Development.Shake.Progress:decay from shake-0.15.5

Percentage Accurate: 66.3% → 86.6%

Time: 21.4s

Alternatives: 17

Speedup: 1.0×

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: 66.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 86.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := \frac{t - a}{b - y}\\ t_3 := z \cdot \left(t - a\right)\\ t_4 := x \cdot \left(\frac{y}{t\_1} + \frac{t\_3}{x \cdot t\_1}\right)\\ \mathbf{if}\;z \leq -9.5 \cdot 10^{+51}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -4.7 \cdot 10^{-105}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-199}:\\ \;\;\;\;\frac{t\_3 + x \cdot y}{t\_1}\\ \mathbf{elif}\;z \leq 90000:\\ \;\;\;\;t\_4\\ \mathbf{else}:\\ \;\;\;\;\left(t\_2 + \frac{y}{z} \cdot \frac{x}{b - y}\right) + \frac{y}{z} \cdot \frac{a - t}{{\left(b - y\right)}^{2}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y))))
        (t_2 (/ (- t a) (- b y)))
        (t_3 (* z (- t a)))
        (t_4 (* x (+ (/ y t_1) (/ t_3 (* x t_1))))))
   (if (<= z -9.5e+51)
     t_2
     (if (<= z -4.7e-105)
       t_4
       (if (<= z 2.9e-199)
         (/ (+ t_3 (* x y)) t_1)
         (if (<= z 90000.0)
           t_4
           (+
            (+ t_2 (* (/ y z) (/ x (- b y))))
            (* (/ y z) (/ (- a t) (pow (- b y) 2.0))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double t_2 = (t - a) / (b - y);
	double t_3 = z * (t - a);
	double t_4 = x * ((y / t_1) + (t_3 / (x * t_1)));
	double tmp;
	if (z <= -9.5e+51) {
		tmp = t_2;
	} else if (z <= -4.7e-105) {
		tmp = t_4;
	} else if (z <= 2.9e-199) {
		tmp = (t_3 + (x * y)) / t_1;
	} else if (z <= 90000.0) {
		tmp = t_4;
	} else {
		tmp = (t_2 + ((y / z) * (x / (b - y)))) + ((y / z) * ((a - t) / pow((b - y), 2.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = y + (z * (b - y))
    t_2 = (t - a) / (b - y)
    t_3 = z * (t - a)
    t_4 = x * ((y / t_1) + (t_3 / (x * t_1)))
    if (z <= (-9.5d+51)) then
        tmp = t_2
    else if (z <= (-4.7d-105)) then
        tmp = t_4
    else if (z <= 2.9d-199) then
        tmp = (t_3 + (x * y)) / t_1
    else if (z <= 90000.0d0) then
        tmp = t_4
    else
        tmp = (t_2 + ((y / z) * (x / (b - y)))) + ((y / z) * ((a - t) / ((b - y) ** 2.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double t_2 = (t - a) / (b - y);
	double t_3 = z * (t - a);
	double t_4 = x * ((y / t_1) + (t_3 / (x * t_1)));
	double tmp;
	if (z <= -9.5e+51) {
		tmp = t_2;
	} else if (z <= -4.7e-105) {
		tmp = t_4;
	} else if (z <= 2.9e-199) {
		tmp = (t_3 + (x * y)) / t_1;
	} else if (z <= 90000.0) {
		tmp = t_4;
	} else {
		tmp = (t_2 + ((y / z) * (x / (b - y)))) + ((y / z) * ((a - t) / Math.pow((b - y), 2.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z * (b - y))
	t_2 = (t - a) / (b - y)
	t_3 = z * (t - a)
	t_4 = x * ((y / t_1) + (t_3 / (x * t_1)))
	tmp = 0
	if z <= -9.5e+51:
		tmp = t_2
	elif z <= -4.7e-105:
		tmp = t_4
	elif z <= 2.9e-199:
		tmp = (t_3 + (x * y)) / t_1
	elif z <= 90000.0:
		tmp = t_4
	else:
		tmp = (t_2 + ((y / z) * (x / (b - y)))) + ((y / z) * ((a - t) / math.pow((b - y), 2.0)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(z * Float64(b - y)))
	t_2 = Float64(Float64(t - a) / Float64(b - y))
	t_3 = Float64(z * Float64(t - a))
	t_4 = Float64(x * Float64(Float64(y / t_1) + Float64(t_3 / Float64(x * t_1))))
	tmp = 0.0
	if (z <= -9.5e+51)
		tmp = t_2;
	elseif (z <= -4.7e-105)
		tmp = t_4;
	elseif (z <= 2.9e-199)
		tmp = Float64(Float64(t_3 + Float64(x * y)) / t_1);
	elseif (z <= 90000.0)
		tmp = t_4;
	else
		tmp = Float64(Float64(t_2 + Float64(Float64(y / z) * Float64(x / Float64(b - y)))) + Float64(Float64(y / z) * Float64(Float64(a - t) / (Float64(b - y) ^ 2.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (z * (b - y));
	t_2 = (t - a) / (b - y);
	t_3 = z * (t - a);
	t_4 = x * ((y / t_1) + (t_3 / (x * t_1)));
	tmp = 0.0;
	if (z <= -9.5e+51)
		tmp = t_2;
	elseif (z <= -4.7e-105)
		tmp = t_4;
	elseif (z <= 2.9e-199)
		tmp = (t_3 + (x * y)) / t_1;
	elseif (z <= 90000.0)
		tmp = t_4;
	else
		tmp = (t_2 + ((y / z) * (x / (b - y)))) + ((y / z) * ((a - t) / ((b - y) ^ 2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(x * N[(N[(y / t$95$1), $MachinePrecision] + N[(t$95$3 / N[(x * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9.5e+51], t$95$2, If[LessEqual[z, -4.7e-105], t$95$4, If[LessEqual[z, 2.9e-199], N[(N[(t$95$3 + N[(x * y), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[z, 90000.0], t$95$4, N[(N[(t$95$2 + N[(N[(y / z), $MachinePrecision] * N[(x / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y / z), $MachinePrecision] * N[(N[(a - t), $MachinePrecision] / N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -9.4999999999999999e51

