Development.Shake.Progress:decay from shake-0.15.5

Percentage Accurate: 66.2% → 90.2%

Time: 16.6s

Alternatives: 15

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: 66.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 90.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ \mathbf{if}\;z \leq -3 \cdot 10^{+28} \lor \neg \left(z \leq 11600000000000\right):\\ \;\;\;\;\left(\frac{y}{z} \cdot \frac{x}{b - y} + \frac{a - t}{y - b}\right) + y \cdot \frac{a - t}{z \cdot {\left(b - y\right)}^{2}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{t\_1} + \frac{z \cdot \left(t - a\right)}{x \cdot t\_1}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y)))))
   (if (or (<= z -3e+28) (not (<= z 11600000000000.0)))
     (+
      (+ (* (/ y z) (/ x (- b y))) (/ (- a t) (- y b)))
      (* y (/ (- a t) (* z (pow (- b y) 2.0)))))
     (* 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 <= -3e+28) || !(z <= 11600000000000.0)) {
		tmp = (((y / z) * (x / (b - y))) + ((a - t) / (y - b))) + (y * ((a - t) / (z * pow((b - y), 2.0))));
	} 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 <= (-3d+28)) .or. (.not. (z <= 11600000000000.0d0))) then
        tmp = (((y / z) * (x / (b - y))) + ((a - t) / (y - b))) + (y * ((a - t) / (z * ((b - y) ** 2.0d0))))
    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 <= -3e+28) || !(z <= 11600000000000.0)) {
		tmp = (((y / z) * (x / (b - y))) + ((a - t) / (y - b))) + (y * ((a - t) / (z * Math.pow((b - y), 2.0))));
	} 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 <= -3e+28) or not (z <= 11600000000000.0):
		tmp = (((y / z) * (x / (b - y))) + ((a - t) / (y - b))) + (y * ((a - t) / (z * math.pow((b - y), 2.0))))
	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 <= -3e+28) || !(z <= 11600000000000.0))
		tmp = Float64(Float64(Float64(Float64(y / z) * Float64(x / Float64(b - y))) + Float64(Float64(a - t) / Float64(y - b))) + Float64(y * Float64(Float64(a - t) / Float64(z * (Float64(b - y) ^ 2.0)))));
	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 <= -3e+28) || ~((z <= 11600000000000.0)))
		tmp = (((y / z) * (x / (b - y))) + ((a - t) / (y - b))) + (y * ((a - t) / (z * ((b - y) ^ 2.0))));
	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, -3e+28], N[Not[LessEqual[z, 11600000000000.0]], $MachinePrecision]], N[(N[(N[(N[(y / z), $MachinePrecision] * N[(x / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(a - t), $MachinePrecision] / N[(y - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * N[(N[(a - t), $MachinePrecision] / N[(z * N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 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 < -3.0000000000000001e28 or 1.16e13 < z

   1. Initial program 42.4%

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

   3. Taylor expanded in z around inf 64.5%

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

      1. associate--r+ 64.5%

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

      2. +-commutative 64.5%

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

      3. associate--l+ 64.5%

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

      4. *-commutative 64.5%

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

      5. times-frac 69.5%

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

      6. div-sub 69.4%

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

      7. associate-/l* 92.5%

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

   5. Simplified 92.5%

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

   if -3.0000000000000001e28 < z < 1.16e13

   1. Initial program 86.9%

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

   3. Taylor expanded in x around inf 91.3%

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

4. Final simplification 91.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+28} \lor \neg \left(z \leq 11600000000000\right):\\ \;\;\;\;\left(\frac{y}{z} \cdot \frac{x}{b - y} + \frac{a - t}{y - b}\right) + y \cdot \frac{a - t}{z \cdot {\left(b - y\right)}^{2}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{y + z \cdot \left(b - y\right)} + \frac{z \cdot \left(t - a\right)}{x \cdot \left(y + z \cdot \left(b - y\right)\right)}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 84.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ \mathbf{if}\;z \leq -5.4 \cdot 10^{+58} \lor \neg \left(z \leq 1.6 \cdot 10^{+94}\right):\\ \;\;\;\;\frac{a - t}{y - b}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{t\_1} + \frac{z \cdot \left(t - a\right)}{x \cdot t\_1}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y)))))
   (if (or (<= z -5.4e+58) (not (<= z 1.6e+94)))
     (/ (- a t) (- y b))
     (* x (+ (/ y t_1) (/ (* z (- t a)) (* x t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double tmp;
	if ((z <= -5.4e+58) || !(z <= 1.6e+94)) {
		tmp = (a - t) / (y - b);
	} else {
		tmp = x * ((y / t_1) + ((z * (t - a)) / (x * t_1)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y + (z * (b - y))
    if ((z <= (-5.4d+58)) .or. (.not. (z <= 1.6d+94))) then
        tmp = (a - t) / (y - b)
    else
        tmp = x * ((y / t_1) + ((z * (t - a)) / (x * t_1)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double tmp;
	if ((z <= -5.4e+58) || !(z <= 1.6e+94)) {
		tmp = (a - t) / (y - b);
	} else {
		tmp = x * ((y / t_1) + ((z * (t - a)) / (x * t_1)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z * (b - y))
	tmp = 0
	if (z <= -5.4e+58) or not (z <= 1.6e+94):
		tmp = (a - t) / (y - b)
	else:
		tmp = x * ((y / t_1) + ((z * (t - a)) / (x * t_1)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(z * Float64(b - y)))
	tmp = 0.0
	if ((z <= -5.4e+58) || !(z <= 1.6e+94))
		tmp = Float64(Float64(a - t) / Float64(y - b));
	else
		tmp = Float64(x * Float64(Float64(y / t_1) + Float64(Float64(z * Float64(t - a)) / Float64(x * t_1))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (z * (b - y));
	tmp = 0.0;
	if ((z <= -5.4e+58) || ~((z <= 1.6e+94)))
		tmp = (a - t) / (y - b);
	else
		tmp = x * ((y / t_1) + ((z * (t - a)) / (x * t_1)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[z, -5.4e+58], N[Not[LessEqual[z, 1.6e+94]], $MachinePrecision]], N[(N[(a - t), $MachinePrecision] / N[(y - b), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y / t$95$1), $MachinePrecision] + N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / N[(x * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.4000000000000002e58 or 1.60000000000000007e94 < z

