Development.Shake.Progress:decay from shake-0.15.5

Percentage Accurate: 66.6% → 89.3%

Time: 24.4s

Alternatives: 23

Speedup: 0.7×

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: 66.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 89.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ t_2 := \frac{x \cdot y - z \cdot \left(a - t\right)}{y + z \cdot \left(b - y\right)}\\ t_3 := t\_1 - \frac{x}{z}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq -1 \cdot 10^{-242}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;t\_1 - \frac{y \cdot \frac{t - a}{{\left(b - y\right)}^{2}} + x \cdot \frac{y}{y - b}}{z}\\ \mathbf{elif}\;t\_2 \leq 4 \cdot 10^{+259}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y)))
        (t_2 (/ (- (* x y) (* z (- a t))) (+ y (* z (- b y)))))
        (t_3 (- t_1 (/ x z))))
   (if (<= t_2 (- INFINITY))
     t_3
     (if (<= t_2 -1e-242)
       t_2
       (if (<= t_2 0.0)
         (-
          t_1
          (/ (+ (* y (/ (- t a) (pow (- b y) 2.0))) (* x (/ y (- y b)))) z))
         (if (<= t_2 4e+259) t_2 t_3))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double t_2 = ((x * y) - (z * (a - t))) / (y + (z * (b - y)));
	double t_3 = t_1 - (x / z);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_3;
	} else if (t_2 <= -1e-242) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = t_1 - (((y * ((t - a) / pow((b - y), 2.0))) + (x * (y / (y - b)))) / z);
	} else if (t_2 <= 4e+259) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

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 t_2 = ((x * y) - (z * (a - t))) / (y + (z * (b - y)));
	double t_3 = t_1 - (x / z);
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_3;
	} else if (t_2 <= -1e-242) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = t_1 - (((y * ((t - a) / Math.pow((b - y), 2.0))) + (x * (y / (y - b)))) / z);
	} else if (t_2 <= 4e+259) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	t_2 = ((x * y) - (z * (a - t))) / (y + (z * (b - y)))
	t_3 = t_1 - (x / z)
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_3
	elif t_2 <= -1e-242:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = t_1 - (((y * ((t - a) / math.pow((b - y), 2.0))) + (x * (y / (y - b)))) / z)
	elif t_2 <= 4e+259:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	t_2 = Float64(Float64(Float64(x * y) - Float64(z * Float64(a - t))) / Float64(y + Float64(z * Float64(b - y))))
	t_3 = Float64(t_1 - Float64(x / z))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_3;
	elseif (t_2 <= -1e-242)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = Float64(t_1 - Float64(Float64(Float64(y * Float64(Float64(t - a) / (Float64(b - y) ^ 2.0))) + Float64(x * Float64(y / Float64(y - b)))) / z));
	elseif (t_2 <= 4e+259)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	t_2 = ((x * y) - (z * (a - t))) / (y + (z * (b - y)));
	t_3 = t_1 - (x / z);
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_3;
	elseif (t_2 <= -1e-242)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = t_1 - (((y * ((t - a) / ((b - y) ^ 2.0))) + (x * (y / (y - b)))) / z);
	elseif (t_2 <= 4e+259)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x * y), $MachinePrecision] - N[(z * N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$1 - N[(x / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$3, If[LessEqual[t$95$2, -1e-242], t$95$2, If[LessEqual[t$95$2, 0.0], N[(t$95$1 - N[(N[(N[(y * N[(N[(t - a), $MachinePrecision] / N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(y / N[(y - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 4e+259], t$95$2, t$95$3]]]]]]]

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 or 4e259 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 17.8%

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

   3. Taylor expanded in z around -inf 40.2%

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

      1. associate--l+ 40.2%

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

      2. mul-1-neg 40.2%

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

      3. distribute-lft-out-- 40.2%

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

      4. associate-/l* 48.1%

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

      5. associate-/l* 74.1%

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

      6. div-sub 74.1%

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

   5. Simplified 74.1%

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

   6. Taylor expanded in y around inf 83.6%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -1e-242 or 0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 4e259

   1. Initial program 99.5%

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

   if -1e-242 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 0.0

   1. Initial program 33.6%

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

   3. Taylor expanded in z around -inf 86.7%

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

      1. associate--l+ 86.7%

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

      2. mul-1-neg 86.7%

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

      3. distribute-lft-out-- 86.7%

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

      4. associate-/l* 86.8%

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

      5. associate-/l* 96.8%

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

      6. div-sub 96.8%

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

   5. Simplified 96.8%

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

4. Final simplification 94.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y - z \cdot \left(a - t\right)}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;\frac{t - a}{b - y} - \frac{x}{z}\\ \mathbf{elif}\;\frac{x \cdot y - z \cdot \left(a - t\right)}{y + z \cdot \left(b - y\right)} \leq -1 \cdot 10^{-242}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(a - t\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y - z \cdot \left(a - t\right)}{y + z \cdot \left(b - y\right)} \leq 0:\\ \;\;\;\;\frac{t - a}{b - y} - \frac{y \cdot \frac{t - a}{{\left(b - y\right)}^{2}} + x \cdot \frac{y}{y - b}}{z}\\ \mathbf{elif}\;\frac{x \cdot y - z \cdot \left(a - t\right)}{y + z \cdot \left(b - y\right)} \leq 4 \cdot 10^{+259}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(a - t\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y} - \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 87.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot y - z \cdot \left(a - t\right)}{y + z \cdot \left(b - y\right)}\\ t_2 := \frac{t - a}{b - y} - \frac{x}{z}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{-294}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;\frac{t}{b - y} + \frac{\frac{x \cdot y}{b - y} - t \cdot \frac{y}{{\left(b - y\right)}^{2}}}{z}\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{+259}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (* x y) (* z (- a t))) (+ y (* z (- b y)))))
        (t_2 (- (/ (- t a) (- b y)) (/ x z))))
   (if (<= t_1 (- INFINITY))
     t_2
     (if (<= t_1 -5e-294)
       t_1
       (if (<= t_1 0.0)
         (+
          (/ t (- b y))
          (/ (- (/ (* x y) (- b y)) (* t (/ y (pow (- b y) 2.0)))) z))
         (if (<= t_1 4e+259) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x * y) - (z * (a - t))) / (y + (z * (b - y)));
	double t_2 = ((t - a) / (b - y)) - (x / z);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = t_2;
	} else if (t_1 <= -5e-294) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = (t / (b - y)) + ((((x * y) / (b - y)) - (t * (y / pow((b - y), 2.0)))) / z);
	} else if (t_1 <= 4e+259) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x * y) - (z * (a - t))) / (y + (z * (b - y)));
	double t_2 = ((t - a) / (b - y)) - (x / z);
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else if (t_1 <= -5e-294) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = (t / (b - y)) + ((((x * y) / (b - y)) - (t * (y / Math.pow((b - y), 2.0)))) / z);
	} else if (t_1 <= 4e+259) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((x * y) - (z * (a - t))) / (y + (z * (b - y)))
	t_2 = ((t - a) / (b - y)) - (x / z)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = t_2
	elif t_1 <= -5e-294:
		tmp = t_1
	elif t_1 <= 0.0:
		tmp = (t / (b - y)) + ((((x * y) / (b - y)) - (t * (y / math.pow((b - y), 2.0)))) / z)
	elif t_1 <= 4e+259:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(x * y) - Float64(z * Float64(a - t))) / Float64(y + Float64(z * Float64(b - y))))
	t_2 = Float64(Float64(Float64(t - a) / Float64(b - y)) - Float64(x / z))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = t_2;
	elseif (t_1 <= -5e-294)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(t / Float64(b - y)) + Float64(Float64(Float64(Float64(x * y) / Float64(b - y)) - Float64(t * Float64(y / (Float64(b - y) ^ 2.0)))) / z));
	elseif (t_1 <= 4e+259)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((x * y) - (z * (a - t))) / (y + (z * (b - y)));
	t_2 = ((t - a) / (b - y)) - (x / z);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = t_2;
	elseif (t_1 <= -5e-294)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = (t / (b - y)) + ((((x * y) / (b - y)) - (t * (y / ((b - y) ^ 2.0)))) / z);
	elseif (t_1 <= 4e+259)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(x * y), $MachinePrecision] - N[(z * N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision] - N[(x / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], t$95$2, If[LessEqual[t$95$1, -5e-294], t$95$1, If[LessEqual[t$95$1, 0.0], N[(N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(N[(x * y), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision] - N[(t * N[(y / N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 4e+259], t$95$1, t$95$2]]]]]]

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 or 4e259 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 17.8%

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

   3. Taylor expanded in z around -inf 40.2%

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

      1. associate--l+ 40.2%

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

      2. mul-1-neg 40.2%

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

      3. distribute-lft-out-- 40.2%

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

      4. associate-/l* 48.1%

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

      5. associate-/l* 74.1%

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

      6. div-sub 74.1%

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

   5. Simplified 74.1%

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

   6. Taylor expanded in y around inf 83.6%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -5.0000000000000003e-294 or 0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 4e259

   1. Initial program 99.5%

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

   if -5.0000000000000003e-294 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 0.0

   1. Initial program 23.3%

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

   3. Taylor expanded in a around 0 23.3%

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

   4. Taylor expanded in z around -inf 70.5%

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

      1. +-commutative 70.5%

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

      2. mul-1-neg 70.5%

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

      3. unsub-neg 70.5%

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

      4. distribute-lft-out-- 70.5%

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

      5. associate-/l* 74.8%

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

   6. Simplified 74.8%

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

4. Final simplification 92.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y - z \cdot \left(a - t\right)}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;\frac{t - a}{b - y} - \frac{x}{z}\\ \mathbf{elif}\;\frac{x \cdot y - z \cdot \left(a - t\right)}{y + z \cdot \left(b - y\right)} \leq -5 \cdot 10^{-294}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(a - t\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y - z \cdot \left(a - t\right)}{y + z \cdot \left(b - y\right)} \leq 0:\\ \;\;\;\;\frac{t}{b - y} + \frac{\frac{x \cdot y}{b - y} - t \cdot \frac{y}{{\left(b - y\right)}^{2}}}{z}\\ \mathbf{elif}\;\frac{x \cdot y - z \cdot \left(a - t\right)}{y + z \cdot \left(b - y\right)} \leq 4 \cdot 10^{+259}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(a - t\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y} - \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 88.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ t_2 := \frac{x \cdot y - z \cdot \left(a - t\right)}{y + z \cdot \left(b - y\right)}\\ t_3 := t\_1 - \frac{x}{z}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{-294}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 4 \cdot 10^{+259}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y)))
        (t_2 (/ (- (* x y) (* z (- a t))) (+ y (* z (- b y)))))
        (t_3 (- t_1 (/ x z))))
   (if (<= t_2 (- INFINITY))
     t_3
     (if (<= t_2 -5e-294)
       t_2
       (if (<= t_2 0.0) t_1 (if (<= t_2 4e+259) t_2 t_3))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double t_2 = ((x * y) - (z * (a - t))) / (y + (z * (b - y)));
	double t_3 = t_1 - (x / z);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_3;
	} else if (t_2 <= -5e-294) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = t_1;
	} else if (t_2 <= 4e+259) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

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 t_2 = ((x * y) - (z * (a - t))) / (y + (z * (b - y)));
	double t_3 = t_1 - (x / z);
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_3;
	} else if (t_2 <= -5e-294) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = t_1;
	} else if (t_2 <= 4e+259) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	t_2 = ((x * y) - (z * (a - t))) / (y + (z * (b - y)))
	t_3 = t_1 - (x / z)
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_3
	elif t_2 <= -5e-294:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = t_1
	elif t_2 <= 4e+259:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	t_2 = Float64(Float64(Float64(x * y) - Float64(z * Float64(a - t))) / Float64(y + Float64(z * Float64(b - y))))
	t_3 = Float64(t_1 - Float64(x / z))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_3;
	elseif (t_2 <= -5e-294)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = t_1;
	elseif (t_2 <= 4e+259)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	t_2 = ((x * y) - (z * (a - t))) / (y + (z * (b - y)));
	t_3 = t_1 - (x / z);
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_3;
	elseif (t_2 <= -5e-294)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = t_1;
	elseif (t_2 <= 4e+259)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x * y), $MachinePrecision] - N[(z * N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$1 - N[(x / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$3, If[LessEqual[t$95$2, -5e-294], t$95$2, If[LessEqual[t$95$2, 0.0], t$95$1, If[LessEqual[t$95$2, 4e+259], t$95$2, t$95$3]]]]]]]

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 or 4e259 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 17.8%

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

   3. Taylor expanded in z around -inf 40.2%

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

      1. associate--l+ 40.2%

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

      2. mul-1-neg 40.2%

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

      3. distribute-lft-out-- 40.2%

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

      4. associate-/l* 48.1%

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

      5. associate-/l* 74.1%

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

      6. div-sub 74.1%

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

   5. Simplified 74.1%

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

   6. Taylor expanded in y around inf 83.6%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -5.0000000000000003e-294 or 0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 4e259

   1. Initial program 99.5%

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

   if -5.0000000000000003e-294 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 0.0

