Development.Shake.Progress:decay from shake-0.15.5

Percentage Accurate: 66.4% → 88.7%

Time: 15.0s

Alternatives: 13

Speedup: 0.9×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 66.4% 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: 88.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{+52} \lor \neg \left(z \leq 68000000\right):\\ \;\;\;\;\frac{\frac{y}{\frac{b - y}{x}} + \frac{a - t}{\frac{{\left(b - y\right)}^{2}}{y}}}{z} + \frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x - z \cdot \left(a - t\right)}{y + \left(z \cdot b - z \cdot y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -2.15e+52) (not (<= z 68000000.0)))
   (+
    (/ (+ (/ y (/ (- b y) x)) (/ (- a t) (/ (pow (- b y) 2.0) y))) z)
    (/ (- t a) (- b y)))
   (/ (- (* y x) (* z (- a t))) (+ y (- (* z b) (* z y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.15e+52) || !(z <= 68000000.0)) {
		tmp = (((y / ((b - y) / x)) + ((a - t) / (pow((b - y), 2.0) / y))) / z) + ((t - a) / (b - y));
	} else {
		tmp = ((y * x) - (z * (a - t))) / (y + ((z * b) - (z * y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-2.15d+52)) .or. (.not. (z <= 68000000.0d0))) then
        tmp = (((y / ((b - y) / x)) + ((a - t) / (((b - y) ** 2.0d0) / y))) / z) + ((t - a) / (b - y))
    else
        tmp = ((y * x) - (z * (a - t))) / (y + ((z * b) - (z * y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.15e+52) || !(z <= 68000000.0)) {
		tmp = (((y / ((b - y) / x)) + ((a - t) / (Math.pow((b - y), 2.0) / y))) / z) + ((t - a) / (b - y));
	} else {
		tmp = ((y * x) - (z * (a - t))) / (y + ((z * b) - (z * y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -2.15e+52) or not (z <= 68000000.0):
		tmp = (((y / ((b - y) / x)) + ((a - t) / (math.pow((b - y), 2.0) / y))) / z) + ((t - a) / (b - y))
	else:
		tmp = ((y * x) - (z * (a - t))) / (y + ((z * b) - (z * y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -2.15e+52) || !(z <= 68000000.0))
		tmp = Float64(Float64(Float64(Float64(y / Float64(Float64(b - y) / x)) + Float64(Float64(a - t) / Float64((Float64(b - y) ^ 2.0) / y))) / z) + Float64(Float64(t - a) / Float64(b - y)));
	else
		tmp = Float64(Float64(Float64(y * x) - Float64(z * Float64(a - t))) / Float64(y + Float64(Float64(z * b) - Float64(z * y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -2.15e+52) || ~((z <= 68000000.0)))
		tmp = (((y / ((b - y) / x)) + ((a - t) / (((b - y) ^ 2.0) / y))) / z) + ((t - a) / (b - y));
	else
		tmp = ((y * x) - (z * (a - t))) / (y + ((z * b) - (z * y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -2.15e+52], N[Not[LessEqual[z, 68000000.0]], $MachinePrecision]], N[(N[(N[(N[(y / N[(N[(b - y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] + N[(N[(a - t), $MachinePrecision] / N[(N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] + N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y * x), $MachinePrecision] - N[(z * N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y + N[(N[(z * b), $MachinePrecision] - N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.15e52 or 6.8e7 < z

   1. Initial program 43.7%

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

   2. Taylor expanded in z around -inf 73.5%

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

      1. +-commutative 73.5%

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

      2. associate--l+ 73.5%

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

   4. Simplified 95.9%

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

   if -2.15e52 < z < 6.8e7

   1. Initial program 90.1%

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

      1. sub-neg 90.1%

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

      2. distribute-lft-in 90.1%

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

   3. Applied egg-rr 90.1%

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

4. Final simplification 92.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{+52} \lor \neg \left(z \leq 68000000\right):\\ \;\;\;\;\frac{\frac{y}{\frac{b - y}{x}} + \frac{a - t}{\frac{{\left(b - y\right)}^{2}}{y}}}{z} + \frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x - z \cdot \left(a - t\right)}{y + \left(z \cdot b - z \cdot y\right)}\\ \end{array} \]

