Development.Shake.Progress:decay from shake-0.15.5

Percentage Accurate: 66.4% → 90.4%

Time: 27.0s

Alternatives: 17

Speedup: 1.1×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 66.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 90.4% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot {\left(b - y\right)}^{2}\\ \mathbf{if}\;z \leq -3.6 \cdot 10^{+34} \lor \neg \left(z \leq 0.00132\right):\\ \;\;\;\;\mathsf{fma}\left(t, \frac{1}{b - y} - \frac{y}{t_1}, \frac{x}{z} \cdot \frac{y}{b - y}\right) - \mathsf{fma}\left(-1, \frac{a}{\frac{t_1}{y}}, \frac{a}{b - y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y + z \cdot \left(b - y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (pow (- b y) 2.0))))
   (if (or (<= z -3.6e+34) (not (<= z 0.00132)))
     (-
      (fma t (- (/ 1.0 (- b y)) (/ y t_1)) (* (/ x z) (/ y (- b y))))
      (fma -1.0 (/ a (/ t_1 y)) (/ a (- b y))))
     (/ (+ (* z (- t a)) (* y x)) (+ y (* z (- b y)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * pow((b - y), 2.0);
	double tmp;
	if ((z <= -3.6e+34) || !(z <= 0.00132)) {
		tmp = fma(t, ((1.0 / (b - y)) - (y / t_1)), ((x / z) * (y / (b - y)))) - fma(-1.0, (a / (t_1 / y)), (a / (b - y)));
	} else {
		tmp = ((z * (t - a)) + (y * x)) / (y + (z * (b - y)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * (Float64(b - y) ^ 2.0))
	tmp = 0.0
	if ((z <= -3.6e+34) || !(z <= 0.00132))
		tmp = Float64(fma(t, Float64(Float64(1.0 / Float64(b - y)) - Float64(y / t_1)), Float64(Float64(x / z) * Float64(y / Float64(b - y)))) - fma(-1.0, Float64(a / Float64(t_1 / y)), Float64(a / Float64(b - y))));
	else
		tmp = Float64(Float64(Float64(z * Float64(t - a)) + Float64(y * x)) / Float64(y + Float64(z * Float64(b - y))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[z, -3.6e+34], N[Not[LessEqual[z, 0.00132]], $MachinePrecision]], N[(N[(t * N[(N[(1.0 / N[(b - y), $MachinePrecision]), $MachinePrecision] - N[(y / t$95$1), $MachinePrecision]), $MachinePrecision] + N[(N[(x / z), $MachinePrecision] * N[(y / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(-1.0 * N[(a / N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision] + N[(a / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] + N[(y * x), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.6e34 or 0.00132 < z

   1. Initial program 37.2%

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

   2. Taylor expanded in z around inf 66.9%

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

      1. associate--r+ 66.9%

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

      2. +-commutative 66.9%

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

      3. associate--l+ 66.9%

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

      4. *-commutative 66.9%

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

      5. times-frac 71.1%

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

      6. div-sub 71.1%

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

      7. *-commutative 71.1%

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

      8. times-frac 92.7%

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

   4. Simplified 92.7%

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

   5. Taylor expanded in t around 0 72.1%

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

      1. fma-def 72.1%

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

      2. times-frac 84.6%

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

      3. fma-def 84.6%

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

      4. associate-/l* 96.3%

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

   7. Simplified 96.3%

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

   if -3.6e34 < z < 0.00132

   1. Initial program 88.0%

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

4. Final simplification 91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+34} \lor \neg \left(z \leq 0.00132\right):\\ \;\;\;\;\mathsf{fma}\left(t, \frac{1}{b - y} - \frac{y}{z \cdot {\left(b - y\right)}^{2}}, \frac{x}{z} \cdot \frac{y}{b - y}\right) - \mathsf{fma}\left(-1, \frac{a}{\frac{z \cdot {\left(b - y\right)}^{2}}{y}}, \frac{a}{b - y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y + z \cdot \left(b - y\right)}\\ \end{array} \]

Alternative 2: 89.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -800000 \lor \neg \left(z \leq 0.00132\right):\\ \;\;\;\;\left(\frac{y}{z} \cdot \frac{x}{b - y} + \frac{t - a}{b - y}\right) + \frac{y}{{\left(b - y\right)}^{2}} \cdot \frac{a - t}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y + z \cdot \left(b - y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -800000.0) (not (<= z 0.00132)))
   (+
    (+ (* (/ y z) (/ x (- b y))) (/ (- t a) (- b y)))
    (* (/ y (pow (- b y) 2.0)) (/ (- a t) z)))
   (/ (+ (* z (- t a)) (* y x)) (+ y (* z (- b y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -800000.0) || !(z <= 0.00132)) {
		tmp = (((y / z) * (x / (b - y))) + ((t - a) / (b - y))) + ((y / pow((b - y), 2.0)) * ((a - t) / z));
	} else {
		tmp = ((z * (t - a)) + (y * x)) / (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 <= (-800000.0d0)) .or. (.not. (z <= 0.00132d0))) then
        tmp = (((y / z) * (x / (b - y))) + ((t - a) / (b - y))) + ((y / ((b - y) ** 2.0d0)) * ((a - t) / z))
    else
        tmp = ((z * (t - a)) + (y * x)) / (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 <= -800000.0) || !(z <= 0.00132)) {
		tmp = (((y / z) * (x / (b - y))) + ((t - a) / (b - y))) + ((y / Math.pow((b - y), 2.0)) * ((a - t) / z));
	} else {
		tmp = ((z * (t - a)) + (y * x)) / (y + (z * (b - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -800000.0) or not (z <= 0.00132):
		tmp = (((y / z) * (x / (b - y))) + ((t - a) / (b - y))) + ((y / math.pow((b - y), 2.0)) * ((a - t) / z))
	else:
		tmp = ((z * (t - a)) + (y * x)) / (y + (z * (b - y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -800000.0) || !(z <= 0.00132))
		tmp = Float64(Float64(Float64(Float64(y / z) * Float64(x / Float64(b - y))) + Float64(Float64(t - a) / Float64(b - y))) + Float64(Float64(y / (Float64(b - y) ^ 2.0)) * Float64(Float64(a - t) / z)));
	else
		tmp = Float64(Float64(Float64(z * Float64(t - a)) + Float64(y * x)) / 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 <= -800000.0) || ~((z <= 0.00132)))
		tmp = (((y / z) * (x / (b - y))) + ((t - a) / (b - y))) + ((y / ((b - y) ^ 2.0)) * ((a - t) / z));
	else
		tmp = ((z * (t - a)) + (y * x)) / (y + (z * (b - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -800000.0], N[Not[LessEqual[z, 0.00132]], $MachinePrecision]], N[(N[(N[(N[(y / z), $MachinePrecision] * N[(x / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y / N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] * N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] + N[(y * x), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8e5 or 0.00132 < z

   1. Initial program 40.9%

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

   2. Taylor expanded in z around inf 68.0%

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

      1. associate--r+ 68.0%

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

      2. +-commutative 68.0%

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

      3. associate--l+ 68.0%

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

      4. *-commutative 68.0%

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

      5. times-frac 72.0%

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

      6. div-sub 72.0%

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

      7. *-commutative 72.0%

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

      8. times-frac 93.1%

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

   4. Simplified 93.1%

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

   if -8e5 < z < 0.00132

   1. Initial program 87.4%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -800000 \lor \neg \left(z \leq 0.00132\right):\\ \;\;\;\;\left(\frac{y}{z} \cdot \frac{x}{b - y} + \frac{t - a}{b - y}\right) + \frac{y}{{\left(b - y\right)}^{2}} \cdot \frac{a - t}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y + z \cdot \left(b - y\right)}\\ \end{array} \]