   1. Initial program 38.6%

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

   3. Taylor expanded in z around inf 86.1%

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

   if -5.4000000000000002e58 < z < 1.60000000000000007e94

   1. Initial program 84.6%

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

   3. Taylor expanded in x around inf 89.1%

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

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{+58} \lor \neg \left(z \leq 1.6 \cdot 10^{+94}\right):\\ \;\;\;\;\frac{a - t}{y - b}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{y + z \cdot \left(b - y\right)} + \frac{z \cdot \left(t - a\right)}{x \cdot \left(y + z \cdot \left(b - y\right)\right)}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 81.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a - t}{y - b}\\ \mathbf{if}\;z \leq -1.9 \cdot 10^{+28}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -0.025:\\ \;\;\;\;\frac{x}{z \cdot \left(\frac{1}{z} + -1\right)}\\ \mathbf{elif}\;z \leq 460000000000:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y + z \cdot b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- a t) (- y b))))
   (if (<= z -1.9e+28)
     t_1
     (if (<= z -0.025)
       (/ x (* z (+ (/ 1.0 z) -1.0)))
       (if (<= z 460000000000.0)
         (/ (+ (* z (- t a)) (* y x)) (+ y (* z b)))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a - t) / (y - b);
	double tmp;
	if (z <= -1.9e+28) {
		tmp = t_1;
	} else if (z <= -0.025) {
		tmp = x / (z * ((1.0 / z) + -1.0));
	} else if (z <= 460000000000.0) {
		tmp = ((z * (t - a)) + (y * x)) / (y + (z * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a - t) / (y - b)
    if (z <= (-1.9d+28)) then
        tmp = t_1
    else if (z <= (-0.025d0)) then
        tmp = x / (z * ((1.0d0 / z) + (-1.0d0)))
    else if (z <= 460000000000.0d0) then
        tmp = ((z * (t - a)) + (y * x)) / (y + (z * b))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a - t) / (y - b);
	double tmp;
	if (z <= -1.9e+28) {
		tmp = t_1;
	} else if (z <= -0.025) {
		tmp = x / (z * ((1.0 / z) + -1.0));
	} else if (z <= 460000000000.0) {
		tmp = ((z * (t - a)) + (y * x)) / (y + (z * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a - t) / (y - b)
	tmp = 0
	if z <= -1.9e+28:
		tmp = t_1
	elif z <= -0.025:
		tmp = x / (z * ((1.0 / z) + -1.0))
	elif z <= 460000000000.0:
		tmp = ((z * (t - a)) + (y * x)) / (y + (z * b))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a - t) / Float64(y - b))
	tmp = 0.0
	if (z <= -1.9e+28)
		tmp = t_1;
	elseif (z <= -0.025)
		tmp = Float64(x / Float64(z * Float64(Float64(1.0 / z) + -1.0)));
	elseif (z <= 460000000000.0)
		tmp = Float64(Float64(Float64(z * Float64(t - a)) + Float64(y * x)) / Float64(y + Float64(z * b)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a - t) / (y - b);
	tmp = 0.0;
	if (z <= -1.9e+28)
		tmp = t_1;
	elseif (z <= -0.025)
		tmp = x / (z * ((1.0 / z) + -1.0));
	elseif (z <= 460000000000.0)
		tmp = ((z * (t - a)) + (y * x)) / (y + (z * b));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a - t), $MachinePrecision] / N[(y - b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.9e+28], t$95$1, If[LessEqual[z, -0.025], N[(x / N[(z * N[(N[(1.0 / z), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 460000000000.0], N[(N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] + N[(y * x), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.8999999999999999e28 or 4.6e11 < z

