Development.Shake.Progress:decay from shake-0.15.5

Percentage Accurate: 66.6% → 93.1%

Time: 20.3s

Alternatives: 19

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: 66.6% 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: 93.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -37000000 \lor \neg \left(z \leq 340000000\right):\\ \;\;\;\;\frac{y}{b - y} \cdot \frac{x}{z} + \frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, z \cdot \left(t - a\right)\right)}{y + z \cdot \left(b - y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -37000000.0) (not (<= z 340000000.0)))
   (+ (* (/ y (- b y)) (/ x z)) (/ (- t a) (- b y)))
   (/ (fma x y (* z (- t a))) (+ y (* z (- b y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -37000000.0) || !(z <= 340000000.0)) {
		tmp = ((y / (b - y)) * (x / z)) + ((t - a) / (b - y));
	} else {
		tmp = fma(x, y, (z * (t - a))) / (y + (z * (b - y)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -37000000.0) || !(z <= 340000000.0))
		tmp = Float64(Float64(Float64(y / Float64(b - y)) * Float64(x / z)) + Float64(Float64(t - a) / Float64(b - y)));
	else
		tmp = Float64(fma(x, y, Float64(z * Float64(t - a))) / Float64(y + Float64(z * Float64(b - y))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -37000000.0], N[Not[LessEqual[z, 340000000.0]], $MachinePrecision]], N[(N[(N[(y / N[(b - y), $MachinePrecision]), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision] + N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * y + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.7e7 or 3.4e8 < z

   1. Initial program 44.8%

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

   3. Taylor expanded in z around -inf 63.8%

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

      1. associate--l+ 63.8%

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

      2. mul-1-neg 63.8%

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

      3. distribute-lft-out-- 63.8%

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

      4. associate-/l* 70.3%

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

      5. associate-/l* 89.8%

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

      6. div-sub 90.5%

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

   5. Simplified 90.5%

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

   6. Taylor expanded in x around inf 82.4%

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

      1. associate-*r/ 82.4%

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

      2. associate-*r* 82.4%

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

      3. times-frac 99.7%

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

      4. mul-1-neg 99.7%

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

   8. Simplified 99.7%

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

   if -3.7e7 < z < 3.4e8

   1. Initial program 87.9%

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

      1. fma-define 87.9%

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

   3. Simplified 87.9%

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

4. Final simplification 93.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -37000000 \lor \neg \left(z \leq 340000000\right):\\ \;\;\;\;\frac{y}{b - y} \cdot \frac{x}{z} + \frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, z \cdot \left(t - a\right)\right)}{y + z \cdot \left(b - y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 87.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ t_2 := \frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;x + z \cdot \frac{t}{y}\\ \mathbf{elif}\;t\_2 \leq -4 \cdot 10^{-290}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+307}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1 - \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y)))
        (t_2 (/ (+ (* z (- t a)) (* x y)) (+ y (* z (- b y))))))
   (if (<= t_2 (- INFINITY))
     (+ x (* z (/ t y)))
     (if (<= t_2 -4e-290)
       t_2
       (if (<= t_2 0.0) t_1 (if (<= t_2 5e+307) t_2 (- t_1 (/ x z))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double t_2 = ((z * (t - a)) + (x * y)) / (y + (z * (b - y)));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = x + (z * (t / y));
	} else if (t_2 <= -4e-290) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = t_1;
	} else if (t_2 <= 5e+307) {
		tmp = t_2;
	} else {
		tmp = t_1 - (x / z);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double t_2 = ((z * (t - a)) + (x * y)) / (y + (z * (b - y)));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = x + (z * (t / y));
	} else if (t_2 <= -4e-290) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = t_1;
	} else if (t_2 <= 5e+307) {
		tmp = t_2;
	} else {
		tmp = t_1 - (x / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	t_2 = ((z * (t - a)) + (x * y)) / (y + (z * (b - y)))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = x + (z * (t / y))
	elif t_2 <= -4e-290:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = t_1
	elif t_2 <= 5e+307:
		tmp = t_2
	else:
		tmp = t_1 - (x / z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	t_2 = Float64(Float64(Float64(z * Float64(t - a)) + Float64(x * y)) / Float64(y + Float64(z * Float64(b - y))))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(x + Float64(z * Float64(t / y)));
	elseif (t_2 <= -4e-290)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = t_1;
	elseif (t_2 <= 5e+307)
		tmp = t_2;
	else
		tmp = Float64(t_1 - Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	t_2 = ((z * (t - a)) + (x * y)) / (y + (z * (b - y)));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = x + (z * (t / y));
	elseif (t_2 <= -4e-290)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = t_1;
	elseif (t_2 <= 5e+307)
		tmp = t_2;
	else
		tmp = t_1 - (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(x + N[(z * N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, -4e-290], t$95$2, If[LessEqual[t$95$2, 0.0], t$95$1, If[LessEqual[t$95$2, 5e+307], t$95$2, N[(t$95$1 - N[(x / z), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -inf.0

   1. Initial program 38.1%

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

   3. Taylor expanded in z around 0 25.7%

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

   4. Taylor expanded in t around inf 66.6%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -4.0000000000000003e-290 or -0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 5e307

   1. Initial program 99.6%

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

   if -4.0000000000000003e-290 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -0.0

   1. Initial program 18.4%

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

   3. Taylor expanded in z around inf 82.7%

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

   if 5e307 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 7.2%

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

   3. Taylor expanded in z around -inf 26.8%

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

      1. associate--l+ 26.8%

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

      2. mul-1-neg 26.8%

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

      3. distribute-lft-out-- 26.8%

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

      4. associate-/l* 39.6%

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

      5. associate-/l* 86.3%

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

      6. div-sub 86.3%

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

   5. Simplified 86.3%

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

   6. Taylor expanded in y around inf 80.4%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;x + z \cdot \frac{t}{y}\\ \mathbf{elif}\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)} \leq -4 \cdot 10^{-290}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)} \leq 0:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)} \leq 5 \cdot 10^{+307}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y} - \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 72.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot y + z \cdot t}{y + z \cdot \left(b - y\right)}\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -2.55 \cdot 10^{+26}:\\ \;\;\;\;t\_2 - \frac{x}{z}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-151}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-67}:\\ \;\;\;\;x - \frac{z \cdot a}{y}\\ \mathbf{elif}\;z \leq 1.52 \cdot 10^{-19}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ (* x y) (* z t)) (+ y (* z (- b y)))))
        (t_2 (/ (- t a) (- b y))))
   (if (<= z -2.55e+26)
     (- t_2 (/ x z))
     (if (<= z 7e-151)
       t_1
       (if (<= z 2.6e-67) (- x (/ (* z a) y)) (if (<= z 1.52e-19) 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)) / (y + (z * (b - y)));
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -2.55e+26) {
		tmp = t_2 - (x / z);
	} else if (z <= 7e-151) {
		tmp = t_1;
	} else if (z <= 2.6e-67) {
		tmp = x - ((z * a) / y);
	} else if (z <= 1.52e-19) {
		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)) / (y + (z * (b - y)))
    t_2 = (t - a) / (b - y)
    if (z <= (-2.55d+26)) then
        tmp = t_2 - (x / z)
    else if (z <= 7d-151) then
        tmp = t_1
    else if (z <= 2.6d-67) then
        tmp = x - ((z * a) / y)
    else if (z <= 1.52d-19) 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)) / (y + (z * (b - y)));
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -2.55e+26) {
		tmp = t_2 - (x / z);
	} else if (z <= 7e-151) {
		tmp = t_1;
	} else if (z <= 2.6e-67) {
		tmp = x - ((z * a) / y);
	} else if (z <= 1.52e-19) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((x * y) + (z * t)) / (y + (z * (b - y)))
	t_2 = (t - a) / (b - y)
	tmp = 0
	if z <= -2.55e+26:
		tmp = t_2 - (x / z)
	elif z <= 7e-151:
		tmp = t_1
	elif z <= 2.6e-67:
		tmp = x - ((z * a) / y)
	elif z <= 1.52e-19:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(x * y) + Float64(z * t)) / Float64(y + Float64(z * Float64(b - y))))
	t_2 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -2.55e+26)
		tmp = Float64(t_2 - Float64(x / z));
	elseif (z <= 7e-151)
		tmp = t_1;
	elseif (z <= 2.6e-67)
		tmp = Float64(x - Float64(Float64(z * a) / y));
	elseif (z <= 1.52e-19)
		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)) / (y + (z * (b - y)));
	t_2 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -2.55e+26)
		tmp = t_2 - (x / z);
	elseif (z <= 7e-151)
		tmp = t_1;
	elseif (z <= 2.6e-67)
		tmp = x - ((z * a) / y);
	elseif (z <= 1.52e-19)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.55e+26], N[(t$95$2 - N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7e-151], t$95$1, If[LessEqual[z, 2.6e-67], N[(x - N[(N[(z * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.52e-19], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.5499999999999999e26