Alternative 3: 69.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z}{\frac{y}{\left(t - a\right) - b \cdot x}}\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -1.02 \cdot 10^{-7}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-60}:\\ \;\;\;\;x - a \cdot \frac{z}{y}\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{-81}:\\ \;\;\;\;\frac{\left(t + \frac{y \cdot x}{z}\right) - a}{b}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-262}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{-185}:\\ \;\;\;\;\frac{y \cdot x}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-8}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (/ z (/ y (- (- t a) (* b x)))))) (t_2 (/ (- t a) (- b y))))
   (if (<= z -1.02e-7)
     t_2
     (if (<= z -5e-60)
       (- x (* a (/ z y)))
       (if (<= z -4.1e-81)
         (/ (- (+ t (/ (* y x) z)) a) b)
         (if (<= z 3.6e-262)
           t_1
           (if (<= z 7.8e-185)
             (/ (* y x) (+ y (* z (- b y))))
             (if (<= z 5.6e-8) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z / (y / ((t - a) - (b * x))));
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -1.02e-7) {
		tmp = t_2;
	} else if (z <= -5e-60) {
		tmp = x - (a * (z / y));
	} else if (z <= -4.1e-81) {
		tmp = ((t + ((y * x) / z)) - a) / b;
	} else if (z <= 3.6e-262) {
		tmp = t_1;
	} else if (z <= 7.8e-185) {
		tmp = (y * x) / (y + (z * (b - y)));
	} else if (z <= 5.6e-8) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (z / (y / ((t - a) - (b * x))))
    t_2 = (t - a) / (b - y)
    if (z <= (-1.02d-7)) then
        tmp = t_2
    else if (z <= (-5d-60)) then
        tmp = x - (a * (z / y))
    else if (z <= (-4.1d-81)) then
        tmp = ((t + ((y * x) / z)) - a) / b
    else if (z <= 3.6d-262) then
        tmp = t_1
    else if (z <= 7.8d-185) then
        tmp = (y * x) / (y + (z * (b - y)))
    else if (z <= 5.6d-8) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z / (y / ((t - a) - (b * x))));
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -1.02e-7) {
		tmp = t_2;
	} else if (z <= -5e-60) {
		tmp = x - (a * (z / y));
	} else if (z <= -4.1e-81) {
		tmp = ((t + ((y * x) / z)) - a) / b;
	} else if (z <= 3.6e-262) {
		tmp = t_1;
	} else if (z <= 7.8e-185) {
		tmp = (y * x) / (y + (z * (b - y)));
	} else if (z <= 5.6e-8) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (z / (y / ((t - a) - (b * x))))
	t_2 = (t - a) / (b - y)
	tmp = 0
	if z <= -1.02e-7:
		tmp = t_2
	elif z <= -5e-60:
		tmp = x - (a * (z / y))
	elif z <= -4.1e-81:
		tmp = ((t + ((y * x) / z)) - a) / b
	elif z <= 3.6e-262:
		tmp = t_1
	elif z <= 7.8e-185:
		tmp = (y * x) / (y + (z * (b - y)))
	elif z <= 5.6e-8:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(z / Float64(y / Float64(Float64(t - a) - Float64(b * x)))))
	t_2 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -1.02e-7)
		tmp = t_2;
	elseif (z <= -5e-60)
		tmp = Float64(x - Float64(a * Float64(z / y)));
	elseif (z <= -4.1e-81)
		tmp = Float64(Float64(Float64(t + Float64(Float64(y * x) / z)) - a) / b);
	elseif (z <= 3.6e-262)
		tmp = t_1;
	elseif (z <= 7.8e-185)
		tmp = Float64(Float64(y * x) / Float64(y + Float64(z * Float64(b - y))));
	elseif (z <= 5.6e-8)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (z / (y / ((t - a) - (b * x))));
	t_2 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -1.02e-7)
		tmp = t_2;
	elseif (z <= -5e-60)
		tmp = x - (a * (z / y));
	elseif (z <= -4.1e-81)
		tmp = ((t + ((y * x) / z)) - a) / b;
	elseif (z <= 3.6e-262)
		tmp = t_1;
	elseif (z <= 7.8e-185)
		tmp = (y * x) / (y + (z * (b - y)));
	elseif (z <= 5.6e-8)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(z / N[(y / N[(N[(t - a), $MachinePrecision] - N[(b * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.02e-7], t$95$2, If[LessEqual[z, -5e-60], N[(x - N[(a * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4.1e-81], N[(N[(N[(t + N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[z, 3.6e-262], t$95$1, If[LessEqual[z, 7.8e-185], N[(N[(y * x), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.6e-8], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.02e-7 or 5.5999999999999999e-8 < z

   1. Initial program 42.9%

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

   2. Taylor expanded in z around inf 77.5%

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

   if -1.02e-7 < z < -5.0000000000000001e-60

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 78.2%

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

   3. Taylor expanded in a around inf 74.0%

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

      1. associate-*r/ 74.0%

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

      2. mul-1-neg 74.0%

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

   5. Simplified 74.0%

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

   6. Taylor expanded in x around 0 76.8%

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

      1. mul-1-neg 76.8%

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

      2. *-commutative 76.8%

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

      3. sub-neg 76.8%

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

      4. associate-/l* 76.7%

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

      5. associate-/r/ 76.8%

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

   8. Simplified 76.8%

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

   if -5.0000000000000001e-60 < z < -4.09999999999999984e-81

   1. Initial program 99.3%

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

   2. Taylor expanded in z around inf 85.5%

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

      1. associate--r+ 85.5%

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

      2. +-commutative 85.5%

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

      3. associate--l+ 85.5%

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

      4. *-commutative 85.5%

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

      5. times-frac 59.9%

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

      6. div-sub 59.9%

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

      7. *-commutative 59.9%

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

      8. times-frac 45.6%

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

   4. Simplified 45.6%

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

   5. Taylor expanded in b around inf 86.0%

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

   if -4.09999999999999984e-81 < z < 3.5999999999999998e-262 or 7.7999999999999999e-185 < z < 5.5999999999999999e-8

   1. Initial program 84.9%

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

   2. Taylor expanded in z around 0 57.9%

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

   3. Taylor expanded in y around 0 69.0%

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

      1. associate-/l* 66.7%

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

      2. associate--r+ 66.7%

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

      3. *-commutative 66.7%

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

   5. Simplified 66.7%

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

   if 3.5999999999999998e-262 < z < 7.7999999999999999e-185

   1. Initial program 88.2%

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

   2. Taylor expanded in x around inf 65.8%

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

      1. *-commutative 65.8%

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

   4. Simplified 65.8%

      \[\leadsto \frac{\color{blue}{y \cdot x}}{y + z \cdot \left(b - y\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{-7}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-60}:\\ \;\;\;\;x - a \cdot \frac{z}{y}\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{-81}:\\ \;\;\;\;\frac{\left(t + \frac{y \cdot x}{z}\right) - a}{b}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-262}:\\ \;\;\;\;x + \frac{z}{\frac{y}{\left(t - a\right) - b \cdot x}}\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{-185}:\\ \;\;\;\;\frac{y \cdot x}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-8}:\\ \;\;\;\;x + \frac{z}{\frac{y}{\left(t - a\right) - b \cdot x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 4: 72.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot x - z \cdot a}{y + z \cdot \left(b - y\right)}\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -1.35 \cdot 10^{-5}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-87}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-211}:\\ \;\;\;\;x + z \cdot \frac{t}{y}\\ \mathbf{elif}\;z \leq 0.0012:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (* y x) (* z a)) (+ y (* z (- b y)))))
        (t_2 (/ (- t a) (- b y))))
   (if (<= z -1.35e-5)
     t_2
     (if (<= z -1.55e-87)
       t_1
       (if (<= z -2.9e-211) (+ x (* z (/ t y))) (if (<= z 0.0012) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y * x) - (z * a)) / (y + (z * (b - y)));
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -1.35e-5) {
		tmp = t_2;
	} else if (z <= -1.55e-87) {
		tmp = t_1;
	} else if (z <= -2.9e-211) {
		tmp = x + (z * (t / y));
	} else if (z <= 0.0012) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((y * x) - (z * a)) / (y + (z * (b - y)))
    t_2 = (t - a) / (b - y)
    if (z <= (-1.35d-5)) then
        tmp = t_2
    else if (z <= (-1.55d-87)) then
        tmp = t_1
    else if (z <= (-2.9d-211)) then
        tmp = x + (z * (t / y))
    else if (z <= 0.0012d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y * x) - (z * a)) / (y + (z * (b - y)));
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -1.35e-5) {
		tmp = t_2;
	} else if (z <= -1.55e-87) {
		tmp = t_1;
	} else if (z <= -2.9e-211) {
		tmp = x + (z * (t / y));
	} else if (z <= 0.0012) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((y * x) - (z * a)) / (y + (z * (b - y)))
	t_2 = (t - a) / (b - y)
	tmp = 0
	if z <= -1.35e-5:
		tmp = t_2
	elif z <= -1.55e-87:
		tmp = t_1
	elif z <= -2.9e-211:
		tmp = x + (z * (t / y))
	elif z <= 0.0012:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(y * x) - Float64(z * a)) / Float64(y + Float64(z * Float64(b - y))))
	t_2 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -1.35e-5)
		tmp = t_2;
	elseif (z <= -1.55e-87)
		tmp = t_1;
	elseif (z <= -2.9e-211)
		tmp = Float64(x + Float64(z * Float64(t / y)));
	elseif (z <= 0.0012)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((y * x) - (z * a)) / (y + (z * (b - y)));
	t_2 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -1.35e-5)
		tmp = t_2;
	elseif (z <= -1.55e-87)
		tmp = t_1;
	elseif (z <= -2.9e-211)
		tmp = x + (z * (t / y));
	elseif (z <= 0.0012)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(y * x), $MachinePrecision] - N[(z * a), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.35e-5], t$95$2, If[LessEqual[z, -1.55e-87], t$95$1, If[LessEqual[z, -2.9e-211], N[(x + N[(z * N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.0012], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.3499999999999999e-5 or 0.00119999999999999989 < z