   1. Initial program 23.3%

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

   3. Taylor expanded in z around inf 74.7%

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

4. Final simplification 92.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y - z \cdot \left(a - t\right)}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;\frac{t - a}{b - y} - \frac{x}{z}\\ \mathbf{elif}\;\frac{x \cdot y - z \cdot \left(a - t\right)}{y + z \cdot \left(b - y\right)} \leq -5 \cdot 10^{-294}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(a - t\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y - z \cdot \left(a - t\right)}{y + z \cdot \left(b - y\right)} \leq 0:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;\frac{x \cdot y - z \cdot \left(a - t\right)}{y + z \cdot \left(b - y\right)} \leq 4 \cdot 10^{+259}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(a - t\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y} - \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 65.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{a - t}{y}\\ t_2 := \frac{t - a}{b - y}\\ t_3 := \frac{x \cdot y - z \cdot \left(a - t\right)}{y}\\ \mathbf{if}\;z \leq -1.2 \cdot 10^{+210}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{+170}:\\ \;\;\;\;\frac{a}{y} - \frac{x}{z}\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{-89}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{-114}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-130}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-149}:\\ \;\;\;\;\frac{x \cdot y}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{-181}:\\ \;\;\;\;x - t\_1\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-224}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-251}:\\ \;\;\;\;x + t \cdot \frac{z}{y}\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-119}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-98}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-32}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+69} \lor \neg \left(z \leq 2.1 \cdot 10^{+130}\right):\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_1 - x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (/ (- a t) y)))
        (t_2 (/ (- t a) (- b y)))
        (t_3 (/ (- (* x y) (* z (- a t))) y)))
   (if (<= z -1.2e+210)
     t_2
     (if (<= z -3.3e+170)
       (- (/ a y) (/ x z))
       (if (<= z -4.4e-89)
         t_2
         (if (<= z -9.2e-114)
           t_3
           (if (<= z -1.7e-130)
             (/ t b)
             (if (<= z -1.25e-149)
               (/ (* x y) (+ y (* z (- b y))))
               (if (<= z -6.6e-181)
                 (- x t_1)
                 (if (<= z -3.2e-224)
                   t_3
                   (if (<= z -6.2e-251)
                     (+ x (* t (/ z y)))
                     (if (<= z 2.7e-119)
                       t_3
                       (if (<= z 1.6e-98)
                         (/ (- t a) b)
                         (if (<= z 1.3e-32)
                           t_3
                           (if (or (<= z 2.9e+69) (not (<= z 2.1e+130)))
                             t_2
                             (/ (- t_1 x) z))))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * ((a - t) / y);
	double t_2 = (t - a) / (b - y);
	double t_3 = ((x * y) - (z * (a - t))) / y;
	double tmp;
	if (z <= -1.2e+210) {
		tmp = t_2;
	} else if (z <= -3.3e+170) {
		tmp = (a / y) - (x / z);
	} else if (z <= -4.4e-89) {
		tmp = t_2;
	} else if (z <= -9.2e-114) {
		tmp = t_3;
	} else if (z <= -1.7e-130) {
		tmp = t / b;
	} else if (z <= -1.25e-149) {
		tmp = (x * y) / (y + (z * (b - y)));
	} else if (z <= -6.6e-181) {
		tmp = x - t_1;
	} else if (z <= -3.2e-224) {
		tmp = t_3;
	} else if (z <= -6.2e-251) {
		tmp = x + (t * (z / y));
	} else if (z <= 2.7e-119) {
		tmp = t_3;
	} else if (z <= 1.6e-98) {
		tmp = (t - a) / b;
	} else if (z <= 1.3e-32) {
		tmp = t_3;
	} else if ((z <= 2.9e+69) || !(z <= 2.1e+130)) {
		tmp = t_2;
	} else {
		tmp = (t_1 - x) / z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = z * ((a - t) / y)
    t_2 = (t - a) / (b - y)
    t_3 = ((x * y) - (z * (a - t))) / y
    if (z <= (-1.2d+210)) then
        tmp = t_2
    else if (z <= (-3.3d+170)) then
        tmp = (a / y) - (x / z)
    else if (z <= (-4.4d-89)) then
        tmp = t_2
    else if (z <= (-9.2d-114)) then
        tmp = t_3
    else if (z <= (-1.7d-130)) then
        tmp = t / b
    else if (z <= (-1.25d-149)) then
        tmp = (x * y) / (y + (z * (b - y)))
    else if (z <= (-6.6d-181)) then
        tmp = x - t_1
    else if (z <= (-3.2d-224)) then
        tmp = t_3
    else if (z <= (-6.2d-251)) then
        tmp = x + (t * (z / y))
    else if (z <= 2.7d-119) then
        tmp = t_3
    else if (z <= 1.6d-98) then
        tmp = (t - a) / b
    else if (z <= 1.3d-32) then
        tmp = t_3
    else if ((z <= 2.9d+69) .or. (.not. (z <= 2.1d+130))) then
        tmp = t_2
    else
        tmp = (t_1 - x) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * ((a - t) / y);
	double t_2 = (t - a) / (b - y);
	double t_3 = ((x * y) - (z * (a - t))) / y;
	double tmp;
	if (z <= -1.2e+210) {
		tmp = t_2;
	} else if (z <= -3.3e+170) {
		tmp = (a / y) - (x / z);
	} else if (z <= -4.4e-89) {
		tmp = t_2;
	} else if (z <= -9.2e-114) {
		tmp = t_3;
	} else if (z <= -1.7e-130) {
		tmp = t / b;
	} else if (z <= -1.25e-149) {
		tmp = (x * y) / (y + (z * (b - y)));
	} else if (z <= -6.6e-181) {
		tmp = x - t_1;
	} else if (z <= -3.2e-224) {
		tmp = t_3;
	} else if (z <= -6.2e-251) {
		tmp = x + (t * (z / y));
	} else if (z <= 2.7e-119) {
		tmp = t_3;
	} else if (z <= 1.6e-98) {
		tmp = (t - a) / b;
	} else if (z <= 1.3e-32) {
		tmp = t_3;
	} else if ((z <= 2.9e+69) || !(z <= 2.1e+130)) {
		tmp = t_2;
	} else {
		tmp = (t_1 - x) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * ((a - t) / y)
	t_2 = (t - a) / (b - y)
	t_3 = ((x * y) - (z * (a - t))) / y
	tmp = 0
	if z <= -1.2e+210:
		tmp = t_2
	elif z <= -3.3e+170:
		tmp = (a / y) - (x / z)
	elif z <= -4.4e-89:
		tmp = t_2
	elif z <= -9.2e-114:
		tmp = t_3
	elif z <= -1.7e-130:
		tmp = t / b
	elif z <= -1.25e-149:
		tmp = (x * y) / (y + (z * (b - y)))
	elif z <= -6.6e-181:
		tmp = x - t_1
	elif z <= -3.2e-224:
		tmp = t_3
	elif z <= -6.2e-251:
		tmp = x + (t * (z / y))
	elif z <= 2.7e-119:
		tmp = t_3
	elif z <= 1.6e-98:
		tmp = (t - a) / b
	elif z <= 1.3e-32:
		tmp = t_3
	elif (z <= 2.9e+69) or not (z <= 2.1e+130):
		tmp = t_2
	else:
		tmp = (t_1 - x) / z
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(Float64(a - t) / y))
	t_2 = Float64(Float64(t - a) / Float64(b - y))
	t_3 = Float64(Float64(Float64(x * y) - Float64(z * Float64(a - t))) / y)
	tmp = 0.0
	if (z <= -1.2e+210)
		tmp = t_2;
	elseif (z <= -3.3e+170)
		tmp = Float64(Float64(a / y) - Float64(x / z));
	elseif (z <= -4.4e-89)
		tmp = t_2;
	elseif (z <= -9.2e-114)
		tmp = t_3;
	elseif (z <= -1.7e-130)
		tmp = Float64(t / b);
	elseif (z <= -1.25e-149)
		tmp = Float64(Float64(x * y) / Float64(y + Float64(z * Float64(b - y))));
	elseif (z <= -6.6e-181)
		tmp = Float64(x - t_1);
	elseif (z <= -3.2e-224)
		tmp = t_3;
	elseif (z <= -6.2e-251)
		tmp = Float64(x + Float64(t * Float64(z / y)));
	elseif (z <= 2.7e-119)
		tmp = t_3;
	elseif (z <= 1.6e-98)
		tmp = Float64(Float64(t - a) / b);
	elseif (z <= 1.3e-32)
		tmp = t_3;
	elseif ((z <= 2.9e+69) || !(z <= 2.1e+130))
		tmp = t_2;
	else
		tmp = Float64(Float64(t_1 - x) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * ((a - t) / y);
	t_2 = (t - a) / (b - y);
	t_3 = ((x * y) - (z * (a - t))) / y;
	tmp = 0.0;
	if (z <= -1.2e+210)
		tmp = t_2;
	elseif (z <= -3.3e+170)
		tmp = (a / y) - (x / z);
	elseif (z <= -4.4e-89)
		tmp = t_2;
	elseif (z <= -9.2e-114)
		tmp = t_3;
	elseif (z <= -1.7e-130)
		tmp = t / b;
	elseif (z <= -1.25e-149)
		tmp = (x * y) / (y + (z * (b - y)));
	elseif (z <= -6.6e-181)
		tmp = x - t_1;
	elseif (z <= -3.2e-224)
		tmp = t_3;
	elseif (z <= -6.2e-251)
		tmp = x + (t * (z / y));
	elseif (z <= 2.7e-119)
		tmp = t_3;
	elseif (z <= 1.6e-98)
		tmp = (t - a) / b;
	elseif (z <= 1.3e-32)
		tmp = t_3;
	elseif ((z <= 2.9e+69) || ~((z <= 2.1e+130)))
		tmp = t_2;
	else
		tmp = (t_1 - x) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(x * y), $MachinePrecision] - N[(z * N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[z, -1.2e+210], t$95$2, If[LessEqual[z, -3.3e+170], N[(N[(a / y), $MachinePrecision] - N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4.4e-89], t$95$2, If[LessEqual[z, -9.2e-114], t$95$3, If[LessEqual[z, -1.7e-130], N[(t / b), $MachinePrecision], If[LessEqual[z, -1.25e-149], N[(N[(x * y), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -6.6e-181], N[(x - t$95$1), $MachinePrecision], If[LessEqual[z, -3.2e-224], t$95$3, If[LessEqual[z, -6.2e-251], N[(x + N[(t * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.7e-119], t$95$3, If[LessEqual[z, 1.6e-98], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[z, 1.3e-32], t$95$3, If[Or[LessEqual[z, 2.9e+69], N[Not[LessEqual[z, 2.1e+130]], $MachinePrecision]], t$95$2, N[(N[(t$95$1 - x), $MachinePrecision] / z), $MachinePrecision]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if z < -1.19999999999999994e210 or -3.30000000000000023e170 < z < -4.40000000000000024e-89 or 1.2999999999999999e-32 < z < 2.8999999999999998e69 or 2.0999999999999999e130 < z

   1. Initial program 51.1%

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

   3. Taylor expanded in z around inf 76.3%

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

   if -1.19999999999999994e210 < z < -3.30000000000000023e170

   1. Initial program 31.0%

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

   3. Taylor expanded in z around -inf 72.3%

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

      1. associate--l+ 72.3%

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

      2. mul-1-neg 72.3%

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

      3. distribute-lft-out-- 72.3%

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

      4. associate-/l* 100.0%

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

      5. associate-/l* 85.7%

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

      6. div-sub 85.7%

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

   5. Simplified 85.7%

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

   6. Taylor expanded in y around inf 89.7%

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

   7. Taylor expanded in y around -inf 89.7%

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

      1. associate-*r/ 89.7%

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

      2. mul-1-neg 89.7%

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

   9. Simplified 89.7%

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

   10. Taylor expanded in t around 0 89.7%

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

   if -4.40000000000000024e-89 < z < -9.1999999999999997e-114 or -6.60000000000000018e-181 < z < -3.1999999999999999e-224 or -6.20000000000000006e-251 < z < 2.70000000000000027e-119 or 1.6e-98 < z < 1.2999999999999999e-32

   1. Initial program 94.0%

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

   3. Taylor expanded in b around inf 94.0%

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

      1. *-commutative 94.0%

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

   5. Simplified 94.0%

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

   6. Taylor expanded in b around 0 76.1%

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

   if -9.1999999999999997e-114 < z < -1.70000000000000003e-130

   1. Initial program 100.0%

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

   3. Taylor expanded in a around 0 100.0%

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

   4. Taylor expanded in y around 0 68.8%

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

   if -1.70000000000000003e-130 < z < -1.24999999999999992e-149

   1. Initial program 86.6%

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

   3. Taylor expanded in x around inf 73.1%

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

      1. *-commutative 73.1%

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

   5. Simplified 73.1%

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

   if -1.24999999999999992e-149 < z < -6.60000000000000018e-181

   1. Initial program 99.7%

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

   3. Taylor expanded in b around inf 99.7%

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

      1. *-commutative 99.7%

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

   5. Simplified 99.7%

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

   6. Taylor expanded in z around 0 83.4%

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

      1. associate--r+ 83.4%

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

      2. div-sub 83.4%

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

      3. associate-/l* 83.4%

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

   8. Simplified 83.4%

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

   9. Taylor expanded in b around 0 83.4%

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

       1. div-sub 83.4%

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

       2. *-commutative 83.4%

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

   11. Simplified 83.4%

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

   if -3.1999999999999999e-224 < z < -6.20000000000000006e-251

   1. Initial program 64.5%

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

   3. Taylor expanded in b around inf 64.5%

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

      1. *-commutative 64.5%

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

   5. Simplified 64.5%

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

   6. Taylor expanded in z around 0 75.4%

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

      1. associate--r+ 75.4%

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

      2. div-sub 75.4%

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

      3. associate-/l* 75.4%

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

   8. Simplified 75.4%

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

   9. Taylor expanded in t around inf 76.5%

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

       1. associate-/l* 76.7%

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

   11. Simplified 76.7%

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

   if 2.70000000000000027e-119 < z < 1.6e-98

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0 100.0%

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

   if 2.8999999999999998e69 < z < 2.0999999999999999e130

   1. Initial program 51.2%

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

   3. Taylor expanded in z around -inf 62.8%

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

      1. associate--l+ 62.8%

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

      2. mul-1-neg 62.8%

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

      3. distribute-lft-out-- 62.8%

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

      4. associate-/l* 62.8%

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

      5. associate-/l* 87.8%

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

      6. div-sub 87.8%

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

   5. Simplified 87.8%

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

   6. Taylor expanded in y around inf 75.8%

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

   7. Taylor expanded in y around -inf 75.8%

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

      1. associate-*r/ 75.8%

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

      2. mul-1-neg 75.8%

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

   9. Simplified 75.8%

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

   10. Taylor expanded in z around 0 76.0%

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

       1. div-sub 76.0%

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

   12. Simplified 76.0%

       \[\leadsto \color{blue}{\frac{z \cdot \frac{a - t}{y} - x}{z}} \]
3. Recombined 9 regimes into one program.

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+210}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{+170}:\\ \;\;\;\;\frac{a}{y} - \frac{x}{z}\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{-89}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{-114}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(a - t\right)}{y}\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-130}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-149}:\\ \;\;\;\;\frac{x \cdot y}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{-181}:\\ \;\;\;\;x - z \cdot \frac{a - t}{y}\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-224}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(a - t\right)}{y}\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-251}:\\ \;\;\;\;x + t \cdot \frac{z}{y}\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-119}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(a - t\right)}{y}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-98}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-32}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(a - t\right)}{y}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+69} \lor \neg \left(z \leq 2.1 \cdot 10^{+130}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \frac{a - t}{y} - x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 65.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a - t}{y}\\ t_2 := \frac{t - a}{b - y}\\ t_3 := \frac{x \cdot y - z \cdot \left(a - t\right)}{y}\\ \mathbf{if}\;z \leq -1.2 \cdot 10^{+210}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{+170}:\\ \;\;\;\;\frac{a}{y} - \frac{x}{z}\\ \mathbf{elif}\;z \leq -2.55 \cdot 10^{-89}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{-114}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-131}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-149}:\\ \;\;\;\;\frac{x \cdot y}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-180}:\\ \;\;\;\;x - z \cdot t\_1\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{-222}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-247}:\\ \;\;\;\;x + t \cdot \frac{z}{y}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-119}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-99}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-33}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+69} \lor \neg \left(z \leq 9.2 \cdot 10^{+131}\right):\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1 - \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- a t) y))
        (t_2 (/ (- t a) (- b y)))
        (t_3 (/ (- (* x y) (* z (- a t))) y)))
   (if (<= z -1.2e+210)
     t_2
     (if (<= z -3.3e+170)
       (- (/ a y) (/ x z))
       (if (<= z -2.55e-89)
         t_2
         (if (<= z -9.2e-114)
           t_3
           (if (<= z -6.5e-131)
             (/ t b)
             (if (<= z -1.25e-149)
               (/ (* x y) (+ y (* z (- b y))))
               (if (<= z -2.4e-180)
                 (- x (* z t_1))
                 (if (<= z -1.85e-222)
                   t_3
                   (if (<= z -2.3e-247)
                     (+ x (* t (/ z y)))
                     (if (<= z 3e-119)
                       t_3
                       (if (<= z 6e-99)
                         (/ (- t a) b)
                         (if (<= z 8.2e-33)
                           t_3
                           (if (or (<= z 2.9e+69) (not (<= z 9.2e+131)))
                             t_2
                             (- t_1 (/ x z)))))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a - t) / y;
	double t_2 = (t - a) / (b - y);
	double t_3 = ((x * y) - (z * (a - t))) / y;
	double tmp;
	if (z <= -1.2e+210) {
		tmp = t_2;
	} else if (z <= -3.3e+170) {
		tmp = (a / y) - (x / z);
	} else if (z <= -2.55e-89) {
		tmp = t_2;
	} else if (z <= -9.2e-114) {
		tmp = t_3;
	} else if (z <= -6.5e-131) {
		tmp = t / b;
	} else if (z <= -1.25e-149) {
		tmp = (x * y) / (y + (z * (b - y)));
	} else if (z <= -2.4e-180) {
		tmp = x - (z * t_1);
	} else if (z <= -1.85e-222) {
		tmp = t_3;
	} else if (z <= -2.3e-247) {
		tmp = x + (t * (z / y));
	} else if (z <= 3e-119) {
		tmp = t_3;
	} else if (z <= 6e-99) {
		tmp = (t - a) / b;
	} else if (z <= 8.2e-33) {
		tmp = t_3;
	} else if ((z <= 2.9e+69) || !(z <= 9.2e+131)) {
		tmp = t_2;
	} else {
		tmp = t_1 - (x / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (a - t) / y
    t_2 = (t - a) / (b - y)
    t_3 = ((x * y) - (z * (a - t))) / y
    if (z <= (-1.2d+210)) then
        tmp = t_2
    else if (z <= (-3.3d+170)) then
        tmp = (a / y) - (x / z)
    else if (z <= (-2.55d-89)) then
        tmp = t_2
    else if (z <= (-9.2d-114)) then
        tmp = t_3
    else if (z <= (-6.5d-131)) then
        tmp = t / b
    else if (z <= (-1.25d-149)) then
        tmp = (x * y) / (y + (z * (b - y)))
    else if (z <= (-2.4d-180)) then
        tmp = x - (z * t_1)
    else if (z <= (-1.85d-222)) then
        tmp = t_3
    else if (z <= (-2.3d-247)) then
        tmp = x + (t * (z / y))
    else if (z <= 3d-119) then
        tmp = t_3
    else if (z <= 6d-99) then
        tmp = (t - a) / b
    else if (z <= 8.2d-33) then
        tmp = t_3
    else if ((z <= 2.9d+69) .or. (.not. (z <= 9.2d+131))) then
        tmp = t_2
    else
        tmp = t_1 - (x / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a - t) / y;
	double t_2 = (t - a) / (b - y);
	double t_3 = ((x * y) - (z * (a - t))) / y;
	double tmp;
	if (z <= -1.2e+210) {
		tmp = t_2;
	} else if (z <= -3.3e+170) {
		tmp = (a / y) - (x / z);
	} else if (z <= -2.55e-89) {
		tmp = t_2;
	} else if (z <= -9.2e-114) {
		tmp = t_3;
	} else if (z <= -6.5e-131) {
		tmp = t / b;
	} else if (z <= -1.25e-149) {
		tmp = (x * y) / (y + (z * (b - y)));
	} else if (z <= -2.4e-180) {
		tmp = x - (z * t_1);
	} else if (z <= -1.85e-222) {
		tmp = t_3;
	} else if (z <= -2.3e-247) {
		tmp = x + (t * (z / y));
	} else if (z <= 3e-119) {
		tmp = t_3;
	} else if (z <= 6e-99) {
		tmp = (t - a) / b;
	} else if (z <= 8.2e-33) {
		tmp = t_3;
	} else if ((z <= 2.9e+69) || !(z <= 9.2e+131)) {
		tmp = t_2;
	} else {
		tmp = t_1 - (x / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a - t) / y
	t_2 = (t - a) / (b - y)
	t_3 = ((x * y) - (z * (a - t))) / y
	tmp = 0
	if z <= -1.2e+210:
		tmp = t_2
	elif z <= -3.3e+170:
		tmp = (a / y) - (x / z)
	elif z <= -2.55e-89:
		tmp = t_2
	elif z <= -9.2e-114:
		tmp = t_3
	elif z <= -6.5e-131:
		tmp = t / b
	elif z <= -1.25e-149:
		tmp = (x * y) / (y + (z * (b - y)))
	elif z <= -2.4e-180:
		tmp = x - (z * t_1)
	elif z <= -1.85e-222:
		tmp = t_3
	elif z <= -2.3e-247:
		tmp = x + (t * (z / y))
	elif z <= 3e-119:
		tmp = t_3
	elif z <= 6e-99:
		tmp = (t - a) / b
	elif z <= 8.2e-33:
		tmp = t_3
	elif (z <= 2.9e+69) or not (z <= 9.2e+131):
		tmp = t_2
	else:
		tmp = t_1 - (x / z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a - t) / y)
	t_2 = Float64(Float64(t - a) / Float64(b - y))
	t_3 = Float64(Float64(Float64(x * y) - Float64(z * Float64(a - t))) / y)
	tmp = 0.0
	if (z <= -1.2e+210)
		tmp = t_2;
	elseif (z <= -3.3e+170)
		tmp = Float64(Float64(a / y) - Float64(x / z));
	elseif (z <= -2.55e-89)
		tmp = t_2;
	elseif (z <= -9.2e-114)
		tmp = t_3;
	elseif (z <= -6.5e-131)
		tmp = Float64(t / b);
	elseif (z <= -1.25e-149)
		tmp = Float64(Float64(x * y) / Float64(y + Float64(z * Float64(b - y))));
	elseif (z <= -2.4e-180)
		tmp = Float64(x - Float64(z * t_1));
	elseif (z <= -1.85e-222)
		tmp = t_3;
	elseif (z <= -2.3e-247)
		tmp = Float64(x + Float64(t * Float64(z / y)));
	elseif (z <= 3e-119)
		tmp = t_3;
	elseif (z <= 6e-99)
		tmp = Float64(Float64(t - a) / b);
	elseif (z <= 8.2e-33)
		tmp = t_3;
	elseif ((z <= 2.9e+69) || !(z <= 9.2e+131))
		tmp = t_2;
	else
		tmp = Float64(t_1 - Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a - t) / y;
	t_2 = (t - a) / (b - y);
	t_3 = ((x * y) - (z * (a - t))) / y;
	tmp = 0.0;
	if (z <= -1.2e+210)
		tmp = t_2;
	elseif (z <= -3.3e+170)
		tmp = (a / y) - (x / z);
	elseif (z <= -2.55e-89)
		tmp = t_2;
	elseif (z <= -9.2e-114)
		tmp = t_3;
	elseif (z <= -6.5e-131)
		tmp = t / b;
	elseif (z <= -1.25e-149)
		tmp = (x * y) / (y + (z * (b - y)));
	elseif (z <= -2.4e-180)
		tmp = x - (z * t_1);
	elseif (z <= -1.85e-222)
		tmp = t_3;
	elseif (z <= -2.3e-247)
		tmp = x + (t * (z / y));
	elseif (z <= 3e-119)
		tmp = t_3;
	elseif (z <= 6e-99)
		tmp = (t - a) / b;
	elseif (z <= 8.2e-33)
		tmp = t_3;
	elseif ((z <= 2.9e+69) || ~((z <= 9.2e+131)))
		tmp = t_2;
	else
		tmp = t_1 - (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(x * y), $MachinePrecision] - N[(z * N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[z, -1.2e+210], t$95$2, If[LessEqual[z, -3.3e+170], N[(N[(a / y), $MachinePrecision] - N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.55e-89], t$95$2, If[LessEqual[z, -9.2e-114], t$95$3, If[LessEqual[z, -6.5e-131], N[(t / b), $MachinePrecision], If[LessEqual[z, -1.25e-149], N[(N[(x * y), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.4e-180], N[(x - N[(z * t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.85e-222], t$95$3, If[LessEqual[z, -2.3e-247], N[(x + N[(t * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3e-119], t$95$3, If[LessEqual[z, 6e-99], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[z, 8.2e-33], t$95$3, If[Or[LessEqual[z, 2.9e+69], N[Not[LessEqual[z, 9.2e+131]], $MachinePrecision]], t$95$2, N[(t$95$1 - N[(x / z), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if z < -1.19999999999999994e210 or -3.30000000000000023e170 < z < -2.55000000000000002e-89 or 8.2e-33 < z < 2.8999999999999998e69 or 9.19999999999999966e131 < z

