Development.Shake.Progress:decay from shake-0.15.5

Percentage Accurate: 65.8% → 86.5%

Time: 26.2s

Alternatives: 20

Speedup: 0.7×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 65.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 86.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -880000000000 \lor \neg \left(z \leq 1.22 \cdot 10^{+62}\right):\\ \;\;\;\;\left(\frac{\frac{x}{z} \cdot y}{b - y} + \frac{t - a}{b - y}\right) - y \cdot \frac{\frac{t - a}{{\left(b - y\right)}^{2}}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, z \cdot \left(t - a\right)\right)}{\mathsf{fma}\left(z, b - y, y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -880000000000.0) (not (<= z 1.22e+62)))
   (-
    (+ (/ (* (/ x z) y) (- b y)) (/ (- t a) (- b y)))
    (* y (/ (/ (- t a) (pow (- b y) 2.0)) z)))
   (/ (fma x y (* z (- t a))) (fma z (- b y) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -880000000000.0) || !(z <= 1.22e+62)) {
		tmp = ((((x / z) * y) / (b - y)) + ((t - a) / (b - y))) - (y * (((t - a) / pow((b - y), 2.0)) / z));
	} else {
		tmp = fma(x, y, (z * (t - a))) / fma(z, (b - y), y);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -880000000000.0) || !(z <= 1.22e+62))
		tmp = Float64(Float64(Float64(Float64(Float64(x / z) * y) / Float64(b - y)) + Float64(Float64(t - a) / Float64(b - y))) - Float64(y * Float64(Float64(Float64(t - a) / (Float64(b - y) ^ 2.0)) / z)));
	else
		tmp = Float64(fma(x, y, Float64(z * Float64(t - a))) / fma(z, Float64(b - y), y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -880000000000.0], N[Not[LessEqual[z, 1.22e+62]], $MachinePrecision]], N[(N[(N[(N[(N[(x / z), $MachinePrecision] * y), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision] + N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * N[(N[(N[(t - a), $MachinePrecision] / N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * y + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * N[(b - y), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.8e11 or 1.21999999999999998e62 < z

   1. Initial program 43.0%

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

   3. Taylor expanded in z around inf 66.7%

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

      1. associate--r+ 66.7%

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

      2. +-commutative 66.7%

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

      3. associate--l+ 66.7%

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

      4. times-frac 77.9%

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

      5. associate-*r/ 74.4%

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

      6. div-sub 75.3%

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

      7. associate-/l* 90.8%

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

      8. *-commutative 90.8%

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

      9. associate-/r* 89.0%

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

   5. Simplified 89.0%

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

   if -8.8e11 < z < 1.21999999999999998e62

   1. Initial program 89.6%

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

      1. fma-define 89.6%

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

      2. +-commutative 89.6%

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

      3. fma-define 89.6%

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

   3. Simplified 89.6%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -880000000000 \lor \neg \left(z \leq 1.22 \cdot 10^{+62}\right):\\ \;\;\;\;\left(\frac{\frac{x}{z} \cdot y}{b - y} + \frac{t - a}{b - y}\right) - y \cdot \frac{\frac{t - a}{{\left(b - y\right)}^{2}}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, z \cdot \left(t - a\right)\right)}{\mathsf{fma}\left(z, b - y, y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 86.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -250000000000 \lor \neg \left(z \leq 1.55 \cdot 10^{+62}\right):\\ \;\;\;\;\left(\frac{\frac{x}{z} \cdot y}{b - y} + \frac{t - a}{b - y}\right) - y \cdot \frac{\frac{t - a}{{\left(b - y\right)}^{2}}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -250000000000.0) (not (<= z 1.55e+62)))
   (-
    (+ (/ (* (/ x z) y) (- b y)) (/ (- t a) (- b y)))
    (* y (/ (/ (- t a) (pow (- b y) 2.0)) z)))
   (/ (+ (* 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 <= -250000000000.0) || !(z <= 1.55e+62)) {
		tmp = ((((x / z) * y) / (b - y)) + ((t - a) / (b - y))) - (y * (((t - a) / pow((b - y), 2.0)) / z));
	} 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 <= (-250000000000.0d0)) .or. (.not. (z <= 1.55d+62))) then
        tmp = ((((x / z) * y) / (b - y)) + ((t - a) / (b - y))) - (y * (((t - a) / ((b - y) ** 2.0d0)) / z))
    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 <= -250000000000.0) || !(z <= 1.55e+62)) {
		tmp = ((((x / z) * y) / (b - y)) + ((t - a) / (b - y))) - (y * (((t - a) / Math.pow((b - y), 2.0)) / z));
	} 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 <= -250000000000.0) or not (z <= 1.55e+62):
		tmp = ((((x / z) * y) / (b - y)) + ((t - a) / (b - y))) - (y * (((t - a) / math.pow((b - y), 2.0)) / z))
	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 <= -250000000000.0) || !(z <= 1.55e+62))
		tmp = Float64(Float64(Float64(Float64(Float64(x / z) * y) / Float64(b - y)) + Float64(Float64(t - a) / Float64(b - y))) - Float64(y * Float64(Float64(Float64(t - a) / (Float64(b - y) ^ 2.0)) / z)));
	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 <= -250000000000.0) || ~((z <= 1.55e+62)))
		tmp = ((((x / z) * y) / (b - y)) + ((t - a) / (b - y))) - (y * (((t - a) / ((b - y) ^ 2.0)) / z));
	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, -250000000000.0], N[Not[LessEqual[z, 1.55e+62]], $MachinePrecision]], N[(N[(N[(N[(N[(x / z), $MachinePrecision] * y), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision] + N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * N[(N[(N[(t - a), $MachinePrecision] / N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] / z), $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 < -2.5e11 or 1.55000000000000007e62 < z

   1. Initial program 43.0%

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

   3. Taylor expanded in z around inf 66.7%

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

      1. associate--r+ 66.7%

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

      2. +-commutative 66.7%

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

      3. associate--l+ 66.7%

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

      4. times-frac 77.9%

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

      5. associate-*r/ 74.4%

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

      6. div-sub 75.3%

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

      7. associate-/l* 90.8%

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

      8. *-commutative 90.8%

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

      9. associate-/r* 89.0%

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

   5. Simplified 89.0%

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

   if -2.5e11 < z < 1.55000000000000007e62

   1. Initial program 89.6%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -250000000000 \lor \neg \left(z \leq 1.55 \cdot 10^{+62}\right):\\ \;\;\;\;\left(\frac{\frac{x}{z} \cdot y}{b - y} + \frac{t - a}{b - y}\right) - y \cdot \frac{\frac{t - a}{{\left(b - y\right)}^{2}}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 84.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ \mathbf{if}\;z \leq -2.05 \cdot 10^{+30} \lor \neg \left(z \leq 8 \cdot 10^{+77}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot a}{z \cdot \left(y - b\right) - y} + \left(\frac{z \cdot t}{t\_1} + \frac{x \cdot y}{t\_1}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y)))))
   (if (or (<= z -2.05e+30) (not (<= z 8e+77)))
     (/ (- t a) (- b y))
     (+ (/ (* z a) (- (* z (- y b)) y)) (+ (/ (* z t) t_1) (/ (* x y) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double tmp;
	if ((z <= -2.05e+30) || !(z <= 8e+77)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((z * a) / ((z * (y - b)) - y)) + (((z * t) / t_1) + ((x * y) / t_1));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y + (z * (b - y))
    if ((z <= (-2.05d+30)) .or. (.not. (z <= 8d+77))) then
        tmp = (t - a) / (b - y)
    else
        tmp = ((z * a) / ((z * (y - b)) - y)) + (((z * t) / t_1) + ((x * y) / t_1))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double tmp;
	if ((z <= -2.05e+30) || !(z <= 8e+77)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((z * a) / ((z * (y - b)) - y)) + (((z * t) / t_1) + ((x * y) / t_1));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z * (b - y))
	tmp = 0
	if (z <= -2.05e+30) or not (z <= 8e+77):
		tmp = (t - a) / (b - y)
	else:
		tmp = ((z * a) / ((z * (y - b)) - y)) + (((z * t) / t_1) + ((x * y) / t_1))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(z * Float64(b - y)))
	tmp = 0.0
	if ((z <= -2.05e+30) || !(z <= 8e+77))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(Float64(Float64(z * a) / Float64(Float64(z * Float64(y - b)) - y)) + Float64(Float64(Float64(z * t) / t_1) + Float64(Float64(x * y) / t_1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (z * (b - y));
	tmp = 0.0;
	if ((z <= -2.05e+30) || ~((z <= 8e+77)))
		tmp = (t - a) / (b - y);
	else
		tmp = ((z * a) / ((z * (y - b)) - y)) + (((z * t) / t_1) + ((x * y) / t_1));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[z, -2.05e+30], N[Not[LessEqual[z, 8e+77]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z * a), $MachinePrecision] / N[(N[(z * N[(y - b), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(z * t), $MachinePrecision] / t$95$1), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.05000000000000003e30 or 7.99999999999999986e77 < z

