Development.Shake.Progress:decay from shake-0.15.5

Percentage Accurate: 67.0% → 89.2%

Time: 18.0s

Alternatives: 17

Speedup: 1.5×

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: 67.0% 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: 89.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -16000000000000 \lor \neg \left(z \leq 4.8 \cdot 10^{+14}\right):\\ \;\;\;\;\frac{\frac{y}{\frac{b - y}{x}} + \frac{a - t}{\frac{{\left(b - y\right)}^{2}}{y}}}{z} + \frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, z \cdot \left(t - a\right)\right)}{\mathsf{fma}\left(z, b - y, y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -16000000000000.0) (not (<= z 4.8e+14)))
   (+
    (/ (+ (/ y (/ (- b y) x)) (/ (- a t) (/ (pow (- b y) 2.0) y))) z)
    (/ (- t a) (- b y)))
   (/ (fma x y (* z (- t a))) (fma z (- b y) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -16000000000000.0) || !(z <= 4.8e+14)) {
		tmp = (((y / ((b - y) / x)) + ((a - t) / (pow((b - y), 2.0) / y))) / z) + ((t - a) / (b - y));
	} else {
		tmp = fma(x, y, (z * (t - a))) / fma(z, (b - y), y);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -16000000000000.0) || !(z <= 4.8e+14))
		tmp = Float64(Float64(Float64(Float64(y / Float64(Float64(b - y) / x)) + Float64(Float64(a - t) / Float64((Float64(b - y) ^ 2.0) / y))) / z) + Float64(Float64(t - a) / Float64(b - y)));
	else
		tmp = Float64(fma(x, y, Float64(z * Float64(t - a))) / fma(z, Float64(b - y), y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -16000000000000.0], N[Not[LessEqual[z, 4.8e+14]], $MachinePrecision]], N[(N[(N[(N[(y / N[(N[(b - y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] + N[(N[(a - t), $MachinePrecision] / N[(N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] + N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * y + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * N[(b - y), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.6e13 or 4.8e14 < z

   1. Initial program 42.0%

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

   2. Taylor expanded in z around -inf 65.6%

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

      1. +-commutative 65.6%

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

      2. associate--l+ 65.6%

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

   4. Simplified 95.8%

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

   if -1.6e13 < z < 4.8e14

   1. Initial program 90.1%

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

      1. fma-def 90.1%

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

      2. +-commutative 90.1%

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

      3. fma-def 90.1%

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

   3. Simplified 90.1%

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

4. Final simplification 92.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -16000000000000 \lor \neg \left(z \leq 4.8 \cdot 10^{+14}\right):\\ \;\;\;\;\frac{\frac{y}{\frac{b - y}{x}} + \frac{a - t}{\frac{{\left(b - y\right)}^{2}}{y}}}{z} + \frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, z \cdot \left(t - a\right)\right)}{\mathsf{fma}\left(z, b - y, y\right)}\\ \end{array} \]

Alternative 2: 89.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ \mathbf{if}\;z \leq -1.25 \cdot 10^{+15} \lor \neg \left(z \leq 10000000000000\right):\\ \;\;\;\;\frac{\frac{y}{\frac{b - y}{x}} + \frac{a - t}{\frac{{\left(b - y\right)}^{2}}{y}}}{z} + \frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{t_1} - \frac{z \cdot \left(a - t\right)}{t_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y)))))
   (if (or (<= z -1.25e+15) (not (<= z 10000000000000.0)))
     (+
      (/ (+ (/ y (/ (- b y) x)) (/ (- a t) (/ (pow (- b y) 2.0) y))) z)
      (/ (- t a) (- b y)))
     (- (/ (* y x) t_1) (/ (* z (- a t)) 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 <= -1.25e+15) || !(z <= 10000000000000.0)) {
		tmp = (((y / ((b - y) / x)) + ((a - t) / (pow((b - y), 2.0) / y))) / z) + ((t - a) / (b - y));
	} else {
		tmp = ((y * x) / t_1) - ((z * (a - t)) / 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 <= (-1.25d+15)) .or. (.not. (z <= 10000000000000.0d0))) then
        tmp = (((y / ((b - y) / x)) + ((a - t) / (((b - y) ** 2.0d0) / y))) / z) + ((t - a) / (b - y))
    else
        tmp = ((y * x) / t_1) - ((z * (a - t)) / 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 <= -1.25e+15) || !(z <= 10000000000000.0)) {
		tmp = (((y / ((b - y) / x)) + ((a - t) / (Math.pow((b - y), 2.0) / y))) / z) + ((t - a) / (b - y));
	} else {
		tmp = ((y * x) / t_1) - ((z * (a - t)) / t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z * (b - y))
	tmp = 0
	if (z <= -1.25e+15) or not (z <= 10000000000000.0):
		tmp = (((y / ((b - y) / x)) + ((a - t) / (math.pow((b - y), 2.0) / y))) / z) + ((t - a) / (b - y))
	else:
		tmp = ((y * x) / t_1) - ((z * (a - t)) / 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 <= -1.25e+15) || !(z <= 10000000000000.0))
		tmp = Float64(Float64(Float64(Float64(y / Float64(Float64(b - y) / x)) + Float64(Float64(a - t) / Float64((Float64(b - y) ^ 2.0) / y))) / z) + Float64(Float64(t - a) / Float64(b - y)));
	else
		tmp = Float64(Float64(Float64(y * x) / t_1) - Float64(Float64(z * Float64(a - t)) / 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 <= -1.25e+15) || ~((z <= 10000000000000.0)))
		tmp = (((y / ((b - y) / x)) + ((a - t) / (((b - y) ^ 2.0) / y))) / z) + ((t - a) / (b - y));
	else
		tmp = ((y * x) / t_1) - ((z * (a - t)) / 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, -1.25e+15], N[Not[LessEqual[z, 10000000000000.0]], $MachinePrecision]], N[(N[(N[(N[(y / N[(N[(b - y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] + N[(N[(a - t), $MachinePrecision] / N[(N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] + N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y * x), $MachinePrecision] / t$95$1), $MachinePrecision] - N[(N[(z * N[(a - t), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.25e15 or 1e13 < z