   1. Initial program 51.1%

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

   3. Taylor expanded in z around inf 76.3%

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

   if -1.19999999999999994e210 < z < -3.30000000000000023e170

   1. Initial program 31.0%

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

   3. Taylor expanded in z around -inf 72.3%

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

      1. associate--l+ 72.3%

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

      2. mul-1-neg 72.3%

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

      3. distribute-lft-out-- 72.3%

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

      4. associate-/l* 100.0%

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

      5. associate-/l* 85.7%

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

      6. div-sub 85.7%

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

   5. Simplified 85.7%

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

   6. Taylor expanded in y around inf 89.7%

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

   7. Taylor expanded in y around -inf 89.7%

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

      1. associate-*r/ 89.7%

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

      2. mul-1-neg 89.7%

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

   9. Simplified 89.7%

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

   10. Taylor expanded in t around 0 89.7%

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

   if -2.55000000000000002e-89 < z < -9.1999999999999997e-114 or -2.39999999999999979e-180 < z < -1.8499999999999999e-222 or -2.3e-247 < z < 3.0000000000000002e-119 or 6.00000000000000012e-99 < z < 8.2e-33

   1. Initial program 94.0%

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

   3. Taylor expanded in b around inf 94.0%

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

      1. *-commutative 94.0%

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

   5. Simplified 94.0%

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

   6. Taylor expanded in b around 0 76.1%

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

   if -9.1999999999999997e-114 < z < -6.5000000000000002e-131

   1. Initial program 100.0%

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

   3. Taylor expanded in a around 0 100.0%

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

   4. Taylor expanded in y around 0 68.8%

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

   if -6.5000000000000002e-131 < z < -1.24999999999999992e-149

   1. Initial program 86.6%

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

   3. Taylor expanded in x around inf 73.1%

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

      1. *-commutative 73.1%

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

   5. Simplified 73.1%

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

   if -1.24999999999999992e-149 < z < -2.39999999999999979e-180

   1. Initial program 99.7%

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

   3. Taylor expanded in b around inf 99.7%

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

      1. *-commutative 99.7%

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

   5. Simplified 99.7%

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

   6. Taylor expanded in z around 0 83.4%

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

      1. associate--r+ 83.4%

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

      2. div-sub 83.4%

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

      3. associate-/l* 83.4%

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

   8. Simplified 83.4%

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

   9. Taylor expanded in b around 0 83.4%

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

       1. div-sub 83.4%

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

       2. *-commutative 83.4%

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

   11. Simplified 83.4%

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

   if -1.8499999999999999e-222 < z < -2.3e-247

   1. Initial program 64.5%

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

   3. Taylor expanded in b around inf 64.5%

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

      1. *-commutative 64.5%

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

   5. Simplified 64.5%

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

   6. Taylor expanded in z around 0 75.4%

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

      1. associate--r+ 75.4%

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

      2. div-sub 75.4%

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

      3. associate-/l* 75.4%

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

   8. Simplified 75.4%

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

   9. Taylor expanded in t around inf 76.5%

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

       1. associate-/l* 76.7%

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

   11. Simplified 76.7%

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

   if 3.0000000000000002e-119 < z < 6.00000000000000012e-99

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0 100.0%

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

   if 2.8999999999999998e69 < z < 9.19999999999999966e131

   1. Initial program 51.2%

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

   3. Taylor expanded in z around -inf 62.8%

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

      1. associate--l+ 62.8%

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

      2. mul-1-neg 62.8%

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

      3. distribute-lft-out-- 62.8%

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

      4. associate-/l* 62.8%

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

      5. associate-/l* 87.8%

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

      6. div-sub 87.8%

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

   5. Simplified 87.8%

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

   6. Taylor expanded in y around inf 75.8%

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

   7. Taylor expanded in y around -inf 75.8%

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

      1. associate-*r/ 75.8%

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

      2. mul-1-neg 75.8%

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

   9. Simplified 75.8%

      \[\leadsto \color{blue}{\frac{-\left(t - a\right)}{y} - \frac{x}{z}} \]
3. Recombined 9 regimes into one program.

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+210}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{+170}:\\ \;\;\;\;\frac{a}{y} - \frac{x}{z}\\ \mathbf{elif}\;z \leq -2.55 \cdot 10^{-89}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{-114}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(a - t\right)}{y}\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-131}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-149}:\\ \;\;\;\;\frac{x \cdot y}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-180}:\\ \;\;\;\;x - z \cdot \frac{a - t}{y}\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{-222}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(a - t\right)}{y}\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-247}:\\ \;\;\;\;x + t \cdot \frac{z}{y}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-119}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(a - t\right)}{y}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-99}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-33}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(a - t\right)}{y}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+69} \lor \neg \left(z \leq 9.2 \cdot 10^{+131}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 67.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ t_2 := x - z \cdot \frac{a - t}{y}\\ \mathbf{if}\;z \leq -1.2 \cdot 10^{+210}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{+170}:\\ \;\;\;\;\frac{a}{y} - \frac{x}{z}\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{-89}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{-114}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-131}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-119}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-99}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-32}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+152} \lor \neg \left(z \leq 1.8 \cdot 10^{+176}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b - y} - \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))) (t_2 (- x (* z (/ (- a t) y)))))
   (if (<= z -1.2e+210)
     t_1
     (if (<= z -3.3e+170)
       (- (/ a y) (/ x z))
       (if (<= z -4.4e-89)
         t_1
         (if (<= z -9.2e-114)
           t_2
           (if (<= z -7.2e-131)
             (/ t b)
             (if (<= z 3e-119)
               t_2
               (if (<= z 6e-99)
                 (/ (- t a) b)
                 (if (<= z 2.15e-32)
                   t_2
                   (if (or (<= z 1.6e+152) (not (<= z 1.8e+176)))
                     t_1
                     (- (/ t (- b y)) (/ x z)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double t_2 = x - (z * ((a - t) / y));
	double tmp;
	if (z <= -1.2e+210) {
		tmp = t_1;
	} else if (z <= -3.3e+170) {
		tmp = (a / y) - (x / z);
	} else if (z <= -4.4e-89) {
		tmp = t_1;
	} else if (z <= -9.2e-114) {
		tmp = t_2;
	} else if (z <= -7.2e-131) {
		tmp = t / b;
	} else if (z <= 3e-119) {
		tmp = t_2;
	} else if (z <= 6e-99) {
		tmp = (t - a) / b;
	} else if (z <= 2.15e-32) {
		tmp = t_2;
	} else if ((z <= 1.6e+152) || !(z <= 1.8e+176)) {
		tmp = t_1;
	} else {
		tmp = (t / (b - y)) - (x / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    t_2 = x - (z * ((a - t) / y))
    if (z <= (-1.2d+210)) then
        tmp = t_1
    else if (z <= (-3.3d+170)) then
        tmp = (a / y) - (x / z)
    else if (z <= (-4.4d-89)) then
        tmp = t_1
    else if (z <= (-9.2d-114)) then
        tmp = t_2
    else if (z <= (-7.2d-131)) then
        tmp = t / b
    else if (z <= 3d-119) then
        tmp = t_2
    else if (z <= 6d-99) then
        tmp = (t - a) / b
    else if (z <= 2.15d-32) then
        tmp = t_2
    else if ((z <= 1.6d+152) .or. (.not. (z <= 1.8d+176))) then
        tmp = t_1
    else
        tmp = (t / (b - y)) - (x / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double t_2 = x - (z * ((a - t) / y));
	double tmp;
	if (z <= -1.2e+210) {
		tmp = t_1;
	} else if (z <= -3.3e+170) {
		tmp = (a / y) - (x / z);
	} else if (z <= -4.4e-89) {
		tmp = t_1;
	} else if (z <= -9.2e-114) {
		tmp = t_2;
	} else if (z <= -7.2e-131) {
		tmp = t / b;
	} else if (z <= 3e-119) {
		tmp = t_2;
	} else if (z <= 6e-99) {
		tmp = (t - a) / b;
	} else if (z <= 2.15e-32) {
		tmp = t_2;
	} else if ((z <= 1.6e+152) || !(z <= 1.8e+176)) {
		tmp = t_1;
	} else {
		tmp = (t / (b - y)) - (x / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	t_2 = x - (z * ((a - t) / y))
	tmp = 0
	if z <= -1.2e+210:
		tmp = t_1
	elif z <= -3.3e+170:
		tmp = (a / y) - (x / z)
	elif z <= -4.4e-89:
		tmp = t_1
	elif z <= -9.2e-114:
		tmp = t_2
	elif z <= -7.2e-131:
		tmp = t / b
	elif z <= 3e-119:
		tmp = t_2
	elif z <= 6e-99:
		tmp = (t - a) / b
	elif z <= 2.15e-32:
		tmp = t_2
	elif (z <= 1.6e+152) or not (z <= 1.8e+176):
		tmp = t_1
	else:
		tmp = (t / (b - y)) - (x / z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	t_2 = Float64(x - Float64(z * Float64(Float64(a - t) / y)))
	tmp = 0.0
	if (z <= -1.2e+210)
		tmp = t_1;
	elseif (z <= -3.3e+170)
		tmp = Float64(Float64(a / y) - Float64(x / z));
	elseif (z <= -4.4e-89)
		tmp = t_1;
	elseif (z <= -9.2e-114)
		tmp = t_2;
	elseif (z <= -7.2e-131)
		tmp = Float64(t / b);
	elseif (z <= 3e-119)
		tmp = t_2;
	elseif (z <= 6e-99)
		tmp = Float64(Float64(t - a) / b);
	elseif (z <= 2.15e-32)
		tmp = t_2;
	elseif ((z <= 1.6e+152) || !(z <= 1.8e+176))
		tmp = t_1;
	else
		tmp = Float64(Float64(t / Float64(b - y)) - Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	t_2 = x - (z * ((a - t) / y));
	tmp = 0.0;
	if (z <= -1.2e+210)
		tmp = t_1;
	elseif (z <= -3.3e+170)
		tmp = (a / y) - (x / z);
	elseif (z <= -4.4e-89)
		tmp = t_1;
	elseif (z <= -9.2e-114)
		tmp = t_2;
	elseif (z <= -7.2e-131)
		tmp = t / b;
	elseif (z <= 3e-119)
		tmp = t_2;
	elseif (z <= 6e-99)
		tmp = (t - a) / b;
	elseif (z <= 2.15e-32)
		tmp = t_2;
	elseif ((z <= 1.6e+152) || ~((z <= 1.8e+176)))
		tmp = t_1;
	else
		tmp = (t / (b - y)) - (x / z);
	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]}, Block[{t$95$2 = N[(x - N[(z * N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.2e+210], t$95$1, If[LessEqual[z, -3.3e+170], N[(N[(a / y), $MachinePrecision] - N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4.4e-89], t$95$1, If[LessEqual[z, -9.2e-114], t$95$2, If[LessEqual[z, -7.2e-131], N[(t / b), $MachinePrecision], If[LessEqual[z, 3e-119], t$95$2, If[LessEqual[z, 6e-99], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[z, 2.15e-32], t$95$2, If[Or[LessEqual[z, 1.6e+152], N[Not[LessEqual[z, 1.8e+176]], $MachinePrecision]], t$95$1, N[(N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision] - N[(x / z), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -1.19999999999999994e210 or -3.30000000000000023e170 < z < -4.40000000000000024e-89 or 2.14999999999999995e-32 < z < 1.60000000000000003e152 or 1.79999999999999996e176 < z

   1. Initial program 51.9%

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

   3. Taylor expanded in z around inf 76.6%

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

   if -1.19999999999999994e210 < z < -3.30000000000000023e170

   1. Initial program 31.0%

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

   3. Taylor expanded in z around -inf 72.3%

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

      1. associate--l+ 72.3%

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

      2. mul-1-neg 72.3%

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

      3. distribute-lft-out-- 72.3%

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

      4. associate-/l* 100.0%

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

      5. associate-/l* 85.7%

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

      6. div-sub 85.7%

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

   5. Simplified 85.7%

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

   6. Taylor expanded in y around inf 89.7%

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

   7. Taylor expanded in y around -inf 89.7%

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

      1. associate-*r/ 89.7%

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

      2. mul-1-neg 89.7%

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

   9. Simplified 89.7%

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

   10. Taylor expanded in t around 0 89.7%

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

   if -4.40000000000000024e-89 < z < -9.1999999999999997e-114 or -7.1999999999999999e-131 < z < 3.0000000000000002e-119 or 6.00000000000000012e-99 < z < 2.14999999999999995e-32

   1. Initial program 91.5%

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

   3. Taylor expanded in b around inf 91.5%

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

      1. *-commutative 91.5%

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

   5. Simplified 91.5%

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

   6. Taylor expanded in z around 0 69.2%

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

      1. associate--r+ 69.2%

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

      2. div-sub 69.2%

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

      3. associate-/l* 69.1%

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

   8. Simplified 69.1%

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

   9. Taylor expanded in b around 0 71.4%

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

       1. div-sub 71.4%

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

       2. *-commutative 71.4%

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

   11. Simplified 71.4%

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

   if -9.1999999999999997e-114 < z < -7.1999999999999999e-131

   1. Initial program 100.0%

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

   3. Taylor expanded in a around 0 100.0%

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

   4. Taylor expanded in y around 0 68.8%

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

   if 3.0000000000000002e-119 < z < 6.00000000000000012e-99

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0 100.0%

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

   if 1.60000000000000003e152 < z < 1.79999999999999996e176

   1. Initial program 33.7%

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

   3. Taylor expanded in z around -inf 51.0%

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

      1. associate--l+ 51.0%

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

      2. mul-1-neg 51.0%

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

      3. distribute-lft-out-- 51.0%

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

      4. associate-/l* 83.3%

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

      5. associate-/l* 100.0%

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

      6. div-sub 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in y around inf 84.2%