   1. Initial program 46.8%

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

   3. Taylor expanded in z around inf 88.1%

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

   if -9.4999999999999999e51 < z < -4.69999999999999986e-105 or 2.9e-199 < z < 9e4

   1. Initial program 78.7%

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

   3. Taylor expanded in x around inf 92.5%

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

   if -4.69999999999999986e-105 < z < 2.9e-199

   1. Initial program 95.6%

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

   if 9e4 < z

   1. Initial program 32.8%

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

   3. Taylor expanded in z around inf 58.5%

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

      1. associate--r+ 58.5%

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

      2. +-commutative 58.5%

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

      3. associate--l+ 58.5%

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

      4. *-commutative 58.5%

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

      5. times-frac 61.0%

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

      6. div-sub 61.0%

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

      7. times-frac 95.0%

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

   5. Simplified 95.0%

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

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+51}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -4.7 \cdot 10^{-105}:\\ \;\;\;\;x \cdot \left(\frac{y}{y + z \cdot \left(b - y\right)} + \frac{z \cdot \left(t - a\right)}{x \cdot \left(y + z \cdot \left(b - y\right)\right)}\right)\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-199}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 90000:\\ \;\;\;\;x \cdot \left(\frac{y}{y + z \cdot \left(b - y\right)} + \frac{z \cdot \left(t - a\right)}{x \cdot \left(y + z \cdot \left(b - y\right)\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{t - a}{b - y} + \frac{y}{z} \cdot \frac{x}{b - y}\right) + \frac{y}{z} \cdot \frac{a - t}{{\left(b - y\right)}^{2}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 89.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ \mathbf{if}\;z \leq -2.45 \cdot 10^{+33} \lor \neg \left(z \leq 90000\right):\\ \;\;\;\;\frac{x \cdot \frac{y}{b - y} - y \cdot \frac{t - a}{{\left(b - y\right)}^{2}}}{z} + \frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{t\_1} + \frac{z \cdot \left(t - a\right)}{x \cdot t\_1}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y)))))
   (if (or (<= z -2.45e+33) (not (<= z 90000.0)))
     (+
      (/ (- (* x (/ y (- b y))) (* y (/ (- t a) (pow (- b y) 2.0)))) z)
      (/ (- t a) (- b y)))
     (* x (+ (/ y t_1) (/ (* z (- t a)) (* x t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double tmp;
	if ((z <= -2.45e+33) || !(z <= 90000.0)) {
		tmp = (((x * (y / (b - y))) - (y * ((t - a) / pow((b - y), 2.0)))) / z) + ((t - a) / (b - y));
	} else {
		tmp = x * ((y / t_1) + ((z * (t - a)) / (x * t_1)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y + (z * (b - y))
    if ((z <= (-2.45d+33)) .or. (.not. (z <= 90000.0d0))) then
        tmp = (((x * (y / (b - y))) - (y * ((t - a) / ((b - y) ** 2.0d0)))) / z) + ((t - a) / (b - y))
    else
        tmp = x * ((y / t_1) + ((z * (t - a)) / (x * t_1)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double tmp;
	if ((z <= -2.45e+33) || !(z <= 90000.0)) {
		tmp = (((x * (y / (b - y))) - (y * ((t - a) / Math.pow((b - y), 2.0)))) / z) + ((t - a) / (b - y));
	} else {
		tmp = x * ((y / t_1) + ((z * (t - a)) / (x * t_1)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z * (b - y))
	tmp = 0
	if (z <= -2.45e+33) or not (z <= 90000.0):
		tmp = (((x * (y / (b - y))) - (y * ((t - a) / math.pow((b - y), 2.0)))) / z) + ((t - a) / (b - y))
	else:
		tmp = x * ((y / t_1) + ((z * (t - a)) / (x * t_1)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(z * Float64(b - y)))
	tmp = 0.0
	if ((z <= -2.45e+33) || !(z <= 90000.0))
		tmp = Float64(Float64(Float64(Float64(x * Float64(y / Float64(b - y))) - Float64(y * Float64(Float64(t - a) / (Float64(b - y) ^ 2.0)))) / z) + Float64(Float64(t - a) / Float64(b - y)));
	else
		tmp = Float64(x * Float64(Float64(y / t_1) + Float64(Float64(z * Float64(t - a)) / Float64(x * t_1))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (z * (b - y));
	tmp = 0.0;
	if ((z <= -2.45e+33) || ~((z <= 90000.0)))
		tmp = (((x * (y / (b - y))) - (y * ((t - a) / ((b - y) ^ 2.0)))) / z) + ((t - a) / (b - y));
	else
		tmp = x * ((y / t_1) + ((z * (t - a)) / (x * t_1)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[z, -2.45e+33], N[Not[LessEqual[z, 90000.0]], $MachinePrecision]], N[(N[(N[(N[(x * N[(y / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * N[(N[(t - a), $MachinePrecision] / N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] + N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y / t$95$1), $MachinePrecision] + N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / N[(x * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.45000000000000007e33 or 9e4 < z

   1. Initial program 39.3%

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

   3. Taylor expanded in z around -inf 66.9%

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

      1. associate--l+ 66.9%

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

      2. mul-1-neg 66.9%

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

      3. distribute-lft-out-- 66.9%

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

      4. associate-/l* 71.9%

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

      5. associate-/l* 95.0%

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

      6. div-sub 95.0%

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

   5. Simplified 95.0%

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

   if -2.45000000000000007e33 < z < 9e4

   1. Initial program 87.9%

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

   3. Taylor expanded in x around inf 90.8%

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

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.45 \cdot 10^{+33} \lor \neg \left(z \leq 90000\right):\\ \;\;\;\;\frac{x \cdot \frac{y}{b - y} - y \cdot \frac{t - a}{{\left(b - y\right)}^{2}}}{z} + \frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{y + z \cdot \left(b - y\right)} + \frac{z \cdot \left(t - a\right)}{x \cdot \left(y + z \cdot \left(b - y\right)\right)}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 84.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := \frac{t - a}{b - y}\\ t_3 := z \cdot \left(t - a\right)\\ t_4 := x \cdot \left(\frac{y}{t\_1} + \frac{t\_3}{x \cdot t\_1}\right)\\ \mathbf{if}\;z \leq -1.7 \cdot 10^{+52}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-103}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-196}:\\ \;\;\;\;\frac{t\_3 + x \cdot y}{t\_1}\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+22}:\\ \;\;\;\;t\_4\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y))))
        (t_2 (/ (- t a) (- b y)))
        (t_3 (* z (- t a)))
        (t_4 (* x (+ (/ y t_1) (/ t_3 (* x t_1))))))
   (if (<= z -1.7e+52)
     t_2
     (if (<= z -1.1e-103)
       t_4
       (if (<= z 6.5e-196)
         (/ (+ t_3 (* x y)) t_1)
         (if (<= z 3.4e+22) t_4 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double t_2 = (t - a) / (b - y);
	double t_3 = z * (t - a);
	double t_4 = x * ((y / t_1) + (t_3 / (x * t_1)));
	double tmp;
	if (z <= -1.7e+52) {
		tmp = t_2;
	} else if (z <= -1.1e-103) {
		tmp = t_4;
	} else if (z <= 6.5e-196) {
		tmp = (t_3 + (x * y)) / t_1;
	} else if (z <= 3.4e+22) {
		tmp = t_4;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = y + (z * (b - y))
    t_2 = (t - a) / (b - y)
    t_3 = z * (t - a)
    t_4 = x * ((y / t_1) + (t_3 / (x * t_1)))
    if (z <= (-1.7d+52)) then
        tmp = t_2
    else if (z <= (-1.1d-103)) then
        tmp = t_4
    else if (z <= 6.5d-196) then
        tmp = (t_3 + (x * y)) / t_1
    else if (z <= 3.4d+22) then
        tmp = t_4
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double t_2 = (t - a) / (b - y);
	double t_3 = z * (t - a);
	double t_4 = x * ((y / t_1) + (t_3 / (x * t_1)));
	double tmp;
	if (z <= -1.7e+52) {
		tmp = t_2;
	} else if (z <= -1.1e-103) {
		tmp = t_4;
	} else if (z <= 6.5e-196) {
		tmp = (t_3 + (x * y)) / t_1;
	} else if (z <= 3.4e+22) {
		tmp = t_4;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z * (b - y))
	t_2 = (t - a) / (b - y)
	t_3 = z * (t - a)
	t_4 = x * ((y / t_1) + (t_3 / (x * t_1)))
	tmp = 0
	if z <= -1.7e+52:
		tmp = t_2
	elif z <= -1.1e-103:
		tmp = t_4
	elif z <= 6.5e-196:
		tmp = (t_3 + (x * y)) / t_1
	elif z <= 3.4e+22:
		tmp = t_4
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(z * Float64(b - y)))
	t_2 = Float64(Float64(t - a) / Float64(b - y))
	t_3 = Float64(z * Float64(t - a))
	t_4 = Float64(x * Float64(Float64(y / t_1) + Float64(t_3 / Float64(x * t_1))))
	tmp = 0.0
	if (z <= -1.7e+52)
		tmp = t_2;
	elseif (z <= -1.1e-103)
		tmp = t_4;
	elseif (z <= 6.5e-196)
		tmp = Float64(Float64(t_3 + Float64(x * y)) / t_1);
	elseif (z <= 3.4e+22)
		tmp = t_4;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (z * (b - y));
	t_2 = (t - a) / (b - y);
	t_3 = z * (t - a);
	t_4 = x * ((y / t_1) + (t_3 / (x * t_1)));
	tmp = 0.0;
	if (z <= -1.7e+52)
		tmp = t_2;
	elseif (z <= -1.1e-103)
		tmp = t_4;
	elseif (z <= 6.5e-196)
		tmp = (t_3 + (x * y)) / t_1;
	elseif (z <= 3.4e+22)
		tmp = t_4;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(x * N[(N[(y / t$95$1), $MachinePrecision] + N[(t$95$3 / N[(x * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.7e+52], t$95$2, If[LessEqual[z, -1.1e-103], t$95$4, If[LessEqual[z, 6.5e-196], N[(N[(t$95$3 + N[(x * y), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[z, 3.4e+22], t$95$4, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.7e52 or 3.4e22 < z

