Development.Shake.Progress:decay from shake-0.15.5

Percentage Accurate: 66.8% → 88.6%

Time: 21.6s

Alternatives: 22

Speedup: 0.6×

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: 66.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 88.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(a - t\right)\\ t_2 := z \cdot \left(y - b\right) - y\\ t_3 := \frac{x \cdot \frac{y}{b - y} + y \cdot \frac{a - t}{{\left(b - y\right)}^{2}}}{z} + \frac{a - t}{y - b}\\ \mathbf{if}\;z \leq -1.7 \cdot 10^{-12}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-307}:\\ \;\;\;\;\frac{t\_1 - x \cdot y}{t\_2}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-170}:\\ \;\;\;\;x \cdot \left(\frac{t\_1}{x \cdot t\_2} - \frac{y}{t\_2}\right)\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{+21}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, z \cdot \left(t - a\right)\right)}{\mathsf{fma}\left(z, b - y, y\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- a t)))
        (t_2 (- (* z (- y b)) y))
        (t_3
         (+
          (/ (+ (* x (/ y (- b y))) (* y (/ (- a t) (pow (- b y) 2.0)))) z)
          (/ (- a t) (- y b)))))
   (if (<= z -1.7e-12)
     t_3
     (if (<= z -3.4e-307)
       (/ (- t_1 (* x y)) t_2)
       (if (<= z 7.5e-170)
         (* x (- (/ t_1 (* x t_2)) (/ y t_2)))
         (if (<= z 1.02e+21)
           (/ (fma x y (* z (- t a))) (fma z (- b y) y))
           t_3))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (a - t);
	double t_2 = (z * (y - b)) - y;
	double t_3 = (((x * (y / (b - y))) + (y * ((a - t) / pow((b - y), 2.0)))) / z) + ((a - t) / (y - b));
	double tmp;
	if (z <= -1.7e-12) {
		tmp = t_3;
	} else if (z <= -3.4e-307) {
		tmp = (t_1 - (x * y)) / t_2;
	} else if (z <= 7.5e-170) {
		tmp = x * ((t_1 / (x * t_2)) - (y / t_2));
	} else if (z <= 1.02e+21) {
		tmp = fma(x, y, (z * (t - a))) / fma(z, (b - y), y);
	} else {
		tmp = t_3;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(a - t))
	t_2 = Float64(Float64(z * Float64(y - b)) - y)
	t_3 = Float64(Float64(Float64(Float64(x * Float64(y / Float64(b - y))) + Float64(y * Float64(Float64(a - t) / (Float64(b - y) ^ 2.0)))) / z) + Float64(Float64(a - t) / Float64(y - b)))
	tmp = 0.0
	if (z <= -1.7e-12)
		tmp = t_3;
	elseif (z <= -3.4e-307)
		tmp = Float64(Float64(t_1 - Float64(x * y)) / t_2);
	elseif (z <= 7.5e-170)
		tmp = Float64(x * Float64(Float64(t_1 / Float64(x * t_2)) - Float64(y / t_2)));
	elseif (z <= 1.02e+21)
		tmp = Float64(fma(x, y, Float64(z * Float64(t - a))) / fma(z, Float64(b - y), y));
	else
		tmp = t_3;
	end
	return 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[(N[(z * N[(y - b), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(N[(x * N[(y / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * N[(N[(a - t), $MachinePrecision] / N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] + N[(N[(a - t), $MachinePrecision] / N[(y - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.7e-12], t$95$3, If[LessEqual[z, -3.4e-307], N[(N[(t$95$1 - N[(x * y), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision], If[LessEqual[z, 7.5e-170], N[(x * N[(N[(t$95$1 / N[(x * t$95$2), $MachinePrecision]), $MachinePrecision] - N[(y / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.02e+21], N[(N[(x * y + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * N[(b - y), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.7e-12 or 1.02e21 < z

   1. Initial program 32.4%

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

   3. Taylor expanded in z around -inf 61.3%

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

      1. associate--l+ 61.3%

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

      2. mul-1-neg 61.3%

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

      3. distribute-lft-out-- 61.3%

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

      4. associate-/l* 70.4%

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

      5. associate-/l* 91.8%

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

      6. div-sub 91.8%

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

   5. Simplified 91.8%

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

   if -1.7e-12 < z < -3.39999999999999989e-307

   1. Initial program 95.5%

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

   if -3.39999999999999989e-307 < z < 7.4999999999999998e-170

   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 x around inf 96.7%

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

   if 7.4999999999999998e-170 < z < 1.02e21

   1. Initial program 99.4%

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

      1. fma-define 99.4%

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

      2. +-commutative 99.4%

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

      3. fma-define 99.4%

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

   3. Simplified 99.4%

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

4. Final simplification 94.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{-12}:\\ \;\;\;\;\frac{x \cdot \frac{y}{b - y} + y \cdot \frac{a - t}{{\left(b - y\right)}^{2}}}{z} + \frac{a - t}{y - b}\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-307}:\\ \;\;\;\;\frac{z \cdot \left(a - t\right) - x \cdot y}{z \cdot \left(y - b\right) - y}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-170}:\\ \;\;\;\;x \cdot \left(\frac{z \cdot \left(a - t\right)}{x \cdot \left(z \cdot \left(y - b\right) - y\right)} - \frac{y}{z \cdot \left(y - b\right) - y}\right)\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{+21}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, z \cdot \left(t - a\right)\right)}{\mathsf{fma}\left(z, b - y, y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{y}{b - y} + y \cdot \frac{a - t}{{\left(b - y\right)}^{2}}}{z} + \frac{a - t}{y - b}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 88.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(a - t\right)\\ t_2 := z \cdot \left(y - b\right) - y\\ t_3 := \frac{x \cdot \frac{y}{b - y} + y \cdot \frac{a - t}{{\left(b - y\right)}^{2}}}{z} + \frac{a - t}{y - b}\\ t_4 := \frac{t\_1 - x \cdot y}{t\_2}\\ \mathbf{if}\;z \leq -1.7 \cdot 10^{-12}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-307}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-169}:\\ \;\;\;\;x \cdot \left(\frac{t\_1}{x \cdot t\_2} - \frac{y}{t\_2}\right)\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{+18}:\\ \;\;\;\;t\_4\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- a t)))
        (t_2 (- (* z (- y b)) y))
        (t_3
         (+
          (/ (+ (* x (/ y (- b y))) (* y (/ (- a t) (pow (- b y) 2.0)))) z)
          (/ (- a t) (- y b))))
        (t_4 (/ (- t_1 (* x y)) t_2)))
   (if (<= z -1.7e-12)
     t_3
     (if (<= z -4.2e-307)
       t_4
       (if (<= z 3.8e-169)
         (* x (- (/ t_1 (* x t_2)) (/ y t_2)))
         (if (<= z 5.6e+18) t_4 t_3))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (a - t);
	double t_2 = (z * (y - b)) - y;
	double t_3 = (((x * (y / (b - y))) + (y * ((a - t) / pow((b - y), 2.0)))) / z) + ((a - t) / (y - b));
	double t_4 = (t_1 - (x * y)) / t_2;
	double tmp;
	if (z <= -1.7e-12) {
		tmp = t_3;
	} else if (z <= -4.2e-307) {
		tmp = t_4;
	} else if (z <= 3.8e-169) {
		tmp = x * ((t_1 / (x * t_2)) - (y / t_2));
	} else if (z <= 5.6e+18) {
		tmp = t_4;
	} 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) :: t_4
    real(8) :: tmp
    t_1 = z * (a - t)
    t_2 = (z * (y - b)) - y
    t_3 = (((x * (y / (b - y))) + (y * ((a - t) / ((b - y) ** 2.0d0)))) / z) + ((a - t) / (y - b))
    t_4 = (t_1 - (x * y)) / t_2
    if (z <= (-1.7d-12)) then
        tmp = t_3
    else if (z <= (-4.2d-307)) then
        tmp = t_4
    else if (z <= 3.8d-169) then
        tmp = x * ((t_1 / (x * t_2)) - (y / t_2))
    else if (z <= 5.6d+18) then
        tmp = t_4
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (a - t);
	double t_2 = (z * (y - b)) - y;
	double t_3 = (((x * (y / (b - y))) + (y * ((a - t) / Math.pow((b - y), 2.0)))) / z) + ((a - t) / (y - b));
	double t_4 = (t_1 - (x * y)) / t_2;
	double tmp;
	if (z <= -1.7e-12) {
		tmp = t_3;
	} else if (z <= -4.2e-307) {
		tmp = t_4;
	} else if (z <= 3.8e-169) {
		tmp = x * ((t_1 / (x * t_2)) - (y / t_2));
	} else if (z <= 5.6e+18) {
		tmp = t_4;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (a - t)
	t_2 = (z * (y - b)) - y
	t_3 = (((x * (y / (b - y))) + (y * ((a - t) / math.pow((b - y), 2.0)))) / z) + ((a - t) / (y - b))
	t_4 = (t_1 - (x * y)) / t_2
	tmp = 0
	if z <= -1.7e-12:
		tmp = t_3
	elif z <= -4.2e-307:
		tmp = t_4
	elif z <= 3.8e-169:
		tmp = x * ((t_1 / (x * t_2)) - (y / t_2))
	elif z <= 5.6e+18:
		tmp = t_4
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(a - t))
	t_2 = Float64(Float64(z * Float64(y - b)) - y)
	t_3 = Float64(Float64(Float64(Float64(x * Float64(y / Float64(b - y))) + Float64(y * Float64(Float64(a - t) / (Float64(b - y) ^ 2.0)))) / z) + Float64(Float64(a - t) / Float64(y - b)))
	t_4 = Float64(Float64(t_1 - Float64(x * y)) / t_2)
	tmp = 0.0
	if (z <= -1.7e-12)
		tmp = t_3;
	elseif (z <= -4.2e-307)
		tmp = t_4;
	elseif (z <= 3.8e-169)
		tmp = Float64(x * Float64(Float64(t_1 / Float64(x * t_2)) - Float64(y / t_2)));
	elseif (z <= 5.6e+18)
		tmp = t_4;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (a - t);
	t_2 = (z * (y - b)) - y;
	t_3 = (((x * (y / (b - y))) + (y * ((a - t) / ((b - y) ^ 2.0)))) / z) + ((a - t) / (y - b));
	t_4 = (t_1 - (x * y)) / t_2;
	tmp = 0.0;
	if (z <= -1.7e-12)
		tmp = t_3;
	elseif (z <= -4.2e-307)
		tmp = t_4;
	elseif (z <= 3.8e-169)
		tmp = x * ((t_1 / (x * t_2)) - (y / t_2));
	elseif (z <= 5.6e+18)
		tmp = t_4;
	else
		tmp = t_3;
	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[(N[(z * N[(y - b), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(N[(x * N[(y / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * N[(N[(a - t), $MachinePrecision] / N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] + N[(N[(a - t), $MachinePrecision] / N[(y - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(t$95$1 - N[(x * y), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]}, If[LessEqual[z, -1.7e-12], t$95$3, If[LessEqual[z, -4.2e-307], t$95$4, If[LessEqual[z, 3.8e-169], N[(x * N[(N[(t$95$1 / N[(x * t$95$2), $MachinePrecision]), $MachinePrecision] - N[(y / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.6e+18], t$95$4, t$95$3]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.7e-12 or 5.6e18 < z