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

   7. Taylor expanded in a around 0 84.2%

      \[\leadsto \color{blue}{\frac{t}{b - y} - \frac{x}{z}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 75.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+210}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{+170}:\\ \;\;\;\;\frac{a}{y} - \frac{x}{z}\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{-89}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{-114}:\\ \;\;\;\;x - z \cdot \frac{a - t}{y}\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-131}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-119}:\\ \;\;\;\;x - z \cdot \frac{a - t}{y}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-99}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-32}:\\ \;\;\;\;x - z \cdot \frac{a - t}{y}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+152} \lor \neg \left(z \leq 1.8 \cdot 10^{+176}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b - y} - \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 66.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a}{y} - \frac{x}{z}\\ t_2 := \frac{t - a}{b - y}\\ t_3 := x - z \cdot \frac{a - t}{y}\\ \mathbf{if}\;z \leq -1.2 \cdot 10^{+210}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{+170}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-89}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{-114}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-130}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 2.85 \cdot 10^{-120}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-99}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-32}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+152} \lor \neg \left(z \leq 1.75 \cdot 10^{+201}\right):\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (/ a y) (/ x z)))
        (t_2 (/ (- t a) (- b y)))
        (t_3 (- x (* z (/ (- a t) y)))))
   (if (<= z -1.2e+210)
     t_2
     (if (<= z -3.3e+170)
       t_1
       (if (<= z -4.2e-89)
         t_2
         (if (<= z -9.2e-114)
           t_3
           (if (<= z -1.7e-130)
             (/ t b)
             (if (<= z 2.85e-120)
               t_3
               (if (<= z 6e-99)
                 (/ (- t a) b)
                 (if (<= z 2.15e-32)
                   t_3
                   (if (or (<= z 3.2e+152) (not (<= z 1.75e+201)))
                     t_2
                     t_1)))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a / y) - (x / z);
	double t_2 = (t - a) / (b - y);
	double t_3 = x - (z * ((a - t) / y));
	double tmp;
	if (z <= -1.2e+210) {
		tmp = t_2;
	} else if (z <= -3.3e+170) {
		tmp = t_1;
	} else if (z <= -4.2e-89) {
		tmp = t_2;
	} else if (z <= -9.2e-114) {
		tmp = t_3;
	} else if (z <= -1.7e-130) {
		tmp = t / b;
	} else if (z <= 2.85e-120) {
		tmp = t_3;
	} else if (z <= 6e-99) {
		tmp = (t - a) / b;
	} else if (z <= 2.15e-32) {
		tmp = t_3;
	} else if ((z <= 3.2e+152) || !(z <= 1.75e+201)) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (a / y) - (x / z)
    t_2 = (t - a) / (b - y)
    t_3 = x - (z * ((a - t) / y))
    if (z <= (-1.2d+210)) then
        tmp = t_2
    else if (z <= (-3.3d+170)) then
        tmp = t_1
    else if (z <= (-4.2d-89)) then
        tmp = t_2
    else if (z <= (-9.2d-114)) then
        tmp = t_3
    else if (z <= (-1.7d-130)) then
        tmp = t / b
    else if (z <= 2.85d-120) then
        tmp = t_3
    else if (z <= 6d-99) then
        tmp = (t - a) / b
    else if (z <= 2.15d-32) then
        tmp = t_3
    else if ((z <= 3.2d+152) .or. (.not. (z <= 1.75d+201))) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a / y) - (x / z);
	double t_2 = (t - a) / (b - y);
	double t_3 = x - (z * ((a - t) / y));
	double tmp;
	if (z <= -1.2e+210) {
		tmp = t_2;
	} else if (z <= -3.3e+170) {
		tmp = t_1;
	} else if (z <= -4.2e-89) {
		tmp = t_2;
	} else if (z <= -9.2e-114) {
		tmp = t_3;
	} else if (z <= -1.7e-130) {
		tmp = t / b;
	} else if (z <= 2.85e-120) {
		tmp = t_3;
	} else if (z <= 6e-99) {
		tmp = (t - a) / b;
	} else if (z <= 2.15e-32) {
		tmp = t_3;
	} else if ((z <= 3.2e+152) || !(z <= 1.75e+201)) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a / y) - (x / z)
	t_2 = (t - a) / (b - y)
	t_3 = x - (z * ((a - t) / y))
	tmp = 0
	if z <= -1.2e+210:
		tmp = t_2
	elif z <= -3.3e+170:
		tmp = t_1
	elif z <= -4.2e-89:
		tmp = t_2
	elif z <= -9.2e-114:
		tmp = t_3
	elif z <= -1.7e-130:
		tmp = t / b
	elif z <= 2.85e-120:
		tmp = t_3
	elif z <= 6e-99:
		tmp = (t - a) / b
	elif z <= 2.15e-32:
		tmp = t_3
	elif (z <= 3.2e+152) or not (z <= 1.75e+201):
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a / y) - Float64(x / z))
	t_2 = Float64(Float64(t - a) / Float64(b - y))
	t_3 = Float64(x - Float64(z * Float64(Float64(a - t) / y)))
	tmp = 0.0
	if (z <= -1.2e+210)
		tmp = t_2;
	elseif (z <= -3.3e+170)
		tmp = t_1;
	elseif (z <= -4.2e-89)
		tmp = t_2;
	elseif (z <= -9.2e-114)
		tmp = t_3;
	elseif (z <= -1.7e-130)
		tmp = Float64(t / b);
	elseif (z <= 2.85e-120)
		tmp = t_3;
	elseif (z <= 6e-99)
		tmp = Float64(Float64(t - a) / b);
	elseif (z <= 2.15e-32)
		tmp = t_3;
	elseif ((z <= 3.2e+152) || !(z <= 1.75e+201))
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a / y) - (x / z);
	t_2 = (t - a) / (b - y);
	t_3 = x - (z * ((a - t) / y));
	tmp = 0.0;
	if (z <= -1.2e+210)
		tmp = t_2;
	elseif (z <= -3.3e+170)
		tmp = t_1;
	elseif (z <= -4.2e-89)
		tmp = t_2;
	elseif (z <= -9.2e-114)
		tmp = t_3;
	elseif (z <= -1.7e-130)
		tmp = t / b;
	elseif (z <= 2.85e-120)
		tmp = t_3;
	elseif (z <= 6e-99)
		tmp = (t - a) / b;
	elseif (z <= 2.15e-32)
		tmp = t_3;
	elseif ((z <= 3.2e+152) || ~((z <= 1.75e+201)))
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a / y), $MachinePrecision] - N[(x / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x - N[(z * N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.2e+210], t$95$2, If[LessEqual[z, -3.3e+170], t$95$1, If[LessEqual[z, -4.2e-89], t$95$2, If[LessEqual[z, -9.2e-114], t$95$3, If[LessEqual[z, -1.7e-130], N[(t / b), $MachinePrecision], If[LessEqual[z, 2.85e-120], t$95$3, If[LessEqual[z, 6e-99], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[z, 2.15e-32], t$95$3, If[Or[LessEqual[z, 3.2e+152], N[Not[LessEqual[z, 1.75e+201]], $MachinePrecision]], t$95$2, t$95$1]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.19999999999999994e210 or -3.30000000000000023e170 < z < -4.2000000000000002e-89 or 2.14999999999999995e-32 < z < 3.20000000000000005e152 or 1.7500000000000001e201 < z

   1. Initial program 53.0%

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

   3. Taylor expanded in z around inf 77.2%

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

   if -1.19999999999999994e210 < z < -3.30000000000000023e170 or 3.20000000000000005e152 < z < 1.7500000000000001e201

   1. Initial program 29.5%

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

   3. Taylor expanded in z around -inf 67.3%

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

      1. associate--l+ 67.3%

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

      2. mul-1-neg 67.3%

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

      3. distribute-lft-out-- 67.3%

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

      4. associate-/l* 88.9%

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

      5. associate-/l* 94.4%

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

      6. div-sub 94.4%

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

   5. Simplified 94.4%

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

   6. Taylor expanded in y around inf 90.7%

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

   7. Taylor expanded in y around -inf 79.6%

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

      1. associate-*r/ 79.6%

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

      2. mul-1-neg 79.6%

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

   9. Simplified 79.6%

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

   10. Taylor expanded in t around 0 74.4%

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

   if -4.2000000000000002e-89 < z < -9.1999999999999997e-114 or -1.70000000000000003e-130 < z < 2.85000000000000015e-120 or 6.00000000000000012e-99 < z < 2.14999999999999995e-32

   1. Initial program 91.5%

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

   3. Taylor expanded in b around inf 91.5%

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

      1. *-commutative 91.5%

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

   5. Simplified 91.5%

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

   6. Taylor expanded in z around 0 69.2%

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

      1. associate--r+ 69.2%

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

      2. div-sub 69.2%

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

      3. associate-/l* 69.1%

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

   8. Simplified 69.1%

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

   9. Taylor expanded in b around 0 71.4%

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

       1. div-sub 71.4%

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

       2. *-commutative 71.4%

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

   11. Simplified 71.4%

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

   if -9.1999999999999997e-114 < z < -1.70000000000000003e-130

   1. Initial program 100.0%

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

   3. Taylor expanded in a around 0 100.0%

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

   4. Taylor expanded in y around 0 68.8%

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

   if 2.85000000000000015e-120 < z < 6.00000000000000012e-99

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0 100.0%

      \[\leadsto \color{blue}{\frac{t - a}{b}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+210}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{+170}:\\ \;\;\;\;\frac{a}{y} - \frac{x}{z}\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-89}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{-114}:\\ \;\;\;\;x - z \cdot \frac{a - t}{y}\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-130}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 2.85 \cdot 10^{-120}:\\ \;\;\;\;x - z \cdot \frac{a - t}{y}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-99}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-32}:\\ \;\;\;\;x - z \cdot \frac{a - t}{y}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+152} \lor \neg \left(z \leq 1.75 \cdot 10^{+201}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{y} - \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 52.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 - z}\\ t_2 := x - z \cdot \frac{a}{y}\\ \mathbf{if}\;y \leq -1 \cdot 10^{+157}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -3700:\\ \;\;\;\;\frac{a - t}{y}\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-18}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{+46}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+78}:\\ \;\;\;\;x + t \cdot \frac{z}{y}\\ \mathbf{elif}\;y \leq 5.7 \cdot 10^{+118}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+186}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 9.6 \cdot 10^{+186}:\\ \;\;\;\;\frac{a}{y}\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+237} \lor \neg \left(y \leq 2.3 \cdot 10^{+256}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{t}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (- 1.0 z))) (t_2 (- x (* z (/ a y)))))
   (if (<= y -1e+157)
     t_1
     (if (<= y -3700.0)
       (/ (- a t) y)
       (if (<= y 6e-18)
         (/ (- t a) b)
         (if (<= y 6.4e+46)
           t_2
           (if (<= y 4.2e+78)
             (+ x (* t (/ z y)))
             (if (<= y 5.7e+118)
               t_2
               (if (<= y 8e+186)
                 t_1
                 (if (<= y 9.6e+186)
                   (/ a y)
                   (if (or (<= y 5e+237) (not (<= y 2.3e+256)))
                     t_1
                     (+ x (* z (/ t y))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 - z);
	double t_2 = x - (z * (a / y));
	double tmp;
	if (y <= -1e+157) {
		tmp = t_1;
	} else if (y <= -3700.0) {
		tmp = (a - t) / y;
	} else if (y <= 6e-18) {
		tmp = (t - a) / b;
	} else if (y <= 6.4e+46) {
		tmp = t_2;
	} else if (y <= 4.2e+78) {
		tmp = x + (t * (z / y));
	} else if (y <= 5.7e+118) {
		tmp = t_2;
	} else if (y <= 8e+186) {
		tmp = t_1;
	} else if (y <= 9.6e+186) {
		tmp = a / y;
	} else if ((y <= 5e+237) || !(y <= 2.3e+256)) {
		tmp = t_1;
	} else {
		tmp = x + (z * (t / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x / (1.0d0 - z)
    t_2 = x - (z * (a / y))
    if (y <= (-1d+157)) then
        tmp = t_1
    else if (y <= (-3700.0d0)) then
        tmp = (a - t) / y
    else if (y <= 6d-18) then
        tmp = (t - a) / b
    else if (y <= 6.4d+46) then
        tmp = t_2
    else if (y <= 4.2d+78) then
        tmp = x + (t * (z / y))
    else if (y <= 5.7d+118) then
        tmp = t_2
    else if (y <= 8d+186) then
        tmp = t_1
    else if (y <= 9.6d+186) then
        tmp = a / y
    else if ((y <= 5d+237) .or. (.not. (y <= 2.3d+256))) then
        tmp = t_1
    else
        tmp = x + (z * (t / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 - z);
	double t_2 = x - (z * (a / y));
	double tmp;
	if (y <= -1e+157) {
		tmp = t_1;
	} else if (y <= -3700.0) {
		tmp = (a - t) / y;
	} else if (y <= 6e-18) {
		tmp = (t - a) / b;
	} else if (y <= 6.4e+46) {
		tmp = t_2;
	} else if (y <= 4.2e+78) {
		tmp = x + (t * (z / y));
	} else if (y <= 5.7e+118) {
		tmp = t_2;
	} else if (y <= 8e+186) {
		tmp = t_1;
	} else if (y <= 9.6e+186) {
		tmp = a / y;
	} else if ((y <= 5e+237) || !(y <= 2.3e+256)) {
		tmp = t_1;
	} else {
		tmp = x + (z * (t / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (1.0 - z)
	t_2 = x - (z * (a / y))
	tmp = 0
	if y <= -1e+157:
		tmp = t_1
	elif y <= -3700.0:
		tmp = (a - t) / y
	elif y <= 6e-18:
		tmp = (t - a) / b
	elif y <= 6.4e+46:
		tmp = t_2
	elif y <= 4.2e+78:
		tmp = x + (t * (z / y))
	elif y <= 5.7e+118:
		tmp = t_2
	elif y <= 8e+186:
		tmp = t_1
	elif y <= 9.6e+186:
		tmp = a / y
	elif (y <= 5e+237) or not (y <= 2.3e+256):
		tmp = t_1
	else:
		tmp = x + (z * (t / y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(1.0 - z))
	t_2 = Float64(x - Float64(z * Float64(a / y)))
	tmp = 0.0
	if (y <= -1e+157)
		tmp = t_1;
	elseif (y <= -3700.0)
		tmp = Float64(Float64(a - t) / y);
	elseif (y <= 6e-18)
		tmp = Float64(Float64(t - a) / b);
	elseif (y <= 6.4e+46)
		tmp = t_2;
	elseif (y <= 4.2e+78)
		tmp = Float64(x + Float64(t * Float64(z / y)));
	elseif (y <= 5.7e+118)
		tmp = t_2;
	elseif (y <= 8e+186)
		tmp = t_1;
	elseif (y <= 9.6e+186)
		tmp = Float64(a / y);
	elseif ((y <= 5e+237) || !(y <= 2.3e+256))
		tmp = t_1;
	else
		tmp = Float64(x + Float64(z * Float64(t / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (1.0 - z);
	t_2 = x - (z * (a / y));
	tmp = 0.0;
	if (y <= -1e+157)
		tmp = t_1;
	elseif (y <= -3700.0)
		tmp = (a - t) / y;
	elseif (y <= 6e-18)
		tmp = (t - a) / b;
	elseif (y <= 6.4e+46)
		tmp = t_2;
	elseif (y <= 4.2e+78)
		tmp = x + (t * (z / y));
	elseif (y <= 5.7e+118)
		tmp = t_2;
	elseif (y <= 8e+186)
		tmp = t_1;
	elseif (y <= 9.6e+186)
		tmp = a / y;
	elseif ((y <= 5e+237) || ~((y <= 2.3e+256)))
		tmp = t_1;
	else
		tmp = x + (z * (t / y));
	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]}, Block[{t$95$2 = N[(x - N[(z * N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1e+157], t$95$1, If[LessEqual[y, -3700.0], N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, 6e-18], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[y, 6.4e+46], t$95$2, If[LessEqual[y, 4.2e+78], N[(x + N[(t * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.7e+118], t$95$2, If[LessEqual[y, 8e+186], t$95$1, If[LessEqual[y, 9.6e+186], N[(a / y), $MachinePrecision], If[Or[LessEqual[y, 5e+237], N[Not[LessEqual[y, 2.3e+256]], $MachinePrecision]], t$95$1, N[(x + N[(z * N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y < -9.99999999999999983e156 or 5.70000000000000002e118 < y < 7.99999999999999984e186 or 9.5999999999999998e186 < y < 5.0000000000000002e237 or 2.2999999999999999e256 < y

   1. Initial program 43.8%

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

   3. Taylor expanded in y around inf 67.9%

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

      1. mul-1-neg 67.9%

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

      2. unsub-neg 67.9%

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

   5. Simplified 67.9%

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

   if -9.99999999999999983e156 < y < -3700

   1. Initial program 53.5%

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

   3. Taylor expanded in z around -inf 49.7%

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

      1. associate--l+ 49.7%

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

      2. mul-1-neg 49.7%

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

      3. distribute-lft-out-- 49.7%

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

      4. associate-/l* 49.8%

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

      5. associate-/l* 69.5%

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

      6. div-sub 69.5%

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

   5. Simplified 69.5%

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

   6. Taylor expanded in y around inf 57.4%

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

   7. Taylor expanded in y around -inf 44.5%

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

      1. associate-*r/ 44.5%

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

      2. mul-1-neg 44.5%

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

   9. Simplified 44.5%

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

   10. Taylor expanded in y around 0 40.0%

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

   if -3700 < y < 5.99999999999999966e-18

   1. Initial program 80.8%

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

   3. Taylor expanded in y around 0 66.2%

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

   if 5.99999999999999966e-18 < y < 6.3999999999999996e46 or 4.2000000000000002e78 < y < 5.70000000000000002e118

   1. Initial program 80.2%

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

   3. Taylor expanded in b around inf 67.9%

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

      1. *-commutative 67.9%

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

   5. Simplified 67.9%

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

   6. Taylor expanded in z around 0 59.7%

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

      1. associate--r+ 59.7%

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

      2. div-sub 59.7%

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

      3. associate-/l* 62.8%

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

   8. Simplified 62.8%

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

   9. Taylor expanded in b around 0 63.0%

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

       1. div-sub 63.0%

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

       2. *-commutative 63.0%

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

   11. Simplified 63.0%

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

   12. Taylor expanded in t around 0 60.2%

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

       1. mul-1-neg 60.2%

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

       2. associate-*r/ 60.2%

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

       3. unsub-neg 60.2%

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

       4. associate-*r/ 60.2%

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

       5. *-commutative 60.2%

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

       6. associate-*r/ 60.1%

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

   14. Simplified 60.1%

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

   if 6.3999999999999996e46 < y < 4.2000000000000002e78

   1. Initial program 84.2%

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

   3. Taylor expanded in b around inf 67.7%

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

      1. *-commutative 67.7%

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

   5. Simplified 67.7%

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

   6. Taylor expanded in z around 0 67.6%

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

      1. associate--r+ 67.6%

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

      2. div-sub 67.6%

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

      3. associate-/l* 67.6%

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

   8. Simplified 67.6%

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

   9. Taylor expanded in t around inf 67.8%

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

       1. associate-/l* 67.8%

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

   11. Simplified 67.8%

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

   if 7.99999999999999984e186 < y < 9.5999999999999998e186

   1. Initial program 50.0%

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

   3. Taylor expanded in z around -inf 50.0%

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

      1. associate--l+ 50.0%

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

      2. mul-1-neg 50.0%

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

      3. distribute-lft-out-- 50.0%

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

      4. associate-/l* 50.0%

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

      5. associate-/l* 100.0%

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

      6. div-sub 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in y around inf 90.9%

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

   7. Taylor expanded in y around -inf 90.9%

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

      1. associate-*r/ 90.9%

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

      2. mul-1-neg 90.9%

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

   9. Simplified 90.9%

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

   10. Taylor expanded in a around inf 100.0%

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

   if 5.0000000000000002e237 < y < 2.2999999999999999e256

   1. Initial program 51.2%

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

   3. Taylor expanded in b around inf 51.8%

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

      1. *-commutative 51.8%

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

   5. Simplified 51.8%

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

   6. Taylor expanded in z around 0 68.9%

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

      1. associate--r+ 68.9%

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

      2. div-sub 68.9%

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

      3. associate-/l* 68.9%

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

   8. Simplified 68.9%

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

   9. Taylor expanded in t around inf 68.9%

      \[\leadsto x + z \cdot \color{blue}{\frac{t}{y}} \]
3. Recombined 7 regimes into one program.

