Development.Shake.Progress:decay from shake-0.15.5

Percentage Accurate: 65.6% → 85.5%

Time: 11.0s

Alternatives: 13

Speedup: 1.3×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 65.6% 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: 85.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{+267} \lor \neg \left(t_1 \leq -1 \cdot 10^{-317}\right) \land \left(t_1 \leq 0 \lor \neg \left(t_1 \leq 10^{+308}\right)\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))))
   (if (or (<= t_1 -5e+267)
           (and (not (<= t_1 -1e-317))
                (or (<= t_1 0.0) (not (<= t_1 1e+308)))))
     (/ (- t a) (- b y))
     t_1)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x * y) + (z * (t - a))) / (y + (z * (b - y)));
	double tmp;
	if ((t_1 <= -5e+267) || (!(t_1 <= -1e-317) && ((t_1 <= 0.0) || !(t_1 <= 1e+308)))) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((x * y) + (z * (t - a))) / (y + (z * (b - y)))
    if ((t_1 <= (-5d+267)) .or. (.not. (t_1 <= (-1d-317))) .and. (t_1 <= 0.0d0) .or. (.not. (t_1 <= 1d+308))) then
        tmp = (t - a) / (b - y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x * y) + (z * (t - a))) / (y + (z * (b - y)));
	double tmp;
	if ((t_1 <= -5e+267) || (!(t_1 <= -1e-317) && ((t_1 <= 0.0) || !(t_1 <= 1e+308)))) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((x * y) + (z * (t - a))) / (y + (z * (b - y)))
	tmp = 0
	if (t_1 <= -5e+267) or (not (t_1 <= -1e-317) and ((t_1 <= 0.0) or not (t_1 <= 1e+308))):
		tmp = (t - a) / (b - y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(x * y) + Float64(z * Float64(t - a))) / Float64(y + Float64(z * Float64(b - y))))
	tmp = 0.0
	if ((t_1 <= -5e+267) || (!(t_1 <= -1e-317) && ((t_1 <= 0.0) || !(t_1 <= 1e+308))))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((x * y) + (z * (t - a))) / (y + (z * (b - y)));
	tmp = 0.0;
	if ((t_1 <= -5e+267) || (~((t_1 <= -1e-317)) && ((t_1 <= 0.0) || ~((t_1 <= 1e+308)))))
		tmp = (t - a) / (b - y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(x * y), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e+267], And[N[Not[LessEqual[t$95$1, -1e-317]], $MachinePrecision], Or[LessEqual[t$95$1, 0.0], N[Not[LessEqual[t$95$1, 1e+308]], $MachinePrecision]]]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], t$95$1]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -4.9999999999999999e267 or -1.00000023e-317 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -0.0 or 1e308 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 19.8%

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

   2. Taylor expanded in z around inf 70.9%

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

   if -4.9999999999999999e267 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -1.00000023e-317 or -0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 1e308

   1. Initial program 99.7%

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

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -5 \cdot 10^{+267} \lor \neg \left(\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -1 \cdot 10^{-317}\right) \land \left(\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 0 \lor \neg \left(\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 10^{+308}\right)\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \end{array} \]

