Development.Shake.Progress:decay from shake-0.15.5

Percentage Accurate: 66.4% → 90.1%

Time: 19.8s

Alternatives: 16

Speedup: 0.9×

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: 66.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 90.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := {\left(b - y\right)}^{2}\\ t_2 := \frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;\frac{\frac{z}{z + -1} \cdot \left(a - t\right) - \frac{b}{\frac{{\left(z + -1\right)}^{2}}{x \cdot z}}}{y} - \frac{x}{z + -1}\\ \mathbf{elif}\;t_2 \leq -5 \cdot 10^{-258}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;\left(\left(\frac{t}{b - y} + \frac{\frac{x \cdot y}{z}}{b - y}\right) - \frac{a}{b - y}\right) + \frac{y}{z} \cdot \frac{a - t}{t_1}\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+291}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{\frac{b - y}{y}} - \frac{y}{\frac{t_1}{t - a}}}{z} + \frac{t - a}{b - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (pow (- b y) 2.0))
        (t_2 (/ (+ (* z (- t a)) (* x y)) (+ y (* z (- b y))))))
   (if (<= t_2 (- INFINITY))
     (-
      (/
       (- (* (/ z (+ z -1.0)) (- a t)) (/ b (/ (pow (+ z -1.0) 2.0) (* x z))))
       y)
      (/ x (+ z -1.0)))
     (if (<= t_2 -5e-258)
       t_2
       (if (<= t_2 0.0)
         (+
          (- (+ (/ t (- b y)) (/ (/ (* x y) z) (- b y))) (/ a (- b y)))
          (* (/ y z) (/ (- a t) t_1)))
         (if (<= t_2 5e+291)
           t_2
           (+
            (/ (- (/ x (/ (- b y) y)) (/ y (/ t_1 (- t a)))) z)
            (/ (- t a) (- b y)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = pow((b - y), 2.0);
	double t_2 = ((z * (t - a)) + (x * y)) / (y + (z * (b - y)));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = ((((z / (z + -1.0)) * (a - t)) - (b / (pow((z + -1.0), 2.0) / (x * z)))) / y) - (x / (z + -1.0));
	} else if (t_2 <= -5e-258) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = (((t / (b - y)) + (((x * y) / z) / (b - y))) - (a / (b - y))) + ((y / z) * ((a - t) / t_1));
	} else if (t_2 <= 5e+291) {
		tmp = t_2;
	} else {
		tmp = (((x / ((b - y) / y)) - (y / (t_1 / (t - a)))) / z) + ((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 = Math.pow((b - y), 2.0);
	double t_2 = ((z * (t - a)) + (x * y)) / (y + (z * (b - y)));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = ((((z / (z + -1.0)) * (a - t)) - (b / (Math.pow((z + -1.0), 2.0) / (x * z)))) / y) - (x / (z + -1.0));
	} else if (t_2 <= -5e-258) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = (((t / (b - y)) + (((x * y) / z) / (b - y))) - (a / (b - y))) + ((y / z) * ((a - t) / t_1));
	} else if (t_2 <= 5e+291) {
		tmp = t_2;
	} else {
		tmp = (((x / ((b - y) / y)) - (y / (t_1 / (t - a)))) / z) + ((t - a) / (b - y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = math.pow((b - y), 2.0)
	t_2 = ((z * (t - a)) + (x * y)) / (y + (z * (b - y)))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = ((((z / (z + -1.0)) * (a - t)) - (b / (math.pow((z + -1.0), 2.0) / (x * z)))) / y) - (x / (z + -1.0))
	elif t_2 <= -5e-258:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = (((t / (b - y)) + (((x * y) / z) / (b - y))) - (a / (b - y))) + ((y / z) * ((a - t) / t_1))
	elif t_2 <= 5e+291:
		tmp = t_2
	else:
		tmp = (((x / ((b - y) / y)) - (y / (t_1 / (t - a)))) / z) + ((t - a) / (b - y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b - y) ^ 2.0
	t_2 = Float64(Float64(Float64(z * Float64(t - a)) + Float64(x * y)) / Float64(y + Float64(z * Float64(b - y))))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(Float64(Float64(Float64(Float64(z / Float64(z + -1.0)) * Float64(a - t)) - Float64(b / Float64((Float64(z + -1.0) ^ 2.0) / Float64(x * z)))) / y) - Float64(x / Float64(z + -1.0)));
	elseif (t_2 <= -5e-258)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = Float64(Float64(Float64(Float64(t / Float64(b - y)) + Float64(Float64(Float64(x * y) / z) / Float64(b - y))) - Float64(a / Float64(b - y))) + Float64(Float64(y / z) * Float64(Float64(a - t) / t_1)));
	elseif (t_2 <= 5e+291)
		tmp = t_2;
	else
		tmp = Float64(Float64(Float64(Float64(x / Float64(Float64(b - y) / y)) - Float64(y / Float64(t_1 / Float64(t - a)))) / z) + Float64(Float64(t - a) / Float64(b - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (b - y) ^ 2.0;
	t_2 = ((z * (t - a)) + (x * y)) / (y + (z * (b - y)));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = ((((z / (z + -1.0)) * (a - t)) - (b / (((z + -1.0) ^ 2.0) / (x * z)))) / y) - (x / (z + -1.0));
	elseif (t_2 <= -5e-258)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = (((t / (b - y)) + (((x * y) / z) / (b - y))) - (a / (b - y))) + ((y / z) * ((a - t) / t_1));
	elseif (t_2 <= 5e+291)
		tmp = t_2;
	else
		tmp = (((x / ((b - y) / y)) - (y / (t_1 / (t - a)))) / z) + ((t - a) / (b - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(N[(N[(N[(N[(z / N[(z + -1.0), $MachinePrecision]), $MachinePrecision] * N[(a - t), $MachinePrecision]), $MachinePrecision] - N[(b / N[(N[Power[N[(z + -1.0), $MachinePrecision], 2.0], $MachinePrecision] / N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] - N[(x / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, -5e-258], t$95$2, If[LessEqual[t$95$2, 0.0], N[(N[(N[(N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y / z), $MachinePrecision] * N[(N[(a - t), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+291], t$95$2, N[(N[(N[(N[(x / N[(N[(b - y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] - N[(y / N[(t$95$1 / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] + N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

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

   1. Initial program 17.2%

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

   3. Taylor expanded in y around -inf 47.9%

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

      1. mul-1-neg 47.9%

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

      2. unsub-neg 47.9%

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

      3. associate-*r/ 47.9%

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

      4. neg-mul-1 47.9%

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

      5. sub-neg 47.9%

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

      6. metadata-eval 47.9%

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

   5. Simplified 69.7%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -4.9999999999999999e-258 or -0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 5.0000000000000001e291

   1. Initial program 99.3%

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

   if -4.9999999999999999e-258 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -0.0

   1. Initial program 29.4%

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

   3. Taylor expanded in z around inf 59.0%

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

      1. associate--r+ 59.0%

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

      2. associate-/r* 89.1%

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

      3. *-commutative 89.1%

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

      4. times-frac 96.2%

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

   5. Simplified 96.2%

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

   if 5.0000000000000001e291 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 9.7%

