Development.Shake.Progress:decay from shake-0.15.5

Percentage Accurate: 66.1% → 88.8%

Time: 17.6s

Alternatives: 19

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 66.1% 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: 88.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+27} \lor \neg \left(z \leq 1.5 \cdot 10^{+28}\right):\\ \;\;\;\;\left(\frac{x \cdot \frac{y}{z}}{b - y} + \frac{t - a}{b - y}\right) + y \cdot \frac{a - t}{z \cdot {\left(b - y\right)}^{2}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -2.2e+27) (not (<= z 1.5e+28)))
   (+
    (+ (/ (* x (/ y z)) (- b y)) (/ (- t a) (- b y)))
    (* y (/ (- a t) (* z (pow (- b y) 2.0)))))
   (/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.2e+27) || !(z <= 1.5e+28)) {
		tmp = (((x * (y / z)) / (b - y)) + ((t - a) / (b - y))) + (y * ((a - t) / (z * pow((b - y), 2.0))));
	} else {
		tmp = ((x * y) + (z * (t - 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 <= (-2.2d+27)) .or. (.not. (z <= 1.5d+28))) then
        tmp = (((x * (y / z)) / (b - y)) + ((t - a) / (b - y))) + (y * ((a - t) / (z * ((b - y) ** 2.0d0))))
    else
        tmp = ((x * y) + (z * (t - 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 <= -2.2e+27) || !(z <= 1.5e+28)) {
		tmp = (((x * (y / z)) / (b - y)) + ((t - a) / (b - y))) + (y * ((a - t) / (z * Math.pow((b - y), 2.0))));
	} else {
		tmp = ((x * y) + (z * (t - a))) / (y + (z * (b - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -2.2e+27) or not (z <= 1.5e+28):
		tmp = (((x * (y / z)) / (b - y)) + ((t - a) / (b - y))) + (y * ((a - t) / (z * math.pow((b - y), 2.0))))
	else:
		tmp = ((x * y) + (z * (t - a))) / (y + (z * (b - y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -2.2e+27) || !(z <= 1.5e+28))
		tmp = Float64(Float64(Float64(Float64(x * Float64(y / z)) / Float64(b - y)) + Float64(Float64(t - a) / Float64(b - y))) + Float64(y * Float64(Float64(a - t) / Float64(z * (Float64(b - y) ^ 2.0)))));
	else
		tmp = Float64(Float64(Float64(x * y) + Float64(z * Float64(t - 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 <= -2.2e+27) || ~((z <= 1.5e+28)))
		tmp = (((x * (y / z)) / (b - y)) + ((t - a) / (b - y))) + (y * ((a - t) / (z * ((b - y) ^ 2.0))));
	else
		tmp = ((x * y) + (z * (t - a))) / (y + (z * (b - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -2.2e+27], N[Not[LessEqual[z, 1.5e+28]], $MachinePrecision]], N[(N[(N[(N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision] + N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * N[(N[(a - t), $MachinePrecision] / N[(z * N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] + N[(z * N[(t - 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 < -2.1999999999999999e27 or 1.5e28 < z

   1. Initial program 44.6%

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

   3. Taylor expanded in z around inf 64.4%

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

      1. associate--r+ 64.4%

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

      2. +-commutative 64.4%

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

      3. associate--l+ 64.4%

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

      4. associate-/r* 68.9%

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

      5. associate-/l* 71.2%

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

      6. div-sub 72.0%

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

      7. associate-/l* 91.5%

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

   5. Simplified 91.5%

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

   if -2.1999999999999999e27 < z < 1.5e28

   1. Initial program 92.3%

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

4. Final simplification 91.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+27} \lor \neg \left(z \leq 1.5 \cdot 10^{+28}\right):\\ \;\;\;\;\left(\frac{x \cdot \frac{y}{z}}{b - y} + \frac{t - a}{b - y}\right) + y \cdot \frac{a - t}{z \cdot {\left(b - y\right)}^{2}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 87.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := z \cdot \left(t - a\right)\\ t_3 := \frac{x \cdot y + t\_2}{t\_1}\\ \mathbf{if}\;t\_3 \leq -\infty:\\ \;\;\;\;x \cdot \left(\frac{y}{t\_1} + \frac{t\_2}{x \cdot t\_1}\right)\\ \mathbf{elif}\;t\_3 \leq -4 \cdot 10^{-276}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_3 \leq 0 \lor \neg \left(t\_3 \leq 10^{+298}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{t\_1} + \frac{t\_2}{t\_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y))))
        (t_2 (* z (- t a)))
        (t_3 (/ (+ (* x y) t_2) t_1)))
   (if (<= t_3 (- INFINITY))
     (* x (+ (/ y t_1) (/ t_2 (* x t_1))))
     (if (<= t_3 -4e-276)
       t_3
       (if (or (<= t_3 0.0) (not (<= t_3 1e+298)))
         (/ (- t a) (- b y))
         (+ (/ (* x y) t_1) (/ t_2 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 t_2 = z * (t - a);
	double t_3 = ((x * y) + t_2) / t_1;
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = x * ((y / t_1) + (t_2 / (x * t_1)));
	} else if (t_3 <= -4e-276) {
		tmp = t_3;
	} else if ((t_3 <= 0.0) || !(t_3 <= 1e+298)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((x * y) / t_1) + (t_2 / t_1);
	}
	return tmp;
}

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 = z * (t - a);
	double t_3 = ((x * y) + t_2) / t_1;
	double tmp;
	if (t_3 <= -Double.POSITIVE_INFINITY) {
		tmp = x * ((y / t_1) + (t_2 / (x * t_1)));
	} else if (t_3 <= -4e-276) {
		tmp = t_3;
	} else if ((t_3 <= 0.0) || !(t_3 <= 1e+298)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((x * y) / t_1) + (t_2 / t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z * (b - y))
	t_2 = z * (t - a)
	t_3 = ((x * y) + t_2) / t_1
	tmp = 0
	if t_3 <= -math.inf:
		tmp = x * ((y / t_1) + (t_2 / (x * t_1)))
	elif t_3 <= -4e-276:
		tmp = t_3
	elif (t_3 <= 0.0) or not (t_3 <= 1e+298):
		tmp = (t - a) / (b - y)
	else:
		tmp = ((x * y) / t_1) + (t_2 / t_1)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(z * Float64(b - y)))
	t_2 = Float64(z * Float64(t - a))
	t_3 = Float64(Float64(Float64(x * y) + t_2) / t_1)
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = Float64(x * Float64(Float64(y / t_1) + Float64(t_2 / Float64(x * t_1))));
	elseif (t_3 <= -4e-276)
		tmp = t_3;
	elseif ((t_3 <= 0.0) || !(t_3 <= 1e+298))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(Float64(Float64(x * y) / t_1) + Float64(t_2 / t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (z * (b - y));
	t_2 = z * (t - a);
	t_3 = ((x * y) + t_2) / t_1;
	tmp = 0.0;
	if (t_3 <= -Inf)
		tmp = x * ((y / t_1) + (t_2 / (x * t_1)));
	elseif (t_3 <= -4e-276)
		tmp = t_3;
	elseif ((t_3 <= 0.0) || ~((t_3 <= 1e+298)))
		tmp = (t - a) / (b - y);
	else
		tmp = ((x * y) / t_1) + (t_2 / 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]}, Block[{t$95$2 = N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(x * y), $MachinePrecision] + t$95$2), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], N[(x * N[(N[(y / t$95$1), $MachinePrecision] + N[(t$95$2 / N[(x * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, -4e-276], t$95$3, If[Or[LessEqual[t$95$3, 0.0], N[Not[LessEqual[t$95$3, 1e+298]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] / t$95$1), $MachinePrecision] + N[(t$95$2 / t$95$1), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -inf.0