   1. Initial program 42.1%

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

   3. Taylor expanded in z around inf 81.0%

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

   if -1.8999999999999999e28 < z < -0.025000000000000001

   1. Initial program 89.2%

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

   3. Taylor expanded in y around inf 79.1%

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

      1. mul-1-neg 79.1%

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

      2. unsub-neg 79.1%

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

   5. Simplified 79.1%

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

   6. Taylor expanded in z around inf 79.3%

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

   if -0.025000000000000001 < z < 4.6e11

   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 b around inf 86.6%

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

      1. *-commutative 86.6%

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

   5. Simplified 86.6%

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

4. Final simplification 83.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+28}:\\ \;\;\;\;\frac{a - t}{y - b}\\ \mathbf{elif}\;z \leq -0.025:\\ \;\;\;\;\frac{x}{z \cdot \left(\frac{1}{z} + -1\right)}\\ \mathbf{elif}\;z \leq 460000000000:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y + z \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\frac{a - t}{y - b}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 82.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+130} \lor \neg \left(z \leq 1.8 \cdot 10^{+94}\right):\\ \;\;\;\;\frac{a - t}{y - b}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y + z \cdot \left(b - y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -3.1e+130) (not (<= z 1.8e+94)))
   (/ (- a t) (- y b))
   (/ (+ (* z (- t a)) (* y x)) (+ y (* z (- b y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -3.1e+130) || !(z <= 1.8e+94)) {
		tmp = (a - t) / (y - b);
	} else {
		tmp = ((z * (t - a)) + (y * x)) / (y + (z * (b - y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-3.1d+130)) .or. (.not. (z <= 1.8d+94))) then
        tmp = (a - t) / (y - b)
    else
        tmp = ((z * (t - a)) + (y * x)) / (y + (z * (b - y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -3.1e+130) || !(z <= 1.8e+94)) {
		tmp = (a - t) / (y - b);
	} else {
		tmp = ((z * (t - a)) + (y * x)) / (y + (z * (b - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -3.1e+130) or not (z <= 1.8e+94):
		tmp = (a - t) / (y - b)
	else:
		tmp = ((z * (t - a)) + (y * x)) / (y + (z * (b - y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -3.1e+130) || !(z <= 1.8e+94))
		tmp = Float64(Float64(a - t) / Float64(y - b));
	else
		tmp = Float64(Float64(Float64(z * Float64(t - a)) + Float64(y * x)) / Float64(y + Float64(z * Float64(b - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -3.1e+130) || ~((z <= 1.8e+94)))
		tmp = (a - t) / (y - b);
	else
		tmp = ((z * (t - a)) + (y * x)) / (y + (z * (b - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -3.1e+130], N[Not[LessEqual[z, 1.8e+94]], $MachinePrecision]], N[(N[(a - t), $MachinePrecision] / N[(y - b), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] + N[(y * x), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.1e130 or 1.79999999999999996e94 < z

   1. Initial program 29.1%

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

   3. Taylor expanded in z around inf 87.6%

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

   if -3.1e130 < z < 1.79999999999999996e94

   1. Initial program 84.5%

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

4. Final simplification 85.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+130} \lor \neg \left(z \leq 1.8 \cdot 10^{+94}\right):\\ \;\;\;\;\frac{a - t}{y - b}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y + z \cdot \left(b - y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 52.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+29}:\\ \;\;\;\;\frac{a}{y - b}\\ \mathbf{elif}\;z \leq -0.00018:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-13}:\\ \;\;\;\;x + \frac{z \cdot t}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b} - \frac{a}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.3e+29)
   (/ a (- y b))
   (if (<= z -0.00018)
     (/ x (- 1.0 z))
     (if (<= z 1.25e-13) (+ x (/ (* z t) y)) (- (/ t b) (/ a b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.3e+29) {
		tmp = a / (y - b);
	} else if (z <= -0.00018) {
		tmp = x / (1.0 - z);
	} else if (z <= 1.25e-13) {
		tmp = x + ((z * t) / y);
	} else {
		tmp = (t / b) - (a / b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-1.3d+29)) then
        tmp = a / (y - b)
    else if (z <= (-0.00018d0)) then
        tmp = x / (1.0d0 - z)
    else if (z <= 1.25d-13) then
        tmp = x + ((z * t) / y)
    else
        tmp = (t / b) - (a / b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.3e+29) {
		tmp = a / (y - b);
	} else if (z <= -0.00018) {
		tmp = x / (1.0 - z);
	} else if (z <= 1.25e-13) {
		tmp = x + ((z * t) / y);
	} else {
		tmp = (t / b) - (a / b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1.3e+29:
		tmp = a / (y - b)
	elif z <= -0.00018:
		tmp = x / (1.0 - z)
	elif z <= 1.25e-13:
		tmp = x + ((z * t) / y)
	else:
		tmp = (t / b) - (a / b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.3e+29)
		tmp = Float64(a / Float64(y - b));
	elseif (z <= -0.00018)
		tmp = Float64(x / Float64(1.0 - z));
	elseif (z <= 1.25e-13)
		tmp = Float64(x + Float64(Float64(z * t) / y));
	else
		tmp = Float64(Float64(t / b) - Float64(a / b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -1.3e+29)
		tmp = a / (y - b);
	elseif (z <= -0.00018)
		tmp = x / (1.0 - z);
	elseif (z <= 1.25e-13)
		tmp = x + ((z * t) / y);
	else
		tmp = (t / b) - (a / b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.3e+29], N[(a / N[(y - b), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -0.00018], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.25e-13], N[(x + N[(N[(z * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(N[(t / b), $MachinePrecision] - N[(a / b), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.3e29