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

   3. Taylor expanded in z around -inf 39.4%

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

      1. associate--l+ 39.4%

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

      2. mul-1-neg 39.4%

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

      3. distribute-lft-out-- 39.4%

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

      4. associate-/l* 48.7%

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

      5. associate-/l* 85.0%

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

      6. div-sub 85.0%

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

   5. Simplified 85.0%

      \[\leadsto \color{blue}{\left(-\frac{-1 \cdot \left(\frac{x}{\frac{b - y}{y}} - \frac{y}{\frac{{\left(b - y\right)}^{2}}{t - a}}\right)}{z}\right) + \frac{t - a}{b - y}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;\frac{\frac{z}{z + -1} \cdot \left(a - t\right) - \frac{b}{\frac{{\left(z + -1\right)}^{2}}{x \cdot z}}}{y} - \frac{x}{z + -1}\\ \mathbf{elif}\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)} \leq -5 \cdot 10^{-258}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)} \leq 0:\\ \;\;\;\;\left(\left(\frac{t}{b - y} + \frac{\frac{x \cdot y}{z}}{b - y}\right) - \frac{a}{b - y}\right) + \frac{y}{z} \cdot \frac{a - t}{{\left(b - y\right)}^{2}}\\ \mathbf{elif}\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)} \leq 5 \cdot 10^{+291}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{\frac{b - y}{y}} - \frac{y}{\frac{{\left(b - y\right)}^{2}}{t - a}}}{z} + \frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 89.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\frac{\frac{z}{z + -1} \cdot \left(a - t\right) - \frac{b}{\frac{{\left(z + -1\right)}^{2}}{x \cdot z}}}{y} - \frac{x}{z + -1}\\ \mathbf{elif}\;t_1 \leq -2 \cdot 10^{-268} \lor \neg \left(t_1 \leq 0\right) \land t_1 \leq 5 \cdot 10^{+291}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{t - a}{b - y} + \frac{x}{\frac{z}{\frac{y}{b - y}}}\right) + \frac{y}{z} \cdot \frac{a - t}{{\left(b - y\right)}^{2}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ (* z (- t a)) (* x y)) (+ y (* z (- b y))))))
   (if (<= t_1 (- INFINITY))
     (-
      (/
       (- (* (/ z (+ z -1.0)) (- a t)) (/ b (/ (pow (+ z -1.0) 2.0) (* x z))))
       y)
      (/ x (+ z -1.0)))
     (if (or (<= t_1 -2e-268) (and (not (<= t_1 0.0)) (<= t_1 5e+291)))
       t_1
       (+
        (+ (/ (- t a) (- b y)) (/ x (/ z (/ y (- b y)))))
        (* (/ y z) (/ (- a t) (pow (- b y) 2.0))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((z * (t - a)) + (x * y)) / (y + (z * (b - y)));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = ((((z / (z + -1.0)) * (a - t)) - (b / (pow((z + -1.0), 2.0) / (x * z)))) / y) - (x / (z + -1.0));
	} else if ((t_1 <= -2e-268) || (!(t_1 <= 0.0) && (t_1 <= 5e+291))) {
		tmp = t_1;
	} else {
		tmp = (((t - a) / (b - y)) + (x / (z / (y / (b - y))))) + ((y / z) * ((a - t) / pow((b - y), 2.0)));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((z * (t - a)) + (x * y)) / (y + (z * (b - y)));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = ((((z / (z + -1.0)) * (a - t)) - (b / (Math.pow((z + -1.0), 2.0) / (x * z)))) / y) - (x / (z + -1.0));
	} else if ((t_1 <= -2e-268) || (!(t_1 <= 0.0) && (t_1 <= 5e+291))) {
		tmp = t_1;
	} else {
		tmp = (((t - a) / (b - y)) + (x / (z / (y / (b - y))))) + ((y / z) * ((a - t) / Math.pow((b - y), 2.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((z * (t - a)) + (x * y)) / (y + (z * (b - y)))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = ((((z / (z + -1.0)) * (a - t)) - (b / (math.pow((z + -1.0), 2.0) / (x * z)))) / y) - (x / (z + -1.0))
	elif (t_1 <= -2e-268) or (not (t_1 <= 0.0) and (t_1 <= 5e+291)):
		tmp = t_1
	else:
		tmp = (((t - a) / (b - y)) + (x / (z / (y / (b - y))))) + ((y / z) * ((a - t) / math.pow((b - y), 2.0)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(z * Float64(t - a)) + Float64(x * y)) / Float64(y + Float64(z * Float64(b - y))))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(Float64(Float64(Float64(z / Float64(z + -1.0)) * Float64(a - t)) - Float64(b / Float64((Float64(z + -1.0) ^ 2.0) / Float64(x * z)))) / y) - Float64(x / Float64(z + -1.0)));
	elseif ((t_1 <= -2e-268) || (!(t_1 <= 0.0) && (t_1 <= 5e+291)))
		tmp = t_1;
	else
		tmp = Float64(Float64(Float64(Float64(t - a) / Float64(b - y)) + Float64(x / Float64(z / Float64(y / Float64(b - y))))) + Float64(Float64(y / z) * Float64(Float64(a - t) / (Float64(b - y) ^ 2.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((z * (t - a)) + (x * y)) / (y + (z * (b - y)));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = ((((z / (z + -1.0)) * (a - t)) - (b / (((z + -1.0) ^ 2.0) / (x * z)))) / y) - (x / (z + -1.0));
	elseif ((t_1 <= -2e-268) || (~((t_1 <= 0.0)) && (t_1 <= 5e+291)))
		tmp = t_1;
	else
		tmp = (((t - a) / (b - y)) + (x / (z / (y / (b - y))))) + ((y / z) * ((a - t) / ((b - y) ^ 2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(N[(N[(N[(z / N[(z + -1.0), $MachinePrecision]), $MachinePrecision] * N[(a - t), $MachinePrecision]), $MachinePrecision] - N[(b / N[(N[Power[N[(z + -1.0), $MachinePrecision], 2.0], $MachinePrecision] / N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] - N[(x / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t$95$1, -2e-268], And[N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision], LessEqual[t$95$1, 5e+291]]], t$95$1, N[(N[(N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision] + N[(x / N[(z / N[(y / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y / z), $MachinePrecision] * N[(N[(a - t), $MachinePrecision] / N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $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 17.2%

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

   3. Taylor expanded in y around -inf 47.9%

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

      1. mul-1-neg 47.9%

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

      2. unsub-neg 47.9%

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

      3. associate-*r/ 47.9%

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

      4. neg-mul-1 47.9%

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

      5. sub-neg 47.9%

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

      6. metadata-eval 47.9%

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

   5. Simplified 69.7%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -1.99999999999999992e-268 or -0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 5.0000000000000001e291

   1. Initial program 99.3%

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

   if -1.99999999999999992e-268 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -0.0 or 5.0000000000000001e291 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 15.5%

