Development.Shake.Progress:decay from shake-0.15.5

Percentage Accurate: 66.3% → 86.5%

Time: 17.4s

Alternatives: 24

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 66.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 86.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z \cdot \left(a - t\right) - x \cdot y}{z \cdot \left(y - b\right) - y}\\ t_2 := y + z \cdot \left(b - y\right)\\ t_3 := y - z \cdot y\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;x \cdot \left(\frac{z}{x} \cdot \frac{t - a}{t\_3} + \frac{y}{t\_3}\right)\\ \mathbf{elif}\;t\_1 \leq -2 \cdot 10^{-246} \lor \neg \left(t\_1 \leq 0\right) \land t\_1 \leq 4 \cdot 10^{+295}:\\ \;\;\;\;\frac{x \cdot y}{t\_2} + \frac{z \cdot \left(t - a\right)}{t\_2}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (* z (- a t)) (* x y)) (- (* z (- y b)) y)))
        (t_2 (+ y (* z (- b y))))
        (t_3 (- y (* z y))))
   (if (<= t_1 (- INFINITY))
     (* x (+ (* (/ z x) (/ (- t a) t_3)) (/ y t_3)))
     (if (or (<= t_1 -2e-246) (and (not (<= t_1 0.0)) (<= t_1 4e+295)))
       (+ (/ (* x y) t_2) (/ (* z (- t a)) 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 * (a - t)) - (x * y)) / ((z * (y - b)) - y);
	double t_2 = y + (z * (b - y));
	double t_3 = y - (z * y);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = x * (((z / x) * ((t - a) / t_3)) + (y / t_3));
	} else if ((t_1 <= -2e-246) || (!(t_1 <= 0.0) && (t_1 <= 4e+295))) {
		tmp = ((x * y) / t_2) + ((z * (t - a)) / 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 * (a - t)) - (x * y)) / ((z * (y - b)) - y);
	double t_2 = y + (z * (b - y));
	double t_3 = y - (z * y);
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = x * (((z / x) * ((t - a) / t_3)) + (y / t_3));
	} else if ((t_1 <= -2e-246) || (!(t_1 <= 0.0) && (t_1 <= 4e+295))) {
		tmp = ((x * y) / t_2) + ((z * (t - a)) / t_2);
	} else {
		tmp = (t - a) / (b - y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((z * (a - t)) - (x * y)) / ((z * (y - b)) - y)
	t_2 = y + (z * (b - y))
	t_3 = y - (z * y)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = x * (((z / x) * ((t - a) / t_3)) + (y / t_3))
	elif (t_1 <= -2e-246) or (not (t_1 <= 0.0) and (t_1 <= 4e+295)):
		tmp = ((x * y) / t_2) + ((z * (t - a)) / t_2)
	else:
		tmp = (t - a) / (b - y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(z * Float64(a - t)) - Float64(x * y)) / Float64(Float64(z * Float64(y - b)) - y))
	t_2 = Float64(y + Float64(z * Float64(b - y)))
	t_3 = Float64(y - Float64(z * y))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(x * Float64(Float64(Float64(z / x) * Float64(Float64(t - a) / t_3)) + Float64(y / t_3)));
	elseif ((t_1 <= -2e-246) || (!(t_1 <= 0.0) && (t_1 <= 4e+295)))
		tmp = Float64(Float64(Float64(x * y) / t_2) + Float64(Float64(z * Float64(t - a)) / 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 * (a - t)) - (x * y)) / ((z * (y - b)) - y);
	t_2 = y + (z * (b - y));
	t_3 = y - (z * y);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = x * (((z / x) * ((t - a) / t_3)) + (y / t_3));
	elseif ((t_1 <= -2e-246) || (~((t_1 <= 0.0)) && (t_1 <= 4e+295)))
		tmp = ((x * y) / t_2) + ((z * (t - a)) / 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[(N[(N[(z * N[(a - t), $MachinePrecision]), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision] / N[(N[(z * N[(y - b), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y - N[(z * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(x * N[(N[(N[(z / x), $MachinePrecision] * N[(N[(t - a), $MachinePrecision] / t$95$3), $MachinePrecision]), $MachinePrecision] + N[(y / t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t$95$1, -2e-246], And[N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision], LessEqual[t$95$1, 4e+295]]], N[(N[(N[(x * y), $MachinePrecision] / t$95$2), $MachinePrecision] + N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision], 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 51.1%

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

   3. Taylor expanded in x around inf 86.6%

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

   4. Taylor expanded in b around 0 72.4%

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

      1. +-commutative 72.4%

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

      2. times-frac 80.9%

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

      3. associate-*r* 80.9%

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

      4. neg-mul-1 80.9%

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

      5. associate-*r* 80.9%

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

      6. neg-mul-1 80.9%

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

   6. Simplified 80.9%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -1.99999999999999991e-246 or 0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 3.9999999999999999e295

   1. Initial program 99.2%

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

   3. Taylor expanded in x around 0 99.2%

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

   if -1.99999999999999991e-246 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 0.0 or 3.9999999999999999e295 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 18.7%

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

   3. Taylor expanded in z around inf 77.5%

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

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z \cdot \left(a - t\right) - x \cdot y}{z \cdot \left(y - b\right) - y} \leq -\infty:\\ \;\;\;\;x \cdot \left(\frac{z}{x} \cdot \frac{t - a}{y - z \cdot y} + \frac{y}{y - z \cdot y}\right)\\ \mathbf{elif}\;\frac{z \cdot \left(a - t\right) - x \cdot y}{z \cdot \left(y - b\right) - y} \leq -2 \cdot 10^{-246} \lor \neg \left(\frac{z \cdot \left(a - t\right) - x \cdot y}{z \cdot \left(y - b\right) - y} \leq 0\right) \land \frac{z \cdot \left(a - t\right) - x \cdot y}{z \cdot \left(y - b\right) - y} \leq 4 \cdot 10^{+295}:\\ \;\;\;\;\frac{x \cdot y}{y + z \cdot \left(b - y\right)} + \frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 86.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(b - y\right)\\ \mathbf{if}\;z \leq -2.4 \cdot 10^{+51} \lor \neg \left(z \leq 57000000000\right):\\ \;\;\;\;\left(x \cdot \frac{y}{t\_1} + \frac{t - a}{b - y}\right) + y \cdot \frac{a - t}{z \cdot {\left(b - y\right)}^{2}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{y + t\_1} + \frac{z \cdot \left(a - t\right)}{x \cdot \left(z \cdot \left(y - b\right) - y\right)}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- b y))))
   (if (or (<= z -2.4e+51) (not (<= z 57000000000.0)))
     (+
      (+ (* x (/ y t_1)) (/ (- t a) (- b y)))
      (* y (/ (- a t) (* z (pow (- b y) 2.0)))))
     (* x (+ (/ y (+ y t_1)) (/ (* z (- a t)) (* x (- (* z (- y b)) y))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (b - y);
	double tmp;
	if ((z <= -2.4e+51) || !(z <= 57000000000.0)) {
		tmp = ((x * (y / t_1)) + ((t - a) / (b - y))) + (y * ((a - t) / (z * pow((b - y), 2.0))));
	} else {
		tmp = x * ((y / (y + t_1)) + ((z * (a - t)) / (x * ((z * (y - 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) :: t_1
    real(8) :: tmp
    t_1 = z * (b - y)
    if ((z <= (-2.4d+51)) .or. (.not. (z <= 57000000000.0d0))) then
        tmp = ((x * (y / t_1)) + ((t - a) / (b - y))) + (y * ((a - t) / (z * ((b - y) ** 2.0d0))))
    else
        tmp = x * ((y / (y + t_1)) + ((z * (a - t)) / (x * ((z * (y - 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 t_1 = z * (b - y);
	double tmp;
	if ((z <= -2.4e+51) || !(z <= 57000000000.0)) {
		tmp = ((x * (y / t_1)) + ((t - a) / (b - y))) + (y * ((a - t) / (z * Math.pow((b - y), 2.0))));
	} else {
		tmp = x * ((y / (y + t_1)) + ((z * (a - t)) / (x * ((z * (y - b)) - y))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (b - y)
	tmp = 0
	if (z <= -2.4e+51) or not (z <= 57000000000.0):
		tmp = ((x * (y / t_1)) + ((t - a) / (b - y))) + (y * ((a - t) / (z * math.pow((b - y), 2.0))))
	else:
		tmp = x * ((y / (y + t_1)) + ((z * (a - t)) / (x * ((z * (y - b)) - y))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(b - y))
	tmp = 0.0
	if ((z <= -2.4e+51) || !(z <= 57000000000.0))
		tmp = Float64(Float64(Float64(x * Float64(y / t_1)) + Float64(Float64(t - a) / Float64(b - y))) + Float64(y * Float64(Float64(a - t) / Float64(z * (Float64(b - y) ^ 2.0)))));
	else
		tmp = Float64(x * Float64(Float64(y / Float64(y + t_1)) + Float64(Float64(z * Float64(a - t)) / Float64(x * Float64(Float64(z * Float64(y - b)) - y)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (b - y);
	tmp = 0.0;
	if ((z <= -2.4e+51) || ~((z <= 57000000000.0)))
		tmp = ((x * (y / t_1)) + ((t - a) / (b - y))) + (y * ((a - t) / (z * ((b - y) ^ 2.0))));
	else
		tmp = x * ((y / (y + t_1)) + ((z * (a - t)) / (x * ((z * (y - b)) - y))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[z, -2.4e+51], N[Not[LessEqual[z, 57000000000.0]], $MachinePrecision]], N[(N[(N[(x * N[(y / t$95$1), $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[(x * N[(N[(y / N[(y + t$95$1), $MachinePrecision]), $MachinePrecision] + N[(N[(z * N[(a - t), $MachinePrecision]), $MachinePrecision] / N[(x * N[(N[(z * N[(y - b), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.3999999999999999e51 or 5.7e10 < z