   1. Initial program 42.0%

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

   2. Taylor expanded in z around -inf 65.6%

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

      1. +-commutative 65.6%

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

      2. associate--l+ 65.6%

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

   4. Simplified 95.8%

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

   if -1.25e15 < z < 1e13

   1. Initial program 90.1%

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

   2. Taylor expanded in x around inf 90.1%

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

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+15} \lor \neg \left(z \leq 10000000000000\right):\\ \;\;\;\;\frac{\frac{y}{\frac{b - y}{x}} + \frac{a - t}{\frac{{\left(b - y\right)}^{2}}{y}}}{z} + \frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{y + z \cdot \left(b - y\right)} - \frac{z \cdot \left(a - t\right)}{y + z \cdot \left(b - y\right)}\\ \end{array} \]

Alternative 3: 80.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := x - \frac{z \cdot \left(a - t\right)}{t_1}\\ t_3 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -270:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-298}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-209}:\\ \;\;\;\;\frac{y \cdot x - z \cdot a}{t_1}\\ \mathbf{elif}\;z \leq 1.55:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y))))
        (t_2 (- x (/ (* z (- a t)) t_1)))
        (t_3 (/ (- t a) (- b y))))
   (if (<= z -270.0)
     t_3
     (if (<= z 3.8e-298)
       t_2
       (if (<= z 1.3e-209)
         (/ (- (* y x) (* z a)) t_1)
         (if (<= z 1.55) t_2 t_3))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double t_2 = x - ((z * (a - t)) / t_1);
	double t_3 = (t - a) / (b - y);
	double tmp;
	if (z <= -270.0) {
		tmp = t_3;
	} else if (z <= 3.8e-298) {
		tmp = t_2;
	} else if (z <= 1.3e-209) {
		tmp = ((y * x) - (z * a)) / t_1;
	} else if (z <= 1.55) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = y + (z * (b - y))
    t_2 = x - ((z * (a - t)) / t_1)
    t_3 = (t - a) / (b - y)
    if (z <= (-270.0d0)) then
        tmp = t_3
    else if (z <= 3.8d-298) then
        tmp = t_2
    else if (z <= 1.3d-209) then
        tmp = ((y * x) - (z * a)) / t_1
    else if (z <= 1.55d0) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double t_2 = x - ((z * (a - t)) / t_1);
	double t_3 = (t - a) / (b - y);
	double tmp;
	if (z <= -270.0) {
		tmp = t_3;
	} else if (z <= 3.8e-298) {
		tmp = t_2;
	} else if (z <= 1.3e-209) {
		tmp = ((y * x) - (z * a)) / t_1;
	} else if (z <= 1.55) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z * (b - y))
	t_2 = x - ((z * (a - t)) / t_1)
	t_3 = (t - a) / (b - y)
	tmp = 0
	if z <= -270.0:
		tmp = t_3
	elif z <= 3.8e-298:
		tmp = t_2
	elif z <= 1.3e-209:
		tmp = ((y * x) - (z * a)) / t_1
	elif z <= 1.55:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(z * Float64(b - y)))
	t_2 = Float64(x - Float64(Float64(z * Float64(a - t)) / t_1))
	t_3 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -270.0)
		tmp = t_3;
	elseif (z <= 3.8e-298)
		tmp = t_2;
	elseif (z <= 1.3e-209)
		tmp = Float64(Float64(Float64(y * x) - Float64(z * a)) / t_1);
	elseif (z <= 1.55)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (z * (b - y));
	t_2 = x - ((z * (a - t)) / t_1);
	t_3 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -270.0)
		tmp = t_3;
	elseif (z <= 3.8e-298)
		tmp = t_2;
	elseif (z <= 1.3e-209)
		tmp = ((y * x) - (z * a)) / t_1;
	elseif (z <= 1.55)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(N[(z * N[(a - t), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -270.0], t$95$3, If[LessEqual[z, 3.8e-298], t$95$2, If[LessEqual[z, 1.3e-209], N[(N[(N[(y * x), $MachinePrecision] - N[(z * a), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[z, 1.55], t$95$2, t$95$3]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -270 or 1.55000000000000004 < z