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

   3. Taylor expanded in z around inf 45.4%

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

      1. associate--r+ 45.4%

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

      2. +-commutative 45.4%

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

      3. associate--l+ 45.4%

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

      4. associate-/l* 50.4%

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

      5. associate-/l* 58.7%

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

      6. div-sub 58.7%

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

      7. times-frac 82.6%

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

   5. Simplified 82.6%

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

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;\frac{\frac{z}{z + -1} \cdot \left(a - t\right) - \frac{b}{\frac{{\left(z + -1\right)}^{2}}{x \cdot z}}}{y} - \frac{x}{z + -1}\\ \mathbf{elif}\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)} \leq -2 \cdot 10^{-268} \lor \neg \left(\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)} \leq 0\right) \land \frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)} \leq 5 \cdot 10^{+291}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{t - a}{b - y} + \frac{x}{\frac{z}{\frac{y}{b - y}}}\right) + \frac{y}{z} \cdot \frac{a - t}{{\left(b - y\right)}^{2}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 90.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\frac{\frac{z}{z + -1} \cdot \left(a - t\right) - \frac{b}{\frac{{\left(z + -1\right)}^{2}}{x \cdot z}}}{y} - \frac{x}{z + -1}\\ \mathbf{elif}\;t_1 \leq -2 \cdot 10^{-268} \lor \neg \left(t_1 \leq 0\right) \land t_1 \leq 5 \cdot 10^{+291}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{\frac{b - y}{y}} - \frac{y}{\frac{{\left(b - y\right)}^{2}}{t - a}}}{z} + \frac{t - a}{b - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ (* z (- t a)) (* x y)) (+ y (* z (- b y))))))
   (if (<= t_1 (- INFINITY))
     (-
      (/
       (- (* (/ z (+ z -1.0)) (- a t)) (/ b (/ (pow (+ z -1.0) 2.0) (* x z))))
       y)
      (/ x (+ z -1.0)))
     (if (or (<= t_1 -2e-268) (and (not (<= t_1 0.0)) (<= t_1 5e+291)))
       t_1
       (+
        (/ (- (/ x (/ (- b y) y)) (/ y (/ (pow (- b y) 2.0) (- t a)))) z)
        (/ (- t a) (- b y)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((z * (t - a)) + (x * y)) / (y + (z * (b - y)));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = ((((z / (z + -1.0)) * (a - t)) - (b / (pow((z + -1.0), 2.0) / (x * z)))) / y) - (x / (z + -1.0));
	} else if ((t_1 <= -2e-268) || (!(t_1 <= 0.0) && (t_1 <= 5e+291))) {
		tmp = t_1;
	} else {
		tmp = (((x / ((b - y) / y)) - (y / (pow((b - y), 2.0) / (t - a)))) / z) + ((t - a) / (b - y));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((z * (t - a)) + (x * y)) / (y + (z * (b - y)));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = ((((z / (z + -1.0)) * (a - t)) - (b / (Math.pow((z + -1.0), 2.0) / (x * z)))) / y) - (x / (z + -1.0));
	} else if ((t_1 <= -2e-268) || (!(t_1 <= 0.0) && (t_1 <= 5e+291))) {
		tmp = t_1;
	} else {
		tmp = (((x / ((b - y) / y)) - (y / (Math.pow((b - y), 2.0) / (t - a)))) / z) + ((t - a) / (b - y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((z * (t - a)) + (x * y)) / (y + (z * (b - y)))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = ((((z / (z + -1.0)) * (a - t)) - (b / (math.pow((z + -1.0), 2.0) / (x * z)))) / y) - (x / (z + -1.0))
	elif (t_1 <= -2e-268) or (not (t_1 <= 0.0) and (t_1 <= 5e+291)):
		tmp = t_1
	else:
		tmp = (((x / ((b - y) / y)) - (y / (math.pow((b - y), 2.0) / (t - a)))) / z) + ((t - a) / (b - y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(z * Float64(t - a)) + Float64(x * y)) / Float64(y + Float64(z * Float64(b - y))))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(Float64(Float64(Float64(z / Float64(z + -1.0)) * Float64(a - t)) - Float64(b / Float64((Float64(z + -1.0) ^ 2.0) / Float64(x * z)))) / y) - Float64(x / Float64(z + -1.0)));
	elseif ((t_1 <= -2e-268) || (!(t_1 <= 0.0) && (t_1 <= 5e+291)))
		tmp = t_1;
	else
		tmp = Float64(Float64(Float64(Float64(x / Float64(Float64(b - y) / y)) - Float64(y / Float64((Float64(b - y) ^ 2.0) / Float64(t - a)))) / z) + Float64(Float64(t - a) / Float64(b - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((z * (t - a)) + (x * y)) / (y + (z * (b - y)));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = ((((z / (z + -1.0)) * (a - t)) - (b / (((z + -1.0) ^ 2.0) / (x * z)))) / y) - (x / (z + -1.0));
	elseif ((t_1 <= -2e-268) || (~((t_1 <= 0.0)) && (t_1 <= 5e+291)))
		tmp = t_1;
	else
		tmp = (((x / ((b - y) / y)) - (y / (((b - y) ^ 2.0) / (t - a)))) / z) + ((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[(t - a), $MachinePrecision]), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(N[(N[(N[(z / N[(z + -1.0), $MachinePrecision]), $MachinePrecision] * N[(a - t), $MachinePrecision]), $MachinePrecision] - N[(b / N[(N[Power[N[(z + -1.0), $MachinePrecision], 2.0], $MachinePrecision] / N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] - N[(x / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t$95$1, -2e-268], And[N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision], LessEqual[t$95$1, 5e+291]]], t$95$1, N[(N[(N[(N[(x / N[(N[(b - y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] - N[(y / N[(N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] + N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $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 17.2%

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

   3. Taylor expanded in y around -inf 47.9%

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

      1. mul-1-neg 47.9%

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

      2. unsub-neg 47.9%

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

      3. associate-*r/ 47.9%

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

      4. neg-mul-1 47.9%

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

      5. sub-neg 47.9%

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

      6. metadata-eval 47.9%

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

   5. Simplified 69.7%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -1.99999999999999992e-268 or -0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 5.0000000000000001e291

   1. Initial program 99.3%

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

   if -1.99999999999999992e-268 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -0.0 or 5.0000000000000001e291 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 15.5%