   1. Initial program 42.9%

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

   2. Taylor expanded in z around inf 77.5%

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

   if -1.3499999999999999e-5 < z < -1.54999999999999999e-87 or -2.90000000000000014e-211 < z < 0.00119999999999999989

   1. Initial program 89.0%

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

   2. Taylor expanded in t around 0 72.9%

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

      1. +-commutative 72.9%

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

      2. mul-1-neg 72.9%

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

      3. unsub-neg 72.9%

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

      4. *-commutative 72.9%

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

      5. *-commutative 72.9%

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

   4. Simplified 72.9%

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

   if -1.54999999999999999e-87 < z < -2.90000000000000014e-211

   1. Initial program 79.4%

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

   2. Taylor expanded in z around 0 57.8%

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

   3. Taylor expanded in t around inf 75.6%

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

4. Final simplification 75.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{-5}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-87}:\\ \;\;\;\;\frac{y \cdot x - z \cdot a}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-211}:\\ \;\;\;\;x + z \cdot \frac{t}{y}\\ \mathbf{elif}\;z \leq 0.0012:\\ \;\;\;\;\frac{y \cdot x - z \cdot a}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 5: 67.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ t_2 := x + z \cdot \frac{t}{y}\\ \mathbf{if}\;z \leq -3.2 \cdot 10^{-8}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{-101}:\\ \;\;\;\;x - a \cdot \frac{z}{y}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-271}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-87}:\\ \;\;\;\;x - \frac{a}{\frac{y}{z}}\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{-55}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+18} \lor \neg \left(z \leq 2.45 \cdot 10^{+27}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))) (t_2 (+ x (* z (/ t y)))))
   (if (<= z -3.2e-8)
     t_1
     (if (<= z -1.45e-101)
       (- x (* a (/ z y)))
       (if (<= z 1.3e-271)
         t_2
         (if (<= z 1.3e-87)
           (- x (/ a (/ y z)))
           (if (<= z 5.4e-55)
             t_2
             (if (or (<= z 7e+18) (not (<= z 2.45e+27)))
               t_1
               (/ (- x) z)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double t_2 = x + (z * (t / y));
	double tmp;
	if (z <= -3.2e-8) {
		tmp = t_1;
	} else if (z <= -1.45e-101) {
		tmp = x - (a * (z / y));
	} else if (z <= 1.3e-271) {
		tmp = t_2;
	} else if (z <= 1.3e-87) {
		tmp = x - (a / (y / z));
	} else if (z <= 5.4e-55) {
		tmp = t_2;
	} else if ((z <= 7e+18) || !(z <= 2.45e+27)) {
		tmp = t_1;
	} else {
		tmp = -x / z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    t_2 = x + (z * (t / y))
    if (z <= (-3.2d-8)) then
        tmp = t_1
    else if (z <= (-1.45d-101)) then
        tmp = x - (a * (z / y))
    else if (z <= 1.3d-271) then
        tmp = t_2
    else if (z <= 1.3d-87) then
        tmp = x - (a / (y / z))
    else if (z <= 5.4d-55) then
        tmp = t_2
    else if ((z <= 7d+18) .or. (.not. (z <= 2.45d+27))) then
        tmp = t_1
    else
        tmp = -x / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double t_2 = x + (z * (t / y));
	double tmp;
	if (z <= -3.2e-8) {
		tmp = t_1;
	} else if (z <= -1.45e-101) {
		tmp = x - (a * (z / y));
	} else if (z <= 1.3e-271) {
		tmp = t_2;
	} else if (z <= 1.3e-87) {
		tmp = x - (a / (y / z));
	} else if (z <= 5.4e-55) {
		tmp = t_2;
	} else if ((z <= 7e+18) || !(z <= 2.45e+27)) {
		tmp = t_1;
	} else {
		tmp = -x / z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	t_2 = x + (z * (t / y))
	tmp = 0
	if z <= -3.2e-8:
		tmp = t_1
	elif z <= -1.45e-101:
		tmp = x - (a * (z / y))
	elif z <= 1.3e-271:
		tmp = t_2
	elif z <= 1.3e-87:
		tmp = x - (a / (y / z))
	elif z <= 5.4e-55:
		tmp = t_2
	elif (z <= 7e+18) or not (z <= 2.45e+27):
		tmp = t_1
	else:
		tmp = -x / z
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	t_2 = Float64(x + Float64(z * Float64(t / y)))
	tmp = 0.0
	if (z <= -3.2e-8)
		tmp = t_1;
	elseif (z <= -1.45e-101)
		tmp = Float64(x - Float64(a * Float64(z / y)));
	elseif (z <= 1.3e-271)
		tmp = t_2;
	elseif (z <= 1.3e-87)
		tmp = Float64(x - Float64(a / Float64(y / z)));
	elseif (z <= 5.4e-55)
		tmp = t_2;
	elseif ((z <= 7e+18) || !(z <= 2.45e+27))
		tmp = t_1;
	else
		tmp = Float64(Float64(-x) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	t_2 = x + (z * (t / y));
	tmp = 0.0;
	if (z <= -3.2e-8)
		tmp = t_1;
	elseif (z <= -1.45e-101)
		tmp = x - (a * (z / y));
	elseif (z <= 1.3e-271)
		tmp = t_2;
	elseif (z <= 1.3e-87)
		tmp = x - (a / (y / z));
	elseif (z <= 5.4e-55)
		tmp = t_2;
	elseif ((z <= 7e+18) || ~((z <= 2.45e+27)))
		tmp = t_1;
	else
		tmp = -x / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(z * N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.2e-8], t$95$1, If[LessEqual[z, -1.45e-101], N[(x - N[(a * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.3e-271], t$95$2, If[LessEqual[z, 1.3e-87], N[(x - N[(a / N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.4e-55], t$95$2, If[Or[LessEqual[z, 7e+18], N[Not[LessEqual[z, 2.45e+27]], $MachinePrecision]], t$95$1, N[((-x) / z), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -3.2000000000000002e-8 or 5.40000000000000008e-55 < z < 7e18 or 2.45000000000000007e27 < z

   1. Initial program 46.2%

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

   2. Taylor expanded in z around inf 76.7%

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

   if -3.2000000000000002e-8 < z < -1.45e-101

   1. Initial program 95.1%

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

   2. Taylor expanded in z around 0 52.9%

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

   3. Taylor expanded in a around inf 56.8%

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

      1. associate-*r/ 56.8%

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

      2. mul-1-neg 56.8%

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

   5. Simplified 56.8%

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

   6. Taylor expanded in x around 0 58.1%

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

      1. mul-1-neg 58.1%

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

      2. *-commutative 58.1%

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

      3. sub-neg 58.1%

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

      4. associate-/l* 58.0%

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

      5. associate-/r/ 58.1%

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

   8. Simplified 58.1%

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

   if -1.45e-101 < z < 1.3e-271 or 1.30000000000000001e-87 < z < 5.40000000000000008e-55