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+157}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq -3700:\\ \;\;\;\;\frac{a - t}{y}\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-18}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{+46}:\\ \;\;\;\;x - z \cdot \frac{a}{y}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+78}:\\ \;\;\;\;x + t \cdot \frac{z}{y}\\ \mathbf{elif}\;y \leq 5.7 \cdot 10^{+118}:\\ \;\;\;\;x - z \cdot \frac{a}{y}\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+186}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq 9.6 \cdot 10^{+186}:\\ \;\;\;\;\frac{a}{y}\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+237} \lor \neg \left(y \leq 2.3 \cdot 10^{+256}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{t}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 52.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 - z}\\ t_2 := x - z \cdot \frac{a}{y}\\ \mathbf{if}\;y \leq -1 \cdot 10^{+157}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -23:\\ \;\;\;\;\frac{a - t}{y}\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-18}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+46}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+77}:\\ \;\;\;\;x + t \cdot \frac{z}{y}\\ \mathbf{elif}\;y \leq 1.26 \cdot 10^{+122}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{+186}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 10^{+187}:\\ \;\;\;\;\frac{a}{y}\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{+214}:\\ \;\;\;\;\frac{a}{y} - \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (- 1.0 z))) (t_2 (- x (* z (/ a y)))))
   (if (<= y -1e+157)
     t_1
     (if (<= y -23.0)
       (/ (- a t) y)
       (if (<= y 6.2e-18)
         (/ (- t a) b)
         (if (<= y 4.8e+46)
           t_2
           (if (<= y 1.25e+77)
             (+ x (* t (/ z y)))
             (if (<= y 1.26e+122)
               t_2
               (if (<= y 8.2e+186)
                 t_1
                 (if (<= y 1e+187)
                   (/ a y)
                   (if (<= y 4.3e+214) (- (/ a y) (/ x z)) 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 t_2 = x - (z * (a / y));
	double tmp;
	if (y <= -1e+157) {
		tmp = t_1;
	} else if (y <= -23.0) {
		tmp = (a - t) / y;
	} else if (y <= 6.2e-18) {
		tmp = (t - a) / b;
	} else if (y <= 4.8e+46) {
		tmp = t_2;
	} else if (y <= 1.25e+77) {
		tmp = x + (t * (z / y));
	} else if (y <= 1.26e+122) {
		tmp = t_2;
	} else if (y <= 8.2e+186) {
		tmp = t_1;
	} else if (y <= 1e+187) {
		tmp = a / y;
	} else if (y <= 4.3e+214) {
		tmp = (a / y) - (x / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x / (1.0d0 - z)
    t_2 = x - (z * (a / y))
    if (y <= (-1d+157)) then
        tmp = t_1
    else if (y <= (-23.0d0)) then
        tmp = (a - t) / y
    else if (y <= 6.2d-18) then
        tmp = (t - a) / b
    else if (y <= 4.8d+46) then
        tmp = t_2
    else if (y <= 1.25d+77) then
        tmp = x + (t * (z / y))
    else if (y <= 1.26d+122) then
        tmp = t_2
    else if (y <= 8.2d+186) then
        tmp = t_1
    else if (y <= 1d+187) then
        tmp = a / y
    else if (y <= 4.3d+214) then
        tmp = (a / y) - (x / z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 - z);
	double t_2 = x - (z * (a / y));
	double tmp;
	if (y <= -1e+157) {
		tmp = t_1;
	} else if (y <= -23.0) {
		tmp = (a - t) / y;
	} else if (y <= 6.2e-18) {
		tmp = (t - a) / b;
	} else if (y <= 4.8e+46) {
		tmp = t_2;
	} else if (y <= 1.25e+77) {
		tmp = x + (t * (z / y));
	} else if (y <= 1.26e+122) {
		tmp = t_2;
	} else if (y <= 8.2e+186) {
		tmp = t_1;
	} else if (y <= 1e+187) {
		tmp = a / y;
	} else if (y <= 4.3e+214) {
		tmp = (a / y) - (x / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (1.0 - z)
	t_2 = x - (z * (a / y))
	tmp = 0
	if y <= -1e+157:
		tmp = t_1
	elif y <= -23.0:
		tmp = (a - t) / y
	elif y <= 6.2e-18:
		tmp = (t - a) / b
	elif y <= 4.8e+46:
		tmp = t_2
	elif y <= 1.25e+77:
		tmp = x + (t * (z / y))
	elif y <= 1.26e+122:
		tmp = t_2
	elif y <= 8.2e+186:
		tmp = t_1
	elif y <= 1e+187:
		tmp = a / y
	elif y <= 4.3e+214:
		tmp = (a / y) - (x / z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(1.0 - z))
	t_2 = Float64(x - Float64(z * Float64(a / y)))
	tmp = 0.0
	if (y <= -1e+157)
		tmp = t_1;
	elseif (y <= -23.0)
		tmp = Float64(Float64(a - t) / y);
	elseif (y <= 6.2e-18)
		tmp = Float64(Float64(t - a) / b);
	elseif (y <= 4.8e+46)
		tmp = t_2;
	elseif (y <= 1.25e+77)
		tmp = Float64(x + Float64(t * Float64(z / y)));
	elseif (y <= 1.26e+122)
		tmp = t_2;
	elseif (y <= 8.2e+186)
		tmp = t_1;
	elseif (y <= 1e+187)
		tmp = Float64(a / y);
	elseif (y <= 4.3e+214)
		tmp = Float64(Float64(a / y) - Float64(x / z));
	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);
	t_2 = x - (z * (a / y));
	tmp = 0.0;
	if (y <= -1e+157)
		tmp = t_1;
	elseif (y <= -23.0)
		tmp = (a - t) / y;
	elseif (y <= 6.2e-18)
		tmp = (t - a) / b;
	elseif (y <= 4.8e+46)
		tmp = t_2;
	elseif (y <= 1.25e+77)
		tmp = x + (t * (z / y));
	elseif (y <= 1.26e+122)
		tmp = t_2;
	elseif (y <= 8.2e+186)
		tmp = t_1;
	elseif (y <= 1e+187)
		tmp = a / y;
	elseif (y <= 4.3e+214)
		tmp = (a / y) - (x / z);
	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]}, Block[{t$95$2 = N[(x - N[(z * N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1e+157], t$95$1, If[LessEqual[y, -23.0], N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, 6.2e-18], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[y, 4.8e+46], t$95$2, If[LessEqual[y, 1.25e+77], N[(x + N[(t * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.26e+122], t$95$2, If[LessEqual[y, 8.2e+186], t$95$1, If[LessEqual[y, 1e+187], N[(a / y), $MachinePrecision], If[LessEqual[y, 4.3e+214], N[(N[(a / y), $MachinePrecision] - N[(x / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y < -9.99999999999999983e156 or 1.25999999999999991e122 < y < 8.2e186 or 4.29999999999999983e214 < y

   1. Initial program 47.9%

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

   3. Taylor expanded in y around inf 68.9%

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

      1. mul-1-neg 68.9%

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

      2. unsub-neg 68.9%

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

   5. Simplified 68.9%

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

   if -9.99999999999999983e156 < y < -23

   1. Initial program 53.5%

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

   3. Taylor expanded in z around -inf 49.7%

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

      1. associate--l+ 49.7%

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

      2. mul-1-neg 49.7%

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

      3. distribute-lft-out-- 49.7%

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

      4. associate-/l* 49.8%

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

      5. associate-/l* 69.5%

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

      6. div-sub 69.5%

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

   5. Simplified 69.5%

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

   6. Taylor expanded in y around inf 57.4%

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

   7. Taylor expanded in y around -inf 44.5%

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

      1. associate-*r/ 44.5%

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

      2. mul-1-neg 44.5%

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

   9. Simplified 44.5%

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

   10. Taylor expanded in y around 0 40.0%

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

   if -23 < y < 6.20000000000000014e-18

   1. Initial program 80.8%

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

   3. Taylor expanded in y around 0 66.2%

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

   if 6.20000000000000014e-18 < y < 4.80000000000000017e46 or 1.25000000000000001e77 < y < 1.25999999999999991e122

   1. Initial program 80.2%

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

   3. Taylor expanded in b around inf 67.9%

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

      1. *-commutative 67.9%

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

   5. Simplified 67.9%

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

   6. Taylor expanded in z around 0 59.7%

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

      1. associate--r+ 59.7%

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

      2. div-sub 59.7%

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

      3. associate-/l* 62.8%

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

   8. Simplified 62.8%

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

   9. Taylor expanded in b around 0 63.0%

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

       1. div-sub 63.0%

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

       2. *-commutative 63.0%

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

   11. Simplified 63.0%

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

   12. Taylor expanded in t around 0 60.2%

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

       1. mul-1-neg 60.2%

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

       2. associate-*r/ 60.2%

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

       3. unsub-neg 60.2%

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

       4. associate-*r/ 60.2%

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

       5. *-commutative 60.2%

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

       6. associate-*r/ 60.1%

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

   14. Simplified 60.1%

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

   if 4.80000000000000017e46 < y < 1.25000000000000001e77

   1. Initial program 84.2%

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

   3. Taylor expanded in b around inf 67.7%

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

      1. *-commutative 67.7%

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

   5. Simplified 67.7%

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

   6. Taylor expanded in z around 0 67.6%

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

      1. associate--r+ 67.6%

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

      2. div-sub 67.6%

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

      3. associate-/l* 67.6%

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

   8. Simplified 67.6%

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

   9. Taylor expanded in t around inf 67.8%

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

       1. associate-/l* 67.8%

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

   11. Simplified 67.8%

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

   if 8.2e186 < y < 9.99999999999999907e186

   1. Initial program 50.0%

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

   3. Taylor expanded in z around -inf 50.0%

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

      1. associate--l+ 50.0%

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

      2. mul-1-neg 50.0%

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

      3. distribute-lft-out-- 50.0%

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

      4. associate-/l* 50.0%

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

      5. associate-/l* 100.0%

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

      6. div-sub 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in y around inf 90.9%

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

   7. Taylor expanded in y around -inf 90.9%

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

      1. associate-*r/ 90.9%

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

      2. mul-1-neg 90.9%

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

   9. Simplified 90.9%

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

   10. Taylor expanded in a around inf 100.0%

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

   if 9.99999999999999907e186 < y < 4.29999999999999983e214

   1. Initial program 16.8%

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

   3. Taylor expanded in z around -inf 14.8%

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

      1. associate--l+ 14.8%

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

      2. mul-1-neg 14.8%

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

      3. distribute-lft-out-- 14.8%

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

      4. associate-/l* 42.7%

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

      5. associate-/l* 72.1%

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

      6. div-sub 72.1%

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

   5. Simplified 72.1%

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

   6. Taylor expanded in y around inf 58.7%

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

   7. Taylor expanded in y around -inf 58.7%

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

      1. associate-*r/ 58.7%

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

      2. mul-1-neg 58.7%

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

   9. Simplified 58.7%

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

   10. Taylor expanded in t around 0 58.7%

       \[\leadsto \color{blue}{\frac{a}{y} - \frac{x}{z}} \]
3. Recombined 7 regimes into one program.
4. Add Preprocessing

Alternative 10: 72.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ t_2 := t\_1 - \frac{x}{z}\\ t_3 := \frac{x \cdot y - z \cdot \left(a - t\right)}{y}\\ \mathbf{if}\;z \leq -1.3:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-139}:\\ \;\;\;\;x - z \cdot \frac{a - t}{y}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-119}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq 2.75 \cdot 10^{-76}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{-30}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq 850000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+172} \lor \neg \left(z \leq 1.85 \cdot 10^{+172}\right):\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y)))
        (t_2 (- t_1 (/ x z)))
        (t_3 (/ (- (* x y) (* z (- a t))) y)))
   (if (<= z -1.3)
     t_2
     (if (<= z -1.6e-139)
       (- x (* z (/ (- a t) y)))
       (if (<= z 3e-119)
         t_3
         (if (<= z 2.75e-76)
           (/ (- t a) b)
           (if (<= z 4.7e-30)
             t_3
             (if (<= z 850000000000.0)
               t_1
               (if (or (<= z 1.8e+172) (not (<= z 1.85e+172)))
                 t_2
                 (/ t b))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double t_2 = t_1 - (x / z);
	double t_3 = ((x * y) - (z * (a - t))) / y;
	double tmp;
	if (z <= -1.3) {
		tmp = t_2;
	} else if (z <= -1.6e-139) {
		tmp = x - (z * ((a - t) / y));
	} else if (z <= 3e-119) {
		tmp = t_3;
	} else if (z <= 2.75e-76) {
		tmp = (t - a) / b;
	} else if (z <= 4.7e-30) {
		tmp = t_3;
	} else if (z <= 850000000000.0) {
		tmp = t_1;
	} else if ((z <= 1.8e+172) || !(z <= 1.85e+172)) {
		tmp = t_2;
	} else {
		tmp = t / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    t_2 = t_1 - (x / z)
    t_3 = ((x * y) - (z * (a - t))) / y
    if (z <= (-1.3d0)) then
        tmp = t_2
    else if (z <= (-1.6d-139)) then
        tmp = x - (z * ((a - t) / y))
    else if (z <= 3d-119) then
        tmp = t_3
    else if (z <= 2.75d-76) then
        tmp = (t - a) / b
    else if (z <= 4.7d-30) then
        tmp = t_3
    else if (z <= 850000000000.0d0) then
        tmp = t_1
    else if ((z <= 1.8d+172) .or. (.not. (z <= 1.85d+172))) then
        tmp = t_2
    else
        tmp = t / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double t_2 = t_1 - (x / z);
	double t_3 = ((x * y) - (z * (a - t))) / y;
	double tmp;
	if (z <= -1.3) {
		tmp = t_2;
	} else if (z <= -1.6e-139) {
		tmp = x - (z * ((a - t) / y));
	} else if (z <= 3e-119) {
		tmp = t_3;
	} else if (z <= 2.75e-76) {
		tmp = (t - a) / b;
	} else if (z <= 4.7e-30) {
		tmp = t_3;
	} else if (z <= 850000000000.0) {
		tmp = t_1;
	} else if ((z <= 1.8e+172) || !(z <= 1.85e+172)) {
		tmp = t_2;
	} else {
		tmp = t / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	t_2 = t_1 - (x / z)
	t_3 = ((x * y) - (z * (a - t))) / y
	tmp = 0
	if z <= -1.3:
		tmp = t_2
	elif z <= -1.6e-139:
		tmp = x - (z * ((a - t) / y))
	elif z <= 3e-119:
		tmp = t_3
	elif z <= 2.75e-76:
		tmp = (t - a) / b
	elif z <= 4.7e-30:
		tmp = t_3
	elif z <= 850000000000.0:
		tmp = t_1
	elif (z <= 1.8e+172) or not (z <= 1.85e+172):
		tmp = t_2
	else:
		tmp = t / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	t_2 = Float64(t_1 - Float64(x / z))
	t_3 = Float64(Float64(Float64(x * y) - Float64(z * Float64(a - t))) / y)
	tmp = 0.0
	if (z <= -1.3)
		tmp = t_2;
	elseif (z <= -1.6e-139)
		tmp = Float64(x - Float64(z * Float64(Float64(a - t) / y)));
	elseif (z <= 3e-119)
		tmp = t_3;
	elseif (z <= 2.75e-76)
		tmp = Float64(Float64(t - a) / b);
	elseif (z <= 4.7e-30)
		tmp = t_3;
	elseif (z <= 850000000000.0)
		tmp = t_1;
	elseif ((z <= 1.8e+172) || !(z <= 1.85e+172))
		tmp = t_2;
	else
		tmp = Float64(t / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	t_2 = t_1 - (x / z);
	t_3 = ((x * y) - (z * (a - t))) / y;
	tmp = 0.0;
	if (z <= -1.3)
		tmp = t_2;
	elseif (z <= -1.6e-139)
		tmp = x - (z * ((a - t) / y));
	elseif (z <= 3e-119)
		tmp = t_3;
	elseif (z <= 2.75e-76)
		tmp = (t - a) / b;
	elseif (z <= 4.7e-30)
		tmp = t_3;
	elseif (z <= 850000000000.0)
		tmp = t_1;
	elseif ((z <= 1.8e+172) || ~((z <= 1.85e+172)))
		tmp = t_2;
	else
		tmp = t / b;
	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]}, Block[{t$95$2 = N[(t$95$1 - N[(x / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(x * y), $MachinePrecision] - N[(z * N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[z, -1.3], t$95$2, If[LessEqual[z, -1.6e-139], N[(x - N[(z * N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3e-119], t$95$3, If[LessEqual[z, 2.75e-76], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[z, 4.7e-30], t$95$3, If[LessEqual[z, 850000000000.0], t$95$1, If[Or[LessEqual[z, 1.8e+172], N[Not[LessEqual[z, 1.85e+172]], $MachinePrecision]], t$95$2, N[(t / b), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -1.30000000000000004 or 8.5e11 < z < 1.79999999999999987e172 or 1.84999999999999986e172 < z

   1. Initial program 41.3%

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

   3. Taylor expanded in z around -inf 68.4%

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

      1. associate--l+ 68.4%

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

      2. mul-1-neg 68.4%

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

      3. distribute-lft-out-- 68.4%

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

      4. associate-/l* 73.3%

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

      5. associate-/l* 92.4%

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

      6. div-sub 92.4%

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

   5. Simplified 92.4%

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

   6. Taylor expanded in y around inf 88.8%

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

   if -1.30000000000000004 < z < -1.6e-139

   1. Initial program 88.8%

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

   3. Taylor expanded in b around inf 85.7%

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

      1. *-commutative 85.7%

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

   5. Simplified 85.7%

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

   6. Taylor expanded in z around 0 52.5%

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

      1. associate--r+ 52.5%

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

      2. div-sub 56.3%

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

      3. associate-/l* 52.5%

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

   8. Simplified 52.5%

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

   9. Taylor expanded in b around 0 52.9%

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

       1. div-sub 56.7%

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

       2. *-commutative 56.7%

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

   11. Simplified 56.7%

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

   if -1.6e-139 < z < 3.0000000000000002e-119 or 2.75000000000000007e-76 < z < 4.69999999999999969e-30