Alternative 2: 83.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot x - z \cdot \left(a - t\right)}{y + z \cdot \left(b - y\right)}\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -4.2 \cdot 10^{+34}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+50}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+89}:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+136}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (* y x) (* z (- a t))) (+ y (* z (- b y)))))
        (t_2 (/ (- t a) (- b y))))
   (if (<= z -4.2e+34)
     t_2
     (if (<= z 3.6e+50)
       t_1
       (if (<= z 3.2e+89)
         (- (/ (- a t) y) (/ x z))
         (if (<= z 1.3e+136) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y * x) - (z * (a - t))) / (y + (z * (b - y)));
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -4.2e+34) {
		tmp = t_2;
	} else if (z <= 3.6e+50) {
		tmp = t_1;
	} else if (z <= 3.2e+89) {
		tmp = ((a - t) / y) - (x / z);
	} else if (z <= 1.3e+136) {
		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 = ((y * x) - (z * (a - t))) / (y + (z * (b - y)))
    t_2 = (t - a) / (b - y)
    if (z <= (-4.2d+34)) then
        tmp = t_2
    else if (z <= 3.6d+50) then
        tmp = t_1
    else if (z <= 3.2d+89) then
        tmp = ((a - t) / y) - (x / z)
    else if (z <= 1.3d+136) 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 = ((y * x) - (z * (a - t))) / (y + (z * (b - y)));
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -4.2e+34) {
		tmp = t_2;
	} else if (z <= 3.6e+50) {
		tmp = t_1;
	} else if (z <= 3.2e+89) {
		tmp = ((a - t) / y) - (x / z);
	} else if (z <= 1.3e+136) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((y * x) - (z * (a - t))) / (y + (z * (b - y)))
	t_2 = (t - a) / (b - y)
	tmp = 0
	if z <= -4.2e+34:
		tmp = t_2
	elif z <= 3.6e+50:
		tmp = t_1
	elif z <= 3.2e+89:
		tmp = ((a - t) / y) - (x / z)
	elif z <= 1.3e+136:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(y * x) - Float64(z * Float64(a - t))) / Float64(y + Float64(z * Float64(b - y))))
	t_2 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -4.2e+34)
		tmp = t_2;
	elseif (z <= 3.6e+50)
		tmp = t_1;
	elseif (z <= 3.2e+89)
		tmp = Float64(Float64(Float64(a - t) / y) - Float64(x / z));
	elseif (z <= 1.3e+136)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((y * x) - (z * (a - t))) / (y + (z * (b - y)));
	t_2 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -4.2e+34)
		tmp = t_2;
	elseif (z <= 3.6e+50)
		tmp = t_1;
	elseif (z <= 3.2e+89)
		tmp = ((a - t) / y) - (x / z);
	elseif (z <= 1.3e+136)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(y * x), $MachinePrecision] - N[(z * N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.2e+34], t$95$2, If[LessEqual[z, 3.6e+50], t$95$1, If[LessEqual[z, 3.2e+89], N[(N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision] - N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.3e+136], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.20000000000000035e34 or 1.3000000000000001e136 < z

   1. Initial program 37.0%

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

   2. Taylor expanded in z around inf 85.8%

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

   if -4.20000000000000035e34 < z < 3.59999999999999986e50 or 3.19999999999999987e89 < z < 1.3000000000000001e136

   1. Initial program 88.1%

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

   if 3.59999999999999986e50 < z < 3.19999999999999987e89

   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 z around inf 50.0%

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

   3. Taylor expanded in y around -inf 90.2%

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

      1. +-commutative 90.2%

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

      2. mul-1-neg 90.2%

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

      3. unsub-neg 90.2%

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

      4. associate-*r/ 90.2%

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

      5. mul-1-neg 90.2%

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

      6. associate--l+ 90.2%

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

      7. associate-/l* 99.8%

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

      8. mul-1-neg 99.8%

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

      9. unsub-neg 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in z around inf 99.8%