   1. Initial program 49.3%

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

      1. fma-define 49.3%

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

   3. Simplified 49.3%

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

   5. Taylor expanded in x around inf 43.2%

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

   6. Taylor expanded in a around inf 32.6%

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

      1. mul-1-neg 32.6%

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

   8. Simplified 32.6%

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

   9. Taylor expanded in z around inf 54.9%

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

       1. associate-*r/ 54.9%

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

       2. neg-mul-1 54.9%

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

   11. Simplified 54.9%

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

   if -1.3e29 < z < -1.80000000000000011e-4

   1. Initial program 89.2%

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

   3. Taylor expanded in y around inf 79.1%

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

      1. mul-1-neg 79.1%

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

      2. unsub-neg 79.1%

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

   5. Simplified 79.1%

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

   if -1.80000000000000011e-4 < z < 1.24999999999999997e-13

   1. Initial program 87.1%

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

      1. fma-define 87.1%

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

   3. Simplified 87.1%

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

   5. Taylor expanded in x around inf 82.4%

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

   6. Taylor expanded in z around 0 64.3%

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

   7. Taylor expanded in x around 0 79.2%

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

   8. Taylor expanded in t around inf 63.4%

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

   if 1.24999999999999997e-13 < z

   1. Initial program 37.0%

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

   3. Taylor expanded in y around 0 49.8%

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

      1. div-sub 49.8%

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

   5. Applied egg-rr 49.8%

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

4. Final simplification 58.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+29}:\\ \;\;\;\;\frac{a}{y - b}\\ \mathbf{elif}\;z \leq -0.00018:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-13}:\\ \;\;\;\;x + \frac{z \cdot t}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b} - \frac{a}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 52.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+29}:\\ \;\;\;\;\frac{a}{y - b}\\ \mathbf{elif}\;z \leq -0.00018:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-11}:\\ \;\;\;\;x + \frac{z \cdot t}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -2.9e+29)
   (/ a (- y b))
   (if (<= z -0.00018)
     (/ x (- 1.0 z))
     (if (<= z 2e-11) (+ x (/ (* z t) y)) (/ (- t a) b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2.9e+29) {
		tmp = a / (y - b);
	} else if (z <= -0.00018) {
		tmp = x / (1.0 - z);
	} else if (z <= 2e-11) {
		tmp = x + ((z * t) / y);
	} else {
		tmp = (t - a) / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-2.9d+29)) then
        tmp = a / (y - b)
    else if (z <= (-0.00018d0)) then
        tmp = x / (1.0d0 - z)
    else if (z <= 2d-11) then
        tmp = x + ((z * t) / y)
    else
        tmp = (t - a) / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2.9e+29) {
		tmp = a / (y - b);
	} else if (z <= -0.00018) {
		tmp = x / (1.0 - z);
	} else if (z <= 2e-11) {
		tmp = x + ((z * t) / y);
	} else {
		tmp = (t - a) / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -2.9e+29:
		tmp = a / (y - b)
	elif z <= -0.00018:
		tmp = x / (1.0 - z)
	elif z <= 2e-11:
		tmp = x + ((z * t) / y)
	else:
		tmp = (t - a) / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -2.9e+29)
		tmp = Float64(a / Float64(y - b));
	elseif (z <= -0.00018)
		tmp = Float64(x / Float64(1.0 - z));
	elseif (z <= 2e-11)
		tmp = Float64(x + Float64(Float64(z * t) / y));
	else
		tmp = Float64(Float64(t - a) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -2.9e+29)
		tmp = a / (y - b);
	elseif (z <= -0.00018)
		tmp = x / (1.0 - z);
	elseif (z <= 2e-11)
		tmp = x + ((z * t) / y);
	else
		tmp = (t - a) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -2.9e+29], N[(a / N[(y - b), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -0.00018], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2e-11], N[(x + N[(N[(z * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.8999999999999999e29