   1. Initial program 27.5%

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

   3. Taylor expanded in x around inf 78.0%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -4e-276

   1. Initial program 99.4%

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

   if -4e-276 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 0.0 or 9.9999999999999996e297 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 16.9%

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

   3. Taylor expanded in z around inf 79.6%

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

   if 0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 9.9999999999999996e297

   1. Initial program 99.6%

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

   3. Taylor expanded in x around 0 99.6%

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

4. Final simplification 91.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;x \cdot \left(\frac{y}{y + z \cdot \left(b - y\right)} + \frac{z \cdot \left(t - a\right)}{x \cdot \left(y + z \cdot \left(b - y\right)\right)}\right)\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -4 \cdot 10^{-276}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 0 \lor \neg \left(\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 10^{+298}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{y + z \cdot \left(b - y\right)} + \frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 87.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := y \cdot \left(1 - z\right)\\ t_3 := z \cdot \left(t - a\right)\\ t_4 := \frac{x \cdot y + t\_3}{t\_1}\\ \mathbf{if}\;t\_4 \leq -\infty:\\ \;\;\;\;x \cdot \frac{y}{t\_2} + z \cdot \frac{t - a}{t\_2}\\ \mathbf{elif}\;t\_4 \leq -4 \cdot 10^{-276}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t\_4 \leq 0 \lor \neg \left(t\_4 \leq 10^{+298}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{t\_1} + \frac{t\_3}{t\_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y))))
        (t_2 (* y (- 1.0 z)))
        (t_3 (* z (- t a)))
        (t_4 (/ (+ (* x y) t_3) t_1)))
   (if (<= t_4 (- INFINITY))
     (+ (* x (/ y t_2)) (* z (/ (- t a) t_2)))
     (if (<= t_4 -4e-276)
       t_4
       (if (or (<= t_4 0.0) (not (<= t_4 1e+298)))
         (/ (- t a) (- b y))
         (+ (/ (* x y) t_1) (/ t_3 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 t_2 = y * (1.0 - z);
	double t_3 = z * (t - a);
	double t_4 = ((x * y) + t_3) / t_1;
	double tmp;
	if (t_4 <= -((double) INFINITY)) {
		tmp = (x * (y / t_2)) + (z * ((t - a) / t_2));
	} else if (t_4 <= -4e-276) {
		tmp = t_4;
	} else if ((t_4 <= 0.0) || !(t_4 <= 1e+298)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((x * y) / t_1) + (t_3 / t_1);
	}
	return tmp;
}

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 = y * (1.0 - z);
	double t_3 = z * (t - a);
	double t_4 = ((x * y) + t_3) / t_1;
	double tmp;
	if (t_4 <= -Double.POSITIVE_INFINITY) {
		tmp = (x * (y / t_2)) + (z * ((t - a) / t_2));
	} else if (t_4 <= -4e-276) {
		tmp = t_4;
	} else if ((t_4 <= 0.0) || !(t_4 <= 1e+298)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((x * y) / t_1) + (t_3 / t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z * (b - y))
	t_2 = y * (1.0 - z)
	t_3 = z * (t - a)
	t_4 = ((x * y) + t_3) / t_1
	tmp = 0
	if t_4 <= -math.inf:
		tmp = (x * (y / t_2)) + (z * ((t - a) / t_2))
	elif t_4 <= -4e-276:
		tmp = t_4
	elif (t_4 <= 0.0) or not (t_4 <= 1e+298):
		tmp = (t - a) / (b - y)
	else:
		tmp = ((x * y) / t_1) + (t_3 / t_1)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(z * Float64(b - y)))
	t_2 = Float64(y * Float64(1.0 - z))
	t_3 = Float64(z * Float64(t - a))
	t_4 = Float64(Float64(Float64(x * y) + t_3) / t_1)
	tmp = 0.0
	if (t_4 <= Float64(-Inf))
		tmp = Float64(Float64(x * Float64(y / t_2)) + Float64(z * Float64(Float64(t - a) / t_2)));
	elseif (t_4 <= -4e-276)
		tmp = t_4;
	elseif ((t_4 <= 0.0) || !(t_4 <= 1e+298))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(Float64(Float64(x * y) / t_1) + Float64(t_3 / t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (z * (b - y));
	t_2 = y * (1.0 - z);
	t_3 = z * (t - a);
	t_4 = ((x * y) + t_3) / t_1;
	tmp = 0.0;
	if (t_4 <= -Inf)
		tmp = (x * (y / t_2)) + (z * ((t - a) / t_2));
	elseif (t_4 <= -4e-276)
		tmp = t_4;
	elseif ((t_4 <= 0.0) || ~((t_4 <= 1e+298)))
		tmp = (t - a) / (b - y);
	else
		tmp = ((x * y) / t_1) + (t_3 / 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]}, Block[{t$95$2 = N[(y * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(x * y), $MachinePrecision] + t$95$3), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[t$95$4, (-Infinity)], N[(N[(x * N[(y / t$95$2), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(t - a), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$4, -4e-276], t$95$4, If[Or[LessEqual[t$95$4, 0.0], N[Not[LessEqual[t$95$4, 1e+298]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] / t$95$1), $MachinePrecision] + N[(t$95$3 / t$95$1), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -inf.0