   1. Initial program 45.2%

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

   2. Taylor expanded in z around inf 72.1%

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

   if -270 < z < 3.8e-298 or 1.29999999999999992e-209 < z < 1.55000000000000004

   1. Initial program 88.1%

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

   2. Taylor expanded in x around inf 88.2%

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

   3. Taylor expanded in z around 0 77.0%

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

   if 3.8e-298 < z < 1.29999999999999992e-209

   1. Initial program 99.7%

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

   2. Taylor expanded in t around 0 94.2%

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

      1. *-commutative 94.2%

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

      2. mul-1-neg 94.2%

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

      3. unsub-neg 94.2%

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

      4. *-commutative 94.2%

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

   4. Simplified 94.2%

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

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -270:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-298}:\\ \;\;\;\;x - \frac{z \cdot \left(a - t\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-209}:\\ \;\;\;\;\frac{y \cdot x - z \cdot a}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 1.55:\\ \;\;\;\;x - \frac{z \cdot \left(a - t\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 4: 84.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.6 \cdot 10^{+86} \lor \neg \left(z \leq 1.26 \cdot 10^{+84}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x + \left(z \cdot t - z \cdot a\right)}{y + z \cdot \left(b - y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -8.6e+86) (not (<= z 1.26e+84)))
   (/ (- t a) (- b y))
   (/ (+ (* y x) (- (* z t) (* z a))) (+ y (* z (- b y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -8.6e+86) || !(z <= 1.26e+84)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((y * x) + ((z * t) - (z * a))) / (y + (z * (b - y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-8.6d+86)) .or. (.not. (z <= 1.26d+84))) then
        tmp = (t - a) / (b - y)
    else
        tmp = ((y * x) + ((z * t) - (z * a))) / (y + (z * (b - y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -8.6e+86) || !(z <= 1.26e+84)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((y * x) + ((z * t) - (z * a))) / (y + (z * (b - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -8.6e+86) or not (z <= 1.26e+84):
		tmp = (t - a) / (b - y)
	else:
		tmp = ((y * x) + ((z * t) - (z * a))) / (y + (z * (b - y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -8.6e+86) || !(z <= 1.26e+84))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(Float64(Float64(y * x) + Float64(Float64(z * t) - Float64(z * a))) / Float64(y + Float64(z * Float64(b - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -8.6e+86) || ~((z <= 1.26e+84)))
		tmp = (t - a) / (b - y);
	else
		tmp = ((y * x) + ((z * t) - (z * a))) / (y + (z * (b - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -8.6e+86], N[Not[LessEqual[z, 1.26e+84]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y * x), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.6000000000000004e86 or 1.26000000000000007e84 < z

   1. Initial program 31.4%

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

   2. Taylor expanded in z around inf 75.4%

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

   if -8.6000000000000004e86 < z < 1.26000000000000007e84

   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. sub-neg 87.1%

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

      2. distribute-lft-in 87.1%

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

   3. Applied egg-rr 87.1%

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

4. Final simplification 83.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.6 \cdot 10^{+86} \lor \neg \left(z \leq 1.26 \cdot 10^{+84}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x + \left(z \cdot t - z \cdot a\right)}{y + z \cdot \left(b - y\right)}\\ \end{array} \]

Alternative 5: 84.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.9 \cdot 10^{+86} \lor \neg \left(z \leq 4.5 \cdot 10^{+84}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x - z \cdot \left(a - t\right)}{y \cdot \left(1 - z\right) + z \cdot b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -7.9e+86) (not (<= z 4.5e+84)))
   (/ (- t a) (- b y))
   (/ (- (* y x) (* z (- a t))) (+ (* y (- 1.0 z)) (* z b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -7.9e+86) || !(z <= 4.5e+84)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((y * x) - (z * (a - t))) / ((y * (1.0 - z)) + (z * 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 <= (-7.9d+86)) .or. (.not. (z <= 4.5d+84))) then
        tmp = (t - a) / (b - y)
    else
        tmp = ((y * x) - (z * (a - t))) / ((y * (1.0d0 - z)) + (z * 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 <= -7.9e+86) || !(z <= 4.5e+84)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((y * x) - (z * (a - t))) / ((y * (1.0 - z)) + (z * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -7.9e+86) or not (z <= 4.5e+84):
		tmp = (t - a) / (b - y)
	else:
		tmp = ((y * x) - (z * (a - t))) / ((y * (1.0 - z)) + (z * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -7.9e+86) || !(z <= 4.5e+84))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(Float64(Float64(y * x) - Float64(z * Float64(a - t))) / Float64(Float64(y * Float64(1.0 - z)) + Float64(z * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -7.9e+86) || ~((z <= 4.5e+84)))
		tmp = (t - a) / (b - y);
	else
		tmp = ((y * x) - (z * (a - t))) / ((y * (1.0 - z)) + (z * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -7.9e+86], N[Not[LessEqual[z, 4.5e+84]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y * x), $MachinePrecision] - N[(z * N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(y * N[(1.0 - z), $MachinePrecision]), $MachinePrecision] + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.90000000000000025e86 or 4.4999999999999997e84 < z