   1. Initial program 83.8%

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

   2. Taylor expanded in z around 0 59.4%

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

   3. Taylor expanded in t around inf 69.2%

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

   if 1.3e-271 < z < 1.30000000000000001e-87

   1. Initial program 88.1%

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

   2. Taylor expanded in z around 0 47.7%

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

   3. Taylor expanded in a around inf 59.8%

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

      1. mul-1-neg 59.8%

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

      2. associate-/l* 59.9%

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

      3. distribute-neg-frac 59.9%

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

   5. Simplified 59.9%

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

   if 7e18 < z < 2.45000000000000007e27

   1. Initial program 27.0%

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

   2. Taylor expanded in y around inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. unsub-neg 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in z around inf 100.0%

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

      1. associate-*r/ 100.0%

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

      2. mul-1-neg 100.0%

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

   7. Simplified 100.0%

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

4. Final simplification 71.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{-8}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{-101}:\\ \;\;\;\;x - a \cdot \frac{z}{y}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-271}:\\ \;\;\;\;x + z \cdot \frac{t}{y}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-87}:\\ \;\;\;\;x - \frac{a}{\frac{y}{z}}\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{-55}:\\ \;\;\;\;x + z \cdot \frac{t}{y}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+18} \lor \neg \left(z \leq 2.45 \cdot 10^{+27}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{z}\\ \end{array} \]

Alternative 6: 85.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+63} \lor \neg \left(z \leq 2.9 \cdot 10^{+30}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y + z \cdot \left(b - y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -5e+63) (not (<= z 2.9e+30)))
   (/ (- t a) (- b y))
   (/ (+ (* z (- t a)) (* y x)) (+ y (* z (- b y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -5e+63) || !(z <= 2.9e+30)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((z * (t - a)) + (y * x)) / (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 <= (-5d+63)) .or. (.not. (z <= 2.9d+30))) then
        tmp = (t - a) / (b - y)
    else
        tmp = ((z * (t - a)) + (y * x)) / (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 <= -5e+63) || !(z <= 2.9e+30)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((z * (t - a)) + (y * x)) / (y + (z * (b - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -5e+63) or not (z <= 2.9e+30):
		tmp = (t - a) / (b - y)
	else:
		tmp = ((z * (t - a)) + (y * x)) / (y + (z * (b - y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -5e+63) || !(z <= 2.9e+30))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(Float64(Float64(z * Float64(t - a)) + Float64(y * x)) / 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 <= -5e+63) || ~((z <= 2.9e+30)))
		tmp = (t - a) / (b - y);
	else
		tmp = ((z * (t - a)) + (y * x)) / (y + (z * (b - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -5e+63], N[Not[LessEqual[z, 2.9e+30]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] + N[(y * x), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.00000000000000011e63 or 2.8999999999999998e30 < z

   1. Initial program 32.8%

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

   2. Taylor expanded in z around inf 81.7%

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

   if -5.00000000000000011e63 < z < 2.8999999999999998e30

   1. Initial program 86.5%

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

4. Final simplification 84.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+63} \lor \neg \left(z \leq 2.9 \cdot 10^{+30}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y + z \cdot \left(b - y\right)}\\ \end{array} \]

Alternative 7: 69.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{z \cdot a}{y}\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -3.2 \cdot 10^{-8}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -8.6 \cdot 10^{-61}:\\ \;\;\;\;x - a \cdot \frac{z}{y}\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{-82}:\\ \;\;\;\;\frac{\left(t + \frac{y \cdot x}{z}\right) - a}{b}\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{-104}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-264}:\\ \;\;\;\;x + z \cdot \frac{t}{y}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-11}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- x (/ (* z a) y))) (t_2 (/ (- t a) (- b y))))
   (if (<= z -3.2e-8)
     t_2
     (if (<= z -8.6e-61)
       (- x (* a (/ z y)))
       (if (<= z -8.2e-82)
         (/ (- (+ t (/ (* y x) z)) a) b)
         (if (<= z -1.85e-104)
           t_1
           (if (<= z -9e-264)
             (+ x (* z (/ t y)))
             (if (<= z 3.5e-11) t_1 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 tmp;
	if (z <= -3.2e-8) {
		tmp = t_2;
	} else if (z <= -8.6e-61) {
		tmp = x - (a * (z / y));
	} else if (z <= -8.2e-82) {
		tmp = ((t + ((y * x) / z)) - a) / b;
	} else if (z <= -1.85e-104) {
		tmp = t_1;
	} else if (z <= -9e-264) {
		tmp = x + (z * (t / y));
	} else if (z <= 3.5e-11) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x - ((z * a) / y)
    t_2 = (t - a) / (b - y)
    if (z <= (-3.2d-8)) then
        tmp = t_2
    else if (z <= (-8.6d-61)) then
        tmp = x - (a * (z / y))
    else if (z <= (-8.2d-82)) then
        tmp = ((t + ((y * x) / z)) - a) / b
    else if (z <= (-1.85d-104)) then
        tmp = t_1
    else if (z <= (-9d-264)) then
        tmp = x + (z * (t / y))
    else if (z <= 3.5d-11) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - ((z * a) / y);
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -3.2e-8) {
		tmp = t_2;
	} else if (z <= -8.6e-61) {
		tmp = x - (a * (z / y));
	} else if (z <= -8.2e-82) {
		tmp = ((t + ((y * x) / z)) - a) / b;
	} else if (z <= -1.85e-104) {
		tmp = t_1;
	} else if (z <= -9e-264) {
		tmp = x + (z * (t / y));
	} else if (z <= 3.5e-11) {
		tmp = t_1;
	} 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)
	tmp = 0
	if z <= -3.2e-8:
		tmp = t_2
	elif z <= -8.6e-61:
		tmp = x - (a * (z / y))
	elif z <= -8.2e-82:
		tmp = ((t + ((y * x) / z)) - a) / b
	elif z <= -1.85e-104:
		tmp = t_1
	elif z <= -9e-264:
		tmp = x + (z * (t / y))
	elif z <= 3.5e-11:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x - Float64(Float64(z * a) / y))
	t_2 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -3.2e-8)
		tmp = t_2;
	elseif (z <= -8.6e-61)
		tmp = Float64(x - Float64(a * Float64(z / y)));
	elseif (z <= -8.2e-82)
		tmp = Float64(Float64(Float64(t + Float64(Float64(y * x) / z)) - a) / b);
	elseif (z <= -1.85e-104)
		tmp = t_1;
	elseif (z <= -9e-264)
		tmp = Float64(x + Float64(z * Float64(t / y)));
	elseif (z <= 3.5e-11)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x - ((z * a) / y);
	t_2 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -3.2e-8)
		tmp = t_2;
	elseif (z <= -8.6e-61)
		tmp = x - (a * (z / y));
	elseif (z <= -8.2e-82)
		tmp = ((t + ((y * x) / z)) - a) / b;
	elseif (z <= -1.85e-104)
		tmp = t_1;
	elseif (z <= -9e-264)
		tmp = x + (z * (t / y));
	elseif (z <= 3.5e-11)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x - N[(N[(z * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.2e-8], t$95$2, If[LessEqual[z, -8.6e-61], N[(x - N[(a * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -8.2e-82], N[(N[(N[(t + N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[z, -1.85e-104], t$95$1, If[LessEqual[z, -9e-264], N[(x + N[(z * N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.5e-11], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -3.2000000000000002e-8 or 3.50000000000000019e-11 < z