   1. Initial program 32.4%

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

   3. Taylor expanded in z around -inf 61.3%

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

      1. associate--l+ 61.3%

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

      2. mul-1-neg 61.3%

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

      3. distribute-lft-out-- 61.3%

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

      4. associate-/l* 70.4%

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

      5. associate-/l* 91.8%

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

      6. div-sub 91.8%

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

   5. Simplified 91.8%

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

   if -1.7e-12 < z < -4.2000000000000002e-307 or 3.8e-169 < z < 5.6e18

   1. Initial program 97.0%

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

   if -4.2000000000000002e-307 < z < 3.8e-169

   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 x around inf 96.7%

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

4. Final simplification 94.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{-12}:\\ \;\;\;\;\frac{x \cdot \frac{y}{b - y} + y \cdot \frac{a - t}{{\left(b - y\right)}^{2}}}{z} + \frac{a - t}{y - b}\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-307}:\\ \;\;\;\;\frac{z \cdot \left(a - t\right) - x \cdot y}{z \cdot \left(y - b\right) - y}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-169}:\\ \;\;\;\;x \cdot \left(\frac{z \cdot \left(a - t\right)}{x \cdot \left(z \cdot \left(y - b\right) - y\right)} - \frac{y}{z \cdot \left(y - b\right) - y}\right)\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{+18}:\\ \;\;\;\;\frac{z \cdot \left(a - t\right) - x \cdot y}{z \cdot \left(y - b\right) - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{y}{b - y} + y \cdot \frac{a - t}{{\left(b - y\right)}^{2}}}{z} + \frac{a - t}{y - b}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 82.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a - t}{y - b}\\ t_2 := z \cdot \left(y - b\right)\\ \mathbf{if}\;z \leq -2.05 \cdot 10^{+154}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.05 \cdot 10^{+125}:\\ \;\;\;\;\frac{x}{1 - z} + x \cdot \frac{\left(\frac{a}{x} - b \cdot \frac{z}{{\left(z + -1\right)}^{2}}\right) - \frac{t}{x}}{y}\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-12}:\\ \;\;\;\;\left(t\_1 - x \cdot \frac{y}{t\_2}\right) + y \cdot \frac{a - t}{z \cdot {\left(b - y\right)}^{2}}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+26}:\\ \;\;\;\;\frac{z \cdot \left(a - t\right) - x \cdot y}{t\_2 - y}\\ \mathbf{elif}\;z \leq 10^{+128}:\\ \;\;\;\;\frac{a - t}{y} - \frac{x + \frac{t - a}{y}}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- a t) (- y b))) (t_2 (* z (- y b))))
   (if (<= z -2.05e+154)
     t_1
     (if (<= z -2.05e+125)
       (+
        (/ x (- 1.0 z))
        (* x (/ (- (- (/ a x) (* b (/ z (pow (+ z -1.0) 2.0)))) (/ t x)) y)))
       (if (<= z -1.7e-12)
         (+ (- t_1 (* x (/ y t_2))) (* y (/ (- a t) (* z (pow (- b y) 2.0)))))
         (if (<= z 1.1e+26)
           (/ (- (* z (- a t)) (* x y)) (- t_2 y))
           (if (<= z 1e+128)
             (- (/ (- a t) y) (/ (+ x (/ (- t a) y)) z))
             t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a - t) / (y - b);
	double t_2 = z * (y - b);
	double tmp;
	if (z <= -2.05e+154) {
		tmp = t_1;
	} else if (z <= -2.05e+125) {
		tmp = (x / (1.0 - z)) + (x * ((((a / x) - (b * (z / pow((z + -1.0), 2.0)))) - (t / x)) / y));
	} else if (z <= -1.7e-12) {
		tmp = (t_1 - (x * (y / t_2))) + (y * ((a - t) / (z * pow((b - y), 2.0))));
	} else if (z <= 1.1e+26) {
		tmp = ((z * (a - t)) - (x * y)) / (t_2 - y);
	} else if (z <= 1e+128) {
		tmp = ((a - t) / y) - ((x + ((t - a) / y)) / 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 = (a - t) / (y - b)
    t_2 = z * (y - b)
    if (z <= (-2.05d+154)) then
        tmp = t_1
    else if (z <= (-2.05d+125)) then
        tmp = (x / (1.0d0 - z)) + (x * ((((a / x) - (b * (z / ((z + (-1.0d0)) ** 2.0d0)))) - (t / x)) / y))
    else if (z <= (-1.7d-12)) then
        tmp = (t_1 - (x * (y / t_2))) + (y * ((a - t) / (z * ((b - y) ** 2.0d0))))
    else if (z <= 1.1d+26) then
        tmp = ((z * (a - t)) - (x * y)) / (t_2 - y)
    else if (z <= 1d+128) then
        tmp = ((a - t) / y) - ((x + ((t - a) / y)) / z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a - t) / (y - b);
	double t_2 = z * (y - b);
	double tmp;
	if (z <= -2.05e+154) {
		tmp = t_1;
	} else if (z <= -2.05e+125) {
		tmp = (x / (1.0 - z)) + (x * ((((a / x) - (b * (z / Math.pow((z + -1.0), 2.0)))) - (t / x)) / y));
	} else if (z <= -1.7e-12) {
		tmp = (t_1 - (x * (y / t_2))) + (y * ((a - t) / (z * Math.pow((b - y), 2.0))));
	} else if (z <= 1.1e+26) {
		tmp = ((z * (a - t)) - (x * y)) / (t_2 - y);
	} else if (z <= 1e+128) {
		tmp = ((a - t) / y) - ((x + ((t - a) / y)) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a - t) / (y - b)
	t_2 = z * (y - b)
	tmp = 0
	if z <= -2.05e+154:
		tmp = t_1
	elif z <= -2.05e+125:
		tmp = (x / (1.0 - z)) + (x * ((((a / x) - (b * (z / math.pow((z + -1.0), 2.0)))) - (t / x)) / y))
	elif z <= -1.7e-12:
		tmp = (t_1 - (x * (y / t_2))) + (y * ((a - t) / (z * math.pow((b - y), 2.0))))
	elif z <= 1.1e+26:
		tmp = ((z * (a - t)) - (x * y)) / (t_2 - y)
	elif z <= 1e+128:
		tmp = ((a - t) / y) - ((x + ((t - a) / y)) / z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a - t) / Float64(y - b))
	t_2 = Float64(z * Float64(y - b))
	tmp = 0.0
	if (z <= -2.05e+154)
		tmp = t_1;
	elseif (z <= -2.05e+125)
		tmp = Float64(Float64(x / Float64(1.0 - z)) + Float64(x * Float64(Float64(Float64(Float64(a / x) - Float64(b * Float64(z / (Float64(z + -1.0) ^ 2.0)))) - Float64(t / x)) / y)));
	elseif (z <= -1.7e-12)
		tmp = Float64(Float64(t_1 - Float64(x * Float64(y / t_2))) + Float64(y * Float64(Float64(a - t) / Float64(z * (Float64(b - y) ^ 2.0)))));
	elseif (z <= 1.1e+26)
		tmp = Float64(Float64(Float64(z * Float64(a - t)) - Float64(x * y)) / Float64(t_2 - y));
	elseif (z <= 1e+128)
		tmp = Float64(Float64(Float64(a - t) / y) - Float64(Float64(x + Float64(Float64(t - a) / y)) / z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a - t) / (y - b);
	t_2 = z * (y - b);
	tmp = 0.0;
	if (z <= -2.05e+154)
		tmp = t_1;
	elseif (z <= -2.05e+125)
		tmp = (x / (1.0 - z)) + (x * ((((a / x) - (b * (z / ((z + -1.0) ^ 2.0)))) - (t / x)) / y));
	elseif (z <= -1.7e-12)
		tmp = (t_1 - (x * (y / t_2))) + (y * ((a - t) / (z * ((b - y) ^ 2.0))));
	elseif (z <= 1.1e+26)
		tmp = ((z * (a - t)) - (x * y)) / (t_2 - y);
	elseif (z <= 1e+128)
		tmp = ((a - t) / y) - ((x + ((t - a) / y)) / z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a - t), $MachinePrecision] / N[(y - b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(y - b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.05e+154], t$95$1, If[LessEqual[z, -2.05e+125], N[(N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(N[(N[(a / x), $MachinePrecision] - N[(b * N[(z / N[Power[N[(z + -1.0), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t / x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.7e-12], N[(N[(t$95$1 - N[(x * N[(y / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * N[(N[(a - t), $MachinePrecision] / N[(z * N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.1e+26], N[(N[(N[(z * N[(a - t), $MachinePrecision]), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision] / N[(t$95$2 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1e+128], N[(N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision] - N[(N[(x + N[(N[(t - a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.05e154 or 1.0000000000000001e128 < z