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

   3. Taylor expanded in z around -inf 56.2%

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

      1. associate--l+ 56.2%

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

      2. mul-1-neg 56.2%

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

      3. distribute-lft-out-- 56.2%

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

      4. associate-/l* 62.4%

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

      5. associate-/l* 88.8%

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

      6. div-sub 88.7%

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

   5. Simplified 88.7%

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

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;\frac{\frac{z}{z + -1} \cdot \left(a - t\right) - \frac{b}{\frac{{\left(z + -1\right)}^{2}}{x \cdot z}}}{y} - \frac{x}{z + -1}\\ \mathbf{elif}\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)} \leq -2 \cdot 10^{-268} \lor \neg \left(\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)} \leq 0\right) \land \frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)} \leq 5 \cdot 10^{+291}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{\frac{b - y}{y}} - \frac{y}{\frac{{\left(b - y\right)}^{2}}{t - a}}}{z} + \frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\frac{\frac{z}{z + -1} \cdot \left(a - t\right) - \frac{b}{\frac{{\left(z + -1\right)}^{2}}{x \cdot z}}}{y} - \frac{x}{z + -1}\\ \mathbf{elif}\;t_1 \leq -2 \cdot 10^{-268}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+286}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{a - t}{y \cdot z} - \left(\frac{a - t}{b - y} - \frac{x}{\frac{z}{\frac{y}{b - y}}}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ (* z (- t a)) (* x y)) (+ y (* z (- b y))))))
   (if (<= t_1 (- INFINITY))
     (-
      (/
       (- (* (/ z (+ z -1.0)) (- a t)) (/ b (/ (pow (+ z -1.0) 2.0) (* x z))))
       y)
      (/ x (+ z -1.0)))
     (if (<= t_1 -2e-268)
       t_1
       (if (<= t_1 0.0)
         (/ (- t a) (- b y))
         (if (<= t_1 2e+286)
           t_1
           (-
            (/ (- a t) (* y z))
            (- (/ (- a t) (- b y)) (/ x (/ z (/ y (- b y))))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((z * (t - a)) + (x * y)) / (y + (z * (b - y)));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = ((((z / (z + -1.0)) * (a - t)) - (b / (pow((z + -1.0), 2.0) / (x * z)))) / y) - (x / (z + -1.0));
	} else if (t_1 <= -2e-268) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = (t - a) / (b - y);
	} else if (t_1 <= 2e+286) {
		tmp = t_1;
	} else {
		tmp = ((a - t) / (y * z)) - (((a - t) / (b - y)) - (x / (z / (y / (b - y)))));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((z * (t - a)) + (x * y)) / (y + (z * (b - y)));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = ((((z / (z + -1.0)) * (a - t)) - (b / (Math.pow((z + -1.0), 2.0) / (x * z)))) / y) - (x / (z + -1.0));
	} else if (t_1 <= -2e-268) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = (t - a) / (b - y);
	} else if (t_1 <= 2e+286) {
		tmp = t_1;
	} else {
		tmp = ((a - t) / (y * z)) - (((a - t) / (b - y)) - (x / (z / (y / (b - y)))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((z * (t - a)) + (x * y)) / (y + (z * (b - y)))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = ((((z / (z + -1.0)) * (a - t)) - (b / (math.pow((z + -1.0), 2.0) / (x * z)))) / y) - (x / (z + -1.0))
	elif t_1 <= -2e-268:
		tmp = t_1
	elif t_1 <= 0.0:
		tmp = (t - a) / (b - y)
	elif t_1 <= 2e+286:
		tmp = t_1
	else:
		tmp = ((a - t) / (y * z)) - (((a - t) / (b - y)) - (x / (z / (y / (b - y)))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(z * Float64(t - a)) + Float64(x * y)) / Float64(y + Float64(z * Float64(b - y))))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(Float64(Float64(Float64(z / Float64(z + -1.0)) * Float64(a - t)) - Float64(b / Float64((Float64(z + -1.0) ^ 2.0) / Float64(x * z)))) / y) - Float64(x / Float64(z + -1.0)));
	elseif (t_1 <= -2e-268)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(t - a) / Float64(b - y));
	elseif (t_1 <= 2e+286)
		tmp = t_1;
	else
		tmp = Float64(Float64(Float64(a - t) / Float64(y * z)) - Float64(Float64(Float64(a - t) / Float64(b - y)) - Float64(x / Float64(z / Float64(y / Float64(b - y))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((z * (t - a)) + (x * y)) / (y + (z * (b - y)));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = ((((z / (z + -1.0)) * (a - t)) - (b / (((z + -1.0) ^ 2.0) / (x * z)))) / y) - (x / (z + -1.0));
	elseif (t_1 <= -2e-268)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = (t - a) / (b - y);
	elseif (t_1 <= 2e+286)
		tmp = t_1;
	else
		tmp = ((a - t) / (y * z)) - (((a - t) / (b - y)) - (x / (z / (y / (b - y)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(N[(N[(N[(z / N[(z + -1.0), $MachinePrecision]), $MachinePrecision] * N[(a - t), $MachinePrecision]), $MachinePrecision] - N[(b / N[(N[Power[N[(z + -1.0), $MachinePrecision], 2.0], $MachinePrecision] / N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] - N[(x / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -2e-268], t$95$1, If[LessEqual[t$95$1, 0.0], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+286], t$95$1, N[(N[(N[(a - t), $MachinePrecision] / N[(y * z), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(a - t), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision] - N[(x / N[(z / N[(y / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

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

   1. Initial program 17.2%

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

   3. Taylor expanded in y around -inf 47.9%

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

      1. mul-1-neg 47.9%

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

      2. unsub-neg 47.9%

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

      3. associate-*r/ 47.9%

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

      4. neg-mul-1 47.9%

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

      5. sub-neg 47.9%

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

      6. metadata-eval 47.9%

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

   5. Simplified 69.7%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -1.99999999999999992e-268 or -0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 2.00000000000000007e286

   1. Initial program 99.3%

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

   if -1.99999999999999992e-268 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -0.0

   1. Initial program 26.8%

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

   3. Taylor expanded in z around inf 64.9%

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

   if 2.00000000000000007e286 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 13.0%

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

   3. Taylor expanded in z around inf 37.9%

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

      1. associate--r+ 37.9%

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

      2. +-commutative 37.9%

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

      3. associate--l+ 37.9%

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

      4. associate-/l* 45.2%

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

      5. associate-/l* 46.9%

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

      6. div-sub 46.9%

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

      7. times-frac 77.9%

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

   5. Simplified 77.9%

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

   6. Taylor expanded in y around inf 79.7%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;\frac{\frac{z}{z + -1} \cdot \left(a - t\right) - \frac{b}{\frac{{\left(z + -1\right)}^{2}}{x \cdot z}}}{y} - \frac{x}{z + -1}\\ \mathbf{elif}\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)} \leq -2 \cdot 10^{-268}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)} \leq 0:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)} \leq 2 \cdot 10^{+286}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{a - t}{y \cdot z} - \left(\frac{a - t}{b - y} - \frac{x}{\frac{z}{\frac{y}{b - y}}}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 83.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;y \cdot \frac{x}{\mathsf{fma}\left(z, b - y, y\right)}\\ \mathbf{elif}\;t_1 \leq -2 \cdot 10^{-268}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+286}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{a - t}{y \cdot z} - \left(\frac{a - t}{b - y} - \frac{x}{\frac{z}{\frac{y}{b - y}}}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ (* z (- t a)) (* x y)) (+ y (* z (- b y))))))
   (if (<= t_1 (- INFINITY))
     (* y (/ x (fma z (- b y) y)))
     (if (<= t_1 -2e-268)
       t_1
       (if (<= t_1 0.0)
         (/ (- t a) (- b y))
         (if (<= t_1 2e+286)
           t_1
           (-
            (/ (- a t) (* y z))
            (- (/ (- a t) (- b y)) (/ x (/ z (/ y (- b y))))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((z * (t - a)) + (x * y)) / (y + (z * (b - y)));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = y * (x / fma(z, (b - y), y));
	} else if (t_1 <= -2e-268) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = (t - a) / (b - y);
	} else if (t_1 <= 2e+286) {
		tmp = t_1;
	} else {
		tmp = ((a - t) / (y * z)) - (((a - t) / (b - y)) - (x / (z / (y / (b - y)))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(z * Float64(t - a)) + Float64(x * y)) / Float64(y + Float64(z * Float64(b - y))))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(y * Float64(x / fma(z, Float64(b - y), y)));
	elseif (t_1 <= -2e-268)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(t - a) / Float64(b - y));
	elseif (t_1 <= 2e+286)
		tmp = t_1;
	else
		tmp = Float64(Float64(Float64(a - t) / Float64(y * z)) - Float64(Float64(Float64(a - t) / Float64(b - y)) - Float64(x / Float64(z / Float64(y / Float64(b - y))))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(y * N[(x / N[(z * N[(b - y), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -2e-268], t$95$1, If[LessEqual[t$95$1, 0.0], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+286], t$95$1, N[(N[(N[(a - t), $MachinePrecision] / N[(y * z), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(a - t), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision] - N[(x / N[(z / N[(y / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