   1. Initial program 39.8%

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

   3. Taylor expanded in z around inf 79.5%

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

   if -2.05000000000000003e30 < z < 7.99999999999999986e77

   1. Initial program 88.9%

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

   3. Taylor expanded in t around 0 89.0%

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

4. Final simplification 85.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.05 \cdot 10^{+30} \lor \neg \left(z \leq 8 \cdot 10^{+77}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot a}{z \cdot \left(y - b\right) - y} + \left(\frac{z \cdot t}{y + z \cdot \left(b - y\right)} + \frac{x \cdot y}{y + z \cdot \left(b - y\right)}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 65.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - z \cdot \frac{a}{y}\\ t_2 := \frac{t - a}{b - y}\\ t_3 := \frac{x \cdot y}{y + z \cdot b}\\ \mathbf{if}\;z \leq -3.8 \cdot 10^{-47}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -4.7 \cdot 10^{-288}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-268}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-128}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-46} \lor \neg \left(z \leq 0.00046\right):\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- x (* z (/ a y))))
        (t_2 (/ (- t a) (- b y)))
        (t_3 (/ (* x y) (+ y (* z b)))))
   (if (<= z -3.8e-47)
     t_2
     (if (<= z -4.7e-288)
       t_1
       (if (<= z 4.4e-268)
         t_3
         (if (<= z 2.5e-128)
           t_1
           (if (or (<= z 2.4e-46) (not (<= z 0.00046))) t_2 t_3)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - (z * (a / y));
	double t_2 = (t - a) / (b - y);
	double t_3 = (x * y) / (y + (z * b));
	double tmp;
	if (z <= -3.8e-47) {
		tmp = t_2;
	} else if (z <= -4.7e-288) {
		tmp = t_1;
	} else if (z <= 4.4e-268) {
		tmp = t_3;
	} else if (z <= 2.5e-128) {
		tmp = t_1;
	} else if ((z <= 2.4e-46) || !(z <= 0.00046)) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x - (z * (a / y))
    t_2 = (t - a) / (b - y)
    t_3 = (x * y) / (y + (z * b))
    if (z <= (-3.8d-47)) then
        tmp = t_2
    else if (z <= (-4.7d-288)) then
        tmp = t_1
    else if (z <= 4.4d-268) then
        tmp = t_3
    else if (z <= 2.5d-128) then
        tmp = t_1
    else if ((z <= 2.4d-46) .or. (.not. (z <= 0.00046d0))) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - (z * (a / y));
	double t_2 = (t - a) / (b - y);
	double t_3 = (x * y) / (y + (z * b));
	double tmp;
	if (z <= -3.8e-47) {
		tmp = t_2;
	} else if (z <= -4.7e-288) {
		tmp = t_1;
	} else if (z <= 4.4e-268) {
		tmp = t_3;
	} else if (z <= 2.5e-128) {
		tmp = t_1;
	} else if ((z <= 2.4e-46) || !(z <= 0.00046)) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x - (z * (a / y))
	t_2 = (t - a) / (b - y)
	t_3 = (x * y) / (y + (z * b))
	tmp = 0
	if z <= -3.8e-47:
		tmp = t_2
	elif z <= -4.7e-288:
		tmp = t_1
	elif z <= 4.4e-268:
		tmp = t_3
	elif z <= 2.5e-128:
		tmp = t_1
	elif (z <= 2.4e-46) or not (z <= 0.00046):
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x - Float64(z * Float64(a / y)))
	t_2 = Float64(Float64(t - a) / Float64(b - y))
	t_3 = Float64(Float64(x * y) / Float64(y + Float64(z * b)))
	tmp = 0.0
	if (z <= -3.8e-47)
		tmp = t_2;
	elseif (z <= -4.7e-288)
		tmp = t_1;
	elseif (z <= 4.4e-268)
		tmp = t_3;
	elseif (z <= 2.5e-128)
		tmp = t_1;
	elseif ((z <= 2.4e-46) || !(z <= 0.00046))
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x - (z * (a / y));
	t_2 = (t - a) / (b - y);
	t_3 = (x * y) / (y + (z * b));
	tmp = 0.0;
	if (z <= -3.8e-47)
		tmp = t_2;
	elseif (z <= -4.7e-288)
		tmp = t_1;
	elseif (z <= 4.4e-268)
		tmp = t_3;
	elseif (z <= 2.5e-128)
		tmp = t_1;
	elseif ((z <= 2.4e-46) || ~((z <= 0.00046)))
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x - N[(z * N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * y), $MachinePrecision] / N[(y + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.8e-47], t$95$2, If[LessEqual[z, -4.7e-288], t$95$1, If[LessEqual[z, 4.4e-268], t$95$3, If[LessEqual[z, 2.5e-128], t$95$1, If[Or[LessEqual[z, 2.4e-46], N[Not[LessEqual[z, 0.00046]], $MachinePrecision]], t$95$2, t$95$3]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.80000000000000015e-47 or 2.5000000000000001e-128 < z < 2.40000000000000013e-46 or 4.6000000000000001e-4 < z

   1. Initial program 56.3%

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

   3. Taylor expanded in z around inf 73.7%

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

   if -3.80000000000000015e-47 < z < -4.6999999999999999e-288 or 4.40000000000000008e-268 < z < 2.5000000000000001e-128

   1. Initial program 85.0%

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

   3. Taylor expanded in z around 0 52.7%

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

   4. Taylor expanded in a around inf 67.4%

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

      1. associate-*r/ 67.4%

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

      2. neg-mul-1 67.4%

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

   6. Simplified 67.4%

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

   if -4.6999999999999999e-288 < z < 4.40000000000000008e-268 or 2.40000000000000013e-46 < z < 4.6000000000000001e-4