   1. Initial program 22.3%

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

   3. Taylor expanded in z around inf 85.5%

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

   if -2.05e154 < z < -2.04999999999999996e125

   1. Initial program 27.3%

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

   3. Taylor expanded in x around inf 40.0%

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

   4. Taylor expanded in z around inf 64.1%

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

   5. Taylor expanded in y around -inf 87.6%

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

      1. distribute-lft-out 87.6%

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

      2. sub-neg 87.6%

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

      3. metadata-eval 87.6%

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

      4. associate-/l* 87.8%

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

      5. associate--l+ 87.8%

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

      6. associate-/l* 94.2%

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

      7. sub-neg 94.2%

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

      8. metadata-eval 94.2%

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

   7. Simplified 94.2%

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

   if -2.04999999999999996e125 < z < -1.7e-12

   1. Initial program 50.6%

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

   3. Taylor expanded in z around inf 64.4%

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

      1. associate--r+ 64.4%

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

      2. +-commutative 64.4%

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

      3. associate--l+ 64.4%

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

      4. associate-/l* 68.4%

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

      5. div-sub 68.4%

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

      6. associate-/l* 89.1%

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

   5. Simplified 89.1%

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

   if -1.7e-12 < z < 1.10000000000000004e26

   1. Initial program 93.5%

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

   if 1.10000000000000004e26 < z < 1.0000000000000001e128

   1. Initial program 42.1%

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

   3. Taylor expanded in y around inf 37.3%

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

      1. mul-1-neg 37.3%

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

      2. unsub-neg 37.3%

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

   5. Simplified 37.3%

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

   6. Taylor expanded in z around -inf 86.5%

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

      1. mul-1-neg 86.5%

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

      2. unsub-neg 86.5%

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

      3. associate-*r/ 86.5%

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

      4. mul-1-neg 86.5%

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

      5. sub-neg 86.5%

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

      6. mul-1-neg 86.5%

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

      7. remove-double-neg 86.5%

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

   8. Simplified 86.5%

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

4. Final simplification 90.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.05 \cdot 10^{+154}:\\ \;\;\;\;\frac{a - t}{y - b}\\ \mathbf{elif}\;z \leq -2.05 \cdot 10^{+125}:\\ \;\;\;\;\frac{x}{1 - z} + x \cdot \frac{\left(\frac{a}{x} - b \cdot \frac{z}{{\left(z + -1\right)}^{2}}\right) - \frac{t}{x}}{y}\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-12}:\\ \;\;\;\;\left(\frac{a - t}{y - b} - x \cdot \frac{y}{z \cdot \left(y - b\right)}\right) + y \cdot \frac{a - t}{z \cdot {\left(b - y\right)}^{2}}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+26}:\\ \;\;\;\;\frac{z \cdot \left(a - t\right) - x \cdot y}{z \cdot \left(y - b\right) - y}\\ \mathbf{elif}\;z \leq 10^{+128}:\\ \;\;\;\;\frac{a - t}{y} - \frac{x + \frac{t - a}{y}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{a - t}{y - b}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 81.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a - t}{y - b}\\ \mathbf{if}\;z \leq -2.05 \cdot 10^{+154}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.05 \cdot 10^{+125}:\\ \;\;\;\;\frac{x}{1 - z} + x \cdot \frac{\left(\frac{a}{x} - b \cdot \frac{z}{{\left(z + -1\right)}^{2}}\right) - \frac{t}{x}}{y}\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{+21}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+26}:\\ \;\;\;\;\frac{z \cdot \left(a - t\right) - x \cdot y}{z \cdot \left(y - b\right) - y}\\ \mathbf{elif}\;z \leq 10^{+128}:\\ \;\;\;\;\frac{a - t}{y} - \frac{x + \frac{t - a}{y}}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- a t) (- y b))))
   (if (<= z -2.05e+154)
     t_1
     (if (<= z -2.05e+125)
       (+
        (/ x (- 1.0 z))
        (* x (/ (- (- (/ a x) (* b (/ z (pow (+ z -1.0) 2.0)))) (/ t x)) y)))
       (if (<= z -1.1e+21)
         t_1
         (if (<= z 1.1e+26)
           (/ (- (* z (- a t)) (* x y)) (- (* z (- y b)) y))
           (if (<= z 1e+128)
             (- (/ (- a t) y) (/ (+ x (/ (- t a) y)) z))
             t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a - t) / (y - b);
	double tmp;
	if (z <= -2.05e+154) {
		tmp = t_1;
	} else if (z <= -2.05e+125) {
		tmp = (x / (1.0 - z)) + (x * ((((a / x) - (b * (z / pow((z + -1.0), 2.0)))) - (t / x)) / y));
	} else if (z <= -1.1e+21) {
		tmp = t_1;
	} else if (z <= 1.1e+26) {
		tmp = ((z * (a - t)) - (x * y)) / ((z * (y - b)) - y);
	} else if (z <= 1e+128) {
		tmp = ((a - t) / y) - ((x + ((t - a) / y)) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a - t) / (y - b)
    if (z <= (-2.05d+154)) then
        tmp = t_1
    else if (z <= (-2.05d+125)) then
        tmp = (x / (1.0d0 - z)) + (x * ((((a / x) - (b * (z / ((z + (-1.0d0)) ** 2.0d0)))) - (t / x)) / y))
    else if (z <= (-1.1d+21)) then
        tmp = t_1
    else if (z <= 1.1d+26) then
        tmp = ((z * (a - t)) - (x * y)) / ((z * (y - b)) - y)
    else if (z <= 1d+128) then
        tmp = ((a - t) / y) - ((x + ((t - a) / y)) / z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a - t) / (y - b);
	double tmp;
	if (z <= -2.05e+154) {
		tmp = t_1;
	} else if (z <= -2.05e+125) {
		tmp = (x / (1.0 - z)) + (x * ((((a / x) - (b * (z / Math.pow((z + -1.0), 2.0)))) - (t / x)) / y));
	} else if (z <= -1.1e+21) {
		tmp = t_1;
	} else if (z <= 1.1e+26) {
		tmp = ((z * (a - t)) - (x * y)) / ((z * (y - b)) - y);
	} else if (z <= 1e+128) {
		tmp = ((a - t) / y) - ((x + ((t - a) / y)) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a - t) / (y - b)
	tmp = 0
	if z <= -2.05e+154:
		tmp = t_1
	elif z <= -2.05e+125:
		tmp = (x / (1.0 - z)) + (x * ((((a / x) - (b * (z / math.pow((z + -1.0), 2.0)))) - (t / x)) / y))
	elif z <= -1.1e+21:
		tmp = t_1
	elif z <= 1.1e+26:
		tmp = ((z * (a - t)) - (x * y)) / ((z * (y - b)) - y)
	elif z <= 1e+128:
		tmp = ((a - t) / y) - ((x + ((t - a) / y)) / z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a - t) / Float64(y - b))
	tmp = 0.0
	if (z <= -2.05e+154)
		tmp = t_1;
	elseif (z <= -2.05e+125)
		tmp = Float64(Float64(x / Float64(1.0 - z)) + Float64(x * Float64(Float64(Float64(Float64(a / x) - Float64(b * Float64(z / (Float64(z + -1.0) ^ 2.0)))) - Float64(t / x)) / y)));
	elseif (z <= -1.1e+21)
		tmp = t_1;
	elseif (z <= 1.1e+26)
		tmp = Float64(Float64(Float64(z * Float64(a - t)) - Float64(x * y)) / Float64(Float64(z * Float64(y - b)) - y));
	elseif (z <= 1e+128)
		tmp = Float64(Float64(Float64(a - t) / y) - Float64(Float64(x + Float64(Float64(t - a) / y)) / z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a - t) / (y - b);
	tmp = 0.0;
	if (z <= -2.05e+154)
		tmp = t_1;
	elseif (z <= -2.05e+125)
		tmp = (x / (1.0 - z)) + (x * ((((a / x) - (b * (z / ((z + -1.0) ^ 2.0)))) - (t / x)) / y));
	elseif (z <= -1.1e+21)
		tmp = t_1;
	elseif (z <= 1.1e+26)
		tmp = ((z * (a - t)) - (x * y)) / ((z * (y - b)) - y);
	elseif (z <= 1e+128)
		tmp = ((a - t) / y) - ((x + ((t - a) / y)) / z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a - t), $MachinePrecision] / N[(y - b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.05e+154], t$95$1, If[LessEqual[z, -2.05e+125], N[(N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(N[(N[(a / x), $MachinePrecision] - N[(b * N[(z / N[Power[N[(z + -1.0), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t / x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.1e+21], t$95$1, If[LessEqual[z, 1.1e+26], N[(N[(N[(z * N[(a - t), $MachinePrecision]), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision] / N[(N[(z * N[(y - b), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1e+128], N[(N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision] - N[(N[(x + N[(N[(t - a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.05e154 or -2.04999999999999996e125 < z < -1.1e21 or 1.0000000000000001e128 < z