   1. Initial program 49.0%

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

   3. Taylor expanded in z around inf 66.5%

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

      1. associate--r+ 66.5%

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

      2. +-commutative 66.5%

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

      3. associate--l+ 66.5%

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

      4. associate-/l* 68.1%

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

      5. div-sub 69.0%

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

      6. associate-/l* 90.7%

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

   5. Simplified 90.7%

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

   if -2.3999999999999999e51 < z < 5.7e10

   1. Initial program 89.3%

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

   3. Taylor expanded in x around inf 91.1%

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

4. Final simplification 90.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+51} \lor \neg \left(z \leq 57000000000\right):\\ \;\;\;\;\left(x \cdot \frac{y}{z \cdot \left(b - y\right)} + \frac{t - a}{b - y}\right) + y \cdot \frac{a - t}{z \cdot {\left(b - y\right)}^{2}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{y + z \cdot \left(b - y\right)} + \frac{z \cdot \left(a - t\right)}{x \cdot \left(z \cdot \left(y - b\right) - y\right)}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 86.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z \cdot \left(a - t\right) - x \cdot y}{z \cdot \left(y - b\right) - y}\\ t_2 := y - z \cdot y\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;x \cdot \left(\frac{z}{x} \cdot \frac{t - a}{t\_2} + \frac{y}{t\_2}\right)\\ \mathbf{elif}\;t\_1 \leq -2 \cdot 10^{-246} \lor \neg \left(t\_1 \leq 0\right) \land t\_1 \leq 4 \cdot 10^{+295}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (* z (- a t)) (* x y)) (- (* z (- y b)) y)))
        (t_2 (- y (* z y))))
   (if (<= t_1 (- INFINITY))
     (* x (+ (* (/ z x) (/ (- t a) t_2)) (/ y t_2)))
     (if (or (<= t_1 -2e-246) (and (not (<= t_1 0.0)) (<= t_1 4e+295)))
       t_1
       (/ (- t a) (- b y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((z * (a - t)) - (x * y)) / ((z * (y - b)) - y);
	double t_2 = y - (z * y);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = x * (((z / x) * ((t - a) / t_2)) + (y / t_2));
	} else if ((t_1 <= -2e-246) || (!(t_1 <= 0.0) && (t_1 <= 4e+295))) {
		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 = ((z * (a - t)) - (x * y)) / ((z * (y - b)) - y);
	double t_2 = y - (z * y);
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = x * (((z / x) * ((t - a) / t_2)) + (y / t_2));
	} else if ((t_1 <= -2e-246) || (!(t_1 <= 0.0) && (t_1 <= 4e+295))) {
		tmp = t_1;
	} else {
		tmp = (t - a) / (b - y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((z * (a - t)) - (x * y)) / ((z * (y - b)) - y)
	t_2 = y - (z * y)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = x * (((z / x) * ((t - a) / t_2)) + (y / t_2))
	elif (t_1 <= -2e-246) or (not (t_1 <= 0.0) and (t_1 <= 4e+295)):
		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(z * Float64(a - t)) - Float64(x * y)) / Float64(Float64(z * Float64(y - b)) - y))
	t_2 = Float64(y - Float64(z * y))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(x * Float64(Float64(Float64(z / x) * Float64(Float64(t - a) / t_2)) + Float64(y / t_2)));
	elseif ((t_1 <= -2e-246) || (!(t_1 <= 0.0) && (t_1 <= 4e+295)))
		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 = ((z * (a - t)) - (x * y)) / ((z * (y - b)) - y);
	t_2 = y - (z * y);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = x * (((z / x) * ((t - a) / t_2)) + (y / t_2));
	elseif ((t_1 <= -2e-246) || (~((t_1 <= 0.0)) && (t_1 <= 4e+295)))
		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[(z * N[(a - t), $MachinePrecision]), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision] / N[(N[(z * N[(y - b), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y - N[(z * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(x * N[(N[(N[(z / x), $MachinePrecision] * N[(N[(t - a), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision] + N[(y / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t$95$1, -2e-246], And[N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision], LessEqual[t$95$1, 4e+295]]], 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 51.1%

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

   3. Taylor expanded in x around inf 86.6%

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

   4. Taylor expanded in b around 0 72.4%

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

      1. +-commutative 72.4%

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

      2. times-frac 80.9%

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

      3. associate-*r* 80.9%

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

      4. neg-mul-1 80.9%

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

      5. associate-*r* 80.9%

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

      6. neg-mul-1 80.9%

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

   6. Simplified 80.9%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -1.99999999999999991e-246 or 0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 3.9999999999999999e295

   1. Initial program 99.2%

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

   if -1.99999999999999991e-246 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 0.0 or 3.9999999999999999e295 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 18.7%

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

   3. Taylor expanded in z around inf 77.5%

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

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z \cdot \left(a - t\right) - x \cdot y}{z \cdot \left(y - b\right) - y} \leq -\infty:\\ \;\;\;\;x \cdot \left(\frac{z}{x} \cdot \frac{t - a}{y - z \cdot y} + \frac{y}{y - z \cdot y}\right)\\ \mathbf{elif}\;\frac{z \cdot \left(a - t\right) - x \cdot y}{z \cdot \left(y - b\right) - y} \leq -2 \cdot 10^{-246} \lor \neg \left(\frac{z \cdot \left(a - t\right) - x \cdot y}{z \cdot \left(y - b\right) - y} \leq 0\right) \land \frac{z \cdot \left(a - t\right) - x \cdot y}{z \cdot \left(y - b\right) - y} \leq 4 \cdot 10^{+295}:\\ \;\;\;\;\frac{z \cdot \left(a - t\right) - x \cdot y}{z \cdot \left(y - b\right) - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+57} \lor \neg \left(z \leq 7.2 \cdot 10^{+72}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{y + z \cdot \left(b - y\right)} + \frac{z \cdot \left(a - t\right)}{x \cdot \left(z \cdot \left(y - b\right) - y\right)}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -9e+57) (not (<= z 7.2e+72)))
   (/ (- t a) (- b y))
   (*
    x
    (+
     (/ y (+ y (* z (- b y))))
     (/ (* z (- a t)) (* x (- (* z (- y b)) y)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -9e+57) || !(z <= 7.2e+72)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x * ((y / (y + (z * (b - y)))) + ((z * (a - t)) / (x * ((z * (y - 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 <= (-9d+57)) .or. (.not. (z <= 7.2d+72))) then
        tmp = (t - a) / (b - y)
    else
        tmp = x * ((y / (y + (z * (b - y)))) + ((z * (a - t)) / (x * ((z * (y - 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 <= -9e+57) || !(z <= 7.2e+72)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x * ((y / (y + (z * (b - y)))) + ((z * (a - t)) / (x * ((z * (y - b)) - y))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -9e+57) or not (z <= 7.2e+72):
		tmp = (t - a) / (b - y)
	else:
		tmp = x * ((y / (y + (z * (b - y)))) + ((z * (a - t)) / (x * ((z * (y - b)) - y))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -9e+57) || !(z <= 7.2e+72))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(x * Float64(Float64(y / Float64(y + Float64(z * Float64(b - y)))) + Float64(Float64(z * Float64(a - t)) / Float64(x * Float64(Float64(z * Float64(y - b)) - y)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -9e+57) || ~((z <= 7.2e+72)))
		tmp = (t - a) / (b - y);
	else
		tmp = x * ((y / (y + (z * (b - y)))) + ((z * (a - t)) / (x * ((z * (y - b)) - y))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -9e+57], N[Not[LessEqual[z, 7.2e+72]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(z * N[(a - t), $MachinePrecision]), $MachinePrecision] / N[(x * N[(N[(z * N[(y - b), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.99999999999999991e57 or 7.20000000000000069e72 < z

   1. Initial program 41.9%

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

   3. Taylor expanded in z around inf 85.0%

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

   if -8.99999999999999991e57 < z < 7.20000000000000069e72

   1. Initial program 88.3%

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

   3. Taylor expanded in x around inf 91.0%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+57} \lor \neg \left(z \leq 7.2 \cdot 10^{+72}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{y + z \cdot \left(b - y\right)} + \frac{z \cdot \left(a - t\right)}{x \cdot \left(z \cdot \left(y - b\right) - y\right)}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 69.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -1.15:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-285}:\\ \;\;\;\;\frac{t \cdot \left(z + x \cdot \frac{y}{t}\right)}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-70}:\\ \;\;\;\;x + z \cdot \left(\frac{t - a}{y} - b \cdot \frac{x}{y}\right)\\ \mathbf{elif}\;z \leq 7800000000:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -1.15)
     t_1
     (if (<= z -3.8e-285)
       (/ (* t (+ z (* x (/ y t)))) (+ y (* z b)))
       (if (<= z 3e-70)
         (+ x (* z (- (/ (- t a) y) (* b (/ x y)))))
         (if (<= z 7800000000.0)
           (/ (* z (- t a)) (+ y (* z (- b y))))
           t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -1.15) {
		tmp = t_1;
	} else if (z <= -3.8e-285) {
		tmp = (t * (z + (x * (y / t)))) / (y + (z * b));
	} else if (z <= 3e-70) {
		tmp = x + (z * (((t - a) / y) - (b * (x / y))));
	} else if (z <= 7800000000.0) {
		tmp = (z * (t - a)) / (y + (z * (b - y)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    if (z <= (-1.15d0)) then
        tmp = t_1
    else if (z <= (-3.8d-285)) then
        tmp = (t * (z + (x * (y / t)))) / (y + (z * b))
    else if (z <= 3d-70) then
        tmp = x + (z * (((t - a) / y) - (b * (x / y))))
    else if (z <= 7800000000.0d0) then
        tmp = (z * (t - a)) / (y + (z * (b - y)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -1.15) {
		tmp = t_1;
	} else if (z <= -3.8e-285) {
		tmp = (t * (z + (x * (y / t)))) / (y + (z * b));
	} else if (z <= 3e-70) {
		tmp = x + (z * (((t - a) / y) - (b * (x / y))));
	} else if (z <= 7800000000.0) {
		tmp = (z * (t - a)) / (y + (z * (b - y)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	tmp = 0
	if z <= -1.15:
		tmp = t_1
	elif z <= -3.8e-285:
		tmp = (t * (z + (x * (y / t)))) / (y + (z * b))
	elif z <= 3e-70:
		tmp = x + (z * (((t - a) / y) - (b * (x / y))))
	elif z <= 7800000000.0:
		tmp = (z * (t - a)) / (y + (z * (b - y)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -1.15)
		tmp = t_1;
	elseif (z <= -3.8e-285)
		tmp = Float64(Float64(t * Float64(z + Float64(x * Float64(y / t)))) / Float64(y + Float64(z * b)));
	elseif (z <= 3e-70)
		tmp = Float64(x + Float64(z * Float64(Float64(Float64(t - a) / y) - Float64(b * Float64(x / y)))));
	elseif (z <= 7800000000.0)
		tmp = Float64(Float64(z * Float64(t - a)) / Float64(y + Float64(z * Float64(b - y))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -1.15)
		tmp = t_1;
	elseif (z <= -3.8e-285)
		tmp = (t * (z + (x * (y / t)))) / (y + (z * b));
	elseif (z <= 3e-70)
		tmp = x + (z * (((t - a) / y) - (b * (x / y))));
	elseif (z <= 7800000000.0)
		tmp = (z * (t - a)) / (y + (z * (b - y)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.15], t$95$1, If[LessEqual[z, -3.8e-285], N[(N[(t * N[(z + N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3e-70], N[(x + N[(z * N[(N[(N[(t - a), $MachinePrecision] / y), $MachinePrecision] - N[(b * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7800000000.0], N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.1499999999999999 or 7.8e9 < z