Alternative 2: 82.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(t - a\right)\\ t_2 := \frac{x \cdot y + t_1}{y + z \cdot b}\\ t_3 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -6.5 \cdot 10^{+36}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-257}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-266}:\\ \;\;\;\;x + \frac{t_1}{y}\\ \mathbf{elif}\;z \leq 12000:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- t a)))
        (t_2 (/ (+ (* x y) t_1) (+ y (* z b))))
        (t_3 (/ (- t a) (- b y))))
   (if (<= z -6.5e+36)
     t_3
     (if (<= z -5e-257)
       t_2
       (if (<= z 3.2e-266) (+ x (/ t_1 y)) (if (<= z 12000.0) t_2 t_3))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (t - a);
	double t_2 = ((x * y) + t_1) / (y + (z * b));
	double t_3 = (t - a) / (b - y);
	double tmp;
	if (z <= -6.5e+36) {
		tmp = t_3;
	} else if (z <= -5e-257) {
		tmp = t_2;
	} else if (z <= 3.2e-266) {
		tmp = x + (t_1 / y);
	} else if (z <= 12000.0) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = z * (t - a)
    t_2 = ((x * y) + t_1) / (y + (z * b))
    t_3 = (t - a) / (b - y)
    if (z <= (-6.5d+36)) then
        tmp = t_3
    else if (z <= (-5d-257)) then
        tmp = t_2
    else if (z <= 3.2d-266) then
        tmp = x + (t_1 / y)
    else if (z <= 12000.0d0) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (t - a);
	double t_2 = ((x * y) + t_1) / (y + (z * b));
	double t_3 = (t - a) / (b - y);
	double tmp;
	if (z <= -6.5e+36) {
		tmp = t_3;
	} else if (z <= -5e-257) {
		tmp = t_2;
	} else if (z <= 3.2e-266) {
		tmp = x + (t_1 / y);
	} else if (z <= 12000.0) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (t - a)
	t_2 = ((x * y) + t_1) / (y + (z * b))
	t_3 = (t - a) / (b - y)
	tmp = 0
	if z <= -6.5e+36:
		tmp = t_3
	elif z <= -5e-257:
		tmp = t_2
	elif z <= 3.2e-266:
		tmp = x + (t_1 / y)
	elif z <= 12000.0:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(t - a))
	t_2 = Float64(Float64(Float64(x * y) + t_1) / Float64(y + Float64(z * b)))
	t_3 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -6.5e+36)
		tmp = t_3;
	elseif (z <= -5e-257)
		tmp = t_2;
	elseif (z <= 3.2e-266)
		tmp = Float64(x + Float64(t_1 / y));
	elseif (z <= 12000.0)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (t - a);
	t_2 = ((x * y) + t_1) / (y + (z * b));
	t_3 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -6.5e+36)
		tmp = t_3;
	elseif (z <= -5e-257)
		tmp = t_2;
	elseif (z <= 3.2e-266)
		tmp = x + (t_1 / y);
	elseif (z <= 12000.0)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x * y), $MachinePrecision] + t$95$1), $MachinePrecision] / N[(y + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.5e+36], t$95$3, If[LessEqual[z, -5e-257], t$95$2, If[LessEqual[z, 3.2e-266], N[(x + N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 12000.0], t$95$2, t$95$3]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.4999999999999998e36 or 12000 < z

   1. Initial program 43.1%

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

   2. Taylor expanded in z around inf 85.7%

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

   if -6.4999999999999998e36 < z < -4.99999999999999989e-257 or 3.2e-266 < z < 12000

   1. Initial program 87.4%

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

   2. Taylor expanded in b around inf 84.7%

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

   if -4.99999999999999989e-257 < z < 3.2e-266

   1. Initial program 79.4%

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

   2. Taylor expanded in b around inf 79.4%

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

   3. Taylor expanded in y around inf 86.3%

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

      1. associate--l+ 86.3%

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

      2. associate-/l* 81.1%

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

      3. associate-*r* 91.2%

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

   5. Simplified 91.2%

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

   6. Taylor expanded in b around 0 96.5%

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

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+36}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-257}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-266}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;z \leq 12000:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 3: 43.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{b - y}\\ \mathbf{if}\;z \leq -4.4 \cdot 10^{-86}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-5}:\\ \;\;\;\;x + x \cdot z\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+215} \lor \neg \left(z \leq 3.8 \cdot 10^{+268}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;-\frac{a}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ t (- b y))))
   (if (<= z -4.4e-86)
     t_1
     (if (<= z 7.5e-5)
       (+ x (* x z))
       (if (or (<= z 3e+215) (not (<= z 3.8e+268))) t_1 (- (/ a b)))))))