   1. Initial program 27.6%

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

   3. Taylor expanded in z around inf 83.1%

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

   if -2.05e154 < z < -2.04999999999999996e125

   1. Initial program 27.3%

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

   3. Taylor expanded in x around inf 40.0%

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

   4. Taylor expanded in z around inf 64.1%

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

   5. Taylor expanded in y around -inf 87.6%

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

      1. distribute-lft-out 87.6%

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

      2. sub-neg 87.6%

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

      3. metadata-eval 87.6%

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

      4. associate-/l* 87.8%

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

      5. associate--l+ 87.8%

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

      6. associate-/l* 94.2%

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

      7. sub-neg 94.2%

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

      8. metadata-eval 94.2%

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

   7. Simplified 94.2%

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

   if -1.1e21 < z < 1.10000000000000004e26

   1. Initial program 92.5%

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

   if 1.10000000000000004e26 < z < 1.0000000000000001e128

   1. Initial program 42.1%

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

   3. Taylor expanded in y around inf 37.3%

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

      1. mul-1-neg 37.3%

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

      2. unsub-neg 37.3%

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

   5. Simplified 37.3%

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

   6. Taylor expanded in z around -inf 86.5%

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

      1. mul-1-neg 86.5%

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

      2. unsub-neg 86.5%

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

      3. associate-*r/ 86.5%

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

      4. mul-1-neg 86.5%

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

      5. sub-neg 86.5%

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

      6. mul-1-neg 86.5%

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

      7. remove-double-neg 86.5%

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

   8. Simplified 86.5%

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

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.05 \cdot 10^{+154}:\\ \;\;\;\;\frac{a - t}{y - b}\\ \mathbf{elif}\;z \leq -2.05 \cdot 10^{+125}:\\ \;\;\;\;\frac{x}{1 - z} + x \cdot \frac{\left(\frac{a}{x} - b \cdot \frac{z}{{\left(z + -1\right)}^{2}}\right) - \frac{t}{x}}{y}\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{+21}:\\ \;\;\;\;\frac{a - t}{y - b}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+26}:\\ \;\;\;\;\frac{z \cdot \left(a - t\right) - x \cdot y}{z \cdot \left(y - b\right) - y}\\ \mathbf{elif}\;z \leq 10^{+128}:\\ \;\;\;\;\frac{a - t}{y} - \frac{x + \frac{t - a}{y}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{a - t}{y - b}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 71.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a - t}{y} - \frac{x + \frac{t - a}{y}}{z}\\ t_2 := \frac{x \cdot \left(\left(\frac{t}{x} + \frac{y}{z}\right) - \frac{a}{x}\right)}{b}\\ t_3 := \frac{a - t}{y - b}\\ \mathbf{if}\;z \leq -2.2 \cdot 10^{+154}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq -2.05 \cdot 10^{+125}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3.9 \cdot 10^{-11}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-67}:\\ \;\;\;\;x - \frac{z \cdot \left(a - t\right)}{y}\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{-48}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 110:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y \cdot \left(1 - z\right)}\\ \mathbf{elif}\;z \leq 43000000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 10^{+128}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (/ (- a t) y) (/ (+ x (/ (- t a) y)) z)))
        (t_2 (/ (* x (- (+ (/ t x) (/ y z)) (/ a x))) b))
        (t_3 (/ (- a t) (- y b))))
   (if (<= z -2.2e+154)
     t_3
     (if (<= z -2.05e+125)
       t_1
       (if (<= z -3.9e-11)
         t_3
         (if (<= z 5.2e-67)
           (- x (/ (* z (- a t)) y))
           (if (<= z 5.3e-48)
             t_2
             (if (<= z 110.0)
               (/ (+ (* x y) (* z (- t a))) (* y (- 1.0 z)))
               (if (<= z 43000000000.0) t_2 (if (<= z 1e+128) t_1 t_3))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((a - t) / y) - ((x + ((t - a) / y)) / z);
	double t_2 = (x * (((t / x) + (y / z)) - (a / x))) / b;
	double t_3 = (a - t) / (y - b);
	double tmp;
	if (z <= -2.2e+154) {
		tmp = t_3;
	} else if (z <= -2.05e+125) {
		tmp = t_1;
	} else if (z <= -3.9e-11) {
		tmp = t_3;
	} else if (z <= 5.2e-67) {
		tmp = x - ((z * (a - t)) / y);
	} else if (z <= 5.3e-48) {
		tmp = t_2;
	} else if (z <= 110.0) {
		tmp = ((x * y) + (z * (t - a))) / (y * (1.0 - z));
	} else if (z <= 43000000000.0) {
		tmp = t_2;
	} else if (z <= 1e+128) {
		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 = ((a - t) / y) - ((x + ((t - a) / y)) / z)
    t_2 = (x * (((t / x) + (y / z)) - (a / x))) / b
    t_3 = (a - t) / (y - b)
    if (z <= (-2.2d+154)) then
        tmp = t_3
    else if (z <= (-2.05d+125)) then
        tmp = t_1
    else if (z <= (-3.9d-11)) then
        tmp = t_3
    else if (z <= 5.2d-67) then
        tmp = x - ((z * (a - t)) / y)
    else if (z <= 5.3d-48) then
        tmp = t_2
    else if (z <= 110.0d0) then
        tmp = ((x * y) + (z * (t - a))) / (y * (1.0d0 - z))
    else if (z <= 43000000000.0d0) then
        tmp = t_2
    else if (z <= 1d+128) 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 = ((a - t) / y) - ((x + ((t - a) / y)) / z);
	double t_2 = (x * (((t / x) + (y / z)) - (a / x))) / b;
	double t_3 = (a - t) / (y - b);
	double tmp;
	if (z <= -2.2e+154) {
		tmp = t_3;
	} else if (z <= -2.05e+125) {
		tmp = t_1;
	} else if (z <= -3.9e-11) {
		tmp = t_3;
	} else if (z <= 5.2e-67) {
		tmp = x - ((z * (a - t)) / y);
	} else if (z <= 5.3e-48) {
		tmp = t_2;
	} else if (z <= 110.0) {
		tmp = ((x * y) + (z * (t - a))) / (y * (1.0 - z));
	} else if (z <= 43000000000.0) {
		tmp = t_2;
	} else if (z <= 1e+128) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((a - t) / y) - ((x + ((t - a) / y)) / z)
	t_2 = (x * (((t / x) + (y / z)) - (a / x))) / b
	t_3 = (a - t) / (y - b)
	tmp = 0
	if z <= -2.2e+154:
		tmp = t_3
	elif z <= -2.05e+125:
		tmp = t_1
	elif z <= -3.9e-11:
		tmp = t_3
	elif z <= 5.2e-67:
		tmp = x - ((z * (a - t)) / y)
	elif z <= 5.3e-48:
		tmp = t_2
	elif z <= 110.0:
		tmp = ((x * y) + (z * (t - a))) / (y * (1.0 - z))
	elif z <= 43000000000.0:
		tmp = t_2
	elif z <= 1e+128:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(a - t) / y) - Float64(Float64(x + Float64(Float64(t - a) / y)) / z))
	t_2 = Float64(Float64(x * Float64(Float64(Float64(t / x) + Float64(y / z)) - Float64(a / x))) / b)
	t_3 = Float64(Float64(a - t) / Float64(y - b))
	tmp = 0.0
	if (z <= -2.2e+154)
		tmp = t_3;
	elseif (z <= -2.05e+125)
		tmp = t_1;
	elseif (z <= -3.9e-11)
		tmp = t_3;
	elseif (z <= 5.2e-67)
		tmp = Float64(x - Float64(Float64(z * Float64(a - t)) / y));
	elseif (z <= 5.3e-48)
		tmp = t_2;
	elseif (z <= 110.0)
		tmp = Float64(Float64(Float64(x * y) + Float64(z * Float64(t - a))) / Float64(y * Float64(1.0 - z)));
	elseif (z <= 43000000000.0)
		tmp = t_2;
	elseif (z <= 1e+128)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((a - t) / y) - ((x + ((t - a) / y)) / z);
	t_2 = (x * (((t / x) + (y / z)) - (a / x))) / b;
	t_3 = (a - t) / (y - b);
	tmp = 0.0;
	if (z <= -2.2e+154)
		tmp = t_3;
	elseif (z <= -2.05e+125)
		tmp = t_1;
	elseif (z <= -3.9e-11)
		tmp = t_3;
	elseif (z <= 5.2e-67)
		tmp = x - ((z * (a - t)) / y);
	elseif (z <= 5.3e-48)
		tmp = t_2;
	elseif (z <= 110.0)
		tmp = ((x * y) + (z * (t - a))) / (y * (1.0 - z));
	elseif (z <= 43000000000.0)
		tmp = t_2;
	elseif (z <= 1e+128)
		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[(a - t), $MachinePrecision] / y), $MachinePrecision] - N[(N[(x + N[(N[(t - a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(N[(N[(t / x), $MachinePrecision] + N[(y / z), $MachinePrecision]), $MachinePrecision] - N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]}, Block[{t$95$3 = N[(N[(a - t), $MachinePrecision] / N[(y - b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.2e+154], t$95$3, If[LessEqual[z, -2.05e+125], t$95$1, If[LessEqual[z, -3.9e-11], t$95$3, If[LessEqual[z, 5.2e-67], N[(x - N[(N[(z * N[(a - t), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.3e-48], t$95$2, If[LessEqual[z, 110.0], N[(N[(N[(x * y), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 43000000000.0], t$95$2, If[LessEqual[z, 1e+128], t$95$1, t$95$3]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.2000000000000001e154 or -2.04999999999999996e125 < z < -3.9000000000000001e-11 or 1.0000000000000001e128 < z

   1. Initial program 30.7%

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

   3. Taylor expanded in z around inf 81.8%

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

   if -2.2000000000000001e154 < z < -2.04999999999999996e125 or 4.3e10 < z < 1.0000000000000001e128

