Development.Shake.Progress:decay from shake-0.15.5

Percentage Accurate: 66.2% → 89.6%

Time: 22.9s

Alternatives: 20

Speedup: 0.6×

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: 66.2% 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: 89.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{-13} \lor \neg \left(z \leq 4800000000000\right):\\ \;\;\;\;\frac{t}{b - y} + \left(\frac{x}{z} \cdot \frac{y}{b - y} + \left(\frac{a}{y - b} + y \cdot \frac{a - t}{z \cdot {\left(b - y\right)}^{2}}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, z \cdot \left(t - a\right)\right)}{\mathsf{fma}\left(z, b - y, y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.05e-13) (not (<= z 4800000000000.0)))
   (+
    (/ t (- b y))
    (+
     (* (/ x z) (/ y (- b y)))
     (+ (/ a (- y b)) (* y (/ (- a t) (* z (pow (- b y) 2.0)))))))
   (/ (fma x y (* z (- t a))) (fma z (- b y) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.05e-13) || !(z <= 4800000000000.0)) {
		tmp = (t / (b - y)) + (((x / z) * (y / (b - y))) + ((a / (y - b)) + (y * ((a - t) / (z * pow((b - y), 2.0))))));
	} else {
		tmp = fma(x, y, (z * (t - a))) / fma(z, (b - y), y);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.05e-13) || !(z <= 4800000000000.0))
		tmp = Float64(Float64(t / Float64(b - y)) + Float64(Float64(Float64(x / z) * Float64(y / Float64(b - y))) + Float64(Float64(a / Float64(y - b)) + Float64(y * Float64(Float64(a - t) / Float64(z * (Float64(b - y) ^ 2.0)))))));
	else
		tmp = Float64(fma(x, y, Float64(z * Float64(t - a))) / fma(z, Float64(b - y), y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.05e-13], N[Not[LessEqual[z, 4800000000000.0]], $MachinePrecision]], N[(N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(x / z), $MachinePrecision] * N[(y / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(a / N[(y - b), $MachinePrecision]), $MachinePrecision] + N[(y * N[(N[(a - t), $MachinePrecision] / N[(z * N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * y + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * N[(b - y), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.04999999999999994e-13 or 4.8e12 < z

   1. Initial program 40.6%

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

   3. Taylor expanded in z around inf 58.8%

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

      1. associate--l+ 58.8%

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

      2. times-frac 67.0%

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

      3. associate-/l* 93.4%

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

   5. Simplified 93.4%

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

   if -1.04999999999999994e-13 < z < 4.8e12

   1. Initial program 91.4%

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

      1. fma-define 91.4%

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

      2. +-commutative 91.4%

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

      3. fma-define 91.4%

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

   3. Simplified 91.4%

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

4. Final simplification 92.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{-13} \lor \neg \left(z \leq 4800000000000\right):\\ \;\;\;\;\frac{t}{b - y} + \left(\frac{x}{z} \cdot \frac{y}{b - y} + \left(\frac{a}{y - b} + y \cdot \frac{a - t}{z \cdot {\left(b - y\right)}^{2}}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, z \cdot \left(t - a\right)\right)}{\mathsf{fma}\left(z, b - y, y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 89.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{-13} \lor \neg \left(z \leq 170000000000\right):\\ \;\;\;\;\frac{t}{b - y} + \left(\frac{x}{z} \cdot \frac{y}{b - y} + \left(\frac{a}{y - b} + y \cdot \frac{a - t}{z \cdot {\left(b - y\right)}^{2}}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x - z \cdot \left(a - t\right)}{y + z \cdot \left(b - y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.05e-13) (not (<= z 170000000000.0)))
   (+
    (/ t (- b y))
    (+
     (* (/ x z) (/ y (- b y)))
     (+ (/ a (- y b)) (* y (/ (- a t) (* z (pow (- b y) 2.0)))))))
   (/ (- (* y x) (* z (- a t))) (+ y (* z (- b y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.05e-13) || !(z <= 170000000000.0)) {
		tmp = (t / (b - y)) + (((x / z) * (y / (b - y))) + ((a / (y - b)) + (y * ((a - t) / (z * pow((b - y), 2.0))))));
	} else {
		tmp = ((y * x) - (z * (a - t))) / (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 <= (-1.05d-13)) .or. (.not. (z <= 170000000000.0d0))) then
        tmp = (t / (b - y)) + (((x / z) * (y / (b - y))) + ((a / (y - b)) + (y * ((a - t) / (z * ((b - y) ** 2.0d0))))))
    else
        tmp = ((y * x) - (z * (a - t))) / (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 <= -1.05e-13) || !(z <= 170000000000.0)) {
		tmp = (t / (b - y)) + (((x / z) * (y / (b - y))) + ((a / (y - b)) + (y * ((a - t) / (z * Math.pow((b - y), 2.0))))));
	} else {
		tmp = ((y * x) - (z * (a - t))) / (y + (z * (b - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.05e-13) or not (z <= 170000000000.0):
		tmp = (t / (b - y)) + (((x / z) * (y / (b - y))) + ((a / (y - b)) + (y * ((a - t) / (z * math.pow((b - y), 2.0))))))
	else:
		tmp = ((y * x) - (z * (a - t))) / (y + (z * (b - y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.05e-13) || !(z <= 170000000000.0))
		tmp = Float64(Float64(t / Float64(b - y)) + Float64(Float64(Float64(x / z) * Float64(y / Float64(b - y))) + Float64(Float64(a / Float64(y - b)) + Float64(y * Float64(Float64(a - t) / Float64(z * (Float64(b - y) ^ 2.0)))))));
	else
		tmp = Float64(Float64(Float64(y * x) - Float64(z * Float64(a - t))) / 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 <= -1.05e-13) || ~((z <= 170000000000.0)))
		tmp = (t / (b - y)) + (((x / z) * (y / (b - y))) + ((a / (y - b)) + (y * ((a - t) / (z * ((b - y) ^ 2.0))))));
	else
		tmp = ((y * x) - (z * (a - t))) / (y + (z * (b - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.05e-13], N[Not[LessEqual[z, 170000000000.0]], $MachinePrecision]], N[(N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(x / z), $MachinePrecision] * N[(y / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(a / N[(y - b), $MachinePrecision]), $MachinePrecision] + N[(y * N[(N[(a - t), $MachinePrecision] / N[(z * N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 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]]

Derivation

1. Split input into 2 regimes

2. if z < -1.04999999999999994e-13 or 1.7e11 < z

   1. Initial program 40.6%

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

   3. Taylor expanded in z around inf 58.8%

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

      1. associate--l+ 58.8%

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

      2. times-frac 67.0%

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

      3. associate-/l* 93.4%

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

   5. Simplified 93.4%

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

   if -1.04999999999999994e-13 < z < 1.7e11

   1. Initial program 91.4%

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

4. Final simplification 92.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{-13} \lor \neg \left(z \leq 170000000000\right):\\ \;\;\;\;\frac{t}{b - y} + \left(\frac{x}{z} \cdot \frac{y}{b - y} + \left(\frac{a}{y - b} + y \cdot \frac{a - t}{z \cdot {\left(b - y\right)}^{2}}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x - z \cdot \left(a - t\right)}{y + z \cdot \left(b - y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 88.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+16} \lor \neg \left(z \leq 170000000\right):\\ \;\;\;\;\frac{x \cdot \frac{y}{b - y} - y \cdot \frac{t - a}{{\left(b - y\right)}^{2}}}{z} + \frac{a - t}{y - b}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x - z \cdot \left(a - t\right)}{y + z \cdot \left(b - y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -6e+16) (not (<= z 170000000.0)))
   (+
    (/ (- (* x (/ y (- b y))) (* y (/ (- t a) (pow (- b y) 2.0)))) z)
    (/ (- a t) (- y b)))
   (/ (- (* y x) (* z (- a t))) (+ y (* z (- b y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -6e+16) || !(z <= 170000000.0)) {
		tmp = (((x * (y / (b - y))) - (y * ((t - a) / pow((b - y), 2.0)))) / z) + ((a - t) / (y - b));
	} else {
		tmp = ((y * x) - (z * (a - t))) / (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 <= (-6d+16)) .or. (.not. (z <= 170000000.0d0))) then
        tmp = (((x * (y / (b - y))) - (y * ((t - a) / ((b - y) ** 2.0d0)))) / z) + ((a - t) / (y - b))
    else
        tmp = ((y * x) - (z * (a - t))) / (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 <= -6e+16) || !(z <= 170000000.0)) {
		tmp = (((x * (y / (b - y))) - (y * ((t - a) / Math.pow((b - y), 2.0)))) / z) + ((a - t) / (y - b));
	} else {
		tmp = ((y * x) - (z * (a - t))) / (y + (z * (b - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -6e+16) or not (z <= 170000000.0):
		tmp = (((x * (y / (b - y))) - (y * ((t - a) / math.pow((b - y), 2.0)))) / z) + ((a - t) / (y - b))
	else:
		tmp = ((y * x) - (z * (a - t))) / (y + (z * (b - y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -6e+16) || !(z <= 170000000.0))
		tmp = Float64(Float64(Float64(Float64(x * Float64(y / Float64(b - y))) - Float64(y * Float64(Float64(t - a) / (Float64(b - y) ^ 2.0)))) / z) + Float64(Float64(a - t) / Float64(y - b)));
	else
		tmp = Float64(Float64(Float64(y * x) - Float64(z * Float64(a - t))) / 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 <= -6e+16) || ~((z <= 170000000.0)))
		tmp = (((x * (y / (b - y))) - (y * ((t - a) / ((b - y) ^ 2.0)))) / z) + ((a - t) / (y - b));
	else
		tmp = ((y * x) - (z * (a - t))) / (y + (z * (b - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -6e+16], N[Not[LessEqual[z, 170000000.0]], $MachinePrecision]], N[(N[(N[(N[(x * N[(y / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * N[(N[(t - a), $MachinePrecision] / N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] + N[(N[(a - t), $MachinePrecision] / N[(y - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 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]]