   1. Initial program 33.8%

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

   3. Taylor expanded in z around -inf 53.9%

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

      1. associate--l+ 53.9%

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

      2. mul-1-neg 53.9%

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

      3. distribute-lft-out-- 53.9%

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

      4. associate-/l* 61.9%

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

      5. associate-/l* 88.9%

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

      6. div-sub 88.9%

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

   5. Simplified 88.9%

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

   6. Taylor expanded in y around inf 77.7%

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

   if -2.5499999999999999e26 < z < 6.99999999999999991e-151 or 2.5999999999999999e-67 < z < 1.5199999999999999e-19

   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 a around 0 71.9%

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

   if 6.99999999999999991e-151 < z < 2.5999999999999999e-67

   1. Initial program 79.9%

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

   3. Taylor expanded in z around 0 54.5%

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

   4. Taylor expanded in a around inf 79.8%

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

   if 1.5199999999999999e-19 < z

   1. Initial program 56.2%

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

   3. Taylor expanded in z around inf 78.8%

      \[\leadsto \color{blue}{\frac{t - a}{b - y}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.55 \cdot 10^{+26}:\\ \;\;\;\;\frac{t - a}{b - y} - \frac{x}{z}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-151}:\\ \;\;\;\;\frac{x \cdot y + z \cdot t}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-67}:\\ \;\;\;\;x - \frac{z \cdot a}{y}\\ \mathbf{elif}\;z \leq 1.52 \cdot 10^{-19}:\\ \;\;\;\;\frac{x \cdot y + z \cdot t}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 73.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ t_2 := y + z \cdot \left(b - y\right)\\ \mathbf{if}\;z \leq -4.2 \cdot 10^{+25}:\\ \;\;\;\;t\_1 - \frac{x}{z}\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-152}:\\ \;\;\;\;\frac{x \cdot y + z \cdot t}{t\_2}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-105}:\\ \;\;\;\;x - \frac{z \cdot a}{y}\\ \mathbf{elif}\;z \leq 1.08 \cdot 10^{+66}:\\ \;\;\;\;\frac{x \cdot y - z \cdot a}{t\_2}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))) (t_2 (+ y (* z (- b y)))))
   (if (<= z -4.2e+25)
     (- t_1 (/ x z))
     (if (<= z 3.3e-152)
       (/ (+ (* x y) (* z t)) t_2)
       (if (<= z 1.2e-105)
         (- x (/ (* z a) y))
         (if (<= z 1.08e+66) (/ (- (* x y) (* z a)) t_2) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double t_2 = y + (z * (b - y));
	double tmp;
	if (z <= -4.2e+25) {
		tmp = t_1 - (x / z);
	} else if (z <= 3.3e-152) {
		tmp = ((x * y) + (z * t)) / t_2;
	} else if (z <= 1.2e-105) {
		tmp = x - ((z * a) / y);
	} else if (z <= 1.08e+66) {
		tmp = ((x * y) - (z * a)) / t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    t_2 = y + (z * (b - y))
    if (z <= (-4.2d+25)) then
        tmp = t_1 - (x / z)
    else if (z <= 3.3d-152) then
        tmp = ((x * y) + (z * t)) / t_2
    else if (z <= 1.2d-105) then
        tmp = x - ((z * a) / y)
    else if (z <= 1.08d+66) then
        tmp = ((x * y) - (z * a)) / t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double t_2 = y + (z * (b - y));
	double tmp;
	if (z <= -4.2e+25) {
		tmp = t_1 - (x / z);
	} else if (z <= 3.3e-152) {
		tmp = ((x * y) + (z * t)) / t_2;
	} else if (z <= 1.2e-105) {
		tmp = x - ((z * a) / y);
	} else if (z <= 1.08e+66) {
		tmp = ((x * y) - (z * a)) / t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	t_2 = y + (z * (b - y))
	tmp = 0
	if z <= -4.2e+25:
		tmp = t_1 - (x / z)
	elif z <= 3.3e-152:
		tmp = ((x * y) + (z * t)) / t_2
	elif z <= 1.2e-105:
		tmp = x - ((z * a) / y)
	elif z <= 1.08e+66:
		tmp = ((x * y) - (z * a)) / t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	t_2 = Float64(y + Float64(z * Float64(b - y)))
	tmp = 0.0
	if (z <= -4.2e+25)
		tmp = Float64(t_1 - Float64(x / z));
	elseif (z <= 3.3e-152)
		tmp = Float64(Float64(Float64(x * y) + Float64(z * t)) / t_2);
	elseif (z <= 1.2e-105)
		tmp = Float64(x - Float64(Float64(z * a) / y));
	elseif (z <= 1.08e+66)
		tmp = Float64(Float64(Float64(x * y) - Float64(z * a)) / t_2);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	t_2 = y + (z * (b - y));
	tmp = 0.0;
	if (z <= -4.2e+25)
		tmp = t_1 - (x / z);
	elseif (z <= 3.3e-152)
		tmp = ((x * y) + (z * t)) / t_2;
	elseif (z <= 1.2e-105)
		tmp = x - ((z * a) / y);
	elseif (z <= 1.08e+66)
		tmp = ((x * y) - (z * a)) / t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.2e+25], N[(t$95$1 - N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.3e-152], N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision], If[LessEqual[z, 1.2e-105], N[(x - N[(N[(z * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.08e+66], N[(N[(N[(x * y), $MachinePrecision] - N[(z * a), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -4.1999999999999998e25