   1. Initial program 92.1%

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

   3. Taylor expanded in b around inf 92.1%

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

      1. *-commutative 92.1%

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

   5. Simplified 92.1%

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

   6. Taylor expanded in b around 0 74.5%

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

   if 3.0000000000000002e-119 < z < 2.75000000000000007e-76

   1. Initial program 92.2%

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

   3. Taylor expanded in y around 0 75.9%

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

   if 4.69999999999999969e-30 < z < 8.5e11

   1. Initial program 92.2%

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

   3. Taylor expanded in z around inf 53.1%

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

   if 1.79999999999999987e172 < z < 1.84999999999999986e172

   1. Initial program 98.4%

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

   3. Taylor expanded in a around 0 98.4%

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

   4. Taylor expanded in y around 0 100.0%

      \[\leadsto \color{blue}{\frac{t}{b}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 78.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3:\\ \;\;\;\;\frac{t - a}{b - y} - \frac{x}{z}\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-139}:\\ \;\;\;\;x - z \cdot \frac{a - t}{y}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-119}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(a - t\right)}{y}\\ \mathbf{elif}\;z \leq 2.75 \cdot 10^{-76}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{-30}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(a - t\right)}{y}\\ \mathbf{elif}\;z \leq 850000000000:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+172} \lor \neg \left(z \leq 1.85 \cdot 10^{+172}\right):\\ \;\;\;\;\frac{t - a}{b - y} - \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 73.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(a - t\right)\\ t_2 := \frac{t\_1}{z \cdot \left(y - b\right) - y}\\ t_3 := \frac{t - a}{b - y}\\ t_4 := t\_3 - \frac{x}{z}\\ \mathbf{if}\;z \leq -38:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{-92}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-138}:\\ \;\;\;\;x - z \cdot \frac{a - t}{y}\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-149}:\\ \;\;\;\;\frac{x \cdot y}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-121}:\\ \;\;\;\;\frac{x \cdot y - t\_1}{y}\\ \mathbf{elif}\;z \leq 220000000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+94}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- a t)))
        (t_2 (/ t_1 (- (* z (- y b)) y)))
        (t_3 (/ (- t a) (- b y)))
        (t_4 (- t_3 (/ x z))))
   (if (<= z -38.0)
     t_4
     (if (<= z -1.35e-92)
       t_2
       (if (<= z -2.6e-138)
         (- x (* z (/ (- a t) y)))
         (if (<= z -1.25e-149)
           (/ (* x y) (+ y (* z b)))
           (if (<= z 1.9e-121)
             (/ (- (* x y) t_1) y)
             (if (<= z 220000000000.0) t_2 (if (<= z 1.4e+94) t_3 t_4)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (a - t);
	double t_2 = t_1 / ((z * (y - b)) - y);
	double t_3 = (t - a) / (b - y);
	double t_4 = t_3 - (x / z);
	double tmp;
	if (z <= -38.0) {
		tmp = t_4;
	} else if (z <= -1.35e-92) {
		tmp = t_2;
	} else if (z <= -2.6e-138) {
		tmp = x - (z * ((a - t) / y));
	} else if (z <= -1.25e-149) {
		tmp = (x * y) / (y + (z * b));
	} else if (z <= 1.9e-121) {
		tmp = ((x * y) - t_1) / y;
	} else if (z <= 220000000000.0) {
		tmp = t_2;
	} else if (z <= 1.4e+94) {
		tmp = t_3;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = z * (a - t)
    t_2 = t_1 / ((z * (y - b)) - y)
    t_3 = (t - a) / (b - y)
    t_4 = t_3 - (x / z)
    if (z <= (-38.0d0)) then
        tmp = t_4
    else if (z <= (-1.35d-92)) then
        tmp = t_2
    else if (z <= (-2.6d-138)) then
        tmp = x - (z * ((a - t) / y))
    else if (z <= (-1.25d-149)) then
        tmp = (x * y) / (y + (z * b))
    else if (z <= 1.9d-121) then
        tmp = ((x * y) - t_1) / y
    else if (z <= 220000000000.0d0) then
        tmp = t_2
    else if (z <= 1.4d+94) then
        tmp = t_3
    else
        tmp = t_4
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (a - t);
	double t_2 = t_1 / ((z * (y - b)) - y);
	double t_3 = (t - a) / (b - y);
	double t_4 = t_3 - (x / z);
	double tmp;
	if (z <= -38.0) {
		tmp = t_4;
	} else if (z <= -1.35e-92) {
		tmp = t_2;
	} else if (z <= -2.6e-138) {
		tmp = x - (z * ((a - t) / y));
	} else if (z <= -1.25e-149) {
		tmp = (x * y) / (y + (z * b));
	} else if (z <= 1.9e-121) {
		tmp = ((x * y) - t_1) / y;
	} else if (z <= 220000000000.0) {
		tmp = t_2;
	} else if (z <= 1.4e+94) {
		tmp = t_3;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (a - t)
	t_2 = t_1 / ((z * (y - b)) - y)
	t_3 = (t - a) / (b - y)
	t_4 = t_3 - (x / z)
	tmp = 0
	if z <= -38.0:
		tmp = t_4
	elif z <= -1.35e-92:
		tmp = t_2
	elif z <= -2.6e-138:
		tmp = x - (z * ((a - t) / y))
	elif z <= -1.25e-149:
		tmp = (x * y) / (y + (z * b))
	elif z <= 1.9e-121:
		tmp = ((x * y) - t_1) / y
	elif z <= 220000000000.0:
		tmp = t_2
	elif z <= 1.4e+94:
		tmp = t_3
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(a - t))
	t_2 = Float64(t_1 / Float64(Float64(z * Float64(y - b)) - y))
	t_3 = Float64(Float64(t - a) / Float64(b - y))
	t_4 = Float64(t_3 - Float64(x / z))
	tmp = 0.0
	if (z <= -38.0)
		tmp = t_4;
	elseif (z <= -1.35e-92)
		tmp = t_2;
	elseif (z <= -2.6e-138)
		tmp = Float64(x - Float64(z * Float64(Float64(a - t) / y)));
	elseif (z <= -1.25e-149)
		tmp = Float64(Float64(x * y) / Float64(y + Float64(z * b)));
	elseif (z <= 1.9e-121)
		tmp = Float64(Float64(Float64(x * y) - t_1) / y);
	elseif (z <= 220000000000.0)
		tmp = t_2;
	elseif (z <= 1.4e+94)
		tmp = t_3;
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (a - t);
	t_2 = t_1 / ((z * (y - b)) - y);
	t_3 = (t - a) / (b - y);
	t_4 = t_3 - (x / z);
	tmp = 0.0;
	if (z <= -38.0)
		tmp = t_4;
	elseif (z <= -1.35e-92)
		tmp = t_2;
	elseif (z <= -2.6e-138)
		tmp = x - (z * ((a - t) / y));
	elseif (z <= -1.25e-149)
		tmp = (x * y) / (y + (z * b));
	elseif (z <= 1.9e-121)
		tmp = ((x * y) - t_1) / y;
	elseif (z <= 220000000000.0)
		tmp = t_2;
	elseif (z <= 1.4e+94)
		tmp = t_3;
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(a - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 / N[(N[(z * N[(y - b), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$3 - N[(x / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -38.0], t$95$4, If[LessEqual[z, -1.35e-92], t$95$2, If[LessEqual[z, -2.6e-138], N[(x - N[(z * N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.25e-149], N[(N[(x * y), $MachinePrecision] / N[(y + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.9e-121], N[(N[(N[(x * y), $MachinePrecision] - t$95$1), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[z, 220000000000.0], t$95$2, If[LessEqual[z, 1.4e+94], t$95$3, t$95$4]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -38 or 1.39999999999999999e94 < z

   1. Initial program 40.3%

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

   3. Taylor expanded in z around -inf 67.2%

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

      1. associate--l+ 67.2%

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

      2. mul-1-neg 67.2%

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

      3. distribute-lft-out-- 67.2%

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

      4. associate-/l* 72.6%

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

      5. associate-/l* 92.5%

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

      6. div-sub 92.5%

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

   5. Simplified 92.5%

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

   6. Taylor expanded in y around inf 89.7%

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

   if -38 < z < -1.34999999999999998e-92 or 1.9e-121 < z < 2.2e11

   1. Initial program 91.5%

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

   3. Taylor expanded in x around 0 78.9%

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

   if -1.34999999999999998e-92 < z < -2.6e-138

   1. Initial program 90.5%

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

   3. Taylor expanded in b around inf 90.5%

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

      1. *-commutative 90.5%

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

   5. Simplified 90.5%

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

   6. Taylor expanded in z around 0 70.9%

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

      1. associate--r+ 70.9%

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

      2. div-sub 70.9%

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

      3. associate-/l* 70.9%

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

   8. Simplified 70.9%

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

   9. Taylor expanded in b around 0 70.9%

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

       1. div-sub 70.9%

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

       2. *-commutative 70.9%

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

   11. Simplified 70.9%

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

   if -2.6e-138 < z < -1.24999999999999992e-149

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 84.2%

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

      1. *-commutative 84.2%

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

   5. Simplified 84.2%

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

   6. Taylor expanded in b around inf 84.2%

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

      1. *-commutative 100.0%

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

   8. Simplified 84.2%

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

   if -1.24999999999999992e-149 < z < 1.9e-121

   1. Initial program 90.8%

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

   3. Taylor expanded in b around inf 90.8%

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

      1. *-commutative 90.8%

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

   5. Simplified 90.8%

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

   6. Taylor expanded in b around 0 74.2%

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

   if 2.2e11 < z < 1.39999999999999999e94

   1. Initial program 60.3%

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

   3. Taylor expanded in z around inf 82.6%

      \[\leadsto \color{blue}{\frac{t - a}{b - y}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 82.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -38:\\ \;\;\;\;\frac{t - a}{b - y} - \frac{x}{z}\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{-92}:\\ \;\;\;\;\frac{z \cdot \left(a - t\right)}{z \cdot \left(y - b\right) - y}\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-138}:\\ \;\;\;\;x - z \cdot \frac{a - t}{y}\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-149}:\\ \;\;\;\;\frac{x \cdot y}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-121}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(a - t\right)}{y}\\ \mathbf{elif}\;z \leq 220000000000:\\ \;\;\;\;\frac{z \cdot \left(a - t\right)}{z \cdot \left(y - b\right) - y}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+94}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y} - \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 74.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + z \cdot t\\ t_2 := \frac{z \cdot \left(a - t\right)}{z \cdot \left(y - b\right) - y}\\ t_3 := \frac{t - a}{b - y}\\ t_4 := t\_3 - \frac{x}{z}\\ \mathbf{if}\;z \leq -60:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;z \leq -2.15 \cdot 10^{-92}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-121}:\\ \;\;\;\;\frac{t\_1}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-47}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+19}:\\ \;\;\;\;\frac{t\_1}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+65}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* z t)))
        (t_2 (/ (* z (- a t)) (- (* z (- y b)) y)))
        (t_3 (/ (- t a) (- b y)))
        (t_4 (- t_3 (/ x z))))
   (if (<= z -60.0)
     t_4
     (if (<= z -2.15e-92)
       t_2
       (if (<= z 2.5e-121)
         (/ t_1 (+ y (* z b)))
         (if (<= z 2.4e-47)
           t_2
           (if (<= z 1.5e+19)
             (/ t_1 (+ y (* z (- b y))))
             (if (<= z 5.8e+65) t_3 t_4))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * y) + (z * t);
	double t_2 = (z * (a - t)) / ((z * (y - b)) - y);
	double t_3 = (t - a) / (b - y);
	double t_4 = t_3 - (x / z);
	double tmp;
	if (z <= -60.0) {
		tmp = t_4;
	} else if (z <= -2.15e-92) {
		tmp = t_2;
	} else if (z <= 2.5e-121) {
		tmp = t_1 / (y + (z * b));
	} else if (z <= 2.4e-47) {
		tmp = t_2;
	} else if (z <= 1.5e+19) {
		tmp = t_1 / (y + (z * (b - y)));
	} else if (z <= 5.8e+65) {
		tmp = t_3;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = (x * y) + (z * t)
    t_2 = (z * (a - t)) / ((z * (y - b)) - y)
    t_3 = (t - a) / (b - y)
    t_4 = t_3 - (x / z)
    if (z <= (-60.0d0)) then
        tmp = t_4
    else if (z <= (-2.15d-92)) then
        tmp = t_2
    else if (z <= 2.5d-121) then
        tmp = t_1 / (y + (z * b))
    else if (z <= 2.4d-47) then
        tmp = t_2
    else if (z <= 1.5d+19) then
        tmp = t_1 / (y + (z * (b - y)))
    else if (z <= 5.8d+65) then
        tmp = t_3
    else
        tmp = t_4
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * y) + (z * t);
	double t_2 = (z * (a - t)) / ((z * (y - b)) - y);
	double t_3 = (t - a) / (b - y);
	double t_4 = t_3 - (x / z);
	double tmp;
	if (z <= -60.0) {
		tmp = t_4;
	} else if (z <= -2.15e-92) {
		tmp = t_2;
	} else if (z <= 2.5e-121) {
		tmp = t_1 / (y + (z * b));
	} else if (z <= 2.4e-47) {
		tmp = t_2;
	} else if (z <= 1.5e+19) {
		tmp = t_1 / (y + (z * (b - y)));
	} else if (z <= 5.8e+65) {
		tmp = t_3;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x * y) + (z * t)
	t_2 = (z * (a - t)) / ((z * (y - b)) - y)
	t_3 = (t - a) / (b - y)
	t_4 = t_3 - (x / z)
	tmp = 0
	if z <= -60.0:
		tmp = t_4
	elif z <= -2.15e-92:
		tmp = t_2
	elif z <= 2.5e-121:
		tmp = t_1 / (y + (z * b))
	elif z <= 2.4e-47:
		tmp = t_2
	elif z <= 1.5e+19:
		tmp = t_1 / (y + (z * (b - y)))
	elif z <= 5.8e+65:
		tmp = t_3
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * y) + Float64(z * t))
	t_2 = Float64(Float64(z * Float64(a - t)) / Float64(Float64(z * Float64(y - b)) - y))
	t_3 = Float64(Float64(t - a) / Float64(b - y))
	t_4 = Float64(t_3 - Float64(x / z))
	tmp = 0.0
	if (z <= -60.0)
		tmp = t_4;
	elseif (z <= -2.15e-92)
		tmp = t_2;
	elseif (z <= 2.5e-121)
		tmp = Float64(t_1 / Float64(y + Float64(z * b)));
	elseif (z <= 2.4e-47)
		tmp = t_2;
	elseif (z <= 1.5e+19)
		tmp = Float64(t_1 / Float64(y + Float64(z * Float64(b - y))));
	elseif (z <= 5.8e+65)
		tmp = t_3;
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x * y) + (z * t);
	t_2 = (z * (a - t)) / ((z * (y - b)) - y);
	t_3 = (t - a) / (b - y);
	t_4 = t_3 - (x / z);
	tmp = 0.0;
	if (z <= -60.0)
		tmp = t_4;
	elseif (z <= -2.15e-92)
		tmp = t_2;
	elseif (z <= 2.5e-121)
		tmp = t_1 / (y + (z * b));
	elseif (z <= 2.4e-47)
		tmp = t_2;
	elseif (z <= 1.5e+19)
		tmp = t_1 / (y + (z * (b - y)));
	elseif (z <= 5.8e+65)
		tmp = t_3;
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z * N[(a - t), $MachinePrecision]), $MachinePrecision] / N[(N[(z * N[(y - b), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$3 - N[(x / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -60.0], t$95$4, If[LessEqual[z, -2.15e-92], t$95$2, If[LessEqual[z, 2.5e-121], N[(t$95$1 / N[(y + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.4e-47], t$95$2, If[LessEqual[z, 1.5e+19], N[(t$95$1 / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.8e+65], t$95$3, t$95$4]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -60 or 5.8000000000000001e65 < z

   1. Initial program 40.5%

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

   3. Taylor expanded in z around -inf 66.9%

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

      1. associate--l+ 66.9%

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

      2. mul-1-neg 66.9%

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

      3. distribute-lft-out-- 66.9%

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

      4. associate-/l* 72.2%

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

      5. associate-/l* 92.7%

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

      6. div-sub 92.7%

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

   5. Simplified 92.7%

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

   6. Taylor expanded in y around inf 89.0%

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

   if -60 < z < -2.15000000000000007e-92 or 2.49999999999999995e-121 < z < 2.3999999999999999e-47