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 <= -4.4e-86) {
		tmp = t_1;
	} else if (z <= 7.5e-5) {
		tmp = x + (x * z);
	} else if ((z <= 3e+215) || !(z <= 3.8e+268)) {
		tmp = t_1;
	} else {
		tmp = -(a / b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t / (b - y)
    if (z <= (-4.4d-86)) then
        tmp = t_1
    else if (z <= 7.5d-5) then
        tmp = x + (x * z)
    else if ((z <= 3d+215) .or. (.not. (z <= 3.8d+268))) then
        tmp = t_1
    else
        tmp = -(a / b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t / (b - y);
	double tmp;
	if (z <= -4.4e-86) {
		tmp = t_1;
	} else if (z <= 7.5e-5) {
		tmp = x + (x * z);
	} else if ((z <= 3e+215) || !(z <= 3.8e+268)) {
		tmp = t_1;
	} else {
		tmp = -(a / b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t / (b - y)
	tmp = 0
	if z <= -4.4e-86:
		tmp = t_1
	elif z <= 7.5e-5:
		tmp = x + (x * z)
	elif (z <= 3e+215) or not (z <= 3.8e+268):
		tmp = t_1
	else:
		tmp = -(a / b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t / Float64(b - y))
	tmp = 0.0
	if (z <= -4.4e-86)
		tmp = t_1;
	elseif (z <= 7.5e-5)
		tmp = Float64(x + Float64(x * z));
	elseif ((z <= 3e+215) || !(z <= 3.8e+268))
		tmp = t_1;
	else
		tmp = Float64(-Float64(a / b));
	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 <= -4.4e-86)
		tmp = t_1;
	elseif (z <= 7.5e-5)
		tmp = x + (x * z);
	elseif ((z <= 3e+215) || ~((z <= 3.8e+268)))
		tmp = t_1;
	else
		tmp = -(a / b);
	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, -4.4e-86], t$95$1, If[LessEqual[z, 7.5e-5], N[(x + N[(x * z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 3e+215], N[Not[LessEqual[z, 3.8e+268]], $MachinePrecision]], t$95$1, (-N[(a / b), $MachinePrecision])]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.4000000000000003e-86 or 7.49999999999999934e-5 < z < 2.9999999999999999e215 or 3.80000000000000027e268 < z

   1. Initial program 51.0%

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

   2. Taylor expanded in z around inf 78.1%

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

   3. Taylor expanded in t around inf 50.2%

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

   if -4.4000000000000003e-86 < z < 7.49999999999999934e-5

   1. Initial program 86.4%

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

   2. Taylor expanded in y around inf 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%

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

   5. Taylor expanded in z around 0 55.6%

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

   if 2.9999999999999999e215 < z < 3.80000000000000027e268

   1. Initial program 35.4%

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

   2. Taylor expanded in a around inf 30.4%

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

      1. mul-1-neg 30.4%

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

      2. distribute-lft-neg-out 30.4%

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

      3. *-commutative 30.4%

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

   4. Simplified 30.4%

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

   5. Taylor expanded in y around 0 62.6%

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

      1. mul-1-neg 62.6%

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

      2. distribute-neg-frac 62.6%

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

   7. Simplified 62.6%

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

4. Final simplification 53.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{-86}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-5}:\\ \;\;\;\;x + x \cdot z\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+215} \lor \neg \left(z \leq 3.8 \cdot 10^{+268}\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;-\frac{a}{b}\\ \end{array} \]

Alternative 4: 43.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{b - y}\\ \mathbf{if}\;z \leq -7.2 \cdot 10^{-85}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+17}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+215} \lor \neg \left(z \leq 5.4 \cdot 10^{+268}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;-\frac{a}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ t (- b y))))
   (if (<= z -7.2e-85)
     t_1
     (if (<= z 1.7e+17)
       (/ x (- 1.0 z))
       (if (or (<= z 4.2e+215) (not (<= z 5.4e+268))) t_1 (- (/ a b)))))))