   1. Initial program 27.5%

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

   3. Taylor expanded in x around 0 27.5%

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

   4. Taylor expanded in b around 0 19.4%

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

      1. associate-/l* 70.3%

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

      2. *-rgt-identity 70.3%

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

      3. mul-1-neg 70.3%

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

      4. *-commutative 70.3%

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

      5. distribute-lft-neg-out 70.3%

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

      6. neg-mul-1 70.3%

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

      7. *-commutative 70.3%

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

      8. distribute-lft-in 70.3%

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

      9. neg-mul-1 70.3%

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

      10. sub-neg 70.3%

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

      11. *-lft-identity 70.3%

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

      12. associate-*r* 70.3%

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

      13. neg-mul-1 70.3%

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

      14. *-commutative 70.3%

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

      15. distribute-rgt-neg-out 70.3%

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

      16. distribute-lft-neg-out 70.3%

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

      17. neg-mul-1 70.3%

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

      18. distribute-rgt-in 70.3%

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

   6. Simplified 70.3%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -4e-276

   1. Initial program 99.4%

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

   if -4e-276 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 0.0 or 9.9999999999999996e297 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 16.9%

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

   3. Taylor expanded in z around inf 79.6%

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

   if 0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 9.9999999999999996e297

   1. Initial program 99.6%

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

   3. Taylor expanded in x around 0 99.6%

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

4. Final simplification 91.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;x \cdot \frac{y}{y \cdot \left(1 - z\right)} + z \cdot \frac{t - a}{y \cdot \left(1 - z\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -4 \cdot 10^{-276}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 0 \lor \neg \left(\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 10^{+298}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{y + z \cdot \left(b - y\right)} + \frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 87.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ t_2 := y \cdot \left(1 - z\right)\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;x \cdot \frac{y}{t\_2} + z \cdot \frac{t - a}{t\_2}\\ \mathbf{elif}\;t\_1 \leq -4 \cdot 10^{-276} \lor \neg \left(t\_1 \leq 0\right) \land t\_1 \leq 10^{+298}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y)))))
        (t_2 (* y (- 1.0 z))))
   (if (<= t_1 (- INFINITY))
     (+ (* x (/ y t_2)) (* z (/ (- t a) t_2)))
     (if (or (<= t_1 -4e-276) (and (not (<= t_1 0.0)) (<= t_1 1e+298)))
       t_1
       (/ (- t a) (- b y))))))

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 t_2 = y * (1.0 - z);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = (x * (y / t_2)) + (z * ((t - a) / t_2));
	} else if ((t_1 <= -4e-276) || (!(t_1 <= 0.0) && (t_1 <= 1e+298))) {
		tmp = t_1;
	} else {
		tmp = (t - a) / (b - y);
	}
	return tmp;
}

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 t_2 = y * (1.0 - z);
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = (x * (y / t_2)) + (z * ((t - a) / t_2));
	} else if ((t_1 <= -4e-276) || (!(t_1 <= 0.0) && (t_1 <= 1e+298))) {
		tmp = t_1;
	} else {
		tmp = (t - a) / (b - y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((x * y) + (z * (t - a))) / (y + (z * (b - y)))
	t_2 = y * (1.0 - z)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = (x * (y / t_2)) + (z * ((t - a) / t_2))
	elif (t_1 <= -4e-276) or (not (t_1 <= 0.0) and (t_1 <= 1e+298)):
		tmp = t_1
	else:
		tmp = (t - a) / (b - y)
	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))))
	t_2 = Float64(y * Float64(1.0 - z))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(x * Float64(y / t_2)) + Float64(z * Float64(Float64(t - a) / t_2)));
	elseif ((t_1 <= -4e-276) || (!(t_1 <= 0.0) && (t_1 <= 1e+298)))
		tmp = t_1;
	else
		tmp = Float64(Float64(t - a) / Float64(b - y));
	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)));
	t_2 = y * (1.0 - z);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = (x * (y / t_2)) + (z * ((t - a) / t_2));
	elseif ((t_1 <= -4e-276) || (~((t_1 <= 0.0)) && (t_1 <= 1e+298)))
		tmp = t_1;
	else
		tmp = (t - a) / (b - y);
	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]}, Block[{t$95$2 = N[(y * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(x * N[(y / t$95$2), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(t - a), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t$95$1, -4e-276], And[N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision], LessEqual[t$95$1, 1e+298]]], t$95$1, N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -inf.0

   1. Initial program 27.5%

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

   3. Taylor expanded in x around 0 27.5%

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

   4. Taylor expanded in b around 0 19.4%

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

      1. associate-/l* 70.3%

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

      2. *-rgt-identity 70.3%

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

      3. mul-1-neg 70.3%

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

      4. *-commutative 70.3%

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

      5. distribute-lft-neg-out 70.3%

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

      6. neg-mul-1 70.3%

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

      7. *-commutative 70.3%

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

      8. distribute-lft-in 70.3%

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

      9. neg-mul-1 70.3%

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

      10. sub-neg 70.3%

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

      11. *-lft-identity 70.3%

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

      12. associate-*r* 70.3%

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

      13. neg-mul-1 70.3%

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

      14. *-commutative 70.3%

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

      15. distribute-rgt-neg-out 70.3%

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

      16. distribute-lft-neg-out 70.3%

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

      17. neg-mul-1 70.3%

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

      18. distribute-rgt-in 70.3%

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

   6. Simplified 70.3%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -4e-276 or 0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 9.9999999999999996e297

   1. Initial program 99.5%

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

   if -4e-276 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 0.0 or 9.9999999999999996e297 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 16.9%

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

   3. Taylor expanded in z around inf 79.6%

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

4. Final simplification 91.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;x \cdot \frac{y}{y \cdot \left(1 - z\right)} + z \cdot \frac{t - a}{y \cdot \left(1 - z\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -4 \cdot 10^{-276} \lor \neg \left(\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 0\right) \land \frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 10^{+298}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 86.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(t - a\right)\\ t_2 := \frac{x \cdot y + t\_1}{y + z \cdot \left(b - y\right)}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;\frac{x}{1 - z} + \frac{t\_1}{y \cdot \left(1 - z\right)}\\ \mathbf{elif}\;t\_2 \leq -4 \cdot 10^{-276} \lor \neg \left(t\_2 \leq 0\right) \land t\_2 \leq 10^{+298}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \end{array} \]

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 y))))))
   (if (<= t_2 (- INFINITY))
     (+ (/ x (- 1.0 z)) (/ t_1 (* y (- 1.0 z))))
     (if (or (<= t_2 -4e-276) (and (not (<= t_2 0.0)) (<= t_2 1e+298)))
       t_2
       (/ (- t a) (- b y))))))

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 - y)));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = (x / (1.0 - z)) + (t_1 / (y * (1.0 - z)));
	} else if ((t_2 <= -4e-276) || (!(t_2 <= 0.0) && (t_2 <= 1e+298))) {
		tmp = t_2;
	} else {
		tmp = (t - a) / (b - y);
	}
	return tmp;
}