Derivation

1. Split input into 2 regimes

2. if z < -6e16 or 1.7e8 < z

   1. Initial program 39.5%

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

   3. Taylor expanded in z around -inf 62.6%

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

      1. associate--l+ 62.6%

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

      2. mul-1-neg 62.6%

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

      3. distribute-lft-out-- 62.6%

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

      4. associate-/l* 66.0%

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

      5. associate-/l* 92.1%

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

      6. div-sub 92.1%

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

   5. Simplified 92.1%

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

   if -6e16 < z < 1.7e8

   1. Initial program 89.8%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+16} \lor \neg \left(z \leq 170000000\right):\\ \;\;\;\;\frac{x \cdot \frac{y}{b - y} - y \cdot \frac{t - a}{{\left(b - y\right)}^{2}}}{z} + \frac{a - t}{y - b}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x - z \cdot \left(a - t\right)}{y + z \cdot \left(b - y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(b - y\right)\\ t_2 := y + t\_1\\ t_3 := \frac{a - t}{y - b}\\ \mathbf{if}\;z \leq -74000000:\\ \;\;\;\;\left(t\_3 + x \cdot \frac{y}{t\_1}\right) + y \cdot \frac{a - t}{z \cdot {\left(b - y\right)}^{2}}\\ \mathbf{elif}\;z \leq 1.78 \cdot 10^{+53}:\\ \;\;\;\;x \cdot \left(\frac{y}{t\_2} + \frac{z \cdot \left(t - a\right)}{x \cdot t\_2}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- b y))) (t_2 (+ y t_1)) (t_3 (/ (- a t) (- y b))))
   (if (<= z -74000000.0)
     (+ (+ t_3 (* x (/ y t_1))) (* y (/ (- a t) (* z (pow (- b y) 2.0)))))
     (if (<= z 1.78e+53)
       (* x (+ (/ y t_2) (/ (* z (- t a)) (* x t_2))))
       t_3))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (b - y);
	double t_2 = y + t_1;
	double t_3 = (a - t) / (y - b);
	double tmp;
	if (z <= -74000000.0) {
		tmp = (t_3 + (x * (y / t_1))) + (y * ((a - t) / (z * pow((b - y), 2.0))));
	} else if (z <= 1.78e+53) {
		tmp = x * ((y / t_2) + ((z * (t - a)) / (x * 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 = z * (b - y)
    t_2 = y + t_1
    t_3 = (a - t) / (y - b)
    if (z <= (-74000000.0d0)) then
        tmp = (t_3 + (x * (y / t_1))) + (y * ((a - t) / (z * ((b - y) ** 2.0d0))))
    else if (z <= 1.78d+53) then
        tmp = x * ((y / t_2) + ((z * (t - a)) / (x * 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 = z * (b - y);
	double t_2 = y + t_1;
	double t_3 = (a - t) / (y - b);
	double tmp;
	if (z <= -74000000.0) {
		tmp = (t_3 + (x * (y / t_1))) + (y * ((a - t) / (z * Math.pow((b - y), 2.0))));
	} else if (z <= 1.78e+53) {
		tmp = x * ((y / t_2) + ((z * (t - a)) / (x * t_2)));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (b - y)
	t_2 = y + t_1
	t_3 = (a - t) / (y - b)
	tmp = 0
	if z <= -74000000.0:
		tmp = (t_3 + (x * (y / t_1))) + (y * ((a - t) / (z * math.pow((b - y), 2.0))))
	elif z <= 1.78e+53:
		tmp = x * ((y / t_2) + ((z * (t - a)) / (x * t_2)))
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(b - y))
	t_2 = Float64(y + t_1)
	t_3 = Float64(Float64(a - t) / Float64(y - b))
	tmp = 0.0
	if (z <= -74000000.0)
		tmp = Float64(Float64(t_3 + Float64(x * Float64(y / t_1))) + Float64(y * Float64(Float64(a - t) / Float64(z * (Float64(b - y) ^ 2.0)))));
	elseif (z <= 1.78e+53)
		tmp = Float64(x * Float64(Float64(y / t_2) + Float64(Float64(z * Float64(t - a)) / Float64(x * t_2))));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (b - y);
	t_2 = y + t_1;
	t_3 = (a - t) / (y - b);
	tmp = 0.0;
	if (z <= -74000000.0)
		tmp = (t_3 + (x * (y / t_1))) + (y * ((a - t) / (z * ((b - y) ^ 2.0))));
	elseif (z <= 1.78e+53)
		tmp = x * ((y / t_2) + ((z * (t - a)) / (x * t_2)));
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y + t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(a - t), $MachinePrecision] / N[(y - b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -74000000.0], N[(N[(t$95$3 + N[(x * N[(y / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * N[(N[(a - t), $MachinePrecision] / N[(z * N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.78e+53], N[(x * N[(N[(y / t$95$2), $MachinePrecision] + N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / N[(x * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.4e7