   1. Initial program 52.6%

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

   3. Taylor expanded in z around inf 82.2%

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

   if -1.1499999999999999 < z < -3.8000000000000002e-285

   1. Initial program 92.7%

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

   3. Taylor expanded in t around -inf 80.7%

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

      1. mul-1-neg 80.7%

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

      2. *-commutative 80.7%

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

      3. distribute-rgt-neg-in 80.7%

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

      4. mul-1-neg 80.7%

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

      5. unsub-neg 80.7%

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

      6. mul-1-neg 80.7%

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

      7. +-commutative 80.7%

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

      8. mul-1-neg 80.7%

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

      9. unsub-neg 80.7%

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

      10. *-commutative 80.7%

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

      11. *-commutative 80.7%

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

   5. Simplified 80.7%

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

   6. Taylor expanded in a around 0 61.9%

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

      1. associate-/l* 60.1%

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

   8. Simplified 60.1%

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

   9. Taylor expanded in b around inf 60.1%

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

   if -3.8000000000000002e-285 < z < 3.0000000000000001e-70

   1. Initial program 82.1%

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

   3. Taylor expanded in b around inf 82.1%

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

      1. *-commutative 82.1%

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

   5. Simplified 82.1%

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

   6. Taylor expanded in z around 0 66.2%

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

      1. associate--r+ 66.2%

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

      2. div-sub 68.0%

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

      3. associate-/l* 71.4%

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

   8. Simplified 71.4%

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

   if 3.0000000000000001e-70 < z < 7.8e9

   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

   3. Taylor expanded in x around 0 93.7%

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

Alternative 6: 67.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -0.305:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-299}:\\ \;\;\;\;\frac{x \cdot y}{t\_1}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-70}:\\ \;\;\;\;x + z \cdot \left(\frac{t - a}{y} - b \cdot \frac{x}{y}\right)\\ \mathbf{elif}\;z \leq 6600000000000:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y)))) (t_2 (/ (- t a) (- b y))))
   (if (<= z -0.305)
     t_2
     (if (<= z 1.95e-299)
       (/ (* x y) t_1)
       (if (<= z 1.7e-70)
         (+ x (* z (- (/ (- t a) y) (* b (/ x y)))))
         (if (<= z 6600000000000.0) (/ (* z (- t a)) t_1) t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -0.305) {
		tmp = t_2;
	} else if (z <= 1.95e-299) {
		tmp = (x * y) / t_1;
	} else if (z <= 1.7e-70) {
		tmp = x + (z * (((t - a) / y) - (b * (x / y))));
	} else if (z <= 6600000000000.0) {
		tmp = (z * (t - a)) / t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y + (z * (b - y))
    t_2 = (t - a) / (b - y)
    if (z <= (-0.305d0)) then
        tmp = t_2
    else if (z <= 1.95d-299) then
        tmp = (x * y) / t_1
    else if (z <= 1.7d-70) then
        tmp = x + (z * (((t - a) / y) - (b * (x / y))))
    else if (z <= 6600000000000.0d0) then
        tmp = (z * (t - a)) / t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -0.305) {
		tmp = t_2;
	} else if (z <= 1.95e-299) {
		tmp = (x * y) / t_1;
	} else if (z <= 1.7e-70) {
		tmp = x + (z * (((t - a) / y) - (b * (x / y))));
	} else if (z <= 6600000000000.0) {
		tmp = (z * (t - a)) / t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z * (b - y))
	t_2 = (t - a) / (b - y)
	tmp = 0
	if z <= -0.305:
		tmp = t_2
	elif z <= 1.95e-299:
		tmp = (x * y) / t_1
	elif z <= 1.7e-70:
		tmp = x + (z * (((t - a) / y) - (b * (x / y))))
	elif z <= 6600000000000.0:
		tmp = (z * (t - a)) / t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(z * Float64(b - y)))
	t_2 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -0.305)
		tmp = t_2;
	elseif (z <= 1.95e-299)
		tmp = Float64(Float64(x * y) / t_1);
	elseif (z <= 1.7e-70)
		tmp = Float64(x + Float64(z * Float64(Float64(Float64(t - a) / y) - Float64(b * Float64(x / y)))));
	elseif (z <= 6600000000000.0)
		tmp = Float64(Float64(z * Float64(t - a)) / t_1);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (z * (b - y));
	t_2 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -0.305)
		tmp = t_2;
	elseif (z <= 1.95e-299)
		tmp = (x * y) / t_1;
	elseif (z <= 1.7e-70)
		tmp = x + (z * (((t - a) / y) - (b * (x / y))));
	elseif (z <= 6600000000000.0)
		tmp = (z * (t - a)) / t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.305], t$95$2, If[LessEqual[z, 1.95e-299], N[(N[(x * y), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[z, 1.7e-70], N[(x + N[(z * N[(N[(N[(t - a), $MachinePrecision] / y), $MachinePrecision] - N[(b * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6600000000000.0], N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -0.304999999999999993 or 6.6e12 < z

   1. Initial program 52.6%

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

   3. Taylor expanded in z around inf 82.2%

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

   if -0.304999999999999993 < z < 1.9499999999999999e-299

   1. Initial program 92.9%

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

   3. Taylor expanded in x around inf 58.6%

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

      1. *-commutative 58.6%

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

   5. Simplified 58.6%

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

   if 1.9499999999999999e-299 < z < 1.69999999999999998e-70

   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 b around inf 80.1%

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

      1. *-commutative 80.1%

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

   5. Simplified 80.1%

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

   6. Taylor expanded in z around 0 66.7%

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

      1. associate--r+ 66.7%

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

      2. div-sub 68.8%

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

      3. associate-/l* 72.8%

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

   8. Simplified 72.8%

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

   if 1.69999999999999998e-70 < z < 6.6e12

   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

   3. Taylor expanded in x around 0 93.7%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.305:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-299}:\\ \;\;\;\;\frac{x \cdot y}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-70}:\\ \;\;\;\;x + z \cdot \left(\frac{t - a}{y} - b \cdot \frac{x}{y}\right)\\ \mathbf{elif}\;z \leq 6600000000000:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 70.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(t - a\right)\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -1550:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-80}:\\ \;\;\;\;\frac{t\_1 + x \cdot y}{z \cdot b}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-71}:\\ \;\;\;\;x + t \cdot \frac{z}{y}\\ \mathbf{elif}\;z \leq 1900000000000:\\ \;\;\;\;\frac{t\_1}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- t a))) (t_2 (/ (- t a) (- b y))))
   (if (<= z -1550.0)
     t_2
     (if (<= z -3e-80)
       (/ (+ t_1 (* x y)) (* z b))
       (if (<= z 9.5e-71)
         (+ x (* t (/ z y)))
         (if (<= z 1900000000000.0) (/ t_1 (+ y (* z (- b y)))) t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (t - a);
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -1550.0) {
		tmp = t_2;
	} else if (z <= -3e-80) {
		tmp = (t_1 + (x * y)) / (z * b);
	} else if (z <= 9.5e-71) {
		tmp = x + (t * (z / y));
	} else if (z <= 1900000000000.0) {
		tmp = t_1 / (y + (z * (b - y)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z * (t - a)
    t_2 = (t - a) / (b - y)
    if (z <= (-1550.0d0)) then
        tmp = t_2
    else if (z <= (-3d-80)) then
        tmp = (t_1 + (x * y)) / (z * b)
    else if (z <= 9.5d-71) then
        tmp = x + (t * (z / y))
    else if (z <= 1900000000000.0d0) then
        tmp = t_1 / (y + (z * (b - y)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (t - a);
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -1550.0) {
		tmp = t_2;
	} else if (z <= -3e-80) {
		tmp = (t_1 + (x * y)) / (z * b);
	} else if (z <= 9.5e-71) {
		tmp = x + (t * (z / y));
	} else if (z <= 1900000000000.0) {
		tmp = t_1 / (y + (z * (b - y)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (t - a)
	t_2 = (t - a) / (b - y)
	tmp = 0
	if z <= -1550.0:
		tmp = t_2
	elif z <= -3e-80:
		tmp = (t_1 + (x * y)) / (z * b)
	elif z <= 9.5e-71:
		tmp = x + (t * (z / y))
	elif z <= 1900000000000.0:
		tmp = t_1 / (y + (z * (b - y)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(t - a))
	t_2 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -1550.0)
		tmp = t_2;
	elseif (z <= -3e-80)
		tmp = Float64(Float64(t_1 + Float64(x * y)) / Float64(z * b));
	elseif (z <= 9.5e-71)
		tmp = Float64(x + Float64(t * Float64(z / y)));
	elseif (z <= 1900000000000.0)
		tmp = Float64(t_1 / Float64(y + Float64(z * Float64(b - y))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (t - a);
	t_2 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -1550.0)
		tmp = t_2;
	elseif (z <= -3e-80)
		tmp = (t_1 + (x * y)) / (z * b);
	elseif (z <= 9.5e-71)
		tmp = x + (t * (z / y));
	elseif (z <= 1900000000000.0)
		tmp = t_1 / (y + (z * (b - y)));
	else
		tmp = t_2;
	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[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1550.0], t$95$2, If[LessEqual[z, -3e-80], N[(N[(t$95$1 + N[(x * y), $MachinePrecision]), $MachinePrecision] / N[(z * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.5e-71], N[(x + N[(t * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1900000000000.0], N[(t$95$1 / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1550 or 1.9e12 < z