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

   1. Initial program 17.2%

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

   3. Taylor expanded in x around inf 4.6%

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

      1. associate-/l* 58.4%

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

      2. +-commutative 58.4%

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

      3. fma-udef 58.4%

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

      4. associate-/r/ 61.9%

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

   5. Simplified 61.9%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -1.99999999999999992e-268 or -0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 2.00000000000000007e286

   1. Initial program 99.3%

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

   if -1.99999999999999992e-268 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -0.0

   1. Initial program 26.8%

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

   3. Taylor expanded in z around inf 64.9%

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

   if 2.00000000000000007e286 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 13.0%

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

   3. Taylor expanded in z around inf 37.9%

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

      1. associate--r+ 37.9%

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

      2. +-commutative 37.9%

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

      3. associate--l+ 37.9%

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

      4. associate-/l* 45.2%

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

      5. associate-/l* 46.9%

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

      6. div-sub 46.9%

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

      7. times-frac 77.9%

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

   5. Simplified 77.9%

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

   6. Taylor expanded in y around inf 79.7%

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

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;y \cdot \frac{x}{\mathsf{fma}\left(z, b - y, y\right)}\\ \mathbf{elif}\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)} \leq -2 \cdot 10^{-268}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)} \leq 0:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)} \leq 2 \cdot 10^{+286}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{a - t}{y \cdot z} - \left(\frac{a - t}{b - y} - \frac{x}{\frac{z}{\frac{y}{b - y}}}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 81.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{+40}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq 410000000000:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{a - t}{y \cdot z} - \left(\frac{a - t}{b - y} - \frac{x}{\frac{z}{\frac{y}{b - y}}}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -2.15e+40)
   (/ (- t a) (- b y))
   (if (<= z 410000000000.0)
     (/ (+ (* z (- t a)) (* x y)) (+ y (* z (- b y))))
     (-
      (/ (- a t) (* y z))
      (- (/ (- a t) (- b y)) (/ x (/ z (/ y (- b y)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2.15e+40) {
		tmp = (t - a) / (b - y);
	} else if (z <= 410000000000.0) {
		tmp = ((z * (t - a)) + (x * y)) / (y + (z * (b - y)));
	} else {
		tmp = ((a - t) / (y * z)) - (((a - t) / (b - y)) - (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 <= (-2.15d+40)) then
        tmp = (t - a) / (b - y)
    else if (z <= 410000000000.0d0) then
        tmp = ((z * (t - a)) + (x * y)) / (y + (z * (b - y)))
    else
        tmp = ((a - t) / (y * z)) - (((a - t) / (b - y)) - (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 <= -2.15e+40) {
		tmp = (t - a) / (b - y);
	} else if (z <= 410000000000.0) {
		tmp = ((z * (t - a)) + (x * y)) / (y + (z * (b - y)));
	} else {
		tmp = ((a - t) / (y * z)) - (((a - t) / (b - y)) - (x / (z / (y / (b - y)))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -2.15e+40:
		tmp = (t - a) / (b - y)
	elif z <= 410000000000.0:
		tmp = ((z * (t - a)) + (x * y)) / (y + (z * (b - y)))
	else:
		tmp = ((a - t) / (y * z)) - (((a - t) / (b - y)) - (x / (z / (y / (b - y)))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -2.15e+40)
		tmp = Float64(Float64(t - a) / Float64(b - y));
	elseif (z <= 410000000000.0)
		tmp = Float64(Float64(Float64(z * Float64(t - a)) + Float64(x * y)) / Float64(y + Float64(z * Float64(b - y))));
	else
		tmp = Float64(Float64(Float64(a - t) / Float64(y * z)) - Float64(Float64(Float64(a - t) / Float64(b - y)) - Float64(x / Float64(z / Float64(y / Float64(b - y))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -2.15e+40)
		tmp = (t - a) / (b - y);
	elseif (z <= 410000000000.0)
		tmp = ((z * (t - a)) + (x * y)) / (y + (z * (b - y)));
	else
		tmp = ((a - t) / (y * z)) - (((a - t) / (b - y)) - (x / (z / (y / (b - y)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -2.15e+40], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 410000000000.0], N[(N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(a - t), $MachinePrecision] / N[(y * z), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(a - t), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision] - N[(x / N[(z / N[(y / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.1500000000000001e40

   1. Initial program 39.1%

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

   3. Taylor expanded in z around inf 81.8%

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

   if -2.1500000000000001e40 < z < 4.1e11

   1. Initial program 86.5%

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

   if 4.1e11 < z

   1. Initial program 41.7%

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

   3. Taylor expanded in z around inf 57.4%

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

      1. associate--r+ 57.4%

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

      2. +-commutative 57.4%

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

      3. associate--l+ 57.4%

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

      4. associate-/l* 60.7%

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

      5. associate-/l* 67.0%

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

      6. div-sub 67.0%

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

      7. times-frac 83.5%

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

   5. Simplified 83.5%

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

   6. Taylor expanded in y around inf 86.4%

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

4. Final simplification 85.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{+40}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq 410000000000:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{a - t}{y \cdot z} - \left(\frac{a - t}{b - y} - \frac{x}{\frac{z}{\frac{y}{b - y}}}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 66.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -3.7 \cdot 10^{+15}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-120}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{t_1}\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-263}:\\ \;\;\;\;\frac{x \cdot y}{t_1}\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-138}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.6:\\ \;\;\;\;\frac{t + \left(\frac{x}{\frac{z}{y}} - a\right)}{b}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