   1. Initial program 33.8%

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

   3. Taylor expanded in z around -inf 53.9%

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

      1. associate--l+ 53.9%

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

      2. mul-1-neg 53.9%

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

      3. distribute-lft-out-- 53.9%

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

      4. associate-/l* 61.9%

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

      5. associate-/l* 88.9%

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

      6. div-sub 88.9%

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

   5. Simplified 88.9%

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

   6. Taylor expanded in y around inf 77.7%

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

   if -4.1999999999999998e25 < z < 3.29999999999999998e-152

   1. Initial program 87.9%

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

   3. Taylor expanded in a around 0 69.6%

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

   if 3.29999999999999998e-152 < z < 1.20000000000000007e-105

   1. Initial program 70.6%

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

   3. Taylor expanded in z around 0 41.4%

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

   4. Taylor expanded in a around inf 85.1%

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

   if 1.20000000000000007e-105 < z < 1.08000000000000008e66

   1. Initial program 96.4%

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

   3. Taylor expanded in t around 0 73.3%

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

      1. +-commutative 73.3%

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

      2. mul-1-neg 73.3%

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

      3. unsub-neg 73.3%

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

      4. *-commutative 73.3%

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

      5. *-commutative 73.3%

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

   5. Simplified 73.3%

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

   if 1.08000000000000008e66 < z

   1. Initial program 47.3%

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

   3. Taylor expanded in z around inf 84.4%

      \[\leadsto \color{blue}{\frac{t - a}{b - y}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 76.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+25}:\\ \;\;\;\;\frac{t - a}{b - y} - \frac{x}{z}\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-152}:\\ \;\;\;\;\frac{x \cdot y + z \cdot t}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-105}:\\ \;\;\;\;x - \frac{z \cdot a}{y}\\ \mathbf{elif}\;z \leq 1.08 \cdot 10^{+66}:\\ \;\;\;\;\frac{x \cdot y - z \cdot a}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 41.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a}{-b}\\ t_2 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -1.15 \cdot 10^{+58}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{-179}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{-264}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{-300}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-125}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ a (- b))) (t_2 (/ x (- 1.0 z))))
   (if (<= y -1.15e+58)
     t_2
     (if (<= y -4.6e-179)
       (/ t (- b y))
       (if (<= y -1.1e-264)
         t_1
         (if (<= y -1.6e-300) (/ t b) (if (<= y 1.9e-125) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a / -b;
	double t_2 = x / (1.0 - z);
	double tmp;
	if (y <= -1.15e+58) {
		tmp = t_2;
	} else if (y <= -4.6e-179) {
		tmp = t / (b - y);
	} else if (y <= -1.1e-264) {
		tmp = t_1;
	} else if (y <= -1.6e-300) {
		tmp = t / b;
	} else if (y <= 1.9e-125) {
		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 = a / -b
    t_2 = x / (1.0d0 - z)
    if (y <= (-1.15d+58)) then
        tmp = t_2
    else if (y <= (-4.6d-179)) then
        tmp = t / (b - y)
    else if (y <= (-1.1d-264)) then
        tmp = t_1
    else if (y <= (-1.6d-300)) then
        tmp = t / b
    else if (y <= 1.9d-125) 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 = a / -b;
	double t_2 = x / (1.0 - z);
	double tmp;
	if (y <= -1.15e+58) {
		tmp = t_2;
	} else if (y <= -4.6e-179) {
		tmp = t / (b - y);
	} else if (y <= -1.1e-264) {
		tmp = t_1;
	} else if (y <= -1.6e-300) {
		tmp = t / b;
	} else if (y <= 1.9e-125) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a / -b
	t_2 = x / (1.0 - z)
	tmp = 0
	if y <= -1.15e+58:
		tmp = t_2
	elif y <= -4.6e-179:
		tmp = t / (b - y)
	elif y <= -1.1e-264:
		tmp = t_1
	elif y <= -1.6e-300:
		tmp = t / b
	elif y <= 1.9e-125:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a / Float64(-b))
	t_2 = Float64(x / Float64(1.0 - z))
	tmp = 0.0
	if (y <= -1.15e+58)
		tmp = t_2;
	elseif (y <= -4.6e-179)
		tmp = Float64(t / Float64(b - y));
	elseif (y <= -1.1e-264)
		tmp = t_1;
	elseif (y <= -1.6e-300)
		tmp = Float64(t / b);
	elseif (y <= 1.9e-125)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a / -b;
	t_2 = x / (1.0 - z);
	tmp = 0.0;
	if (y <= -1.15e+58)
		tmp = t_2;
	elseif (y <= -4.6e-179)
		tmp = t / (b - y);
	elseif (y <= -1.1e-264)
		tmp = t_1;
	elseif (y <= -1.6e-300)
		tmp = t / b;
	elseif (y <= 1.9e-125)
		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[(a / (-b)), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.15e+58], t$95$2, If[LessEqual[y, -4.6e-179], N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.1e-264], t$95$1, If[LessEqual[y, -1.6e-300], N[(t / b), $MachinePrecision], If[LessEqual[y, 1.9e-125], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.15000000000000001e58 or 1.9000000000000001e-125 < y

   1. Initial program 51.8%

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

   3. Taylor expanded in y around inf 51.6%

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

      1. mul-1-neg 51.6%

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

      2. unsub-neg 51.6%

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

   5. Simplified 51.6%

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

   if -1.15000000000000001e58 < y < -4.59999999999999975e-179

   1. Initial program 79.3%

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

   3. Taylor expanded in t around inf 37.3%

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

      1. *-commutative 37.3%

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

   5. Simplified 37.3%

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

   6. Taylor expanded in z around inf 38.5%

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

   if -4.59999999999999975e-179 < y < -1.09999999999999997e-264 or -1.60000000000000011e-300 < y < 1.9000000000000001e-125

   1. Initial program 85.1%

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

   3. Taylor expanded in b around inf 61.6%

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

   4. Taylor expanded in a around inf 45.8%

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

      1. associate-*r/ 45.8%

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

      2. neg-mul-1 45.8%

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

   6. Simplified 45.8%

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

   if -1.09999999999999997e-264 < y < -1.60000000000000011e-300

   1. Initial program 90.9%

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

   3. Taylor expanded in t around inf 58.1%

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

      1. *-commutative 58.1%

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

   5. Simplified 58.1%

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

   6. Taylor expanded in y around 0 67.0%

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

4. Final simplification 48.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+58}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{-179}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{-264}:\\ \;\;\;\;\frac{a}{-b}\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{-300}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-125}:\\ \;\;\;\;\frac{a}{-b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 66.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -7.8 \cdot 10^{+33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{-26}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;z \leq -6.4 \cdot 10^{-27}:\\ \;\;\;\;\frac{a}{-b}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-35}:\\ \;\;\;\;x + z \cdot \frac{t}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -7.8e+33)
     t_1
     (if (<= z -9.2e-26)
       (/ x (- 1.0 z))
       (if (<= z -6.4e-27)
         (/ a (- b))
         (if (<= z 1.8e-35) (+ x (* z (/ t y))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -7.8e+33) {
		tmp = t_1;
	} else if (z <= -9.2e-26) {
		tmp = x / (1.0 - z);
	} else if (z <= -6.4e-27) {
		tmp = a / -b;
	} else if (z <= 1.8e-35) {
		tmp = x + (z * (t / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    if (z <= (-7.8d+33)) then
        tmp = t_1
    else if (z <= (-9.2d-26)) then
        tmp = x / (1.0d0 - z)
    else if (z <= (-6.4d-27)) then
        tmp = a / -b
    else if (z <= 1.8d-35) then
        tmp = x + (z * (t / y))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -7.8e+33) {
		tmp = t_1;
	} else if (z <= -9.2e-26) {
		tmp = x / (1.0 - z);
	} else if (z <= -6.4e-27) {
		tmp = a / -b;
	} else if (z <= 1.8e-35) {
		tmp = x + (z * (t / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	tmp = 0
	if z <= -7.8e+33:
		tmp = t_1
	elif z <= -9.2e-26:
		tmp = x / (1.0 - z)
	elif z <= -6.4e-27:
		tmp = a / -b
	elif z <= 1.8e-35:
		tmp = x + (z * (t / y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -7.8e+33)
		tmp = t_1;
	elseif (z <= -9.2e-26)
		tmp = Float64(x / Float64(1.0 - z));
	elseif (z <= -6.4e-27)
		tmp = Float64(a / Float64(-b));
	elseif (z <= 1.8e-35)
		tmp = Float64(x + Float64(z * Float64(t / y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -7.8e+33)
		tmp = t_1;
	elseif (z <= -9.2e-26)
		tmp = x / (1.0 - z);
	elseif (z <= -6.4e-27)
		tmp = a / -b;
	elseif (z <= 1.8e-35)
		tmp = x + (z * (t / y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.8e+33], t$95$1, If[LessEqual[z, -9.2e-26], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -6.4e-27], N[(a / (-b)), $MachinePrecision], If[LessEqual[z, 1.8e-35], N[(x + N[(z * N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -7.8000000000000004e33 or 1.80000000000000009e-35 < z