   1. Initial program 52.2%

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

   3. Taylor expanded in z around inf 82.0%

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

   if -1550 < z < -3.00000000000000007e-80

   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

   3. Taylor expanded in b around inf 64.7%

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

   if -3.00000000000000007e-80 < z < 9.4999999999999994e-71

   1. Initial program 85.1%

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

   3. Taylor expanded in t around -inf 78.8%

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

      1. mul-1-neg 78.8%

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

      2. *-commutative 78.8%

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

      3. distribute-rgt-neg-in 78.8%

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

      4. mul-1-neg 78.8%

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

      5. unsub-neg 78.8%

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

      6. mul-1-neg 78.8%

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

      7. +-commutative 78.8%

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

      8. mul-1-neg 78.8%

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

      9. unsub-neg 78.8%

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

      10. *-commutative 78.8%

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

      11. *-commutative 78.8%

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

   5. Simplified 78.8%

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

   6. Taylor expanded in a around 0 64.9%

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

      1. associate-/l* 59.7%

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

   8. Simplified 59.7%

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

   9. Taylor expanded in z around 0 46.8%

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

   10. Taylor expanded in t around inf 64.8%

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

       1. associate-/l* 65.0%

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

   12. Simplified 65.0%

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

   if 9.4999999999999994e-71 < z < 1.9e12

   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

   3. Taylor expanded in x around 0 93.7%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1550:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-80}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + x \cdot y}{z \cdot b}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-71}:\\ \;\;\;\;x + t \cdot \frac{z}{y}\\ \mathbf{elif}\;z \leq 1900000000000:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 70.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -245:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-80}:\\ \;\;\;\;x \cdot \frac{y}{z \cdot b} - \frac{a - t}{b}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-70}:\\ \;\;\;\;x + t \cdot \frac{z}{y}\\ \mathbf{elif}\;z \leq 36000000000000:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -245.0)
     t_1
     (if (<= z -6.5e-80)
       (- (* x (/ y (* z b))) (/ (- a t) b))
       (if (<= z 3.2e-70)
         (+ x (* t (/ z y)))
         (if (<= z 36000000000000.0)
           (/ (* z (- t a)) (+ y (* z (- b y))))
           t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -245.0) {
		tmp = t_1;
	} else if (z <= -6.5e-80) {
		tmp = (x * (y / (z * b))) - ((a - t) / b);
	} else if (z <= 3.2e-70) {
		tmp = x + (t * (z / y));
	} else if (z <= 36000000000000.0) {
		tmp = (z * (t - a)) / (y + (z * (b - y)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    if (z <= (-245.0d0)) then
        tmp = t_1
    else if (z <= (-6.5d-80)) then
        tmp = (x * (y / (z * b))) - ((a - t) / b)
    else if (z <= 3.2d-70) then
        tmp = x + (t * (z / y))
    else if (z <= 36000000000000.0d0) then
        tmp = (z * (t - a)) / (y + (z * (b - y)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -245.0) {
		tmp = t_1;
	} else if (z <= -6.5e-80) {
		tmp = (x * (y / (z * b))) - ((a - t) / b);
	} else if (z <= 3.2e-70) {
		tmp = x + (t * (z / y));
	} else if (z <= 36000000000000.0) {
		tmp = (z * (t - a)) / (y + (z * (b - y)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	tmp = 0
	if z <= -245.0:
		tmp = t_1
	elif z <= -6.5e-80:
		tmp = (x * (y / (z * b))) - ((a - t) / b)
	elif z <= 3.2e-70:
		tmp = x + (t * (z / y))
	elif z <= 36000000000000.0:
		tmp = (z * (t - a)) / (y + (z * (b - y)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -245.0)
		tmp = t_1;
	elseif (z <= -6.5e-80)
		tmp = Float64(Float64(x * Float64(y / Float64(z * b))) - Float64(Float64(a - t) / b));
	elseif (z <= 3.2e-70)
		tmp = Float64(x + Float64(t * Float64(z / y)));
	elseif (z <= 36000000000000.0)
		tmp = Float64(Float64(z * Float64(t - a)) / Float64(y + Float64(z * Float64(b - y))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -245.0)
		tmp = t_1;
	elseif (z <= -6.5e-80)
		tmp = (x * (y / (z * b))) - ((a - t) / b);
	elseif (z <= 3.2e-70)
		tmp = x + (t * (z / y));
	elseif (z <= 36000000000000.0)
		tmp = (z * (t - a)) / (y + (z * (b - y)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -245.0], t$95$1, If[LessEqual[z, -6.5e-80], N[(N[(x * N[(y / N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(a - t), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.2e-70], N[(x + N[(t * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 36000000000000.0], N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -245 or 3.6e13 < z

   1. Initial program 52.2%

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

   3. Taylor expanded in z around inf 82.0%

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

   if -245 < z < -6.49999999999999984e-80

   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

   3. Taylor expanded in y around 0 53.1%

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

      1. associate--l+ 53.1%

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

      2. *-commutative 53.1%

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

      3. associate-/l* 53.1%

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

      4. mul-1-neg 53.1%

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

      5. *-commutative 53.1%

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

      6. div-sub 53.1%

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

   5. Simplified 53.1%

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

   6. Taylor expanded in x around inf 64.5%

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

      1. associate-/l* 64.4%

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

      2. *-commutative 64.4%

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

   8. Simplified 64.4%

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

   if -6.49999999999999984e-80 < z < 3.1999999999999997e-70

   1. Initial program 85.1%

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

   3. Taylor expanded in t around -inf 78.8%

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

      1. mul-1-neg 78.8%

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

      2. *-commutative 78.8%

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

      3. distribute-rgt-neg-in 78.8%

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

      4. mul-1-neg 78.8%

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

      5. unsub-neg 78.8%

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

      6. mul-1-neg 78.8%

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

      7. +-commutative 78.8%

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

      8. mul-1-neg 78.8%

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

      9. unsub-neg 78.8%

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

      10. *-commutative 78.8%

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

      11. *-commutative 78.8%

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

   5. Simplified 78.8%

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

   6. Taylor expanded in a around 0 64.9%

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

      1. associate-/l* 59.7%

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

   8. Simplified 59.7%

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

   9. Taylor expanded in z around 0 46.8%

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

   10. Taylor expanded in t around inf 64.8%

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

       1. associate-/l* 65.0%

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

   12. Simplified 65.0%

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

   if 3.1999999999999997e-70 < z < 3.6e13

   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

   3. Taylor expanded in x around 0 93.7%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -245:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-80}:\\ \;\;\;\;x \cdot \frac{y}{z \cdot b} - \frac{a - t}{b}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-70}:\\ \;\;\;\;x + t \cdot \frac{z}{y}\\ \mathbf{elif}\;z \leq 36000000000000:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 84.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+58} \lor \neg \left(z \leq 2.9 \cdot 10^{+112}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(a - t\right) - x \cdot y}{z \cdot \left(y - b\right) - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1e+58) (not (<= z 2.9e+112)))
   (/ (- t a) (- b y))
   (/ (- (* z (- a t)) (* x y)) (- (* z (- y b)) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1e+58) || !(z <= 2.9e+112)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((z * (a - t)) - (x * y)) / ((z * (y - 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 <= (-1d+58)) .or. (.not. (z <= 2.9d+112))) then
        tmp = (t - a) / (b - y)
    else
        tmp = ((z * (a - t)) - (x * y)) / ((z * (y - 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 <= -1e+58) || !(z <= 2.9e+112)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((z * (a - t)) - (x * y)) / ((z * (y - b)) - y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1e+58) or not (z <= 2.9e+112):
		tmp = (t - a) / (b - y)
	else:
		tmp = ((z * (a - t)) - (x * y)) / ((z * (y - b)) - y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1e+58) || !(z <= 2.9e+112))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(Float64(Float64(z * Float64(a - t)) - Float64(x * y)) / Float64(Float64(z * Float64(y - b)) - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1e+58) || ~((z <= 2.9e+112)))
		tmp = (t - a) / (b - y);
	else
		tmp = ((z * (a - t)) - (x * y)) / ((z * (y - b)) - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1e+58], N[Not[LessEqual[z, 2.9e+112]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z * N[(a - t), $MachinePrecision]), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision] / N[(N[(z * N[(y - b), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.99999999999999944e57 or 2.9000000000000002e112 < z