   1. Initial program 40.5%

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

   3. Taylor expanded in z around inf 54.8%

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

      1. associate--r+ 54.8%

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

      2. +-commutative 54.8%

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

      3. associate--l+ 54.8%

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

      4. associate-/l* 56.6%

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

      5. div-sub 56.6%

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

      6. associate-/l* 76.8%

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

   5. Simplified 76.8%

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

   if -7.4e7 < z < 1.77999999999999999e53

   1. Initial program 88.8%

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

   3. Taylor expanded in x around inf 90.5%

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

   if 1.77999999999999999e53 < z

   1. Initial program 37.5%

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

   3. Taylor expanded in z around inf 92.9%

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

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -74000000:\\ \;\;\;\;\left(\frac{a - t}{y - b} + x \cdot \frac{y}{z \cdot \left(b - y\right)}\right) + y \cdot \frac{a - t}{z \cdot {\left(b - y\right)}^{2}}\\ \mathbf{elif}\;z \leq 1.78 \cdot 10^{+53}:\\ \;\;\;\;x \cdot \left(\frac{y}{y + z \cdot \left(b - y\right)} + \frac{z \cdot \left(t - a\right)}{x \cdot \left(y + z \cdot \left(b - y\right)\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{a - t}{y - b}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 64.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(t - a\right)\\ t_2 := \frac{t\_1}{y + z \cdot \left(b - y\right)}\\ t_3 := \frac{a - t}{y - b}\\ t_4 := \frac{y \cdot x - z \cdot a}{y}\\ \mathbf{if}\;z \leq -6 \cdot 10^{+16}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{-92}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-251}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;z \leq -2.05 \cdot 10^{-288}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-261}:\\ \;\;\;\;\frac{y \cdot x}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 10^{-197}:\\ \;\;\;\;\frac{x \cdot \left(y + \frac{t\_1}{x}\right)}{y}\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{-60}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-50}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-20}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 1.78 \cdot 10^{+53}:\\ \;\;\;\;\frac{1}{\frac{1 - z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- t a)))
        (t_2 (/ t_1 (+ y (* z (- b y)))))
        (t_3 (/ (- a t) (- y b)))
        (t_4 (/ (- (* y x) (* z a)) y)))
   (if (<= z -6e+16)
     t_3
     (if (<= z -7.8e-92)
       t_2
       (if (<= z -3.3e-251)
         t_4
         (if (<= z -2.05e-288)
           t_2
           (if (<= z 7e-261)
             (/ (* y x) (+ y (* z b)))
             (if (<= z 1e-197)
               (/ (* x (+ y (/ t_1 x))) y)
               (if (<= z 7.8e-60)
                 t_2
                 (if (<= z 7.5e-50)
                   t_4
                   (if (<= z 2.1e-20)
                     t_2
                     (if (<= z 1.78e+53)
                       (/ 1.0 (/ (- 1.0 z) x))
                       t_3))))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (t - a);
	double t_2 = t_1 / (y + (z * (b - y)));
	double t_3 = (a - t) / (y - b);
	double t_4 = ((y * x) - (z * a)) / y;
	double tmp;
	if (z <= -6e+16) {
		tmp = t_3;
	} else if (z <= -7.8e-92) {
		tmp = t_2;
	} else if (z <= -3.3e-251) {
		tmp = t_4;
	} else if (z <= -2.05e-288) {
		tmp = t_2;
	} else if (z <= 7e-261) {
		tmp = (y * x) / (y + (z * b));
	} else if (z <= 1e-197) {
		tmp = (x * (y + (t_1 / x))) / y;
	} else if (z <= 7.8e-60) {
		tmp = t_2;
	} else if (z <= 7.5e-50) {
		tmp = t_4;
	} else if (z <= 2.1e-20) {
		tmp = t_2;
	} else if (z <= 1.78e+53) {
		tmp = 1.0 / ((1.0 - z) / x);
	} 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) :: t_4
    real(8) :: tmp
    t_1 = z * (t - a)
    t_2 = t_1 / (y + (z * (b - y)))
    t_3 = (a - t) / (y - b)
    t_4 = ((y * x) - (z * a)) / y
    if (z <= (-6d+16)) then
        tmp = t_3
    else if (z <= (-7.8d-92)) then
        tmp = t_2
    else if (z <= (-3.3d-251)) then
        tmp = t_4
    else if (z <= (-2.05d-288)) then
        tmp = t_2
    else if (z <= 7d-261) then
        tmp = (y * x) / (y + (z * b))
    else if (z <= 1d-197) then
        tmp = (x * (y + (t_1 / x))) / y
    else if (z <= 7.8d-60) then
        tmp = t_2
    else if (z <= 7.5d-50) then
        tmp = t_4
    else if (z <= 2.1d-20) then
        tmp = t_2
    else if (z <= 1.78d+53) then
        tmp = 1.0d0 / ((1.0d0 - z) / x)
    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 = z * (t - a);
	double t_2 = t_1 / (y + (z * (b - y)));
	double t_3 = (a - t) / (y - b);
	double t_4 = ((y * x) - (z * a)) / y;
	double tmp;
	if (z <= -6e+16) {
		tmp = t_3;
	} else if (z <= -7.8e-92) {
		tmp = t_2;
	} else if (z <= -3.3e-251) {
		tmp = t_4;
	} else if (z <= -2.05e-288) {
		tmp = t_2;
	} else if (z <= 7e-261) {
		tmp = (y * x) / (y + (z * b));
	} else if (z <= 1e-197) {
		tmp = (x * (y + (t_1 / x))) / y;
	} else if (z <= 7.8e-60) {
		tmp = t_2;
	} else if (z <= 7.5e-50) {
		tmp = t_4;
	} else if (z <= 2.1e-20) {
		tmp = t_2;
	} else if (z <= 1.78e+53) {
		tmp = 1.0 / ((1.0 - z) / x);
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (t - a)
	t_2 = t_1 / (y + (z * (b - y)))
	t_3 = (a - t) / (y - b)
	t_4 = ((y * x) - (z * a)) / y
	tmp = 0
	if z <= -6e+16:
		tmp = t_3
	elif z <= -7.8e-92:
		tmp = t_2
	elif z <= -3.3e-251:
		tmp = t_4
	elif z <= -2.05e-288:
		tmp = t_2
	elif z <= 7e-261:
		tmp = (y * x) / (y + (z * b))
	elif z <= 1e-197:
		tmp = (x * (y + (t_1 / x))) / y
	elif z <= 7.8e-60:
		tmp = t_2
	elif z <= 7.5e-50:
		tmp = t_4
	elif z <= 2.1e-20:
		tmp = t_2
	elif z <= 1.78e+53:
		tmp = 1.0 / ((1.0 - z) / x)
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(t - a))
	t_2 = Float64(t_1 / Float64(y + Float64(z * Float64(b - y))))
	t_3 = Float64(Float64(a - t) / Float64(y - b))
	t_4 = Float64(Float64(Float64(y * x) - Float64(z * a)) / y)
	tmp = 0.0
	if (z <= -6e+16)
		tmp = t_3;
	elseif (z <= -7.8e-92)
		tmp = t_2;
	elseif (z <= -3.3e-251)
		tmp = t_4;
	elseif (z <= -2.05e-288)
		tmp = t_2;
	elseif (z <= 7e-261)
		tmp = Float64(Float64(y * x) / Float64(y + Float64(z * b)));
	elseif (z <= 1e-197)
		tmp = Float64(Float64(x * Float64(y + Float64(t_1 / x))) / y);
	elseif (z <= 7.8e-60)
		tmp = t_2;
	elseif (z <= 7.5e-50)
		tmp = t_4;
	elseif (z <= 2.1e-20)
		tmp = t_2;
	elseif (z <= 1.78e+53)
		tmp = Float64(1.0 / Float64(Float64(1.0 - z) / x));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (t - a);
	t_2 = t_1 / (y + (z * (b - y)));
	t_3 = (a - t) / (y - b);
	t_4 = ((y * x) - (z * a)) / y;
	tmp = 0.0;
	if (z <= -6e+16)
		tmp = t_3;
	elseif (z <= -7.8e-92)
		tmp = t_2;
	elseif (z <= -3.3e-251)
		tmp = t_4;
	elseif (z <= -2.05e-288)
		tmp = t_2;
	elseif (z <= 7e-261)
		tmp = (y * x) / (y + (z * b));
	elseif (z <= 1e-197)
		tmp = (x * (y + (t_1 / x))) / y;
	elseif (z <= 7.8e-60)
		tmp = t_2;
	elseif (z <= 7.5e-50)
		tmp = t_4;
	elseif (z <= 2.1e-20)
		tmp = t_2;
	elseif (z <= 1.78e+53)
		tmp = 1.0 / ((1.0 - z) / x);
	else
		tmp = t_3;
	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[(t$95$1 / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(a - t), $MachinePrecision] / N[(y - b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(y * x), $MachinePrecision] - N[(z * a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[z, -6e+16], t$95$3, If[LessEqual[z, -7.8e-92], t$95$2, If[LessEqual[z, -3.3e-251], t$95$4, If[LessEqual[z, -2.05e-288], t$95$2, If[LessEqual[z, 7e-261], N[(N[(y * x), $MachinePrecision] / N[(y + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1e-197], N[(N[(x * N[(y + N[(t$95$1 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[z, 7.8e-60], t$95$2, If[LessEqual[z, 7.5e-50], t$95$4, If[LessEqual[z, 2.1e-20], t$95$2, If[LessEqual[z, 1.78e+53], N[(1.0 / N[(N[(1.0 - z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -6e16 or 1.77999999999999999e53 < z

   1. Initial program 37.9%

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

   3. Taylor expanded in z around inf 83.4%

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

   if -6e16 < z < -7.7999999999999993e-92 or -3.3e-251 < z < -2.05000000000000004e-288 or 9.9999999999999999e-198 < z < 7.8000000000000004e-60 or 7.5e-50 < z < 2.0999999999999999e-20

   1. Initial program 86.7%

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

   3. Taylor expanded in x around 0 68.3%

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

   if -7.7999999999999993e-92 < z < -3.3e-251 or 7.8000000000000004e-60 < z < 7.5e-50

   1. Initial program 94.9%

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

   3. Taylor expanded in t around 0 85.1%

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

      1. +-commutative 85.1%

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

      2. mul-1-neg 85.1%

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

      3. unsub-neg 85.1%

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

      4. *-commutative 85.1%

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

      5. *-commutative 85.1%

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

   5. Simplified 85.1%

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

   6. Taylor expanded in z around 0 66.1%

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

   if -2.05000000000000004e-288 < z < 6.9999999999999995e-261

   1. Initial program 94.1%

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

   3. Taylor expanded in t around 0 94.0%

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

      1. +-commutative 94.0%

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

      2. mul-1-neg 94.0%

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

      3. unsub-neg 94.0%

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

      4. *-commutative 94.0%

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

      5. *-commutative 94.0%

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

   5. Simplified 94.0%

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

   6. Taylor expanded in b around inf 94.0%

      \[\leadsto \frac{y \cdot x - z \cdot a}{y + \color{blue}{b \cdot z}} \]
   7. Step-by-step derivation

      1. *-commutative 94.0%

         \[\leadsto \frac{y \cdot x - z \cdot a}{y + \color{blue}{z \cdot b}} \]

   8. Simplified 94.0%

      \[\leadsto \frac{y \cdot x - z \cdot a}{y + \color{blue}{z \cdot b}} \]

   9. Taylor expanded in x around inf 88.0%

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

   if 6.9999999999999995e-261 < z < 9.9999999999999999e-198

   1. Initial program 90.5%

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

   3. Taylor expanded in x around inf 90.3%

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

   4. Taylor expanded in z around 0 76.4%

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

   if 2.0999999999999999e-20 < z < 1.77999999999999999e53

   1. Initial program 64.1%

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

      1. fma-define 64.1%

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

      2. clear-num 64.1%

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

      3. inv-pow 64.1%

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

      4. +-commutative 64.1%

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

      5. fma-undefine 64.1%

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

      6. fma-define 64.1%

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

      7. +-commutative 64.1%

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

      8. fma-define 64.1%

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

   4. Applied egg-rr 64.1%

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

      1. unpow-1 64.1%

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

      2. *-commutative 64.1%

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

   6. Simplified 64.1%

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

   7. Taylor expanded in y around inf 65.4%

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

      1. neg-mul-1 65.4%

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

   9. Simplified 65.4%

      \[\leadsto \frac{1}{\color{blue}{\frac{1 + \left(-z\right)}{x}}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+16}:\\ \;\;\;\;\frac{a - t}{y - b}\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{-92}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-251}:\\ \;\;\;\;\frac{y \cdot x - z \cdot a}{y}\\ \mathbf{elif}\;z \leq -2.05 \cdot 10^{-288}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-261}:\\ \;\;\;\;\frac{y \cdot x}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 10^{-197}:\\ \;\;\;\;\frac{x \cdot \left(y + \frac{z \cdot \left(t - a\right)}{x}\right)}{y}\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{-60}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-50}:\\ \;\;\;\;\frac{y \cdot x - z \cdot a}{y}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-20}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 1.78 \cdot 10^{+53}:\\ \;\;\;\;\frac{1}{\frac{1 - z}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{a - t}{y - b}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 85.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ \mathbf{if}\;z \leq -2.6 \cdot 10^{+60} \lor \neg \left(z \leq 1.85 \cdot 10^{+53}\right):\\ \;\;\;\;\frac{a - t}{y - b}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{t\_1} + \frac{z \cdot \left(t - a\right)}{x \cdot t\_1}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y)))))
   (if (or (<= z -2.6e+60) (not (<= z 1.85e+53)))
     (/ (- a t) (- y b))
     (* x (+ (/ y t_1) (/ (* z (- t a)) (* x t_1)))))))