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 73.3%

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

      1. *-commutative 73.3%

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

   5. Simplified 73.3%

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

   6. Taylor expanded in b around inf 73.3%

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

      1. *-commutative 73.3%

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

   8. Simplified 73.3%

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

4. Final simplification 71.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{-47}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -4.7 \cdot 10^{-288}:\\ \;\;\;\;x - z \cdot \frac{a}{y}\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-268}:\\ \;\;\;\;\frac{x \cdot y}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-128}:\\ \;\;\;\;x - z \cdot \frac{a}{y}\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-46} \lor \neg \left(z \leq 0.00046\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{y + z \cdot b}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 65.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - z \cdot \frac{a}{y}\\ t_2 := \frac{t - a}{b - y}\\ t_3 := \frac{x \cdot y}{y + z \cdot b}\\ \mathbf{if}\;z \leq -1.85 \cdot 10^{-50}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-288}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{-268}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-112}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-49}:\\ \;\;\;\;\frac{z \cdot a}{\left(-y\right) - z \cdot b}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-8}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- x (* z (/ a y))))
        (t_2 (/ (- t a) (- b y)))
        (t_3 (/ (* x y) (+ y (* z b)))))
   (if (<= z -1.85e-50)
     t_2
     (if (<= z -1.2e-288)
       t_1
       (if (<= z 4.1e-268)
         t_3
         (if (<= z 3.4e-112)
           t_1
           (if (<= z 9.2e-49)
             (/ (* z a) (- (- y) (* z b)))
             (if (<= z 6.2e-8) t_3 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - (z * (a / y));
	double t_2 = (t - a) / (b - y);
	double t_3 = (x * y) / (y + (z * b));
	double tmp;
	if (z <= -1.85e-50) {
		tmp = t_2;
	} else if (z <= -1.2e-288) {
		tmp = t_1;
	} else if (z <= 4.1e-268) {
		tmp = t_3;
	} else if (z <= 3.4e-112) {
		tmp = t_1;
	} else if (z <= 9.2e-49) {
		tmp = (z * a) / (-y - (z * b));
	} else if (z <= 6.2e-8) {
		tmp = t_3;
	} 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) :: t_3
    real(8) :: tmp
    t_1 = x - (z * (a / y))
    t_2 = (t - a) / (b - y)
    t_3 = (x * y) / (y + (z * b))
    if (z <= (-1.85d-50)) then
        tmp = t_2
    else if (z <= (-1.2d-288)) then
        tmp = t_1
    else if (z <= 4.1d-268) then
        tmp = t_3
    else if (z <= 3.4d-112) then
        tmp = t_1
    else if (z <= 9.2d-49) then
        tmp = (z * a) / (-y - (z * b))
    else if (z <= 6.2d-8) then
        tmp = t_3
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - (z * (a / y));
	double t_2 = (t - a) / (b - y);
	double t_3 = (x * y) / (y + (z * b));
	double tmp;
	if (z <= -1.85e-50) {
		tmp = t_2;
	} else if (z <= -1.2e-288) {
		tmp = t_1;
	} else if (z <= 4.1e-268) {
		tmp = t_3;
	} else if (z <= 3.4e-112) {
		tmp = t_1;
	} else if (z <= 9.2e-49) {
		tmp = (z * a) / (-y - (z * b));
	} else if (z <= 6.2e-8) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x - (z * (a / y))
	t_2 = (t - a) / (b - y)
	t_3 = (x * y) / (y + (z * b))
	tmp = 0
	if z <= -1.85e-50:
		tmp = t_2
	elif z <= -1.2e-288:
		tmp = t_1
	elif z <= 4.1e-268:
		tmp = t_3
	elif z <= 3.4e-112:
		tmp = t_1
	elif z <= 9.2e-49:
		tmp = (z * a) / (-y - (z * b))
	elif z <= 6.2e-8:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x - Float64(z * Float64(a / y)))
	t_2 = Float64(Float64(t - a) / Float64(b - y))
	t_3 = Float64(Float64(x * y) / Float64(y + Float64(z * b)))
	tmp = 0.0
	if (z <= -1.85e-50)
		tmp = t_2;
	elseif (z <= -1.2e-288)
		tmp = t_1;
	elseif (z <= 4.1e-268)
		tmp = t_3;
	elseif (z <= 3.4e-112)
		tmp = t_1;
	elseif (z <= 9.2e-49)
		tmp = Float64(Float64(z * a) / Float64(Float64(-y) - Float64(z * b)));
	elseif (z <= 6.2e-8)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x - (z * (a / y));
	t_2 = (t - a) / (b - y);
	t_3 = (x * y) / (y + (z * b));
	tmp = 0.0;
	if (z <= -1.85e-50)
		tmp = t_2;
	elseif (z <= -1.2e-288)
		tmp = t_1;
	elseif (z <= 4.1e-268)
		tmp = t_3;
	elseif (z <= 3.4e-112)
		tmp = t_1;
	elseif (z <= 9.2e-49)
		tmp = (z * a) / (-y - (z * b));
	elseif (z <= 6.2e-8)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x - N[(z * N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * y), $MachinePrecision] / N[(y + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.85e-50], t$95$2, If[LessEqual[z, -1.2e-288], t$95$1, If[LessEqual[z, 4.1e-268], t$95$3, If[LessEqual[z, 3.4e-112], t$95$1, If[LessEqual[z, 9.2e-49], N[(N[(z * a), $MachinePrecision] / N[((-y) - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.2e-8], t$95$3, t$95$2]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.85e-50 or 6.2e-8 < z

   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 z around inf 76.7%

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

   if -1.85e-50 < z < -1.1999999999999999e-288 or 4.0999999999999999e-268 < z < 3.3999999999999998e-112

   1. Initial program 85.0%

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

   3. Taylor expanded in z around 0 50.2%

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

   4. Taylor expanded in a around inf 65.2%

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

      1. associate-*r/ 65.2%

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

      2. neg-mul-1 65.2%

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

   6. Simplified 65.2%

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

   if -1.1999999999999999e-288 < z < 4.0999999999999999e-268 or 9.1999999999999996e-49 < z < 6.2e-8

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 73.3%

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

      1. *-commutative 73.3%

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

   5. Simplified 73.3%

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

   6. Taylor expanded in b around inf 73.3%

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

      1. *-commutative 73.3%

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

   8. Simplified 73.3%

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

   if 3.3999999999999998e-112 < z < 9.1999999999999996e-49

   1. Initial program 91.9%

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

   3. Taylor expanded in a around inf 59.4%

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

      1. mul-1-neg 59.4%

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

      2. distribute-lft-neg-out 59.4%

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

      3. *-commutative 59.4%

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

   5. Simplified 59.4%

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

   6. Taylor expanded in b around inf 59.4%

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

      1. *-commutative 19.6%

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

   8. Simplified 59.4%

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

4. Final simplification 71.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{-50}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-288}:\\ \;\;\;\;x - z \cdot \frac{a}{y}\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{-268}:\\ \;\;\;\;\frac{x \cdot y}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-112}:\\ \;\;\;\;x - z \cdot \frac{a}{y}\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-49}:\\ \;\;\;\;\frac{z \cdot a}{\left(-y\right) - z \cdot b}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-8}:\\ \;\;\;\;\frac{x \cdot y}{y + z \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 71.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ t_2 := z \cdot \left(t - a\right)\\ \mathbf{if}\;z \leq -3.1 \cdot 10^{-12}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-128}:\\ \;\;\;\;x + a \cdot \frac{z}{z \cdot \left(y - b\right) - y}\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{-49}:\\ \;\;\;\;\frac{t\_2}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 58:\\ \;\;\;\;\frac{t\_2 + x \cdot y}{y \cdot \left(1 - z\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))) (t_2 (* z (- t a))))
   (if (<= z -3.1e-12)
     t_1
     (if (<= z 2.15e-128)
       (+ x (* a (/ z (- (* z (- y b)) y))))
       (if (<= z 7.6e-49)
         (/ t_2 (+ y (* z (- b y))))
         (if (<= z 58.0) (/ (+ t_2 (* x y)) (* y (- 1.0 z))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double t_2 = z * (t - a);
	double tmp;
	if (z <= -3.1e-12) {
		tmp = t_1;
	} else if (z <= 2.15e-128) {
		tmp = x + (a * (z / ((z * (y - b)) - y)));
	} else if (z <= 7.6e-49) {
		tmp = t_2 / (y + (z * (b - y)));
	} else if (z <= 58.0) {
		tmp = (t_2 + (x * y)) / (y * (1.0 - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    t_2 = z * (t - a)
    if (z <= (-3.1d-12)) then
        tmp = t_1
    else if (z <= 2.15d-128) then
        tmp = x + (a * (z / ((z * (y - b)) - y)))
    else if (z <= 7.6d-49) then
        tmp = t_2 / (y + (z * (b - y)))
    else if (z <= 58.0d0) then
        tmp = (t_2 + (x * y)) / (y * (1.0d0 - z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double t_2 = z * (t - a);
	double tmp;
	if (z <= -3.1e-12) {
		tmp = t_1;
	} else if (z <= 2.15e-128) {
		tmp = x + (a * (z / ((z * (y - b)) - y)));
	} else if (z <= 7.6e-49) {
		tmp = t_2 / (y + (z * (b - y)));
	} else if (z <= 58.0) {
		tmp = (t_2 + (x * y)) / (y * (1.0 - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	t_2 = z * (t - a)
	tmp = 0
	if z <= -3.1e-12:
		tmp = t_1
	elif z <= 2.15e-128:
		tmp = x + (a * (z / ((z * (y - b)) - y)))
	elif z <= 7.6e-49:
		tmp = t_2 / (y + (z * (b - y)))
	elif z <= 58.0:
		tmp = (t_2 + (x * y)) / (y * (1.0 - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	t_2 = Float64(z * Float64(t - a))
	tmp = 0.0
	if (z <= -3.1e-12)
		tmp = t_1;
	elseif (z <= 2.15e-128)
		tmp = Float64(x + Float64(a * Float64(z / Float64(Float64(z * Float64(y - b)) - y))));
	elseif (z <= 7.6e-49)
		tmp = Float64(t_2 / Float64(y + Float64(z * Float64(b - y))));
	elseif (z <= 58.0)
		tmp = Float64(Float64(t_2 + Float64(x * y)) / Float64(y * Float64(1.0 - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	t_2 = z * (t - a);
	tmp = 0.0;
	if (z <= -3.1e-12)
		tmp = t_1;
	elseif (z <= 2.15e-128)
		tmp = x + (a * (z / ((z * (y - b)) - y)));
	elseif (z <= 7.6e-49)
		tmp = t_2 / (y + (z * (b - y)));
	elseif (z <= 58.0)
		tmp = (t_2 + (x * y)) / (y * (1.0 - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.1e-12], t$95$1, If[LessEqual[z, 2.15e-128], N[(x + N[(a * N[(z / N[(N[(z * N[(y - b), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.6e-49], N[(t$95$2 / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 58.0], N[(N[(t$95$2 + N[(x * y), $MachinePrecision]), $MachinePrecision] / N[(y * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.1000000000000001e-12 or 58 < z