   1. Initial program 49.3%

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

      1. fma-define 49.3%

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

   3. Simplified 49.3%

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

   5. Taylor expanded in x around inf 43.2%

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

   6. Taylor expanded in a around inf 32.6%

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

      1. mul-1-neg 32.6%

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

   8. Simplified 32.6%

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

   9. Taylor expanded in z around inf 54.9%

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

       1. associate-*r/ 54.9%

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

       2. neg-mul-1 54.9%

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

   11. Simplified 54.9%

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

   if -2.8999999999999999e29 < z < -1.80000000000000011e-4

   1. Initial program 89.2%

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

   3. Taylor expanded in y around inf 79.1%

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

      1. mul-1-neg 79.1%

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

      2. unsub-neg 79.1%

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

   5. Simplified 79.1%

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

   if -1.80000000000000011e-4 < z < 1.99999999999999988e-11

   1. Initial program 87.1%

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

      1. fma-define 87.1%

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

   3. Simplified 87.1%

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

   5. Taylor expanded in x around inf 82.4%

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

   6. Taylor expanded in z around 0 64.3%

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

   7. Taylor expanded in x around 0 79.2%

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

   8. Taylor expanded in t around inf 63.4%

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

   if 1.99999999999999988e-11 < z

   1. Initial program 37.0%

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

   3. Taylor expanded in y around 0 49.8%

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

4. Final simplification 58.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+29}:\\ \;\;\;\;\frac{a}{y - b}\\ \mathbf{elif}\;z \leq -0.00018:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-11}:\\ \;\;\;\;x + \frac{z \cdot t}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 43.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -5 \cdot 10^{+46}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-134}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{-49}:\\ \;\;\;\;\frac{a}{-b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (- 1.0 z))))
   (if (<= y -5e+46)
     t_1
     (if (<= y 1.6e-134) (/ t (- b y)) (if (<= y 4.7e-49) (/ 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 <= -5e+46) {
		tmp = t_1;
	} else if (y <= 1.6e-134) {
		tmp = t / (b - y);
	} else if (y <= 4.7e-49) {
		tmp = 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 <= (-5d+46)) then
        tmp = t_1
    else if (y <= 1.6d-134) then
        tmp = t / (b - y)
    else if (y <= 4.7d-49) then
        tmp = 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 <= -5e+46) {
		tmp = t_1;
	} else if (y <= 1.6e-134) {
		tmp = t / (b - y);
	} else if (y <= 4.7e-49) {
		tmp = 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 <= -5e+46:
		tmp = t_1
	elif y <= 1.6e-134:
		tmp = t / (b - y)
	elif y <= 4.7e-49:
		tmp = 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 <= -5e+46)
		tmp = t_1;
	elseif (y <= 1.6e-134)
		tmp = Float64(t / Float64(b - y));
	elseif (y <= 4.7e-49)
		tmp = Float64(a / Float64(-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 <= -5e+46)
		tmp = t_1;
	elseif (y <= 1.6e-134)
		tmp = t / (b - y);
	elseif (y <= 4.7e-49)
		tmp = 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, -5e+46], t$95$1, If[LessEqual[y, 1.6e-134], N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.7e-49], N[(a / (-b)), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.0000000000000002e46 or 4.70000000000000021e-49 < y

   1. Initial program 58.3%

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

   3. Taylor expanded in y around inf 51.7%

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

      1. mul-1-neg 51.7%

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

      2. unsub-neg 51.7%

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

   5. Simplified 51.7%

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

   if -5.0000000000000002e46 < y < 1.6000000000000001e-134

   1. Initial program 78.1%

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

      1. fma-define 78.2%

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

   3. Simplified 78.2%

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

   5. Taylor expanded in x around inf 76.0%

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

   6. Taylor expanded in t around inf 50.4%

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

      1. associate-/l* 46.8%

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

   8. Simplified 46.8%

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

   9. Taylor expanded in z around inf 42.5%

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

   if 1.6000000000000001e-134 < y < 4.70000000000000021e-49

   1. Initial program 67.5%

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

   3. Taylor expanded in x around inf 56.3%

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

   4. Taylor expanded in y around 0 40.4%

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

      1. div-sub 40.4%

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

   6. Simplified 40.4%

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

   7. Taylor expanded in t around 0 51.5%

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

      1. associate-*r/ 51.5%

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

      2. mul-1-neg 51.5%

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

   9. Simplified 51.5%

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

4. Final simplification 48.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+46}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-134}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{-49}:\\ \;\;\;\;\frac{a}{-b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 42.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{b - y}\\ \mathbf{if}\;z \leq -3 \cdot 10^{-100}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 410000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+117}:\\ \;\;\;\;\frac{x}{-z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ t (- b y))))
   (if (<= z -3e-100)
     t_1
     (if (<= z 410000000000.0) x (if (<= z 1.8e+117) (/ x (- z)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t / (b - y);
	double tmp;
	if (z <= -3e-100) {
		tmp = t_1;
	} else if (z <= 410000000000.0) {
		tmp = x;
	} else if (z <= 1.8e+117) {
		tmp = x / -z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t / (b - y)
    if (z <= (-3d-100)) then
        tmp = t_1
    else if (z <= 410000000000.0d0) then
        tmp = x
    else if (z <= 1.8d+117) then
        tmp = x / -z
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t / (b - y);
	double tmp;
	if (z <= -3e-100) {
		tmp = t_1;
	} else if (z <= 410000000000.0) {
		tmp = x;
	} else if (z <= 1.8e+117) {
		tmp = x / -z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t / (b - y)
	tmp = 0
	if z <= -3e-100:
		tmp = t_1
	elif z <= 410000000000.0:
		tmp = x
	elif z <= 1.8e+117:
		tmp = x / -z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t / Float64(b - y))
	tmp = 0.0
	if (z <= -3e-100)
		tmp = t_1;
	elseif (z <= 410000000000.0)
		tmp = x;
	elseif (z <= 1.8e+117)
		tmp = Float64(x / Float64(-z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t / (b - y);
	tmp = 0.0;
	if (z <= -3e-100)
		tmp = t_1;
	elseif (z <= 410000000000.0)
		tmp = x;
	elseif (z <= 1.8e+117)
		tmp = x / -z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3e-100], t$95$1, If[LessEqual[z, 410000000000.0], x, If[LessEqual[z, 1.8e+117], N[(x / (-z)), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.0000000000000001e-100 or 1.80000000000000006e117 < z