   1. Initial program 40.2%

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

   3. Taylor expanded in y around inf 36.7%

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

      1. mul-1-neg 36.7%

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

      2. unsub-neg 36.7%

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

   5. Simplified 36.7%

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

   6. Taylor expanded in z around -inf 88.1%

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

      1. mul-1-neg 88.1%

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

      2. unsub-neg 88.1%

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

      3. associate-*r/ 88.1%

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

      4. mul-1-neg 88.1%

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

      5. sub-neg 88.1%

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

      6. mul-1-neg 88.1%

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

      7. remove-double-neg 88.1%

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

   8. Simplified 88.1%

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

   if -3.9000000000000001e-11 < z < 5.1999999999999998e-67

   1. Initial program 91.6%

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

   3. Taylor expanded in z around 0 67.2%

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

   4. Taylor expanded in x around 0 75.1%

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

   if 5.1999999999999998e-67 < z < 5.3e-48 or 110 < z < 4.3e10

   1. Initial program 99.0%

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

   3. Taylor expanded in x around inf 67.3%

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

   4. Taylor expanded in b around inf 99.8%

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

   if 5.3e-48 < z < 110

   1. Initial program 99.4%

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

   3. Taylor expanded in y around inf 69.8%

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

      1. mul-1-neg 69.8%

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

      2. unsub-neg 69.8%

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

   5. Simplified 69.8%

      \[\leadsto \frac{x \cdot y + z \cdot \left(t - a\right)}{\color{blue}{y \cdot \left(1 - z\right)}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+154}:\\ \;\;\;\;\frac{a - t}{y - b}\\ \mathbf{elif}\;z \leq -2.05 \cdot 10^{+125}:\\ \;\;\;\;\frac{a - t}{y} - \frac{x + \frac{t - a}{y}}{z}\\ \mathbf{elif}\;z \leq -3.9 \cdot 10^{-11}:\\ \;\;\;\;\frac{a - t}{y - b}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-67}:\\ \;\;\;\;x - \frac{z \cdot \left(a - t\right)}{y}\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{-48}:\\ \;\;\;\;\frac{x \cdot \left(\left(\frac{t}{x} + \frac{y}{z}\right) - \frac{a}{x}\right)}{b}\\ \mathbf{elif}\;z \leq 110:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y \cdot \left(1 - z\right)}\\ \mathbf{elif}\;z \leq 43000000000:\\ \;\;\;\;\frac{x \cdot \left(\left(\frac{t}{x} + \frac{y}{z}\right) - \frac{a}{x}\right)}{b}\\ \mathbf{elif}\;z \leq 10^{+128}:\\ \;\;\;\;\frac{a - t}{y} - \frac{x + \frac{t - a}{y}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{a - t}{y - b}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 82.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a - t}{y - b}\\ \mathbf{if}\;z \leq -2.06 \cdot 10^{+154}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{+125}:\\ \;\;\;\;t \cdot \left(\frac{z}{y \cdot \left(1 - z\right)} - \frac{\frac{a}{y} \cdot \frac{z}{1 - z} + \frac{x}{z + -1}}{t}\right)\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{+23}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{+25}:\\ \;\;\;\;\frac{z \cdot \left(a - t\right) - x \cdot y}{z \cdot \left(y - b\right) - y}\\ \mathbf{elif}\;z \leq 10^{+128}:\\ \;\;\;\;\frac{a - t}{y} - \frac{x + \frac{t - a}{y}}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- a t) (- y b))))
   (if (<= z -2.06e+154)
     t_1
     (if (<= z -1.55e+125)
       (*
        t
        (-
         (/ z (* y (- 1.0 z)))
         (/ (+ (* (/ a y) (/ z (- 1.0 z))) (/ x (+ z -1.0))) t)))
       (if (<= z -2.6e+23)
         t_1
         (if (<= z 4.7e+25)
           (/ (- (* z (- a t)) (* x y)) (- (* z (- y b)) y))
           (if (<= z 1e+128)
             (- (/ (- a t) y) (/ (+ x (/ (- t a) y)) z))
             t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a - t) / (y - b);
	double tmp;
	if (z <= -2.06e+154) {
		tmp = t_1;
	} else if (z <= -1.55e+125) {
		tmp = t * ((z / (y * (1.0 - z))) - ((((a / y) * (z / (1.0 - z))) + (x / (z + -1.0))) / t));
	} else if (z <= -2.6e+23) {
		tmp = t_1;
	} else if (z <= 4.7e+25) {
		tmp = ((z * (a - t)) - (x * y)) / ((z * (y - b)) - y);
	} else if (z <= 1e+128) {
		tmp = ((a - t) / y) - ((x + ((t - a) / y)) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a - t) / (y - b)
    if (z <= (-2.06d+154)) then
        tmp = t_1
    else if (z <= (-1.55d+125)) then
        tmp = t * ((z / (y * (1.0d0 - z))) - ((((a / y) * (z / (1.0d0 - z))) + (x / (z + (-1.0d0)))) / t))
    else if (z <= (-2.6d+23)) then
        tmp = t_1
    else if (z <= 4.7d+25) then
        tmp = ((z * (a - t)) - (x * y)) / ((z * (y - b)) - y)
    else if (z <= 1d+128) then
        tmp = ((a - t) / y) - ((x + ((t - a) / y)) / z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a - t) / (y - b);
	double tmp;
	if (z <= -2.06e+154) {
		tmp = t_1;
	} else if (z <= -1.55e+125) {
		tmp = t * ((z / (y * (1.0 - z))) - ((((a / y) * (z / (1.0 - z))) + (x / (z + -1.0))) / t));
	} else if (z <= -2.6e+23) {
		tmp = t_1;
	} else if (z <= 4.7e+25) {
		tmp = ((z * (a - t)) - (x * y)) / ((z * (y - b)) - y);
	} else if (z <= 1e+128) {
		tmp = ((a - t) / y) - ((x + ((t - a) / y)) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a - t) / (y - b)
	tmp = 0
	if z <= -2.06e+154:
		tmp = t_1
	elif z <= -1.55e+125:
		tmp = t * ((z / (y * (1.0 - z))) - ((((a / y) * (z / (1.0 - z))) + (x / (z + -1.0))) / t))
	elif z <= -2.6e+23:
		tmp = t_1
	elif z <= 4.7e+25:
		tmp = ((z * (a - t)) - (x * y)) / ((z * (y - b)) - y)
	elif z <= 1e+128:
		tmp = ((a - t) / y) - ((x + ((t - a) / y)) / z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a - t) / Float64(y - b))
	tmp = 0.0
	if (z <= -2.06e+154)
		tmp = t_1;
	elseif (z <= -1.55e+125)
		tmp = Float64(t * Float64(Float64(z / Float64(y * Float64(1.0 - z))) - Float64(Float64(Float64(Float64(a / y) * Float64(z / Float64(1.0 - z))) + Float64(x / Float64(z + -1.0))) / t)));
	elseif (z <= -2.6e+23)
		tmp = t_1;
	elseif (z <= 4.7e+25)
		tmp = Float64(Float64(Float64(z * Float64(a - t)) - Float64(x * y)) / Float64(Float64(z * Float64(y - b)) - y));
	elseif (z <= 1e+128)
		tmp = Float64(Float64(Float64(a - t) / y) - Float64(Float64(x + Float64(Float64(t - a) / y)) / z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a - t) / (y - b);
	tmp = 0.0;
	if (z <= -2.06e+154)
		tmp = t_1;
	elseif (z <= -1.55e+125)
		tmp = t * ((z / (y * (1.0 - z))) - ((((a / y) * (z / (1.0 - z))) + (x / (z + -1.0))) / t));
	elseif (z <= -2.6e+23)
		tmp = t_1;
	elseif (z <= 4.7e+25)
		tmp = ((z * (a - t)) - (x * y)) / ((z * (y - b)) - y);
	elseif (z <= 1e+128)
		tmp = ((a - t) / y) - ((x + ((t - a) / y)) / z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a - t), $MachinePrecision] / N[(y - b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.06e+154], t$95$1, If[LessEqual[z, -1.55e+125], N[(t * N[(N[(z / N[(y * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(N[(a / y), $MachinePrecision] * N[(z / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.6e+23], t$95$1, If[LessEqual[z, 4.7e+25], N[(N[(N[(z * N[(a - t), $MachinePrecision]), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision] / N[(N[(z * N[(y - b), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1e+128], N[(N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision] - N[(N[(x + N[(N[(t - a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.05999999999999988e154 or -1.55e125 < z < -2.59999999999999992e23 or 1.0000000000000001e128 < z