   1. Initial program 90.6%

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

   3. Taylor expanded in x around 0 84.4%

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

   if -2.15000000000000007e-92 < z < 2.49999999999999995e-121

   1. Initial program 91.4%

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

   3. Taylor expanded in a around 0 75.7%

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

   4. Taylor expanded in b around inf 75.7%

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

      1. *-commutative 91.4%

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

   6. Simplified 75.7%

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

   if 2.3999999999999999e-47 < z < 1.5e19

   1. Initial program 94.3%

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

   3. Taylor expanded in a around 0 72.5%

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

   if 1.5e19 < z < 5.8000000000000001e65

   1. Initial program 46.1%

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

   3. Taylor expanded in z around inf 100.0%

      \[\leadsto \color{blue}{\frac{t - a}{b - y}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 83.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -60:\\ \;\;\;\;\frac{t - a}{b - y} - \frac{x}{z}\\ \mathbf{elif}\;z \leq -2.15 \cdot 10^{-92}:\\ \;\;\;\;\frac{z \cdot \left(a - t\right)}{z \cdot \left(y - b\right) - y}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-121}:\\ \;\;\;\;\frac{x \cdot y + z \cdot t}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-47}:\\ \;\;\;\;\frac{z \cdot \left(a - t\right)}{z \cdot \left(y - b\right) - y}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+19}:\\ \;\;\;\;\frac{x \cdot y + z \cdot t}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+65}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y} - \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 74.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot y + z \cdot t}{y + z \cdot b}\\ t_2 := \frac{z \cdot \left(a - t\right)}{z \cdot \left(y - b\right) - y}\\ t_3 := \frac{t - a}{b - y} - \frac{x}{z}\\ \mathbf{if}\;z \leq -60:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-92}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-121}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-47}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{-6}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ (* x y) (* z t)) (+ y (* z b))))
        (t_2 (/ (* z (- a t)) (- (* z (- y b)) y)))
        (t_3 (- (/ (- t a) (- b y)) (/ x z))))
   (if (<= z -60.0)
     t_3
     (if (<= z -1.1e-92)
       t_2
       (if (<= z 1.65e-121)
         t_1
         (if (<= z 5.5e-47) t_2 (if (<= z 6.4e-6) t_1 t_3)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x * y) + (z * t)) / (y + (z * b));
	double t_2 = (z * (a - t)) / ((z * (y - b)) - y);
	double t_3 = ((t - a) / (b - y)) - (x / z);
	double tmp;
	if (z <= -60.0) {
		tmp = t_3;
	} else if (z <= -1.1e-92) {
		tmp = t_2;
	} else if (z <= 1.65e-121) {
		tmp = t_1;
	} else if (z <= 5.5e-47) {
		tmp = t_2;
	} else if (z <= 6.4e-6) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = ((x * y) + (z * t)) / (y + (z * b))
    t_2 = (z * (a - t)) / ((z * (y - b)) - y)
    t_3 = ((t - a) / (b - y)) - (x / z)
    if (z <= (-60.0d0)) then
        tmp = t_3
    else if (z <= (-1.1d-92)) then
        tmp = t_2
    else if (z <= 1.65d-121) then
        tmp = t_1
    else if (z <= 5.5d-47) then
        tmp = t_2
    else if (z <= 6.4d-6) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x * y) + (z * t)) / (y + (z * b));
	double t_2 = (z * (a - t)) / ((z * (y - b)) - y);
	double t_3 = ((t - a) / (b - y)) - (x / z);
	double tmp;
	if (z <= -60.0) {
		tmp = t_3;
	} else if (z <= -1.1e-92) {
		tmp = t_2;
	} else if (z <= 1.65e-121) {
		tmp = t_1;
	} else if (z <= 5.5e-47) {
		tmp = t_2;
	} else if (z <= 6.4e-6) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((x * y) + (z * t)) / (y + (z * b))
	t_2 = (z * (a - t)) / ((z * (y - b)) - y)
	t_3 = ((t - a) / (b - y)) - (x / z)
	tmp = 0
	if z <= -60.0:
		tmp = t_3
	elif z <= -1.1e-92:
		tmp = t_2
	elif z <= 1.65e-121:
		tmp = t_1
	elif z <= 5.5e-47:
		tmp = t_2
	elif z <= 6.4e-6:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(x * y) + Float64(z * t)) / Float64(y + Float64(z * b)))
	t_2 = Float64(Float64(z * Float64(a - t)) / Float64(Float64(z * Float64(y - b)) - y))
	t_3 = Float64(Float64(Float64(t - a) / Float64(b - y)) - Float64(x / z))
	tmp = 0.0
	if (z <= -60.0)
		tmp = t_3;
	elseif (z <= -1.1e-92)
		tmp = t_2;
	elseif (z <= 1.65e-121)
		tmp = t_1;
	elseif (z <= 5.5e-47)
		tmp = t_2;
	elseif (z <= 6.4e-6)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((x * y) + (z * t)) / (y + (z * b));
	t_2 = (z * (a - t)) / ((z * (y - b)) - y);
	t_3 = ((t - a) / (b - y)) - (x / z);
	tmp = 0.0;
	if (z <= -60.0)
		tmp = t_3;
	elseif (z <= -1.1e-92)
		tmp = t_2;
	elseif (z <= 1.65e-121)
		tmp = t_1;
	elseif (z <= 5.5e-47)
		tmp = t_2;
	elseif (z <= 6.4e-6)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z * N[(a - t), $MachinePrecision]), $MachinePrecision] / N[(N[(z * N[(y - b), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision] - N[(x / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -60.0], t$95$3, If[LessEqual[z, -1.1e-92], t$95$2, If[LessEqual[z, 1.65e-121], t$95$1, If[LessEqual[z, 5.5e-47], t$95$2, If[LessEqual[z, 6.4e-6], t$95$1, t$95$3]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -60 or 6.3999999999999997e-6 < z

   1. Initial program 44.5%

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

   3. Taylor expanded in z around -inf 67.0%

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

      1. associate--l+ 67.0%

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

      2. mul-1-neg 67.0%

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

      3. distribute-lft-out-- 67.0%

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

      4. associate-/l* 71.7%

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

      5. associate-/l* 90.4%

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

      6. div-sub 90.4%

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

   5. Simplified 90.4%

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

   6. Taylor expanded in y around inf 85.2%

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

   if -60 < z < -1.09999999999999994e-92 or 1.65000000000000005e-121 < z < 5.5000000000000002e-47

   1. Initial program 90.6%

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

   3. Taylor expanded in x around 0 84.4%

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

   if -1.09999999999999994e-92 < z < 1.65000000000000005e-121 or 5.5000000000000002e-47 < z < 6.3999999999999997e-6

   1. Initial program 91.3%

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

   3. Taylor expanded in a around 0 75.1%

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

   4. Taylor expanded in b around inf 75.1%

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

      1. *-commutative 91.3%

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

   6. Simplified 75.1%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -60:\\ \;\;\;\;\frac{t - a}{b - y} - \frac{x}{z}\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-92}:\\ \;\;\;\;\frac{z \cdot \left(a - t\right)}{z \cdot \left(y - b\right) - y}\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-121}:\\ \;\;\;\;\frac{x \cdot y + z \cdot t}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-47}:\\ \;\;\;\;\frac{z \cdot \left(a - t\right)}{z \cdot \left(y - b\right) - y}\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{-6}:\\ \;\;\;\;\frac{x \cdot y + z \cdot t}{y + z \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y} - \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 67.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -1.2 \cdot 10^{+210}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{+170}:\\ \;\;\;\;\frac{a}{y} - \frac{x}{z}\\ \mathbf{elif}\;z \leq -2.35 \cdot 10^{-92}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-121}:\\ \;\;\;\;x + \frac{z \cdot t}{y}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-99}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;z \leq 2.65 \cdot 10^{-42}:\\ \;\;\;\;x - z \cdot \frac{a}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -1.2e+210)
     t_1
     (if (<= z -3.3e+170)
       (- (/ a y) (/ x z))
       (if (<= z -2.35e-92)
         t_1
         (if (<= z 2.1e-121)
           (+ x (/ (* z t) y))
           (if (<= z 6e-99)
             (/ (- t a) b)
             (if (<= z 2.65e-42) (- x (* z (/ a y))) t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -1.2e+210) {
		tmp = t_1;
	} else if (z <= -3.3e+170) {
		tmp = (a / y) - (x / z);
	} else if (z <= -2.35e-92) {
		tmp = t_1;
	} else if (z <= 2.1e-121) {
		tmp = x + ((z * t) / y);
	} else if (z <= 6e-99) {
		tmp = (t - a) / b;
	} else if (z <= 2.65e-42) {
		tmp = x - (z * (a / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    if (z <= (-1.2d+210)) then
        tmp = t_1
    else if (z <= (-3.3d+170)) then
        tmp = (a / y) - (x / z)
    else if (z <= (-2.35d-92)) then
        tmp = t_1
    else if (z <= 2.1d-121) then
        tmp = x + ((z * t) / y)
    else if (z <= 6d-99) then
        tmp = (t - a) / b
    else if (z <= 2.65d-42) then
        tmp = x - (z * (a / y))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -1.2e+210) {
		tmp = t_1;
	} else if (z <= -3.3e+170) {
		tmp = (a / y) - (x / z);
	} else if (z <= -2.35e-92) {
		tmp = t_1;
	} else if (z <= 2.1e-121) {
		tmp = x + ((z * t) / y);
	} else if (z <= 6e-99) {
		tmp = (t - a) / b;
	} else if (z <= 2.65e-42) {
		tmp = x - (z * (a / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	tmp = 0
	if z <= -1.2e+210:
		tmp = t_1
	elif z <= -3.3e+170:
		tmp = (a / y) - (x / z)
	elif z <= -2.35e-92:
		tmp = t_1
	elif z <= 2.1e-121:
		tmp = x + ((z * t) / y)
	elif z <= 6e-99:
		tmp = (t - a) / b
	elif z <= 2.65e-42:
		tmp = x - (z * (a / y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -1.2e+210)
		tmp = t_1;
	elseif (z <= -3.3e+170)
		tmp = Float64(Float64(a / y) - Float64(x / z));
	elseif (z <= -2.35e-92)
		tmp = t_1;
	elseif (z <= 2.1e-121)
		tmp = Float64(x + Float64(Float64(z * t) / y));
	elseif (z <= 6e-99)
		tmp = Float64(Float64(t - a) / b);
	elseif (z <= 2.65e-42)
		tmp = Float64(x - Float64(z * Float64(a / y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -1.2e+210)
		tmp = t_1;
	elseif (z <= -3.3e+170)
		tmp = (a / y) - (x / z);
	elseif (z <= -2.35e-92)
		tmp = t_1;
	elseif (z <= 2.1e-121)
		tmp = x + ((z * t) / y);
	elseif (z <= 6e-99)
		tmp = (t - a) / b;
	elseif (z <= 2.65e-42)
		tmp = x - (z * (a / y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.2e+210], t$95$1, If[LessEqual[z, -3.3e+170], N[(N[(a / y), $MachinePrecision] - N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.35e-92], t$95$1, If[LessEqual[z, 2.1e-121], N[(x + N[(N[(z * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6e-99], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[z, 2.65e-42], N[(x - N[(z * N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.19999999999999994e210 or -3.30000000000000023e170 < z < -2.34999999999999996e-92 or 2.65e-42 < z

   1. Initial program 52.4%

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

   3. Taylor expanded in z around inf 73.5%

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

   if -1.19999999999999994e210 < z < -3.30000000000000023e170

   1. Initial program 31.0%

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

   3. Taylor expanded in z around -inf 72.3%

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

      1. associate--l+ 72.3%

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

      2. mul-1-neg 72.3%

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

      3. distribute-lft-out-- 72.3%

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

      4. associate-/l* 100.0%

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

      5. associate-/l* 85.7%

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

      6. div-sub 85.7%

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

   5. Simplified 85.7%

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

   6. Taylor expanded in y around inf 89.7%

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

   7. Taylor expanded in y around -inf 89.7%

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

      1. associate-*r/ 89.7%

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

      2. mul-1-neg 89.7%

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

   9. Simplified 89.7%

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

   10. Taylor expanded in t around 0 89.7%

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

   if -2.34999999999999996e-92 < z < 2.0999999999999999e-121

   1. Initial program 91.4%

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

   3. Taylor expanded in b around inf 91.4%

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

      1. *-commutative 91.4%

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

   5. Simplified 91.4%

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

   6. Taylor expanded in z around 0 68.7%

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

      1. associate--r+ 68.7%

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

      2. div-sub 68.7%

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

      3. associate-/l* 68.6%

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

   8. Simplified 68.6%

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

   9. Taylor expanded in t around inf 67.4%

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

   if 2.0999999999999999e-121 < z < 6.00000000000000012e-99

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 85.8%

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

   if 6.00000000000000012e-99 < z < 2.65e-42

   1. Initial program 90.8%

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

   3. Taylor expanded in b around inf 90.8%

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

      1. *-commutative 90.8%

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

   5. Simplified 90.8%

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

   6. Taylor expanded in z around 0 61.3%

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

      1. associate--r+ 61.3%

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

      2. div-sub 61.3%

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

      3. associate-/l* 61.3%

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

   8. Simplified 61.3%

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

   9. Taylor expanded in b around 0 62.0%

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

       1. div-sub 62.0%

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

       2. *-commutative 62.0%

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

   11. Simplified 62.0%

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

   12. Taylor expanded in t around 0 51.6%

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

       1. mul-1-neg 51.6%

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

       2. associate-*r/ 46.3%

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

       3. unsub-neg 46.3%

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

       4. associate-*r/ 51.6%

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

       5. *-commutative 51.6%

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

       6. associate-*r/ 51.6%

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

   14. Simplified 51.6%

       \[\leadsto \color{blue}{x - z \cdot \frac{a}{y}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 71.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+210}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{+170}:\\ \;\;\;\;\frac{a}{y} - \frac{x}{z}\\ \mathbf{elif}\;z \leq -2.35 \cdot 10^{-92}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-121}:\\ \;\;\;\;x + \frac{z \cdot t}{y}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-99}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;z \leq 2.65 \cdot 10^{-42}:\\ \;\;\;\;x - z \cdot \frac{a}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 52.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -1.1 \cdot 10^{+157}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -165000:\\ \;\;\;\;\frac{a - t}{y}\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-18}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{+186} \lor \neg \left(y \leq 9.6 \cdot 10^{+186}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (- 1.0 z))))
   (if (<= y -1.1e+157)
     t_1
     (if (<= y -165000.0)
       (/ (- a t) y)
       (if (<= y 6e-18)
         (/ (- t a) b)
         (if (or (<= y 8.2e+186) (not (<= y 9.6e+186))) t_1 (/ a y)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 - z);
	double tmp;
	if (y <= -1.1e+157) {
		tmp = t_1;
	} else if (y <= -165000.0) {
		tmp = (a - t) / y;
	} else if (y <= 6e-18) {
		tmp = (t - a) / b;
	} else if ((y <= 8.2e+186) || !(y <= 9.6e+186)) {
		tmp = t_1;
	} else {
		tmp = a / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (1.0d0 - z)
    if (y <= (-1.1d+157)) then
        tmp = t_1
    else if (y <= (-165000.0d0)) then
        tmp = (a - t) / y
    else if (y <= 6d-18) then
        tmp = (t - a) / b
    else if ((y <= 8.2d+186) .or. (.not. (y <= 9.6d+186))) then
        tmp = t_1
    else
        tmp = a / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 - z);
	double tmp;
	if (y <= -1.1e+157) {
		tmp = t_1;
	} else if (y <= -165000.0) {
		tmp = (a - t) / y;
	} else if (y <= 6e-18) {
		tmp = (t - a) / b;
	} else if ((y <= 8.2e+186) || !(y <= 9.6e+186)) {
		tmp = t_1;
	} else {
		tmp = a / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (1.0 - z)
	tmp = 0
	if y <= -1.1e+157:
		tmp = t_1
	elif y <= -165000.0:
		tmp = (a - t) / y
	elif y <= 6e-18:
		tmp = (t - a) / b
	elif (y <= 8.2e+186) or not (y <= 9.6e+186):
		tmp = t_1
	else:
		tmp = a / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(1.0 - z))
	tmp = 0.0
	if (y <= -1.1e+157)
		tmp = t_1;
	elseif (y <= -165000.0)
		tmp = Float64(Float64(a - t) / y);
	elseif (y <= 6e-18)
		tmp = Float64(Float64(t - a) / b);
	elseif ((y <= 8.2e+186) || !(y <= 9.6e+186))
		tmp = t_1;
	else
		tmp = Float64(a / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (1.0 - z);
	tmp = 0.0;
	if (y <= -1.1e+157)
		tmp = t_1;
	elseif (y <= -165000.0)
		tmp = (a - t) / y;
	elseif (y <= 6e-18)
		tmp = (t - a) / b;
	elseif ((y <= 8.2e+186) || ~((y <= 9.6e+186)))
		tmp = t_1;
	else
		tmp = a / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.1e+157], t$95$1, If[LessEqual[y, -165000.0], N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, 6e-18], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision], If[Or[LessEqual[y, 8.2e+186], N[Not[LessEqual[y, 9.6e+186]], $MachinePrecision]], t$95$1, N[(a / y), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.1000000000000001e157 or 5.99999999999999966e-18 < y < 8.2e186 or 9.5999999999999998e186 < y

   1. Initial program 57.4%

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

   3. Taylor expanded in y around inf 59.9%

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

      1. mul-1-neg 59.9%

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

      2. unsub-neg 59.9%

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

   5. Simplified 59.9%

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

   if -1.1000000000000001e157 < y < -165000

   1. Initial program 53.5%

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

   3. Taylor expanded in z around -inf 49.7%

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

      1. associate--l+ 49.7%

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

      2. mul-1-neg 49.7%

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

      3. distribute-lft-out-- 49.7%

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

      4. associate-/l* 49.8%

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

      5. associate-/l* 69.5%

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

      6. div-sub 69.5%

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

   5. Simplified 69.5%

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

   6. Taylor expanded in y around inf 57.4%

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

   7. Taylor expanded in y around -inf 44.5%

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

      1. associate-*r/ 44.5%

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

      2. mul-1-neg 44.5%

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

   9. Simplified 44.5%

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

   10. Taylor expanded in y around 0 40.0%

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

   if -165000 < y < 5.99999999999999966e-18

   1. Initial program 80.8%

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

   3. Taylor expanded in y around 0 66.2%

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

   if 8.2e186 < y < 9.5999999999999998e186

   1. Initial program 50.0%

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

   3. Taylor expanded in z around -inf 50.0%

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

      1. associate--l+ 50.0%

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

      2. mul-1-neg 50.0%

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

      3. distribute-lft-out-- 50.0%

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

      4. associate-/l* 50.0%

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

      5. associate-/l* 100.0%

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

      6. div-sub 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in y around inf 90.9%

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

   7. Taylor expanded in y around -inf 90.9%

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

      1. associate-*r/ 90.9%

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

      2. mul-1-neg 90.9%

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

   9. Simplified 90.9%

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

   10. Taylor expanded in a around inf 100.0%

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

4. Final simplification 60.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+157}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq -165000:\\ \;\;\;\;\frac{a - t}{y}\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-18}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{+186} \lor \neg \left(y \leq 9.6 \cdot 10^{+186}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 52.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -1 \cdot 10^{+157}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -11500000:\\ \;\;\;\;\frac{a - t}{y}\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-81}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+56}:\\ \;\;\;\;x + t \cdot \frac{z}{y}\\ \mathbf{elif}\;y \leq 2.95 \cdot 10^{+56}:\\ \;\;\;\;\frac{a}{-b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (- 1.0 z))))
   (if (<= y -1e+157)
     t_1
     (if (<= y -11500000.0)
       (/ (- a t) y)
       (if (<= y 8e-81)
         (/ (- t a) b)
         (if (<= y 2.8e+56)
           (+ x (* t (/ z y)))
           (if (<= y 2.95e+56) (/ a (- b)) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 - z);
	double tmp;
	if (y <= -1e+157) {
		tmp = t_1;
	} else if (y <= -11500000.0) {
		tmp = (a - t) / y;
	} else if (y <= 8e-81) {
		tmp = (t - a) / b;
	} else if (y <= 2.8e+56) {
		tmp = x + (t * (z / y));
	} else if (y <= 2.95e+56) {
		tmp = a / -b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (1.0d0 - z)
    if (y <= (-1d+157)) then
        tmp = t_1
    else if (y <= (-11500000.0d0)) then
        tmp = (a - t) / y
    else if (y <= 8d-81) then
        tmp = (t - a) / b
    else if (y <= 2.8d+56) then
        tmp = x + (t * (z / y))
    else if (y <= 2.95d+56) then
        tmp = a / -b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 - z);
	double tmp;
	if (y <= -1e+157) {
		tmp = t_1;
	} else if (y <= -11500000.0) {
		tmp = (a - t) / y;
	} else if (y <= 8e-81) {
		tmp = (t - a) / b;
	} else if (y <= 2.8e+56) {
		tmp = x + (t * (z / y));
	} else if (y <= 2.95e+56) {
		tmp = a / -b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (1.0 - z)
	tmp = 0
	if y <= -1e+157:
		tmp = t_1
	elif y <= -11500000.0:
		tmp = (a - t) / y
	elif y <= 8e-81:
		tmp = (t - a) / b
	elif y <= 2.8e+56:
		tmp = x + (t * (z / y))
	elif y <= 2.95e+56:
		tmp = a / -b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(1.0 - z))
	tmp = 0.0
	if (y <= -1e+157)
		tmp = t_1;
	elseif (y <= -11500000.0)
		tmp = Float64(Float64(a - t) / y);
	elseif (y <= 8e-81)
		tmp = Float64(Float64(t - a) / b);
	elseif (y <= 2.8e+56)
		tmp = Float64(x + Float64(t * Float64(z / y)));
	elseif (y <= 2.95e+56)
		tmp = Float64(a / Float64(-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 <= -1e+157)
		tmp = t_1;
	elseif (y <= -11500000.0)
		tmp = (a - t) / y;
	elseif (y <= 8e-81)
		tmp = (t - a) / b;
	elseif (y <= 2.8e+56)
		tmp = x + (t * (z / y));
	elseif (y <= 2.95e+56)
		tmp = a / -b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1e+157], t$95$1, If[LessEqual[y, -11500000.0], N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, 8e-81], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[y, 2.8e+56], N[(x + N[(t * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.95e+56], N[(a / (-b)), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -9.99999999999999983e156 or 2.9500000000000001e56 < y