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 -3.7e+15)
     t_2
     (if (<= z -4.5e-120)
       (/ (* z (- t a)) t_1)
       (if (<= z -4e-263)
         (/ (* x y) t_1)
         (if (<= z 4.8e-138)
           x
           (if (<= z 2.6) (/ (+ t (- (/ x (/ z y)) a)) b) 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 <= -3.7e+15) {
		tmp = t_2;
	} else if (z <= -4.5e-120) {
		tmp = (z * (t - a)) / t_1;
	} else if (z <= -4e-263) {
		tmp = (x * y) / t_1;
	} else if (z <= 4.8e-138) {
		tmp = x;
	} else if (z <= 2.6) {
		tmp = (t + ((x / (z / y)) - a)) / b;
	} 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 <= (-3.7d+15)) then
        tmp = t_2
    else if (z <= (-4.5d-120)) then
        tmp = (z * (t - a)) / t_1
    else if (z <= (-4d-263)) then
        tmp = (x * y) / t_1
    else if (z <= 4.8d-138) then
        tmp = x
    else if (z <= 2.6d0) then
        tmp = (t + ((x / (z / y)) - a)) / b
    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 <= -3.7e+15) {
		tmp = t_2;
	} else if (z <= -4.5e-120) {
		tmp = (z * (t - a)) / t_1;
	} else if (z <= -4e-263) {
		tmp = (x * y) / t_1;
	} else if (z <= 4.8e-138) {
		tmp = x;
	} else if (z <= 2.6) {
		tmp = (t + ((x / (z / y)) - a)) / b;
	} 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 <= -3.7e+15:
		tmp = t_2
	elif z <= -4.5e-120:
		tmp = (z * (t - a)) / t_1
	elif z <= -4e-263:
		tmp = (x * y) / t_1
	elif z <= 4.8e-138:
		tmp = x
	elif z <= 2.6:
		tmp = (t + ((x / (z / y)) - a)) / b
	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 <= -3.7e+15)
		tmp = t_2;
	elseif (z <= -4.5e-120)
		tmp = Float64(Float64(z * Float64(t - a)) / t_1);
	elseif (z <= -4e-263)
		tmp = Float64(Float64(x * y) / t_1);
	elseif (z <= 4.8e-138)
		tmp = x;
	elseif (z <= 2.6)
		tmp = Float64(Float64(t + Float64(Float64(x / Float64(z / y)) - a)) / b);
	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 <= -3.7e+15)
		tmp = t_2;
	elseif (z <= -4.5e-120)
		tmp = (z * (t - a)) / t_1;
	elseif (z <= -4e-263)
		tmp = (x * y) / t_1;
	elseif (z <= 4.8e-138)
		tmp = x;
	elseif (z <= 2.6)
		tmp = (t + ((x / (z / y)) - a)) / b;
	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, -3.7e+15], t$95$2, If[LessEqual[z, -4.5e-120], N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[z, -4e-263], N[(N[(x * y), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[z, 4.8e-138], x, If[LessEqual[z, 2.6], N[(N[(t + N[(N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -3.7e15 or 2.60000000000000009 < z

   1. Initial program 42.5%

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

   3. Taylor expanded in z around inf 77.9%

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

   if -3.7e15 < z < -4.5e-120

   1. Initial program 88.1%

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

   3. Taylor expanded in x around 0 59.2%

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

   if -4.5e-120 < z < -4e-263

   1. Initial program 93.5%

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

   3. Taylor expanded in x around inf 64.9%

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

      1. *-commutative 64.9%

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

   5. Simplified 64.9%

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

   if -4e-263 < z < 4.7999999999999998e-138

   1. Initial program 78.3%

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

   3. Taylor expanded in z around 0 58.8%

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

   if 4.7999999999999998e-138 < z < 2.60000000000000009

   1. Initial program 92.4%

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

   3. Taylor expanded in y around 0 55.5%

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

      1. associate--l+ 55.5%

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

      2. associate-/r* 55.5%

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

      3. times-frac 51.5%

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

      4. mul-1-neg 51.5%

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

      5. div-sub 51.5%

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

   5. Simplified 51.5%

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

   6. Taylor expanded in b around inf 66.6%

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

      1. associate--l+ 66.6%

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

      2. associate-/l* 66.6%

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

   8. Simplified 66.6%

      \[\leadsto \color{blue}{\frac{t + \left(\frac{x}{\frac{z}{y}} - a\right)}{b}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{+15}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-120}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-263}:\\ \;\;\;\;\frac{x \cdot y}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-138}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.6:\\ \;\;\;\;\frac{t + \left(\frac{x}{\frac{z}{y}} - a\right)}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 83.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{+39} \lor \neg \left(z \leq 4.8 \cdot 10^{+111}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -3.7e+39) (not (<= z 4.8e+111)))
   (/ (- t a) (- b y))
   (/ (+ (* z (- t a)) (* x y)) (+ y (* z (- b y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -3.7e+39) || !(z <= 4.8e+111)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((z * (t - a)) + (x * y)) / (y + (z * (b - y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-3.7d+39)) .or. (.not. (z <= 4.8d+111))) then
        tmp = (t - a) / (b - y)
    else
        tmp = ((z * (t - a)) + (x * y)) / (y + (z * (b - y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -3.7e+39) || !(z <= 4.8e+111)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((z * (t - a)) + (x * y)) / (y + (z * (b - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -3.7e+39) or not (z <= 4.8e+111):
		tmp = (t - a) / (b - y)
	else:
		tmp = ((z * (t - a)) + (x * y)) / (y + (z * (b - y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -3.7e+39) || !(z <= 4.8e+111))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(Float64(Float64(z * Float64(t - a)) + Float64(x * y)) / Float64(y + Float64(z * Float64(b - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -3.7e+39) || ~((z <= 4.8e+111)))
		tmp = (t - a) / (b - y);
	else
		tmp = ((z * (t - a)) + (x * y)) / (y + (z * (b - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -3.7e+39], N[Not[LessEqual[z, 4.8e+111]], $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 * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.70000000000000012e39 or 4.80000000000000011e111 < z

   1. Initial program 36.4%

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

   3. Taylor expanded in z around inf 82.9%

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

   if -3.70000000000000012e39 < z < 4.80000000000000011e111

   1. Initial program 84.7%

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

4. Final simplification 84.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{+39} \lor \neg \left(z \leq 4.8 \cdot 10^{+111}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 73.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.0043 \lor \neg \left(z \leq 9.5 \cdot 10^{-13}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot a}{y + z \cdot \left(b - y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -0.0043) (not (<= z 9.5e-13)))
   (/ (- t a) (- b y))
   (/ (- (* x y) (* z a)) (+ y (* z (- b y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -0.0043) || !(z <= 9.5e-13)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((x * y) - (z * a)) / (y + (z * (b - y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-0.0043d0)) .or. (.not. (z <= 9.5d-13))) then
        tmp = (t - a) / (b - y)
    else
        tmp = ((x * y) - (z * a)) / (y + (z * (b - y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -0.0043) || !(z <= 9.5e-13)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((x * y) - (z * a)) / (y + (z * (b - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -0.0043) or not (z <= 9.5e-13):
		tmp = (t - a) / (b - y)
	else:
		tmp = ((x * y) - (z * a)) / (y + (z * (b - y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -0.0043) || !(z <= 9.5e-13))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(Float64(Float64(x * y) - Float64(z * a)) / Float64(y + Float64(z * Float64(b - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -0.0043) || ~((z <= 9.5e-13)))
		tmp = (t - a) / (b - y);
	else
		tmp = ((x * y) - (z * a)) / (y + (z * (b - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -0.0043], N[Not[LessEqual[z, 9.5e-13]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] - N[(z * a), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.0043 or 9.49999999999999991e-13 < z