   1. Initial program 27.6%

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

   3. Taylor expanded in z around inf 83.1%

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

   if -2.05999999999999988e154 < z < -1.55e125

   1. Initial program 27.3%

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

   3. Taylor expanded in y around inf 27.3%

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

      1. mul-1-neg 27.3%

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

      2. unsub-neg 27.3%

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

   5. Simplified 27.3%

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

   6. Taylor expanded in t around -inf 67.0%

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

      1. mul-1-neg 67.0%

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

      2. distribute-rgt-neg-in 67.0%

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

      3. mul-1-neg 67.0%

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

      4. unsub-neg 67.0%

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

      5. associate-*r/ 67.0%

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

      6. mul-1-neg 67.0%

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

   8. Simplified 92.0%

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

   if -2.59999999999999992e23 < z < 4.6999999999999998e25

   1. Initial program 92.5%

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

   if 4.6999999999999998e25 < z < 1.0000000000000001e128

   1. Initial program 42.1%

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

   3. Taylor expanded in y around inf 37.3%

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

      1. mul-1-neg 37.3%

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

      2. unsub-neg 37.3%

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

   5. Simplified 37.3%

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

   6. Taylor expanded in z around -inf 86.5%

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

      1. mul-1-neg 86.5%

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

      2. unsub-neg 86.5%

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

      3. associate-*r/ 86.5%

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

      4. mul-1-neg 86.5%

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

      5. sub-neg 86.5%

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

      6. mul-1-neg 86.5%

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

      7. remove-double-neg 86.5%

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

   8. Simplified 86.5%

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

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.06 \cdot 10^{+154}:\\ \;\;\;\;\frac{a - t}{y - b}\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{+125}:\\ \;\;\;\;t \cdot \left(\frac{z}{y \cdot \left(1 - z\right)} - \frac{\frac{a}{y} \cdot \frac{z}{1 - z} + \frac{x}{z + -1}}{t}\right)\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{+23}:\\ \;\;\;\;\frac{a - t}{y - b}\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{+25}:\\ \;\;\;\;\frac{z \cdot \left(a - t\right) - x \cdot y}{z \cdot \left(y - b\right) - y}\\ \mathbf{elif}\;z \leq 10^{+128}:\\ \;\;\;\;\frac{a - t}{y} - \frac{x + \frac{t - a}{y}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{a - t}{y - b}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 82.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a - t}{y} - \frac{x + \frac{t - a}{y}}{z}\\ t_2 := \frac{a - t}{y - b}\\ \mathbf{if}\;z \leq -2.05 \cdot 10^{+154}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{+125}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{+23}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+26}:\\ \;\;\;\;\frac{z \cdot \left(a - t\right) - x \cdot y}{z \cdot \left(y - b\right) - y}\\ \mathbf{elif}\;z \leq 10^{+128}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (/ (- a t) y) (/ (+ x (/ (- t a) y)) z)))
        (t_2 (/ (- a t) (- y b))))
   (if (<= z -2.05e+154)
     t_2
     (if (<= z -1.8e+125)
       t_1
       (if (<= z -2.6e+23)
         t_2
         (if (<= z 1.1e+26)
           (/ (- (* z (- a t)) (* x y)) (- (* z (- y b)) y))
           (if (<= z 1e+128) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((a - t) / y) - ((x + ((t - a) / y)) / z);
	double t_2 = (a - t) / (y - b);
	double tmp;
	if (z <= -2.05e+154) {
		tmp = t_2;
	} else if (z <= -1.8e+125) {
		tmp = t_1;
	} else if (z <= -2.6e+23) {
		tmp = t_2;
	} else if (z <= 1.1e+26) {
		tmp = ((z * (a - t)) - (x * y)) / ((z * (y - b)) - y);
	} else if (z <= 1e+128) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((a - t) / y) - ((x + ((t - a) / y)) / z)
    t_2 = (a - t) / (y - b)
    if (z <= (-2.05d+154)) then
        tmp = t_2
    else if (z <= (-1.8d+125)) then
        tmp = t_1
    else if (z <= (-2.6d+23)) then
        tmp = t_2
    else if (z <= 1.1d+26) then
        tmp = ((z * (a - t)) - (x * y)) / ((z * (y - b)) - y)
    else if (z <= 1d+128) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((a - t) / y) - ((x + ((t - a) / y)) / z);
	double t_2 = (a - t) / (y - b);
	double tmp;
	if (z <= -2.05e+154) {
		tmp = t_2;
	} else if (z <= -1.8e+125) {
		tmp = t_1;
	} else if (z <= -2.6e+23) {
		tmp = t_2;
	} else if (z <= 1.1e+26) {
		tmp = ((z * (a - t)) - (x * y)) / ((z * (y - b)) - y);
	} else if (z <= 1e+128) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((a - t) / y) - ((x + ((t - a) / y)) / z)
	t_2 = (a - t) / (y - b)
	tmp = 0
	if z <= -2.05e+154:
		tmp = t_2
	elif z <= -1.8e+125:
		tmp = t_1
	elif z <= -2.6e+23:
		tmp = t_2
	elif z <= 1.1e+26:
		tmp = ((z * (a - t)) - (x * y)) / ((z * (y - b)) - y)
	elif z <= 1e+128:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(a - t) / y) - Float64(Float64(x + Float64(Float64(t - a) / y)) / z))
	t_2 = Float64(Float64(a - t) / Float64(y - b))
	tmp = 0.0
	if (z <= -2.05e+154)
		tmp = t_2;
	elseif (z <= -1.8e+125)
		tmp = t_1;
	elseif (z <= -2.6e+23)
		tmp = t_2;
	elseif (z <= 1.1e+26)
		tmp = Float64(Float64(Float64(z * Float64(a - t)) - Float64(x * y)) / Float64(Float64(z * Float64(y - b)) - y));
	elseif (z <= 1e+128)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((a - t) / y) - ((x + ((t - a) / y)) / z);
	t_2 = (a - t) / (y - b);
	tmp = 0.0;
	if (z <= -2.05e+154)
		tmp = t_2;
	elseif (z <= -1.8e+125)
		tmp = t_1;
	elseif (z <= -2.6e+23)
		tmp = t_2;
	elseif (z <= 1.1e+26)
		tmp = ((z * (a - t)) - (x * y)) / ((z * (y - b)) - y);
	elseif (z <= 1e+128)
		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[(a - t), $MachinePrecision] / y), $MachinePrecision] - N[(N[(x + N[(N[(t - a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a - t), $MachinePrecision] / N[(y - b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.05e+154], t$95$2, If[LessEqual[z, -1.8e+125], t$95$1, If[LessEqual[z, -2.6e+23], t$95$2, If[LessEqual[z, 1.1e+26], N[(N[(N[(z * N[(a - t), $MachinePrecision]), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision] / N[(N[(z * N[(y - b), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1e+128], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.05e154 or -1.8000000000000002e125 < z < -2.59999999999999992e23 or 1.0000000000000001e128 < z

   1. Initial program 27.6%

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

   3. Taylor expanded in z around inf 83.1%

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

   if -2.05e154 < z < -1.8000000000000002e125 or 1.10000000000000004e26 < z < 1.0000000000000001e128

   1. Initial program 38.2%

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

   3. Taylor expanded in y around inf 34.6%

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

      1. mul-1-neg 34.6%

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

      2. unsub-neg 34.6%

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

   5. Simplified 34.6%

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

   6. Taylor expanded in z around -inf 87.9%

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

      1. mul-1-neg 87.9%

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

      2. unsub-neg 87.9%

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

      3. associate-*r/ 87.9%

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

      4. mul-1-neg 87.9%

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

      5. sub-neg 87.9%

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

      6. mul-1-neg 87.9%

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

      7. remove-double-neg 87.9%

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

   8. Simplified 87.9%

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

   if -2.59999999999999992e23 < z < 1.10000000000000004e26

   1. Initial program 92.5%

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

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.05 \cdot 10^{+154}:\\ \;\;\;\;\frac{a - t}{y - b}\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{+125}:\\ \;\;\;\;\frac{a - t}{y} - \frac{x + \frac{t - a}{y}}{z}\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{+23}:\\ \;\;\;\;\frac{a - t}{y - b}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+26}:\\ \;\;\;\;\frac{z \cdot \left(a - t\right) - x \cdot y}{z \cdot \left(y - b\right) - y}\\ \mathbf{elif}\;z \leq 10^{+128}:\\ \;\;\;\;\frac{a - t}{y} - \frac{x + \frac{t - a}{y}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{a - t}{y - b}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 71.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a - t}{y - b}\\ \mathbf{if}\;z \leq -1.45 \cdot 10^{-11}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-67}:\\ \;\;\;\;x - \frac{z \cdot \left(a - t\right)}{y}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-48}:\\ \;\;\;\;\frac{x \cdot \left(\left(\frac{t}{x} + \frac{y}{z}\right) - \frac{a}{x}\right)}{b}\\ \mathbf{elif}\;z \leq 850:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y \cdot \left(1 - z\right)}\\ \mathbf{elif}\;z \leq 3.05 \cdot 10^{+71} \lor \neg \left(z \leq 10^{+128}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- a t) (- y b))))
   (if (<= z -1.45e-11)
     t_1
     (if (<= z 2e-67)
       (- x (/ (* z (- a t)) y))
       (if (<= z 3.5e-48)
         (/ (* x (- (+ (/ t x) (/ y z)) (/ a x))) b)
         (if (<= z 850.0)
           (/ (+ (* x y) (* z (- t a))) (* y (- 1.0 z)))
           (if (or (<= z 3.05e+71) (not (<= z 1e+128)))
             t_1
             (/ x (- 1.0 z)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a - t) / (y - b);
	double tmp;
	if (z <= -1.45e-11) {
		tmp = t_1;
	} else if (z <= 2e-67) {
		tmp = x - ((z * (a - t)) / y);
	} else if (z <= 3.5e-48) {
		tmp = (x * (((t / x) + (y / z)) - (a / x))) / b;
	} else if (z <= 850.0) {
		tmp = ((x * y) + (z * (t - a))) / (y * (1.0 - z));
	} else if ((z <= 3.05e+71) || !(z <= 1e+128)) {
		tmp = t_1;
	} else {
		tmp = x / (1.0 - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a - t) / (y - b)
    if (z <= (-1.45d-11)) then
        tmp = t_1
    else if (z <= 2d-67) then
        tmp = x - ((z * (a - t)) / y)
    else if (z <= 3.5d-48) then
        tmp = (x * (((t / x) + (y / z)) - (a / x))) / b
    else if (z <= 850.0d0) then
        tmp = ((x * y) + (z * (t - a))) / (y * (1.0d0 - z))
    else if ((z <= 3.05d+71) .or. (.not. (z <= 1d+128))) then
        tmp = t_1
    else
        tmp = x / (1.0d0 - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a - t) / (y - b);
	double tmp;
	if (z <= -1.45e-11) {
		tmp = t_1;
	} else if (z <= 2e-67) {
		tmp = x - ((z * (a - t)) / y);
	} else if (z <= 3.5e-48) {
		tmp = (x * (((t / x) + (y / z)) - (a / x))) / b;
	} else if (z <= 850.0) {
		tmp = ((x * y) + (z * (t - a))) / (y * (1.0 - z));
	} else if ((z <= 3.05e+71) || !(z <= 1e+128)) {
		tmp = t_1;
	} else {
		tmp = x / (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a - t) / (y - b)
	tmp = 0
	if z <= -1.45e-11:
		tmp = t_1
	elif z <= 2e-67:
		tmp = x - ((z * (a - t)) / y)
	elif z <= 3.5e-48:
		tmp = (x * (((t / x) + (y / z)) - (a / x))) / b
	elif z <= 850.0:
		tmp = ((x * y) + (z * (t - a))) / (y * (1.0 - z))
	elif (z <= 3.05e+71) or not (z <= 1e+128):
		tmp = t_1
	else:
		tmp = x / (1.0 - z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a - t) / Float64(y - b))
	tmp = 0.0
	if (z <= -1.45e-11)
		tmp = t_1;
	elseif (z <= 2e-67)
		tmp = Float64(x - Float64(Float64(z * Float64(a - t)) / y));
	elseif (z <= 3.5e-48)
		tmp = Float64(Float64(x * Float64(Float64(Float64(t / x) + Float64(y / z)) - Float64(a / x))) / b);
	elseif (z <= 850.0)
		tmp = Float64(Float64(Float64(x * y) + Float64(z * Float64(t - a))) / Float64(y * Float64(1.0 - z)));
	elseif ((z <= 3.05e+71) || !(z <= 1e+128))
		tmp = t_1;
	else
		tmp = Float64(x / Float64(1.0 - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a - t) / (y - b);
	tmp = 0.0;
	if (z <= -1.45e-11)
		tmp = t_1;
	elseif (z <= 2e-67)
		tmp = x - ((z * (a - t)) / y);
	elseif (z <= 3.5e-48)
		tmp = (x * (((t / x) + (y / z)) - (a / x))) / b;
	elseif (z <= 850.0)
		tmp = ((x * y) + (z * (t - a))) / (y * (1.0 - z));
	elseif ((z <= 3.05e+71) || ~((z <= 1e+128)))
		tmp = t_1;
	else
		tmp = x / (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a - t), $MachinePrecision] / N[(y - b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.45e-11], t$95$1, If[LessEqual[z, 2e-67], N[(x - N[(N[(z * N[(a - t), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.5e-48], N[(N[(x * N[(N[(N[(t / x), $MachinePrecision] + N[(y / z), $MachinePrecision]), $MachinePrecision] - N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[z, 850.0], N[(N[(N[(x * y), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 3.05e+71], N[Not[LessEqual[z, 1e+128]], $MachinePrecision]], t$95$1, N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.45e-11 or 850 < z < 3.0500000000000002e71 or 1.0000000000000001e128 < z