   1. Initial program 42.9%

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

   2. Taylor expanded in z around inf 77.5%

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

   if -3.2000000000000002e-8 < z < -8.6000000000000007e-61

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 78.2%

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

   3. Taylor expanded in a around inf 74.0%

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

      1. associate-*r/ 74.0%

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

      2. mul-1-neg 74.0%

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

   5. Simplified 74.0%

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

   6. Taylor expanded in x around 0 76.8%

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

      1. mul-1-neg 76.8%

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

      2. *-commutative 76.8%

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

      3. sub-neg 76.8%

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

      4. associate-/l* 76.7%

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

      5. associate-/r/ 76.8%

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

   8. Simplified 76.8%

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

   if -8.6000000000000007e-61 < z < -8.19999999999999992e-82

   1. Initial program 99.3%

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

   2. Taylor expanded in z around inf 85.5%

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

      1. associate--r+ 85.5%

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

      2. +-commutative 85.5%

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

      3. associate--l+ 85.5%

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

      4. *-commutative 85.5%

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

      5. times-frac 59.9%

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

      6. div-sub 59.9%

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

      7. *-commutative 59.9%

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

      8. times-frac 45.6%

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

   4. Simplified 45.6%

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

   5. Taylor expanded in b around inf 86.0%

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

   if -8.19999999999999992e-82 < z < -1.85e-104 or -9.0000000000000001e-264 < z < 3.50000000000000019e-11

   1. Initial program 88.0%

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

   2. Taylor expanded in z around 0 54.1%

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

   3. Taylor expanded in a around inf 57.0%

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

      1. associate-*r/ 57.0%

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

      2. mul-1-neg 57.0%

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

   5. Simplified 57.0%

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

   6. Taylor expanded in z around 0 60.1%

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

      1. associate-*r/ 60.1%

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

      2. associate-*r* 60.1%

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

      3. neg-mul-1 60.1%

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

   8. Simplified 60.1%

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

   if -1.85e-104 < z < -9.0000000000000001e-264

   1. Initial program 79.7%

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

   2. Taylor expanded in z around 0 54.0%

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

   3. Taylor expanded in t around inf 70.2%

      \[\leadsto x + z \cdot \color{blue}{\frac{t}{y}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 71.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{-8}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -8.6 \cdot 10^{-61}:\\ \;\;\;\;x - a \cdot \frac{z}{y}\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{-82}:\\ \;\;\;\;\frac{\left(t + \frac{y \cdot x}{z}\right) - a}{b}\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{-104}:\\ \;\;\;\;x - \frac{z \cdot a}{y}\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-264}:\\ \;\;\;\;x + z \cdot \frac{t}{y}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-11}:\\ \;\;\;\;x - \frac{z \cdot a}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 8: 41.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{b - y}\\ t_2 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -6.5 \cdot 10^{-88}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-193}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+28}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+56}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+124}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ t (- b y))) (t_2 (/ x (- 1.0 z))))
   (if (<= y -6.5e-88)
     t_2
     (if (<= y -3e-193)
       (/ (- a) b)
       (if (<= y 6.5e+28)
         t_1
         (if (<= y 2.2e+56) x (if (<= y 7.2e+124) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t / (b - y);
	double t_2 = x / (1.0 - z);
	double tmp;
	if (y <= -6.5e-88) {
		tmp = t_2;
	} else if (y <= -3e-193) {
		tmp = -a / b;
	} else if (y <= 6.5e+28) {
		tmp = t_1;
	} else if (y <= 2.2e+56) {
		tmp = x;
	} else if (y <= 7.2e+124) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t / (b - y)
    t_2 = x / (1.0d0 - z)
    if (y <= (-6.5d-88)) then
        tmp = t_2
    else if (y <= (-3d-193)) then
        tmp = -a / b
    else if (y <= 6.5d+28) then
        tmp = t_1
    else if (y <= 2.2d+56) then
        tmp = x
    else if (y <= 7.2d+124) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t / (b - y);
	double t_2 = x / (1.0 - z);
	double tmp;
	if (y <= -6.5e-88) {
		tmp = t_2;
	} else if (y <= -3e-193) {
		tmp = -a / b;
	} else if (y <= 6.5e+28) {
		tmp = t_1;
	} else if (y <= 2.2e+56) {
		tmp = x;
	} else if (y <= 7.2e+124) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t / (b - y)
	t_2 = x / (1.0 - z)
	tmp = 0
	if y <= -6.5e-88:
		tmp = t_2
	elif y <= -3e-193:
		tmp = -a / b
	elif y <= 6.5e+28:
		tmp = t_1
	elif y <= 2.2e+56:
		tmp = x
	elif y <= 7.2e+124:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t / Float64(b - y))
	t_2 = Float64(x / Float64(1.0 - z))
	tmp = 0.0
	if (y <= -6.5e-88)
		tmp = t_2;
	elseif (y <= -3e-193)
		tmp = Float64(Float64(-a) / b);
	elseif (y <= 6.5e+28)
		tmp = t_1;
	elseif (y <= 2.2e+56)
		tmp = x;
	elseif (y <= 7.2e+124)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t / (b - y);
	t_2 = x / (1.0 - z);
	tmp = 0.0;
	if (y <= -6.5e-88)
		tmp = t_2;
	elseif (y <= -3e-193)
		tmp = -a / b;
	elseif (y <= 6.5e+28)
		tmp = t_1;
	elseif (y <= 2.2e+56)
		tmp = x;
	elseif (y <= 7.2e+124)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.5e-88], t$95$2, If[LessEqual[y, -3e-193], N[((-a) / b), $MachinePrecision], If[LessEqual[y, 6.5e+28], t$95$1, If[LessEqual[y, 2.2e+56], x, If[LessEqual[y, 7.2e+124], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -6.50000000000000006e-88 or 7.19999999999999972e124 < y

   1. Initial program 59.7%

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

   2. Taylor expanded in y around inf 60.2%

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

      1. mul-1-neg 60.2%

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

      2. unsub-neg 60.2%

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

   4. Simplified 60.2%

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

   if -6.50000000000000006e-88 < y < -2.9999999999999999e-193

   1. Initial program 78.5%

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

   2. Taylor expanded in y around 0 75.1%

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

   3. Taylor expanded in t around 0 53.5%

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

      1. associate-*r/ 53.5%

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

      2. neg-mul-1 53.5%

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

   5. Simplified 53.5%

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

   if -2.9999999999999999e-193 < y < 6.5000000000000001e28 or 2.20000000000000016e56 < y < 7.19999999999999972e124

   1. Initial program 68.9%

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

   2. Taylor expanded in t around inf 31.9%

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

      1. *-commutative 31.9%

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

   4. Simplified 31.9%

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

   5. Taylor expanded in z around inf 43.4%

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

   if 6.5000000000000001e28 < y < 2.20000000000000016e56

   1. Initial program 78.9%

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

   2. Taylor expanded in z around 0 47.6%

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

4. Final simplification 51.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{-88}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-193}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+28}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+56}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+124}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]

Alternative 9: 68.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - a \cdot \frac{z}{y}\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -3.4 \cdot 10^{-8}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-100}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-269}:\\ \;\;\;\;x + z \cdot \frac{t}{y}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-12}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- x (* a (/ z y)))) (t_2 (/ (- t a) (- b y))))
   (if (<= z -3.4e-8)
     t_2
     (if (<= z -2.5e-100)
       t_1
       (if (<= z 1.1e-269) (+ x (* z (/ t y))) (if (<= z 5.2e-12) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - (a * (z / y));
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -3.4e-8) {
		tmp = t_2;
	} else if (z <= -2.5e-100) {
		tmp = t_1;
	} else if (z <= 1.1e-269) {
		tmp = x + (z * (t / y));
	} else if (z <= 5.2e-12) {
		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 - (a * (z / y))
    t_2 = (t - a) / (b - y)
    if (z <= (-3.4d-8)) then
        tmp = t_2
    else if (z <= (-2.5d-100)) then
        tmp = t_1
    else if (z <= 1.1d-269) then
        tmp = x + (z * (t / y))
    else if (z <= 5.2d-12) 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 - (a * (z / y));
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -3.4e-8) {
		tmp = t_2;
	} else if (z <= -2.5e-100) {
		tmp = t_1;
	} else if (z <= 1.1e-269) {
		tmp = x + (z * (t / y));
	} else if (z <= 5.2e-12) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x - (a * (z / y))
	t_2 = (t - a) / (b - y)
	tmp = 0
	if z <= -3.4e-8:
		tmp = t_2
	elif z <= -2.5e-100:
		tmp = t_1
	elif z <= 1.1e-269:
		tmp = x + (z * (t / y))
	elif z <= 5.2e-12:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x - Float64(a * Float64(z / y)))
	t_2 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -3.4e-8)
		tmp = t_2;
	elseif (z <= -2.5e-100)
		tmp = t_1;
	elseif (z <= 1.1e-269)
		tmp = Float64(x + Float64(z * Float64(t / y)));
	elseif (z <= 5.2e-12)
		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 - (a * (z / y));
	t_2 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -3.4e-8)
		tmp = t_2;
	elseif (z <= -2.5e-100)
		tmp = t_1;
	elseif (z <= 1.1e-269)
		tmp = x + (z * (t / y));
	elseif (z <= 5.2e-12)
		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[(a * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.4e-8], t$95$2, If[LessEqual[z, -2.5e-100], t$95$1, If[LessEqual[z, 1.1e-269], N[(x + N[(z * N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.2e-12], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.4e-8 or 5.19999999999999965e-12 < z