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 - y)));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = (x / (1.0 - z)) + (t_1 / (y * (1.0 - z)));
	} else if ((t_2 <= -4e-276) || (!(t_2 <= 0.0) && (t_2 <= 1e+298))) {
		tmp = t_2;
	} else {
		tmp = (t - a) / (b - y);
	}
	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 - y)))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = (x / (1.0 - z)) + (t_1 / (y * (1.0 - z)))
	elif (t_2 <= -4e-276) or (not (t_2 <= 0.0) and (t_2 <= 1e+298)):
		tmp = t_2
	else:
		tmp = (t - a) / (b - y)
	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 * Float64(b - y))))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(Float64(x / Float64(1.0 - z)) + Float64(t_1 / Float64(y * Float64(1.0 - z))));
	elseif ((t_2 <= -4e-276) || (!(t_2 <= 0.0) && (t_2 <= 1e+298)))
		tmp = t_2;
	else
		tmp = Float64(Float64(t - a) / Float64(b - y));
	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 - y)));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = (x / (1.0 - z)) + (t_1 / (y * (1.0 - z)));
	elseif ((t_2 <= -4e-276) || (~((t_2 <= 0.0)) && (t_2 <= 1e+298)))
		tmp = t_2;
	else
		tmp = (t - a) / (b - y);
	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 * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision] + N[(t$95$1 / N[(y * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t$95$2, -4e-276], And[N[Not[LessEqual[t$95$2, 0.0]], $MachinePrecision], LessEqual[t$95$2, 1e+298]]], t$95$2, N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -inf.0

   1. Initial program 27.5%

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

   3. Taylor expanded in b around 0 19.4%

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

      1. mul-1-neg 19.4%

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

      2. *-commutative 19.4%

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

   5. Simplified 19.4%

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

   6. Taylor expanded in y around inf 70.3%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -4e-276 or 0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 9.9999999999999996e297

   1. Initial program 99.5%

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

   if -4e-276 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 0.0 or 9.9999999999999996e297 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 16.9%

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

   3. Taylor expanded in z around inf 79.6%

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

4. Final simplification 91.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;\frac{x}{1 - z} + \frac{z \cdot \left(t - a\right)}{y \cdot \left(1 - z\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -4 \cdot 10^{-276} \lor \neg \left(\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 0\right) \land \frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 10^{+298}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 83.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3900000000000 \lor \neg \left(z \leq 1.32 \cdot 10^{+20}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -3900000000000.0) (not (<= z 1.32e+20)))
   (/ (- t a) (- b y))
   (/ (+ (* x y) (* z (- t a))) (+ y (* z b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -3900000000000.0) || !(z <= 1.32e+20)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((x * y) + (z * (t - a))) / (y + (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 <= (-3900000000000.0d0)) .or. (.not. (z <= 1.32d+20))) then
        tmp = (t - a) / (b - y)
    else
        tmp = ((x * y) + (z * (t - a))) / (y + (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 <= -3900000000000.0) || !(z <= 1.32e+20)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((x * y) + (z * (t - a))) / (y + (z * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -3900000000000.0) or not (z <= 1.32e+20):
		tmp = (t - a) / (b - y)
	else:
		tmp = ((x * y) + (z * (t - a))) / (y + (z * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -3900000000000.0) || !(z <= 1.32e+20))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(Float64(Float64(x * y) + Float64(z * Float64(t - a))) / Float64(y + Float64(z * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -3900000000000.0) || ~((z <= 1.32e+20)))
		tmp = (t - a) / (b - y);
	else
		tmp = ((x * y) + (z * (t - a))) / (y + (z * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -3900000000000.0], N[Not[LessEqual[z, 1.32e+20]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.9e12 or 1.32e20 < z

   1. Initial program 45.9%

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

   3. Taylor expanded in z around inf 82.5%

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

   if -3.9e12 < z < 1.32e20

   1. Initial program 92.1%

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

   3. Taylor expanded in b around inf 90.2%

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

      1. *-commutative 90.2%

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

   5. Simplified 90.2%

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

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3900000000000 \lor \neg \left(z \leq 1.32 \cdot 10^{+20}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot b}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 53.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+226}:\\ \;\;\;\;\frac{a - t}{y}\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{-23} \lor \neg \left(z \leq 1.9 \cdot 10^{-7}\right):\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot t}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -2.2e+226)
   (/ (- a t) y)
   (if (or (<= z -6.6e-23) (not (<= z 1.9e-7)))
     (/ (- t a) b)
     (+ x (/ (* z t) y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2.2e+226) {
		tmp = (a - t) / y;
	} else if ((z <= -6.6e-23) || !(z <= 1.9e-7)) {
		tmp = (t - a) / b;
	} else {
		tmp = x + ((z * t) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-2.2d+226)) then
        tmp = (a - t) / y
    else if ((z <= (-6.6d-23)) .or. (.not. (z <= 1.9d-7))) then
        tmp = (t - a) / b
    else
        tmp = x + ((z * t) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2.2e+226) {
		tmp = (a - t) / y;
	} else if ((z <= -6.6e-23) || !(z <= 1.9e-7)) {
		tmp = (t - a) / b;
	} else {
		tmp = x + ((z * t) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -2.2e+226:
		tmp = (a - t) / y
	elif (z <= -6.6e-23) or not (z <= 1.9e-7):
		tmp = (t - a) / b
	else:
		tmp = x + ((z * t) / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -2.2e+226)
		tmp = Float64(Float64(a - t) / y);
	elseif ((z <= -6.6e-23) || !(z <= 1.9e-7))
		tmp = Float64(Float64(t - a) / b);
	else
		tmp = Float64(x + Float64(Float64(z * t) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -2.2e+226)
		tmp = (a - t) / y;
	elseif ((z <= -6.6e-23) || ~((z <= 1.9e-7)))
		tmp = (t - a) / b;
	else
		tmp = x + ((z * t) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -2.2e+226], N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision], If[Or[LessEqual[z, -6.6e-23], N[Not[LessEqual[z, 1.9e-7]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision], N[(x + N[(N[(z * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.19999999999999994e226

   1. Initial program 28.7%

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

   3. Taylor expanded in b around 0 29.0%

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

      1. mul-1-neg 29.0%

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

      2. *-commutative 29.0%

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

   5. Simplified 29.0%

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

   6. Taylor expanded in z around -inf 65.6%

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

      1. mul-1-neg 65.6%

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

      2. unsub-neg 65.6%

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

      3. associate-*r/ 65.6%

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

      4. mul-1-neg 65.6%

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

      5. sub-neg 65.6%

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

      6. mul-1-neg 65.6%

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

      7. remove-double-neg 65.6%

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

   8. Simplified 65.6%

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

   9. Taylor expanded in z around inf 65.6%

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

       1. div-sub 74.7%

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

   11. Simplified 74.7%

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

   if -2.19999999999999994e226 < z < -6.60000000000000041e-23 or 1.90000000000000007e-7 < z