   1. Initial program 34.0%

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

   3. Taylor expanded in z around inf 76.2%

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

   if -1.45e-11 < z < 1.99999999999999989e-67

   1. Initial program 91.6%

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

   3. Taylor expanded in z around 0 67.2%

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

   4. Taylor expanded in x around 0 75.1%

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

   if 1.99999999999999989e-67 < z < 3.49999999999999991e-48

   1. Initial program 99.0%

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

   3. Taylor expanded in x around inf 83.0%

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

   4. Taylor expanded in b around inf 99.7%

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

   if 3.49999999999999991e-48 < z < 850

   1. Initial program 99.4%

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

   3. Taylor expanded in y around inf 69.8%

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

      1. mul-1-neg 69.8%

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

      2. unsub-neg 69.8%

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

   5. Simplified 69.8%

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

   if 3.0500000000000002e71 < z < 1.0000000000000001e128

   1. Initial program 40.8%

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

   3. Taylor expanded in y around inf 74.0%

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

      1. mul-1-neg 74.0%

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

      2. unsub-neg 74.0%

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

   5. Simplified 74.0%

      \[\leadsto \color{blue}{\frac{x}{1 - z}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{-11}:\\ \;\;\;\;\frac{a - t}{y - b}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-67}:\\ \;\;\;\;x - \frac{z \cdot \left(a - t\right)}{y}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-48}:\\ \;\;\;\;\frac{x \cdot \left(\left(\frac{t}{x} + \frac{y}{z}\right) - \frac{a}{x}\right)}{b}\\ \mathbf{elif}\;z \leq 850:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y \cdot \left(1 - z\right)}\\ \mathbf{elif}\;z \leq 3.05 \cdot 10^{+71} \lor \neg \left(z \leq 10^{+128}\right):\\ \;\;\;\;\frac{a - t}{y - b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 71.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a - t}{y - b}\\ \mathbf{if}\;z \leq -2.5 \cdot 10^{-10}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-66}:\\ \;\;\;\;x - \frac{z \cdot \left(a - t\right)}{y}\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{-48}:\\ \;\;\;\;\frac{x \cdot \left(\left(\frac{t}{x} + \frac{y}{z}\right) - \frac{a}{x}\right)}{b}\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{-8}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;z \leq 3.05 \cdot 10^{+71} \lor \neg \left(z \leq 10^{+128}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- a t) (- y b))))
   (if (<= z -2.5e-10)
     t_1
     (if (<= z 3.2e-66)
       (- x (/ (* z (- a t)) y))
       (if (<= z 5.3e-48)
         (/ (* x (- (+ (/ t x) (/ y z)) (/ a x))) b)
         (if (<= z 2.45e-8)
           (/ (+ (* x y) (* z (- t a))) y)
           (if (or (<= z 3.05e+71) (not (<= z 1e+128)))
             t_1
             (/ x (- 1.0 z)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a - t) / (y - b);
	double tmp;
	if (z <= -2.5e-10) {
		tmp = t_1;
	} else if (z <= 3.2e-66) {
		tmp = x - ((z * (a - t)) / y);
	} else if (z <= 5.3e-48) {
		tmp = (x * (((t / x) + (y / z)) - (a / x))) / b;
	} else if (z <= 2.45e-8) {
		tmp = ((x * y) + (z * (t - a))) / y;
	} else if ((z <= 3.05e+71) || !(z <= 1e+128)) {
		tmp = t_1;
	} else {
		tmp = x / (1.0 - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a - t) / (y - b)
    if (z <= (-2.5d-10)) then
        tmp = t_1
    else if (z <= 3.2d-66) then
        tmp = x - ((z * (a - t)) / y)
    else if (z <= 5.3d-48) then
        tmp = (x * (((t / x) + (y / z)) - (a / x))) / b
    else if (z <= 2.45d-8) then
        tmp = ((x * y) + (z * (t - a))) / y
    else if ((z <= 3.05d+71) .or. (.not. (z <= 1d+128))) then
        tmp = t_1
    else
        tmp = x / (1.0d0 - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a - t) / (y - b);
	double tmp;
	if (z <= -2.5e-10) {
		tmp = t_1;
	} else if (z <= 3.2e-66) {
		tmp = x - ((z * (a - t)) / y);
	} else if (z <= 5.3e-48) {
		tmp = (x * (((t / x) + (y / z)) - (a / x))) / b;
	} else if (z <= 2.45e-8) {
		tmp = ((x * y) + (z * (t - a))) / y;
	} else if ((z <= 3.05e+71) || !(z <= 1e+128)) {
		tmp = t_1;
	} else {
		tmp = x / (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a - t) / (y - b)
	tmp = 0
	if z <= -2.5e-10:
		tmp = t_1
	elif z <= 3.2e-66:
		tmp = x - ((z * (a - t)) / y)
	elif z <= 5.3e-48:
		tmp = (x * (((t / x) + (y / z)) - (a / x))) / b
	elif z <= 2.45e-8:
		tmp = ((x * y) + (z * (t - a))) / y
	elif (z <= 3.05e+71) or not (z <= 1e+128):
		tmp = t_1
	else:
		tmp = x / (1.0 - z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a - t) / Float64(y - b))
	tmp = 0.0
	if (z <= -2.5e-10)
		tmp = t_1;
	elseif (z <= 3.2e-66)
		tmp = Float64(x - Float64(Float64(z * Float64(a - t)) / y));
	elseif (z <= 5.3e-48)
		tmp = Float64(Float64(x * Float64(Float64(Float64(t / x) + Float64(y / z)) - Float64(a / x))) / b);
	elseif (z <= 2.45e-8)
		tmp = Float64(Float64(Float64(x * y) + Float64(z * Float64(t - a))) / y);
	elseif ((z <= 3.05e+71) || !(z <= 1e+128))
		tmp = t_1;
	else
		tmp = Float64(x / Float64(1.0 - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a - t) / (y - b);
	tmp = 0.0;
	if (z <= -2.5e-10)
		tmp = t_1;
	elseif (z <= 3.2e-66)
		tmp = x - ((z * (a - t)) / y);
	elseif (z <= 5.3e-48)
		tmp = (x * (((t / x) + (y / z)) - (a / x))) / b;
	elseif (z <= 2.45e-8)
		tmp = ((x * y) + (z * (t - a))) / y;
	elseif ((z <= 3.05e+71) || ~((z <= 1e+128)))
		tmp = t_1;
	else
		tmp = x / (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a - t), $MachinePrecision] / N[(y - b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.5e-10], t$95$1, If[LessEqual[z, 3.2e-66], N[(x - N[(N[(z * N[(a - t), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.3e-48], N[(N[(x * N[(N[(N[(t / x), $MachinePrecision] + N[(y / z), $MachinePrecision]), $MachinePrecision] - N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[z, 2.45e-8], N[(N[(N[(x * y), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[Or[LessEqual[z, 3.05e+71], N[Not[LessEqual[z, 1e+128]], $MachinePrecision]], t$95$1, N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.50000000000000016e-10 or 2.4500000000000001e-8 < z < 3.0500000000000002e71 or 1.0000000000000001e128 < z