   1. Initial program 37.7%

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

   3. Taylor expanded in z around inf 86.6%

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

   if -1.7e52 < z < -1.1e-103 or 6.5000000000000004e-196 < z < 3.4e22

   1. Initial program 78.6%

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

   3. Taylor expanded in x around inf 91.7%

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

   if -1.1e-103 < z < 6.5000000000000004e-196

   1. Initial program 95.6%

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

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+52}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-103}:\\ \;\;\;\;x \cdot \left(\frac{y}{y + z \cdot \left(b - y\right)} + \frac{z \cdot \left(t - a\right)}{x \cdot \left(y + z \cdot \left(b - y\right)\right)}\right)\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-196}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+22}:\\ \;\;\;\;x \cdot \left(\frac{y}{y + z \cdot \left(b - y\right)} + \frac{z \cdot \left(t - a\right)}{x \cdot \left(y + z \cdot \left(b - y\right)\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 72.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot y + z \cdot t}{y + z \cdot \left(b - y\right)}\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -1.5 \cdot 10^{+20}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-71}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-34}:\\ \;\;\;\;x - \frac{z \cdot a}{y}\\ \mathbf{elif}\;z \leq 0.0021:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ (* x y) (* z t)) (+ y (* z (- b y)))))
        (t_2 (/ (- t a) (- b y))))
   (if (<= z -1.5e+20)
     t_2
     (if (<= z 5.8e-71)
       t_1
       (if (<= z 3.4e-34) (- x (/ (* z a) y)) (if (<= z 0.0021) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x * y) + (z * t)) / (y + (z * (b - y)));
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -1.5e+20) {
		tmp = t_2;
	} else if (z <= 5.8e-71) {
		tmp = t_1;
	} else if (z <= 3.4e-34) {
		tmp = x - ((z * a) / y);
	} else if (z <= 0.0021) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((x * y) + (z * t)) / (y + (z * (b - y)))
    t_2 = (t - a) / (b - y)
    if (z <= (-1.5d+20)) then
        tmp = t_2
    else if (z <= 5.8d-71) then
        tmp = t_1
    else if (z <= 3.4d-34) then
        tmp = x - ((z * a) / y)
    else if (z <= 0.0021d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x * y) + (z * t)) / (y + (z * (b - y)));
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -1.5e+20) {
		tmp = t_2;
	} else if (z <= 5.8e-71) {
		tmp = t_1;
	} else if (z <= 3.4e-34) {
		tmp = x - ((z * a) / y);
	} else if (z <= 0.0021) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((x * y) + (z * t)) / (y + (z * (b - y)))
	t_2 = (t - a) / (b - y)
	tmp = 0
	if z <= -1.5e+20:
		tmp = t_2
	elif z <= 5.8e-71:
		tmp = t_1
	elif z <= 3.4e-34:
		tmp = x - ((z * a) / y)
	elif z <= 0.0021:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(x * y) + Float64(z * t)) / Float64(y + Float64(z * Float64(b - y))))
	t_2 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -1.5e+20)
		tmp = t_2;
	elseif (z <= 5.8e-71)
		tmp = t_1;
	elseif (z <= 3.4e-34)
		tmp = Float64(x - Float64(Float64(z * a) / y));
	elseif (z <= 0.0021)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((x * y) + (z * t)) / (y + (z * (b - y)));
	t_2 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -1.5e+20)
		tmp = t_2;
	elseif (z <= 5.8e-71)
		tmp = t_1;
	elseif (z <= 3.4e-34)
		tmp = x - ((z * a) / y);
	elseif (z <= 0.0021)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.5e+20], t$95$2, If[LessEqual[z, 5.8e-71], t$95$1, If[LessEqual[z, 3.4e-34], N[(x - N[(N[(z * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.0021], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.5e20 or 0.00209999999999999987 < z

   1. Initial program 42.8%

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

   3. Taylor expanded in z around inf 85.1%

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

   if -1.5e20 < z < 5.7999999999999997e-71 or 3.4000000000000001e-34 < z < 0.00209999999999999987