   1. Initial program 31.4%

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

   2. Taylor expanded in z around inf 75.4%

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

   if -7.90000000000000025e86 < z < 4.4999999999999997e84

   1. Initial program 87.1%

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

   2. Taylor expanded in y around 0 87.1%

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

4. Final simplification 83.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.9 \cdot 10^{+86} \lor \neg \left(z \leq 4.5 \cdot 10^{+84}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x - z \cdot \left(a - t\right)}{y \cdot \left(1 - z\right) + z \cdot b}\\ \end{array} \]

Alternative 6: 84.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+86} \lor \neg \left(z \leq 1.1 \cdot 10^{+85}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x - z \cdot \left(a - t\right)}{y + z \cdot \left(b - y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -9.5e+86) (not (<= z 1.1e+85)))
   (/ (- t a) (- b y))
   (/ (- (* y x) (* z (- a t))) (+ y (* z (- b y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -9.5e+86) || !(z <= 1.1e+85)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((y * x) - (z * (a - t))) / (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 <= (-9.5d+86)) .or. (.not. (z <= 1.1d+85))) then
        tmp = (t - a) / (b - y)
    else
        tmp = ((y * x) - (z * (a - t))) / (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 <= -9.5e+86) || !(z <= 1.1e+85)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((y * x) - (z * (a - t))) / (y + (z * (b - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -9.5e+86) or not (z <= 1.1e+85):
		tmp = (t - a) / (b - y)
	else:
		tmp = ((y * x) - (z * (a - t))) / (y + (z * (b - y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -9.5e+86) || !(z <= 1.1e+85))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(Float64(Float64(y * x) - Float64(z * Float64(a - t))) / 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 <= -9.5e+86) || ~((z <= 1.1e+85)))
		tmp = (t - a) / (b - y);
	else
		tmp = ((y * x) - (z * (a - t))) / (y + (z * (b - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -9.5e+86], N[Not[LessEqual[z, 1.1e+85]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y * x), $MachinePrecision] - N[(z * N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.50000000000000028e86 or 1.1000000000000001e85 < z

   1. Initial program 31.4%

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

   2. Taylor expanded in z around inf 75.4%

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

   if -9.50000000000000028e86 < z < 1.1000000000000001e85

   1. Initial program 87.1%

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

4. Final simplification 83.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+86} \lor \neg \left(z \leq 1.1 \cdot 10^{+85}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x - z \cdot \left(a - t\right)}{y + z \cdot \left(b - y\right)}\\ \end{array} \]

Alternative 7: 81.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -125 \lor \neg \left(z \leq 1.05\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z \cdot \left(a - t\right)}{y + z \cdot \left(b - y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -125.0) (not (<= z 1.05)))
   (/ (- t a) (- b y))
   (- x (/ (* z (- a t)) (+ y (* z (- b y)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -125.0) || !(z <= 1.05)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x - ((z * (a - t)) / (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 <= (-125.0d0)) .or. (.not. (z <= 1.05d0))) then
        tmp = (t - a) / (b - y)
    else
        tmp = x - ((z * (a - t)) / (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 <= -125.0) || !(z <= 1.05)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x - ((z * (a - t)) / (y + (z * (b - y))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -125.0) or not (z <= 1.05):
		tmp = (t - a) / (b - y)
	else:
		tmp = x - ((z * (a - t)) / (y + (z * (b - y))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -125.0) || !(z <= 1.05))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(x - Float64(Float64(z * Float64(a - t)) / 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 <= -125.0) || ~((z <= 1.05)))
		tmp = (t - a) / (b - y);
	else
		tmp = x - ((z * (a - t)) / (y + (z * (b - y))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -125.0], N[Not[LessEqual[z, 1.05]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(z * N[(a - t), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -125 or 1.05000000000000004 < z

   1. Initial program 45.2%

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

   2. Taylor expanded in z around inf 72.1%

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

   if -125 < z < 1.05000000000000004

   1. Initial program 89.6%

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

   2. Taylor expanded in x around inf 89.7%

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

   3. Taylor expanded in z around 0 74.8%

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

4. Final simplification 73.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -125 \lor \neg \left(z \leq 1.05\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z \cdot \left(a - t\right)}{y + z \cdot \left(b - y\right)}\\ \end{array} \]

Alternative 8: 39.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+90}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;z \leq -5.3 \cdot 10^{+41}:\\ \;\;\;\;-\frac{x}{z}\\ \mathbf{elif}\;z \leq -110000000000 \lor \neg \left(z \leq 5 \cdot 10^{-87}\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -7.5e+90)
   (/ (- a) b)
   (if (<= z -5.3e+41)
     (- (/ x z))
     (if (or (<= z -110000000000.0) (not (<= z 5e-87))) (/ t (- b y)) x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -7.5e+90) {
		tmp = -a / b;
	} else if (z <= -5.3e+41) {
		tmp = -(x / z);
	} else if ((z <= -110000000000.0) || !(z <= 5e-87)) {
		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 <= (-7.5d+90)) then
        tmp = -a / b
    else if (z <= (-5.3d+41)) then
        tmp = -(x / z)
    else if ((z <= (-110000000000.0d0)) .or. (.not. (z <= 5d-87))) 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 <= -7.5e+90) {
		tmp = -a / b;
	} else if (z <= -5.3e+41) {
		tmp = -(x / z);
	} else if ((z <= -110000000000.0) || !(z <= 5e-87)) {
		tmp = t / (b - y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -7.5e+90:
		tmp = -a / b
	elif z <= -5.3e+41:
		tmp = -(x / z)
	elif (z <= -110000000000.0) or not (z <= 5e-87):
		tmp = t / (b - y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -7.5e+90)
		tmp = Float64(Float64(-a) / b);
	elseif (z <= -5.3e+41)
		tmp = Float64(-Float64(x / z));
	elseif ((z <= -110000000000.0) || !(z <= 5e-87))
		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 <= -7.5e+90)
		tmp = -a / b;
	elseif (z <= -5.3e+41)
		tmp = -(x / z);
	elseif ((z <= -110000000000.0) || ~((z <= 5e-87)))
		tmp = t / (b - y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -7.5e+90], N[((-a) / b), $MachinePrecision], If[LessEqual[z, -5.3e+41], (-N[(x / z), $MachinePrecision]), If[Or[LessEqual[z, -110000000000.0], N[Not[LessEqual[z, 5e-87]], $MachinePrecision]], N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision], x]]]

