = a / y;
	else
		tmp = t / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -0.74], N[(t / b), $MachinePrecision], If[LessEqual[z, 1.9e-38], x, If[LessEqual[z, 4.8e+50], N[(t / b), $MachinePrecision], If[LessEqual[z, 3.6e+180], N[(a / y), $MachinePrecision], N[(t / b), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.73999999999999999 or 1.9e-38 < z < 4.8000000000000004e50 or 3.6000000000000002e180 < z

   1. Initial program 52.0%

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

   2. Taylor expanded in x around inf 52.0%

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

   3. Taylor expanded in b around inf 56.9%

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

   4. Taylor expanded in t around inf 37.5%

      \[\leadsto \color{blue}{\frac{t}{b}} \]

   if -0.73999999999999999 < z < 1.9e-38

   1. Initial program 88.9%

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

   2. Taylor expanded in z around 0 51.6%

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

   if 4.8000000000000004e50 < z < 3.6000000000000002e180

   1. Initial program 60.2%

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

   2. Taylor expanded in z around inf 96.3%

      \[\leadsto \color{blue}{\frac{t - a}{b - y}} \]

   3. Taylor expanded in b around 0 61.2%

      \[\leadsto \color{blue}{-1 \cdot \frac{t - a}{y}} \]
   4. Step-by-step derivation

      1. associate-*r/ 61.2%

         \[\leadsto \color{blue}{\frac{-1 \cdot \left(t - a\right)}{y}} \]

      2. mul-1-neg 61.2%

         \[\leadsto \frac{\color{blue}{-\left(t - a\right)}}{y} \]

   5. Simplified 61.2%

      \[\leadsto \color{blue}{\frac{-\left(t - a\right)}{y}} \]

   6. Taylor expanded in t around 0 40.5%

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

4. Final simplification 44.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.74:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-38}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+50}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+180}:\\ \;\;\;\;\frac{a}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \]

Alternative 16: 62.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.78 \lor \neg \left(z \leq 2.95 \cdot 10^{-149}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{1 - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -0.78) (not (<= z 2.95e-149)))
   (/ (- t a) (- b y))
   (* x (/ 1.0 (- 1.0 z)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -0.78) || !(z <= 2.95e-149)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x * (1.0 / (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 <= (-0.78d0)) .or. (.not. (z <= 2.95d-149))) then
        tmp = (t - a) / (b - y)
    else
        tmp = x * (1.0d0 / (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 <= -0.78) || !(z <= 2.95e-149)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x * (1.0 / (1.0 - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -0.78) or not (z <= 2.95e-149):
		tmp = (t - a) / (b - y)
	else:
		tmp = x * (1.0 / (1.0 - z))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -0.78) || !(z <= 2.95e-149))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(x * Float64(1.0 / Float64(1.0 - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -0.78) || ~((z <= 2.95e-149)))
		tmp = (t - a) / (b - y);
	else
		tmp = x * (1.0 / (1.0 - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -0.78], N[Not[LessEqual[z, 2.95e-149]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.78000000000000003 or 2.9500000000000001e-149 < z

   1. Initial program 60.0%

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

   2. Taylor expanded in z around inf 72.9%

      \[\leadsto \color{blue}{\frac{t - a}{b - y}} \]

   if -0.78000000000000003 < z < 2.9500000000000001e-149

   1. Initial program 87.9%

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

   2. Taylor expanded in y around inf 62.3%

      \[\leadsto \color{blue}{\frac{x}{-1 \cdot z + 1}} \]
   3. Step-by-step derivation

      1. +-commutative 62.3%

         \[\leadsto \frac{x}{\color{blue}{1 + -1 \cdot z}} \]

      2. mul-1-neg 62.3%

         \[\leadsto \frac{x}{1 + \color{blue}{\left(-z\right)}} \]

      3. unsub-neg 62.3%

         \[\leadsto \frac{x}{\color{blue}{1 - z}} \]

   4. Simplified 62.3%

      \[\leadsto \color{blue}{\frac{x}{1 - z}} \]
   5. Step-by-step derivation

      1. div-inv 62.3%

         \[\leadsto \color{blue}{x \cdot \frac{1}{1 - z}} \]

   6. Applied egg-rr 62.3%

      \[\leadsto \color{blue}{x \cdot \frac{1}{1 - z}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.78 \lor \neg \left(z \leq 2.95 \cdot 10^{-149}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{1 - z}\\ \end{array} \]