   1. Initial program 42.9%

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

   2. Taylor expanded in z around inf 77.5%

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

   if -3.4e-8 < z < -2.5e-100 or 1.09999999999999992e-269 < z < 5.19999999999999965e-12

   1. Initial program 90.6%

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

   2. Taylor expanded in z around 0 51.1%

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

   3. Taylor expanded in a around inf 54.9%

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

      1. associate-*r/ 54.9%

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

      2. mul-1-neg 54.9%

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

   5. Simplified 54.9%

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

   6. Taylor expanded in x around 0 56.4%

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

      1. mul-1-neg 56.4%

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

      2. *-commutative 56.4%

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

      3. sub-neg 56.4%

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

      4. associate-/l* 55.2%

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

      5. associate-/r/ 56.4%

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

   8. Simplified 56.4%

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

   if -2.5e-100 < z < 1.09999999999999992e-269

   1. Initial program 82.8%

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

   2. Taylor expanded in z around 0 56.8%

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

   3. Taylor expanded in t around inf 67.2%

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

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{-8}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-100}:\\ \;\;\;\;x - a \cdot \frac{z}{y}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-269}:\\ \;\;\;\;x + z \cdot \frac{t}{y}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-12}:\\ \;\;\;\;x - a \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 10: 69.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -3.2 \cdot 10^{-8}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{-101}:\\ \;\;\;\;x - a \cdot \frac{z}{y}\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-264}:\\ \;\;\;\;x + z \cdot \frac{t}{y}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-12}:\\ \;\;\;\;x - \frac{z \cdot a}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -3.2e-8)
     t_1
     (if (<= z -1.45e-101)
       (- x (* a (/ z y)))
       (if (<= z -7.2e-264)
         (+ x (* z (/ t y)))
         (if (<= z 1.9e-12) (- x (/ (* z a) y)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -3.2e-8) {
		tmp = t_1;
	} else if (z <= -1.45e-101) {
		tmp = x - (a * (z / y));
	} else if (z <= -7.2e-264) {
		tmp = x + (z * (t / y));
	} else if (z <= 1.9e-12) {
		tmp = x - ((z * a) / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    if (z <= (-3.2d-8)) then
        tmp = t_1
    else if (z <= (-1.45d-101)) then
        tmp = x - (a * (z / y))
    else if (z <= (-7.2d-264)) then
        tmp = x + (z * (t / y))
    else if (z <= 1.9d-12) then
        tmp = x - ((z * a) / y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -3.2e-8) {
		tmp = t_1;
	} else if (z <= -1.45e-101) {
		tmp = x - (a * (z / y));
	} else if (z <= -7.2e-264) {
		tmp = x + (z * (t / y));
	} else if (z <= 1.9e-12) {
		tmp = x - ((z * a) / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	tmp = 0
	if z <= -3.2e-8:
		tmp = t_1
	elif z <= -1.45e-101:
		tmp = x - (a * (z / y))
	elif z <= -7.2e-264:
		tmp = x + (z * (t / y))
	elif z <= 1.9e-12:
		tmp = x - ((z * a) / y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -3.2e-8)
		tmp = t_1;
	elseif (z <= -1.45e-101)
		tmp = Float64(x - Float64(a * Float64(z / y)));
	elseif (z <= -7.2e-264)
		tmp = Float64(x + Float64(z * Float64(t / y)));
	elseif (z <= 1.9e-12)
		tmp = Float64(x - Float64(Float64(z * a) / y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -3.2e-8)
		tmp = t_1;
	elseif (z <= -1.45e-101)
		tmp = x - (a * (z / y));
	elseif (z <= -7.2e-264)
		tmp = x + (z * (t / y));
	elseif (z <= 1.9e-12)
		tmp = x - ((z * a) / y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.2e-8], t$95$1, If[LessEqual[z, -1.45e-101], N[(x - N[(a * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -7.2e-264], N[(x + N[(z * N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.9e-12], N[(x - N[(N[(z * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.2000000000000002e-8 or 1.89999999999999998e-12 < z

   1. Initial program 42.9%

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

   2. Taylor expanded in z around inf 77.5%

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

   if -3.2000000000000002e-8 < z < -1.45e-101

   1. Initial program 95.1%

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

   2. Taylor expanded in z around 0 52.9%

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

   3. Taylor expanded in a around inf 56.8%

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

      1. associate-*r/ 56.8%

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

      2. mul-1-neg 56.8%

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

   5. Simplified 56.8%

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

   6. Taylor expanded in x around 0 58.1%

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

      1. mul-1-neg 58.1%

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

      2. *-commutative 58.1%

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

      3. sub-neg 58.1%

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

      4. associate-/l* 58.0%

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

      5. associate-/r/ 58.1%

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

   8. Simplified 58.1%

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

   if -1.45e-101 < z < -7.2000000000000004e-264

   1. Initial program 79.7%

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

   2. Taylor expanded in z around 0 54.0%

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

   3. Taylor expanded in t around inf 70.2%

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

   if -7.2000000000000004e-264 < z < 1.89999999999999998e-12

   1. Initial program 88.5%

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

   2. Taylor expanded in z around 0 53.7%

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

   3. Taylor expanded in a around inf 55.4%

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

      1. associate-*r/ 55.4%

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

      2. mul-1-neg 55.4%

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

   5. Simplified 55.4%

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

   6. Taylor expanded in z around 0 58.6%

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

      1. associate-*r/ 58.6%

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

      2. associate-*r* 58.6%

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

      3. neg-mul-1 58.6%

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

   8. Simplified 58.6%

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

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{-8}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{-101}:\\ \;\;\;\;x - a \cdot \frac{z}{y}\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-264}:\\ \;\;\;\;x + z \cdot \frac{t}{y}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-12}:\\ \;\;\;\;x - \frac{z \cdot a}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 11: 44.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{b - y}\\ \mathbf{if}\;z \leq -6.6 \cdot 10^{+135}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{+28}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-7} \lor \neg \left(z \leq 1.9 \cdot 10^{-54}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ t (- b y))))
   (if (<= z -6.6e+135)
     t_1
     (if (<= z -3.6e+28)
       (/ (- a) b)
       (if (or (<= z -1e-7) (not (<= z 1.9e-54))) t_1 (+ x (* z x)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t / (b - y);
	double tmp;
	if (z <= -6.6e+135) {
		tmp = t_1;
	} else if (z <= -3.6e+28) {
		tmp = -a / b;
	} else if ((z <= -1e-7) || !(z <= 1.9e-54)) {
		tmp = t_1;
	} else {
		tmp = x + (z * x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t / (b - y)
    if (z <= (-6.6d+135)) then
        tmp = t_1
    else if (z <= (-3.6d+28)) then
        tmp = -a / b
    else if ((z <= (-1d-7)) .or. (.not. (z <= 1.9d-54))) then
        tmp = t_1
    else
        tmp = x + (z * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t / (b - y);
	double tmp;
	if (z <= -6.6e+135) {
		tmp = t_1;
	} else if (z <= -3.6e+28) {
		tmp = -a / b;
	} else if ((z <= -1e-7) || !(z <= 1.9e-54)) {
		tmp = t_1;
	} else {
		tmp = x + (z * x);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t / (b - y)
	tmp = 0
	if z <= -6.6e+135:
		tmp = t_1
	elif z <= -3.6e+28:
		tmp = -a / b
	elif (z <= -1e-7) or not (z <= 1.9e-54):
		tmp = t_1
	else:
		tmp = x + (z * x)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t / Float64(b - y))
	tmp = 0.0
	if (z <= -6.6e+135)
		tmp = t_1;
	elseif (z <= -3.6e+28)
		tmp = Float64(Float64(-a) / b);
	elseif ((z <= -1e-7) || !(z <= 1.9e-54))
		tmp = t_1;
	else
		tmp = Float64(x + Float64(z * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t / (b - y);
	tmp = 0.0;
	if (z <= -6.6e+135)
		tmp = t_1;
	elseif (z <= -3.6e+28)
		tmp = -a / b;
	elseif ((z <= -1e-7) || ~((z <= 1.9e-54)))
		tmp = t_1;
	else
		tmp = x + (z * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.6e+135], t$95$1, If[LessEqual[z, -3.6e+28], N[((-a) / b), $MachinePrecision], If[Or[LessEqual[z, -1e-7], N[Not[LessEqual[z, 1.9e-54]], $MachinePrecision]], t$95$1, N[(x + N[(z * x), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.5999999999999998e135 or -3.5999999999999999e28 < z < -9.9999999999999995e-8 or 1.9000000000000001e-54 < z