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 <= -7.2e-85) {
		tmp = t_1;
	} else if (z <= 1.7e+17) {
		tmp = x / (1.0 - z);
	} else if ((z <= 4.2e+215) || !(z <= 5.4e+268)) {
		tmp = t_1;
	} else {
		tmp = -(a / b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t / (b - y)
    if (z <= (-7.2d-85)) then
        tmp = t_1
    else if (z <= 1.7d+17) then
        tmp = x / (1.0d0 - z)
    else if ((z <= 4.2d+215) .or. (.not. (z <= 5.4d+268))) then
        tmp = t_1
    else
        tmp = -(a / b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t / (b - y);
	double tmp;
	if (z <= -7.2e-85) {
		tmp = t_1;
	} else if (z <= 1.7e+17) {
		tmp = x / (1.0 - z);
	} else if ((z <= 4.2e+215) || !(z <= 5.4e+268)) {
		tmp = t_1;
	} else {
		tmp = -(a / b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t / (b - y)
	tmp = 0
	if z <= -7.2e-85:
		tmp = t_1
	elif z <= 1.7e+17:
		tmp = x / (1.0 - z)
	elif (z <= 4.2e+215) or not (z <= 5.4e+268):
		tmp = t_1
	else:
		tmp = -(a / b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t / Float64(b - y))
	tmp = 0.0
	if (z <= -7.2e-85)
		tmp = t_1;
	elseif (z <= 1.7e+17)
		tmp = Float64(x / Float64(1.0 - z));
	elseif ((z <= 4.2e+215) || !(z <= 5.4e+268))
		tmp = t_1;
	else
		tmp = Float64(-Float64(a / b));
	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 <= -7.2e-85)
		tmp = t_1;
	elseif (z <= 1.7e+17)
		tmp = x / (1.0 - z);
	elseif ((z <= 4.2e+215) || ~((z <= 5.4e+268)))
		tmp = t_1;
	else
		tmp = -(a / b);
	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, -7.2e-85], t$95$1, If[LessEqual[z, 1.7e+17], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 4.2e+215], N[Not[LessEqual[z, 5.4e+268]], $MachinePrecision]], t$95$1, (-N[(a / b), $MachinePrecision])]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.1999999999999996e-85 or 1.7e17 < z < 4.2000000000000003e215 or 5.40000000000000022e268 < z

   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 z around inf 80.1%

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

   3. Taylor expanded in t around inf 52.5%

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

   if -7.1999999999999996e-85 < z < 1.7e17

   1. Initial program 84.4%

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

   2. Taylor expanded in y around inf 54.0%

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

      1. +-commutative 54.0%

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

      2. mul-1-neg 54.0%

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

      3. unsub-neg 54.0%

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

   4. Simplified 54.0%

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

   if 4.2000000000000003e215 < z < 5.40000000000000022e268

   1. Initial program 35.4%

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

   2. Taylor expanded in a around inf 30.4%

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

      1. mul-1-neg 30.4%

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

      2. distribute-lft-neg-out 30.4%

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

      3. *-commutative 30.4%

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

   4. Simplified 30.4%

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

   5. Taylor expanded in y around 0 62.6%

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

      1. mul-1-neg 62.6%

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

      2. distribute-neg-frac 62.6%

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

   7. Simplified 62.6%

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

4. Final simplification 53.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{-85}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+17}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+215} \lor \neg \left(z \leq 5.4 \cdot 10^{+268}\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;-\frac{a}{b}\\ \end{array} \]