   1. Initial program 48.7%

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

   3. Taylor expanded in z around inf 79.4%

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

   if -3.1000000000000001e-12 < z < 2.14999999999999997e-128

   1. Initial program 89.1%

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

   3. Taylor expanded in x around 0 89.0%

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

   4. Taylor expanded in t around 0 89.1%

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

   5. Taylor expanded in z around 0 80.4%

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

   6. Taylor expanded in a around inf 70.2%

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

      1. mul-1-neg 70.2%

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

      2. associate-/l* 69.3%

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

      3. distribute-rgt-neg-in 69.3%

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

   8. Simplified 69.3%

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

   if 2.14999999999999997e-128 < z < 7.5999999999999994e-49

   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 x around 0 73.7%

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

   if 7.5999999999999994e-49 < z < 58

   1. Initial program 90.7%

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

   3. Taylor expanded in y around inf 71.3%

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

      1. mul-1-neg 71.3%

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

      2. unsub-neg 71.3%

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

   5. Simplified 71.3%

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

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{-12}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-128}:\\ \;\;\;\;x + a \cdot \frac{z}{z \cdot \left(y - b\right) - y}\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{-49}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 58:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y \cdot \left(1 - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 67.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y}{y + z \cdot \left(b - y\right)}\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -5.3 \cdot 10^{-52}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-107}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-50}:\\ \;\;\;\;\frac{z \cdot a}{\left(-y\right) - z \cdot b}\\ \mathbf{elif}\;z \leq 650:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (/ y (+ y (* z (- b y)))))) (t_2 (/ (- t a) (- b y))))
   (if (<= z -5.3e-52)
     t_2
     (if (<= z 2.5e-107)
       t_1
       (if (<= z 7e-50)
         (/ (* z a) (- (- y) (* z b)))
         (if (<= z 650.0) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * (y / (y + (z * (b - y))));
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -5.3e-52) {
		tmp = t_2;
	} else if (z <= 2.5e-107) {
		tmp = t_1;
	} else if (z <= 7e-50) {
		tmp = (z * a) / (-y - (z * b));
	} else if (z <= 650.0) {
		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 / (y + (z * (b - y))))
    t_2 = (t - a) / (b - y)
    if (z <= (-5.3d-52)) then
        tmp = t_2
    else if (z <= 2.5d-107) then
        tmp = t_1
    else if (z <= 7d-50) then
        tmp = (z * a) / (-y - (z * b))
    else if (z <= 650.0d0) 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 / (y + (z * (b - y))));
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -5.3e-52) {
		tmp = t_2;
	} else if (z <= 2.5e-107) {
		tmp = t_1;
	} else if (z <= 7e-50) {
		tmp = (z * a) / (-y - (z * b));
	} else if (z <= 650.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * (y / (y + (z * (b - y))))
	t_2 = (t - a) / (b - y)
	tmp = 0
	if z <= -5.3e-52:
		tmp = t_2
	elif z <= 2.5e-107:
		tmp = t_1
	elif z <= 7e-50:
		tmp = (z * a) / (-y - (z * b))
	elif z <= 650.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * Float64(y / Float64(y + Float64(z * Float64(b - y)))))
	t_2 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -5.3e-52)
		tmp = t_2;
	elseif (z <= 2.5e-107)
		tmp = t_1;
	elseif (z <= 7e-50)
		tmp = Float64(Float64(z * a) / Float64(Float64(-y) - Float64(z * b)));
	elseif (z <= 650.0)
		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 / (y + (z * (b - y))));
	t_2 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -5.3e-52)
		tmp = t_2;
	elseif (z <= 2.5e-107)
		tmp = t_1;
	elseif (z <= 7e-50)
		tmp = (z * a) / (-y - (z * b));
	elseif (z <= 650.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x * N[(y / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.3e-52], t$95$2, If[LessEqual[z, 2.5e-107], t$95$1, If[LessEqual[z, 7e-50], N[(N[(z * a), $MachinePrecision] / N[((-y) - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 650.0], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.3000000000000003e-52 or 650 < z

   1. Initial program 52.2%

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

   3. Taylor expanded in z around inf 77.2%

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

   if -5.3000000000000003e-52 < z < 2.49999999999999985e-107 or 6.99999999999999993e-50 < z < 650