   1. Initial program 51.4%

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

      1. fma-define 51.5%

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

   3. Simplified 51.5%

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

   5. Taylor expanded in x around inf 46.1%

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

   6. Taylor expanded in t around inf 28.5%

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

      1. associate-/l* 24.7%

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

   8. Simplified 24.7%

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

   9. Taylor expanded in z around inf 36.2%

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

   if -3.0000000000000001e-100 < z < 4.1e11

   1. Initial program 85.4%

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

   3. Taylor expanded in z around 0 54.1%

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

   if 4.1e11 < z < 1.80000000000000006e117

   1. Initial program 57.8%

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

   3. Taylor expanded in y around inf 45.5%

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

      1. mul-1-neg 45.5%

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

      2. unsub-neg 45.5%

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

   5. Simplified 45.5%

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

   6. Taylor expanded in z around inf 44.5%

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

      1. associate-*r/ 44.5%

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

      2. mul-1-neg 44.5%

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

   8. Simplified 44.5%

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

4. Final simplification 44.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{-100}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;z \leq 410000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+117}:\\ \;\;\;\;\frac{x}{-z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 75.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{-16} \lor \neg \left(z \leq 1.16 \cdot 10^{-14}\right):\\ \;\;\;\;\frac{a - t}{y - b}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -3.5e-16) (not (<= z 1.16e-14)))
   (/ (- a t) (- y b))
   (+ x (/ (* z (- t a)) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -3.5e-16) || !(z <= 1.16e-14)) {
		tmp = (a - t) / (y - b);
	} else {
		tmp = x + ((z * (t - 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 <= (-3.5d-16)) .or. (.not. (z <= 1.16d-14))) then
        tmp = (a - t) / (y - b)
    else
        tmp = x + ((z * (t - 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 <= -3.5e-16) || !(z <= 1.16e-14)) {
		tmp = (a - t) / (y - b);
	} else {
		tmp = x + ((z * (t - a)) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -3.5e-16) or not (z <= 1.16e-14):
		tmp = (a - t) / (y - b)
	else:
		tmp = x + ((z * (t - a)) / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -3.5e-16) || !(z <= 1.16e-14))
		tmp = Float64(Float64(a - t) / Float64(y - b));
	else
		tmp = Float64(x + Float64(Float64(z * Float64(t - a)) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -3.5e-16) || ~((z <= 1.16e-14)))
		tmp = (a - t) / (y - b);
	else
		tmp = x + ((z * (t - a)) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -3.5e-16], N[Not[LessEqual[z, 1.16e-14]], $MachinePrecision]], N[(N[(a - t), $MachinePrecision] / N[(y - b), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.50000000000000017e-16 or 1.16000000000000007e-14 < z