   1. Initial program 47.9%

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

   3. Taylor expanded in z around inf 78.2%

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

   if -7.8000000000000004e33 < z < -9.20000000000000035e-26

   1. Initial program 60.8%

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

   3. Taylor expanded in y around inf 55.6%

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

      1. mul-1-neg 55.6%

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

      2. unsub-neg 55.6%

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

   5. Simplified 55.6%

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

   if -9.20000000000000035e-26 < z < -6.39999999999999982e-27

   1. Initial program 98.4%

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

   3. Taylor expanded in b around inf 98.4%

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

   4. Taylor expanded in a around inf 100.0%

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

      1. associate-*r/ 100.0%

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

      2. neg-mul-1 100.0%

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

   6. Simplified 100.0%

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

   if -6.39999999999999982e-27 < z < 1.80000000000000009e-35

   1. Initial program 89.2%

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

   3. Taylor expanded in z around 0 53.5%

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

   4. Taylor expanded in t around inf 59.4%

      \[\leadsto x + z \cdot \color{blue}{\frac{t}{y}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{+33}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{-26}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;z \leq -6.4 \cdot 10^{-27}:\\ \;\;\;\;\frac{a}{-b}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-35}:\\ \;\;\;\;x + z \cdot \frac{t}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 66.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -7.8 \cdot 10^{+33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-87}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-110}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-36}:\\ \;\;\;\;x - a \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -7.8e+33)
     t_1
     (if (<= z -7.5e-87)
       (/ x (- 1.0 z))
       (if (<= z -1.05e-110)
         (/ (- t a) b)
         (if (<= z 4e-36) (- x (* a (/ z y))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -7.8e+33) {
		tmp = t_1;
	} else if (z <= -7.5e-87) {
		tmp = x / (1.0 - z);
	} else if (z <= -1.05e-110) {
		tmp = (t - a) / b;
	} else if (z <= 4e-36) {
		tmp = x - (a * (z / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    if (z <= (-7.8d+33)) then
        tmp = t_1
    else if (z <= (-7.5d-87)) then
        tmp = x / (1.0d0 - z)
    else if (z <= (-1.05d-110)) then
        tmp = (t - a) / b
    else if (z <= 4d-36) then
        tmp = x - (a * (z / y))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -7.8e+33) {
		tmp = t_1;
	} else if (z <= -7.5e-87) {
		tmp = x / (1.0 - z);
	} else if (z <= -1.05e-110) {
		tmp = (t - a) / b;
	} else if (z <= 4e-36) {
		tmp = x - (a * (z / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	tmp = 0
	if z <= -7.8e+33:
		tmp = t_1
	elif z <= -7.5e-87:
		tmp = x / (1.0 - z)
	elif z <= -1.05e-110:
		tmp = (t - a) / b
	elif z <= 4e-36:
		tmp = x - (a * (z / y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -7.8e+33)
		tmp = t_1;
	elseif (z <= -7.5e-87)
		tmp = Float64(x / Float64(1.0 - z));
	elseif (z <= -1.05e-110)
		tmp = Float64(Float64(t - a) / b);
	elseif (z <= 4e-36)
		tmp = Float64(x - Float64(a * Float64(z / y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -7.8e+33)
		tmp = t_1;
	elseif (z <= -7.5e-87)
		tmp = x / (1.0 - z);
	elseif (z <= -1.05e-110)
		tmp = (t - a) / b;
	elseif (z <= 4e-36)
		tmp = x - (a * (z / y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.8e+33], t$95$1, If[LessEqual[z, -7.5e-87], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.05e-110], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[z, 4e-36], N[(x - N[(a * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -7.8000000000000004e33 or 3.9999999999999998e-36 < z

   1. Initial program 47.9%

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

   3. Taylor expanded in z around inf 78.2%

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

   if -7.8000000000000004e33 < z < -7.5000000000000002e-87

   1. Initial program 77.2%

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

   3. Taylor expanded in y around inf 51.4%

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

      1. mul-1-neg 51.4%

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

      2. unsub-neg 51.4%

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

   5. Simplified 51.4%

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

   if -7.5000000000000002e-87 < z < -1.05000000000000001e-110

   1. Initial program 99.4%

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

   3. Taylor expanded in y around 0 80.3%

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

   if -1.05000000000000001e-110 < z < 3.9999999999999998e-36

   1. Initial program 88.4%

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

   3. Taylor expanded in z around 0 55.0%

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

   4. Taylor expanded in a around inf 62.7%

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

      1. mul-1-neg 62.7%

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

      2. associate-/l* 61.7%

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

   6. Simplified 61.7%

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

4. Final simplification 69.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{+33}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-87}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-110}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-36}:\\ \;\;\;\;x - a \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 66.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -7.8 \cdot 10^{+33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-87}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-111}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-36}:\\ \;\;\;\;x - \frac{z \cdot a}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -7.8e+33)
     t_1
     (if (<= z -3.2e-87)
       (/ x (- 1.0 z))
       (if (<= z -4.8e-111)
         (/ (- t a) b)
         (if (<= z 2e-36) (- x (/ (* z a) y)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -7.8e+33) {
		tmp = t_1;
	} else if (z <= -3.2e-87) {
		tmp = x / (1.0 - z);
	} else if (z <= -4.8e-111) {
		tmp = (t - a) / b;
	} else if (z <= 2e-36) {
		tmp = x - ((z * a) / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    if (z <= (-7.8d+33)) then
        tmp = t_1
    else if (z <= (-3.2d-87)) then
        tmp = x / (1.0d0 - z)
    else if (z <= (-4.8d-111)) then
        tmp = (t - a) / b
    else if (z <= 2d-36) then
        tmp = x - ((z * a) / y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -7.8e+33) {
		tmp = t_1;
	} else if (z <= -3.2e-87) {
		tmp = x / (1.0 - z);
	} else if (z <= -4.8e-111) {
		tmp = (t - a) / b;
	} else if (z <= 2e-36) {
		tmp = x - ((z * a) / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	tmp = 0
	if z <= -7.8e+33:
		tmp = t_1
	elif z <= -3.2e-87:
		tmp = x / (1.0 - z)
	elif z <= -4.8e-111:
		tmp = (t - a) / b
	elif z <= 2e-36:
		tmp = x - ((z * a) / y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -7.8e+33)
		tmp = t_1;
	elseif (z <= -3.2e-87)
		tmp = Float64(x / Float64(1.0 - z));
	elseif (z <= -4.8e-111)
		tmp = Float64(Float64(t - a) / b);
	elseif (z <= 2e-36)
		tmp = Float64(x - Float64(Float64(z * a) / y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -7.8e+33)
		tmp = t_1;
	elseif (z <= -3.2e-87)
		tmp = x / (1.0 - z);
	elseif (z <= -4.8e-111)
		tmp = (t - a) / b;
	elseif (z <= 2e-36)
		tmp = x - ((z * a) / y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.8e+33], t$95$1, If[LessEqual[z, -3.2e-87], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4.8e-111], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[z, 2e-36], N[(x - N[(N[(z * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -7.8000000000000004e33 or 1.9999999999999999e-36 < z