   1. Initial program 88.2%

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

   3. Taylor expanded in x around inf 57.5%

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

      1. *-commutative 57.5%

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

   5. Simplified 57.5%

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

   6. Taylor expanded in x around 0 57.5%

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

      1. associate-/l* 67.4%

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

   8. Simplified 67.4%

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

   if 2.49999999999999985e-107 < z < 6.99999999999999993e-50

   1. Initial program 91.3%

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

   3. Taylor expanded in a around inf 64.4%

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

      1. mul-1-neg 64.4%

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

      2. distribute-lft-neg-out 64.4%

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

      3. *-commutative 64.4%

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

   5. Simplified 64.4%

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

   6. Taylor expanded in b around inf 64.4%

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

      1. *-commutative 12.4%

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

   8. Simplified 64.4%

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

4. Final simplification 72.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.3 \cdot 10^{-52}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-107}:\\ \;\;\;\;x \cdot \frac{y}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-50}:\\ \;\;\;\;\frac{z \cdot a}{\left(-y\right) - z \cdot b}\\ \mathbf{elif}\;z \leq 650:\\ \;\;\;\;x \cdot \frac{y}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 69.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := x \cdot \frac{y}{t\_1}\\ t_3 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -2.15 \cdot 10^{-47}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{-107}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-48}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{t\_1}\\ \mathbf{elif}\;z \leq 43000:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y))))
        (t_2 (* x (/ y t_1)))
        (t_3 (/ (- t a) (- b y))))
   (if (<= z -2.15e-47)
     t_3
     (if (<= z 2.35e-107)
       t_2
       (if (<= z 1.3e-48)
         (/ (* z (- t a)) t_1)
         (if (<= z 43000.0) t_2 t_3))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double t_2 = x * (y / t_1);
	double t_3 = (t - a) / (b - y);
	double tmp;
	if (z <= -2.15e-47) {
		tmp = t_3;
	} else if (z <= 2.35e-107) {
		tmp = t_2;
	} else if (z <= 1.3e-48) {
		tmp = (z * (t - a)) / t_1;
	} else if (z <= 43000.0) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = y + (z * (b - y))
    t_2 = x * (y / t_1)
    t_3 = (t - a) / (b - y)
    if (z <= (-2.15d-47)) then
        tmp = t_3
    else if (z <= 2.35d-107) then
        tmp = t_2
    else if (z <= 1.3d-48) then
        tmp = (z * (t - a)) / t_1
    else if (z <= 43000.0d0) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double t_2 = x * (y / t_1);
	double t_3 = (t - a) / (b - y);
	double tmp;
	if (z <= -2.15e-47) {
		tmp = t_3;
	} else if (z <= 2.35e-107) {
		tmp = t_2;
	} else if (z <= 1.3e-48) {
		tmp = (z * (t - a)) / t_1;
	} else if (z <= 43000.0) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z * (b - y))
	t_2 = x * (y / t_1)
	t_3 = (t - a) / (b - y)
	tmp = 0
	if z <= -2.15e-47:
		tmp = t_3
	elif z <= 2.35e-107:
		tmp = t_2
	elif z <= 1.3e-48:
		tmp = (z * (t - a)) / t_1
	elif z <= 43000.0:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(z * Float64(b - y)))
	t_2 = Float64(x * Float64(y / t_1))
	t_3 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -2.15e-47)
		tmp = t_3;
	elseif (z <= 2.35e-107)
		tmp = t_2;
	elseif (z <= 1.3e-48)
		tmp = Float64(Float64(z * Float64(t - a)) / t_1);
	elseif (z <= 43000.0)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (z * (b - y));
	t_2 = x * (y / t_1);
	t_3 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -2.15e-47)
		tmp = t_3;
	elseif (z <= 2.35e-107)
		tmp = t_2;
	elseif (z <= 1.3e-48)
		tmp = (z * (t - a)) / t_1;
	elseif (z <= 43000.0)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(y / t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.15e-47], t$95$3, If[LessEqual[z, 2.35e-107], t$95$2, If[LessEqual[z, 1.3e-48], N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[z, 43000.0], t$95$2, t$95$3]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.1499999999999999e-47 or 43000 < z

   1. Initial program 52.2%

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

   3. Taylor expanded in z around inf 77.2%

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

   if -2.1499999999999999e-47 < z < 2.34999999999999999e-107 or 1.29999999999999994e-48 < z < 43000

   1. Initial program 88.2%

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

   3. Taylor expanded in x around inf 57.5%

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

      1. *-commutative 57.5%

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

   5. Simplified 57.5%

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

   6. Taylor expanded in x around 0 57.5%

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

      1. associate-/l* 67.4%

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

   8. Simplified 67.4%

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

   if 2.34999999999999999e-107 < z < 1.29999999999999994e-48

   1. Initial program 91.3%

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

   3. Taylor expanded in x around 0 90.7%

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

4. Final simplification 73.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{-47}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{-107}:\\ \;\;\;\;x \cdot \frac{y}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-48}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 43000:\\ \;\;\;\;x \cdot \frac{y}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 71.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -3.3 \cdot 10^{-12}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-128}:\\ \;\;\;\;x + a \cdot \frac{z}{z \cdot \left(y - b\right) - y}\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{-46}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{t\_1}\\ \mathbf{elif}\;z \leq 2.1:\\ \;\;\;\;x \cdot \frac{y}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y)))) (t_2 (/ (- t a) (- b y))))
   (if (<= z -3.3e-12)
     t_2
     (if (<= z 1.95e-128)
       (+ x (* a (/ z (- (* z (- y b)) y))))
       (if (<= z 2.45e-46)
         (/ (* z (- t a)) t_1)
         (if (<= z 2.1) (* x (/ y t_1)) t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -3.3e-12) {
		tmp = t_2;
	} else if (z <= 1.95e-128) {
		tmp = x + (a * (z / ((z * (y - b)) - y)));
	} else if (z <= 2.45e-46) {
		tmp = (z * (t - a)) / t_1;
	} else if (z <= 2.1) {
		tmp = x * (y / t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y + (z * (b - y))
    t_2 = (t - a) / (b - y)
    if (z <= (-3.3d-12)) then
        tmp = t_2
    else if (z <= 1.95d-128) then
        tmp = x + (a * (z / ((z * (y - b)) - y)))
    else if (z <= 2.45d-46) then
        tmp = (z * (t - a)) / t_1
    else if (z <= 2.1d0) then
        tmp = x * (y / t_1)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -3.3e-12) {
		tmp = t_2;
	} else if (z <= 1.95e-128) {
		tmp = x + (a * (z / ((z * (y - b)) - y)));
	} else if (z <= 2.45e-46) {
		tmp = (z * (t - a)) / t_1;
	} else if (z <= 2.1) {
		tmp = x * (y / t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z * (b - y))
	t_2 = (t - a) / (b - y)
	tmp = 0
	if z <= -3.3e-12:
		tmp = t_2
	elif z <= 1.95e-128:
		tmp = x + (a * (z / ((z * (y - b)) - y)))
	elif z <= 2.45e-46:
		tmp = (z * (t - a)) / t_1
	elif z <= 2.1:
		tmp = x * (y / t_1)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(z * Float64(b - y)))
	t_2 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -3.3e-12)
		tmp = t_2;
	elseif (z <= 1.95e-128)
		tmp = Float64(x + Float64(a * Float64(z / Float64(Float64(z * Float64(y - b)) - y))));
	elseif (z <= 2.45e-46)
		tmp = Float64(Float64(z * Float64(t - a)) / t_1);
	elseif (z <= 2.1)
		tmp = Float64(x * Float64(y / t_1));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (z * (b - y));
	t_2 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -3.3e-12)
		tmp = t_2;
	elseif (z <= 1.95e-128)
		tmp = x + (a * (z / ((z * (y - b)) - y)));
	elseif (z <= 2.45e-46)
		tmp = (z * (t - a)) / t_1;
	elseif (z <= 2.1)
		tmp = x * (y / t_1);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.3e-12], t$95$2, If[LessEqual[z, 1.95e-128], N[(x + N[(a * N[(z / N[(N[(z * N[(y - b), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.45e-46], N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[z, 2.1], N[(x * N[(y / t$95$1), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.3000000000000001e-12 or 2.10000000000000009 < z