Alternative 5: 71.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{-37} \lor \neg \left(z \leq 1700\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{t - a}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -4.8e-37) (not (<= z 1700.0)))
   (/ (- t a) (- b y))
   (+ x (* z (/ (- t a) y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -4.8e-37) || !(z <= 1700.0)) {
		tmp = (t - a) / (b - y);
	} 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 <= (-4.8d-37)) .or. (.not. (z <= 1700.0d0))) then
        tmp = (t - a) / (b - y)
    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 <= -4.8e-37) || !(z <= 1700.0)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x + (z * ((t - a) / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -4.8e-37) or not (z <= 1700.0):
		tmp = (t - a) / (b - y)
	else:
		tmp = x + (z * ((t - a) / y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -4.8e-37) || !(z <= 1700.0))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(x + Float64(z * Float64(Float64(t - a) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -4.8e-37) || ~((z <= 1700.0)))
		tmp = (t - a) / (b - y);
	else
		tmp = x + (z * ((t - a) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -4.8e-37], N[Not[LessEqual[z, 1700.0]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(N[(t - a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.79999999999999982e-37 or 1700 < z

   1. Initial program 46.9%

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

   2. Taylor expanded in z around inf 83.4%

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

   if -4.79999999999999982e-37 < z < 1700

   1. Initial program 86.0%

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

   2. Taylor expanded in b around inf 84.8%

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

   3. Taylor expanded in y around inf 71.4%

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

      1. associate--l+ 71.4%

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

      2. associate-/l* 69.8%

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

      3. associate-*r* 73.4%

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

   5. Simplified 73.4%

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

   6. Taylor expanded in b around 0 76.0%

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

      1. +-commutative 76.0%

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

      2. associate-/l* 74.4%

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

      3. div-sub 74.4%

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

      4. associate-/r/ 71.1%

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

      5. associate-/r/ 69.3%

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

      6. distribute-rgt-out-- 69.2%

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

      7. div-sub 69.3%

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

   8. Simplified 69.3%

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

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{-37} \lor \neg \left(z \leq 1700\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{t - a}{y}\\ \end{array} \]

Alternative 6: 74.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{-35} \lor \neg \left(z \leq 1700\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.6e-35) (not (<= z 1700.0)))
   (/ (- t a) (- b y))
   (+ x (/ (* z (- t a)) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.6e-35) || !(z <= 1700.0)) {
		tmp = (t - a) / (b - y);
	} 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 <= (-1.6d-35)) .or. (.not. (z <= 1700.0d0))) then
        tmp = (t - a) / (b - y)
    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 <= -1.6e-35) || !(z <= 1700.0)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x + ((z * (t - a)) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.6e-35) or not (z <= 1700.0):
		tmp = (t - a) / (b - y)
	else:
		tmp = x + ((z * (t - a)) / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.6e-35) || !(z <= 1700.0))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	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 <= -1.6e-35) || ~((z <= 1700.0)))
		tmp = (t - a) / (b - y);
	else
		tmp = x + ((z * (t - a)) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.6e-35], N[Not[LessEqual[z, 1700.0]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $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 < -1.5999999999999999e-35 or 1700 < z

   1. Initial program 46.9%

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

   2. Taylor expanded in z around inf 83.4%

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

   if -1.5999999999999999e-35 < z < 1700

   1. Initial program 86.0%

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

   2. Taylor expanded in b around inf 84.8%

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

   3. Taylor expanded in y around inf 71.4%

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

      1. associate--l+ 71.4%

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

      2. associate-/l* 69.8%

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

      3. associate-*r* 73.4%

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

   5. Simplified 73.4%

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

   6. Taylor expanded in b around 0 76.0%

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

4. Final simplification 79.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{-35} \lor \neg \left(z \leq 1700\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y}\\ \end{array} \]