   1. Initial program 47.7%

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

   3. Taylor expanded in z around inf 77.1%

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

   if -3.50000000000000017e-16 < z < 1.16000000000000007e-14

   1. Initial program 86.8%

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

      1. fma-define 86.8%

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

   3. Simplified 86.8%

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

   5. Taylor expanded in x around inf 81.9%

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

   6. Taylor expanded in z around 0 64.9%

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

   7. Taylor expanded in x around 0 80.2%

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

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{-16} \lor \neg \left(z \leq 1.16 \cdot 10^{-14}\right):\\ \;\;\;\;\frac{a - t}{y - b}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 36.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a}{-b}\\ \mathbf{if}\;z \leq -1.3 \cdot 10^{+63}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-99}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-10}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ a (- b))))
   (if (<= z -1.3e+63)
     t_1
     (if (<= z -1.9e-99) (/ t b) (if (<= z 1.15e-10) 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 <= -1.3e+63) {
		tmp = t_1;
	} else if (z <= -1.9e-99) {
		tmp = t / b;
	} else if (z <= 1.15e-10) {
		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 <= (-1.3d+63)) then
        tmp = t_1
    else if (z <= (-1.9d-99)) then
        tmp = t / b
    else if (z <= 1.15d-10) 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 <= -1.3e+63) {
		tmp = t_1;
	} else if (z <= -1.9e-99) {
		tmp = t / b;
	} else if (z <= 1.15e-10) {
		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 <= -1.3e+63:
		tmp = t_1
	elif z <= -1.9e-99:
		tmp = t / b
	elif z <= 1.15e-10:
		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 <= -1.3e+63)
		tmp = t_1;
	elseif (z <= -1.9e-99)
		tmp = Float64(t / b);
	elseif (z <= 1.15e-10)
		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 <= -1.3e+63)
		tmp = t_1;
	elseif (z <= -1.9e-99)
		tmp = t / b;
	elseif (z <= 1.15e-10)
		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, -1.3e+63], t$95$1, If[LessEqual[z, -1.9e-99], N[(t / b), $MachinePrecision], If[LessEqual[z, 1.15e-10], x, t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.3000000000000001e63 or 1.15000000000000004e-10 < z

   1. Initial program 41.6%

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

   3. Taylor expanded in x around inf 35.4%

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

   4. Taylor expanded in y around 0 36.5%

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

      1. div-sub 38.3%

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

   6. Simplified 38.3%

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

   7. Taylor expanded in t around 0 33.0%

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

      1. associate-*r/ 33.0%

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

      2. mul-1-neg 33.0%

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

   9. Simplified 33.0%

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

   if -1.3000000000000001e63 < z < -1.8999999999999998e-99

   1. Initial program 88.8%

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

   3. Taylor expanded in x around inf 81.8%

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

   4. Taylor expanded in y around 0 28.7%

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

      1. div-sub 28.9%

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

   6. Simplified 28.9%

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

   7. Taylor expanded in t around inf 29.1%

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

   if -1.8999999999999998e-99 < z < 1.15000000000000004e-10

   1. Initial program 85.0%

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

   3. Taylor expanded in z around 0 55.6%

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

4. Final simplification 41.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+63}:\\ \;\;\;\;\frac{a}{-b}\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-99}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-10}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{-b}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 69.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{-20} \lor \neg \left(z \leq 1.05 \cdot 10^{-11}\right):\\ \;\;\;\;\frac{a - t}{y - b}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z \cdot a}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -2.1e-20) (not (<= z 1.05e-11)))
   (/ (- a t) (- y b))
   (- x (/ (* z a) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.1e-20) || !(z <= 1.05e-11)) {
		tmp = (a - t) / (y - b);
	} 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 <= (-2.1d-20)) .or. (.not. (z <= 1.05d-11))) then
        tmp = (a - t) / (y - b)
    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 <= -2.1e-20) || !(z <= 1.05e-11)) {
		tmp = (a - t) / (y - b);
	} else {
		tmp = x - ((z * a) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -2.1e-20) or not (z <= 1.05e-11):
		tmp = (a - t) / (y - b)
	else:
		tmp = x - ((z * a) / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -2.1e-20) || !(z <= 1.05e-11))
		tmp = Float64(Float64(a - t) / Float64(y - b));
	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 <= -2.1e-20) || ~((z <= 1.05e-11)))
		tmp = (a - t) / (y - b);
	else
		tmp = x - ((z * a) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -2.1e-20], N[Not[LessEqual[z, 1.05e-11]], $MachinePrecision]], N[(N[(a - t), $MachinePrecision] / N[(y - b), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(z * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.0999999999999999e-20 or 1.0499999999999999e-11 < 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 76.6%

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

   if -2.0999999999999999e-20 < z < 1.0499999999999999e-11

   1. Initial program 86.7%

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

      1. fma-define 86.7%

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

   3. Simplified 86.7%

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

   5. Taylor expanded in x around inf 81.8%

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

   6. Taylor expanded in z around 0 64.6%

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

   7. Taylor expanded in x around 0 80.1%

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

   8. Taylor expanded in t around 0 66.5%

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

      1. associate-*r/ 66.5%

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

      2. neg-mul-1 66.5%

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

      3. distribute-lft-neg-in 66.5%

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

      4. *-commutative 66.5%

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

   10. Simplified 66.5%

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

4. Final simplification 72.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{-20} \lor \neg \left(z \leq 1.05 \cdot 10^{-11}\right):\\ \;\;\;\;\frac{a - t}{y - b}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z \cdot a}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 69.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{-59} \lor \neg \left(z \leq 1.7 \cdot 10^{-16}\right):\\ \;\;\;\;\frac{a - t}{y - b}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot t}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -6.2e-59) (not (<= z 1.7e-16)))
   (/ (- a t) (- y b))
   (+ x (/ (* z t) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -6.2e-59) || !(z <= 1.7e-16)) {
		tmp = (a - t) / (y - b);
	} else {
		tmp = x + ((z * t) / 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 <= (-6.2d-59)) .or. (.not. (z <= 1.7d-16))) then
        tmp = (a - t) / (y - b)
    else
        tmp = x + ((z * t) / 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 <= -6.2e-59) || !(z <= 1.7e-16)) {
		tmp = (a - t) / (y - b);
	} else {
		tmp = x + ((z * t) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -6.2e-59) or not (z <= 1.7e-16):
		tmp = (a - t) / (y - b)
	else:
		tmp = x + ((z * t) / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -6.2e-59) || !(z <= 1.7e-16))
		tmp = Float64(Float64(a - t) / Float64(y - b));
	else
		tmp = Float64(x + Float64(Float64(z * t) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -6.2e-59) || ~((z <= 1.7e-16)))
		tmp = (a - t) / (y - b);
	else
		tmp = x + ((z * t) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -6.2e-59], N[Not[LessEqual[z, 1.7e-16]], $MachinePrecision]], N[(N[(a - t), $MachinePrecision] / N[(y - b), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.19999999999999998e-59 or 1.7e-16 < z