Derivation

1. Split input into 4 regimes

2. if z < -7.50000000000000014e90

   1. Initial program 39.7%

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

   2. Taylor expanded in b around inf 24.5%

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

   3. Taylor expanded in a around inf 34.8%

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

      1. mul-1-neg 34.8%

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

   5. Simplified 34.8%

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

   if -7.50000000000000014e90 < z < -5.2999999999999997e41

   1. Initial program 41.4%

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

   2. Taylor expanded in y around inf 54.8%

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

      1. +-commutative 54.8%

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

      2. mul-1-neg 54.8%

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

      3. unsub-neg 54.8%

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

   4. Simplified 54.8%

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

   5. Taylor expanded in z around inf 54.8%

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

      1. associate-*r/ 54.8%

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

      2. mul-1-neg 54.8%

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

   7. Simplified 54.8%

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

   if -5.2999999999999997e41 < z < -1.1e11 or 5.00000000000000042e-87 < z

   1. Initial program 54.3%

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

      1. sub-neg 54.3%

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

      2. distribute-lft-in 54.3%

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

   3. Applied egg-rr 54.3%

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

   4. Taylor expanded in t around inf 27.4%

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

      1. *-commutative 27.4%

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

   6. Simplified 27.4%

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

   7. Taylor expanded in z around inf 40.3%

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

   if -1.1e11 < z < 5.00000000000000042e-87

   1. Initial program 90.8%

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

   2. Taylor expanded in z around 0 40.7%

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

4. Final simplification 40.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+90}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;z \leq -5.3 \cdot 10^{+41}:\\ \;\;\;\;-\frac{x}{z}\\ \mathbf{elif}\;z \leq -110000000000 \lor \neg \left(z \leq 5 \cdot 10^{-87}\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9: 54.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -1.02 \cdot 10^{+30}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -3900000:\\ \;\;\;\;\frac{y \cdot x}{z \cdot b}\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{-14}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-7}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (- 1.0 z))))
   (if (<= y -1.02e+30)
     t_1
     (if (<= y -3900000.0)
       (/ (* y x) (* z b))
       (if (<= y -7.5e-14) x (if (<= y 1.2e-7) (/ (- 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 <= -1.02e+30) {
		tmp = t_1;
	} else if (y <= -3900000.0) {
		tmp = (y * x) / (z * b);
	} else if (y <= -7.5e-14) {
		tmp = x;
	} else if (y <= 1.2e-7) {
		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 <= (-1.02d+30)) then
        tmp = t_1
    else if (y <= (-3900000.0d0)) then
        tmp = (y * x) / (z * b)
    else if (y <= (-7.5d-14)) then
        tmp = x
    else if (y <= 1.2d-7) 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 <= -1.02e+30) {
		tmp = t_1;
	} else if (y <= -3900000.0) {
		tmp = (y * x) / (z * b);
	} else if (y <= -7.5e-14) {
		tmp = x;
	} else if (y <= 1.2e-7) {
		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 <= -1.02e+30:
		tmp = t_1
	elif y <= -3900000.0:
		tmp = (y * x) / (z * b)
	elif y <= -7.5e-14:
		tmp = x
	elif y <= 1.2e-7:
		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 <= -1.02e+30)
		tmp = t_1;
	elseif (y <= -3900000.0)
		tmp = Float64(Float64(y * x) / Float64(z * b));
	elseif (y <= -7.5e-14)
		tmp = x;
	elseif (y <= 1.2e-7)
		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 <= -1.02e+30)
		tmp = t_1;
	elseif (y <= -3900000.0)
		tmp = (y * x) / (z * b);
	elseif (y <= -7.5e-14)
		tmp = x;
	elseif (y <= 1.2e-7)
		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, -1.02e+30], t$95$1, If[LessEqual[y, -3900000.0], N[(N[(y * x), $MachinePrecision] / N[(z * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -7.5e-14], x, If[LessEqual[y, 1.2e-7], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.02e30 or 1.19999999999999989e-7 < y