   1. Initial program 47.9%

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

   3. Taylor expanded in z around inf 78.2%

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

   if -7.8000000000000004e33 < z < -3.19999999999999979e-87

   1. Initial program 77.2%

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

   3. Taylor expanded in y around inf 51.4%

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

      1. mul-1-neg 51.4%

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

      2. unsub-neg 51.4%

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

   5. Simplified 51.4%

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

   if -3.19999999999999979e-87 < z < -4.8000000000000001e-111

   1. Initial program 99.4%

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

   3. Taylor expanded in y around 0 80.3%

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

   if -4.8000000000000001e-111 < z < 1.9999999999999999e-36

   1. Initial program 88.4%

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

   3. Taylor expanded in z around 0 55.0%

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

   4. Taylor expanded in a around inf 62.7%

      \[\leadsto x + \color{blue}{-1 \cdot \frac{a \cdot z}{y}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 70.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{+33}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-87}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-111}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-36}:\\ \;\;\;\;x - \frac{z \cdot a}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 66.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -7.8 \cdot 10^{+33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-87}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-155}:\\ \;\;\;\;\frac{\left(t - a\right) + x \cdot \frac{y}{z}}{b}\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-35}:\\ \;\;\;\;x - \frac{z \cdot a}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -7.8e+33)
     t_1
     (if (<= z -1.8e-87)
       (/ x (- 1.0 z))
       (if (<= z -1.4e-155)
         (/ (+ (- t a) (* x (/ y z))) b)
         (if (<= z 2.4e-35) (- x (/ (* z a) y)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -7.8e+33) {
		tmp = t_1;
	} else if (z <= -1.8e-87) {
		tmp = x / (1.0 - z);
	} else if (z <= -1.4e-155) {
		tmp = ((t - a) + (x * (y / z))) / b;
	} else if (z <= 2.4e-35) {
		tmp = x - ((z * a) / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    if (z <= (-7.8d+33)) then
        tmp = t_1
    else if (z <= (-1.8d-87)) then
        tmp = x / (1.0d0 - z)
    else if (z <= (-1.4d-155)) then
        tmp = ((t - a) + (x * (y / z))) / b
    else if (z <= 2.4d-35) then
        tmp = x - ((z * a) / y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -7.8e+33) {
		tmp = t_1;
	} else if (z <= -1.8e-87) {
		tmp = x / (1.0 - z);
	} else if (z <= -1.4e-155) {
		tmp = ((t - a) + (x * (y / z))) / b;
	} else if (z <= 2.4e-35) {
		tmp = x - ((z * a) / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	tmp = 0
	if z <= -7.8e+33:
		tmp = t_1
	elif z <= -1.8e-87:
		tmp = x / (1.0 - z)
	elif z <= -1.4e-155:
		tmp = ((t - a) + (x * (y / z))) / b
	elif z <= 2.4e-35:
		tmp = x - ((z * a) / y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -7.8e+33)
		tmp = t_1;
	elseif (z <= -1.8e-87)
		tmp = Float64(x / Float64(1.0 - z));
	elseif (z <= -1.4e-155)
		tmp = Float64(Float64(Float64(t - a) + Float64(x * Float64(y / z))) / b);
	elseif (z <= 2.4e-35)
		tmp = Float64(x - Float64(Float64(z * a) / y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -7.8e+33)
		tmp = t_1;
	elseif (z <= -1.8e-87)
		tmp = x / (1.0 - z);
	elseif (z <= -1.4e-155)
		tmp = ((t - a) + (x * (y / z))) / b;
	elseif (z <= 2.4e-35)
		tmp = x - ((z * a) / y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.8e+33], t$95$1, If[LessEqual[z, -1.8e-87], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.4e-155], N[(N[(N[(t - a), $MachinePrecision] + N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[z, 2.4e-35], N[(x - N[(N[(z * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -7.8000000000000004e33 or 2.4000000000000001e-35 < z

   1. Initial program 47.9%

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

   3. Taylor expanded in z around inf 78.2%

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

   if -7.8000000000000004e33 < z < -1.79999999999999996e-87

   1. Initial program 77.2%

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

   3. Taylor expanded in y around inf 51.4%

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

      1. mul-1-neg 51.4%

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

      2. unsub-neg 51.4%

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

   5. Simplified 51.4%

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

   if -1.79999999999999996e-87 < z < -1.4e-155

   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 z around -inf 54.6%

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

      1. associate--l+ 54.6%

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

      2. mul-1-neg 54.6%

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

      3. distribute-lft-out-- 54.6%

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

      4. associate-/l* 54.6%

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

      5. associate-/l* 43.2%

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

      6. div-sub 49.1%

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

   5. Simplified 49.1%

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

   6. Taylor expanded in x around inf 66.4%

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

      1. associate-*r/ 66.4%

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

      2. associate-*r* 66.4%

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

      3. times-frac 60.9%

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

      4. mul-1-neg 60.9%

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

   8. Simplified 60.9%

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

   9. Taylor expanded in b around inf 65.9%

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

       1. mul-1-neg 65.9%

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

       2. associate--r+ 65.9%

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

       3. associate-*l/ 65.8%

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

       4. distribute-lft-neg-in 65.8%

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

       5. cancel-sign-sub 65.8%

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

       6. associate-*l/ 65.9%

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

       7. associate-/l* 65.9%

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

   11. Simplified 65.9%

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

   if -1.4e-155 < z < 2.4000000000000001e-35

   1. Initial program 89.0%

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

   3. Taylor expanded in z around 0 58.0%

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

   4. Taylor expanded in a around inf 65.6%

      \[\leadsto x + \color{blue}{-1 \cdot \frac{a \cdot z}{y}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 70.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{+33}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-87}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-155}:\\ \;\;\;\;\frac{\left(t - a\right) + x \cdot \frac{y}{z}}{b}\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-35}:\\ \;\;\;\;x - \frac{z \cdot a}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 68.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -0.03:\\ \;\;\;\;t\_1 - \frac{x}{z}\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-85}:\\ \;\;\;\;x + z \cdot \frac{t}{y}\\ \mathbf{elif}\;z \leq -1.32 \cdot 10^{-164}:\\ \;\;\;\;\frac{\left(t - a\right) + x \cdot \frac{y}{z}}{b}\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-35}:\\ \;\;\;\;x - \frac{z \cdot a}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -0.03)
     (- t_1 (/ x z))
     (if (<= z -3.5e-85)
       (+ x (* z (/ t y)))
       (if (<= z -1.32e-164)
         (/ (+ (- t a) (* x (/ y z))) b)
         (if (<= z 1.75e-35) (- x (/ (* z a) y)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -0.03) {
		tmp = t_1 - (x / z);
	} else if (z <= -3.5e-85) {
		tmp = x + (z * (t / y));
	} else if (z <= -1.32e-164) {
		tmp = ((t - a) + (x * (y / z))) / b;
	} else if (z <= 1.75e-35) {
		tmp = x - ((z * a) / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    if (z <= (-0.03d0)) then
        tmp = t_1 - (x / z)
    else if (z <= (-3.5d-85)) then
        tmp = x + (z * (t / y))
    else if (z <= (-1.32d-164)) then
        tmp = ((t - a) + (x * (y / z))) / b
    else if (z <= 1.75d-35) then
        tmp = x - ((z * a) / y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -0.03) {
		tmp = t_1 - (x / z);
	} else if (z <= -3.5e-85) {
		tmp = x + (z * (t / y));
	} else if (z <= -1.32e-164) {
		tmp = ((t - a) + (x * (y / z))) / b;
	} else if (z <= 1.75e-35) {
		tmp = x - ((z * a) / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	tmp = 0
	if z <= -0.03:
		tmp = t_1 - (x / z)
	elif z <= -3.5e-85:
		tmp = x + (z * (t / y))
	elif z <= -1.32e-164:
		tmp = ((t - a) + (x * (y / z))) / b
	elif z <= 1.75e-35:
		tmp = x - ((z * a) / y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -0.03)
		tmp = Float64(t_1 - Float64(x / z));
	elseif (z <= -3.5e-85)
		tmp = Float64(x + Float64(z * Float64(t / y)));
	elseif (z <= -1.32e-164)
		tmp = Float64(Float64(Float64(t - a) + Float64(x * Float64(y / z))) / b);
	elseif (z <= 1.75e-35)
		tmp = Float64(x - Float64(Float64(z * a) / y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -0.03)
		tmp = t_1 - (x / z);
	elseif (z <= -3.5e-85)
		tmp = x + (z * (t / y));
	elseif (z <= -1.32e-164)
		tmp = ((t - a) + (x * (y / z))) / b;
	elseif (z <= 1.75e-35)
		tmp = x - ((z * a) / y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.03], N[(t$95$1 - N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.5e-85], N[(x + N[(z * N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.32e-164], N[(N[(N[(t - a), $MachinePrecision] + N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[z, 1.75e-35], N[(x - N[(N[(z * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -0.029999999999999999