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

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+34}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+50}:\\ \;\;\;\;\frac{y \cdot x - z \cdot \left(a - t\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+89}:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+136}:\\ \;\;\;\;\frac{y \cdot x - z \cdot \left(a - t\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 3: 83.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot x - z \cdot \left(a - t\right)\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -2.2 \cdot 10^{+34}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{+50}:\\ \;\;\;\;\frac{t_1}{y + \left(z \cdot b - z \cdot y\right)}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+89}:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+136}:\\ \;\;\;\;\frac{t_1}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (* y x) (* z (- a t)))) (t_2 (/ (- t a) (- b y))))
   (if (<= z -2.2e+34)
     t_2
     (if (<= z 3.9e+50)
       (/ t_1 (+ y (- (* z b) (* z y))))
       (if (<= z 5e+89)
         (- (/ (- a t) y) (/ x z))
         (if (<= z 1.3e+136) (/ t_1 (+ y (* z (- b y)))) t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y * x) - (z * (a - t));
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -2.2e+34) {
		tmp = t_2;
	} else if (z <= 3.9e+50) {
		tmp = t_1 / (y + ((z * b) - (z * y)));
	} else if (z <= 5e+89) {
		tmp = ((a - t) / y) - (x / z);
	} else if (z <= 1.3e+136) {
		tmp = t_1 / (y + (z * (b - y)));
	} 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 * x) - (z * (a - t))
    t_2 = (t - a) / (b - y)
    if (z <= (-2.2d+34)) then
        tmp = t_2
    else if (z <= 3.9d+50) then
        tmp = t_1 / (y + ((z * b) - (z * y)))
    else if (z <= 5d+89) then
        tmp = ((a - t) / y) - (x / z)
    else if (z <= 1.3d+136) then
        tmp = t_1 / (y + (z * (b - y)))
    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 * x) - (z * (a - t));
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -2.2e+34) {
		tmp = t_2;
	} else if (z <= 3.9e+50) {
		tmp = t_1 / (y + ((z * b) - (z * y)));
	} else if (z <= 5e+89) {
		tmp = ((a - t) / y) - (x / z);
	} else if (z <= 1.3e+136) {
		tmp = t_1 / (y + (z * (b - y)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (y * x) - (z * (a - t))
	t_2 = (t - a) / (b - y)
	tmp = 0
	if z <= -2.2e+34:
		tmp = t_2
	elif z <= 3.9e+50:
		tmp = t_1 / (y + ((z * b) - (z * y)))
	elif z <= 5e+89:
		tmp = ((a - t) / y) - (x / z)
	elif z <= 1.3e+136:
		tmp = t_1 / (y + (z * (b - y)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y * x) - Float64(z * Float64(a - t)))
	t_2 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -2.2e+34)
		tmp = t_2;
	elseif (z <= 3.9e+50)
		tmp = Float64(t_1 / Float64(y + Float64(Float64(z * b) - Float64(z * y))));
	elseif (z <= 5e+89)
		tmp = Float64(Float64(Float64(a - t) / y) - Float64(x / z));
	elseif (z <= 1.3e+136)
		tmp = Float64(t_1 / Float64(y + Float64(z * Float64(b - y))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (y * x) - (z * (a - t));
	t_2 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -2.2e+34)
		tmp = t_2;
	elseif (z <= 3.9e+50)
		tmp = t_1 / (y + ((z * b) - (z * y)));
	elseif (z <= 5e+89)
		tmp = ((a - t) / y) - (x / z);
	elseif (z <= 1.3e+136)
		tmp = t_1 / (y + (z * (b - y)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y * x), $MachinePrecision] - N[(z * N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.2e+34], t$95$2, If[LessEqual[z, 3.9e+50], N[(t$95$1 / N[(y + N[(N[(z * b), $MachinePrecision] - N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5e+89], N[(N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision] - N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.3e+136], N[(t$95$1 / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.2000000000000002e34 or 1.3000000000000001e136 < z

   1. Initial program 37.0%

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

   2. Taylor expanded in z around inf 85.8%

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

   if -2.2000000000000002e34 < z < 3.89999999999999967e50

   1. Initial program 90.2%

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

      1. sub-neg 90.2%

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

      2. distribute-lft-in 90.2%

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

   3. Applied egg-rr 90.2%

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

   if 3.89999999999999967e50 < z < 4.99999999999999983e89

   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 z around inf 50.0%

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

   3. Taylor expanded in y around -inf 90.2%

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

      1. +-commutative 90.2%

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

      2. mul-1-neg 90.2%

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

      3. unsub-neg 90.2%

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

      4. associate-*r/ 90.2%

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

      5. mul-1-neg 90.2%

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

      6. associate--l+ 90.2%

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

      7. associate-/l* 99.8%

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

      8. mul-1-neg 99.8%

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

      9. unsub-neg 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in z around inf 99.8%