   1. Initial program 47.1%

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

   3. Taylor expanded in y around inf 64.2%

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

      1. mul-1-neg 64.2%

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

      2. unsub-neg 64.2%

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

   5. Simplified 64.2%

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

   if -9.99999999999999983e156 < y < -1.15e7

   1. Initial program 53.5%

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

   3. Taylor expanded in z around -inf 49.7%

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

      1. associate--l+ 49.7%

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

      2. mul-1-neg 49.7%

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

      3. distribute-lft-out-- 49.7%

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

      4. associate-/l* 49.8%

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

      5. associate-/l* 69.5%

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

      6. div-sub 69.5%

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

   5. Simplified 69.5%

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

   6. Taylor expanded in y around inf 57.4%

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

   7. Taylor expanded in y around -inf 44.5%

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

      1. associate-*r/ 44.5%

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

      2. mul-1-neg 44.5%

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

   9. Simplified 44.5%

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

   10. Taylor expanded in y around 0 40.0%

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

   if -1.15e7 < y < 7.9999999999999997e-81

   1. Initial program 80.3%

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

   3. Taylor expanded in y around 0 71.4%

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

   if 7.9999999999999997e-81 < y < 2.80000000000000008e56

   1. Initial program 90.1%

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

   3. Taylor expanded in b around inf 72.1%

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

      1. *-commutative 72.1%

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

   5. Simplified 72.1%

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

   6. Taylor expanded in z around 0 52.3%

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

      1. associate--r+ 52.3%

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

      2. div-sub 52.3%

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

      3. associate-/l* 52.3%

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

   8. Simplified 52.3%

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

   9. Taylor expanded in t around inf 42.4%

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

       1. associate-/l* 42.4%

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

   11. Simplified 42.4%

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

   if 2.80000000000000008e56 < y < 2.9500000000000001e56

   1. Initial program 5.3%

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

   3. Taylor expanded in z around inf 5.3%

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

      1. associate--l+ 5.3%

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

      2. associate-/l* 5.3%

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

   5. Simplified 5.3%

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

   6. Taylor expanded in a around inf 5.3%

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

      1. associate-*r* 5.3%

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

      2. neg-mul-1 5.3%

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

   8. Simplified 5.3%

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

   9. Taylor expanded in y around 0 100.0%

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

       1. mul-1-neg 100.0%

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

   11. Simplified 100.0%

       \[\leadsto \color{blue}{-\frac{a}{b}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 61.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+157}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq -11500000:\\ \;\;\;\;\frac{a - t}{y}\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-81}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+56}:\\ \;\;\;\;x + t \cdot \frac{z}{y}\\ \mathbf{elif}\;y \leq 2.95 \cdot 10^{+56}:\\ \;\;\;\;\frac{a}{-b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 42.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -1 \cdot 10^{+157}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -105:\\ \;\;\;\;\frac{a - t}{y}\\ \mathbf{elif}\;y \leq -0.025 \lor \neg \left(y \leq 7 \cdot 10^{-29}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (- 1.0 z))))
   (if (<= y -1e+157)
     t_1
     (if (<= y -105.0)
       (/ (- a t) y)
       (if (or (<= y -0.025) (not (<= y 7e-29))) t_1 (/ t (- b y)))))))

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 <= -1e+157) {
		tmp = t_1;
	} else if (y <= -105.0) {
		tmp = (a - t) / y;
	} else if ((y <= -0.025) || !(y <= 7e-29)) {
		tmp = t_1;
	} else {
		tmp = t / (b - y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (1.0d0 - z)
    if (y <= (-1d+157)) then
        tmp = t_1
    else if (y <= (-105.0d0)) then
        tmp = (a - t) / y
    else if ((y <= (-0.025d0)) .or. (.not. (y <= 7d-29))) then
        tmp = t_1
    else
        tmp = t / (b - y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 - z);
	double tmp;
	if (y <= -1e+157) {
		tmp = t_1;
	} else if (y <= -105.0) {
		tmp = (a - t) / y;
	} else if ((y <= -0.025) || !(y <= 7e-29)) {
		tmp = t_1;
	} else {
		tmp = t / (b - y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (1.0 - z)
	tmp = 0
	if y <= -1e+157:
		tmp = t_1
	elif y <= -105.0:
		tmp = (a - t) / y
	elif (y <= -0.025) or not (y <= 7e-29):
		tmp = t_1
	else:
		tmp = t / (b - y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(1.0 - z))
	tmp = 0.0
	if (y <= -1e+157)
		tmp = t_1;
	elseif (y <= -105.0)
		tmp = Float64(Float64(a - t) / y);
	elseif ((y <= -0.025) || !(y <= 7e-29))
		tmp = t_1;
	else
		tmp = Float64(t / Float64(b - y));
	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 <= -1e+157)
		tmp = t_1;
	elseif (y <= -105.0)
		tmp = (a - t) / y;
	elseif ((y <= -0.025) || ~((y <= 7e-29)))
		tmp = t_1;
	else
		tmp = t / (b - y);
	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, -1e+157], t$95$1, If[LessEqual[y, -105.0], N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision], If[Or[LessEqual[y, -0.025], N[Not[LessEqual[y, 7e-29]], $MachinePrecision]], t$95$1, N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.99999999999999983e156 or -105 < y < -0.025000000000000001 or 6.9999999999999995e-29 < y

   1. Initial program 59.8%

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

   3. Taylor expanded in y around inf 56.6%

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

      1. mul-1-neg 56.6%

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

      2. unsub-neg 56.6%

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

   5. Simplified 56.6%

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

   if -9.99999999999999983e156 < y < -105

   1. Initial program 53.5%

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

   3. Taylor expanded in z around -inf 49.7%

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

      1. associate--l+ 49.7%

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

      2. mul-1-neg 49.7%

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

      3. distribute-lft-out-- 49.7%

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

      4. associate-/l* 49.8%

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

      5. associate-/l* 69.5%

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

      6. div-sub 69.5%

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

   5. Simplified 69.5%

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

   6. Taylor expanded in y around inf 57.4%

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

   7. Taylor expanded in y around -inf 44.5%

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

      1. associate-*r/ 44.5%

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

      2. mul-1-neg 44.5%

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

   9. Simplified 44.5%

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

   10. Taylor expanded in y around 0 40.0%

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

   if -0.025000000000000001 < y < 6.9999999999999995e-29

   1. Initial program 80.1%

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

   3. Taylor expanded in a around 0 57.9%

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

   4. Taylor expanded in z around inf 52.0%

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

4. Final simplification 52.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+157}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq -105:\\ \;\;\;\;\frac{a - t}{y}\\ \mathbf{elif}\;y \leq -0.025 \lor \neg \left(y \leq 7 \cdot 10^{-29}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 85.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{+17} \lor \neg \left(z \leq 58000\right):\\ \;\;\;\;\frac{t - a}{b - y} - \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(a - t\right)}{y + z \cdot b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -7.8e+17) (not (<= z 58000.0)))
   (- (/ (- t a) (- b y)) (/ x z))
   (/ (- (* x y) (* z (- a t))) (+ y (* z b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -7.8e+17) || !(z <= 58000.0)) {
		tmp = ((t - a) / (b - y)) - (x / z);
	} else {
		tmp = ((x * y) - (z * (a - t))) / (y + (z * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-7.8d+17)) .or. (.not. (z <= 58000.0d0))) then
        tmp = ((t - a) / (b - y)) - (x / z)
    else
        tmp = ((x * y) - (z * (a - t))) / (y + (z * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -7.8e+17) || !(z <= 58000.0)) {
		tmp = ((t - a) / (b - y)) - (x / z);
	} else {
		tmp = ((x * y) - (z * (a - t))) / (y + (z * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -7.8e+17) or not (z <= 58000.0):
		tmp = ((t - a) / (b - y)) - (x / z)
	else:
		tmp = ((x * y) - (z * (a - t))) / (y + (z * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -7.8e+17) || !(z <= 58000.0))
		tmp = Float64(Float64(Float64(t - a) / Float64(b - y)) - Float64(x / z));
	else
		tmp = Float64(Float64(Float64(x * y) - Float64(z * Float64(a - t))) / Float64(y + Float64(z * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -7.8e+17) || ~((z <= 58000.0)))
		tmp = ((t - a) / (b - y)) - (x / z);
	else
		tmp = ((x * y) - (z * (a - t))) / (y + (z * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -7.8e+17], N[Not[LessEqual[z, 58000.0]], $MachinePrecision]], N[(N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision] - N[(x / z), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] - N[(z * N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.8e17 or 58000 < z

   1. Initial program 40.0%

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

   3. Taylor expanded in z around -inf 68.2%

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

      1. associate--l+ 68.2%

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

      2. mul-1-neg 68.2%

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

      3. distribute-lft-out-- 68.2%

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

      4. associate-/l* 73.3%

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

      5. associate-/l* 93.2%

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

      6. div-sub 93.2%

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

   5. Simplified 93.2%

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

   6. Taylor expanded in y around inf 88.8%

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

   if -7.8e17 < z < 58000

   1. Initial program 91.1%

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

   3. Taylor expanded in b around inf 88.6%

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

      1. *-commutative 88.6%

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

   5. Simplified 88.6%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{+17} \lor \neg \left(z \leq 58000\right):\\ \;\;\;\;\frac{t - a}{b - y} - \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(a - t\right)}{y + z \cdot b}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 41.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+159} \lor \neg \left(y \leq 8.2 \cdot 10^{-30}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -4.4e+159) (not (<= y 8.2e-30))) (/ x (- 1.0 z)) (/ t (- b y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -4.4e+159) || !(y <= 8.2e-30)) {
		tmp = x / (1.0 - z);
	} else {
		tmp = t / (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 ((y <= (-4.4d+159)) .or. (.not. (y <= 8.2d-30))) then
        tmp = x / (1.0d0 - z)
    else
        tmp = t / (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 ((y <= -4.4e+159) || !(y <= 8.2e-30)) {
		tmp = x / (1.0 - z);
	} else {
		tmp = t / (b - y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -4.4e+159) or not (y <= 8.2e-30):
		tmp = x / (1.0 - z)
	else:
		tmp = t / (b - y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -4.4e+159) || !(y <= 8.2e-30))
		tmp = Float64(x / Float64(1.0 - z));
	else
		tmp = Float64(t / Float64(b - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -4.4e+159) || ~((y <= 8.2e-30)))
		tmp = x / (1.0 - z);
	else
		tmp = t / (b - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -4.4e+159], N[Not[LessEqual[y, 8.2e-30]], $MachinePrecision]], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.3999999999999998e159 or 8.2000000000000007e-30 < y

   1. Initial program 58.7%

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

   3. Taylor expanded in y around inf 55.4%

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

      1. mul-1-neg 55.4%

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

      2. unsub-neg 55.4%

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

   5. Simplified 55.4%

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

   if -4.3999999999999998e159 < y < 8.2000000000000007e-30

   1. Initial program 74.9%

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

   3. Taylor expanded in a around 0 55.8%

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

   4. Taylor expanded in z around inf 47.5%

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

4. Final simplification 50.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+159} \lor \neg \left(y \leq 8.2 \cdot 10^{-30}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 32.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.85 \cdot 10^{+256}:\\ \;\;\;\;\frac{x}{-z}\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-55}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -2.85e+256) (/ x (- z)) (if (<= y 5e-55) (/ t (- b y)) x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.85e+256) {
		tmp = x / -z;
	} else if (y <= 5e-55) {
		tmp = t / (b - y);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-2.85d+256)) then
        tmp = x / -z
    else if (y <= 5d-55) then
        tmp = t / (b - y)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.85e+256) {
		tmp = x / -z;
	} else if (y <= 5e-55) {
		tmp = t / (b - y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -2.85e+256:
		tmp = x / -z
	elif y <= 5e-55:
		tmp = t / (b - y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -2.85e+256)
		tmp = Float64(x / Float64(-z));
	elseif (y <= 5e-55)
		tmp = Float64(t / Float64(b - y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -2.85e+256)
		tmp = x / -z;
	elseif (y <= 5e-55)
		tmp = t / (b - y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -2.85e+256], N[(x / (-z)), $MachinePrecision], If[LessEqual[y, 5e-55], N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 3 regimes

2. if y < -2.8499999999999999e256

   1. Initial program 33.4%

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

   3. Taylor expanded in z around -inf 16.0%

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

      1. associate--l+ 16.0%

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

      2. mul-1-neg 16.0%

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

      3. distribute-lft-out-- 16.0%

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

      4. associate-/l* 23.4%

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

      5. associate-/l* 55.1%

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

      6. div-sub 55.1%

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

   5. Simplified 55.1%

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

   6. Taylor expanded in y around inf 41.3%

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

      1. associate-*r/ 41.3%

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

      2. mul-1-neg 41.3%

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

   8. Simplified 41.3%

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

   if -2.8499999999999999e256 < y < 5.0000000000000002e-55

   1. Initial program 71.7%

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

   3. Taylor expanded in a around 0 54.2%

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

   4. Taylor expanded in z around inf 43.7%

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

   if 5.0000000000000002e-55 < y

   1. Initial program 66.6%

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

   3. Taylor expanded in z around 0 38.3%

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

4. Final simplification 41.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.85 \cdot 10^{+256}:\\ \;\;\;\;\frac{x}{-z}\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-55}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 32.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+170} \lor \neg \left(z \leq 3 \cdot 10^{-21}\right):\\ \;\;\;\;\frac{a}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -3.4e+170) (not (<= z 3e-21))) (/ a y) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -3.4e+170) || !(z <= 3e-21)) {
		tmp = a / y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-3.4d+170)) .or. (.not. (z <= 3d-21))) then
        tmp = a / y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -3.4e+170) || !(z <= 3e-21)) {
		tmp = a / y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -3.4e+170) or not (z <= 3e-21):
		tmp = a / y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -3.4e+170) || !(z <= 3e-21))
		tmp = Float64(a / y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -3.4e+170) || ~((z <= 3e-21)))
		tmp = a / y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -3.4e+170], N[Not[LessEqual[z, 3e-21]], $MachinePrecision]], N[(a / y), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -3.4000000000000001e170 or 2.99999999999999991e-21 < z

   1. Initial program 43.8%

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

   3. Taylor expanded in z around -inf 71.1%

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

      1. associate--l+ 71.1%

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

      2. mul-1-neg 71.1%

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

      3. distribute-lft-out-- 71.1%

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

      4. associate-/l* 77.4%

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

      5. associate-/l* 89.2%

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

      6. div-sub 89.2%

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

   5. Simplified 89.2%

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

   6. Taylor expanded in y around inf 82.7%

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

   7. Taylor expanded in y around -inf 51.2%

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

      1. associate-*r/ 51.2%

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

      2. mul-1-neg 51.2%

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

   9. Simplified 51.2%

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

   10. Taylor expanded in a around inf 18.5%

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

   if -3.4000000000000001e170 < z < 2.99999999999999991e-21

   1. Initial program 81.8%

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

   3. Taylor expanded in z around 0 33.0%

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

4. Final simplification 27.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+170} \lor \neg \left(z \leq 3 \cdot 10^{-21}\right):\\ \;\;\;\;\frac{a}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 35.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{-59}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-58}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -3.2e-59) x (if (<= y 2.9e-58) (/ t b) x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -3.2e-59) {
		tmp = x;
	} else if (y <= 2.9e-58) {
		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 <= (-3.2d-59)) then
        tmp = x
    else if (y <= 2.9d-58) 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 <= -3.2e-59) {
		tmp = x;
	} else if (y <= 2.9e-58) {
		tmp = t / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -3.2e-59:
		tmp = x
	elif y <= 2.9e-58:
		tmp = t / b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -3.2e-59)
		tmp = x;
	elseif (y <= 2.9e-58)
		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 <= -3.2e-59)
		tmp = x;
	elseif (y <= 2.9e-58)
		tmp = t / b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -3.2e-59], x, If[LessEqual[y, 2.9e-58], N[(t / b), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -3.1999999999999999e-59 or 2.8999999999999999e-58 < y

   1. Initial program 60.8%

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

   3. Taylor expanded in z around 0 32.4%

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

   if -3.1999999999999999e-59 < y < 2.8999999999999999e-58

   1. Initial program 79.0%

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

   3. Taylor expanded in a around 0 57.7%

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

   4. Taylor expanded in y around 0 53.4%

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

Alternative 23: 25.8% accurate, 17.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 68.2%

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

3. Taylor expanded in z around 0 22.7%

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

Developer target: 73.9% 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 2024107 
(FPCore (x y z t a b)
  :name "Development.Shake.Progress:decay from shake-0.15.5"
  :precision binary64

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

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