   1. Initial program 88.8%

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

   3. Taylor expanded in a around 0 74.0%

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

   if 5.7999999999999997e-71 < z < 3.4000000000000001e-34

   1. Initial program 54.4%

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

   3. Taylor expanded in z around 0 37.4%

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

   4. Taylor expanded in a around inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. associate-/l* 99.7%

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

   6. Simplified 99.7%

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

      1. unsub-neg 99.7%

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

      2. associate-*r/ 100.0%

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

      3. *-commutative 100.0%

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

   8. Applied egg-rr 100.0%

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

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+20}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-71}:\\ \;\;\;\;\frac{x \cdot y + z \cdot t}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-34}:\\ \;\;\;\;x - \frac{z \cdot a}{y}\\ \mathbf{elif}\;z \leq 0.0021:\\ \;\;\;\;\frac{x \cdot y + z \cdot t}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 68.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(t - a\right) + x \cdot y\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -4.1 \cdot 10^{-79}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-211}:\\ \;\;\;\;\frac{t\_1}{y}\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-175}:\\ \;\;\;\;\frac{t\_1}{z \cdot b}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-5}:\\ \;\;\;\;x + t \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (* z (- t a)) (* x y))) (t_2 (/ (- t a) (- b y))))
   (if (<= z -4.1e-79)
     t_2
     (if (<= z 5.6e-211)
       (/ t_1 y)
       (if (<= z 3.3e-175)
         (/ t_1 (* z b))
         (if (<= z 1.7e-5) (+ x (* t (/ z y))) t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z * (t - a)) + (x * y);
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -4.1e-79) {
		tmp = t_2;
	} else if (z <= 5.6e-211) {
		tmp = t_1 / y;
	} else if (z <= 3.3e-175) {
		tmp = t_1 / (z * b);
	} else if (z <= 1.7e-5) {
		tmp = x + (t * (z / y));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (z * (t - a)) + (x * y)
    t_2 = (t - a) / (b - y)
    if (z <= (-4.1d-79)) then
        tmp = t_2
    else if (z <= 5.6d-211) then
        tmp = t_1 / y
    else if (z <= 3.3d-175) then
        tmp = t_1 / (z * b)
    else if (z <= 1.7d-5) then
        tmp = x + (t * (z / y))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z * (t - a)) + (x * y);
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -4.1e-79) {
		tmp = t_2;
	} else if (z <= 5.6e-211) {
		tmp = t_1 / y;
	} else if (z <= 3.3e-175) {
		tmp = t_1 / (z * b);
	} else if (z <= 1.7e-5) {
		tmp = x + (t * (z / y));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z * (t - a)) + (x * y)
	t_2 = (t - a) / (b - y)
	tmp = 0
	if z <= -4.1e-79:
		tmp = t_2
	elif z <= 5.6e-211:
		tmp = t_1 / y
	elif z <= 3.3e-175:
		tmp = t_1 / (z * b)
	elif z <= 1.7e-5:
		tmp = x + (t * (z / y))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z * Float64(t - a)) + Float64(x * y))
	t_2 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -4.1e-79)
		tmp = t_2;
	elseif (z <= 5.6e-211)
		tmp = Float64(t_1 / y);
	elseif (z <= 3.3e-175)
		tmp = Float64(t_1 / Float64(z * b));
	elseif (z <= 1.7e-5)
		tmp = Float64(x + Float64(t * Float64(z / y)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z * (t - a)) + (x * y);
	t_2 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -4.1e-79)
		tmp = t_2;
	elseif (z <= 5.6e-211)
		tmp = t_1 / y;
	elseif (z <= 3.3e-175)
		tmp = t_1 / (z * b);
	elseif (z <= 1.7e-5)
		tmp = x + (t * (z / y));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.1e-79], t$95$2, If[LessEqual[z, 5.6e-211], N[(t$95$1 / y), $MachinePrecision], If[LessEqual[z, 3.3e-175], N[(t$95$1 / N[(z * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.7e-5], N[(x + N[(t * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.09999999999999994e-79 or 1.7e-5 < z

   1. Initial program 48.1%

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

   3. Taylor expanded in z around inf 79.4%

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

   if -4.09999999999999994e-79 < z < 5.5999999999999996e-211

   1. Initial program 92.0%

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

   3. Taylor expanded in z around 0 70.3%

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

   if 5.5999999999999996e-211 < z < 3.29999999999999999e-175

   1. Initial program 89.3%

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

   3. Taylor expanded in y around 0 78.6%

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

      1. *-commutative 78.6%

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

   5. Simplified 78.6%

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

   if 3.29999999999999999e-175 < z < 1.7e-5

   1. Initial program 82.5%

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

   3. Taylor expanded in z around 0 57.8%

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

   4. Taylor expanded in x around inf 72.1%

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

   5. Taylor expanded in t around inf 68.2%

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

      1. associate-/l* 65.2%

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

   7. Simplified 65.2%

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

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{-79}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-211}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y}\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-175}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + x \cdot y}{z \cdot b}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-5}:\\ \;\;\;\;x + t \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 68.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -1.7 \cdot 10^{-42}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-226}:\\ \;\;\;\;x - \frac{z \cdot a}{y}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-153}:\\ \;\;\;\;\frac{x \cdot y}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-9}:\\ \;\;\;\;x + t \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -1.7e-42)
     t_1
     (if (<= z 1.1e-226)
       (- x (/ (* z a) y))
       (if (<= z 9e-153)
         (/ (* x y) (+ y (* z (- b y))))
         (if (<= z 1.5e-9) (+ x (* t (/ z y))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -1.7e-42) {
		tmp = t_1;
	} else if (z <= 1.1e-226) {
		tmp = x - ((z * a) / y);
	} else if (z <= 9e-153) {
		tmp = (x * y) / (y + (z * (b - y)));
	} else if (z <= 1.5e-9) {
		tmp = x + (t * (z / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    if (z <= (-1.7d-42)) then
        tmp = t_1
    else if (z <= 1.1d-226) then
        tmp = x - ((z * a) / y)
    else if (z <= 9d-153) then
        tmp = (x * y) / (y + (z * (b - y)))
    else if (z <= 1.5d-9) then
        tmp = x + (t * (z / y))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -1.7e-42) {
		tmp = t_1;
	} else if (z <= 1.1e-226) {
		tmp = x - ((z * a) / y);
	} else if (z <= 9e-153) {
		tmp = (x * y) / (y + (z * (b - y)));
	} else if (z <= 1.5e-9) {
		tmp = x + (t * (z / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	tmp = 0
	if z <= -1.7e-42:
		tmp = t_1
	elif z <= 1.1e-226:
		tmp = x - ((z * a) / y)
	elif z <= 9e-153:
		tmp = (x * y) / (y + (z * (b - y)))
	elif z <= 1.5e-9:
		tmp = x + (t * (z / y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -1.7e-42)
		tmp = t_1;
	elseif (z <= 1.1e-226)
		tmp = Float64(x - Float64(Float64(z * a) / y));
	elseif (z <= 9e-153)
		tmp = Float64(Float64(x * y) / Float64(y + Float64(z * Float64(b - y))));
	elseif (z <= 1.5e-9)
		tmp = Float64(x + Float64(t * Float64(z / y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -1.7e-42)
		tmp = t_1;
	elseif (z <= 1.1e-226)
		tmp = x - ((z * a) / y);
	elseif (z <= 9e-153)
		tmp = (x * y) / (y + (z * (b - y)));
	elseif (z <= 1.5e-9)
		tmp = x + (t * (z / y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.7e-42], t$95$1, If[LessEqual[z, 1.1e-226], N[(x - N[(N[(z * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9e-153], N[(N[(x * y), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.5e-9], N[(x + N[(t * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.70000000000000011e-42 or 1.49999999999999999e-9 < z