Alternative 7: 63.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{-85} \lor \neg \left(z \leq 1700000000\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.05e-85) (not (<= z 1700000000.0)))
   (/ (- t a) (- b y))
   (/ x (- 1.0 z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.05e-85) || !(z <= 1700000000.0)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x / (1.0 - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-1.05d-85)) .or. (.not. (z <= 1700000000.0d0))) then
        tmp = (t - a) / (b - y)
    else
        tmp = x / (1.0d0 - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.05e-85) || !(z <= 1700000000.0)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x / (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.05e-85) or not (z <= 1700000000.0):
		tmp = (t - a) / (b - y)
	else:
		tmp = x / (1.0 - z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.05e-85) || !(z <= 1700000000.0))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(x / Float64(1.0 - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1.05e-85) || ~((z <= 1700000000.0)))
		tmp = (t - a) / (b - y);
	else
		tmp = x / (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.05e-85], N[Not[LessEqual[z, 1700000000.0]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.05e-85 or 1.7e9 < z

   1. Initial program 49.6%

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

   2. Taylor expanded in z around inf 81.5%

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

   if -1.05e-85 < z < 1.7e9

   1. Initial program 85.2%

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

   2. Taylor expanded in y around inf 55.1%

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

      1. +-commutative 55.1%

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

      2. mul-1-neg 55.1%

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

      3. unsub-neg 55.1%

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

   4. Simplified 55.1%

      \[\leadsto \color{blue}{\frac{x}{1 - z}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{-85} \lor \neg \left(z \leq 1700000000\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]

Alternative 8: 54.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.02 \cdot 10^{-26} \lor \neg \left(y \leq 2.2 \cdot 10^{+34}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.02e-26) (not (<= y 2.2e+34))) (/ 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 <= -1.02e-26) || !(y <= 2.2e+34)) {
		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 <= (-1.02d-26)) .or. (.not. (y <= 2.2d+34))) 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 <= -1.02e-26) || !(y <= 2.2e+34)) {
		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 <= -1.02e-26) or not (y <= 2.2e+34):
		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 <= -1.02e-26) || !(y <= 2.2e+34))
		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 <= -1.02e-26) || ~((y <= 2.2e+34)))
		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, -1.02e-26], N[Not[LessEqual[y, 2.2e+34]], $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 < -1.02e-26 or 2.2000000000000002e34 < y

   1. Initial program 56.1%

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

   2. Taylor expanded in y around inf 56.3%

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

      1. +-commutative 56.3%

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

      2. mul-1-neg 56.3%

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

      3. unsub-neg 56.3%

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

   4. Simplified 56.3%

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

   if -1.02e-26 < y < 2.2000000000000002e34

   1. Initial program 75.2%

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

   2. Taylor expanded in y around 0 61.3%

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

4. Final simplification 59.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.02 \cdot 10^{-26} \lor \neg \left(y \leq 2.2 \cdot 10^{+34}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \]

Alternative 9: 36.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{-85}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 1700:\\ \;\;\;\;x + x \cdot z\\ \mathbf{else}:\\ \;\;\;\;-\frac{a}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -7.2e-85) (/ t b) (if (<= z 1700.0) (+ x (* x z)) (- (/ a b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -7.2e-85) {
		tmp = t / b;
	} else if (z <= 1700.0) {
		tmp = x + (x * z);
	} else {
		tmp = -(a / b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-7.2d-85)) then
        tmp = t / b
    else if (z <= 1700.0d0) then
        tmp = x + (x * z)
    else
        tmp = -(a / b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -7.2e-85) {
		tmp = t / b;
	} else if (z <= 1700.0) {
		tmp = x + (x * z);
	} else {
		tmp = -(a / b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -7.2e-85:
		tmp = t / b
	elif z <= 1700.0:
		tmp = x + (x * z)
	else:
		tmp = -(a / b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -7.2e-85)
		tmp = Float64(t / b);
	elseif (z <= 1700.0)
		tmp = Float64(x + Float64(x * z));
	else
		tmp = Float64(-Float64(a / b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -7.2e-85)
		tmp = t / b;
	elseif (z <= 1700.0)
		tmp = x + (x * z);
	else
		tmp = -(a / b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -7.2e-85], N[(t / b), $MachinePrecision], If[LessEqual[z, 1700.0], N[(x + N[(x * z), $MachinePrecision]), $MachinePrecision], (-N[(a / b), $MachinePrecision])]]