   1. Initial program 53.9%

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

   3. Taylor expanded in y around 0 51.7%

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

   if -6.60000000000000041e-23 < z < 1.90000000000000007e-7

   1. Initial program 91.6%

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

   3. Taylor expanded in b around 0 68.9%

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

      1. mul-1-neg 68.9%

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

      2. *-commutative 68.9%

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

   5. Simplified 68.9%

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

   6. Taylor expanded in z around 0 68.2%

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

      1. mul-1-neg 68.2%

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

      2. +-commutative 68.2%

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

      3. unsub-neg 68.2%

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

   8. Simplified 68.2%

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

   9. Taylor expanded in t around inf 58.6%

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

4. Final simplification 55.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+226}:\\ \;\;\;\;\frac{a - t}{y}\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{-23} \lor \neg \left(z \leq 1.9 \cdot 10^{-7}\right):\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot t}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 51.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{+227}:\\ \;\;\;\;\frac{a - t}{y}\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-28} \lor \neg \left(z \leq 1.5 \cdot 10^{-7}\right):\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{t}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.02e+227)
   (/ (- a t) y)
   (if (or (<= z -3.4e-28) (not (<= z 1.5e-7)))
     (/ (- t a) b)
     (+ x (* z (/ t y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.02e+227) {
		tmp = (a - t) / y;
	} else if ((z <= -3.4e-28) || !(z <= 1.5e-7)) {
		tmp = (t - a) / b;
	} else {
		tmp = x + (z * (t / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-1.02d+227)) then
        tmp = (a - t) / y
    else if ((z <= (-3.4d-28)) .or. (.not. (z <= 1.5d-7))) then
        tmp = (t - a) / b
    else
        tmp = x + (z * (t / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.02e+227) {
		tmp = (a - t) / y;
	} else if ((z <= -3.4e-28) || !(z <= 1.5e-7)) {
		tmp = (t - a) / b;
	} else {
		tmp = x + (z * (t / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1.02e+227:
		tmp = (a - t) / y
	elif (z <= -3.4e-28) or not (z <= 1.5e-7):
		tmp = (t - a) / b
	else:
		tmp = x + (z * (t / y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.02e+227)
		tmp = Float64(Float64(a - t) / y);
	elseif ((z <= -3.4e-28) || !(z <= 1.5e-7))
		tmp = Float64(Float64(t - a) / b);
	else
		tmp = Float64(x + Float64(z * Float64(t / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -1.02e+227)
		tmp = (a - t) / y;
	elseif ((z <= -3.4e-28) || ~((z <= 1.5e-7)))
		tmp = (t - a) / b;
	else
		tmp = x + (z * (t / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.02e+227], N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision], If[Or[LessEqual[z, -3.4e-28], N[Not[LessEqual[z, 1.5e-7]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision], N[(x + N[(z * N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.0200000000000001e227

   1. Initial program 28.7%

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

   3. Taylor expanded in b around 0 29.0%

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

      1. mul-1-neg 29.0%

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

      2. *-commutative 29.0%

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

   5. Simplified 29.0%

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

   6. Taylor expanded in z around -inf 65.6%

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

      1. mul-1-neg 65.6%

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

      2. unsub-neg 65.6%

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

      3. associate-*r/ 65.6%

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

      4. mul-1-neg 65.6%

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

      5. sub-neg 65.6%

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

      6. mul-1-neg 65.6%

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

      7. remove-double-neg 65.6%

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

   8. Simplified 65.6%

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

   9. Taylor expanded in z around inf 65.6%

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

       1. div-sub 74.7%

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

   11. Simplified 74.7%

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

   if -1.0200000000000001e227 < z < -3.4000000000000001e-28 or 1.4999999999999999e-7 < z

   1. Initial program 53.9%

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

   3. Taylor expanded in y around 0 51.7%

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

   if -3.4000000000000001e-28 < z < 1.4999999999999999e-7

   1. Initial program 91.6%

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

   3. Taylor expanded in b around 0 68.9%

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

      1. mul-1-neg 68.9%

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

      2. *-commutative 68.9%

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

   5. Simplified 68.9%

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

   6. Taylor expanded in z around 0 68.2%

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

      1. mul-1-neg 68.2%

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

      2. +-commutative 68.2%

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

      3. unsub-neg 68.2%

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

   8. Simplified 68.2%

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

   9. Taylor expanded in t around inf 57.7%

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

4. Final simplification 55.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{+227}:\\ \;\;\;\;\frac{a - t}{y}\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-28} \lor \neg \left(z \leq 1.5 \cdot 10^{-7}\right):\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{t}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 42.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a - t}{y}\\ \mathbf{if}\;z \leq -1.55 \cdot 10^{+83}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-17}:\\ \;\;\;\;\frac{a}{-b}\\ \mathbf{elif}\;z \leq 23000000000:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- a t) y)))
   (if (<= z -1.55e+83)
     t_1
     (if (<= z -3.5e-17)
       (/ a (- b))
       (if (<= z 23000000000.0) (/ x (- 1.0 z)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a - t) / y;
	double tmp;
	if (z <= -1.55e+83) {
		tmp = t_1;
	} else if (z <= -3.5e-17) {
		tmp = a / -b;
	} else if (z <= 23000000000.0) {
		tmp = x / (1.0 - z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a - t) / y
    if (z <= (-1.55d+83)) then
        tmp = t_1
    else if (z <= (-3.5d-17)) then
        tmp = a / -b
    else if (z <= 23000000000.0d0) then
        tmp = x / (1.0d0 - z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a - t) / y;
	double tmp;
	if (z <= -1.55e+83) {
		tmp = t_1;
	} else if (z <= -3.5e-17) {
		tmp = a / -b;
	} else if (z <= 23000000000.0) {
		tmp = x / (1.0 - z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a - t) / y
	tmp = 0
	if z <= -1.55e+83:
		tmp = t_1
	elif z <= -3.5e-17:
		tmp = a / -b
	elif z <= 23000000000.0:
		tmp = x / (1.0 - z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a - t) / y)
	tmp = 0.0
	if (z <= -1.55e+83)
		tmp = t_1;
	elseif (z <= -3.5e-17)
		tmp = Float64(a / Float64(-b));
	elseif (z <= 23000000000.0)
		tmp = Float64(x / Float64(1.0 - z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a - t) / y;
	tmp = 0.0;
	if (z <= -1.55e+83)
		tmp = t_1;
	elseif (z <= -3.5e-17)
		tmp = a / -b;
	elseif (z <= 23000000000.0)
		tmp = x / (1.0 - z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[z, -1.55e+83], t$95$1, If[LessEqual[z, -3.5e-17], N[(a / (-b)), $MachinePrecision], If[LessEqual[z, 23000000000.0], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.54999999999999996e83 or 2.3e10 < z