   1. Initial program 37.7%

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

   3. Taylor expanded in z around -inf 54.1%

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

      1. associate--l+ 54.1%

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

      2. mul-1-neg 54.1%

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

      3. distribute-lft-out-- 54.1%

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

      4. associate-/l* 61.8%

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

      5. associate-/l* 86.6%

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

      6. div-sub 86.6%

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

   5. Simplified 86.6%

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

   6. Taylor expanded in y around inf 74.8%

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

   if -0.029999999999999999 < z < -3.49999999999999978e-85

   1. Initial program 80.0%

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

   3. Taylor expanded in z around 0 42.9%

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

   4. Taylor expanded in t around inf 60.4%

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

   if -3.49999999999999978e-85 < z < -1.3199999999999999e-164

   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 z around -inf 53.8%

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

      1. associate--l+ 53.8%

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

      2. mul-1-neg 53.8%

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

      3. distribute-lft-out-- 53.8%

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

      4. associate-/l* 53.7%

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

      5. associate-/l* 44.5%

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

      6. div-sub 49.2%

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

   5. Simplified 49.2%

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

   6. Taylor expanded in x around inf 63.3%

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

      1. associate-*r/ 63.3%

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

      2. associate-*r* 63.3%

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

      3. times-frac 54.5%

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

      4. mul-1-neg 54.5%

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

   8. Simplified 54.5%

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

   9. Taylor expanded in b around inf 62.9%

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

       1. mul-1-neg 62.9%

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

       2. associate--r+ 62.9%

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

       3. associate-*l/ 58.2%

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

       4. distribute-lft-neg-in 58.2%

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

       5. cancel-sign-sub 58.2%

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

       6. associate-*l/ 62.9%

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

       7. associate-/l* 62.9%

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

   11. Simplified 62.9%

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

   if -1.3199999999999999e-164 < z < 1.74999999999999998e-35

   1. Initial program 88.4%

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

   3. Taylor expanded in z around 0 59.6%

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

   4. Taylor expanded in a around inf 66.3%

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

   if 1.74999999999999998e-35 < z

   1. Initial program 57.3%

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

   3. Taylor expanded in z around inf 78.1%

      \[\leadsto \color{blue}{\frac{t - a}{b - y}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 71.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.03:\\ \;\;\;\;\frac{t - a}{b - y} - \frac{x}{z}\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-85}:\\ \;\;\;\;x + z \cdot \frac{t}{y}\\ \mathbf{elif}\;z \leq -1.32 \cdot 10^{-164}:\\ \;\;\;\;\frac{\left(t - a\right) + x \cdot \frac{y}{z}}{b}\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-35}:\\ \;\;\;\;x - \frac{z \cdot a}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 93.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -56000000000 \lor \neg \left(z \leq 1000000000\right):\\ \;\;\;\;\frac{y}{b - y} \cdot \frac{x}{z} + \frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -56000000000.0) (not (<= z 1000000000.0)))
   (+ (* (/ y (- b y)) (/ x z)) (/ (- t a) (- b y)))
   (/ (+ (* z (- t a)) (* x y)) (+ y (* z (- b y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -56000000000.0) || !(z <= 1000000000.0)) {
		tmp = ((y / (b - y)) * (x / z)) + ((t - a) / (b - y));
	} else {
		tmp = ((z * (t - a)) + (x * y)) / (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 <= (-56000000000.0d0)) .or. (.not. (z <= 1000000000.0d0))) then
        tmp = ((y / (b - y)) * (x / z)) + ((t - a) / (b - y))
    else
        tmp = ((z * (t - a)) + (x * y)) / (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 <= -56000000000.0) || !(z <= 1000000000.0)) {
		tmp = ((y / (b - y)) * (x / z)) + ((t - a) / (b - y));
	} else {
		tmp = ((z * (t - a)) + (x * y)) / (y + (z * (b - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -56000000000.0) or not (z <= 1000000000.0):
		tmp = ((y / (b - y)) * (x / z)) + ((t - a) / (b - y))
	else:
		tmp = ((z * (t - a)) + (x * y)) / (y + (z * (b - y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -56000000000.0) || !(z <= 1000000000.0))
		tmp = Float64(Float64(Float64(y / Float64(b - y)) * Float64(x / z)) + Float64(Float64(t - a) / Float64(b - y)));
	else
		tmp = Float64(Float64(Float64(z * Float64(t - a)) + Float64(x * y)) / 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 <= -56000000000.0) || ~((z <= 1000000000.0)))
		tmp = ((y / (b - y)) * (x / z)) + ((t - a) / (b - y));
	else
		tmp = ((z * (t - a)) + (x * y)) / (y + (z * (b - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -56000000000.0], N[Not[LessEqual[z, 1000000000.0]], $MachinePrecision]], N[(N[(N[(y / N[(b - y), $MachinePrecision]), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision] + N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.6e10 or 1e9 < z

   1. Initial program 44.8%

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

   3. Taylor expanded in z around -inf 63.8%

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

      1. associate--l+ 63.8%

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

      2. mul-1-neg 63.8%

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

      3. distribute-lft-out-- 63.8%

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

      4. associate-/l* 70.3%

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

      5. associate-/l* 89.8%

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

      6. div-sub 90.5%

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

   5. Simplified 90.5%

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

   6. Taylor expanded in x around inf 82.4%

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

      1. associate-*r/ 82.4%

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

      2. associate-*r* 82.4%

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

      3. times-frac 99.7%

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

      4. mul-1-neg 99.7%

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

   8. Simplified 99.7%

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

   if -5.6e10 < z < 1e9

   1. Initial program 87.9%

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

4. Final simplification 93.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -56000000000 \lor \neg \left(z \leq 1000000000\right):\\ \;\;\;\;\frac{y}{b - y} \cdot \frac{x}{z} + \frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 44.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a}{-b}\\ t_2 := \frac{t}{b - y}\\ \mathbf{if}\;z \leq -1.6 \cdot 10^{+85}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -6.4 \cdot 10^{-27}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{-20}:\\ \;\;\;\;x + z \cdot x\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+42}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ a (- b))) (t_2 (/ t (- b y))))
   (if (<= z -1.6e+85)
     t_2
     (if (<= z -6.4e-27)
       t_1
       (if (<= z 6.6e-20) (+ x (* z x)) (if (<= z 2.5e+42) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a / -b;
	double t_2 = t / (b - y);
	double tmp;
	if (z <= -1.6e+85) {
		tmp = t_2;
	} else if (z <= -6.4e-27) {
		tmp = t_1;
	} else if (z <= 6.6e-20) {
		tmp = x + (z * x);
	} else if (z <= 2.5e+42) {
		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 = a / -b
    t_2 = t / (b - y)
    if (z <= (-1.6d+85)) then
        tmp = t_2
    else if (z <= (-6.4d-27)) then
        tmp = t_1
    else if (z <= 6.6d-20) then
        tmp = x + (z * x)
    else if (z <= 2.5d+42) 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 = a / -b;
	double t_2 = t / (b - y);
	double tmp;
	if (z <= -1.6e+85) {
		tmp = t_2;
	} else if (z <= -6.4e-27) {
		tmp = t_1;
	} else if (z <= 6.6e-20) {
		tmp = x + (z * x);
	} else if (z <= 2.5e+42) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a / -b
	t_2 = t / (b - y)
	tmp = 0
	if z <= -1.6e+85:
		tmp = t_2
	elif z <= -6.4e-27:
		tmp = t_1
	elif z <= 6.6e-20:
		tmp = x + (z * x)
	elif z <= 2.5e+42:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a / Float64(-b))
	t_2 = Float64(t / Float64(b - y))
	tmp = 0.0
	if (z <= -1.6e+85)
		tmp = t_2;
	elseif (z <= -6.4e-27)
		tmp = t_1;
	elseif (z <= 6.6e-20)
		tmp = Float64(x + Float64(z * x));
	elseif (z <= 2.5e+42)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a / -b;
	t_2 = t / (b - y);
	tmp = 0.0;
	if (z <= -1.6e+85)
		tmp = t_2;
	elseif (z <= -6.4e-27)
		tmp = t_1;
	elseif (z <= 6.6e-20)
		tmp = x + (z * x);
	elseif (z <= 2.5e+42)
		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[(a / (-b)), $MachinePrecision]}, Block[{t$95$2 = N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.6e+85], t$95$2, If[LessEqual[z, -6.4e-27], t$95$1, If[LessEqual[z, 6.6e-20], N[(x + N[(z * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.5e+42], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.60000000000000009e85 or 2.50000000000000003e42 < z

   1. Initial program 39.9%

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

   3. Taylor expanded in t around inf 19.9%

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

      1. *-commutative 19.9%

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

   5. Simplified 19.9%

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

   6. Taylor expanded in z around inf 41.3%

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

   if -1.60000000000000009e85 < z < -6.39999999999999982e-27 or 6.6e-20 < z < 2.50000000000000003e42