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 <= -2.6e+60) || !(z <= 1.85e+53)) {
		tmp = (a - t) / (y - b);
	} else {
		tmp = x * ((y / t_1) + ((z * (t - a)) / (x * 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 = y + (z * (b - y))
    if ((z <= (-2.6d+60)) .or. (.not. (z <= 1.85d+53))) then
        tmp = (a - t) / (y - b)
    else
        tmp = x * ((y / t_1) + ((z * (t - a)) / (x * 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 = y + (z * (b - y));
	double tmp;
	if ((z <= -2.6e+60) || !(z <= 1.85e+53)) {
		tmp = (a - t) / (y - b);
	} else {
		tmp = x * ((y / t_1) + ((z * (t - a)) / (x * t_1)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z * (b - y))
	tmp = 0
	if (z <= -2.6e+60) or not (z <= 1.85e+53):
		tmp = (a - t) / (y - b)
	else:
		tmp = x * ((y / t_1) + ((z * (t - a)) / (x * t_1)))
	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 <= -2.6e+60) || !(z <= 1.85e+53))
		tmp = Float64(Float64(a - t) / Float64(y - b));
	else
		tmp = Float64(x * Float64(Float64(y / t_1) + Float64(Float64(z * Float64(t - a)) / Float64(x * t_1))));
	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 <= -2.6e+60) || ~((z <= 1.85e+53)))
		tmp = (a - t) / (y - b);
	else
		tmp = x * ((y / t_1) + ((z * (t - a)) / (x * t_1)));
	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, -2.6e+60], N[Not[LessEqual[z, 1.85e+53]], $MachinePrecision]], N[(N[(a - t), $MachinePrecision] / N[(y - b), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y / t$95$1), $MachinePrecision] + N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / N[(x * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.60000000000000008e60 or 1.85e53 < z

   1. Initial program 36.6%

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

   3. Taylor expanded in z around inf 87.7%

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

   if -2.60000000000000008e60 < z < 1.85e53

   1. Initial program 86.5%

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

   3. Taylor expanded in x around inf 87.6%

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

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+60} \lor \neg \left(z \leq 1.85 \cdot 10^{+53}\right):\\ \;\;\;\;\frac{a - t}{y - b}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{y + z \cdot \left(b - y\right)} + \frac{z \cdot \left(t - a\right)}{x \cdot \left(y + z \cdot \left(b - y\right)\right)}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 53.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a - t}{y}\\ t_2 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -1.15 \cdot 10^{+198}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{+142}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{+58}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{+25}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-31} \lor \neg \left(y \leq 3.1 \cdot 10^{+37}\right):\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- a t) y)) (t_2 (/ x (- 1.0 z))))
   (if (<= y -1.15e+198)
     t_2
     (if (<= y -2.5e+142)
       t_1
       (if (<= y -7.5e+58)
         t_2
         (if (<= y -1.8e+25)
           t_1
           (if (or (<= y -1.7e-31) (not (<= y 3.1e+37)))
             t_2
             (/ (- t a) b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a - t) / y;
	double t_2 = x / (1.0 - z);
	double tmp;
	if (y <= -1.15e+198) {
		tmp = t_2;
	} else if (y <= -2.5e+142) {
		tmp = t_1;
	} else if (y <= -7.5e+58) {
		tmp = t_2;
	} else if (y <= -1.8e+25) {
		tmp = t_1;
	} else if ((y <= -1.7e-31) || !(y <= 3.1e+37)) {
		tmp = t_2;
	} 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (a - t) / y
    t_2 = x / (1.0d0 - z)
    if (y <= (-1.15d+198)) then
        tmp = t_2
    else if (y <= (-2.5d+142)) then
        tmp = t_1
    else if (y <= (-7.5d+58)) then
        tmp = t_2
    else if (y <= (-1.8d+25)) then
        tmp = t_1
    else if ((y <= (-1.7d-31)) .or. (.not. (y <= 3.1d+37))) then
        tmp = t_2
    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 t_1 = (a - t) / y;
	double t_2 = x / (1.0 - z);
	double tmp;
	if (y <= -1.15e+198) {
		tmp = t_2;
	} else if (y <= -2.5e+142) {
		tmp = t_1;
	} else if (y <= -7.5e+58) {
		tmp = t_2;
	} else if (y <= -1.8e+25) {
		tmp = t_1;
	} else if ((y <= -1.7e-31) || !(y <= 3.1e+37)) {
		tmp = t_2;
	} else {
		tmp = (t - a) / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a - t) / y
	t_2 = x / (1.0 - z)
	tmp = 0
	if y <= -1.15e+198:
		tmp = t_2
	elif y <= -2.5e+142:
		tmp = t_1
	elif y <= -7.5e+58:
		tmp = t_2
	elif y <= -1.8e+25:
		tmp = t_1
	elif (y <= -1.7e-31) or not (y <= 3.1e+37):
		tmp = t_2
	else:
		tmp = (t - a) / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a - t) / y)
	t_2 = Float64(x / Float64(1.0 - z))
	tmp = 0.0
	if (y <= -1.15e+198)
		tmp = t_2;
	elseif (y <= -2.5e+142)
		tmp = t_1;
	elseif (y <= -7.5e+58)
		tmp = t_2;
	elseif (y <= -1.8e+25)
		tmp = t_1;
	elseif ((y <= -1.7e-31) || !(y <= 3.1e+37))
		tmp = t_2;
	else
		tmp = Float64(Float64(t - a) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a - t) / y;
	t_2 = x / (1.0 - z);
	tmp = 0.0;
	if (y <= -1.15e+198)
		tmp = t_2;
	elseif (y <= -2.5e+142)
		tmp = t_1;
	elseif (y <= -7.5e+58)
		tmp = t_2;
	elseif (y <= -1.8e+25)
		tmp = t_1;
	elseif ((y <= -1.7e-31) || ~((y <= 3.1e+37)))
		tmp = t_2;
	else
		tmp = (t - a) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.15e+198], t$95$2, If[LessEqual[y, -2.5e+142], t$95$1, If[LessEqual[y, -7.5e+58], t$95$2, If[LessEqual[y, -1.8e+25], t$95$1, If[Or[LessEqual[y, -1.7e-31], N[Not[LessEqual[y, 3.1e+37]], $MachinePrecision]], t$95$2, N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.15e198 or -2.5000000000000001e142 < y < -7.5000000000000001e58 or -1.80000000000000008e25 < y < -1.7000000000000001e-31 or 3.1000000000000002e37 < y

   1. Initial program 56.7%

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

   3. Taylor expanded in y around inf 62.0%

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

      1. mul-1-neg 62.0%

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

      2. unsub-neg 62.0%

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

   5. Simplified 62.0%

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

   if -1.15e198 < y < -2.5000000000000001e142 or -7.5000000000000001e58 < y < -1.80000000000000008e25