   1. Initial program 37.3%

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

   3. Taylor expanded in z around inf 86.5%

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

   if -9.99999999999999944e57 < z < 2.9000000000000002e112

   1. Initial program 87.8%

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

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+58} \lor \neg \left(z \leq 2.9 \cdot 10^{+112}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(a - t\right) - x \cdot y}{z \cdot \left(y - b\right) - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 83.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1720 \lor \neg \left(z \leq 23.5\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1720.0) (not (<= z 23.5)))
   (/ (- t a) (- b y))
   (/ (+ (* z (- t a)) (* x y)) (+ y (* z b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1720.0) || !(z <= 23.5)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((z * (t - a)) + (x * y)) / (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 <= (-1720.0d0)) .or. (.not. (z <= 23.5d0))) then
        tmp = (t - a) / (b - y)
    else
        tmp = ((z * (t - a)) + (x * y)) / (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 <= -1720.0) || !(z <= 23.5)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((z * (t - a)) + (x * y)) / (y + (z * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1720.0) or not (z <= 23.5):
		tmp = (t - a) / (b - y)
	else:
		tmp = ((z * (t - a)) + (x * y)) / (y + (z * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1720.0) || !(z <= 23.5))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(Float64(Float64(z * Float64(t - a)) + Float64(x * y)) / 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 <= -1720.0) || ~((z <= 23.5)))
		tmp = (t - a) / (b - y);
	else
		tmp = ((z * (t - a)) + (x * y)) / (y + (z * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1720.0], N[Not[LessEqual[z, 23.5]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1720 or 23.5 < z

   1. Initial program 53.0%

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

   3. Taylor expanded in z around inf 82.0%

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

   if -1720 < z < 23.5

   1. Initial program 89.1%

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

   3. Taylor expanded in b around inf 88.1%

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

      1. *-commutative 88.1%

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

   5. Simplified 88.1%

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

4. Final simplification 85.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1720 \lor \neg \left(z \leq 23.5\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot b}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 37.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -\frac{a}{b}\\ \mathbf{if}\;z \leq -6.2 \cdot 10^{+58}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-36}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-66}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{+46}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (/ a b))))
   (if (<= z -6.2e+58)
     (/ t b)
     (if (<= z -2.8e-36)
       t_1
       (if (<= z 4.6e-66) x (if (<= z 6.6e+46) t_1 (/ t b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -(a / b);
	double tmp;
	if (z <= -6.2e+58) {
		tmp = t / b;
	} else if (z <= -2.8e-36) {
		tmp = t_1;
	} else if (z <= 4.6e-66) {
		tmp = x;
	} else if (z <= 6.6e+46) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = -(a / b)
    if (z <= (-6.2d+58)) then
        tmp = t / b
    else if (z <= (-2.8d-36)) then
        tmp = t_1
    else if (z <= 4.6d-66) then
        tmp = x
    else if (z <= 6.6d+46) then
        tmp = t_1
    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 t_1 = -(a / b);
	double tmp;
	if (z <= -6.2e+58) {
		tmp = t / b;
	} else if (z <= -2.8e-36) {
		tmp = t_1;
	} else if (z <= 4.6e-66) {
		tmp = x;
	} else if (z <= 6.6e+46) {
		tmp = t_1;
	} else {
		tmp = t / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = -(a / b)
	tmp = 0
	if z <= -6.2e+58:
		tmp = t / b
	elif z <= -2.8e-36:
		tmp = t_1
	elif z <= 4.6e-66:
		tmp = x
	elif z <= 6.6e+46:
		tmp = t_1
	else:
		tmp = t / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(-Float64(a / b))
	tmp = 0.0
	if (z <= -6.2e+58)
		tmp = Float64(t / b);
	elseif (z <= -2.8e-36)
		tmp = t_1;
	elseif (z <= 4.6e-66)
		tmp = x;
	elseif (z <= 6.6e+46)
		tmp = t_1;
	else
		tmp = Float64(t / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = -(a / b);
	tmp = 0.0;
	if (z <= -6.2e+58)
		tmp = t / b;
	elseif (z <= -2.8e-36)
		tmp = t_1;
	elseif (z <= 4.6e-66)
		tmp = x;
	elseif (z <= 6.6e+46)
		tmp = t_1;
	else
		tmp = t / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = (-N[(a / b), $MachinePrecision])}, If[LessEqual[z, -6.2e+58], N[(t / b), $MachinePrecision], If[LessEqual[z, -2.8e-36], t$95$1, If[LessEqual[z, 4.6e-66], x, If[LessEqual[z, 6.6e+46], t$95$1, N[(t / b), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.1999999999999998e58 or 6.5999999999999996e46 < z

   1. Initial program 46.4%

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

   3. Taylor expanded in y around 0 28.9%

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

      1. associate--l+ 28.9%

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

      2. *-commutative 28.9%

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

      3. associate-/l* 44.4%

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

      4. mul-1-neg 44.4%

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

      5. *-commutative 44.4%

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

      6. div-sub 44.4%

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

   5. Simplified 44.4%

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

   6. Taylor expanded in b around inf 56.8%

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

      1. associate-/l* 57.8%

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

   8. Simplified 57.8%

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

   9. Taylor expanded in t around inf 37.9%

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

   if -6.1999999999999998e58 < z < -2.8000000000000001e-36 or 4.59999999999999984e-66 < z < 6.5999999999999996e46

   1. Initial program 89.7%

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

   3. Taylor expanded in a around inf 54.7%

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

      1. mul-1-neg 54.7%

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

      2. distribute-lft-neg-out 54.7%

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

      3. *-commutative 54.7%

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

   5. Simplified 54.7%

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

   6. Taylor expanded in y around 0 40.4%

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

      1. associate-*r/ 40.4%

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

      2. neg-mul-1 40.4%

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

   8. Simplified 40.4%

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

   if -2.8000000000000001e-36 < z < 4.59999999999999984e-66

   1. Initial program 86.7%

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

   3. Taylor expanded in z around 0 51.0%

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

4. Final simplification 43.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+58}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-36}:\\ \;\;\;\;-\frac{a}{b}\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-66}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{+46}:\\ \;\;\;\;-\frac{a}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 69.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -1150:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-81}:\\ \;\;\;\;x \cdot \frac{y}{z \cdot b} - \frac{a - t}{b}\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{-30}:\\ \;\;\;\;x + t \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -1150.0)
     t_1
     (if (<= z -4.2e-81)
       (- (* x (/ y (* z b))) (/ (- a t) b))
       (if (<= z 5.3e-30) (+ x (* t (/ z y))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -1150.0) {
		tmp = t_1;
	} else if (z <= -4.2e-81) {
		tmp = (x * (y / (z * b))) - ((a - t) / b);
	} else if (z <= 5.3e-30) {
		tmp = x + (t * (z / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    if (z <= (-1150.0d0)) then
        tmp = t_1
    else if (z <= (-4.2d-81)) then
        tmp = (x * (y / (z * b))) - ((a - t) / b)
    else if (z <= 5.3d-30) then
        tmp = x + (t * (z / y))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -1150.0) {
		tmp = t_1;
	} else if (z <= -4.2e-81) {
		tmp = (x * (y / (z * b))) - ((a - t) / b);
	} else if (z <= 5.3e-30) {
		tmp = x + (t * (z / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	tmp = 0
	if z <= -1150.0:
		tmp = t_1
	elif z <= -4.2e-81:
		tmp = (x * (y / (z * b))) - ((a - t) / b)
	elif z <= 5.3e-30:
		tmp = x + (t * (z / y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -1150.0)
		tmp = t_1;
	elseif (z <= -4.2e-81)
		tmp = Float64(Float64(x * Float64(y / Float64(z * b))) - Float64(Float64(a - t) / b));
	elseif (z <= 5.3e-30)
		tmp = Float64(x + Float64(t * Float64(z / y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -1150.0)
		tmp = t_1;
	elseif (z <= -4.2e-81)
		tmp = (x * (y / (z * b))) - ((a - t) / b);
	elseif (z <= 5.3e-30)
		tmp = x + (t * (z / y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1150.0], t$95$1, If[LessEqual[z, -4.2e-81], N[(N[(x * N[(y / N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(a - t), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.3e-30], N[(x + N[(t * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1150 or 5.29999999999999974e-30 < z