Alternative 17: 54.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{-34} \lor \neg \left(y \leq 6.5 \cdot 10^{-71}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.35e-34) (not (<= y 6.5e-71))) (/ x (- 1.0 z)) (/ (- t a) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.35e-34) || !(y <= 6.5e-71)) {
		tmp = x / (1.0 - z);
	} else {
		tmp = (t - a) / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-1.35d-34)) .or. (.not. (y <= 6.5d-71))) then
        tmp = x / (1.0d0 - z)
    else
        tmp = (t - a) / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.35e-34) || !(y <= 6.5e-71)) {
		tmp = x / (1.0 - z);
	} else {
		tmp = (t - a) / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.35e-34) or not (y <= 6.5e-71):
		tmp = x / (1.0 - z)
	else:
		tmp = (t - a) / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.35e-34) || !(y <= 6.5e-71))
		tmp = Float64(x / Float64(1.0 - z));
	else
		tmp = Float64(Float64(t - a) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.35e-34) || ~((y <= 6.5e-71)))
		tmp = x / (1.0 - z);
	else
		tmp = (t - a) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.35e-34], N[Not[LessEqual[y, 6.5e-71]], $MachinePrecision]], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.35000000000000008e-34 or 6.50000000000000005e-71 < y

   1. Initial program 61.4%

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

   2. Taylor expanded in y around inf 52.4%

      \[\leadsto \color{blue}{\frac{x}{-1 \cdot z + 1}} \]
   3. Step-by-step derivation

      1. +-commutative 52.4%

         \[\leadsto \frac{x}{\color{blue}{1 + -1 \cdot z}} \]

      2. mul-1-neg 52.4%

         \[\leadsto \frac{x}{1 + \color{blue}{\left(-z\right)}} \]

      3. unsub-neg 52.4%

         \[\leadsto \frac{x}{\color{blue}{1 - z}} \]

   4. Simplified 52.4%

      \[\leadsto \color{blue}{\frac{x}{1 - z}} \]

   if -1.35000000000000008e-34 < y < 6.50000000000000005e-71

   1. Initial program 81.8%

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

   2. Taylor expanded in y around 0 61.5%

      \[\leadsto \color{blue}{\frac{t - a}{b}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 56.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{-34} \lor \neg \left(y \leq 6.5 \cdot 10^{-71}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \]

Alternative 18: 33.9% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.25 \cdot 10^{-7}:\\ \;\;\;\;\frac{a}{y}\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{-16}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -2.25e-7) (/ a y) (if (<= z 7.6e-16) x (/ a y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2.25e-7) {
		tmp = a / y;
	} else if (z <= 7.6e-16) {
		tmp = x;
	} 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 <= (-2.25d-7)) then
        tmp = a / y
    else if (z <= 7.6d-16) then
        tmp = x
    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 <= -2.25e-7) {
		tmp = a / y;
	} else if (z <= 7.6e-16) {
		tmp = x;
	} else {
		tmp = a / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -2.25e-7:
		tmp = a / y
	elif z <= 7.6e-16:
		tmp = x
	else:
		tmp = a / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -2.25e-7)
		tmp = Float64(a / y);
	elseif (z <= 7.6e-16)
		tmp = x;
	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 <= -2.25e-7)
		tmp = a / y;
	elseif (z <= 7.6e-16)
		tmp = x;
	else
		tmp = a / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -2.25e-7], N[(a / y), $MachinePrecision], If[LessEqual[z, 7.6e-16], x, N[(a / y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.2499999999999999e-7 or 7.60000000000000024e-16 < z

   1. Initial program 53.3%

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

   2. Taylor expanded in z around inf 81.1%

      \[\leadsto \color{blue}{\frac{t - a}{b - y}} \]

   3. Taylor expanded in b around 0 37.6%

      \[\leadsto \color{blue}{-1 \cdot \frac{t - a}{y}} \]
   4. Step-by-step derivation

      1. associate-*r/ 37.6%

         \[\leadsto \color{blue}{\frac{-1 \cdot \left(t - a\right)}{y}} \]

      2. mul-1-neg 37.6%

         \[\leadsto \frac{\color{blue}{-\left(t - a\right)}}{y} \]

   5. Simplified 37.6%

      \[\leadsto \color{blue}{\frac{-\left(t - a\right)}{y}} \]

   6. Taylor expanded in t around 0 22.7%

      \[\leadsto \color{blue}{\frac{a}{y}} \]

   if -2.2499999999999999e-7 < z < 7.60000000000000024e-16

   1. Initial program 89.0%

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

   2. Taylor expanded in z around 0 51.7%

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

4. Final simplification 36.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.25 \cdot 10^{-7}:\\ \;\;\;\;\frac{a}{y}\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{-16}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{y}\\ \end{array} \]

Alternative 19: 25.1% 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

1. Initial program 70.4%

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

2. Taylor expanded in z around 0 26.8%

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

3. Final simplification 26.8%

   \[\leadsto x \]

Developer target: 73.0% 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 2023228 
(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)))))