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

   if 4.99999999999999983e89 < z < 1.3000000000000001e136

   1. Initial program 67.3%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+34}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{+50}:\\ \;\;\;\;\frac{y \cdot x - z \cdot \left(a - t\right)}{y + \left(z \cdot b - z \cdot y\right)}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+89}:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+136}:\\ \;\;\;\;\frac{y \cdot x - z \cdot \left(a - t\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 4: 66.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot x - z \cdot \left(a - t\right)}{y}\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -8.2 \cdot 10^{+24}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -4.3 \cdot 10^{-76}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-189}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 0.36:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (* y x) (* z (- a t))) y)) (t_2 (/ (- t a) (- b y))))
   (if (<= z -8.2e+24)
     t_2
     (if (<= z -4.3e-76)
       t_1
       (if (<= z -3.6e-189) x (if (<= z 0.36) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y * x) - (z * (a - t))) / y;
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -8.2e+24) {
		tmp = t_2;
	} else if (z <= -4.3e-76) {
		tmp = t_1;
	} else if (z <= -3.6e-189) {
		tmp = x;
	} else if (z <= 0.36) {
		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 = ((y * x) - (z * (a - t))) / y
    t_2 = (t - a) / (b - y)
    if (z <= (-8.2d+24)) then
        tmp = t_2
    else if (z <= (-4.3d-76)) then
        tmp = t_1
    else if (z <= (-3.6d-189)) then
        tmp = x
    else if (z <= 0.36d0) 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 = ((y * x) - (z * (a - t))) / y;
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -8.2e+24) {
		tmp = t_2;
	} else if (z <= -4.3e-76) {
		tmp = t_1;
	} else if (z <= -3.6e-189) {
		tmp = x;
	} else if (z <= 0.36) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((y * x) - (z * (a - t))) / y
	t_2 = (t - a) / (b - y)
	tmp = 0
	if z <= -8.2e+24:
		tmp = t_2
	elif z <= -4.3e-76:
		tmp = t_1
	elif z <= -3.6e-189:
		tmp = x
	elif z <= 0.36:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(y * x) - Float64(z * Float64(a - t))) / y)
	t_2 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -8.2e+24)
		tmp = t_2;
	elseif (z <= -4.3e-76)
		tmp = t_1;
	elseif (z <= -3.6e-189)
		tmp = x;
	elseif (z <= 0.36)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((y * x) - (z * (a - t))) / y;
	t_2 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -8.2e+24)
		tmp = t_2;
	elseif (z <= -4.3e-76)
		tmp = t_1;
	elseif (z <= -3.6e-189)
		tmp = x;
	elseif (z <= 0.36)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(y * x), $MachinePrecision] - N[(z * N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8.2e+24], t$95$2, If[LessEqual[z, -4.3e-76], t$95$1, If[LessEqual[z, -3.6e-189], x, If[LessEqual[z, 0.36], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.2000000000000002e24 or 0.35999999999999999 < z

   1. Initial program 47.7%

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

   2. Taylor expanded in z around inf 77.3%

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

   if -8.2000000000000002e24 < z < -4.2999999999999999e-76 or -3.60000000000000017e-189 < z < 0.35999999999999999

   1. Initial program 94.4%

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

   2. Taylor expanded in z around 0 61.5%

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

   if -4.2999999999999999e-76 < z < -3.60000000000000017e-189

   1. Initial program 75.3%

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

   2. Taylor expanded in z around 0 60.9%

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

4. Final simplification 68.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+24}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -4.3 \cdot 10^{-76}:\\ \;\;\;\;\frac{y \cdot x - z \cdot \left(a - t\right)}{y}\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-189}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 0.36:\\ \;\;\;\;\frac{y \cdot x - z \cdot \left(a - t\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 5: 42.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{b - y}\\ t_2 := \frac{-a}{b}\\ t_3 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -5.2 \cdot 10^{-97}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-248}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-306}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-217}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{+14}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ t (- b y))) (t_2 (/ (- a) b)) (t_3 (/ x (- 1.0 z))))
   (if (<= y -5.2e-97)
     t_3
     (if (<= y -4.2e-248)
       t_1
       (if (<= y 2.5e-306)
         t_2
         (if (<= y 3.4e-217) t_1 (if (<= y 4.7e+14) t_2 t_3)))))))

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 t_3 = x / (1.0 - z);
	double tmp;
	if (y <= -5.2e-97) {
		tmp = t_3;
	} else if (y <= -4.2e-248) {
		tmp = t_1;
	} else if (y <= 2.5e-306) {
		tmp = t_2;
	} else if (y <= 3.4e-217) {
		tmp = t_1;
	} else if (y <= 4.7e+14) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = t / (b - y)
    t_2 = -a / b
    t_3 = x / (1.0d0 - z)
    if (y <= (-5.2d-97)) then
        tmp = t_3
    else if (y <= (-4.2d-248)) then
        tmp = t_1
    else if (y <= 2.5d-306) then
        tmp = t_2
    else if (y <= 3.4d-217) then
        tmp = t_1
    else if (y <= 4.7d+14) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t / (b - y);
	double t_2 = -a / b;
	double t_3 = x / (1.0 - z);
	double tmp;
	if (y <= -5.2e-97) {
		tmp = t_3;
	} else if (y <= -4.2e-248) {
		tmp = t_1;
	} else if (y <= 2.5e-306) {
		tmp = t_2;
	} else if (y <= 3.4e-217) {
		tmp = t_1;
	} else if (y <= 4.7e+14) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t / (b - y)
	t_2 = -a / b
	t_3 = x / (1.0 - z)
	tmp = 0
	if y <= -5.2e-97:
		tmp = t_3
	elif y <= -4.2e-248:
		tmp = t_1
	elif y <= 2.5e-306:
		tmp = t_2
	elif y <= 3.4e-217:
		tmp = t_1
	elif y <= 4.7e+14:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t / Float64(b - y))
	t_2 = Float64(Float64(-a) / b)
	t_3 = Float64(x / Float64(1.0 - z))
	tmp = 0.0
	if (y <= -5.2e-97)
		tmp = t_3;
	elseif (y <= -4.2e-248)
		tmp = t_1;
	elseif (y <= 2.5e-306)
		tmp = t_2;
	elseif (y <= 3.4e-217)
		tmp = t_1;
	elseif (y <= 4.7e+14)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t / (b - y);
	t_2 = -a / b;
	t_3 = x / (1.0 - z);
	tmp = 0.0;
	if (y <= -5.2e-97)
		tmp = t_3;
	elseif (y <= -4.2e-248)
		tmp = t_1;
	elseif (y <= 2.5e-306)
		tmp = t_2;
	elseif (y <= 3.4e-217)
		tmp = t_1;
	elseif (y <= 4.7e+14)
		tmp = t_2;
	else
		tmp = t_3;
	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]}, Block[{t$95$3 = N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.2e-97], t$95$3, If[LessEqual[y, -4.2e-248], t$95$1, If[LessEqual[y, 2.5e-306], t$95$2, If[LessEqual[y, 3.4e-217], t$95$1, If[LessEqual[y, 4.7e+14], t$95$2, t$95$3]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.20000000000000014e-97 or 4.7e14 < y