   1. Initial program 50.5%

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

   2. Taylor expanded in y around inf 55.5%

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

      1. +-commutative 55.5%

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

      2. mul-1-neg 55.5%

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

      3. unsub-neg 55.5%

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

   4. Simplified 55.5%

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

   if -1.02e30 < y < -3.9e6

   1. Initial program 99.7%

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

   2. Taylor expanded in b around inf 79.6%

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

   3. Taylor expanded in z around 0 79.8%

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

   if -3.9e6 < y < -7.4999999999999996e-14

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 100.0%

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

   if -7.4999999999999996e-14 < y < 1.19999999999999989e-7

   1. Initial program 83.4%

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

   2. Taylor expanded in y around 0 54.9%

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

4. Final simplification 56.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.02 \cdot 10^{+30}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq -3900000:\\ \;\;\;\;\frac{y \cdot x}{z \cdot b}\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{-14}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-7}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]

Alternative 10: 75.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.7 \lor \neg \left(z \leq 3.5 \cdot 10^{-6}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z \cdot \left(a - t\right)}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -0.7) (not (<= z 3.5e-6)))
   (/ (- t a) (- b y))
   (- x (/ (* z (- a t)) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -0.7) || !(z <= 3.5e-6)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x - ((z * (a - 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 <= (-0.7d0)) .or. (.not. (z <= 3.5d-6))) then
        tmp = (t - a) / (b - y)
    else
        tmp = x - ((z * (a - 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 <= -0.7) || !(z <= 3.5e-6)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x - ((z * (a - t)) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -0.7) or not (z <= 3.5e-6):
		tmp = (t - a) / (b - y)
	else:
		tmp = x - ((z * (a - t)) / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -0.7) || !(z <= 3.5e-6))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(x - Float64(Float64(z * Float64(a - t)) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -0.7) || ~((z <= 3.5e-6)))
		tmp = (t - a) / (b - y);
	else
		tmp = x - ((z * (a - t)) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -0.7], N[Not[LessEqual[z, 3.5e-6]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(z * N[(a - t), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.69999999999999996 or 3.49999999999999995e-6 < z

   1. Initial program 45.2%

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

   2. Taylor expanded in z around inf 72.1%

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

   if -0.69999999999999996 < z < 3.49999999999999995e-6

   1. Initial program 89.6%

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

      1. +-commutative 89.6%

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

      2. *-commutative 89.6%

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

      3. add-cube-cbrt 89.2%

         \[\leadsto \frac{x \cdot y + z \cdot \left(t - a\right)}{\color{blue}{\left(\left(\sqrt[3]{b - y} \cdot \sqrt[3]{b - y}\right) \cdot \sqrt[3]{b - y}\right)} \cdot z + y} \]

      4. associate-*l* 89.2%

         \[\leadsto \frac{x \cdot y + z \cdot \left(t - a\right)}{\color{blue}{\left(\sqrt[3]{b - y} \cdot \sqrt[3]{b - y}\right) \cdot \left(\sqrt[3]{b - y} \cdot z\right)} + y} \]

      5. fma-def 89.2%

         \[\leadsto \frac{x \cdot y + z \cdot \left(t - a\right)}{\color{blue}{\mathsf{fma}\left(\sqrt[3]{b - y} \cdot \sqrt[3]{b - y}, \sqrt[3]{b - y} \cdot z, y\right)}} \]

      6. pow2 89.2%

         \[\leadsto \frac{x \cdot y + z \cdot \left(t - a\right)}{\mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{b - y}\right)}^{2}}, \sqrt[3]{b - y} \cdot z, y\right)} \]

   3. Applied egg-rr 89.2%

      \[\leadsto \frac{x \cdot y + z \cdot \left(t - a\right)}{\color{blue}{\mathsf{fma}\left({\left(\sqrt[3]{b - y}\right)}^{2}, \sqrt[3]{b - y} \cdot z, y\right)}} \]

   4. Taylor expanded in y around inf 64.4%

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

4. Final simplification 68.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.7 \lor \neg \left(z \leq 3.5 \cdot 10^{-6}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z \cdot \left(a - t\right)}{y}\\ \end{array} \]

Alternative 11: 42.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -5.2 \cdot 10^{+40}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-178}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-18}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (- 1.0 z))))
   (if (<= y -5.2e+40)
     t_1
     (if (<= y -6e-178) (/ t (- b y)) (if (<= y 6.8e-18) (/ (- 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 <= -5.2e+40) {
		tmp = t_1;
	} else if (y <= -6e-178) {
		tmp = t / (b - y);
	} else if (y <= 6.8e-18) {
		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 <= (-5.2d+40)) then
        tmp = t_1
    else if (y <= (-6d-178)) then
        tmp = t / (b - y)
    else if (y <= 6.8d-18) 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 <= -5.2e+40) {
		tmp = t_1;
	} else if (y <= -6e-178) {
		tmp = t / (b - y);
	} else if (y <= 6.8e-18) {
		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 <= -5.2e+40:
		tmp = t_1
	elif y <= -6e-178:
		tmp = t / (b - y)
	elif y <= 6.8e-18:
		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 <= -5.2e+40)
		tmp = t_1;
	elseif (y <= -6e-178)
		tmp = Float64(t / Float64(b - y));
	elseif (y <= 6.8e-18)
		tmp = Float64(Float64(-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 <= -5.2e+40)
		tmp = t_1;
	elseif (y <= -6e-178)
		tmp = t / (b - y);
	elseif (y <= 6.8e-18)
		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, -5.2e+40], t$95$1, If[LessEqual[y, -6e-178], N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.8e-18], N[((-a) / b), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.2000000000000001e40 or 6.80000000000000002e-18 < y