   1. Initial program 57.0%

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

   3. Taylor expanded in z around inf 66.5%

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

   4. Taylor expanded in b around 0 55.5%

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

      1. associate-*r/ 55.5%

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

      2. mul-1-neg 55.5%

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

   6. Simplified 55.5%

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

   if -1.7000000000000001e-31 < y < 3.1000000000000002e37

   1. Initial program 78.8%

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

   3. Taylor expanded in y around 0 53.6%

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

4. Final simplification 57.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+198}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{+142}:\\ \;\;\;\;\frac{a - t}{y}\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{+58}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{+25}:\\ \;\;\;\;\frac{a - t}{y}\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-31} \lor \neg \left(y \leq 3.1 \cdot 10^{+37}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 72.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := \frac{a - t}{y - b}\\ \mathbf{if}\;z \leq -6.5 \cdot 10^{+16}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-91}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{t\_1}\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{-221}:\\ \;\;\;\;\frac{y \cdot x - z \cdot a}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 1.78 \cdot 10^{+53}:\\ \;\;\;\;\frac{y \cdot x + z \cdot t}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y)))) (t_2 (/ (- a t) (- y b))))
   (if (<= z -6.5e+16)
     t_2
     (if (<= z -1.55e-91)
       (/ (* z (- t a)) t_1)
       (if (<= z -6.8e-221)
         (/ (- (* y x) (* z a)) (+ y (* z b)))
         (if (<= z 1.78e+53) (/ (+ (* 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 = (a - t) / (y - b);
	double tmp;
	if (z <= -6.5e+16) {
		tmp = t_2;
	} else if (z <= -1.55e-91) {
		tmp = (z * (t - a)) / t_1;
	} else if (z <= -6.8e-221) {
		tmp = ((y * x) - (z * a)) / (y + (z * b));
	} else if (z <= 1.78e+53) {
		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 = (a - t) / (y - b)
    if (z <= (-6.5d+16)) then
        tmp = t_2
    else if (z <= (-1.55d-91)) then
        tmp = (z * (t - a)) / t_1
    else if (z <= (-6.8d-221)) then
        tmp = ((y * x) - (z * a)) / (y + (z * b))
    else if (z <= 1.78d+53) 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 = (a - t) / (y - b);
	double tmp;
	if (z <= -6.5e+16) {
		tmp = t_2;
	} else if (z <= -1.55e-91) {
		tmp = (z * (t - a)) / t_1;
	} else if (z <= -6.8e-221) {
		tmp = ((y * x) - (z * a)) / (y + (z * b));
	} else if (z <= 1.78e+53) {
		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 = (a - t) / (y - b)
	tmp = 0
	if z <= -6.5e+16:
		tmp = t_2
	elif z <= -1.55e-91:
		tmp = (z * (t - a)) / t_1
	elif z <= -6.8e-221:
		tmp = ((y * x) - (z * a)) / (y + (z * b))
	elif z <= 1.78e+53:
		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(a - t) / Float64(y - b))
	tmp = 0.0
	if (z <= -6.5e+16)
		tmp = t_2;
	elseif (z <= -1.55e-91)
		tmp = Float64(Float64(z * Float64(t - a)) / t_1);
	elseif (z <= -6.8e-221)
		tmp = Float64(Float64(Float64(y * x) - Float64(z * a)) / Float64(y + Float64(z * b)));
	elseif (z <= 1.78e+53)
		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 = (a - t) / (y - b);
	tmp = 0.0;
	if (z <= -6.5e+16)
		tmp = t_2;
	elseif (z <= -1.55e-91)
		tmp = (z * (t - a)) / t_1;
	elseif (z <= -6.8e-221)
		tmp = ((y * x) - (z * a)) / (y + (z * b));
	elseif (z <= 1.78e+53)
		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[(a - t), $MachinePrecision] / N[(y - b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.5e+16], t$95$2, If[LessEqual[z, -1.55e-91], N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[z, -6.8e-221], N[(N[(N[(y * x), $MachinePrecision] - N[(z * a), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.78e+53], N[(N[(N[(y * x), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -6.5e16 or 1.77999999999999999e53 < z

   1. Initial program 37.9%

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

   3. Taylor expanded in z around inf 83.4%

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

   if -6.5e16 < z < -1.5499999999999999e-91

   1. Initial program 82.6%

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

   3. Taylor expanded in x around 0 76.4%

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

   if -1.5499999999999999e-91 < z < -6.8000000000000003e-221

   1. Initial program 93.4%

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

   3. Taylor expanded in t around 0 80.5%

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

      1. +-commutative 80.5%

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

      2. mul-1-neg 80.5%

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

      3. unsub-neg 80.5%

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

      4. *-commutative 80.5%

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

      5. *-commutative 80.5%

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

   5. Simplified 80.5%

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

   6. Taylor expanded in b around inf 80.5%

      \[\leadsto \frac{y \cdot x - z \cdot a}{y + \color{blue}{b \cdot z}} \]
   7. Step-by-step derivation

      1. *-commutative 80.5%

         \[\leadsto \frac{y \cdot x - z \cdot a}{y + \color{blue}{z \cdot b}} \]

   8. Simplified 80.5%

      \[\leadsto \frac{y \cdot x - z \cdot a}{y + \color{blue}{z \cdot b}} \]

   if -6.8000000000000003e-221 < z < 1.77999999999999999e53

   1. Initial program 88.7%

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

   3. Taylor expanded in a around 0 71.9%

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

4. Final simplification 78.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+16}:\\ \;\;\;\;\frac{a - t}{y - b}\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-91}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{-221}:\\ \;\;\;\;\frac{y \cdot x - z \cdot a}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 1.78 \cdot 10^{+53}:\\ \;\;\;\;\frac{y \cdot x + z \cdot t}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{a - t}{y - b}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 67.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot \left(y + \frac{z \cdot \left(t - a\right)}{x}\right)}{y}\\ t_2 := \frac{a - t}{y - b}\\ \mathbf{if}\;z \leq -4.8 \cdot 10^{-37}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -9.6 \cdot 10^{-289}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-262}:\\ \;\;\;\;\frac{y \cdot x}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-14}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* x (+ y (/ (* z (- t a)) x))) y)) (t_2 (/ (- a t) (- y b))))
   (if (<= z -4.8e-37)
     t_2
     (if (<= z -9.6e-289)
       t_1
       (if (<= z 2.6e-262)
         (/ (* y x) (+ y (* z b)))
         (if (<= z 4.5e-14) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * (y + ((z * (t - a)) / x))) / y;
	double t_2 = (a - t) / (y - b);
	double tmp;
	if (z <= -4.8e-37) {
		tmp = t_2;
	} else if (z <= -9.6e-289) {
		tmp = t_1;
	} else if (z <= 2.6e-262) {
		tmp = (y * x) / (y + (z * b));
	} else if (z <= 4.5e-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 * (y + ((z * (t - a)) / x))) / y
    t_2 = (a - t) / (y - b)
    if (z <= (-4.8d-37)) then
        tmp = t_2
    else if (z <= (-9.6d-289)) then
        tmp = t_1
    else if (z <= 2.6d-262) then
        tmp = (y * x) / (y + (z * b))
    else if (z <= 4.5d-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 * (y + ((z * (t - a)) / x))) / y;
	double t_2 = (a - t) / (y - b);
	double tmp;
	if (z <= -4.8e-37) {
		tmp = t_2;
	} else if (z <= -9.6e-289) {
		tmp = t_1;
	} else if (z <= 2.6e-262) {
		tmp = (y * x) / (y + (z * b));
	} else if (z <= 4.5e-14) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x * (y + ((z * (t - a)) / x))) / y
	t_2 = (a - t) / (y - b)
	tmp = 0
	if z <= -4.8e-37:
		tmp = t_2
	elif z <= -9.6e-289:
		tmp = t_1
	elif z <= 2.6e-262:
		tmp = (y * x) / (y + (z * b))
	elif z <= 4.5e-14:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * Float64(y + Float64(Float64(z * Float64(t - a)) / x))) / y)
	t_2 = Float64(Float64(a - t) / Float64(y - b))
	tmp = 0.0
	if (z <= -4.8e-37)
		tmp = t_2;
	elseif (z <= -9.6e-289)
		tmp = t_1;
	elseif (z <= 2.6e-262)
		tmp = Float64(Float64(y * x) / Float64(y + Float64(z * b)));
	elseif (z <= 4.5e-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 * (y + ((z * (t - a)) / x))) / y;
	t_2 = (a - t) / (y - b);
	tmp = 0.0;
	if (z <= -4.8e-37)
		tmp = t_2;
	elseif (z <= -9.6e-289)
		tmp = t_1;
	elseif (z <= 2.6e-262)
		tmp = (y * x) / (y + (z * b));
	elseif (z <= 4.5e-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[(N[(x * N[(y + N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a - t), $MachinePrecision] / N[(y - b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.8e-37], t$95$2, If[LessEqual[z, -9.6e-289], t$95$1, If[LessEqual[z, 2.6e-262], N[(N[(y * x), $MachinePrecision] / N[(y + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.5e-14], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.79999999999999982e-37 or 4.4999999999999998e-14 < z

   1. Initial program 43.0%

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

   3. Taylor expanded in z around inf 78.0%

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

   if -4.79999999999999982e-37 < z < -9.59999999999999975e-289 or 2.5999999999999999e-262 < z < 4.4999999999999998e-14

   1. Initial program 90.7%

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

   3. Taylor expanded in x around inf 85.5%

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

   4. Taylor expanded in z around 0 60.2%

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

   if -9.59999999999999975e-289 < z < 2.5999999999999999e-262

   1. Initial program 94.1%

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

   3. Taylor expanded in t around 0 94.0%

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

      1. +-commutative 94.0%

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

      2. mul-1-neg 94.0%

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

      3. unsub-neg 94.0%

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

      4. *-commutative 94.0%

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

      5. *-commutative 94.0%

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

   5. Simplified 94.0%

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

   6. Taylor expanded in b around inf 94.0%

      \[\leadsto \frac{y \cdot x - z \cdot a}{y + \color{blue}{b \cdot z}} \]
   7. Step-by-step derivation

      1. *-commutative 94.0%

         \[\leadsto \frac{y \cdot x - z \cdot a}{y + \color{blue}{z \cdot b}} \]

   8. Simplified 94.0%

      \[\leadsto \frac{y \cdot x - z \cdot a}{y + \color{blue}{z \cdot b}} \]