   1. Initial program 46.8%

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

   3. Taylor expanded in b around 0 26.1%

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

      1. mul-1-neg 26.1%

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

      2. *-commutative 26.1%

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

   5. Simplified 26.1%

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

   6. Taylor expanded in z around -inf 49.3%

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

      1. mul-1-neg 49.3%

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

      2. unsub-neg 49.3%

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

      3. associate-*r/ 49.3%

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

      4. mul-1-neg 49.3%

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

      5. sub-neg 49.3%

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

      6. mul-1-neg 49.3%

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

      7. remove-double-neg 49.3%

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

   8. Simplified 49.3%

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

   9. Taylor expanded in z around inf 42.3%

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

       1. div-sub 43.2%

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

   11. Simplified 43.2%

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

   if -1.54999999999999996e83 < z < -3.5000000000000002e-17

   1. Initial program 66.6%

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

   3. Taylor expanded in x around 0 66.7%

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

   4. Taylor expanded in b around inf 69.1%

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

      1. +-commutative 69.1%

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

      2. *-commutative 69.1%

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

   6. Simplified 69.1%

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

   7. Taylor expanded in a around inf 48.9%

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

      1. neg-mul-1 48.9%

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

   9. Simplified 48.9%

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

   if -3.5000000000000002e-17 < z < 2.3e10

   1. Initial program 91.3%

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

   3. Taylor expanded in y around inf 48.5%

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

      1. mul-1-neg 48.5%

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

      2. unsub-neg 48.5%

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

   5. Simplified 48.5%

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

4. Final simplification 46.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+83}:\\ \;\;\;\;\frac{a - t}{y}\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-17}:\\ \;\;\;\;\frac{a}{-b}\\ \mathbf{elif}\;z \leq 23000000000:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{a - t}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 36.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+156}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-18}:\\ \;\;\;\;\frac{a}{-b}\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-7}:\\ \;\;\;\;x + z \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -2.5e+156)
   (/ t b)
   (if (<= z -1.3e-18) (/ a (- b)) (if (<= z 2.4e-7) (+ x (* z x)) (/ t b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2.5e+156) {
		tmp = t / b;
	} else if (z <= -1.3e-18) {
		tmp = a / -b;
	} else if (z <= 2.4e-7) {
		tmp = x + (z * 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 <= (-2.5d+156)) then
        tmp = t / b
    else if (z <= (-1.3d-18)) then
        tmp = a / -b
    else if (z <= 2.4d-7) then
        tmp = x + (z * 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 <= -2.5e+156) {
		tmp = t / b;
	} else if (z <= -1.3e-18) {
		tmp = a / -b;
	} else if (z <= 2.4e-7) {
		tmp = x + (z * x);
	} else {
		tmp = t / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -2.5e+156:
		tmp = t / b
	elif z <= -1.3e-18:
		tmp = a / -b
	elif z <= 2.4e-7:
		tmp = x + (z * x)
	else:
		tmp = t / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -2.5e+156)
		tmp = Float64(t / b);
	elseif (z <= -1.3e-18)
		tmp = Float64(a / Float64(-b));
	elseif (z <= 2.4e-7)
		tmp = Float64(x + Float64(z * 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 <= -2.5e+156)
		tmp = t / b;
	elseif (z <= -1.3e-18)
		tmp = a / -b;
	elseif (z <= 2.4e-7)
		tmp = x + (z * x);
	else
		tmp = t / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -2.5e+156], N[(t / b), $MachinePrecision], If[LessEqual[z, -1.3e-18], N[(a / (-b)), $MachinePrecision], If[LessEqual[z, 2.4e-7], N[(x + N[(z * x), $MachinePrecision]), $MachinePrecision], N[(t / b), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.49999999999999996e156 or 2.39999999999999979e-7 < z

   1. Initial program 48.0%

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

   3. Taylor expanded in x around 0 48.0%

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

   4. Taylor expanded in b around inf 51.1%

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

      1. +-commutative 51.1%

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

      2. *-commutative 51.1%

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

   6. Simplified 51.1%

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

   7. Taylor expanded in t around inf 29.4%

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

   if -2.49999999999999996e156 < z < -1.3e-18

   1. Initial program 58.4%

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

   3. Taylor expanded in x around 0 58.5%

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

   4. Taylor expanded in b around inf 64.2%

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

      1. +-commutative 64.2%

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

      2. *-commutative 64.2%

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

   6. Simplified 64.2%

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

   7. Taylor expanded in a around inf 41.9%

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

      1. neg-mul-1 41.9%

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

   9. Simplified 41.9%

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

   if -1.3e-18 < z < 2.39999999999999979e-7

   1. Initial program 91.8%

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

   3. Taylor expanded in y around inf 49.3%

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

      1. mul-1-neg 49.3%

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

      2. unsub-neg 49.3%

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

   5. Simplified 49.3%

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

   6. Taylor expanded in z around 0 49.2%

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

      1. *-commutative 49.2%

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

   8. Simplified 49.2%

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

4. Final simplification 40.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+156}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-18}:\\ \;\;\;\;\frac{a}{-b}\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-7}:\\ \;\;\;\;x + z \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 75.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{-23} \lor \neg \left(z \leq 2.25 \cdot 10^{-7}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -2.2e-23) (not (<= z 2.25e-7)))
   (/ (- 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 <= -2.2e-23) || !(z <= 2.25e-7)) {
		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 <= (-2.2d-23)) .or. (.not. (z <= 2.25d-7))) 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 <= -2.2e-23) || !(z <= 2.25e-7)) {
		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 <= -2.2e-23) or not (z <= 2.25e-7):
		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 <= -2.2e-23) || !(z <= 2.25e-7))
		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 <= -2.2e-23) || ~((z <= 2.25e-7)))
		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, -2.2e-23], N[Not[LessEqual[z, 2.25e-7]], $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 < -2.1999999999999999e-23 or 2.2499999999999999e-7 < z