Derivation

1. Split input into 3 regimes

2. if z < -7.1999999999999996e-85

   1. Initial program 51.7%

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

      1. div-inv 51.6%

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

      2. fma-def 51.6%

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

      3. +-commutative 51.6%

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

      4. fma-def 51.6%

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

   3. Applied egg-rr 51.6%

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

   4. Taylor expanded in a around 0 37.7%

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

   5. Taylor expanded in y around 0 32.4%

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

   if -7.1999999999999996e-85 < z < 1700

   1. Initial program 85.8%

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

   2. Taylor expanded in y around inf 54.7%

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

      1. +-commutative 54.7%

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

      2. mul-1-neg 54.7%

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

      3. unsub-neg 54.7%

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

   4. Simplified 54.7%

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

   5. Taylor expanded in z around 0 54.7%

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

   if 1700 < 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 a around inf 29.3%

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

      1. mul-1-neg 29.3%

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

      2. distribute-lft-neg-out 29.3%

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

      3. *-commutative 29.3%

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

   4. Simplified 29.3%

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

   5. Taylor expanded in y around 0 38.3%

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

      1. mul-1-neg 38.3%

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

      2. distribute-neg-frac 38.3%

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

   7. Simplified 38.3%

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

4. Final simplification 44.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{-85}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 1700:\\ \;\;\;\;x + x \cdot z\\ \mathbf{else}:\\ \;\;\;\;-\frac{a}{b}\\ \end{array} \]

Alternative 10: 36.3% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{-87}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-22}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;-\frac{a}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -3.2e-87) (/ t b) (if (<= z 1.9e-22) x (- (/ a b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -3.2e-87) {
		tmp = t / b;
	} else if (z <= 1.9e-22) {
		tmp = x;
	} else {
		tmp = -(a / b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-3.2d-87)) then
        tmp = t / b
    else if (z <= 1.9d-22) then
        tmp = x
    else
        tmp = -(a / b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -3.2e-87) {
		tmp = t / b;
	} else if (z <= 1.9e-22) {
		tmp = x;
	} else {
		tmp = -(a / b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -3.2e-87:
		tmp = t / b
	elif z <= 1.9e-22:
		tmp = x
	else:
		tmp = -(a / b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -3.2e-87)
		tmp = Float64(t / b);
	elseif (z <= 1.9e-22)
		tmp = x;
	else
		tmp = Float64(-Float64(a / b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -3.2e-87)
		tmp = t / b;
	elseif (z <= 1.9e-22)
		tmp = x;
	else
		tmp = -(a / b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -3.2e-87], N[(t / b), $MachinePrecision], If[LessEqual[z, 1.9e-22], x, (-N[(a / b), $MachinePrecision])]]

Derivation

1. Split input into 3 regimes

2. if z < -3.19999999999999979e-87

   1. Initial program 51.7%

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

      1. div-inv 51.6%

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

      2. fma-def 51.6%

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

      3. +-commutative 51.6%

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

      4. fma-def 51.6%

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

   3. Applied egg-rr 51.6%

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

   4. Taylor expanded in a around 0 37.7%

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

   5. Taylor expanded in y around 0 32.4%

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

   if -3.19999999999999979e-87 < z < 1.90000000000000012e-22

   1. Initial program 85.9%

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

   2. Taylor expanded in z around 0 56.5%

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

   if 1.90000000000000012e-22 < z

   1. Initial program 49.8%

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

   2. Taylor expanded in a around inf 30.4%

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

      1. mul-1-neg 30.4%

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

      2. distribute-lft-neg-out 30.4%

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

      3. *-commutative 30.4%

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

   4. Simplified 30.4%

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

   5. Taylor expanded in y around 0 36.5%

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

      1. mul-1-neg 36.5%

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

      2. distribute-neg-frac 36.5%

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

   7. Simplified 36.5%

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

4. Final simplification 44.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{-87}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-22}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;-\frac{a}{b}\\ \end{array} \]