   1. Initial program 51.6%

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

   3. Taylor expanded in z around inf 73.7%

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

   if -6.19999999999999998e-59 < z < 1.7e-16

   1. Initial program 85.4%

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

      1. fma-define 85.4%

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

   3. Simplified 85.4%

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

   5. Taylor expanded in x around inf 81.0%

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

   6. Taylor expanded in z around 0 66.8%

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

   7. Taylor expanded in x around 0 82.8%

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

   8. Taylor expanded in t around inf 67.6%

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

4. Final simplification 71.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{-59} \lor \neg \left(z \leq 1.7 \cdot 10^{-16}\right):\\ \;\;\;\;\frac{a - t}{y - b}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot t}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 54.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+46} \lor \neg \left(y \leq 3.2 \cdot 10^{-48}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -6e+46) (not (<= y 3.2e-48))) (/ x (- 1.0 z)) (/ (- t a) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -6e+46) || !(y <= 3.2e-48)) {
		tmp = x / (1.0 - z);
	} else {
		tmp = (t - a) / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-6d+46)) .or. (.not. (y <= 3.2d-48))) then
        tmp = x / (1.0d0 - z)
    else
        tmp = (t - a) / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -6e+46) || !(y <= 3.2e-48)) {
		tmp = x / (1.0 - z);
	} else {
		tmp = (t - a) / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -6e+46) or not (y <= 3.2e-48):
		tmp = x / (1.0 - z)
	else:
		tmp = (t - a) / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -6e+46) || !(y <= 3.2e-48))
		tmp = Float64(x / Float64(1.0 - z));
	else
		tmp = Float64(Float64(t - a) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -6e+46) || ~((y <= 3.2e-48)))
		tmp = x / (1.0 - z);
	else
		tmp = (t - a) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -6e+46], N[Not[LessEqual[y, 3.2e-48]], $MachinePrecision]], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.00000000000000047e46 or 3.1999999999999998e-48 < y

   1. Initial program 58.3%

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

   3. Taylor expanded in y around inf 51.7%

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

      1. mul-1-neg 51.7%

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

      2. unsub-neg 51.7%

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

   5. Simplified 51.7%

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

   if -6.00000000000000047e46 < y < 3.1999999999999998e-48

   1. Initial program 76.3%

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

   3. Taylor expanded in y around 0 60.3%

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

4. Final simplification 55.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+46} \lor \neg \left(y \leq 3.2 \cdot 10^{-48}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 35.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{-99} \lor \neg \left(z \leq 410000000000\right):\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.9e-99) (not (<= z 410000000000.0))) (/ t b) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.9e-99) || !(z <= 410000000000.0)) {
		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 ((z <= (-1.9d-99)) .or. (.not. (z <= 410000000000.0d0))) 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 ((z <= -1.9e-99) || !(z <= 410000000000.0)) {
		tmp = t / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.9e-99) or not (z <= 410000000000.0):
		tmp = t / b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.9e-99) || !(z <= 410000000000.0))
		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 ((z <= -1.9e-99) || ~((z <= 410000000000.0)))
		tmp = t / b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.9e-99], N[Not[LessEqual[z, 410000000000.0]], $MachinePrecision]], N[(t / b), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.8999999999999998e-99 or 4.1e11 < z

   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 x around inf 45.5%

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

   4. Taylor expanded in y around 0 34.6%

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

      1. div-sub 36.1%

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

   6. Simplified 36.1%

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

   7. Taylor expanded in t around inf 25.2%

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

   if -1.8999999999999998e-99 < z < 4.1e11

   1. Initial program 85.4%

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

   3. Taylor expanded in z around 0 54.1%

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

4. Final simplification 37.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{-99} \lor \neg \left(z \leq 410000000000\right):\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 25.8% 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 25.5%

   \[\leadsto \color{blue}{x} \]
4. Add Preprocessing

Developer Target 1: 73.7% 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 2024172 
(FPCore (x y z t a b)
  :name "Development.Shake.Progress:decay from shake-0.15.5"
  :precision binary64

  :alt
  (! :herbie-platform default (- (/ (+ (* z t) (* y x)) (+ y (* z (- b y)))) (/ a (+ (- b y) (/ y z)))))

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