   1. Initial program 46.5%

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

   3. Taylor expanded in z around inf 82.1%

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

   if -1.70000000000000011e-42 < z < 1.1e-226

   1. Initial program 88.7%

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

   3. Taylor expanded in z around 0 51.9%

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

   4. Taylor expanded in a around inf 63.4%

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

      1. mul-1-neg 63.4%

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

      2. associate-/l* 62.5%

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

   6. Simplified 62.5%

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

      1. unsub-neg 62.5%

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

      2. associate-*r/ 63.4%

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

      3. *-commutative 63.4%

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

   8. Applied egg-rr 63.4%

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

   if 1.1e-226 < z < 9e-153

   1. Initial program 94.7%

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

   3. Taylor expanded in x around inf 62.5%

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

      1. *-commutative 62.5%

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

   5. Simplified 62.5%

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

   if 9e-153 < z < 1.49999999999999999e-9

   1. Initial program 80.0%

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

   3. Taylor expanded in z around 0 51.9%

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

   4. Taylor expanded in x around inf 71.6%

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

   5. Taylor expanded in t around inf 68.1%

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

      1. associate-/l* 68.1%

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

   7. Simplified 68.1%

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

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{-42}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-226}:\\ \;\;\;\;x - \frac{z \cdot a}{y}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-153}:\\ \;\;\;\;\frac{x \cdot y}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-9}:\\ \;\;\;\;x + t \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 68.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -4.1 \cdot 10^{-79}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 10^{-218}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y}\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-175}:\\ \;\;\;\;\frac{x \cdot y}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-9}:\\ \;\;\;\;x + t \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -4.1e-79)
     t_1
     (if (<= z 1e-218)
       (/ (+ (* z (- t a)) (* x y)) y)
       (if (<= z 3.3e-175)
         (/ (* x y) (+ y (* z (- b y))))
         (if (<= z 4e-9) (+ x (* t (/ z y))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -4.1e-79) {
		tmp = t_1;
	} else if (z <= 1e-218) {
		tmp = ((z * (t - a)) + (x * y)) / y;
	} else if (z <= 3.3e-175) {
		tmp = (x * y) / (y + (z * (b - y)));
	} else if (z <= 4e-9) {
		tmp = x + (t * (z / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    if (z <= (-4.1d-79)) then
        tmp = t_1
    else if (z <= 1d-218) then
        tmp = ((z * (t - a)) + (x * y)) / y
    else if (z <= 3.3d-175) then
        tmp = (x * y) / (y + (z * (b - y)))
    else if (z <= 4d-9) then
        tmp = x + (t * (z / y))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -4.1e-79) {
		tmp = t_1;
	} else if (z <= 1e-218) {
		tmp = ((z * (t - a)) + (x * y)) / y;
	} else if (z <= 3.3e-175) {
		tmp = (x * y) / (y + (z * (b - y)));
	} else if (z <= 4e-9) {
		tmp = x + (t * (z / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	tmp = 0
	if z <= -4.1e-79:
		tmp = t_1
	elif z <= 1e-218:
		tmp = ((z * (t - a)) + (x * y)) / y
	elif z <= 3.3e-175:
		tmp = (x * y) / (y + (z * (b - y)))
	elif z <= 4e-9:
		tmp = x + (t * (z / y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -4.1e-79)
		tmp = t_1;
	elseif (z <= 1e-218)
		tmp = Float64(Float64(Float64(z * Float64(t - a)) + Float64(x * y)) / y);
	elseif (z <= 3.3e-175)
		tmp = Float64(Float64(x * y) / Float64(y + Float64(z * Float64(b - y))));
	elseif (z <= 4e-9)
		tmp = Float64(x + Float64(t * Float64(z / y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -4.1e-79)
		tmp = t_1;
	elseif (z <= 1e-218)
		tmp = ((z * (t - a)) + (x * y)) / y;
	elseif (z <= 3.3e-175)
		tmp = (x * y) / (y + (z * (b - y)));
	elseif (z <= 4e-9)
		tmp = x + (t * (z / y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.1e-79], t$95$1, If[LessEqual[z, 1e-218], N[(N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[z, 3.3e-175], N[(N[(x * y), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4e-9], N[(x + N[(t * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.09999999999999994e-79 or 4.00000000000000025e-9 < z

   1. Initial program 48.1%

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

   3. Taylor expanded in z around inf 79.4%

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

   if -4.09999999999999994e-79 < z < 1e-218

   1. Initial program 91.8%

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

   3. Taylor expanded in z around 0 70.8%

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

   if 1e-218 < z < 3.29999999999999999e-175

   1. Initial program 91.3%

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

   3. Taylor expanded in x around inf 64.7%

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

      1. *-commutative 64.7%

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

   5. Simplified 64.7%

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

   if 3.29999999999999999e-175 < z < 4.00000000000000025e-9

   1. Initial program 82.5%

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

   3. Taylor expanded in z around 0 57.8%

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

   4. Taylor expanded in x around inf 72.1%

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

   5. Taylor expanded in t around inf 68.2%

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

      1. associate-/l* 65.2%

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

   7. Simplified 65.2%

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

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{-79}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq 10^{-218}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y}\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-175}:\\ \;\;\;\;\frac{x \cdot y}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-9}:\\ \;\;\;\;x + t \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 84.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+31} \lor \neg \left(z \leq 9 \cdot 10^{+20}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -3.1e+31) (not (<= z 9e+20)))
   (/ (- t a) (- b y))
   (/ (+ (* z (- t a)) (* x y)) (+ y (* z (- b y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -3.1e+31) || !(z <= 9e+20)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((z * (t - a)) + (x * y)) / (y + (z * (b - y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-3.1d+31)) .or. (.not. (z <= 9d+20))) then
        tmp = (t - a) / (b - y)
    else
        tmp = ((z * (t - a)) + (x * y)) / (y + (z * (b - y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -3.1e+31) || !(z <= 9e+20)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((z * (t - a)) + (x * y)) / (y + (z * (b - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -3.1e+31) or not (z <= 9e+20):
		tmp = (t - a) / (b - y)
	else:
		tmp = ((z * (t - a)) + (x * y)) / (y + (z * (b - y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -3.1e+31) || !(z <= 9e+20))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(Float64(Float64(z * Float64(t - a)) + Float64(x * y)) / Float64(y + Float64(z * Float64(b - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -3.1e+31) || ~((z <= 9e+20)))
		tmp = (t - a) / (b - y);
	else
		tmp = ((z * (t - a)) + (x * y)) / (y + (z * (b - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -3.1e+31], N[Not[LessEqual[z, 9e+20]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.1000000000000002e31 or 9e20 < z