   1. Initial program 59.8%

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

   2. Taylor expanded in y around inf 48.1%

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

      1. +-commutative 48.1%

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

      2. mul-1-neg 48.1%

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

      3. unsub-neg 48.1%

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

   4. Simplified 48.1%

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

   if -5.20000000000000014e-97 < y < -4.2e-248 or 2.49999999999999999e-306 < y < 3.40000000000000016e-217

   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 z around inf 66.2%

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

   3. Taylor expanded in t around inf 49.5%

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

   if -4.2e-248 < y < 2.49999999999999999e-306 or 3.40000000000000016e-217 < y < 4.7e14

   1. Initial program 79.7%

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

   2. Taylor expanded in a around inf 38.1%

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

      1. mul-1-neg 38.1%

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

      2. distribute-rgt-neg-in 38.1%

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

   4. Simplified 38.1%

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

   5. Taylor expanded in y around 0 47.3%

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

      1. associate-*r/ 47.3%

         \[\leadsto \color{blue}{\frac{-1 \cdot a}{b}} \]

      2. mul-1-neg 47.3%

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

   7. Simplified 47.3%

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

4. Final simplification 48.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{-97}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-248}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-306}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-217}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{+14}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]

Alternative 6: 60.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{+264}:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z}\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{+71} \lor \neg \left(y \leq 6.5 \cdot 10^{+90}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.55e+264)
   (- (/ (- a t) y) (/ x z))
   (if (or (<= y -2.9e+71) (not (<= y 6.5e+90)))
     (/ x (- 1.0 z))
     (/ (- t a) (- b y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.55e+264) {
		tmp = ((a - t) / y) - (x / z);
	} else if ((y <= -2.9e+71) || !(y <= 6.5e+90)) {
		tmp = x / (1.0 - z);
	} else {
		tmp = (t - a) / (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 (y <= (-1.55d+264)) then
        tmp = ((a - t) / y) - (x / z)
    else if ((y <= (-2.9d+71)) .or. (.not. (y <= 6.5d+90))) then
        tmp = x / (1.0d0 - z)
    else
        tmp = (t - a) / (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 (y <= -1.55e+264) {
		tmp = ((a - t) / y) - (x / z);
	} else if ((y <= -2.9e+71) || !(y <= 6.5e+90)) {
		tmp = x / (1.0 - z);
	} else {
		tmp = (t - a) / (b - y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.55e+264:
		tmp = ((a - t) / y) - (x / z)
	elif (y <= -2.9e+71) or not (y <= 6.5e+90):
		tmp = x / (1.0 - z)
	else:
		tmp = (t - a) / (b - y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.55e+264)
		tmp = Float64(Float64(Float64(a - t) / y) - Float64(x / z));
	elseif ((y <= -2.9e+71) || !(y <= 6.5e+90))
		tmp = Float64(x / Float64(1.0 - z));
	else
		tmp = Float64(Float64(t - a) / Float64(b - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -1.55e+264)
		tmp = ((a - t) / y) - (x / z);
	elseif ((y <= -2.9e+71) || ~((y <= 6.5e+90)))
		tmp = x / (1.0 - z);
	else
		tmp = (t - a) / (b - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.55e+264], N[(N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision] - N[(x / z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -2.9e+71], N[Not[LessEqual[y, 6.5e+90]], $MachinePrecision]], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.54999999999999991e264