   1. Initial program 48.7%

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

   3. Taylor expanded in z around inf 79.4%

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

   if -3.3000000000000001e-12 < z < 1.94999999999999998e-128

   1. Initial program 89.1%

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

   3. Taylor expanded in x around 0 89.0%

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

   4. Taylor expanded in t around 0 89.1%

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

   5. Taylor expanded in z around 0 80.4%

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

   6. Taylor expanded in a around inf 70.2%

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

      1. mul-1-neg 70.2%

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

      2. associate-/l* 69.3%

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

      3. distribute-rgt-neg-in 69.3%

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

   8. Simplified 69.3%

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

   if 1.94999999999999998e-128 < z < 2.45e-46

   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 x around 0 73.7%

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

   if 2.45e-46 < z < 2.10000000000000009

   1. Initial program 90.7%

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

   3. Taylor expanded in x around inf 61.7%

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

      1. *-commutative 61.7%

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

   5. Simplified 61.7%

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

   6. Taylor expanded in x around 0 61.7%

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

      1. associate-/l* 70.4%

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

   8. Simplified 70.4%

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

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{-12}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-128}:\\ \;\;\;\;x + a \cdot \frac{z}{z \cdot \left(y - b\right) - y}\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{-46}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 2.1:\\ \;\;\;\;x \cdot \frac{y}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 54.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b}\\ t_2 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -50000000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{-31}:\\ \;\;\;\;\frac{a - t}{y}\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-52}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-7}:\\ \;\;\;\;x + z \cdot \frac{t}{y}\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+17}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) b)) (t_2 (/ x (- 1.0 z))))
   (if (<= y -50000000000.0)
     t_2
     (if (<= y -2.6e-31)
       (/ (- a t) y)
       (if (<= y 8.2e-52)
         t_1
         (if (<= y 3.2e-7)
           (+ x (* z (/ t y)))
           (if (<= y 2.8e+17) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / b;
	double t_2 = x / (1.0 - z);
	double tmp;
	if (y <= -50000000000.0) {
		tmp = t_2;
	} else if (y <= -2.6e-31) {
		tmp = (a - t) / y;
	} else if (y <= 8.2e-52) {
		tmp = t_1;
	} else if (y <= 3.2e-7) {
		tmp = x + (z * (t / y));
	} else if (y <= 2.8e+17) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (t - a) / b
    t_2 = x / (1.0d0 - z)
    if (y <= (-50000000000.0d0)) then
        tmp = t_2
    else if (y <= (-2.6d-31)) then
        tmp = (a - t) / y
    else if (y <= 8.2d-52) then
        tmp = t_1
    else if (y <= 3.2d-7) then
        tmp = x + (z * (t / y))
    else if (y <= 2.8d+17) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / b;
	double t_2 = x / (1.0 - z);
	double tmp;
	if (y <= -50000000000.0) {
		tmp = t_2;
	} else if (y <= -2.6e-31) {
		tmp = (a - t) / y;
	} else if (y <= 8.2e-52) {
		tmp = t_1;
	} else if (y <= 3.2e-7) {
		tmp = x + (z * (t / y));
	} else if (y <= 2.8e+17) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / b
	t_2 = x / (1.0 - z)
	tmp = 0
	if y <= -50000000000.0:
		tmp = t_2
	elif y <= -2.6e-31:
		tmp = (a - t) / y
	elif y <= 8.2e-52:
		tmp = t_1
	elif y <= 3.2e-7:
		tmp = x + (z * (t / y))
	elif y <= 2.8e+17:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / b)
	t_2 = Float64(x / Float64(1.0 - z))
	tmp = 0.0
	if (y <= -50000000000.0)
		tmp = t_2;
	elseif (y <= -2.6e-31)
		tmp = Float64(Float64(a - t) / y);
	elseif (y <= 8.2e-52)
		tmp = t_1;
	elseif (y <= 3.2e-7)
		tmp = Float64(x + Float64(z * Float64(t / y)));
	elseif (y <= 2.8e+17)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / b;
	t_2 = x / (1.0 - z);
	tmp = 0.0;
	if (y <= -50000000000.0)
		tmp = t_2;
	elseif (y <= -2.6e-31)
		tmp = (a - t) / y;
	elseif (y <= 8.2e-52)
		tmp = t_1;
	elseif (y <= 3.2e-7)
		tmp = x + (z * (t / y));
	elseif (y <= 2.8e+17)
		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[(t - a), $MachinePrecision] / b), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -50000000000.0], t$95$2, If[LessEqual[y, -2.6e-31], N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, 8.2e-52], t$95$1, If[LessEqual[y, 3.2e-7], N[(x + N[(z * N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.8e+17], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5e10 or 2.8e17 < y

   1. Initial program 56.5%

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

   3. Taylor expanded in y around inf 60.0%

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

      1. mul-1-neg 60.0%

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

      2. unsub-neg 60.0%

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

   5. Simplified 60.0%

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

   if -5e10 < y < -2.59999999999999995e-31

   1. Initial program 58.2%

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

   3. Taylor expanded in b around 0 48.3%

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

      1. +-commutative 48.3%

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

      2. fma-define 48.3%

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

      3. *-commutative 48.3%

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

      4. *-rgt-identity 48.3%

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

      5. mul-1-neg 48.3%

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

      6. distribute-rgt-neg-in 48.3%

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

      7. mul-1-neg 48.3%

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

      8. distribute-lft-in 48.3%

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

      9. mul-1-neg 48.3%

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

      10. unsub-neg 48.3%

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

   5. Simplified 48.3%

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

   6. Taylor expanded in z around inf 69.6%

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

      1. mul-1-neg 69.6%

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

      2. distribute-neg-frac2 69.6%

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

   8. Simplified 69.6%

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

   if -2.59999999999999995e-31 < y < 8.19999999999999977e-52 or 3.2000000000000001e-7 < y < 2.8e17

   1. Initial program 81.8%

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

   3. Taylor expanded in y around 0 66.7%

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

   if 8.19999999999999977e-52 < y < 3.2000000000000001e-7

   1. Initial program 90.4%

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

   3. Taylor expanded in z around 0 61.6%

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

   4. Taylor expanded in t around inf 80.5%

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

4. Final simplification 64.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -50000000000:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{-31}:\\ \;\;\;\;\frac{a - t}{y}\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-52}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-7}:\\ \;\;\;\;x + z \cdot \frac{t}{y}\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+17}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 66.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{-49} \lor \neg \left(z \leq 2.2 \cdot 10^{-128} \lor \neg \left(z \leq 3.7 \cdot 10^{-47}\right) \land z \leq 6.2 \cdot 10^{-8}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{a}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.45e-49)
         (not (or (<= z 2.2e-128) (and (not (<= z 3.7e-47)) (<= z 6.2e-8)))))
   (/ (- t a) (- b y))
   (- x (* z (/ a y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.45e-49) || !((z <= 2.2e-128) || (!(z <= 3.7e-47) && (z <= 6.2e-8)))) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x - (z * (a / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-1.45d-49)) .or. (.not. (z <= 2.2d-128) .or. (.not. (z <= 3.7d-47)) .and. (z <= 6.2d-8))) then
        tmp = (t - a) / (b - y)
    else
        tmp = x - (z * (a / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.45e-49) || !((z <= 2.2e-128) || (!(z <= 3.7e-47) && (z <= 6.2e-8)))) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x - (z * (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.45e-49) or not ((z <= 2.2e-128) or (not (z <= 3.7e-47) and (z <= 6.2e-8))):
		tmp = (t - a) / (b - y)
	else:
		tmp = x - (z * (a / y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.45e-49) || !((z <= 2.2e-128) || (!(z <= 3.7e-47) && (z <= 6.2e-8))))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(x - Float64(z * Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1.45e-49) || ~(((z <= 2.2e-128) || (~((z <= 3.7e-47)) && (z <= 6.2e-8)))))
		tmp = (t - a) / (b - y);
	else
		tmp = x - (z * (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.45e-49], N[Not[Or[LessEqual[z, 2.2e-128], And[N[Not[LessEqual[z, 3.7e-47]], $MachinePrecision], LessEqual[z, 6.2e-8]]]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x - N[(z * N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.45e-49 or 2.20000000000000009e-128 < z < 3.7e-47 or 6.2e-8 < z