   1. Initial program 45.3%

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

   3. Taylor expanded in z around inf 77.7%

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

   if -0.0043 < z < 9.49999999999999991e-13

   1. Initial program 86.4%

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

   3. Taylor expanded in t around 0 64.6%

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

      1. +-commutative 64.6%

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

      2. mul-1-neg 64.6%

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

      3. unsub-neg 64.6%

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

      4. *-commutative 64.6%

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

      5. *-commutative 64.6%

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

   5. Simplified 64.6%

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

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.0043 \lor \neg \left(z \leq 9.5 \cdot 10^{-13}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot a}{y + z \cdot \left(b - y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 41.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -3.6 \cdot 10^{+50}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{-95}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{-152}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{-274}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-99}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;y \leq 6.1 \cdot 10^{-34}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (- 1.0 z))))
   (if (<= y -3.6e+50)
     t_1
     (if (<= y -2.7e-95)
       (/ t b)
       (if (<= y -8.5e-152)
         t_1
         (if (<= y -1.25e-274)
           (/ t b)
           (if (<= y 1.8e-99)
             (/ (- a) b)
             (if (<= y 6.1e-34) (/ t b) t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 - z);
	double tmp;
	if (y <= -3.6e+50) {
		tmp = t_1;
	} else if (y <= -2.7e-95) {
		tmp = t / b;
	} else if (y <= -8.5e-152) {
		tmp = t_1;
	} else if (y <= -1.25e-274) {
		tmp = t / b;
	} else if (y <= 1.8e-99) {
		tmp = -a / b;
	} else if (y <= 6.1e-34) {
		tmp = t / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (1.0d0 - z)
    if (y <= (-3.6d+50)) then
        tmp = t_1
    else if (y <= (-2.7d-95)) then
        tmp = t / b
    else if (y <= (-8.5d-152)) then
        tmp = t_1
    else if (y <= (-1.25d-274)) then
        tmp = t / b
    else if (y <= 1.8d-99) then
        tmp = -a / b
    else if (y <= 6.1d-34) then
        tmp = t / b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 - z);
	double tmp;
	if (y <= -3.6e+50) {
		tmp = t_1;
	} else if (y <= -2.7e-95) {
		tmp = t / b;
	} else if (y <= -8.5e-152) {
		tmp = t_1;
	} else if (y <= -1.25e-274) {
		tmp = t / b;
	} else if (y <= 1.8e-99) {
		tmp = -a / b;
	} else if (y <= 6.1e-34) {
		tmp = t / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (1.0 - z)
	tmp = 0
	if y <= -3.6e+50:
		tmp = t_1
	elif y <= -2.7e-95:
		tmp = t / b
	elif y <= -8.5e-152:
		tmp = t_1
	elif y <= -1.25e-274:
		tmp = t / b
	elif y <= 1.8e-99:
		tmp = -a / b
	elif y <= 6.1e-34:
		tmp = t / b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(1.0 - z))
	tmp = 0.0
	if (y <= -3.6e+50)
		tmp = t_1;
	elseif (y <= -2.7e-95)
		tmp = Float64(t / b);
	elseif (y <= -8.5e-152)
		tmp = t_1;
	elseif (y <= -1.25e-274)
		tmp = Float64(t / b);
	elseif (y <= 1.8e-99)
		tmp = Float64(Float64(-a) / b);
	elseif (y <= 6.1e-34)
		tmp = Float64(t / b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (1.0 - z);
	tmp = 0.0;
	if (y <= -3.6e+50)
		tmp = t_1;
	elseif (y <= -2.7e-95)
		tmp = t / b;
	elseif (y <= -8.5e-152)
		tmp = t_1;
	elseif (y <= -1.25e-274)
		tmp = t / b;
	elseif (y <= 1.8e-99)
		tmp = -a / b;
	elseif (y <= 6.1e-34)
		tmp = t / b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.6e+50], t$95$1, If[LessEqual[y, -2.7e-95], N[(t / b), $MachinePrecision], If[LessEqual[y, -8.5e-152], t$95$1, If[LessEqual[y, -1.25e-274], N[(t / b), $MachinePrecision], If[LessEqual[y, 1.8e-99], N[((-a) / b), $MachinePrecision], If[LessEqual[y, 6.1e-34], N[(t / b), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.59999999999999986e50 or -2.7e-95 < y < -8.5000000000000007e-152 or 6.0999999999999998e-34 < y

   1. Initial program 49.2%

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

   3. Taylor expanded in y around inf 54.1%

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

      1. mul-1-neg 54.1%

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

      2. unsub-neg 54.1%

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

   5. Simplified 54.1%

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

   if -3.59999999999999986e50 < y < -2.7e-95 or -8.5000000000000007e-152 < y < -1.25e-274 or 1.8e-99 < y < 6.0999999999999998e-34

   1. Initial program 77.8%

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

   3. Taylor expanded in b around inf 51.6%

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

   4. Taylor expanded in t around inf 40.5%

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

   if -1.25e-274 < y < 1.8e-99

   1. Initial program 85.2%

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

   3. Taylor expanded in a around inf 45.0%

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

      1. mul-1-neg 45.0%

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

      2. distribute-lft-neg-out 45.0%

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

      3. *-commutative 45.0%

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

   5. Simplified 45.0%

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

   6. Taylor expanded in y around 0 42.8%

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

      1. associate-*r/ 42.8%

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

      2. neg-mul-1 42.8%

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

   8. Simplified 42.8%

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

4. Final simplification 47.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+50}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{-95}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{-152}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{-274}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-99}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;y \leq 6.1 \cdot 10^{-34}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 65.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -1 \cdot 10^{-53}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-138}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.2:\\ \;\;\;\;\frac{t + \left(\frac{x}{\frac{z}{y}} - a\right)}{b}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -1e-53)
     t_1
     (if (<= z 9.5e-138)
       x
       (if (<= z 5.2) (/ (+ t (- (/ x (/ z y)) a)) b) 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 <= -1e-53) {
		tmp = t_1;
	} else if (z <= 9.5e-138) {
		tmp = x;
	} else if (z <= 5.2) {
		tmp = (t + ((x / (z / y)) - 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 - a) / (b - y)
    if (z <= (-1d-53)) then
        tmp = t_1
    else if (z <= 9.5d-138) then
        tmp = x
    else if (z <= 5.2d0) then
        tmp = (t + ((x / (z / y)) - 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 - a) / (b - y);
	double tmp;
	if (z <= -1e-53) {
		tmp = t_1;
	} else if (z <= 9.5e-138) {
		tmp = x;
	} else if (z <= 5.2) {
		tmp = (t + ((x / (z / y)) - a)) / b;
	} 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 <= -1e-53:
		tmp = t_1
	elif z <= 9.5e-138:
		tmp = x
	elif z <= 5.2:
		tmp = (t + ((x / (z / y)) - a)) / b
	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 <= -1e-53)
		tmp = t_1;
	elseif (z <= 9.5e-138)
		tmp = x;
	elseif (z <= 5.2)
		tmp = Float64(Float64(t + Float64(Float64(x / Float64(z / y)) - a)) / b);
	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 <= -1e-53)
		tmp = t_1;
	elseif (z <= 9.5e-138)
		tmp = x;
	elseif (z <= 5.2)
		tmp = (t + ((x / (z / y)) - a)) / b;
	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, -1e-53], t$95$1, If[LessEqual[z, 9.5e-138], x, If[LessEqual[z, 5.2], N[(N[(t + N[(N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.00000000000000003e-53 or 5.20000000000000018 < z