   1. Initial program 56.3%

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

   3. Taylor expanded in z around inf 81.1%

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

   if -1150 < z < -4.1999999999999998e-81

   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

   3. Taylor expanded in y around 0 53.1%

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

      1. associate--l+ 53.1%

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

      2. *-commutative 53.1%

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

      3. associate-/l* 53.1%

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

      4. mul-1-neg 53.1%

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

      5. *-commutative 53.1%

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

      6. div-sub 53.1%

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

   5. Simplified 53.1%

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

   6. Taylor expanded in x around inf 64.5%

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

      1. associate-/l* 64.4%

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

      2. *-commutative 64.4%

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

   8. Simplified 64.4%

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

   if -4.1999999999999998e-81 < z < 5.29999999999999974e-30

   1. Initial program 86.1%

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

   3. Taylor expanded in t around -inf 78.3%

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

      1. mul-1-neg 78.3%

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

      2. *-commutative 78.3%

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

      3. distribute-rgt-neg-in 78.3%

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

      4. mul-1-neg 78.3%

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

      5. unsub-neg 78.3%

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

      6. mul-1-neg 78.3%

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

      7. +-commutative 78.3%

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

      8. mul-1-neg 78.3%

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

      9. unsub-neg 78.3%

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

      10. *-commutative 78.3%

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

      11. *-commutative 78.3%

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

   5. Simplified 78.3%

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

   6. Taylor expanded in a around 0 64.7%

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

      1. associate-/l* 59.7%

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

   8. Simplified 59.7%

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

   9. Taylor expanded in z around 0 46.8%

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

   10. Taylor expanded in t around inf 63.6%

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

       1. associate-/l* 63.8%

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

   12. Simplified 63.8%

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

4. Final simplification 73.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1150:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-81}:\\ \;\;\;\;x \cdot \frac{y}{z \cdot b} - \frac{a - t}{b}\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{-30}:\\ \;\;\;\;x + t \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 69.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -440:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -5.6 \cdot 10^{-80}:\\ \;\;\;\;\frac{\left(t + \frac{x \cdot y}{z}\right) - a}{b}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-32}:\\ \;\;\;\;x + t \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -440.0)
     t_1
     (if (<= z -5.6e-80)
       (/ (- (+ t (/ (* x y) z)) a) b)
       (if (<= z 2.1e-32) (+ x (* t (/ z y))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -440.0) {
		tmp = t_1;
	} else if (z <= -5.6e-80) {
		tmp = ((t + ((x * y) / z)) - a) / b;
	} else if (z <= 2.1e-32) {
		tmp = x + (t * (z / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    if (z <= (-440.0d0)) then
        tmp = t_1
    else if (z <= (-5.6d-80)) then
        tmp = ((t + ((x * y) / z)) - a) / b
    else if (z <= 2.1d-32) then
        tmp = x + (t * (z / y))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -440.0) {
		tmp = t_1;
	} else if (z <= -5.6e-80) {
		tmp = ((t + ((x * y) / z)) - a) / b;
	} else if (z <= 2.1e-32) {
		tmp = x + (t * (z / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	tmp = 0
	if z <= -440.0:
		tmp = t_1
	elif z <= -5.6e-80:
		tmp = ((t + ((x * y) / z)) - a) / b
	elif z <= 2.1e-32:
		tmp = x + (t * (z / y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -440.0)
		tmp = t_1;
	elseif (z <= -5.6e-80)
		tmp = Float64(Float64(Float64(t + Float64(Float64(x * y) / z)) - a) / b);
	elseif (z <= 2.1e-32)
		tmp = Float64(x + Float64(t * Float64(z / y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -440.0)
		tmp = t_1;
	elseif (z <= -5.6e-80)
		tmp = ((t + ((x * y) / z)) - a) / b;
	elseif (z <= 2.1e-32)
		tmp = x + (t * (z / y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -440.0], t$95$1, If[LessEqual[z, -5.6e-80], N[(N[(N[(t + N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[z, 2.1e-32], N[(x + N[(t * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -440 or 2.0999999999999999e-32 < z

   1. Initial program 56.3%

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

   3. Taylor expanded in z around inf 81.1%

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

   if -440 < z < -5.59999999999999978e-80

   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

   3. Taylor expanded in y around 0 53.1%

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

      1. associate--l+ 53.1%

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

      2. *-commutative 53.1%

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

      3. associate-/l* 53.1%

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

      4. mul-1-neg 53.1%

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

      5. *-commutative 53.1%

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

      6. div-sub 53.1%

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

   5. Simplified 53.1%

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

   6. Taylor expanded in b around inf 60.1%

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

   if -5.59999999999999978e-80 < z < 2.0999999999999999e-32

   1. Initial program 86.1%

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

   3. Taylor expanded in t around -inf 78.3%

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

      1. mul-1-neg 78.3%

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

      2. *-commutative 78.3%

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

      3. distribute-rgt-neg-in 78.3%

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

      4. mul-1-neg 78.3%

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

      5. unsub-neg 78.3%

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

      6. mul-1-neg 78.3%

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

      7. +-commutative 78.3%

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

      8. mul-1-neg 78.3%

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

      9. unsub-neg 78.3%

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

      10. *-commutative 78.3%

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

      11. *-commutative 78.3%

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

   5. Simplified 78.3%

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

   6. Taylor expanded in a around 0 64.7%

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

      1. associate-/l* 59.7%

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

   8. Simplified 59.7%

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

   9. Taylor expanded in z around 0 46.8%

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

   10. Taylor expanded in t around inf 63.6%

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

       1. associate-/l* 63.8%

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

   12. Simplified 63.8%

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

Alternative 14: 69.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -1150:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-80}:\\ \;\;\;\;\frac{\left(t + x \cdot \frac{y}{z}\right) - a}{b}\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{-31}:\\ \;\;\;\;x + t \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -1150.0)
     t_1
     (if (<= z -5.5e-80)
       (/ (- (+ t (* x (/ y z))) a) b)
       (if (<= z 6.4e-31) (+ x (* t (/ z y))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -1150.0) {
		tmp = t_1;
	} else if (z <= -5.5e-80) {
		tmp = ((t + (x * (y / z))) - a) / b;
	} else if (z <= 6.4e-31) {
		tmp = x + (t * (z / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    if (z <= (-1150.0d0)) then
        tmp = t_1
    else if (z <= (-5.5d-80)) then
        tmp = ((t + (x * (y / z))) - a) / b
    else if (z <= 6.4d-31) then
        tmp = x + (t * (z / y))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -1150.0) {
		tmp = t_1;
	} else if (z <= -5.5e-80) {
		tmp = ((t + (x * (y / z))) - a) / b;
	} else if (z <= 6.4e-31) {
		tmp = x + (t * (z / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	tmp = 0
	if z <= -1150.0:
		tmp = t_1
	elif z <= -5.5e-80:
		tmp = ((t + (x * (y / z))) - a) / b
	elif z <= 6.4e-31:
		tmp = x + (t * (z / y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -1150.0)
		tmp = t_1;
	elseif (z <= -5.5e-80)
		tmp = Float64(Float64(Float64(t + Float64(x * Float64(y / z))) - a) / b);
	elseif (z <= 6.4e-31)
		tmp = Float64(x + Float64(t * Float64(z / y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -1150.0)
		tmp = t_1;
	elseif (z <= -5.5e-80)
		tmp = ((t + (x * (y / z))) - a) / b;
	elseif (z <= 6.4e-31)
		tmp = x + (t * (z / y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1150.0], t$95$1, If[LessEqual[z, -5.5e-80], N[(N[(N[(t + N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[z, 6.4e-31], N[(x + N[(t * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1150 or 6.40000000000000036e-31 < z

   1. Initial program 56.3%

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

   3. Taylor expanded in z around inf 81.1%

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

   if -1150 < z < -5.4999999999999997e-80

   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

   3. Taylor expanded in y around 0 53.1%

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

      1. associate--l+ 53.1%

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

      2. *-commutative 53.1%

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

      3. associate-/l* 53.1%

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

      4. mul-1-neg 53.1%

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

      5. *-commutative 53.1%

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

      6. div-sub 53.1%

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

   5. Simplified 53.1%

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

   6. Taylor expanded in b around inf 60.1%

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

      1. associate-/l* 59.9%

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

   8. Simplified 59.9%

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

   if -5.4999999999999997e-80 < z < 6.40000000000000036e-31

   1. Initial program 86.1%

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

   3. Taylor expanded in t around -inf 78.3%

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

      1. mul-1-neg 78.3%

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

      2. *-commutative 78.3%

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

      3. distribute-rgt-neg-in 78.3%

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

      4. mul-1-neg 78.3%

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

      5. unsub-neg 78.3%

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

      6. mul-1-neg 78.3%

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

      7. +-commutative 78.3%

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

      8. mul-1-neg 78.3%

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

      9. unsub-neg 78.3%

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

      10. *-commutative 78.3%

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

      11. *-commutative 78.3%

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

   5. Simplified 78.3%

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

   6. Taylor expanded in a around 0 64.7%

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

      1. associate-/l* 59.7%

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

   8. Simplified 59.7%

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

   9. Taylor expanded in z around 0 46.8%

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

   10. Taylor expanded in t around inf 63.6%

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

       1. associate-/l* 63.8%

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

   12. Simplified 63.8%

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

Alternative 15: 65.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -1.4:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-299}:\\ \;\;\;\;\frac{x \cdot y}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-31}:\\ \;\;\;\;x + t \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -1.4)
     t_1
     (if (<= z 1.95e-299)
       (/ (* x y) (+ y (* z (- b y))))
       (if (<= z 7.2e-31) (+ x (* t (/ z y))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -1.4) {
		tmp = t_1;
	} else if (z <= 1.95e-299) {
		tmp = (x * y) / (y + (z * (b - y)));
	} else if (z <= 7.2e-31) {
		tmp = x + (t * (z / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    if (z <= (-1.4d0)) then
        tmp = t_1
    else if (z <= 1.95d-299) then
        tmp = (x * y) / (y + (z * (b - y)))
    else if (z <= 7.2d-31) then
        tmp = x + (t * (z / y))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -1.4) {
		tmp = t_1;
	} else if (z <= 1.95e-299) {
		tmp = (x * y) / (y + (z * (b - y)));
	} else if (z <= 7.2e-31) {
		tmp = x + (t * (z / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	tmp = 0
	if z <= -1.4:
		tmp = t_1
	elif z <= 1.95e-299:
		tmp = (x * y) / (y + (z * (b - y)))
	elif z <= 7.2e-31:
		tmp = x + (t * (z / y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -1.4)
		tmp = t_1;
	elseif (z <= 1.95e-299)
		tmp = Float64(Float64(x * y) / Float64(y + Float64(z * Float64(b - y))));
	elseif (z <= 7.2e-31)
		tmp = Float64(x + Float64(t * Float64(z / y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -1.4)
		tmp = t_1;
	elseif (z <= 1.95e-299)
		tmp = (x * y) / (y + (z * (b - y)));
	elseif (z <= 7.2e-31)
		tmp = x + (t * (z / y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.4], t$95$1, If[LessEqual[z, 1.95e-299], N[(N[(x * y), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.2e-31], N[(x + N[(t * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.3999999999999999 or 7.20000000000000007e-31 < z