   9. Taylor expanded in x around inf 88.0%

      \[\leadsto \color{blue}{\frac{x \cdot y}{y + b \cdot z}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 70.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{-37}:\\ \;\;\;\;\frac{a - t}{y - b}\\ \mathbf{elif}\;z \leq -9.6 \cdot 10^{-289}:\\ \;\;\;\;\frac{x \cdot \left(y + \frac{z \cdot \left(t - a\right)}{x}\right)}{y}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-262}:\\ \;\;\;\;\frac{y \cdot x}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-14}:\\ \;\;\;\;\frac{x \cdot \left(y + \frac{z \cdot \left(t - a\right)}{x}\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{a - t}{y - b}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 63.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot x - z \cdot a}{y}\\ t_2 := \frac{a - t}{y - b}\\ \mathbf{if}\;z \leq -7.2 \cdot 10^{-38}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-288}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-228}:\\ \;\;\;\;\frac{y \cdot x}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-11}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (* y x) (* z a)) y)) (t_2 (/ (- a t) (- y b))))
   (if (<= z -7.2e-38)
     t_2
     (if (<= z -4e-288)
       t_1
       (if (<= z 1.55e-228)
         (/ (* y x) (+ y (* z b)))
         (if (<= z 8.5e-11) 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)) / y;
	double t_2 = (a - t) / (y - b);
	double tmp;
	if (z <= -7.2e-38) {
		tmp = t_2;
	} else if (z <= -4e-288) {
		tmp = t_1;
	} else if (z <= 1.55e-228) {
		tmp = (y * x) / (y + (z * b));
	} else if (z <= 8.5e-11) {
		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)) / y
    t_2 = (a - t) / (y - b)
    if (z <= (-7.2d-38)) then
        tmp = t_2
    else if (z <= (-4d-288)) then
        tmp = t_1
    else if (z <= 1.55d-228) then
        tmp = (y * x) / (y + (z * b))
    else if (z <= 8.5d-11) 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)) / y;
	double t_2 = (a - t) / (y - b);
	double tmp;
	if (z <= -7.2e-38) {
		tmp = t_2;
	} else if (z <= -4e-288) {
		tmp = t_1;
	} else if (z <= 1.55e-228) {
		tmp = (y * x) / (y + (z * b));
	} else if (z <= 8.5e-11) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((y * x) - (z * a)) / y
	t_2 = (a - t) / (y - b)
	tmp = 0
	if z <= -7.2e-38:
		tmp = t_2
	elif z <= -4e-288:
		tmp = t_1
	elif z <= 1.55e-228:
		tmp = (y * x) / (y + (z * b))
	elif z <= 8.5e-11:
		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 * a)) / y)
	t_2 = Float64(Float64(a - t) / Float64(y - b))
	tmp = 0.0
	if (z <= -7.2e-38)
		tmp = t_2;
	elseif (z <= -4e-288)
		tmp = t_1;
	elseif (z <= 1.55e-228)
		tmp = Float64(Float64(y * x) / Float64(y + Float64(z * b)));
	elseif (z <= 8.5e-11)
		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)) / y;
	t_2 = (a - t) / (y - b);
	tmp = 0.0;
	if (z <= -7.2e-38)
		tmp = t_2;
	elseif (z <= -4e-288)
		tmp = t_1;
	elseif (z <= 1.55e-228)
		tmp = (y * x) / (y + (z * b));
	elseif (z <= 8.5e-11)
		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 * a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a - t), $MachinePrecision] / N[(y - b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.2e-38], t$95$2, If[LessEqual[z, -4e-288], t$95$1, If[LessEqual[z, 1.55e-228], N[(N[(y * x), $MachinePrecision] / N[(y + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.5e-11], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.2000000000000001e-38 or 8.50000000000000037e-11 < z

   1. Initial program 43.0%

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

   3. Taylor expanded in z around inf 78.0%

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

   if -7.2000000000000001e-38 < z < -4.00000000000000023e-288 or 1.5499999999999999e-228 < z < 8.50000000000000037e-11

   1. Initial program 90.6%

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

   3. Taylor expanded in t around 0 65.7%

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

      1. +-commutative 65.7%

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

      2. mul-1-neg 65.7%

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

      3. unsub-neg 65.7%

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

      4. *-commutative 65.7%

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

      5. *-commutative 65.7%

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

   5. Simplified 65.7%

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

   6. Taylor expanded in z around 0 50.9%

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

   if -4.00000000000000023e-288 < z < 1.5499999999999999e-228

   1. Initial program 92.9%

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

   3. Taylor expanded in t around 0 82.5%

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

      1. +-commutative 82.5%

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

      2. mul-1-neg 82.5%

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

      3. unsub-neg 82.5%

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

      4. *-commutative 82.5%

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

      5. *-commutative 82.5%

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

   5. Simplified 82.5%

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

   6. Taylor expanded in b around inf 82.5%

      \[\leadsto \frac{y \cdot x - z \cdot a}{y + \color{blue}{b \cdot z}} \]
   7. Step-by-step derivation

      1. *-commutative 82.5%

         \[\leadsto \frac{y \cdot x - z \cdot a}{y + \color{blue}{z \cdot b}} \]

   8. Simplified 82.5%

      \[\leadsto \frac{y \cdot x - z \cdot a}{y + \color{blue}{z \cdot b}} \]

   9. Taylor expanded in x around inf 75.4%

      \[\leadsto \color{blue}{\frac{x \cdot y}{y + b \cdot z}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 66.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{-38}:\\ \;\;\;\;\frac{a - t}{y - b}\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-288}:\\ \;\;\;\;\frac{y \cdot x - z \cdot a}{y}\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-228}:\\ \;\;\;\;\frac{y \cdot x}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-11}:\\ \;\;\;\;\frac{y \cdot x - z \cdot a}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{a - t}{y - b}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 72.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a - t}{y - b}\\ \mathbf{if}\;z \leq -6 \cdot 10^{+16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-92}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 2.2:\\ \;\;\;\;\frac{y \cdot x - z \cdot a}{y + z \cdot b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- a t) (- y b))))
   (if (<= z -6e+16)
     t_1
     (if (<= z -9e-92)
       (/ (* z (- t a)) (+ y (* z (- b y))))
       (if (<= z 2.2) (/ (- (* y x) (* 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 = (a - t) / (y - b);
	double tmp;
	if (z <= -6e+16) {
		tmp = t_1;
	} else if (z <= -9e-92) {
		tmp = (z * (t - a)) / (y + (z * (b - y)));
	} else if (z <= 2.2) {
		tmp = ((y * x) - (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 = (a - t) / (y - b)
    if (z <= (-6d+16)) then
        tmp = t_1
    else if (z <= (-9d-92)) then
        tmp = (z * (t - a)) / (y + (z * (b - y)))
    else if (z <= 2.2d0) then
        tmp = ((y * x) - (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 = (a - t) / (y - b);
	double tmp;
	if (z <= -6e+16) {
		tmp = t_1;
	} else if (z <= -9e-92) {
		tmp = (z * (t - a)) / (y + (z * (b - y)));
	} else if (z <= 2.2) {
		tmp = ((y * x) - (z * a)) / (y + (z * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a - t) / (y - b)
	tmp = 0
	if z <= -6e+16:
		tmp = t_1
	elif z <= -9e-92:
		tmp = (z * (t - a)) / (y + (z * (b - y)))
	elif z <= 2.2:
		tmp = ((y * x) - (z * a)) / (y + (z * b))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a - t) / Float64(y - b))
	tmp = 0.0
	if (z <= -6e+16)
		tmp = t_1;
	elseif (z <= -9e-92)
		tmp = Float64(Float64(z * Float64(t - a)) / Float64(y + Float64(z * Float64(b - y))));
	elseif (z <= 2.2)
		tmp = Float64(Float64(Float64(y * x) - Float64(z * 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 = (a - t) / (y - b);
	tmp = 0.0;
	if (z <= -6e+16)
		tmp = t_1;
	elseif (z <= -9e-92)
		tmp = (z * (t - a)) / (y + (z * (b - y)));
	elseif (z <= 2.2)
		tmp = ((y * x) - (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[(a - t), $MachinePrecision] / N[(y - b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6e+16], t$95$1, If[LessEqual[z, -9e-92], N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.2], N[(N[(N[(y * x), $MachinePrecision] - N[(z * a), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6e16 or 2.2000000000000002 < z

   1. Initial program 39.5%

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

   3. Taylor expanded in z around inf 81.1%

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

   if -6e16 < z < -9.0000000000000001e-92

   1. Initial program 82.6%

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

   3. Taylor expanded in x around 0 76.4%

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

   if -9.0000000000000001e-92 < z < 2.2000000000000002

   1. Initial program 90.8%

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

   3. Taylor expanded in t around 0 69.5%

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

      1. +-commutative 69.5%

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

      2. mul-1-neg 69.5%

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

      3. unsub-neg 69.5%

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

      4. *-commutative 69.5%

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

      5. *-commutative 69.5%

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

   5. Simplified 69.5%

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

   6. Taylor expanded in b around inf 69.5%

      \[\leadsto \frac{y \cdot x - z \cdot a}{y + \color{blue}{b \cdot z}} \]
   7. Step-by-step derivation

      1. *-commutative 69.5%

         \[\leadsto \frac{y \cdot x - z \cdot a}{y + \color{blue}{z \cdot b}} \]