   1. Initial program 39.6%

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

   3. Taylor expanded in z around inf 85.9%

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

   if -3.1000000000000002e31 < z < 9e20

   1. Initial program 87.3%

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

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+31} \lor \neg \left(z \leq 9 \cdot 10^{+20}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 42.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{b - y}\\ t_2 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -1 \cdot 10^{+98}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -3.1 \cdot 10^{-273}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.52 \cdot 10^{-148}:\\ \;\;\;\;\frac{a}{-b}\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{+60}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ t (- b y))) (t_2 (/ x (- 1.0 z))))
   (if (<= y -1e+98)
     t_2
     (if (<= y -3.1e-273)
       t_1
       (if (<= y 1.52e-148) (/ a (- b)) (if (<= y 6.4e+60) 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 <= -1e+98) {
		tmp = t_2;
	} else if (y <= -3.1e-273) {
		tmp = t_1;
	} else if (y <= 1.52e-148) {
		tmp = a / -b;
	} else if (y <= 6.4e+60) {
		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 <= (-1d+98)) then
        tmp = t_2
    else if (y <= (-3.1d-273)) then
        tmp = t_1
    else if (y <= 1.52d-148) then
        tmp = a / -b
    else if (y <= 6.4d+60) 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 <= -1e+98) {
		tmp = t_2;
	} else if (y <= -3.1e-273) {
		tmp = t_1;
	} else if (y <= 1.52e-148) {
		tmp = a / -b;
	} else if (y <= 6.4e+60) {
		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 <= -1e+98:
		tmp = t_2
	elif y <= -3.1e-273:
		tmp = t_1
	elif y <= 1.52e-148:
		tmp = a / -b
	elif y <= 6.4e+60:
		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 <= -1e+98)
		tmp = t_2;
	elseif (y <= -3.1e-273)
		tmp = t_1;
	elseif (y <= 1.52e-148)
		tmp = Float64(a / Float64(-b));
	elseif (y <= 6.4e+60)
		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 <= -1e+98)
		tmp = t_2;
	elseif (y <= -3.1e-273)
		tmp = t_1;
	elseif (y <= 1.52e-148)
		tmp = a / -b;
	elseif (y <= 6.4e+60)
		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, -1e+98], t$95$2, If[LessEqual[y, -3.1e-273], t$95$1, If[LessEqual[y, 1.52e-148], N[(a / (-b)), $MachinePrecision], If[LessEqual[y, 6.4e+60], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.99999999999999998e97 or 6.39999999999999982e60 < y

   1. Initial program 50.2%

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

   3. Taylor expanded in y around inf 63.0%

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

      1. mul-1-neg 63.0%

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

      2. unsub-neg 63.0%

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

   5. Simplified 63.0%

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

   if -9.99999999999999998e97 < y < -3.09999999999999988e-273 or 1.52000000000000002e-148 < y < 6.39999999999999982e60

   1. Initial program 78.6%

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

   3. Taylor expanded in t around inf 33.5%

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

      1. *-commutative 33.5%

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

   5. Simplified 33.5%

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

   6. Taylor expanded in z around inf 32.9%

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

   if -3.09999999999999988e-273 < y < 1.52000000000000002e-148

   1. Initial program 67.7%

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

   3. Taylor expanded in a around inf 38.2%

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

      1. mul-1-neg 38.2%

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

      2. distribute-rgt-neg-in 38.2%

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

   5. Simplified 38.2%

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

   6. Taylor expanded in y around 0 55.9%

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

      1. associate-*r/ 55.9%

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

      2. neg-mul-1 55.9%

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

   8. Simplified 55.9%

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

4. Final simplification 47.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+98}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq -3.1 \cdot 10^{-273}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;y \leq 1.52 \cdot 10^{-148}:\\ \;\;\;\;\frac{a}{-b}\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{+60}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 53.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -3.1 \cdot 10^{+97}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -490000000:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-35}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+19}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (- 1.0 z))))
   (if (<= y -3.1e+97)
     t_1
     (if (<= y -490000000.0)
       (/ t (- b y))
       (if (<= y -1.8e-35) x (if (<= y 1.35e+19) (/ (- t a) b) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 - z);
	double tmp;
	if (y <= -3.1e+97) {
		tmp = t_1;
	} else if (y <= -490000000.0) {
		tmp = t / (b - y);
	} else if (y <= -1.8e-35) {
		tmp = x;
	} else if (y <= 1.35e+19) {
		tmp = (t - a) / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (1.0d0 - z)
    if (y <= (-3.1d+97)) then
        tmp = t_1
    else if (y <= (-490000000.0d0)) then
        tmp = t / (b - y)
    else if (y <= (-1.8d-35)) then
        tmp = x
    else if (y <= 1.35d+19) then
        tmp = (t - a) / b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 - z);
	double tmp;
	if (y <= -3.1e+97) {
		tmp = t_1;
	} else if (y <= -490000000.0) {
		tmp = t / (b - y);
	} else if (y <= -1.8e-35) {
		tmp = x;
	} else if (y <= 1.35e+19) {
		tmp = (t - a) / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (1.0 - z)
	tmp = 0
	if y <= -3.1e+97:
		tmp = t_1
	elif y <= -490000000.0:
		tmp = t / (b - y)
	elif y <= -1.8e-35:
		tmp = x
	elif y <= 1.35e+19:
		tmp = (t - a) / b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(1.0 - z))
	tmp = 0.0
	if (y <= -3.1e+97)
		tmp = t_1;
	elseif (y <= -490000000.0)
		tmp = Float64(t / Float64(b - y));
	elseif (y <= -1.8e-35)
		tmp = x;
	elseif (y <= 1.35e+19)
		tmp = Float64(Float64(t - a) / b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (1.0 - z);
	tmp = 0.0;
	if (y <= -3.1e+97)
		tmp = t_1;
	elseif (y <= -490000000.0)
		tmp = t / (b - y);
	elseif (y <= -1.8e-35)
		tmp = x;
	elseif (y <= 1.35e+19)
		tmp = (t - a) / b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.1e+97], t$95$1, If[LessEqual[y, -490000000.0], N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.8e-35], x, If[LessEqual[y, 1.35e+19], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.09999999999999981e97 or 1.35e19 < y