   1. Initial program 27.1%

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

   2. Taylor expanded in z around inf 11.0%

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

   3. Taylor expanded in y around -inf 71.0%

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

      1. +-commutative 71.0%

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

      2. mul-1-neg 71.0%

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

      3. unsub-neg 71.0%

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

      4. associate-*r/ 71.0%

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

      5. mul-1-neg 71.0%

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

      6. associate--l+ 71.0%

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

      7. associate-/l* 71.0%

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

      8. mul-1-neg 71.0%

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

      9. unsub-neg 71.0%

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

   5. Simplified 71.0%

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

   6. Taylor expanded in z around inf 71.7%

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

   if -1.54999999999999991e264 < y < -2.90000000000000007e71 or 6.5000000000000001e90 < y

   1. Initial program 56.0%

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

   2. Taylor expanded in y around inf 59.7%

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

      1. +-commutative 59.7%

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

      2. mul-1-neg 59.7%

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

      3. unsub-neg 59.7%

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

   4. Simplified 59.7%

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

   if -2.90000000000000007e71 < y < 6.5000000000000001e90

   1. Initial program 81.4%

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

   2. Taylor expanded in z around inf 62.9%

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

4. Final simplification 62.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{+264}:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z}\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{+71} \lor \neg \left(y \leq 6.5 \cdot 10^{+90}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 7: 61.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{+71} \lor \neg \left(y \leq 1.5 \cdot 10^{+91}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -4.6e+71) (not (<= y 1.5e+91)))
   (/ x (- 1.0 z))
   (/ (- t a) (- b y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -4.6e+71) || !(y <= 1.5e+91)) {
		tmp = x / (1.0 - z);
	} else {
		tmp = (t - a) / (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 ((y <= (-4.6d+71)) .or. (.not. (y <= 1.5d+91))) then
        tmp = x / (1.0d0 - z)
    else
        tmp = (t - a) / (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 ((y <= -4.6e+71) || !(y <= 1.5e+91)) {
		tmp = x / (1.0 - z);
	} else {
		tmp = (t - a) / (b - y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -4.6e+71) or not (y <= 1.5e+91):
		tmp = x / (1.0 - z)
	else:
		tmp = (t - a) / (b - y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -4.6e+71) || !(y <= 1.5e+91))
		tmp = Float64(x / Float64(1.0 - z));
	else
		tmp = Float64(Float64(t - a) / Float64(b - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -4.6e+71) || ~((y <= 1.5e+91)))
		tmp = x / (1.0 - z);
	else
		tmp = (t - a) / (b - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -4.6e+71], N[Not[LessEqual[y, 1.5e+91]], $MachinePrecision]], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.6000000000000005e71 or 1.50000000000000003e91 < y

   1. Initial program 53.0%

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

   2. Taylor expanded in y around inf 56.7%

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

      1. +-commutative 56.7%

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

      2. mul-1-neg 56.7%

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

      3. unsub-neg 56.7%

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

   4. Simplified 56.7%

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

   if -4.6000000000000005e71 < y < 1.50000000000000003e91

   1. Initial program 81.4%

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

   2. Taylor expanded in z around inf 62.9%

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

4. Final simplification 60.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{+71} \lor \neg \left(y \leq 1.5 \cdot 10^{+91}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 8: 54.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+71} \lor \neg \left(y \leq 2100\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -5.5e+71) (not (<= y 2100.0))) (/ 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 <= -5.5e+71) || !(y <= 2100.0)) {
		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 <= (-5.5d+71)) .or. (.not. (y <= 2100.0d0))) 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 <= -5.5e+71) || !(y <= 2100.0)) {
		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 <= -5.5e+71) or not (y <= 2100.0):
		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 <= -5.5e+71) || !(y <= 2100.0))
		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 <= -5.5e+71) || ~((y <= 2100.0)))
		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, -5.5e+71], N[Not[LessEqual[y, 2100.0]], $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 < -5.5e71 or 2100 < y

   1. Initial program 54.6%

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

   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%

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

   if -5.5e71 < y < 2100

   1. Initial program 82.5%

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

   2. Taylor expanded in y around 0 57.2%

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

4. Final simplification 55.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+71} \lor \neg \left(y \leq 2100\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \]