   8. Simplified 69.5%

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

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+16}:\\ \;\;\;\;\frac{a - t}{y - b}\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-92}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 2.2:\\ \;\;\;\;\frac{y \cdot x - z \cdot a}{y + z \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\frac{a - t}{y - b}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 84.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+50} \lor \neg \left(z \leq 2.4 \cdot 10^{+53}\right):\\ \;\;\;\;\frac{a - t}{y - b}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x - z \cdot \left(a - t\right)}{y + z \cdot \left(b - y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -3.4e+50) (not (<= z 2.4e+53)))
   (/ (- a t) (- y b))
   (/ (- (* y x) (* z (- a t))) (+ y (* z (- b y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -3.4e+50) || !(z <= 2.4e+53)) {
		tmp = (a - t) / (y - b);
	} else {
		tmp = ((y * x) - (z * (a - t))) / (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 <= (-3.4d+50)) .or. (.not. (z <= 2.4d+53))) then
        tmp = (a - t) / (y - b)
    else
        tmp = ((y * x) - (z * (a - t))) / (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 <= -3.4e+50) || !(z <= 2.4e+53)) {
		tmp = (a - t) / (y - b);
	} else {
		tmp = ((y * x) - (z * (a - t))) / (y + (z * (b - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -3.4e+50) or not (z <= 2.4e+53):
		tmp = (a - t) / (y - b)
	else:
		tmp = ((y * x) - (z * (a - t))) / (y + (z * (b - y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -3.4e+50) || !(z <= 2.4e+53))
		tmp = Float64(Float64(a - t) / Float64(y - b));
	else
		tmp = Float64(Float64(Float64(y * x) - Float64(z * Float64(a - t))) / 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 <= -3.4e+50) || ~((z <= 2.4e+53)))
		tmp = (a - t) / (y - b);
	else
		tmp = ((y * x) - (z * (a - t))) / (y + (z * (b - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -3.4e+50], N[Not[LessEqual[z, 2.4e+53]], $MachinePrecision]], N[(N[(a - t), $MachinePrecision] / N[(y - b), $MachinePrecision]), $MachinePrecision], 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]]

Derivation

1. Split input into 2 regimes

2. if z < -3.3999999999999998e50 or 2.4e53 < z

   1. Initial program 36.6%

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

   3. Taylor expanded in z around inf 87.7%

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

   if -3.3999999999999998e50 < z < 2.4e53

   1. Initial program 86.5%

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

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+50} \lor \neg \left(z \leq 2.4 \cdot 10^{+53}\right):\\ \;\;\;\;\frac{a - t}{y - b}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x - z \cdot \left(a - t\right)}{y + z \cdot \left(b - y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 54.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -4.5 \cdot 10^{+58}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{+25}:\\ \;\;\;\;\frac{a}{y - b}\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{-31} \lor \neg \left(y \leq 2.7 \cdot 10^{+37}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (- 1.0 z))))
   (if (<= y -4.5e+58)
     t_1
     (if (<= y -3.5e+25)
       (/ a (- y b))
       (if (or (<= y -2.3e-31) (not (<= y 2.7e+37))) t_1 (/ (- t a) b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 - z);
	double tmp;
	if (y <= -4.5e+58) {
		tmp = t_1;
	} else if (y <= -3.5e+25) {
		tmp = a / (y - b);
	} else if ((y <= -2.3e-31) || !(y <= 2.7e+37)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x / (1.0d0 - z)
    if (y <= (-4.5d+58)) then
        tmp = t_1
    else if (y <= (-3.5d+25)) then
        tmp = a / (y - b)
    else if ((y <= (-2.3d-31)) .or. (.not. (y <= 2.7d+37))) then
        tmp = t_1
    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 t_1 = x / (1.0 - z);
	double tmp;
	if (y <= -4.5e+58) {
		tmp = t_1;
	} else if (y <= -3.5e+25) {
		tmp = a / (y - b);
	} else if ((y <= -2.3e-31) || !(y <= 2.7e+37)) {
		tmp = t_1;
	} else {
		tmp = (t - a) / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (1.0 - z)
	tmp = 0
	if y <= -4.5e+58:
		tmp = t_1
	elif y <= -3.5e+25:
		tmp = a / (y - b)
	elif (y <= -2.3e-31) or not (y <= 2.7e+37):
		tmp = t_1
	else:
		tmp = (t - a) / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(1.0 - z))
	tmp = 0.0
	if (y <= -4.5e+58)
		tmp = t_1;
	elseif (y <= -3.5e+25)
		tmp = Float64(a / Float64(y - b));
	elseif ((y <= -2.3e-31) || !(y <= 2.7e+37))
		tmp = t_1;
	else
		tmp = Float64(Float64(t - a) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (1.0 - z);
	tmp = 0.0;
	if (y <= -4.5e+58)
		tmp = t_1;
	elseif (y <= -3.5e+25)
		tmp = a / (y - b);
	elseif ((y <= -2.3e-31) || ~((y <= 2.7e+37)))
		tmp = t_1;
	else
		tmp = (t - a) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.5e+58], t$95$1, If[LessEqual[y, -3.5e+25], N[(a / N[(y - b), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -2.3e-31], N[Not[LessEqual[y, 2.7e+37]], $MachinePrecision]], t$95$1, N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.4999999999999998e58 or -3.49999999999999999e25 < y < -2.2999999999999998e-31 or 2.69999999999999986e37 < y

   1. Initial program 57.2%

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

   3. Taylor expanded in y around inf 57.7%

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

      1. mul-1-neg 57.7%

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

      2. unsub-neg 57.7%

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

   5. Simplified 57.7%

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

   if -4.4999999999999998e58 < y < -3.49999999999999999e25

   1. Initial program 51.3%

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

   3. Taylor expanded in a around inf 31.9%

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

      1. mul-1-neg 31.9%

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

      2. distribute-lft-neg-out 31.9%

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

      3. *-commutative 31.9%

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

   5. Simplified 31.9%

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

   6. Taylor expanded in z around inf 49.5%

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

      1. associate-*r/ 49.5%

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

      2. mul-1-neg 49.5%

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

   8. Simplified 49.5%

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

   if -2.2999999999999998e-31 < y < 2.69999999999999986e37

   1. Initial program 78.8%

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

   3. Taylor expanded in y around 0 53.6%

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

4. Final simplification 55.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+58}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{+25}:\\ \;\;\;\;\frac{a}{y - b}\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{-31} \lor \neg \left(y \leq 2.7 \cdot 10^{+37}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 63.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.12 \cdot 10^{-91} \lor \neg \left(z \leq 1.16 \cdot 10^{-49}\right):\\ \;\;\;\;\frac{a - t}{y - b}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{y + z \cdot b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.12e-91) (not (<= z 1.16e-49)))
   (/ (- a t) (- y b))
   (/ (* y x) (+ y (* z b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.12e-91) || !(z <= 1.16e-49)) {
		tmp = (a - t) / (y - b);
	} else {
		tmp = (y * x) / (y + (z * 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 <= (-1.12d-91)) .or. (.not. (z <= 1.16d-49))) then
        tmp = (a - t) / (y - b)
    else
        tmp = (y * x) / (y + (z * 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 <= -1.12e-91) || !(z <= 1.16e-49)) {
		tmp = (a - t) / (y - b);
	} else {
		tmp = (y * x) / (y + (z * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.12e-91) or not (z <= 1.16e-49):
		tmp = (a - t) / (y - b)
	else:
		tmp = (y * x) / (y + (z * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.12e-91) || !(z <= 1.16e-49))
		tmp = Float64(Float64(a - t) / Float64(y - b));
	else
		tmp = Float64(Float64(y * x) / Float64(y + Float64(z * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1.12e-91) || ~((z <= 1.16e-49)))
		tmp = (a - t) / (y - b);
	else
		tmp = (y * x) / (y + (z * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.12e-91], N[Not[LessEqual[z, 1.16e-49]], $MachinePrecision]], N[(N[(a - t), $MachinePrecision] / N[(y - b), $MachinePrecision]), $MachinePrecision], N[(N[(y * x), $MachinePrecision] / N[(y + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.12e-91 or 1.16000000000000003e-49 < z

   1. Initial program 47.0%

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

   3. Taylor expanded in z around inf 71.8%

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

   if -1.12e-91 < z < 1.16000000000000003e-49

   1. Initial program 93.2%

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

   3. Taylor expanded in t around 0 73.1%

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

      1. +-commutative 73.1%

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

      2. mul-1-neg 73.1%

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

      3. unsub-neg 73.1%

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

      4. *-commutative 73.1%

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

      5. *-commutative 73.1%

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

   5. Simplified 73.1%

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

   6. Taylor expanded in b around inf 73.1%

      \[\leadsto \frac{y \cdot x - z \cdot a}{y + \color{blue}{b \cdot z}} \]
   7. Step-by-step derivation

      1. *-commutative 73.1%

         \[\leadsto \frac{y \cdot x - z \cdot a}{y + \color{blue}{z \cdot b}} \]

   8. Simplified 73.1%

      \[\leadsto \frac{y \cdot x - z \cdot a}{y + \color{blue}{z \cdot b}} \]