   1. Initial program 52.1%

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

   3. Taylor expanded in y around inf 58.4%

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

      1. mul-1-neg 58.4%

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

      2. unsub-neg 58.4%

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

   5. Simplified 58.4%

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

   if -3.09999999999999981e97 < y < -4.9e8

   1. Initial program 69.9%

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

   3. Taylor expanded in t around inf 36.5%

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

      1. *-commutative 36.5%

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

   5. Simplified 36.5%

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

   6. Taylor expanded in z around inf 47.1%

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

   if -4.9e8 < y < -1.80000000000000009e-35

   1. Initial program 79.9%

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

   3. Taylor expanded in z around 0 31.9%

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

   if -1.80000000000000009e-35 < y < 1.35e19

   1. Initial program 77.7%

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

   3. Taylor expanded in y around 0 59.6%

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

4. Final simplification 56.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+97}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq -490000000:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-35}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+19}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 53.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -3.1 \cdot 10^{+97}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{+15}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-35}:\\ \;\;\;\;\frac{a}{y - b}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+18}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (- 1.0 z))))
   (if (<= y -3.1e+97)
     t_1
     (if (<= y -2.3e+15)
       (/ t (- b y))
       (if (<= y -1.3e-35)
         (/ a (- y b))
         (if (<= y 3.5e+18) (/ (- t a) b) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 - z);
	double tmp;
	if (y <= -3.1e+97) {
		tmp = t_1;
	} else if (y <= -2.3e+15) {
		tmp = t / (b - y);
	} else if (y <= -1.3e-35) {
		tmp = a / (y - b);
	} else if (y <= 3.5e+18) {
		tmp = (t - a) / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (1.0d0 - z)
    if (y <= (-3.1d+97)) then
        tmp = t_1
    else if (y <= (-2.3d+15)) then
        tmp = t / (b - y)
    else if (y <= (-1.3d-35)) then
        tmp = a / (y - b)
    else if (y <= 3.5d+18) then
        tmp = (t - a) / b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 - z);
	double tmp;
	if (y <= -3.1e+97) {
		tmp = t_1;
	} else if (y <= -2.3e+15) {
		tmp = t / (b - y);
	} else if (y <= -1.3e-35) {
		tmp = a / (y - b);
	} else if (y <= 3.5e+18) {
		tmp = (t - a) / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (1.0 - z)
	tmp = 0
	if y <= -3.1e+97:
		tmp = t_1
	elif y <= -2.3e+15:
		tmp = t / (b - y)
	elif y <= -1.3e-35:
		tmp = a / (y - b)
	elif y <= 3.5e+18:
		tmp = (t - a) / b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(1.0 - z))
	tmp = 0.0
	if (y <= -3.1e+97)
		tmp = t_1;
	elseif (y <= -2.3e+15)
		tmp = Float64(t / Float64(b - y));
	elseif (y <= -1.3e-35)
		tmp = Float64(a / Float64(y - b));
	elseif (y <= 3.5e+18)
		tmp = Float64(Float64(t - a) / b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (1.0 - z);
	tmp = 0.0;
	if (y <= -3.1e+97)
		tmp = t_1;
	elseif (y <= -2.3e+15)
		tmp = t / (b - y);
	elseif (y <= -1.3e-35)
		tmp = a / (y - b);
	elseif (y <= 3.5e+18)
		tmp = (t - a) / b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.1e+97], t$95$1, If[LessEqual[y, -2.3e+15], N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.3e-35], N[(a / N[(y - b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.5e+18], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.09999999999999981e97 or 3.5e18 < y

   1. Initial program 52.1%

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

   3. Taylor expanded in y around inf 58.4%

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

      1. mul-1-neg 58.4%

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

      2. unsub-neg 58.4%

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

   5. Simplified 58.4%

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

   if -3.09999999999999981e97 < y < -2.3e15

   1. Initial program 68.0%

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

   3. Taylor expanded in t around inf 38.7%

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

      1. *-commutative 38.7%

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

   5. Simplified 38.7%

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

   6. Taylor expanded in z around inf 49.9%

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

   if -2.3e15 < y < -1.30000000000000002e-35

   1. Initial program 81.2%

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

   3. Taylor expanded in a around inf 22.6%

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

      1. mul-1-neg 22.6%

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

      2. distribute-rgt-neg-in 22.6%

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

   5. Simplified 22.6%

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

   6. Taylor expanded in z around inf 35.1%

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

      1. associate-*r/ 35.1%

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

      2. neg-mul-1 35.1%

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

   8. Simplified 35.1%

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

   if -1.30000000000000002e-35 < y < 3.5e18

   1. Initial program 77.7%

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

   3. Taylor expanded in y around 0 59.6%

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

4. Final simplification 57.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+97}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{+15}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-35}:\\ \;\;\;\;\frac{a}{y - b}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+18}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 53.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -1.05 \cdot 10^{+98}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -140000000:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-35}:\\ \;\;\;\;x + t \cdot \frac{z}{y}\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+19}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (- 1.0 z))))
   (if (<= y -1.05e+98)
     t_1
     (if (<= y -140000000.0)
       (/ t (- b y))
       (if (<= y -1.4e-35)
         (+ x (* t (/ z y)))
         (if (<= y 2.1e+19) (/ (- t a) b) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 - z);
	double tmp;
	if (y <= -1.05e+98) {
		tmp = t_1;
	} else if (y <= -140000000.0) {
		tmp = t / (b - y);
	} else if (y <= -1.4e-35) {
		tmp = x + (t * (z / y));
	} else if (y <= 2.1e+19) {
		tmp = (t - a) / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (1.0d0 - z)
    if (y <= (-1.05d+98)) then
        tmp = t_1
    else if (y <= (-140000000.0d0)) then
        tmp = t / (b - y)
    else if (y <= (-1.4d-35)) then
        tmp = x + (t * (z / y))
    else if (y <= 2.1d+19) then
        tmp = (t - a) / b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 - z);
	double tmp;
	if (y <= -1.05e+98) {
		tmp = t_1;
	} else if (y <= -140000000.0) {
		tmp = t / (b - y);
	} else if (y <= -1.4e-35) {
		tmp = x + (t * (z / y));
	} else if (y <= 2.1e+19) {
		tmp = (t - a) / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (1.0 - z)
	tmp = 0
	if y <= -1.05e+98:
		tmp = t_1
	elif y <= -140000000.0:
		tmp = t / (b - y)
	elif y <= -1.4e-35:
		tmp = x + (t * (z / y))
	elif y <= 2.1e+19:
		tmp = (t - a) / b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(1.0 - z))
	tmp = 0.0
	if (y <= -1.05e+98)
		tmp = t_1;
	elseif (y <= -140000000.0)
		tmp = Float64(t / Float64(b - y));
	elseif (y <= -1.4e-35)
		tmp = Float64(x + Float64(t * Float64(z / y)));
	elseif (y <= 2.1e+19)
		tmp = Float64(Float64(t - a) / b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (1.0 - z);
	tmp = 0.0;
	if (y <= -1.05e+98)
		tmp = t_1;
	elseif (y <= -140000000.0)
		tmp = t / (b - y);
	elseif (y <= -1.4e-35)
		tmp = x + (t * (z / y));
	elseif (y <= 2.1e+19)
		tmp = (t - a) / b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.05e+98], t$95$1, If[LessEqual[y, -140000000.0], N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.4e-35], N[(x + N[(t * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.1e+19], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.05000000000000002e98 or 2.1e19 < y