   1. Initial program 43.1%

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

   2. Taylor expanded in t around inf 22.1%

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

      1. *-commutative 22.1%

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

   4. Simplified 22.1%

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

   5. Taylor expanded in z around inf 48.9%

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

   if -6.5999999999999998e135 < z < -3.5999999999999999e28

   1. Initial program 63.7%

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

   2. Taylor expanded in y around 0 44.0%

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

   3. Taylor expanded in t around 0 43.8%

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

      1. associate-*r/ 43.8%

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

      2. neg-mul-1 43.8%

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

   5. Simplified 43.8%

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

   if -9.9999999999999995e-8 < z < 1.9000000000000001e-54

   1. Initial program 87.0%

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

   2. Taylor expanded in y around inf 45.5%

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

      1. mul-1-neg 45.5%

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

      2. unsub-neg 45.5%

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

   4. Simplified 45.5%

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

   5. Taylor expanded in z around 0 45.4%

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

4. Final simplification 46.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{+135}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{+28}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-7} \lor \neg \left(z \leq 1.9 \cdot 10^{-54}\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot x\\ \end{array} \]

Alternative 12: 52.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -2.5 \cdot 10^{-86}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+29}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{+65}:\\ \;\;\;\;x + z \cdot x\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+96}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (- 1.0 z))))
   (if (<= y -2.5e-86)
     t_1
     (if (<= y 1.55e+29)
       (/ (- t a) b)
       (if (<= y 1.02e+65)
         (+ x (* z x))
         (if (<= y 6.2e+96) (/ t (- b y)) 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 <= -2.5e-86) {
		tmp = t_1;
	} else if (y <= 1.55e+29) {
		tmp = (t - a) / b;
	} else if (y <= 1.02e+65) {
		tmp = x + (z * x);
	} else if (y <= 6.2e+96) {
		tmp = t / (b - y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (1.0d0 - z)
    if (y <= (-2.5d-86)) then
        tmp = t_1
    else if (y <= 1.55d+29) then
        tmp = (t - a) / b
    else if (y <= 1.02d+65) then
        tmp = x + (z * x)
    else if (y <= 6.2d+96) then
        tmp = t / (b - y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 - z);
	double tmp;
	if (y <= -2.5e-86) {
		tmp = t_1;
	} else if (y <= 1.55e+29) {
		tmp = (t - a) / b;
	} else if (y <= 1.02e+65) {
		tmp = x + (z * x);
	} else if (y <= 6.2e+96) {
		tmp = t / (b - y);
	} 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 <= -2.5e-86:
		tmp = t_1
	elif y <= 1.55e+29:
		tmp = (t - a) / b
	elif y <= 1.02e+65:
		tmp = x + (z * x)
	elif y <= 6.2e+96:
		tmp = t / (b - y)
	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 <= -2.5e-86)
		tmp = t_1;
	elseif (y <= 1.55e+29)
		tmp = Float64(Float64(t - a) / b);
	elseif (y <= 1.02e+65)
		tmp = Float64(x + Float64(z * x));
	elseif (y <= 6.2e+96)
		tmp = Float64(t / Float64(b - y));
	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 <= -2.5e-86)
		tmp = t_1;
	elseif (y <= 1.55e+29)
		tmp = (t - a) / b;
	elseif (y <= 1.02e+65)
		tmp = x + (z * x);
	elseif (y <= 6.2e+96)
		tmp = t / (b - y);
	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, -2.5e-86], t$95$1, If[LessEqual[y, 1.55e+29], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[y, 1.02e+65], N[(x + N[(z * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.2e+96], N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.4999999999999999e-86 or 6.1999999999999996e96 < y

   1. Initial program 59.4%

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

   2. Taylor expanded in y around inf 59.0%

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

      1. mul-1-neg 59.0%

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

      2. unsub-neg 59.0%

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

   4. Simplified 59.0%

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

   if -2.4999999999999999e-86 < y < 1.5499999999999999e29

   1. Initial program 72.2%

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

   2. Taylor expanded in y around 0 60.7%

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

   if 1.5499999999999999e29 < y < 1.02000000000000005e65

   1. Initial program 76.0%

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

   2. Taylor expanded in y around inf 43.9%

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

      1. mul-1-neg 43.9%

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

      2. unsub-neg 43.9%

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

   4. Simplified 43.9%

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

   5. Taylor expanded in z around 0 44.5%

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

   if 1.02000000000000005e65 < y < 6.1999999999999996e96

   1. Initial program 56.5%

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

   2. Taylor expanded in t around inf 35.0%

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

      1. *-commutative 35.0%

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

   4. Simplified 35.0%

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

   5. Taylor expanded in z around inf 56.5%

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

4. Final simplification 59.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{-86}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+29}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{+65}:\\ \;\;\;\;x + z \cdot x\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+96}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]

Alternative 13: 51.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -2.5 \cdot 10^{-86}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+27}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+56}:\\ \;\;\;\;x + z \cdot \frac{t}{y}\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+124}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (- 1.0 z))))
   (if (<= y -2.5e-86)
     t_1
     (if (<= y 1.6e+27)
       (/ (- t a) b)
       (if (<= y 2.1e+56)
         (+ x (* z (/ t y)))
         (if (<= y 7.2e+124) (/ t (- b y)) 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 <= -2.5e-86) {
		tmp = t_1;
	} else if (y <= 1.6e+27) {
		tmp = (t - a) / b;
	} else if (y <= 2.1e+56) {
		tmp = x + (z * (t / y));
	} else if (y <= 7.2e+124) {
		tmp = t / (b - y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (1.0d0 - z)
    if (y <= (-2.5d-86)) then
        tmp = t_1
    else if (y <= 1.6d+27) then
        tmp = (t - a) / b
    else if (y <= 2.1d+56) then
        tmp = x + (z * (t / y))
    else if (y <= 7.2d+124) then
        tmp = t / (b - y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 - z);
	double tmp;
	if (y <= -2.5e-86) {
		tmp = t_1;
	} else if (y <= 1.6e+27) {
		tmp = (t - a) / b;
	} else if (y <= 2.1e+56) {
		tmp = x + (z * (t / y));
	} else if (y <= 7.2e+124) {
		tmp = t / (b - y);
	} 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 <= -2.5e-86:
		tmp = t_1
	elif y <= 1.6e+27:
		tmp = (t - a) / b
	elif y <= 2.1e+56:
		tmp = x + (z * (t / y))
	elif y <= 7.2e+124:
		tmp = t / (b - y)
	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 <= -2.5e-86)
		tmp = t_1;
	elseif (y <= 1.6e+27)
		tmp = Float64(Float64(t - a) / b);
	elseif (y <= 2.1e+56)
		tmp = Float64(x + Float64(z * Float64(t / y)));
	elseif (y <= 7.2e+124)
		tmp = Float64(t / Float64(b - y));
	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 <= -2.5e-86)
		tmp = t_1;
	elseif (y <= 1.6e+27)
		tmp = (t - a) / b;
	elseif (y <= 2.1e+56)
		tmp = x + (z * (t / y));
	elseif (y <= 7.2e+124)
		tmp = t / (b - y);
	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, -2.5e-86], t$95$1, If[LessEqual[y, 1.6e+27], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[y, 2.1e+56], N[(x + N[(z * N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.2e+124], N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.4999999999999999e-86 or 7.19999999999999972e124 < y