   1. Initial program 48.0%

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

   3. Taylor expanded in z around inf 75.1%

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

   if -1.00000000000000003e-53 < z < 9.49999999999999997e-138

   1. Initial program 84.8%

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

   3. Taylor expanded in z around 0 55.3%

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

   if 9.49999999999999997e-138 < z < 5.20000000000000018

   1. Initial program 92.4%

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

   3. Taylor expanded in y around 0 55.5%

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

      1. associate--l+ 55.5%

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

      2. associate-/r* 55.5%

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

      3. times-frac 51.5%

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

      4. mul-1-neg 51.5%

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

      5. div-sub 51.5%

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

   5. Simplified 51.5%

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

   6. Taylor expanded in b around inf 66.6%

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

      1. associate--l+ 66.6%

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

      2. associate-/l* 66.6%

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

   8. Simplified 66.6%

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

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{-53}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-138}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.2:\\ \;\;\;\;\frac{t + \left(\frac{x}{\frac{z}{y}} - a\right)}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 64.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{-52} \lor \neg \left(z \leq 9.8 \cdot 10^{-138}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -6e-52) (not (<= z 9.8e-138))) (/ (- t a) (- b y)) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -6e-52) || !(z <= 9.8e-138)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-6d-52)) .or. (.not. (z <= 9.8d-138))) then
        tmp = (t - a) / (b - y)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -6e-52) || !(z <= 9.8e-138)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -6e-52) or not (z <= 9.8e-138):
		tmp = (t - a) / (b - y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -6e-52) || !(z <= 9.8e-138))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -6e-52) || ~((z <= 9.8e-138)))
		tmp = (t - a) / (b - y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -6e-52], N[Not[LessEqual[z, 9.8e-138]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -6e-52 or 9.80000000000000033e-138 < z

   1. Initial program 54.4%

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

   3. Taylor expanded in z around inf 71.4%

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

   if -6e-52 < z < 9.80000000000000033e-138

   1. Initial program 84.8%

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

   3. Taylor expanded in z around 0 55.3%

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

4. Final simplification 65.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{-52} \lor \neg \left(z \leq 9.8 \cdot 10^{-138}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 54.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{+80} \lor \neg \left(y \leq 2.9 \cdot 10^{-32}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.45e+80) (not (<= y 2.9e-32))) (/ x (- 1.0 z)) (/ (- t a) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.45e+80) || !(y <= 2.9e-32)) {
		tmp = x / (1.0 - z);
	} else {
		tmp = (t - a) / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-1.45d+80)) .or. (.not. (y <= 2.9d-32))) then
        tmp = x / (1.0d0 - z)
    else
        tmp = (t - a) / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.45e+80) || !(y <= 2.9e-32)) {
		tmp = x / (1.0 - z);
	} else {
		tmp = (t - a) / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.45e+80) or not (y <= 2.9e-32):
		tmp = x / (1.0 - z)
	else:
		tmp = (t - a) / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.45e+80) || !(y <= 2.9e-32))
		tmp = Float64(x / Float64(1.0 - z));
	else
		tmp = Float64(Float64(t - a) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.45e+80) || ~((y <= 2.9e-32)))
		tmp = x / (1.0 - z);
	else
		tmp = (t - a) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.45e+80], N[Not[LessEqual[y, 2.9e-32]], $MachinePrecision]], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.44999999999999993e80 or 2.89999999999999996e-32 < y

   1. Initial program 45.2%

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

   3. Taylor expanded in y around inf 57.8%

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

      1. mul-1-neg 57.8%

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

      2. unsub-neg 57.8%

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

   5. Simplified 57.8%

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

   if -1.44999999999999993e80 < y < 2.89999999999999996e-32

   1. Initial program 79.8%

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

   3. Taylor expanded in y around 0 54.8%

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

4. Final simplification 56.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{+80} \lor \neg \left(y \leq 2.9 \cdot 10^{-32}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 34.5% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+50}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{-32}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -6e+50) x (if (<= y 4.9e-32) (/ t b) x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -6e+50) {
		tmp = x;
	} else if (y <= 4.9e-32) {
		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 (y <= (-6d+50)) then
        tmp = x
    else if (y <= 4.9d-32) 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 (y <= -6e+50) {
		tmp = x;
	} else if (y <= 4.9e-32) {
		tmp = t / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -6e+50:
		tmp = x
	elif y <= 4.9e-32:
		tmp = t / b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -6e+50)
		tmp = x;
	elseif (y <= 4.9e-32)
		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 (y <= -6e+50)
		tmp = x;
	elseif (y <= 4.9e-32)
		tmp = t / b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -6e+50], x, If[LessEqual[y, 4.9e-32], N[(t / b), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -5.9999999999999996e50 or 4.8999999999999998e-32 < y

   1. Initial program 45.5%

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

   3. Taylor expanded in z around 0 41.9%

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

   if -5.9999999999999996e50 < y < 4.8999999999999998e-32

   1. Initial program 81.0%

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

   3. Taylor expanded in b around inf 52.2%

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

   4. Taylor expanded in t around inf 33.1%

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

4. Final simplification 37.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+50}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{-32}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 36.1% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{-18}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{-138}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.15e-18) (/ (- a) b) (if (<= z 9.8e-138) x (/ t b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.15e-18) {
		tmp = -a / b;
	} else if (z <= 9.8e-138) {
		tmp = x;
	} else {
		tmp = t / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-1.15d-18)) then
        tmp = -a / b
    else if (z <= 9.8d-138) then
        tmp = x
    else
        tmp = t / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.15e-18) {
		tmp = -a / b;
	} else if (z <= 9.8e-138) {
		tmp = x;
	} else {
		tmp = t / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1.15e-18:
		tmp = -a / b
	elif z <= 9.8e-138:
		tmp = x
	else:
		tmp = t / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.15e-18)
		tmp = Float64(Float64(-a) / b);
	elseif (z <= 9.8e-138)
		tmp = x;
	else
		tmp = Float64(t / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -1.15e-18)
		tmp = -a / b;
	elseif (z <= 9.8e-138)
		tmp = x;
	else
		tmp = t / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.15e-18], N[((-a) / b), $MachinePrecision], If[LessEqual[z, 9.8e-138], x, N[(t / b), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.15e-18

   1. Initial program 45.9%

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

   3. Taylor expanded in a around inf 18.9%

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

      1. mul-1-neg 18.9%

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

      2. distribute-lft-neg-out 18.9%

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

      3. *-commutative 18.9%

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

   5. Simplified 18.9%

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

   6. Taylor expanded in y around 0 29.8%

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

      1. associate-*r/ 29.8%

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

      2. neg-mul-1 29.8%

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

   8. Simplified 29.8%

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

   if -1.15e-18 < z < 9.80000000000000033e-138

   1. Initial program 85.3%

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

   3. Taylor expanded in z around 0 53.9%

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

   if 9.80000000000000033e-138 < z

   1. Initial program 57.2%

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

   3. Taylor expanded in b around inf 39.7%

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

   4. Taylor expanded in t around inf 24.9%

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

4. Final simplification 37.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{-18}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{-138}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 26.1% accurate, 17.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 65.1%

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

3. Taylor expanded in z around 0 25.2%

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

4. Final simplification 25.2%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 73.4% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024010 
(FPCore (x y z t a b)
  :name "Development.Shake.Progress:decay from shake-0.15.5"
  :precision binary64

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

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