   1. Initial program 56.3%

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

   3. Taylor expanded in z around inf 73.7%

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

   if -1.45e-49 < z < 2.20000000000000009e-128 or 3.7e-47 < z < 6.2e-8

   1. Initial program 89.1%

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

   3. Taylor expanded in z around 0 56.0%

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

   4. Taylor expanded in a around inf 64.5%

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

      1. associate-*r/ 64.5%

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

      2. neg-mul-1 64.5%

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

   6. Simplified 64.5%

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

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{-49} \lor \neg \left(z \leq 2.2 \cdot 10^{-128} \lor \neg \left(z \leq 3.7 \cdot 10^{-47}\right) \land z \leq 6.2 \cdot 10^{-8}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{a}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 66.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -1.56 \cdot 10^{-49}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-128}:\\ \;\;\;\;x + z \cdot \frac{t}{y}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-49} \lor \neg \left(z \leq 53\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -1.56e-49)
     t_1
     (if (<= z 2.5e-128)
       (+ x (* z (/ t y)))
       (if (or (<= z 7e-49) (not (<= z 53.0))) t_1 (/ x (- 1.0 z)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -1.56e-49) {
		tmp = t_1;
	} else if (z <= 2.5e-128) {
		tmp = x + (z * (t / y));
	} else if ((z <= 7e-49) || !(z <= 53.0)) {
		tmp = t_1;
	} else {
		tmp = x / (1.0 - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    if (z <= (-1.56d-49)) then
        tmp = t_1
    else if (z <= 2.5d-128) then
        tmp = x + (z * (t / y))
    else if ((z <= 7d-49) .or. (.not. (z <= 53.0d0))) then
        tmp = t_1
    else
        tmp = x / (1.0d0 - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -1.56e-49) {
		tmp = t_1;
	} else if (z <= 2.5e-128) {
		tmp = x + (z * (t / y));
	} else if ((z <= 7e-49) || !(z <= 53.0)) {
		tmp = t_1;
	} else {
		tmp = x / (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	tmp = 0
	if z <= -1.56e-49:
		tmp = t_1
	elif z <= 2.5e-128:
		tmp = x + (z * (t / y))
	elif (z <= 7e-49) or not (z <= 53.0):
		tmp = t_1
	else:
		tmp = x / (1.0 - z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -1.56e-49)
		tmp = t_1;
	elseif (z <= 2.5e-128)
		tmp = Float64(x + Float64(z * Float64(t / y)));
	elseif ((z <= 7e-49) || !(z <= 53.0))
		tmp = t_1;
	else
		tmp = Float64(x / Float64(1.0 - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -1.56e-49)
		tmp = t_1;
	elseif (z <= 2.5e-128)
		tmp = x + (z * (t / y));
	elseif ((z <= 7e-49) || ~((z <= 53.0)))
		tmp = t_1;
	else
		tmp = x / (1.0 - 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]}, If[LessEqual[z, -1.56e-49], t$95$1, If[LessEqual[z, 2.5e-128], N[(x + N[(z * N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 7e-49], N[Not[LessEqual[z, 53.0]], $MachinePrecision]], t$95$1, N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.56000000000000008e-49 or 2.5000000000000001e-128 < z < 7.00000000000000012e-49 or 53 < z

   1. Initial program 56.6%

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

   3. Taylor expanded in z around inf 74.2%

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

   if -1.56000000000000008e-49 < z < 2.5000000000000001e-128

   1. Initial program 88.1%

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

   3. Taylor expanded in z around 0 54.4%

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

   4. Taylor expanded in t around inf 61.3%

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

   if 7.00000000000000012e-49 < z < 53

   1. Initial program 90.7%

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

   3. Taylor expanded in y around inf 59.0%

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

      1. mul-1-neg 59.0%

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

      2. unsub-neg 59.0%

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

   5. Simplified 59.0%

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

4. Final simplification 68.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.56 \cdot 10^{-49}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-128}:\\ \;\;\;\;x + z \cdot \frac{t}{y}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-49} \lor \neg \left(z \leq 53\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 84.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+30} \lor \neg \left(z \leq 7.2 \cdot 10^{+77}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -3.6e+30) (not (<= z 7.2e+77)))
   (/ (- 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 <= -3.6e+30) || !(z <= 7.2e+77)) {
		tmp = (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 <= (-3.6d+30)) .or. (.not. (z <= 7.2d+77))) then
        tmp = (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 <= -3.6e+30) || !(z <= 7.2e+77)) {
		tmp = (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 <= -3.6e+30) or not (z <= 7.2e+77):
		tmp = (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 <= -3.6e+30) || !(z <= 7.2e+77))
		tmp = 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 <= -3.6e+30) || ~((z <= 7.2e+77)))
		tmp = (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, -3.6e+30], N[Not[LessEqual[z, 7.2e+77]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $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 < -3.6000000000000002e30 or 7.1999999999999996e77 < z

   1. Initial program 39.8%

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

   3. Taylor expanded in z around inf 79.5%

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

   if -3.6000000000000002e30 < z < 7.1999999999999996e77

   1. Initial program 88.9%

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

4. Final simplification 85.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+30} \lor \neg \left(z \leq 7.2 \cdot 10^{+77}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 73.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{-6} \lor \neg \left(z \leq 760000000000\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot a}{y + z \cdot \left(b - y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -3.2e-6) (not (<= z 760000000000.0)))
   (/ (- t a) (- b y))
   (/ (- (* x y) (* z a)) (+ y (* z (- b y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -3.2e-6) || !(z <= 760000000000.0)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((x * y) - (z * a)) / (y + (z * (b - y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-3.2d-6)) .or. (.not. (z <= 760000000000.0d0))) then
        tmp = (t - a) / (b - y)
    else
        tmp = ((x * y) - (z * a)) / (y + (z * (b - y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -3.2e-6) || !(z <= 760000000000.0)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((x * y) - (z * a)) / (y + (z * (b - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -3.2e-6) or not (z <= 760000000000.0):
		tmp = (t - a) / (b - y)
	else:
		tmp = ((x * y) - (z * a)) / (y + (z * (b - y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -3.2e-6) || !(z <= 760000000000.0))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(Float64(Float64(x * y) - Float64(z * a)) / Float64(y + Float64(z * Float64(b - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -3.2e-6) || ~((z <= 760000000000.0)))
		tmp = (t - a) / (b - y);
	else
		tmp = ((x * y) - (z * a)) / (y + (z * (b - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -3.2e-6], N[Not[LessEqual[z, 760000000000.0]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] - N[(z * a), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.1999999999999999e-6 or 7.6e11 < z

   1. Initial program 48.7%

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

   3. Taylor expanded in z around inf 79.4%

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

   if -3.1999999999999999e-6 < z < 7.6e11

   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 t around 0 70.9%

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

      1. +-commutative 70.9%

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

      2. mul-1-neg 70.9%

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

      3. unsub-neg 70.9%

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

      4. *-commutative 70.9%

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

      5. *-commutative 70.9%

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

   5. Simplified 70.9%

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

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{-6} \lor \neg \left(z \leq 760000000000\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot a}{y + z \cdot \left(b - y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 54.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -170000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-31}:\\ \;\;\;\;\frac{a - t}{y}\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-44}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (- 1.0 z))))
   (if (<= y -170000000.0)
     t_1
     (if (<= y -3e-31) (/ (- a t) y) (if (<= y 8e-44) (/ (- t a) b) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 - z);
	double tmp;
	if (y <= -170000000.0) {
		tmp = t_1;
	} else if (y <= -3e-31) {
		tmp = (a - t) / y;
	} else if (y <= 8e-44) {
		tmp = (t - a) / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (1.0d0 - z)
    if (y <= (-170000000.0d0)) then
        tmp = t_1
    else if (y <= (-3d-31)) then
        tmp = (a - t) / y
    else if (y <= 8d-44) then
        tmp = (t - a) / b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 - z);
	double tmp;
	if (y <= -170000000.0) {
		tmp = t_1;
	} else if (y <= -3e-31) {
		tmp = (a - t) / y;
	} else if (y <= 8e-44) {
		tmp = (t - a) / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (1.0 - z)
	tmp = 0
	if y <= -170000000.0:
		tmp = t_1
	elif y <= -3e-31:
		tmp = (a - t) / y
	elif y <= 8e-44:
		tmp = (t - a) / b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(1.0 - z))
	tmp = 0.0
	if (y <= -170000000.0)
		tmp = t_1;
	elseif (y <= -3e-31)
		tmp = Float64(Float64(a - t) / y);
	elseif (y <= 8e-44)
		tmp = Float64(Float64(t - a) / b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (1.0 - z);
	tmp = 0.0;
	if (y <= -170000000.0)
		tmp = t_1;
	elseif (y <= -3e-31)
		tmp = (a - t) / y;
	elseif (y <= 8e-44)
		tmp = (t - a) / b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -170000000.0], t$95$1, If[LessEqual[y, -3e-31], N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, 8e-44], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.7e8 or 7.99999999999999962e-44 < y