   1. Initial program 59.7%

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

   2. Taylor expanded in y around inf 60.2%

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

      1. mul-1-neg 60.2%

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

      2. unsub-neg 60.2%

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

   4. Simplified 60.2%

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

   if -2.4999999999999999e-86 < y < 1.60000000000000008e27

   1. Initial program 72.2%

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

   2. Taylor expanded in y around 0 60.7%

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

   if 1.60000000000000008e27 < y < 2.10000000000000017e56

   1. Initial program 78.9%

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

   2. Taylor expanded in z around 0 66.8%

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

   3. Taylor expanded in t around inf 68.8%

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

   if 2.10000000000000017e56 < y < 7.19999999999999972e124

   1. Initial program 57.2%

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

   2. Taylor expanded in t around inf 27.2%

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

      1. *-commutative 27.2%

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

   4. Simplified 27.2%

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

   5. Taylor expanded in z around inf 52.7%

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

4. Final simplification 60.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{-86}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+27}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+56}:\\ \;\;\;\;x + z \cdot \frac{t}{y}\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+124}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]

Alternative 14: 34.1% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.85 \cdot 10^{-89}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{-192}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{+27}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -2.85e-89)
   x
   (if (<= y -2.7e-192)
     (/ (- a) b)
     (if (<= y 5.8e+27) (/ t b) (+ x (* z x))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.85e-89) {
		tmp = x;
	} else if (y <= -2.7e-192) {
		tmp = -a / b;
	} else if (y <= 5.8e+27) {
		tmp = t / b;
	} else {
		tmp = x + (z * x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-2.85d-89)) then
        tmp = x
    else if (y <= (-2.7d-192)) then
        tmp = -a / b
    else if (y <= 5.8d+27) then
        tmp = t / b
    else
        tmp = x + (z * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.85e-89) {
		tmp = x;
	} else if (y <= -2.7e-192) {
		tmp = -a / b;
	} else if (y <= 5.8e+27) {
		tmp = t / b;
	} else {
		tmp = x + (z * x);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -2.85e-89:
		tmp = x
	elif y <= -2.7e-192:
		tmp = -a / b
	elif y <= 5.8e+27:
		tmp = t / b
	else:
		tmp = x + (z * x)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -2.85e-89)
		tmp = x;
	elseif (y <= -2.7e-192)
		tmp = Float64(Float64(-a) / b);
	elseif (y <= 5.8e+27)
		tmp = Float64(t / b);
	else
		tmp = Float64(x + Float64(z * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -2.85e-89)
		tmp = x;
	elseif (y <= -2.7e-192)
		tmp = -a / b;
	elseif (y <= 5.8e+27)
		tmp = t / b;
	else
		tmp = x + (z * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -2.85e-89], x, If[LessEqual[y, -2.7e-192], N[((-a) / b), $MachinePrecision], If[LessEqual[y, 5.8e+27], N[(t / b), $MachinePrecision], N[(x + N[(z * x), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.8500000000000001e-89

   1. Initial program 66.3%

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

   2. Taylor expanded in z around 0 34.1%

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

   if -2.8500000000000001e-89 < y < -2.69999999999999991e-192

   1. Initial program 78.5%

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

   2. Taylor expanded in y around 0 75.1%

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

   3. Taylor expanded in t around 0 53.5%

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

      1. associate-*r/ 53.5%

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

      2. neg-mul-1 53.5%

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

   5. Simplified 53.5%

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

   if -2.69999999999999991e-192 < y < 5.8000000000000002e27

   1. Initial program 70.8%

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

   2. Taylor expanded in t around inf 32.7%

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

      1. *-commutative 32.7%

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

   4. Simplified 32.7%

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

   5. Taylor expanded in y around 0 38.9%

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

   if 5.8000000000000002e27 < y

   1. Initial program 54.5%

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

   2. Taylor expanded in y around inf 58.1%

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

      1. mul-1-neg 58.1%

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

      2. unsub-neg 58.1%

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

   4. Simplified 58.1%

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

   5. Taylor expanded in z around 0 43.8%

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

4. Final simplification 40.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.85 \cdot 10^{-89}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{-192}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{+27}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot x\\ \end{array} \]

Alternative 15: 34.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{-88}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{-192}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+27}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.8e-88)
   x
   (if (<= y -1.2e-192) (/ (- a) b) (if (<= y 1.6e+27) (/ t b) x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.8e-88) {
		tmp = x;
	} else if (y <= -1.2e-192) {
		tmp = -a / b;
	} else if (y <= 1.6e+27) {
		tmp = t / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-1.8d-88)) then
        tmp = x
    else if (y <= (-1.2d-192)) then
        tmp = -a / b
    else if (y <= 1.6d+27) then
        tmp = t / b
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.8e-88) {
		tmp = x;
	} else if (y <= -1.2e-192) {
		tmp = -a / b;
	} else if (y <= 1.6e+27) {
		tmp = t / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.8e-88:
		tmp = x
	elif y <= -1.2e-192:
		tmp = -a / b
	elif y <= 1.6e+27:
		tmp = t / b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.8e-88)
		tmp = x;
	elseif (y <= -1.2e-192)
		tmp = Float64(Float64(-a) / b);
	elseif (y <= 1.6e+27)
		tmp = Float64(t / b);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -1.8e-88)
		tmp = x;
	elseif (y <= -1.2e-192)
		tmp = -a / b;
	elseif (y <= 1.6e+27)
		tmp = t / b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.8e-88], x, If[LessEqual[y, -1.2e-192], N[((-a) / b), $MachinePrecision], If[LessEqual[y, 1.6e+27], N[(t / b), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.8e-88 or 1.60000000000000008e27 < y

   1. Initial program 60.7%

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

   2. Taylor expanded in z around 0 38.5%

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

   if -1.8e-88 < y < -1.2e-192

   1. Initial program 78.5%

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

   2. Taylor expanded in y around 0 75.1%

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

   3. Taylor expanded in t around 0 53.5%

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

      1. associate-*r/ 53.5%

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

      2. neg-mul-1 53.5%

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

   5. Simplified 53.5%

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

   if -1.2e-192 < y < 1.60000000000000008e27

   1. Initial program 70.8%

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

   2. Taylor expanded in t around inf 32.7%

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

      1. *-commutative 32.7%

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

   4. Simplified 32.7%

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

   5. Taylor expanded in y around 0 38.9%

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

4. Final simplification 40.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{-88}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{-192}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+27}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 16: 34.4% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{-87}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+28}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -6e-87) x (if (<= y 8e+28) (/ t b) x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -6e-87) {
		tmp = x;
	} else if (y <= 8e+28) {
		tmp = t / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-6d-87)) then
        tmp = x
    else if (y <= 8d+28) then
        tmp = t / b
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -6e-87) {
		tmp = x;
	} else if (y <= 8e+28) {
		tmp = t / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -6e-87:
		tmp = x
	elif y <= 8e+28:
		tmp = t / b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -6e-87)
		tmp = x;
	elseif (y <= 8e+28)
		tmp = Float64(t / b);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -6e-87)
		tmp = x;
	elseif (y <= 8e+28)
		tmp = t / b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -6e-87], x, If[LessEqual[y, 8e+28], N[(t / b), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -6.00000000000000033e-87 or 7.99999999999999967e28 < y

   1. Initial program 60.7%

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

   2. Taylor expanded in z around 0 38.5%

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

   if -6.00000000000000033e-87 < y < 7.99999999999999967e28

   1. Initial program 72.2%

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

   2. Taylor expanded in t around inf 29.5%

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

      1. *-commutative 29.5%

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

   4. Simplified 29.5%

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

   5. Taylor expanded in y around 0 36.3%

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

4. Final simplification 37.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{-87}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+28}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 17: 25.7% accurate, 17.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 66.2%

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

2. Taylor expanded in z around 0 24.9%

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

3. Final simplification 24.9%

   \[\leadsto x \]

Developer target: 73.6% 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 2023275 
(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)))))