   1. Initial program 52.0%

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

   3. Taylor expanded in z around inf 79.9%

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

   if -2.1999999999999999e-23 < z < 2.2499999999999999e-7

   1. Initial program 91.6%

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

   3. Taylor expanded in b around 0 68.9%

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

      1. mul-1-neg 68.9%

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

      2. *-commutative 68.9%

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

   5. Simplified 68.9%

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

   6. Taylor expanded in z around 0 68.2%

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

      1. mul-1-neg 68.2%

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

      2. +-commutative 68.2%

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

      3. unsub-neg 68.2%

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

   8. Simplified 68.2%

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

   9. Taylor expanded in y around 0 76.5%

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

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{-23} \lor \neg \left(z \leq 2.25 \cdot 10^{-7}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 36.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.3 \cdot 10^{+156}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq -6.9 \cdot 10^{-18}:\\ \;\;\;\;\frac{a}{-b}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-7}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -6.3e+156)
   (/ t b)
   (if (<= z -6.9e-18) (/ a (- b)) (if (<= z 1.5e-7) x (/ t b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -6.3e+156) {
		tmp = t / b;
	} else if (z <= -6.9e-18) {
		tmp = a / -b;
	} else if (z <= 1.5e-7) {
		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 <= (-6.3d+156)) then
        tmp = t / b
    else if (z <= (-6.9d-18)) then
        tmp = a / -b
    else if (z <= 1.5d-7) 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 <= -6.3e+156) {
		tmp = t / b;
	} else if (z <= -6.9e-18) {
		tmp = a / -b;
	} else if (z <= 1.5e-7) {
		tmp = x;
	} else {
		tmp = t / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -6.3e+156:
		tmp = t / b
	elif z <= -6.9e-18:
		tmp = a / -b
	elif z <= 1.5e-7:
		tmp = x
	else:
		tmp = t / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -6.3e+156)
		tmp = Float64(t / b);
	elseif (z <= -6.9e-18)
		tmp = Float64(a / Float64(-b));
	elseif (z <= 1.5e-7)
		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 <= -6.3e+156)
		tmp = t / b;
	elseif (z <= -6.9e-18)
		tmp = a / -b;
	elseif (z <= 1.5e-7)
		tmp = x;
	else
		tmp = t / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -6.3e+156], N[(t / b), $MachinePrecision], If[LessEqual[z, -6.9e-18], N[(a / (-b)), $MachinePrecision], If[LessEqual[z, 1.5e-7], x, N[(t / b), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.29999999999999982e156 or 1.4999999999999999e-7 < z

   1. Initial program 48.0%

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

   3. Taylor expanded in x around 0 48.0%

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

   4. Taylor expanded in b around inf 51.1%

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

      1. +-commutative 51.1%

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

      2. *-commutative 51.1%

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

   6. Simplified 51.1%

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

   7. Taylor expanded in t around inf 29.4%

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

   if -6.29999999999999982e156 < z < -6.9000000000000003e-18

   1. Initial program 58.4%

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

   3. Taylor expanded in x around 0 58.5%

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

   4. Taylor expanded in b around inf 64.2%

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

      1. +-commutative 64.2%

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

      2. *-commutative 64.2%

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

   6. Simplified 64.2%

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

   7. Taylor expanded in a around inf 41.9%

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

      1. neg-mul-1 41.9%

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

   9. Simplified 41.9%

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

   if -6.9000000000000003e-18 < z < 1.4999999999999999e-7

   1. Initial program 91.8%

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

   3. Taylor expanded in z around 0 48.9%

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

4. Final simplification 39.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.3 \cdot 10^{+156}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq -6.9 \cdot 10^{-18}:\\ \;\;\;\;\frac{a}{-b}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-7}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 69.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{-28} \lor \neg \left(z \leq 1.5 \cdot 10^{-7}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z \cdot a}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -2.7e-28) (not (<= z 1.5e-7)))
   (/ (- t a) (- b y))
   (- x (/ (* z a) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.7e-28) || !(z <= 1.5e-7)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x - ((z * a) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-2.7d-28)) .or. (.not. (z <= 1.5d-7))) then
        tmp = (t - a) / (b - y)
    else
        tmp = x - ((z * a) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.7e-28) || !(z <= 1.5e-7)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x - ((z * a) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -2.7e-28) or not (z <= 1.5e-7):
		tmp = (t - a) / (b - y)
	else:
		tmp = x - ((z * a) / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -2.7e-28) || !(z <= 1.5e-7))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(x - Float64(Float64(z * a) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -2.7e-28) || ~((z <= 1.5e-7)))
		tmp = (t - a) / (b - y);
	else
		tmp = x - ((z * a) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -2.7e-28], N[Not[LessEqual[z, 1.5e-7]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(z * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.6999999999999999e-28 or 1.4999999999999999e-7 < z

   1. Initial program 52.0%

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

   3. Taylor expanded in z around inf 79.9%

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

   if -2.6999999999999999e-28 < z < 1.4999999999999999e-7

   1. Initial program 91.6%

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

   3. Taylor expanded in b around 0 68.9%

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

      1. mul-1-neg 68.9%

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

      2. *-commutative 68.9%

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

   5. Simplified 68.9%

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

   6. Taylor expanded in z around 0 68.2%

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

      1. mul-1-neg 68.2%

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

      2. +-commutative 68.2%

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

      3. unsub-neg 68.2%

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

   8. Simplified 68.2%

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

   9. Taylor expanded in a around inf 67.5%

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

       1. associate-*r/ 67.5%

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

       2. mul-1-neg 67.5%

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

       3. *-commutative 67.5%

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

   11. Simplified 67.5%

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

4. Final simplification 74.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{-28} \lor \neg \left(z \leq 1.5 \cdot 10^{-7}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z \cdot a}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 69.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{-23} \lor \neg \left(z \leq 1.55 \cdot 10^{-7}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -2.2e-23) (not (<= z 1.55e-7)))
   (/ (- t a) (- b y))
   (- x (* a (/ z y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.2e-23) || !(z <= 1.55e-7)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x - (a * (z / 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 <= (-2.2d-23)) .or. (.not. (z <= 1.55d-7))) then
        tmp = (t - a) / (b - y)
    else
        tmp = x - (a * (z / 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 <= -2.2e-23) || !(z <= 1.55e-7)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x - (a * (z / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -2.2e-23) or not (z <= 1.55e-7):
		tmp = (t - a) / (b - y)
	else:
		tmp = x - (a * (z / y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -2.2e-23) || !(z <= 1.55e-7))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(x - Float64(a * Float64(z / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -2.2e-23) || ~((z <= 1.55e-7)))
		tmp = (t - a) / (b - y);
	else
		tmp = x - (a * (z / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -2.2e-23], N[Not[LessEqual[z, 1.55e-7]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x - N[(a * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.1999999999999999e-23 or 1.55e-7 < z