   1. Initial program 52.1%

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

   3. Taylor expanded in y around inf 58.4%

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

      1. mul-1-neg 58.4%

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

      2. unsub-neg 58.4%

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

   5. Simplified 58.4%

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

   if -1.05000000000000002e98 < y < -1.4e8

   1. Initial program 69.9%

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

   3. Taylor expanded in t around inf 36.5%

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

      1. *-commutative 36.5%

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

   5. Simplified 36.5%

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

   6. Taylor expanded in z around inf 47.1%

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

   if -1.4e8 < y < -1.4e-35

   1. Initial program 79.9%

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

   3. Taylor expanded in z around 0 38.3%

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

   4. Taylor expanded in x around inf 38.2%

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

   5. Taylor expanded in t around inf 37.9%

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

      1. associate-/l* 37.9%

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

   7. Simplified 37.9%

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

   if -1.4e-35 < y < 2.1e19

   1. Initial program 77.7%

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

   3. Taylor expanded in y around 0 59.6%

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

4. Final simplification 57.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+98}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq -140000000:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-35}:\\ \;\;\;\;x + t \cdot \frac{z}{y}\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+19}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 36.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a}{-b}\\ \mathbf{if}\;z \leq -1.4 \cdot 10^{+51}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-41}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-27}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ a (- b))))
   (if (<= z -1.4e+51)
     t_1
     (if (<= z -8e-41) (/ t b) (if (<= z 1.3e-27) x t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a / -b;
	double tmp;
	if (z <= -1.4e+51) {
		tmp = t_1;
	} else if (z <= -8e-41) {
		tmp = t / b;
	} else if (z <= 1.3e-27) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a / -b
    if (z <= (-1.4d+51)) then
        tmp = t_1
    else if (z <= (-8d-41)) then
        tmp = t / b
    else if (z <= 1.3d-27) then
        tmp = x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a / -b;
	double tmp;
	if (z <= -1.4e+51) {
		tmp = t_1;
	} else if (z <= -8e-41) {
		tmp = t / b;
	} else if (z <= 1.3e-27) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a / -b
	tmp = 0
	if z <= -1.4e+51:
		tmp = t_1
	elif z <= -8e-41:
		tmp = t / b
	elif z <= 1.3e-27:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a / Float64(-b))
	tmp = 0.0
	if (z <= -1.4e+51)
		tmp = t_1;
	elseif (z <= -8e-41)
		tmp = Float64(t / b);
	elseif (z <= 1.3e-27)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a / -b;
	tmp = 0.0;
	if (z <= -1.4e+51)
		tmp = t_1;
	elseif (z <= -8e-41)
		tmp = t / b;
	elseif (z <= 1.3e-27)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a / (-b)), $MachinePrecision]}, If[LessEqual[z, -1.4e+51], t$95$1, If[LessEqual[z, -8e-41], N[(t / b), $MachinePrecision], If[LessEqual[z, 1.3e-27], x, t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.40000000000000002e51 or 1.30000000000000009e-27 < z

   1. Initial program 40.4%

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

   3. Taylor expanded in a around inf 23.7%

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

      1. mul-1-neg 23.7%

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

      2. distribute-rgt-neg-in 23.7%

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

   5. Simplified 23.7%

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

   6. Taylor expanded in y around 0 29.5%

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

      1. associate-*r/ 29.5%

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

      2. neg-mul-1 29.5%

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

   8. Simplified 29.5%

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

   if -1.40000000000000002e51 < z < -8.00000000000000005e-41

   1. Initial program 82.9%

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

   3. Taylor expanded in t around inf 34.3%

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

      1. *-commutative 34.3%

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

   5. Simplified 34.3%

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

   6. Taylor expanded in y around 0 38.5%

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

   if -8.00000000000000005e-41 < z < 1.30000000000000009e-27

   1. Initial program 87.4%

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

   3. Taylor expanded in z around 0 48.3%

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

4. Final simplification 39.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+51}:\\ \;\;\;\;\frac{a}{-b}\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-41}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-27}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{-b}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 69.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{-47} \lor \neg \left(z \leq 4 \cdot 10^{-28}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z \cdot a}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -8.8e-47) (not (<= z 4e-28)))
   (/ (- t a) (- b y))
   (- x (/ (* z a) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -8.8e-47) || !(z <= 4e-28)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x - ((z * a) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-8.8d-47)) .or. (.not. (z <= 4d-28))) then
        tmp = (t - a) / (b - y)
    else
        tmp = x - ((z * a) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -8.8e-47) || !(z <= 4e-28)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x - ((z * a) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -8.8e-47) or not (z <= 4e-28):
		tmp = (t - a) / (b - y)
	else:
		tmp = x - ((z * a) / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -8.8e-47) || !(z <= 4e-28))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(x - Float64(Float64(z * a) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -8.8e-47) || ~((z <= 4e-28)))
		tmp = (t - a) / (b - y);
	else
		tmp = x - ((z * a) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -8.8e-47], N[Not[LessEqual[z, 4e-28]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(z * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.80000000000000075e-47 or 3.99999999999999988e-28 < z

   1. Initial program 47.2%

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

   3. Taylor expanded in z around inf 80.9%

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

   if -8.80000000000000075e-47 < z < 3.99999999999999988e-28

   1. Initial program 87.4%

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

   3. Taylor expanded in z around 0 50.9%

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

   4. Taylor expanded in a around inf 59.8%

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

      1. mul-1-neg 59.8%

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

      2. associate-/l* 58.4%

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

   6. Simplified 58.4%

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

      1. unsub-neg 58.4%

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

      2. associate-*r/ 59.8%

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

      3. *-commutative 59.8%

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

   8. Applied egg-rr 59.8%

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

4. Final simplification 71.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{-47} \lor \neg \left(z \leq 4 \cdot 10^{-28}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z \cdot a}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 45.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.55 \cdot 10^{-41} \lor \neg \left(z \leq 9 \cdot 10^{-28}\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -4.55e-41) (not (<= z 9e-28))) (/ t (- b y)) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -4.55e-41) || !(z <= 9e-28)) {
		tmp = t / (b - y);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-4.55d-41)) .or. (.not. (z <= 9d-28))) then
        tmp = t / (b - y)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -4.55e-41) || !(z <= 9e-28)) {
		tmp = t / (b - y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -4.55e-41) or not (z <= 9e-28):
		tmp = t / (b - y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -4.55e-41) || !(z <= 9e-28))
		tmp = Float64(t / Float64(b - y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -4.55e-41) || ~((z <= 9e-28)))
		tmp = t / (b - y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -4.55e-41], N[Not[LessEqual[z, 9e-28]], $MachinePrecision]], N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -4.55000000000000015e-41 or 8.9999999999999996e-28 < z

   1. Initial program 47.2%

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

   3. Taylor expanded in t around inf 22.3%

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

      1. *-commutative 22.3%

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

   5. Simplified 22.3%

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

   6. Taylor expanded in z around inf 37.3%

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

   if -4.55000000000000015e-41 < z < 8.9999999999999996e-28

   1. Initial program 87.4%

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

   3. Taylor expanded in z around 0 48.3%

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

4. Final simplification 42.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.55 \cdot 10^{-41} \lor \neg \left(z \leq 9 \cdot 10^{-28}\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 34.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{-36}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{+18}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -2.2e-36) x (if (<= y 3.7e+18) (/ t b) x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.2e-36) {
		tmp = x;
	} else if (y <= 3.7e+18) {
		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 <= (-2.2d-36)) then
        tmp = x
    else if (y <= 3.7d+18) 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 <= -2.2e-36) {
		tmp = x;
	} else if (y <= 3.7e+18) {
		tmp = t / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -2.2e-36:
		tmp = x
	elif y <= 3.7e+18:
		tmp = t / b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -2.2e-36)
		tmp = x;
	elseif (y <= 3.7e+18)
		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 <= -2.2e-36)
		tmp = x;
	elseif (y <= 3.7e+18)
		tmp = t / b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -2.2e-36], x, If[LessEqual[y, 3.7e+18], N[(t / b), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -2.1999999999999999e-36 or 3.7e18 < y

   1. Initial program 57.1%

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

   3. Taylor expanded in z around 0 37.9%

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

   if -2.1999999999999999e-36 < y < 3.7e18

   1. Initial program 77.5%

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

   3. Taylor expanded in t around inf 35.4%

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

      1. *-commutative 35.4%

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

   5. Simplified 35.4%

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

   6. Taylor expanded in y around 0 34.9%

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

4. Final simplification 36.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{-36}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{+18}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 25.3% 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 65.9%

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

3. Taylor expanded in z around 0 24.8%

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

4. Final simplification 24.8%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 73.3% 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 2024096 
(FPCore (x y z t a b)
  :name "Development.Shake.Progress:decay from shake-0.15.5"
  :precision binary64

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

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