Alternative 9: 34.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{-8}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-5}:\\ \;\;\;\;x + z \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.2e-8) (/ (- a) b) (if (<= z 3.6e-5) (+ x (* z x)) (/ (- x) z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.2e-8) {
		tmp = -a / b;
	} else if (z <= 3.6e-5) {
		tmp = x + (z * x);
	} else {
		tmp = -x / 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 <= (-1.2d-8)) then
        tmp = -a / b
    else if (z <= 3.6d-5) then
        tmp = x + (z * x)
    else
        tmp = -x / 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 <= -1.2e-8) {
		tmp = -a / b;
	} else if (z <= 3.6e-5) {
		tmp = x + (z * x);
	} else {
		tmp = -x / z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1.2e-8:
		tmp = -a / b
	elif z <= 3.6e-5:
		tmp = x + (z * x)
	else:
		tmp = -x / z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.2e-8)
		tmp = Float64(Float64(-a) / b);
	elseif (z <= 3.6e-5)
		tmp = Float64(x + Float64(z * x));
	else
		tmp = Float64(Float64(-x) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -1.2e-8)
		tmp = -a / b;
	elseif (z <= 3.6e-5)
		tmp = x + (z * x);
	else
		tmp = -x / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.2e-8], N[((-a) / b), $MachinePrecision], If[LessEqual[z, 3.6e-5], N[(x + N[(z * x), $MachinePrecision]), $MachinePrecision], N[((-x) / z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.19999999999999999e-8

   1. Initial program 46.5%

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

   2. Taylor expanded in a around inf 24.4%

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

      1. mul-1-neg 24.4%

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

      2. distribute-rgt-neg-in 24.4%

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

   4. Simplified 24.4%

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

   5. Taylor expanded in y around 0 41.1%

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

      1. associate-*r/ 41.1%

         \[\leadsto \color{blue}{\frac{-1 \cdot a}{b}} \]

      2. mul-1-neg 41.1%

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

   7. Simplified 41.1%

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

   if -1.19999999999999999e-8 < z < 3.60000000000000009e-5

   1. Initial program 90.4%

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

   2. Taylor expanded in y around inf 41.7%

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

      1. +-commutative 41.7%

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

      2. mul-1-neg 41.7%

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

      3. unsub-neg 41.7%

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

   4. Simplified 41.7%

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

   5. Taylor expanded in z around 0 41.5%

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

   if 3.60000000000000009e-5 < z

   1. Initial program 51.7%

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

   2. Taylor expanded in y around inf 24.9%

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

      1. +-commutative 24.9%

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

      2. mul-1-neg 24.9%

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

      3. unsub-neg 24.9%

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

   4. Simplified 24.9%

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

   5. Taylor expanded in z around inf 24.2%

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

      1. associate-*r/ 24.2%

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

      2. mul-1-neg 24.2%

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

   7. Simplified 24.2%

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

4. Final simplification 36.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{-8}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-5}:\\ \;\;\;\;x + z \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{z}\\ \end{array} \]

Alternative 10: 39.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{-7}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;z \leq 1.32 \cdot 10^{+14}:\\ \;\;\;\;x + z \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -3.7e-7)
   (/ (- a) b)
   (if (<= z 1.32e+14) (+ x (* z x)) (/ t (- b y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -3.7e-7) {
		tmp = -a / b;
	} else if (z <= 1.32e+14) {
		tmp = x + (z * x);
	} else {
		tmp = t / (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 <= (-3.7d-7)) then
        tmp = -a / b
    else if (z <= 1.32d+14) then
        tmp = x + (z * x)
    else
        tmp = t / (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 <= -3.7e-7) {
		tmp = -a / b;
	} else if (z <= 1.32e+14) {
		tmp = x + (z * x);
	} else {
		tmp = t / (b - y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -3.7e-7:
		tmp = -a / b
	elif z <= 1.32e+14:
		tmp = x + (z * x)
	else:
		tmp = t / (b - y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -3.7e-7)
		tmp = Float64(Float64(-a) / b);
	elseif (z <= 1.32e+14)
		tmp = Float64(x + Float64(z * x));
	else
		tmp = Float64(t / Float64(b - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -3.7e-7)
		tmp = -a / b;
	elseif (z <= 1.32e+14)
		tmp = x + (z * x);
	else
		tmp = t / (b - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -3.7e-7], N[((-a) / b), $MachinePrecision], If[LessEqual[z, 1.32e+14], N[(x + N[(z * x), $MachinePrecision]), $MachinePrecision], N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.70000000000000004e-7

   1. Initial program 46.5%

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

   2. Taylor expanded in a around inf 24.4%

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

      1. mul-1-neg 24.4%

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

      2. distribute-rgt-neg-in 24.4%

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

   4. Simplified 24.4%

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

   5. Taylor expanded in y around 0 41.1%

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

      1. associate-*r/ 41.1%

         \[\leadsto \color{blue}{\frac{-1 \cdot a}{b}} \]