   1. Initial program 56.7%

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

   3. Taylor expanded in z around inf 81.3%

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

   if -1.3999999999999999 < z < 1.9499999999999999e-299

   1. Initial program 92.9%

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

   3. Taylor expanded in x around inf 58.6%

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

      1. *-commutative 58.6%

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

   5. Simplified 58.6%

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

   if 1.9499999999999999e-299 < z < 7.20000000000000007e-31

   1. Initial program 82.6%

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

   3. Taylor expanded in t around -inf 77.1%

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

      1. mul-1-neg 77.1%

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

      2. *-commutative 77.1%

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

      3. distribute-rgt-neg-in 77.1%

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

      4. mul-1-neg 77.1%

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

      5. unsub-neg 77.1%

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

      6. mul-1-neg 77.1%

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

      7. +-commutative 77.1%

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

      8. mul-1-neg 77.1%

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

      9. unsub-neg 77.1%

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

      10. *-commutative 77.1%

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

      11. *-commutative 77.1%

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

   5. Simplified 77.1%

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

   6. Taylor expanded in a around 0 65.9%

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

      1. associate-/l* 58.5%

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

   8. Simplified 58.5%

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

   9. Taylor expanded in z around 0 49.5%

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

   10. Taylor expanded in t around inf 66.9%

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

       1. associate-/l* 67.4%

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

   12. Simplified 67.4%

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

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-299}:\\ \;\;\;\;\frac{x \cdot y}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-31}:\\ \;\;\;\;x + t \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 65.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -0.26:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-299}:\\ \;\;\;\;\frac{x \cdot y}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-32}:\\ \;\;\;\;x + t \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -0.26)
     t_1
     (if (<= z 1.02e-299)
       (/ (* x y) (+ y (* z b)))
       (if (<= z 1.9e-32) (+ x (* t (/ z y))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -0.26) {
		tmp = t_1;
	} else if (z <= 1.02e-299) {
		tmp = (x * y) / (y + (z * b));
	} else if (z <= 1.9e-32) {
		tmp = x + (t * (z / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    if (z <= (-0.26d0)) then
        tmp = t_1
    else if (z <= 1.02d-299) then
        tmp = (x * y) / (y + (z * b))
    else if (z <= 1.9d-32) then
        tmp = x + (t * (z / y))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -0.26) {
		tmp = t_1;
	} else if (z <= 1.02e-299) {
		tmp = (x * y) / (y + (z * b));
	} else if (z <= 1.9e-32) {
		tmp = x + (t * (z / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	tmp = 0
	if z <= -0.26:
		tmp = t_1
	elif z <= 1.02e-299:
		tmp = (x * y) / (y + (z * b))
	elif z <= 1.9e-32:
		tmp = x + (t * (z / y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -0.26)
		tmp = t_1;
	elseif (z <= 1.02e-299)
		tmp = Float64(Float64(x * y) / Float64(y + Float64(z * b)));
	elseif (z <= 1.9e-32)
		tmp = Float64(x + Float64(t * Float64(z / y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -0.26)
		tmp = t_1;
	elseif (z <= 1.02e-299)
		tmp = (x * y) / (y + (z * b));
	elseif (z <= 1.9e-32)
		tmp = x + (t * (z / y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.26], t$95$1, If[LessEqual[z, 1.02e-299], N[(N[(x * y), $MachinePrecision] / N[(y + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.9e-32], N[(x + N[(t * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.26000000000000001 or 1.90000000000000004e-32 < z

   1. Initial program 56.7%

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

   3. Taylor expanded in z around inf 81.3%

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

   if -0.26000000000000001 < z < 1.02e-299

   1. Initial program 92.9%

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

   3. Taylor expanded in b around inf 92.2%

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

      1. *-commutative 92.2%

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

   5. Simplified 92.2%

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

   6. Taylor expanded in x around inf 57.9%

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

      1. *-commutative 58.6%

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

   8. Simplified 57.9%

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

   if 1.02e-299 < z < 1.90000000000000004e-32

   1. Initial program 82.6%

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

   3. Taylor expanded in t around -inf 77.1%

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

      1. mul-1-neg 77.1%

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

      2. *-commutative 77.1%

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

      3. distribute-rgt-neg-in 77.1%

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

      4. mul-1-neg 77.1%

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

      5. unsub-neg 77.1%

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

      6. mul-1-neg 77.1%

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

      7. +-commutative 77.1%

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

      8. mul-1-neg 77.1%

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

      9. unsub-neg 77.1%

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

      10. *-commutative 77.1%

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

      11. *-commutative 77.1%

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

   5. Simplified 77.1%

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

   6. Taylor expanded in a around 0 65.9%

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

      1. associate-/l* 58.5%

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

   8. Simplified 58.5%

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

   9. Taylor expanded in z around 0 49.5%

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

   10. Taylor expanded in t around inf 66.9%

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

       1. associate-/l* 67.4%

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

   12. Simplified 67.4%

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

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.26:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-299}:\\ \;\;\;\;\frac{x \cdot y}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-32}:\\ \;\;\;\;x + t \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 44.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{b - y}\\ \mathbf{if}\;z \leq -3.5 \cdot 10^{-6}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-66}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;z \leq 10^{+46}:\\ \;\;\;\;-\frac{a}{b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ t (- b y))))
   (if (<= z -3.5e-6)
     t_1
     (if (<= z 2.7e-66) (/ x (- 1.0 z)) (if (<= z 1e+46) (- (/ a b)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t / (b - y);
	double tmp;
	if (z <= -3.5e-6) {
		tmp = t_1;
	} else if (z <= 2.7e-66) {
		tmp = x / (1.0 - z);
	} else if (z <= 1e+46) {
		tmp = -(a / b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t / (b - y)
    if (z <= (-3.5d-6)) then
        tmp = t_1
    else if (z <= 2.7d-66) then
        tmp = x / (1.0d0 - z)
    else if (z <= 1d+46) then
        tmp = -(a / b)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t / (b - y);
	double tmp;
	if (z <= -3.5e-6) {
		tmp = t_1;
	} else if (z <= 2.7e-66) {
		tmp = x / (1.0 - z);
	} else if (z <= 1e+46) {
		tmp = -(a / b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t / (b - y)
	tmp = 0
	if z <= -3.5e-6:
		tmp = t_1
	elif z <= 2.7e-66:
		tmp = x / (1.0 - z)
	elif z <= 1e+46:
		tmp = -(a / b)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t / Float64(b - y))
	tmp = 0.0
	if (z <= -3.5e-6)
		tmp = t_1;
	elseif (z <= 2.7e-66)
		tmp = Float64(x / Float64(1.0 - z));
	elseif (z <= 1e+46)
		tmp = Float64(-Float64(a / b));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t / (b - y);
	tmp = 0.0;
	if (z <= -3.5e-6)
		tmp = t_1;
	elseif (z <= 2.7e-66)
		tmp = x / (1.0 - z);
	elseif (z <= 1e+46)
		tmp = -(a / b);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.5e-6], t$95$1, If[LessEqual[z, 2.7e-66], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1e+46], (-N[(a / b), $MachinePrecision]), t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.49999999999999995e-6 or 9.9999999999999999e45 < z

   1. Initial program 52.3%

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

   3. Taylor expanded in z around inf 81.9%

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

   4. Taylor expanded in t around inf 47.1%

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

   if -3.49999999999999995e-6 < z < 2.69999999999999996e-66

   1. Initial program 87.6%

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

   3. Taylor expanded in 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%

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

   if 2.69999999999999996e-66 < z < 9.9999999999999999e45

   1. Initial program 87.6%

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

   3. Taylor expanded in a around inf 52.3%

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

      1. mul-1-neg 52.3%

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

      2. distribute-lft-neg-out 52.3%

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

      3. *-commutative 52.3%

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

   5. Simplified 52.3%

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

   6. Taylor expanded in y around 0 47.5%

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

      1. associate-*r/ 47.5%

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

      2. neg-mul-1 47.5%

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

   8. Simplified 47.5%

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

4. Final simplification 47.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{-6}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-66}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;z \leq 10^{+46}:\\ \;\;\;\;-\frac{a}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 44.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{b - y}\\ \mathbf{if}\;z \leq -1 \cdot 10^{-22}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-66}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+48}:\\ \;\;\;\;-\frac{a}{b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ t (- b y))))
   (if (<= z -1e-22)
     t_1
     (if (<= z 4.6e-66) x (if (<= z 1.8e+48) (- (/ a b)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t / (b - y);
	double tmp;
	if (z <= -1e-22) {
		tmp = t_1;
	} else if (z <= 4.6e-66) {
		tmp = x;
	} else if (z <= 1.8e+48) {
		tmp = -(a / b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t / (b - y)
    if (z <= (-1d-22)) then
        tmp = t_1
    else if (z <= 4.6d-66) then
        tmp = x
    else if (z <= 1.8d+48) then
        tmp = -(a / b)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t / (b - y);
	double tmp;
	if (z <= -1e-22) {
		tmp = t_1;
	} else if (z <= 4.6e-66) {
		tmp = x;
	} else if (z <= 1.8e+48) {
		tmp = -(a / b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t / (b - y)
	tmp = 0
	if z <= -1e-22:
		tmp = t_1
	elif z <= 4.6e-66:
		tmp = x
	elif z <= 1.8e+48:
		tmp = -(a / b)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t / Float64(b - y))
	tmp = 0.0
	if (z <= -1e-22)
		tmp = t_1;
	elseif (z <= 4.6e-66)
		tmp = x;
	elseif (z <= 1.8e+48)
		tmp = Float64(-Float64(a / b));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t / (b - y);
	tmp = 0.0;
	if (z <= -1e-22)
		tmp = t_1;
	elseif (z <= 4.6e-66)
		tmp = x;
	elseif (z <= 1.8e+48)
		tmp = -(a / b);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1e-22], t$95$1, If[LessEqual[z, 4.6e-66], x, If[LessEqual[z, 1.8e+48], (-N[(a / b), $MachinePrecision]), t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1e-22 or 1.79999999999999992e48 < z