Alternative 11: 34.8% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{+37}:\\ \;\;\;\;\frac{a}{y}\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -2.15e+37) (/ a y) (if (<= z 1.0) x (/ a y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2.15e+37) {
		tmp = a / y;
	} else if (z <= 1.0) {
		tmp = x;
	} else {
		tmp = 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 <= (-2.15d+37)) then
        tmp = a / y
    else if (z <= 1.0d0) then
        tmp = x
    else
        tmp = 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 <= -2.15e+37) {
		tmp = a / y;
	} else if (z <= 1.0) {
		tmp = x;
	} else {
		tmp = a / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -2.15e+37:
		tmp = a / y
	elif z <= 1.0:
		tmp = x
	else:
		tmp = a / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -2.15e+37)
		tmp = Float64(a / y);
	elseif (z <= 1.0)
		tmp = x;
	else
		tmp = Float64(a / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -2.15e+37)
		tmp = a / y;
	elseif (z <= 1.0)
		tmp = x;
	else
		tmp = a / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -2.15e+37], N[(a / y), $MachinePrecision], If[LessEqual[z, 1.0], x, N[(a / y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.1499999999999998e37 or 1 < z

   1. Initial program 42.7%

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

   2. Taylor expanded in z around inf 85.1%

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

   3. Taylor expanded in t around 0 46.0%

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

      1. mul-1-neg 46.0%

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

      2. distribute-neg-frac 46.0%

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

   5. Simplified 46.0%

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

   6. Taylor expanded in b around 0 16.8%

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

   if -2.1499999999999998e37 < z < 1

   1. Initial program 86.4%

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

   2. Taylor expanded in z around 0 48.5%

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

4. Final simplification 33.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{+37}:\\ \;\;\;\;\frac{a}{y}\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{y}\\ \end{array} \]

Alternative 12: 35.8% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{-85}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 17200000000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -4.5e-85) (/ t b) (if (<= z 17200000000000.0) x (/ t b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -4.5e-85) {
		tmp = t / b;
	} else if (z <= 17200000000000.0) {
		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 <= (-4.5d-85)) then
        tmp = t / b
    else if (z <= 17200000000000.0d0) 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 <= -4.5e-85) {
		tmp = t / b;
	} else if (z <= 17200000000000.0) {
		tmp = x;
	} else {
		tmp = t / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -4.5e-85:
		tmp = t / b
	elif z <= 17200000000000.0:
		tmp = x
	else:
		tmp = t / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -4.5e-85)
		tmp = Float64(t / b);
	elseif (z <= 17200000000000.0)
		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 <= -4.5e-85)
		tmp = t / b;
	elseif (z <= 17200000000000.0)
		tmp = x;
	else
		tmp = t / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -4.5e-85], N[(t / b), $MachinePrecision], If[LessEqual[z, 17200000000000.0], x, N[(t / b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -4.50000000000000004e-85 or 1.72e13 < z

   1. Initial program 48.8%

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

      1. div-inv 48.7%

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

      2. fma-def 48.8%

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

      3. +-commutative 48.8%

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

      4. fma-def 48.8%

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

   3. Applied egg-rr 48.8%

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

   4. Taylor expanded in a around 0 33.0%

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

   5. Taylor expanded in y around 0 33.2%

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

   if -4.50000000000000004e-85 < z < 1.72e13

   1. Initial program 84.9%

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

   2. Taylor expanded in z around 0 52.4%

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

4. Final simplification 42.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{-85}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 17200000000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \]

Alternative 13: 25.6% accurate, 17.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 66.3%

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

2. Taylor expanded in z around 0 27.8%

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

3. Final simplification 27.8%

   \[\leadsto x \]

Developer target: 72.8% 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 2023185 
(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)))))