   1. Initial program 51.2%

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

   2. Taylor expanded in y around inf 55.6%

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

      1. +-commutative 55.6%

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

      2. mul-1-neg 55.6%

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

      3. unsub-neg 55.6%

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

   4. Simplified 55.6%

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

   if -5.2000000000000001e40 < y < -5.9999999999999997e-178

   1. Initial program 76.4%

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

      1. sub-neg 76.4%

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

      2. distribute-lft-in 76.3%

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

   3. Applied egg-rr 76.3%

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

   4. Taylor expanded in t around inf 32.5%

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

      1. *-commutative 32.5%

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

   6. Simplified 32.5%

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

   7. Taylor expanded in z around inf 30.4%

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

   if -5.9999999999999997e-178 < y < 6.80000000000000002e-18

   1. Initial program 88.0%

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

   2. Taylor expanded in b around inf 58.8%

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

   3. Taylor expanded in a around inf 37.9%

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

      1. mul-1-neg 37.9%

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

   5. Simplified 37.9%

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

4. Final simplification 45.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{+40}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-178}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-18}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]

Alternative 12: 68.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.7 \lor \neg \left(z \leq 1.35 \cdot 10^{-69}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot t}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -0.7) (not (<= z 1.35e-69)))
   (/ (- t a) (- b y))
   (+ x (/ (* z t) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -0.7) || !(z <= 1.35e-69)) {
		tmp = (t - a) / (b - y);
	} 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 <= (-0.7d0)) .or. (.not. (z <= 1.35d-69))) then
        tmp = (t - a) / (b - y)
    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 <= -0.7) || !(z <= 1.35e-69)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x + ((z * t) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -0.7) or not (z <= 1.35e-69):
		tmp = (t - a) / (b - y)
	else:
		tmp = x + ((z * t) / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -0.7) || !(z <= 1.35e-69))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	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 <= -0.7) || ~((z <= 1.35e-69)))
		tmp = (t - a) / (b - y);
	else
		tmp = x + ((z * t) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -0.7], N[Not[LessEqual[z, 1.35e-69]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.69999999999999996 or 1.3499999999999999e-69 < z

   1. Initial program 48.3%

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

   2. Taylor expanded in z around inf 69.1%

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

   if -0.69999999999999996 < z < 1.3499999999999999e-69

   1. Initial program 90.9%

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

   2. Taylor expanded in z around 0 47.5%

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

   3. Taylor expanded in t around inf 59.3%

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

      1. *-commutative 59.3%

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

   5. Simplified 59.3%

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

4. Final simplification 64.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.7 \lor \neg \left(z \leq 1.35 \cdot 10^{-69}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot t}{y}\\ \end{array} \]

Alternative 13: 34.3% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+90}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;z \leq -1 \lor \neg \left(z \leq 1.8 \cdot 10^{-7}\right):\\ \;\;\;\;-\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -2.2e+90)
   (/ (- a) b)
   (if (or (<= z -1.0) (not (<= z 1.8e-7))) (- (/ x z)) x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2.2e+90) {
		tmp = -a / b;
	} else if ((z <= -1.0) || !(z <= 1.8e-7)) {
		tmp = -(x / z);
	} 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 <= (-2.2d+90)) then
        tmp = -a / b
    else if ((z <= (-1.0d0)) .or. (.not. (z <= 1.8d-7))) then
        tmp = -(x / z)
    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 <= -2.2e+90) {
		tmp = -a / b;
	} else if ((z <= -1.0) || !(z <= 1.8e-7)) {
		tmp = -(x / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -2.2e+90:
		tmp = -a / b
	elif (z <= -1.0) or not (z <= 1.8e-7):
		tmp = -(x / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -2.2e+90)
		tmp = Float64(Float64(-a) / b);
	elseif ((z <= -1.0) || !(z <= 1.8e-7))
		tmp = Float64(-Float64(x / z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -2.2e+90)
		tmp = -a / b;
	elseif ((z <= -1.0) || ~((z <= 1.8e-7)))
		tmp = -(x / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -2.2e+90], N[((-a) / b), $MachinePrecision], If[Or[LessEqual[z, -1.0], N[Not[LessEqual[z, 1.8e-7]], $MachinePrecision]], (-N[(x / z), $MachinePrecision]), x]]