   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 z around inf 80.8%

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

   4. Taylor expanded in t around inf 46.8%

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

   if -1e-22 < z < 4.59999999999999984e-66

   1. Initial program 87.3%

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

   3. Taylor expanded in z around 0 48.9%

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

   if 4.59999999999999984e-66 < z < 1.79999999999999992e48

   1. Initial program 87.6%

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

   3. Taylor expanded in a around inf 52.3%

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

      1. mul-1-neg 52.3%

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

      2. distribute-lft-neg-out 52.3%

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

      3. *-commutative 52.3%

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

   5. Simplified 52.3%

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

   6. Taylor expanded in y around 0 47.5%

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

      1. associate-*r/ 47.5%

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

      2. neg-mul-1 47.5%

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

   8. Simplified 47.5%

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

4. Final simplification 47.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{-22}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-66}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+48}:\\ \;\;\;\;-\frac{a}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 69.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{-80} \lor \neg \left(z \leq 3.8 \cdot 10^{-30}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -5.8e-80) (not (<= z 3.8e-30)))
   (/ (- t a) (- b y))
   (+ x (* t (/ z y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -5.8e-80) || !(z <= 3.8e-30)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x + (t * (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 <= (-5.8d-80)) .or. (.not. (z <= 3.8d-30))) then
        tmp = (t - a) / (b - y)
    else
        tmp = x + (t * (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 <= -5.8e-80) || !(z <= 3.8e-30)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x + (t * (z / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -5.8e-80) or not (z <= 3.8e-30):
		tmp = (t - a) / (b - y)
	else:
		tmp = x + (t * (z / y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -5.8e-80) || !(z <= 3.8e-30))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(x + Float64(t * Float64(z / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -5.8e-80) || ~((z <= 3.8e-30)))
		tmp = (t - a) / (b - y);
	else
		tmp = x + (t * (z / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -5.8e-80], N[Not[LessEqual[z, 3.8e-30]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.79999999999999996e-80 or 3.8000000000000003e-30 < z

   1. Initial program 61.6%

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

   3. Taylor expanded in z around inf 75.5%

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

   if -5.79999999999999996e-80 < z < 3.8000000000000003e-30

   1. Initial program 86.1%

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

   3. Taylor expanded in t around -inf 78.3%

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

      1. mul-1-neg 78.3%

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

      2. *-commutative 78.3%

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

      3. distribute-rgt-neg-in 78.3%

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

      4. mul-1-neg 78.3%

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

      5. unsub-neg 78.3%

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

      6. mul-1-neg 78.3%

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

      7. +-commutative 78.3%

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

      8. mul-1-neg 78.3%

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

      9. unsub-neg 78.3%

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

      10. *-commutative 78.3%

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

      11. *-commutative 78.3%

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

   5. Simplified 78.3%

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

   6. Taylor expanded in a around 0 64.7%

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

      1. associate-/l* 59.7%

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

   8. Simplified 59.7%

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

   9. Taylor expanded in z around 0 46.8%

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

   10. Taylor expanded in t around inf 63.6%

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

       1. associate-/l* 63.8%

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

   12. Simplified 63.8%

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

4. Final simplification 71.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{-80} \lor \neg \left(z \leq 3.8 \cdot 10^{-30}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 53.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{-80} \lor \neg \left(z \leq 2.35 \cdot 10^{-32}\right):\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -6.5e-80) (not (<= z 2.35e-32)))
   (/ (- t a) b)
   (+ x (* t (/ z y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -6.5e-80) || !(z <= 2.35e-32)) {
		tmp = (t - a) / b;
	} else {
		tmp = x + (t * (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 <= (-6.5d-80)) .or. (.not. (z <= 2.35d-32))) then
        tmp = (t - a) / b
    else
        tmp = x + (t * (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 <= -6.5e-80) || !(z <= 2.35e-32)) {
		tmp = (t - a) / b;
	} else {
		tmp = x + (t * (z / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -6.5e-80) or not (z <= 2.35e-32):
		tmp = (t - a) / b
	else:
		tmp = x + (t * (z / y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -6.5e-80) || !(z <= 2.35e-32))
		tmp = Float64(Float64(t - a) / b);
	else
		tmp = Float64(x + Float64(t * Float64(z / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -6.5e-80) || ~((z <= 2.35e-32)))
		tmp = (t - a) / b;
	else
		tmp = x + (t * (z / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -6.5e-80], N[Not[LessEqual[z, 2.35e-32]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision], N[(x + N[(t * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.49999999999999984e-80 or 2.3500000000000001e-32 < z

   1. Initial program 61.6%

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

   3. Taylor expanded in y around 0 52.1%

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

   if -6.49999999999999984e-80 < z < 2.3500000000000001e-32

   1. Initial program 86.1%

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

   3. Taylor expanded in t around -inf 78.3%

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

      1. mul-1-neg 78.3%

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

      2. *-commutative 78.3%

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

      3. distribute-rgt-neg-in 78.3%

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

      4. mul-1-neg 78.3%

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

      5. unsub-neg 78.3%

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

      6. mul-1-neg 78.3%

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

      7. +-commutative 78.3%

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

      8. mul-1-neg 78.3%

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

      9. unsub-neg 78.3%

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

      10. *-commutative 78.3%

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

      11. *-commutative 78.3%

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

   5. Simplified 78.3%

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

   6. Taylor expanded in a around 0 64.7%

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

      1. associate-/l* 59.7%

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

   8. Simplified 59.7%

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

   9. Taylor expanded in z around 0 46.8%

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

   10. Taylor expanded in t around inf 63.6%

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

       1. associate-/l* 63.8%

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

   12. Simplified 63.8%

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

4. Final simplification 56.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{-80} \lor \neg \left(z \leq 2.35 \cdot 10^{-32}\right):\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 54.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{-47} \lor \neg \left(y \leq 350000000\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -4e-47) (not (<= y 350000000.0)))
   (/ 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 <= -4e-47) || !(y <= 350000000.0)) {
		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 <= (-4d-47)) .or. (.not. (y <= 350000000.0d0))) 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 <= -4e-47) || !(y <= 350000000.0)) {
		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 <= -4e-47) or not (y <= 350000000.0):
		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 <= -4e-47) || !(y <= 350000000.0))
		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 <= -4e-47) || ~((y <= 350000000.0)))
		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, -4e-47], N[Not[LessEqual[y, 350000000.0]], $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 < -3.9999999999999999e-47 or 3.5e8 < y

   1. Initial program 60.0%

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

   3. Taylor expanded in y around inf 46.0%

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

      1. mul-1-neg 46.0%

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

      2. unsub-neg 46.0%

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

   5. Simplified 46.0%

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

   if -3.9999999999999999e-47 < y < 3.5e8

   1. Initial program 83.0%

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

   3. Taylor expanded in y around 0 64.2%

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

4. Final simplification 54.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{-47} \lor \neg \left(y \leq 350000000\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 36.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{-80} \lor \neg \left(z \leq 4.2 \cdot 10^{-66}\right):\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -5.4e-80) (not (<= z 4.2e-66))) (/ t b) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -5.4e-80) || !(z <= 4.2e-66)) {
		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 <= (-5.4d-80)) .or. (.not. (z <= 4.2d-66))) 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 <= -5.4e-80) || !(z <= 4.2e-66)) {
		tmp = t / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -5.4e-80) or not (z <= 4.2e-66):
		tmp = t / b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -5.4e-80) || !(z <= 4.2e-66))
		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 <= -5.4e-80) || ~((z <= 4.2e-66)))
		tmp = t / b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -5.4e-80], N[Not[LessEqual[z, 4.2e-66]], $MachinePrecision]], N[(t / b), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -5.4000000000000004e-80 or 4.2000000000000001e-66 < z

   1. Initial program 62.5%

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

   3. Taylor expanded in y around 0 36.1%

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

      1. associate--l+ 36.1%

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

      2. *-commutative 36.1%

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

      3. associate-/l* 46.0%

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

      4. mul-1-neg 46.0%

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

      5. *-commutative 46.0%

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

      6. div-sub 46.0%

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

   5. Simplified 46.0%

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

   6. Taylor expanded in b around inf 58.0%

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

      1. associate-/l* 58.6%

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

   8. Simplified 58.6%

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

   9. Taylor expanded in t around inf 31.5%

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

   if -5.4000000000000004e-80 < z < 4.2000000000000001e-66

   1. Initial program 85.5%

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

   3. Taylor expanded in z around 0 53.5%

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

4. Final simplification 39.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{-80} \lor \neg \left(z \leq 4.2 \cdot 10^{-66}\right):\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 34.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.000185 \lor \neg \left(z \leq 2900000\right):\\ \;\;\;\;\frac{a}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -0.000185) (not (<= z 2900000.0))) (/ a y) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -0.000185) || !(z <= 2900000.0)) {
		tmp = a / y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-0.000185d0)) .or. (.not. (z <= 2900000.0d0))) then
        tmp = a / y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -0.000185) || !(z <= 2900000.0)) {
		tmp = a / y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -0.000185) or not (z <= 2900000.0):
		tmp = a / y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -0.000185) || !(z <= 2900000.0))
		tmp = Float64(a / y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -0.000185) || ~((z <= 2900000.0)))
		tmp = a / y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -0.000185], N[Not[LessEqual[z, 2900000.0]], $MachinePrecision]], N[(a / y), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.85e-4 or 2.9e6 < z

   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 z around inf 81.3%

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

   4. Taylor expanded in b around 0 38.1%

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

      1. neg-mul-1 38.1%

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

   6. Simplified 38.1%

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

   7. Taylor expanded in t around 0 21.8%

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

   if -1.85e-4 < z < 2.9e6

   1. Initial program 89.0%

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

   3. Taylor expanded in z around 0 42.9%

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

4. Final simplification 32.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.000185 \lor \neg \left(z \leq 2900000\right):\\ \;\;\;\;\frac{a}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 25.4% accurate, 17.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 71.0%

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

3. Taylor expanded in z around 0 23.1%

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

Developer Target 1: 73.2% 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 2024135 
(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)))))