   9. Taylor expanded in x around inf 52.6%

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

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.12 \cdot 10^{-91} \lor \neg \left(z \leq 1.16 \cdot 10^{-49}\right):\\ \;\;\;\;\frac{a - t}{y - b}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{y + z \cdot b}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 62.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{-92} \lor \neg \left(z \leq 1.78 \cdot 10^{+53}\right):\\ \;\;\;\;\frac{a - t}{y - b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -7.5e-92) (not (<= z 1.78e+53)))
   (/ (- a t) (- y b))
   (/ x (- 1.0 z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -7.5e-92) || !(z <= 1.78e+53)) {
		tmp = (a - t) / (y - b);
	} else {
		tmp = x / (1.0 - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-7.5d-92)) .or. (.not. (z <= 1.78d+53))) then
        tmp = (a - t) / (y - b)
    else
        tmp = x / (1.0d0 - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -7.5e-92) || !(z <= 1.78e+53)) {
		tmp = (a - t) / (y - b);
	} else {
		tmp = x / (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -7.5e-92) or not (z <= 1.78e+53):
		tmp = (a - t) / (y - b)
	else:
		tmp = x / (1.0 - z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -7.5e-92) || !(z <= 1.78e+53))
		tmp = Float64(Float64(a - t) / Float64(y - b));
	else
		tmp = Float64(x / Float64(1.0 - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -7.5e-92) || ~((z <= 1.78e+53)))
		tmp = (a - t) / (y - b);
	else
		tmp = x / (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -7.5e-92], N[Not[LessEqual[z, 1.78e+53]], $MachinePrecision]], N[(N[(a - t), $MachinePrecision] / N[(y - b), $MachinePrecision]), $MachinePrecision], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.5000000000000005e-92 or 1.77999999999999999e53 < z

   1. Initial program 44.0%

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

   3. Taylor expanded in z around inf 77.8%

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

   if -7.5000000000000005e-92 < z < 1.77999999999999999e53

   1. Initial program 89.7%

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

   3. Taylor expanded in y around inf 49.1%

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

      1. mul-1-neg 49.1%

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

      2. unsub-neg 49.1%

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

   5. Simplified 49.1%

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

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{-92} \lor \neg \left(z \leq 1.78 \cdot 10^{+53}\right):\\ \;\;\;\;\frac{a - t}{y - b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 45.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{-91} \lor \neg \left(z \leq 1.55 \cdot 10^{-11}\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.05e-91) (not (<= z 1.55e-11))) (/ t (- b y)) (+ x (* z x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.05e-91) || !(z <= 1.55e-11)) {
		tmp = t / (b - y);
	} else {
		tmp = x + (z * 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 <= (-1.05d-91)) .or. (.not. (z <= 1.55d-11))) then
        tmp = t / (b - y)
    else
        tmp = x + (z * 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 <= -1.05e-91) || !(z <= 1.55e-11)) {
		tmp = t / (b - y);
	} else {
		tmp = x + (z * x);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.05e-91) or not (z <= 1.55e-11):
		tmp = t / (b - y)
	else:
		tmp = x + (z * x)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.05e-91) || !(z <= 1.55e-11))
		tmp = Float64(t / Float64(b - y));
	else
		tmp = Float64(x + Float64(z * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1.05e-91) || ~((z <= 1.55e-11)))
		tmp = t / (b - y);
	else
		tmp = x + (z * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.05e-91], N[Not[LessEqual[z, 1.55e-11]], $MachinePrecision]], N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.05e-91 or 1.55000000000000014e-11 < z

   1. Initial program 45.1%

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

   3. Taylor expanded in t around inf 26.8%

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

      1. associate-/l* 37.8%

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

      2. +-commutative 37.8%

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

      3. fma-define 37.8%

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

   5. Simplified 37.8%

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

   6. Taylor expanded in z around inf 45.9%

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

   if -1.05e-91 < z < 1.55000000000000014e-11

   1. Initial program 90.8%

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

      1. fma-define 90.8%

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

      2. clear-num 90.6%

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

      3. inv-pow 90.6%

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

      4. +-commutative 90.6%

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

      5. fma-undefine 90.6%

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

      6. fma-define 90.6%

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

      7. +-commutative 90.6%

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

      8. fma-define 90.5%

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

   4. Applied egg-rr 90.5%

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

      1. unpow-1 90.5%

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

      2. *-commutative 90.5%

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

   6. Simplified 90.5%

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

   7. Taylor expanded in y around inf 48.8%

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

      1. neg-mul-1 48.8%

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

   9. Simplified 48.8%

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

   10. Taylor expanded in z around 0 48.9%

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

4. Final simplification 47.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{-91} \lor \neg \left(z \leq 1.55 \cdot 10^{-11}\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 45.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.9 \cdot 10^{-47} \lor \neg \left(y \leq 2.1 \cdot 10^{-22}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -3.9e-47) (not (<= y 2.1e-22))) (/ x (- 1.0 z)) (/ t (- b y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -3.9e-47) || !(y <= 2.1e-22)) {
		tmp = x / (1.0 - z);
	} 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 ((y <= (-3.9d-47)) .or. (.not. (y <= 2.1d-22))) then
        tmp = x / (1.0d0 - z)
    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 ((y <= -3.9e-47) || !(y <= 2.1e-22)) {
		tmp = x / (1.0 - z);
	} else {
		tmp = t / (b - y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -3.9e-47) or not (y <= 2.1e-22):
		tmp = x / (1.0 - z)
	else:
		tmp = t / (b - y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -3.9e-47) || !(y <= 2.1e-22))
		tmp = Float64(x / Float64(1.0 - z));
	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 ((y <= -3.9e-47) || ~((y <= 2.1e-22)))
		tmp = x / (1.0 - z);
	else
		tmp = t / (b - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -3.9e-47], N[Not[LessEqual[y, 2.1e-22]], $MachinePrecision]], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.89999999999999978e-47 or 2.10000000000000008e-22 < y

   1. Initial program 57.8%

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

   3. Taylor expanded in y around inf 50.5%

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

      1. mul-1-neg 50.5%

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

      2. unsub-neg 50.5%

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

   5. Simplified 50.5%

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

   if -3.89999999999999978e-47 < y < 2.10000000000000008e-22

   1. Initial program 80.4%

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

   3. Taylor expanded in t around inf 37.8%

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

      1. associate-/l* 45.6%

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

      2. +-commutative 45.6%

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

      3. fma-define 45.6%

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

   5. Simplified 45.6%

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

   6. Taylor expanded in z around inf 45.9%

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

4. Final simplification 48.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.9 \cdot 10^{-47} \lor \neg \left(y \leq 2.1 \cdot 10^{-22}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 55.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{-31} \lor \neg \left(y \leq 2.8 \cdot 10^{+37}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.55e-31) (not (<= y 2.8e+37))) (/ 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 <= -1.55e-31) || !(y <= 2.8e+37)) {
		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 <= (-1.55d-31)) .or. (.not. (y <= 2.8d+37))) 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 <= -1.55e-31) || !(y <= 2.8e+37)) {
		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 <= -1.55e-31) or not (y <= 2.8e+37):
		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 <= -1.55e-31) || !(y <= 2.8e+37))
		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 <= -1.55e-31) || ~((y <= 2.8e+37)))
		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, -1.55e-31], N[Not[LessEqual[y, 2.8e+37]], $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 < -1.55e-31 or 2.7999999999999998e37 < y

   1. Initial program 56.7%

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

   3. Taylor expanded in y around inf 53.6%

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

      1. mul-1-neg 53.6%

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

      2. unsub-neg 53.6%

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

   5. Simplified 53.6%

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

   if -1.55e-31 < y < 2.7999999999999998e37

   1. Initial program 78.8%

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

   3. Taylor expanded in y around 0 53.6%

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

4. Final simplification 53.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{-31} \lor \neg \left(y \leq 2.8 \cdot 10^{+37}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 36.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{-31}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-32}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.55e-31) x (if (<= y 1.15e-32) (/ t b) x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.55e-31) {
		tmp = x;
	} else if (y <= 1.15e-32) {
		tmp = t / 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 (y <= (-1.55d-31)) then
        tmp = x
    else if (y <= 1.15d-32) then
        tmp = t / 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 (y <= -1.55e-31) {
		tmp = x;
	} else if (y <= 1.15e-32) {
		tmp = t / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.55e-31:
		tmp = x
	elif y <= 1.15e-32:
		tmp = t / b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.55e-31)
		tmp = x;
	elseif (y <= 1.15e-32)
		tmp = Float64(t / b);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -1.55e-31)
		tmp = x;
	elseif (y <= 1.15e-32)
		tmp = t / b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.55e-31], x, If[LessEqual[y, 1.15e-32], N[(t / b), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -1.55e-31 or 1.15e-32 < y

   1. Initial program 56.9%

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

   3. Taylor expanded in z around 0 38.8%

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

   if -1.55e-31 < y < 1.15e-32

   1. Initial program 80.9%

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

   3. Taylor expanded in t around inf 36.9%

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

      1. associate-/l* 44.5%

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

      2. +-commutative 44.5%

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

      3. fma-define 44.5%

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

   5. Simplified 44.5%

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

   6. Taylor expanded in b around inf 38.2%

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

4. Final simplification 38.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{-31}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-32}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 26.1% 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 67.4%

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

3. Taylor expanded in z around 0 25.7%

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

4. Final simplification 25.7%

   \[\leadsto x \]
5. Add Preprocessing

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 2024055 
(FPCore (x y z t a b)
  :name "Development.Shake.Progress:decay from shake-0.15.5"
  :precision binary64

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

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