Derivation

1. Split input into 3 regimes

2. if z < -2.1999999999999999e90

   1. Initial program 39.7%

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

   2. Taylor expanded in b around inf 24.5%

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

   3. Taylor expanded in a around inf 34.8%

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

      1. mul-1-neg 34.8%

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

   5. Simplified 34.8%

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

   if -2.1999999999999999e90 < z < -1 or 1.79999999999999997e-7 < z

   1. Initial program 48.9%

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

   2. Taylor expanded in y around inf 25.5%

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

      1. +-commutative 25.5%

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

      2. mul-1-neg 25.5%

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

      3. unsub-neg 25.5%

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

   4. Simplified 25.5%

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

   5. Taylor expanded in z around inf 25.1%

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

      1. associate-*r/ 25.1%

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

      2. mul-1-neg 25.1%

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

   7. Simplified 25.1%

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

   if -1 < z < 1.79999999999999997e-7

   1. Initial program 89.5%

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

   2. Taylor expanded in z around 0 39.1%

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

4. Final simplification 33.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+90}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;z \leq -1 \lor \neg \left(z \leq 1.8 \cdot 10^{-7}\right):\\ \;\;\;\;-\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 14: 55.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{-5} \lor \neg \left(y \leq 1.1 \cdot 10^{-6}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.65e-5) (not (<= y 1.1e-6))) (/ 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 <= -1.65e-5) || !(y <= 1.1e-6)) {
		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 <= (-1.65d-5)) .or. (.not. (y <= 1.1d-6))) 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 <= -1.65e-5) || !(y <= 1.1e-6)) {
		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 <= -1.65e-5) or not (y <= 1.1e-6):
		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 <= -1.65e-5) || !(y <= 1.1e-6))
		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 <= -1.65e-5) || ~((y <= 1.1e-6)))
		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, -1.65e-5], N[Not[LessEqual[y, 1.1e-6]], $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 < -1.6500000000000001e-5 or 1.1000000000000001e-6 < y

   1. Initial program 53.1%

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

   2. Taylor expanded in y around inf 53.5%

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

      1. +-commutative 53.5%

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

      2. mul-1-neg 53.5%

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

      3. unsub-neg 53.5%

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

   4. Simplified 53.5%

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

   if -1.6500000000000001e-5 < y < 1.1000000000000001e-6

   1. Initial program 83.4%

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

   2. Taylor expanded in y around 0 54.9%

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

4. Final simplification 54.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{-5} \lor \neg \left(y \leq 1.1 \cdot 10^{-6}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \]

Alternative 15: 35.0% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.52 \cdot 10^{-9}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 140000000:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.52e-9) x (if (<= y 140000000.0) (/ (- a) b) x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.52e-9) {
		tmp = x;
	} else if (y <= 140000000.0) {
		tmp = -a / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-1.52d-9)) then
        tmp = x
    else if (y <= 140000000.0d0) then
        tmp = -a / b
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.52e-9) {
		tmp = x;
	} else if (y <= 140000000.0) {
		tmp = -a / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.52e-9:
		tmp = x
	elif y <= 140000000.0:
		tmp = -a / b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.52e-9)
		tmp = x;
	elseif (y <= 140000000.0)
		tmp = Float64(Float64(-a) / b);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -1.52e-9)
		tmp = x;
	elseif (y <= 140000000.0)
		tmp = -a / b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.52e-9], x, If[LessEqual[y, 140000000.0], N[((-a) / b), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -1.51999999999999992e-9 or 1.4e8 < y

   1. Initial program 51.6%

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

   2. Taylor expanded in z around 0 32.8%

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

   if -1.51999999999999992e-9 < y < 1.4e8

   1. Initial program 83.9%

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

   2. Taylor expanded in b around inf 50.6%

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

   3. Taylor expanded in a around inf 31.5%

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

      1. mul-1-neg 31.5%

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

   5. Simplified 31.5%

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

4. Final simplification 32.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.52 \cdot 10^{-9}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 140000000:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 16: 36.0% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+31}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-87}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -3.8e+31) (/ t b) (if (<= z 5e-87) x (/ t b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -3.8e+31) {
		tmp = t / b;
	} else if (z <= 5e-87) {
		tmp = x;
	} else {
		tmp = t / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-3.8d+31)) then
        tmp = t / b
    else if (z <= 5d-87) then
        tmp = x
    else
        tmp = t / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -3.8e+31) {
		tmp = t / b;
	} else if (z <= 5e-87) {
		tmp = x;
	} else {
		tmp = t / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -3.8e+31:
		tmp = t / b
	elif z <= 5e-87:
		tmp = x
	else:
		tmp = t / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -3.8e+31)
		tmp = Float64(t / b);
	elseif (z <= 5e-87)
		tmp = x;
	else
		tmp = Float64(t / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -3.8e+31)
		tmp = t / b;
	elseif (z <= 5e-87)
		tmp = x;
	else
		tmp = t / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -3.8e+31], N[(t / b), $MachinePrecision], If[LessEqual[z, 5e-87], x, N[(t / b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.8000000000000001e31 or 5.00000000000000042e-87 < z

   1. Initial program 46.4%

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

   2. Taylor expanded in b around inf 26.7%

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

   3. Taylor expanded in t around inf 21.3%

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

   if -3.8000000000000001e31 < z < 5.00000000000000042e-87

   1. Initial program 91.2%

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

   2. Taylor expanded in z around 0 38.9%

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

4. Final simplification 29.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+31}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-87}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \]

Alternative 17: 25.4% 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 67.9%

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

2. Taylor expanded in z around 0 21.7%

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

3. Final simplification 21.7%

   \[\leadsto x \]

Developer target: 73.4% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023196 
(FPCore (x y z t a b)
  :name "Development.Shake.Progress:decay from shake-0.15.5"
  :precision binary64

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

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