   1. Initial program 52.0%

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

   3. Taylor expanded in z around inf 79.9%

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

   if -2.1999999999999999e-23 < z < 1.55e-7

   1. Initial program 91.6%

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

   3. Taylor expanded in b around 0 68.9%

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

      1. mul-1-neg 68.9%

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

      2. *-commutative 68.9%

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

   5. Simplified 68.9%

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

   6. Taylor expanded in z around 0 68.2%

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

      1. mul-1-neg 68.2%

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

      2. +-commutative 68.2%

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

      3. unsub-neg 68.2%

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

   8. Simplified 68.2%

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

   9. Taylor expanded in a around inf 67.5%

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

       1. mul-1-neg 67.5%

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

       2. associate-/l* 62.4%

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

       3. distribute-rgt-neg-in 62.4%

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

       4. mul-1-neg 62.4%

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

       5. associate-*r/ 62.4%

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

       6. mul-1-neg 62.4%

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

   11. Simplified 62.4%

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

4. Final simplification 72.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{-23} \lor \neg \left(z \leq 1.55 \cdot 10^{-7}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 69.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{-35} \lor \neg \left(z \leq 1.6 \cdot 10^{-7}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot t}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -9e-35) (not (<= z 1.6e-7)))
   (/ (- 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 <= -9e-35) || !(z <= 1.6e-7)) {
		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 <= (-9d-35)) .or. (.not. (z <= 1.6d-7))) 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 <= -9e-35) || !(z <= 1.6e-7)) {
		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 <= -9e-35) or not (z <= 1.6e-7):
		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 <= -9e-35) || !(z <= 1.6e-7))
		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 <= -9e-35) || ~((z <= 1.6e-7)))
		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, -9e-35], N[Not[LessEqual[z, 1.6e-7]], $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 < -9.0000000000000002e-35 or 1.6e-7 < z

   1. Initial program 52.4%

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

   3. Taylor expanded in z around inf 79.5%

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

   if -9.0000000000000002e-35 < z < 1.6e-7

   1. Initial program 91.5%

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

   3. Taylor expanded in b around 0 68.6%

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

      1. mul-1-neg 68.6%

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

      2. *-commutative 68.6%

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

   5. Simplified 68.6%

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

   6. Taylor expanded in z around 0 67.9%

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

      1. mul-1-neg 67.9%

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

      2. +-commutative 67.9%

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

      3. unsub-neg 67.9%

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

   8. Simplified 67.9%

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

   9. Taylor expanded in t around inf 59.1%

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

4. Final simplification 71.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{-35} \lor \neg \left(z \leq 1.6 \cdot 10^{-7}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot t}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 54.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{-13} \lor \neg \left(y \leq 7.5 \cdot 10^{+44}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.55e-13) (not (<= y 7.5e+44))) (/ 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 <= -1.55e-13) || !(y <= 7.5e+44)) {
		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 <= (-1.55d-13)) .or. (.not. (y <= 7.5d+44))) 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 <= -1.55e-13) || !(y <= 7.5e+44)) {
		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 <= -1.55e-13) or not (y <= 7.5e+44):
		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 <= -1.55e-13) || !(y <= 7.5e+44))
		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 <= -1.55e-13) || ~((y <= 7.5e+44)))
		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, -1.55e-13], N[Not[LessEqual[y, 7.5e+44]], $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 < -1.55e-13 or 7.50000000000000027e44 < y

   1. Initial program 53.4%

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

   3. Taylor expanded in y around inf 48.0%

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

      1. mul-1-neg 48.0%

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

      2. unsub-neg 48.0%

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

   5. Simplified 48.0%

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

   if -1.55e-13 < y < 7.50000000000000027e44

   1. Initial program 80.4%

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

   3. Taylor expanded in y around 0 55.7%

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

4. Final simplification 52.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{-13} \lor \neg \left(y \leq 7.5 \cdot 10^{+44}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 41.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{-19} \lor \neg \left(y \leq 1.65 \cdot 10^{+21}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.85e-19) (not (<= y 1.65e+21))) (/ x (- 1.0 z)) (/ t b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.85e-19) || !(y <= 1.65e+21)) {
		tmp = x / (1.0 - z);
	} 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 ((y <= (-1.85d-19)) .or. (.not. (y <= 1.65d+21))) then
        tmp = x / (1.0d0 - z)
    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 ((y <= -1.85e-19) || !(y <= 1.65e+21)) {
		tmp = x / (1.0 - z);
	} else {
		tmp = t / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.85e-19) or not (y <= 1.65e+21):
		tmp = x / (1.0 - z)
	else:
		tmp = t / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.85e-19) || !(y <= 1.65e+21))
		tmp = Float64(x / Float64(1.0 - z));
	else
		tmp = Float64(t / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.85e-19) || ~((y <= 1.65e+21)))
		tmp = x / (1.0 - z);
	else
		tmp = t / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.85e-19], N[Not[LessEqual[y, 1.65e+21]], $MachinePrecision]], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(t / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.85000000000000003e-19 or 1.65e21 < y

   1. Initial program 56.0%

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

   3. Taylor expanded in y around inf 45.9%

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

      1. mul-1-neg 45.9%

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

      2. unsub-neg 45.9%

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

   5. Simplified 45.9%

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

   if -1.85000000000000003e-19 < y < 1.65e21

   1. Initial program 80.1%

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

   3. Taylor expanded in x around 0 80.1%

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

   4. Taylor expanded in b around inf 65.6%

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

      1. +-commutative 65.6%

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

      2. *-commutative 65.6%

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

   6. Simplified 65.6%

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

   7. Taylor expanded in t around inf 32.5%

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

4. Final simplification 39.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{-19} \lor \neg \left(y \leq 1.65 \cdot 10^{+21}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 36.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{-32} \lor \neg \left(z \leq 1.5 \cdot 10^{-7}\right):\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -2.6e-32) (not (<= z 1.5e-7))) (/ t b) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.6e-32) || !(z <= 1.5e-7)) {
		tmp = t / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-2.6d-32)) .or. (.not. (z <= 1.5d-7))) then
        tmp = t / b
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.6e-32) || !(z <= 1.5e-7)) {
		tmp = t / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -2.6e-32) or not (z <= 1.5e-7):
		tmp = t / b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -2.6e-32) || !(z <= 1.5e-7))
		tmp = Float64(t / b);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -2.6e-32) || ~((z <= 1.5e-7)))
		tmp = t / b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -2.6e-32], N[Not[LessEqual[z, 1.5e-7]], $MachinePrecision]], N[(t / b), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -2.5999999999999997e-32 or 1.4999999999999999e-7 < z

   1. Initial program 52.4%

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

   3. Taylor expanded in x around 0 52.4%

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

   4. Taylor expanded in b around inf 55.5%

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

      1. +-commutative 55.5%

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

      2. *-commutative 55.5%

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

   6. Simplified 55.5%

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

   7. Taylor expanded in t around inf 28.3%

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

   if -2.5999999999999997e-32 < z < 1.4999999999999999e-7

   1. Initial program 91.5%

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

   3. Taylor expanded in z around 0 50.5%

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

4. Final simplification 37.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{-32} \lor \neg \left(z \leq 1.5 \cdot 10^{-7}\right):\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 25.0% 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 68.4%

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

3. Taylor expanded in z around 0 23.2%

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

Developer Target 1: 73.6% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024145 
(FPCore (x y z t a b)
  :name "Development.Shake.Progress:decay from shake-0.15.5"
  :precision binary64

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

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