      2. mul-1-neg 41.1%

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

   7. Simplified 41.1%

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

   if -3.70000000000000004e-7 < z < 1.32e14

   1. Initial program 90.6%

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

   2. Taylor expanded in y around inf 41.2%

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

      1. +-commutative 41.2%

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

      2. mul-1-neg 41.2%

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

      3. unsub-neg 41.2%

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

   4. Simplified 41.2%

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

   5. Taylor expanded in z around 0 40.3%

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

   if 1.32e14 < z

   1. Initial program 48.7%

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

   2. Taylor expanded in z around inf 74.3%

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

   3. Taylor expanded in t around inf 44.1%

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

4. Final simplification 41.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{-7}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;z \leq 1.32 \cdot 10^{+14}:\\ \;\;\;\;x + z \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b - y}\\ \end{array} \]

Alternative 11: 36.3% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+20} \lor \neg \left(z \leq 6 \cdot 10^{-74}\right):\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.8e+20) (not (<= z 6e-74))) (/ (- a) b) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.8e+20) || !(z <= 6e-74)) {
		tmp = -a / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-1.8d+20)) .or. (.not. (z <= 6d-74))) then
        tmp = -a / b
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.8e+20) || !(z <= 6e-74)) {
		tmp = -a / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.8e+20) or not (z <= 6e-74):
		tmp = -a / b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.8e+20) || !(z <= 6e-74))
		tmp = Float64(Float64(-a) / b);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1.8e+20) || ~((z <= 6e-74)))
		tmp = -a / b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.8e+20], N[Not[LessEqual[z, 6e-74]], $MachinePrecision]], N[((-a) / b), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.8e20 or 6.00000000000000014e-74 < 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 a around inf 26.0%

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

      1. mul-1-neg 26.0%

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

      2. distribute-rgt-neg-in 26.0%

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

   4. Simplified 26.0%

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

   5. Taylor expanded in y around 0 30.0%

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

      1. associate-*r/ 30.0%

         \[\leadsto \color{blue}{\frac{-1 \cdot a}{b}} \]

      2. mul-1-neg 30.0%

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

   7. Simplified 30.0%

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

   if -1.8e20 < z < 6.00000000000000014e-74

   1. Initial program 91.6%

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

   2. Taylor expanded in z around 0 42.9%

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

4. Final simplification 35.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+20} \lor \neg \left(z \leq 6 \cdot 10^{-74}\right):\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 12: 34.4% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+15}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-5}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -3.8e+15) (/ (- a) b) (if (<= z 3.4e-5) x (/ (- x) z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -3.8e+15) {
		tmp = -a / b;
	} else if (z <= 3.4e-5) {
		tmp = x;
	} else {
		tmp = -x / 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 <= (-3.8d+15)) then
        tmp = -a / b
    else if (z <= 3.4d-5) then
        tmp = x
    else
        tmp = -x / 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 <= -3.8e+15) {
		tmp = -a / b;
	} else if (z <= 3.4e-5) {
		tmp = x;
	} else {
		tmp = -x / z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -3.8e+15:
		tmp = -a / b
	elif z <= 3.4e-5:
		tmp = x
	else:
		tmp = -x / z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -3.8e+15)
		tmp = Float64(Float64(-a) / b);
	elseif (z <= 3.4e-5)
		tmp = x;
	else
		tmp = Float64(Float64(-x) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -3.8e+15)
		tmp = -a / b;
	elseif (z <= 3.4e-5)
		tmp = x;
	else
		tmp = -x / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -3.8e+15], N[((-a) / b), $MachinePrecision], If[LessEqual[z, 3.4e-5], x, N[((-x) / z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.8e15

   1. Initial program 45.5%

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

   2. Taylor expanded in a around inf 24.7%

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

      1. mul-1-neg 24.7%

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

      2. distribute-rgt-neg-in 24.7%

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

   4. Simplified 24.7%

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

   5. Taylor expanded in y around 0 41.8%

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

      1. associate-*r/ 41.8%

         \[\leadsto \color{blue}{\frac{-1 \cdot a}{b}} \]

      2. mul-1-neg 41.8%

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

   7. Simplified 41.8%

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

   if -3.8e15 < z < 3.4e-5

   1. Initial program 90.4%

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

   2. Taylor expanded in z around 0 40.7%

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

   if 3.4e-5 < z

   1. Initial program 51.7%

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

   2. Taylor expanded in y around inf 24.9%

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

      1. +-commutative 24.9%

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

      2. mul-1-neg 24.9%

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

      3. unsub-neg 24.9%

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

   4. Simplified 24.9%

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

   5. Taylor expanded in z around inf 24.2%

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

      1. associate-*r/ 24.2%

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

      2. mul-1-neg 24.2%

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

   7. Simplified 24.2%

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

4. Final simplification 36.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+15}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-5}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{z}\\ \end{array} \]

Alternative 13: 24.6% accurate, 17.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 70.5%

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

2. Taylor expanded in z around 0 22.7%

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

3. Final simplification 22.7%

   \[\leadsto x \]

Developer target: 74.1% 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 2023195 
(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)))))