   1. Initial program 78.1%

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

   3. Taylor expanded in b around inf 52.2%

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

   4. Taylor expanded in a around inf 38.1%

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

      1. associate-*r/ 38.1%

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

      2. neg-mul-1 38.1%

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

   6. Simplified 38.1%

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

   if -6.39999999999999982e-27 < z < 6.6e-20

   1. Initial program 89.4%

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

   3. Taylor expanded in z around 0 53.5%

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

   4. Taylor expanded in y around inf 49.4%

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

      1. *-commutative 49.4%

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

   6. Simplified 49.4%

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

4. Final simplification 44.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+85}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;z \leq -6.4 \cdot 10^{-27}:\\ \;\;\;\;\frac{a}{-b}\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{-20}:\\ \;\;\;\;x + z \cdot x\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+42}:\\ \;\;\;\;\frac{a}{-b}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 36.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a}{-b}\\ \mathbf{if}\;z \leq -5.7 \cdot 10^{+141}:\\ \;\;\;\;\frac{a}{y}\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-27}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-20}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{+163}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ a (- b))))
   (if (<= z -5.7e+141)
     (/ a y)
     (if (<= z -6.2e-27)
       t_1
       (if (<= z 9.5e-20) x (if (<= z 5.4e+163) t_1 (/ t b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a / -b;
	double tmp;
	if (z <= -5.7e+141) {
		tmp = a / y;
	} else if (z <= -6.2e-27) {
		tmp = t_1;
	} else if (z <= 9.5e-20) {
		tmp = x;
	} else if (z <= 5.4e+163) {
		tmp = t_1;
	} else {
		tmp = t / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a / -b
    if (z <= (-5.7d+141)) then
        tmp = a / y
    else if (z <= (-6.2d-27)) then
        tmp = t_1
    else if (z <= 9.5d-20) then
        tmp = x
    else if (z <= 5.4d+163) then
        tmp = t_1
    else
        tmp = t / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a / -b;
	double tmp;
	if (z <= -5.7e+141) {
		tmp = a / y;
	} else if (z <= -6.2e-27) {
		tmp = t_1;
	} else if (z <= 9.5e-20) {
		tmp = x;
	} else if (z <= 5.4e+163) {
		tmp = t_1;
	} else {
		tmp = t / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a / -b
	tmp = 0
	if z <= -5.7e+141:
		tmp = a / y
	elif z <= -6.2e-27:
		tmp = t_1
	elif z <= 9.5e-20:
		tmp = x
	elif z <= 5.4e+163:
		tmp = t_1
	else:
		tmp = t / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a / Float64(-b))
	tmp = 0.0
	if (z <= -5.7e+141)
		tmp = Float64(a / y);
	elseif (z <= -6.2e-27)
		tmp = t_1;
	elseif (z <= 9.5e-20)
		tmp = x;
	elseif (z <= 5.4e+163)
		tmp = t_1;
	else
		tmp = Float64(t / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a / -b;
	tmp = 0.0;
	if (z <= -5.7e+141)
		tmp = a / y;
	elseif (z <= -6.2e-27)
		tmp = t_1;
	elseif (z <= 9.5e-20)
		tmp = x;
	elseif (z <= 5.4e+163)
		tmp = t_1;
	else
		tmp = t / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a / (-b)), $MachinePrecision]}, If[LessEqual[z, -5.7e+141], N[(a / y), $MachinePrecision], If[LessEqual[z, -6.2e-27], t$95$1, If[LessEqual[z, 9.5e-20], x, If[LessEqual[z, 5.4e+163], t$95$1, N[(t / b), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.69999999999999998e141

   1. Initial program 25.9%

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

   3. Taylor expanded in z around inf 87.4%

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

   4. Taylor expanded in b around 0 47.5%

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

      1. associate-*r/ 47.5%

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

      2. mul-1-neg 47.5%

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

   6. Simplified 47.5%

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

   7. Taylor expanded in t around 0 38.4%

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

   if -5.69999999999999998e141 < z < -6.1999999999999997e-27 or 9.5e-20 < z < 5.39999999999999998e163

   1. Initial program 63.4%

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

   3. Taylor expanded in b around inf 41.7%

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

   4. Taylor expanded in a around inf 31.9%

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

      1. associate-*r/ 31.9%

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

      2. neg-mul-1 31.9%

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

   6. Simplified 31.9%

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

   if -6.1999999999999997e-27 < z < 9.5e-20

   1. Initial program 89.4%

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

   3. Taylor expanded in z around 0 49.4%

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

   if 5.39999999999999998e163 < z

   1. Initial program 41.3%

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

   3. Taylor expanded in t around inf 23.8%

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

      1. *-commutative 23.8%

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

   5. Simplified 23.8%

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

   6. Taylor expanded in y around 0 35.0%

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

4. Final simplification 40.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.7 \cdot 10^{+141}:\\ \;\;\;\;\frac{a}{y}\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-27}:\\ \;\;\;\;\frac{a}{-b}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-20}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{+163}:\\ \;\;\;\;\frac{a}{-b}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 36.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a}{-b}\\ \mathbf{if}\;z \leq -8.5 \cdot 10^{+141}:\\ \;\;\;\;\frac{a}{y}\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-27}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.85 \cdot 10^{-21}:\\ \;\;\;\;x + z \cdot x\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+161}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ a (- b))))
   (if (<= z -8.5e+141)
     (/ a y)
     (if (<= z -6.2e-27)
       t_1
       (if (<= z 2.85e-21) (+ x (* z x)) (if (<= z 1.6e+161) t_1 (/ t b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a / -b;
	double tmp;
	if (z <= -8.5e+141) {
		tmp = a / y;
	} else if (z <= -6.2e-27) {
		tmp = t_1;
	} else if (z <= 2.85e-21) {
		tmp = x + (z * x);
	} else if (z <= 1.6e+161) {
		tmp = t_1;
	} else {
		tmp = t / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a / -b
    if (z <= (-8.5d+141)) then
        tmp = a / y
    else if (z <= (-6.2d-27)) then
        tmp = t_1
    else if (z <= 2.85d-21) then
        tmp = x + (z * x)
    else if (z <= 1.6d+161) then
        tmp = t_1
    else
        tmp = t / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a / -b;
	double tmp;
	if (z <= -8.5e+141) {
		tmp = a / y;
	} else if (z <= -6.2e-27) {
		tmp = t_1;
	} else if (z <= 2.85e-21) {
		tmp = x + (z * x);
	} else if (z <= 1.6e+161) {
		tmp = t_1;
	} else {
		tmp = t / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a / -b
	tmp = 0
	if z <= -8.5e+141:
		tmp = a / y
	elif z <= -6.2e-27:
		tmp = t_1
	elif z <= 2.85e-21:
		tmp = x + (z * x)
	elif z <= 1.6e+161:
		tmp = t_1
	else:
		tmp = t / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a / Float64(-b))
	tmp = 0.0
	if (z <= -8.5e+141)
		tmp = Float64(a / y);
	elseif (z <= -6.2e-27)
		tmp = t_1;
	elseif (z <= 2.85e-21)
		tmp = Float64(x + Float64(z * x));
	elseif (z <= 1.6e+161)
		tmp = t_1;
	else
		tmp = Float64(t / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a / -b;
	tmp = 0.0;
	if (z <= -8.5e+141)
		tmp = a / y;
	elseif (z <= -6.2e-27)
		tmp = t_1;
	elseif (z <= 2.85e-21)
		tmp = x + (z * x);
	elseif (z <= 1.6e+161)
		tmp = t_1;
	else
		tmp = t / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a / (-b)), $MachinePrecision]}, If[LessEqual[z, -8.5e+141], N[(a / y), $MachinePrecision], If[LessEqual[z, -6.2e-27], t$95$1, If[LessEqual[z, 2.85e-21], N[(x + N[(z * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.6e+161], t$95$1, N[(t / b), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -8.4999999999999996e141

   1. Initial program 25.9%

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

   3. Taylor expanded in z around inf 87.4%

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

   4. Taylor expanded in b around 0 47.5%

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

      1. associate-*r/ 47.5%

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

      2. mul-1-neg 47.5%

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

   6. Simplified 47.5%

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

   7. Taylor expanded in t around 0 38.4%

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

   if -8.4999999999999996e141 < z < -6.1999999999999997e-27 or 2.8499999999999998e-21 < z < 1.60000000000000001e161