   1. Initial program 59.0%

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

   3. Taylor expanded in y around inf 58.4%

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

      1. mul-1-neg 58.4%

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

      2. unsub-neg 58.4%

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

   5. Simplified 58.4%

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

   if -1.7e8 < y < -2.99999999999999981e-31

   1. Initial program 58.2%

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

   3. Taylor expanded in b around 0 48.3%

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

      1. +-commutative 48.3%

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

      2. fma-define 48.3%

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

      3. *-commutative 48.3%

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

      4. *-rgt-identity 48.3%

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

      5. mul-1-neg 48.3%

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

      6. distribute-rgt-neg-in 48.3%

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

      7. mul-1-neg 48.3%

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

      8. distribute-lft-in 48.3%

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

      9. mul-1-neg 48.3%

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

      10. unsub-neg 48.3%

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

   5. Simplified 48.3%

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

   6. Taylor expanded in z around inf 69.6%

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

      1. mul-1-neg 69.6%

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

      2. distribute-neg-frac2 69.6%

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

   8. Simplified 69.6%

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

   if -2.99999999999999981e-31 < y < 7.99999999999999962e-44

   1. Initial program 82.3%

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

   3. Taylor expanded in y around 0 66.1%

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

4. Final simplification 62.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -170000000:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-31}:\\ \;\;\;\;\frac{a - t}{y}\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-44}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 42.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{-110} \lor \neg \left(y \leq 8.2 \cdot 10^{-45}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{-a}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -3.2e-110) (not (<= y 8.2e-45))) (/ x (- 1.0 z)) (/ (- a) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -3.2e-110) || !(y <= 8.2e-45)) {
		tmp = x / (1.0 - z);
	} else {
		tmp = -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 <= (-3.2d-110)) .or. (.not. (y <= 8.2d-45))) then
        tmp = x / (1.0d0 - z)
    else
        tmp = -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 <= -3.2e-110) || !(y <= 8.2e-45)) {
		tmp = x / (1.0 - z);
	} else {
		tmp = -a / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -3.2e-110) or not (y <= 8.2e-45):
		tmp = x / (1.0 - z)
	else:
		tmp = -a / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -3.2e-110) || !(y <= 8.2e-45))
		tmp = Float64(x / Float64(1.0 - z));
	else
		tmp = Float64(Float64(-a) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -3.2e-110) || ~((y <= 8.2e-45)))
		tmp = x / (1.0 - z);
	else
		tmp = -a / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -3.2e-110], N[Not[LessEqual[y, 8.2e-45]], $MachinePrecision]], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[((-a) / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.20000000000000028e-110 or 8.1999999999999998e-45 < y

   1. Initial program 60.3%

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

   3. Taylor expanded in y around inf 53.2%

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

      1. mul-1-neg 53.2%

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

      2. unsub-neg 53.2%

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

   5. Simplified 53.2%

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

   if -3.20000000000000028e-110 < y < 8.1999999999999998e-45

   1. Initial program 83.2%

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

   3. Taylor expanded in t around 0 48.8%

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

      1. +-commutative 48.8%

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

      2. mul-1-neg 48.8%

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

      3. unsub-neg 48.8%

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

      4. *-commutative 48.8%

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

      5. *-commutative 48.8%

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

   5. Simplified 48.8%

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

   6. Taylor expanded in y around 0 39.5%

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

      1. associate-*r/ 39.5%

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

      2. neg-mul-1 39.5%

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

   8. Simplified 39.5%

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

4. Final simplification 47.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{-110} \lor \neg \left(y \leq 8.2 \cdot 10^{-45}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{-a}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 54.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{-51} \lor \neg \left(y \leq 2.15 \cdot 10^{-44}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -8e-51) (not (<= y 2.15e-44))) (/ 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 <= -8e-51) || !(y <= 2.15e-44)) {
		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 <= (-8d-51)) .or. (.not. (y <= 2.15d-44))) 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 <= -8e-51) || !(y <= 2.15e-44)) {
		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 <= -8e-51) or not (y <= 2.15e-44):
		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 <= -8e-51) || !(y <= 2.15e-44))
		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 <= -8e-51) || ~((y <= 2.15e-44)))
		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, -8e-51], N[Not[LessEqual[y, 2.15e-44]], $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 < -8.0000000000000001e-51 or 2.15000000000000007e-44 < y

   1. Initial program 59.4%

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

   3. Taylor expanded in y around inf 55.4%

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

      1. mul-1-neg 55.4%

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

      2. unsub-neg 55.4%

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

   5. Simplified 55.4%

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

   if -8.0000000000000001e-51 < y < 2.15000000000000007e-44

   1. Initial program 82.6%

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

   3. Taylor expanded in y around 0 67.5%

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

4. Final simplification 60.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{-51} \lor \neg \left(y \leq 2.15 \cdot 10^{-44}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 34.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{-64}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-45}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -4.2e-64) x (if (<= y 3.2e-45) (/ (- a) b) x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -4.2e-64) {
		tmp = x;
	} else if (y <= 3.2e-45) {
		tmp = -a / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-4.2d-64)) then
        tmp = x
    else if (y <= 3.2d-45) then
        tmp = -a / b
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -4.2e-64) {
		tmp = x;
	} else if (y <= 3.2e-45) {
		tmp = -a / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -4.2e-64:
		tmp = x
	elif y <= 3.2e-45:
		tmp = -a / b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -4.2e-64)
		tmp = x;
	elseif (y <= 3.2e-45)
		tmp = Float64(Float64(-a) / b);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -4.2e-64)
		tmp = x;
	elseif (y <= 3.2e-45)
		tmp = -a / b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -4.2e-64], x, If[LessEqual[y, 3.2e-45], N[((-a) / b), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -4.20000000000000023e-64 or 3.20000000000000007e-45 < y

   1. Initial program 59.7%

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

   3. Taylor expanded in z around 0 42.1%

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

   if -4.20000000000000023e-64 < y < 3.20000000000000007e-45

   1. Initial program 82.5%

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

   3. Taylor expanded in t around 0 49.3%

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

      1. +-commutative 49.3%

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

      2. mul-1-neg 49.3%

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

      3. unsub-neg 49.3%

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

      4. *-commutative 49.3%

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

      5. *-commutative 49.3%

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

   5. Simplified 49.3%

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

   6. Taylor expanded in y around 0 38.0%

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

      1. associate-*r/ 38.0%

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

      2. neg-mul-1 38.0%

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

   8. Simplified 38.0%

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

4. Final simplification 40.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{-64}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-45}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 34.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{-6} \lor \neg \left(z \leq 1\right):\\ \;\;\;\;\frac{a}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -8.5e-6) (not (<= z 1.0))) (/ a y) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -8.5e-6) || !(z <= 1.0)) {
		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 <= (-8.5d-6)) .or. (.not. (z <= 1.0d0))) 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 <= -8.5e-6) || !(z <= 1.0)) {
		tmp = a / y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -8.5e-6) or not (z <= 1.0):
		tmp = a / y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -8.5e-6) || !(z <= 1.0))
		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 <= -8.5e-6) || ~((z <= 1.0)))
		tmp = a / y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -8.5e-6], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(a / y), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -8.4999999999999999e-6 or 1 < z

   1. Initial program 48.0%

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

   3. Taylor expanded in b around 0 25.2%

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

      1. +-commutative 25.2%

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

      2. fma-define 25.2%

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

      3. *-commutative 25.2%

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

      4. *-rgt-identity 25.2%

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

      5. mul-1-neg 25.2%

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

      6. distribute-rgt-neg-in 25.2%

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

      7. mul-1-neg 25.2%

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

      8. distribute-lft-in 25.2%

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

      9. mul-1-neg 25.2%

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

      10. unsub-neg 25.2%

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

   5. Simplified 25.2%

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

   6. Taylor expanded in z around inf 35.1%

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

      1. mul-1-neg 35.1%

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

      2. distribute-neg-frac2 35.1%

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

   8. Simplified 35.1%

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

   9. Taylor expanded in t around 0 17.0%

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

   if -8.4999999999999999e-6 < z < 1

   1. Initial program 89.9%

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

   3. Taylor expanded in z around 0 49.8%

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

4. Final simplification 34.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{-6} \lor \neg \left(z \leq 1\right):\\ \;\;\;\;\frac{a}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 25.0% 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 69.7%

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

3. Taylor expanded in z around 0 27.5%

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

4. Final simplification 27.5%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 73.4% 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 2024039 
(FPCore (x y z t a b)
  :name "Development.Shake.Progress:decay from shake-0.15.5"
  :precision binary64

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

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