   1. Initial program 63.4%

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

   3. Taylor expanded in b around inf 41.7%

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

   4. Taylor expanded in a around inf 31.9%

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

      1. associate-*r/ 31.9%

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

      2. neg-mul-1 31.9%

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

   6. Simplified 31.9%

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

   if -6.1999999999999997e-27 < z < 2.8499999999999998e-21

   1. Initial program 89.4%

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

   3. Taylor expanded in z around 0 53.5%

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

   4. Taylor expanded in y around inf 49.4%

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

      1. *-commutative 49.4%

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

   6. Simplified 49.4%

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

   if 1.60000000000000001e161 < z

   1. Initial program 41.3%

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

   3. Taylor expanded in t around inf 23.8%

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

      1. *-commutative 23.8%

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

   5. Simplified 23.8%

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

   6. Taylor expanded in y around 0 35.0%

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

4. Final simplification 40.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+141}:\\ \;\;\;\;\frac{a}{y}\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-27}:\\ \;\;\;\;\frac{a}{-b}\\ \mathbf{elif}\;z \leq 2.85 \cdot 10^{-21}:\\ \;\;\;\;x + z \cdot x\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+161}:\\ \;\;\;\;\frac{a}{-b}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 35.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -18:\\ \;\;\;\;\frac{a}{y}\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{-11}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.7 \cdot 10^{+94}:\\ \;\;\;\;\frac{t}{-y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -18.0)
   (/ a y)
   (if (<= z 2.45e-11) x (if (<= z 5.7e+94) (/ t (- y)) (/ t b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -18.0) {
		tmp = a / y;
	} else if (z <= 2.45e-11) {
		tmp = x;
	} else if (z <= 5.7e+94) {
		tmp = t / -y;
	} else {
		tmp = t / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-18.0d0)) then
        tmp = a / y
    else if (z <= 2.45d-11) then
        tmp = x
    else if (z <= 5.7d+94) then
        tmp = t / -y
    else
        tmp = t / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -18.0) {
		tmp = a / y;
	} else if (z <= 2.45e-11) {
		tmp = x;
	} else if (z <= 5.7e+94) {
		tmp = t / -y;
	} else {
		tmp = t / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -18.0:
		tmp = a / y
	elif z <= 2.45e-11:
		tmp = x
	elif z <= 5.7e+94:
		tmp = t / -y
	else:
		tmp = t / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -18.0)
		tmp = Float64(a / y);
	elseif (z <= 2.45e-11)
		tmp = x;
	elseif (z <= 5.7e+94)
		tmp = Float64(t / Float64(-y));
	else
		tmp = Float64(t / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -18.0)
		tmp = a / y;
	elseif (z <= 2.45e-11)
		tmp = x;
	elseif (z <= 5.7e+94)
		tmp = t / -y;
	else
		tmp = t / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -18.0], N[(a / y), $MachinePrecision], If[LessEqual[z, 2.45e-11], x, If[LessEqual[z, 5.7e+94], N[(t / (-y)), $MachinePrecision], N[(t / b), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -18

   1. Initial program 38.2%

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

   3. Taylor expanded in z around inf 72.7%

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

   4. Taylor expanded in b around 0 33.1%

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

      1. associate-*r/ 33.1%

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

      2. mul-1-neg 33.1%

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

   6. Simplified 33.1%

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

   7. Taylor expanded in t around 0 26.2%

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

   if -18 < z < 2.4499999999999999e-11

   1. Initial program 87.1%

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

   3. Taylor expanded in z around 0 47.5%

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

   if 2.4499999999999999e-11 < z < 5.7000000000000002e94

   1. Initial program 86.2%

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

   3. Taylor expanded in z around inf 65.0%

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

   4. Taylor expanded in b around 0 34.7%

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

      1. associate-*r/ 34.7%

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

      2. mul-1-neg 34.7%

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

   6. Simplified 34.7%

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

   7. Taylor expanded in t around inf 26.2%

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

      1. mul-1-neg 26.2%

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

      2. distribute-neg-frac2 26.2%

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

   9. Simplified 26.2%

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

   if 5.7000000000000002e94 < z

   1. Initial program 43.4%

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

   3. Taylor expanded in t around inf 23.6%

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

      1. *-commutative 23.6%

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

   5. Simplified 23.6%

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

   6. Taylor expanded in y around 0 31.6%

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

4. Final simplification 37.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -18:\\ \;\;\;\;\frac{a}{y}\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{-11}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.7 \cdot 10^{+94}:\\ \;\;\;\;\frac{t}{-y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 53.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+57} \lor \neg \left(y \leq 2.5 \cdot 10^{-77}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -3.8e+57) (not (<= y 2.5e-77))) (/ 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 <= -3.8e+57) || !(y <= 2.5e-77)) {
		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 <= (-3.8d+57)) .or. (.not. (y <= 2.5d-77))) 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 <= -3.8e+57) || !(y <= 2.5e-77)) {
		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 <= -3.8e+57) or not (y <= 2.5e-77):
		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 <= -3.8e+57) || !(y <= 2.5e-77))
		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 <= -3.8e+57) || ~((y <= 2.5e-77)))
		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, -3.8e+57], N[Not[LessEqual[y, 2.5e-77]], $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 < -3.7999999999999999e57 or 2.49999999999999982e-77 < y

   1. Initial program 51.1%

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

   3. Taylor expanded in y around inf 52.4%

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

      1. mul-1-neg 52.4%

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

      2. unsub-neg 52.4%

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

   5. Simplified 52.4%

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

   if -3.7999999999999999e57 < y < 2.49999999999999982e-77

   1. Initial program 83.0%

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

   3. Taylor expanded in y around 0 62.4%

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

4. Final simplification 57.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+57} \lor \neg \left(y \leq 2.5 \cdot 10^{-77}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 35.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -16 \lor \neg \left(z \leq 580\right):\\ \;\;\;\;\frac{a}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -16.0) (not (<= z 580.0))) (/ a y) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -16.0) || !(z <= 580.0)) {
		tmp = a / y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-16.0d0)) .or. (.not. (z <= 580.0d0))) then
        tmp = a / y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -16.0) || !(z <= 580.0)) {
		tmp = a / y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -16.0) or not (z <= 580.0):
		tmp = a / y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -16.0) || !(z <= 580.0))
		tmp = Float64(a / y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -16.0) || ~((z <= 580.0)))
		tmp = a / y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -16.0], N[Not[LessEqual[z, 580.0]], $MachinePrecision]], N[(a / y), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -16 or 580 < z

   1. Initial program 46.0%

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

   3. Taylor expanded in z around inf 76.5%

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

   4. Taylor expanded in b around 0 34.9%

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

      1. associate-*r/ 34.9%

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

      2. mul-1-neg 34.9%

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

   6. Simplified 34.9%

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

   7. Taylor expanded in t around 0 23.2%

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

   if -16 < z < 580

   1. Initial program 87.6%

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

   3. Taylor expanded in z around 0 45.8%

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

4. Final simplification 34.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -16 \lor \neg \left(z \leq 580\right):\\ \;\;\;\;\frac{a}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 34.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+53}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-87}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -7e+53) x (if (<= y 3e-87) (/ t b) x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -7e+53) {
		tmp = x;
	} else if (y <= 3e-87) {
		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 <= (-7d+53)) then
        tmp = x
    else if (y <= 3d-87) 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 <= -7e+53) {
		tmp = x;
	} else if (y <= 3e-87) {
		tmp = t / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -7e+53:
		tmp = x
	elif y <= 3e-87:
		tmp = t / b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -7e+53)
		tmp = x;
	elseif (y <= 3e-87)
		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 <= -7e+53)
		tmp = x;
	elseif (y <= 3e-87)
		tmp = t / b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -7e+53], x, If[LessEqual[y, 3e-87], N[(t / b), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -7.00000000000000038e53 or 3.00000000000000016e-87 < y

   1. Initial program 51.4%

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

   3. Taylor expanded in z around 0 37.7%

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

   if -7.00000000000000038e53 < y < 3.00000000000000016e-87

   1. Initial program 82.9%

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

   3. Taylor expanded in t around inf 33.0%

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

      1. *-commutative 33.0%

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

   5. Simplified 33.0%

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

   6. Taylor expanded in y around 0 33.3%

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

4. Final simplification 35.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+53}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-87}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 26.0% 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 66.2%

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

3. Taylor expanded in z around 0 23.8%

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

4. Final simplification 23.8%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 73.2% 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 2024082 
(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)))))