   1. Initial program 35.2%

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

   3. Taylor expanded in z around inf 75.7%

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

   if -2.50000000000000016e-10 < z < 3.19999999999999982e-66

   1. Initial program 91.6%

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

   3. Taylor expanded in z around 0 67.2%

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

   4. Taylor expanded in x around 0 75.1%

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

   if 3.19999999999999982e-66 < z < 5.3e-48

   1. Initial program 99.0%

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

   3. Taylor expanded in x around inf 83.0%

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

   4. Taylor expanded in b around inf 99.7%

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

   if 5.3e-48 < z < 2.4500000000000001e-8

   1. Initial program 99.5%

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

   3. Taylor expanded in z around 0 68.7%

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

   if 3.0500000000000002e71 < z < 1.0000000000000001e128

   1. Initial program 40.8%

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

   3. Taylor expanded in y around inf 74.0%

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

      1. mul-1-neg 74.0%

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

      2. unsub-neg 74.0%

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

   5. Simplified 74.0%

      \[\leadsto \color{blue}{\frac{x}{1 - z}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 75.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{-10}:\\ \;\;\;\;\frac{a - t}{y - b}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-66}:\\ \;\;\;\;x - \frac{z \cdot \left(a - t\right)}{y}\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{-48}:\\ \;\;\;\;\frac{x \cdot \left(\left(\frac{t}{x} + \frac{y}{z}\right) - \frac{a}{x}\right)}{b}\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{-8}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;z \leq 3.05 \cdot 10^{+71} \lor \neg \left(z \leq 10^{+128}\right):\\ \;\;\;\;\frac{a - t}{y - b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 71.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a - t}{y - b}\\ \mathbf{if}\;z \leq -5.8 \cdot 10^{-12}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-65}:\\ \;\;\;\;x - \frac{z \cdot \left(a - t\right)}{y}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-48}:\\ \;\;\;\;x \cdot \frac{\frac{t}{x} + \left(\frac{y}{z} - \frac{a}{x}\right)}{b}\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-8}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;z \leq 3.05 \cdot 10^{+71} \lor \neg \left(z \leq 10^{+128}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- a t) (- y b))))
   (if (<= z -5.8e-12)
     t_1
     (if (<= z 2.1e-65)
       (- x (/ (* z (- a t)) y))
       (if (<= z 1.9e-48)
         (* x (/ (+ (/ t x) (- (/ y z) (/ a x))) b))
         (if (<= z 1.05e-8)
           (/ (+ (* x y) (* z (- t a))) y)
           (if (or (<= z 3.05e+71) (not (<= z 1e+128)))
             t_1
             (/ x (- 1.0 z)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a - t) / (y - b);
	double tmp;
	if (z <= -5.8e-12) {
		tmp = t_1;
	} else if (z <= 2.1e-65) {
		tmp = x - ((z * (a - t)) / y);
	} else if (z <= 1.9e-48) {
		tmp = x * (((t / x) + ((y / z) - (a / x))) / b);
	} else if (z <= 1.05e-8) {
		tmp = ((x * y) + (z * (t - a))) / y;
	} else if ((z <= 3.05e+71) || !(z <= 1e+128)) {
		tmp = t_1;
	} else {
		tmp = x / (1.0 - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a - t) / (y - b)
    if (z <= (-5.8d-12)) then
        tmp = t_1
    else if (z <= 2.1d-65) then
        tmp = x - ((z * (a - t)) / y)
    else if (z <= 1.9d-48) then
        tmp = x * (((t / x) + ((y / z) - (a / x))) / b)
    else if (z <= 1.05d-8) then
        tmp = ((x * y) + (z * (t - a))) / y
    else if ((z <= 3.05d+71) .or. (.not. (z <= 1d+128))) then
        tmp = t_1
    else
        tmp = x / (1.0d0 - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a - t) / (y - b);
	double tmp;
	if (z <= -5.8e-12) {
		tmp = t_1;
	} else if (z <= 2.1e-65) {
		tmp = x - ((z * (a - t)) / y);
	} else if (z <= 1.9e-48) {
		tmp = x * (((t / x) + ((y / z) - (a / x))) / b);
	} else if (z <= 1.05e-8) {
		tmp = ((x * y) + (z * (t - a))) / y;
	} else if ((z <= 3.05e+71) || !(z <= 1e+128)) {
		tmp = t_1;
	} else {
		tmp = x / (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a - t) / (y - b)
	tmp = 0
	if z <= -5.8e-12:
		tmp = t_1
	elif z <= 2.1e-65:
		tmp = x - ((z * (a - t)) / y)
	elif z <= 1.9e-48:
		tmp = x * (((t / x) + ((y / z) - (a / x))) / b)
	elif z <= 1.05e-8:
		tmp = ((x * y) + (z * (t - a))) / y
	elif (z <= 3.05e+71) or not (z <= 1e+128):
		tmp = t_1
	else:
		tmp = x / (1.0 - z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a - t) / Float64(y - b))
	tmp = 0.0
	if (z <= -5.8e-12)
		tmp = t_1;
	elseif (z <= 2.1e-65)
		tmp = Float64(x - Float64(Float64(z * Float64(a - t)) / y));
	elseif (z <= 1.9e-48)
		tmp = Float64(x * Float64(Float64(Float64(t / x) + Float64(Float64(y / z) - Float64(a / x))) / b));
	elseif (z <= 1.05e-8)
		tmp = Float64(Float64(Float64(x * y) + Float64(z * Float64(t - a))) / y);
	elseif ((z <= 3.05e+71) || !(z <= 1e+128))
		tmp = t_1;
	else
		tmp = Float64(x / Float64(1.0 - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a - t) / (y - b);
	tmp = 0.0;
	if (z <= -5.8e-12)
		tmp = t_1;
	elseif (z <= 2.1e-65)
		tmp = x - ((z * (a - t)) / y);
	elseif (z <= 1.9e-48)
		tmp = x * (((t / x) + ((y / z) - (a / x))) / b);
	elseif (z <= 1.05e-8)
		tmp = ((x * y) + (z * (t - a))) / y;
	elseif ((z <= 3.05e+71) || ~((z <= 1e+128)))
		tmp = t_1;
	else
		tmp = x / (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a - t), $MachinePrecision] / N[(y - b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.8e-12], t$95$1, If[LessEqual[z, 2.1e-65], N[(x - N[(N[(z * N[(a - t), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.9e-48], N[(x * N[(N[(N[(t / x), $MachinePrecision] + N[(N[(y / z), $MachinePrecision] - N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.05e-8], N[(N[(N[(x * y), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[Or[LessEqual[z, 3.05e+71], N[Not[LessEqual[z, 1e+128]], $MachinePrecision]], t$95$1, N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -5.8000000000000003e-12 or 1.04999999999999997e-8 < z < 3.0500000000000002e71 or 1.0000000000000001e128 < z

   1. Initial program 35.2%

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

   3. Taylor expanded in z around inf 75.7%

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

   if -5.8000000000000003e-12 < z < 2.10000000000000003e-65

   1. Initial program 91.6%

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

   3. Taylor expanded in z around 0 67.2%

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

   4. Taylor expanded in x around 0 75.1%

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

   if 2.10000000000000003e-65 < z < 1.90000000000000001e-48

   1. Initial program 99.0%

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

   3. Taylor expanded in x around inf 83.0%

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

   4. Taylor expanded in b around inf 99.7%

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

      1. associate-/l* 99.2%

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

      2. associate--l+ 99.2%

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

   6. Simplified 99.2%

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

   if 1.90000000000000001e-48 < z < 1.04999999999999997e-8

   1. Initial program 99.5%

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

   3. Taylor expanded in z around 0 68.7%

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

   if 3.0500000000000002e71 < z < 1.0000000000000001e128

   1. Initial program 40.8%

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

   3. Taylor expanded in y around inf 74.0%

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

      1. mul-1-neg 74.0%

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

      2. unsub-neg 74.0%

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

   5. Simplified 74.0%

      \[\leadsto \color{blue}{\frac{x}{1 - z}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 75.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{-12}:\\ \;\;\;\;\frac{a - t}{y - b}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-65}:\\ \;\;\;\;x - \frac{z \cdot \left(a - t\right)}{y}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-48}:\\ \;\;\;\;x \cdot \frac{\frac{t}{x} + \left(\frac{y}{z} - \frac{a}{x}\right)}{b}\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-8}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;z \leq 3.05 \cdot 10^{+71} \lor \neg \left(z \leq 10^{+128}\right):\\ \;\;\;\;\frac{a - t}{y - b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 71.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a - t}{y - b}\\ t_2 := x \cdot y + z \cdot \left(t - a\right)\\ \mathbf{if}\;z \leq -8 \cdot 10^{-10}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{-65}:\\ \;\;\;\;x - \frac{z \cdot \left(a - t\right)}{y}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-48}:\\ \;\;\;\;\frac{t\_2}{z \cdot b}\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{-8}:\\ \;\;\;\;\frac{t\_2}{y}\\ \mathbf{elif}\;z \leq 3.05 \cdot 10^{+71} \lor \neg \left(z \leq 10^{+128}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- a t) (- y b))) (t_2 (+ (* x y) (* z (- t a)))))
   (if (<= z -8e-10)
     t_1
     (if (<= z 2.25e-65)
       (- x (/ (* z (- a t)) y))
       (if (<= z 2e-48)
         (/ t_2 (* z b))
         (if (<= z 5.1e-8)
           (/ t_2 y)
           (if (or (<= z 3.05e+71) (not (<= z 1e+128)))
             t_1
             (/ x (- 1.0 z)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a - t) / (y - b);
	double t_2 = (x * y) + (z * (t - a));
	double tmp;
	if (z <= -8e-10) {
		tmp = t_1;
	} else if (z <= 2.25e-65) {
		tmp = x - ((z * (a - t)) / y);
	} else if (z <= 2e-48) {
		tmp = t_2 / (z * b);
	} else if (z <= 5.1e-8) {
		tmp = t_2 / y;
	} else if ((z <= 3.05e+71) || !(z <= 1e+128)) {
		tmp = t_1;
	} else {
		tmp = x / (1.0 - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (a - t) / (y - b)
    t_2 = (x * y) + (z * (t - a))
    if (z <= (-8d-10)) then
        tmp = t_1
    else if (z <= 2.25d-65) then
        tmp = x - ((z * (a - t)) / y)
    else if (z <= 2d-48) then
        tmp = t_2 / (z * b)
    else if (z <= 5.1d-8) then
        tmp = t_2 / y
    else if ((z <= 3.05d+71) .or. (.not. (z <= 1d+128))) then
        tmp = t_1
    else
        tmp = x / (1.0d0 - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a - t) / (y - b);
	double t_2 = (x * y) + (z * (t - a));
	double tmp;
	if (z <= -8e-10) {
		tmp = t_1;
	} else if (z <= 2.25e-65) {
		tmp = x - ((z * (a - t)) / y);
	} else if (z <= 2e-48) {
		tmp = t_2 / (z * b);
	} else if (z <= 5.1e-8) {
		tmp = t_2 / y;
	} else if ((z <= 3.05e+71) || !(z <= 1e+128)) {
		tmp = t_1;
	} else {
		tmp = x / (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a - t) / (y - b)
	t_2 = (x * y) + (z * (t - a))
	tmp = 0
	if z <= -8e-10:
		tmp = t_1
	elif z <= 2.25e-65:
		tmp = x - ((z * (a - t)) / y)
	elif z <= 2e-48:
		tmp = t_2 / (z * b)
	elif z <= 5.1e-8:
		tmp = t_2 / y
	elif (z <= 3.05e+71) or not (z <= 1e+128):
		tmp = t_1
	else:
		tmp = x / (1.0 - z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a - t) / Float64(y - b))
	t_2 = Float64(Float64(x * y) + Float64(z * Float64(t - a)))
	tmp = 0.0
	if (z <= -8e-10)
		tmp = t_1;
	elseif (z <= 2.25e-65)
		tmp = Float64(x - Float64(Float64(z * Float64(a - t)) / y));
	elseif (z <= 2e-48)
		tmp = Float64(t_2 / Float64(z * b));
	elseif (z <= 5.1e-8)
		tmp = Float64(t_2 / y);
	elseif ((z <= 3.05e+71) || !(z <= 1e+128))
		tmp = t_1;
	else
		tmp = Float64(x / Float64(1.0 - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a - t) / (y - b);
	t_2 = (x * y) + (z * (t - a));
	tmp = 0.0;
	if (z <= -8e-10)
		tmp = t_1;
	elseif (z <= 2.25e-65)
		tmp = x - ((z * (a - t)) / y);
	elseif (z <= 2e-48)
		tmp = t_2 / (z * b);
	elseif (z <= 5.1e-8)
		tmp = t_2 / y;
	elseif ((z <= 3.05e+71) || ~((z <= 1e+128)))
		tmp = t_1;
	else
		tmp = x / (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a - t), $MachinePrecision] / N[(y - b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8e-10], t$95$1, If[LessEqual[z, 2.25e-65], N[(x - N[(N[(z * N[(a - t), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2e-48], N[(t$95$2 / N[(z * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.1e-8], N[(t$95$2 / y), $MachinePrecision], If[Or[LessEqual[z, 3.05e+71], N[Not[LessEqual[z, 1e+128]], $MachinePrecision]], t$95$1, N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -8.00000000000000029e-10 or 5.10000000000000001e-8 < z < 3.0500000000000002e71 or 1.0000000000000001e128 < z

   1. Initial program 35.2%

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

   3. Taylor expanded in z around inf 75.7%

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

   if -8.00000000000000029e-10 < z < 2.2499999999999999e-65

   1. Initial program 91.6%

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

   3. Taylor expanded in z around 0 67.2%

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

   4. Taylor expanded in x around 0 75.1%

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

   if 2.2499999999999999e-65 < z < 1.9999999999999999e-48

   1. Initial program 99.0%

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

   3. Taylor expanded in y around 0 99.0%

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

      1. *-commutative 99.0%

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

   5. Simplified 99.0%

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

   if 1.9999999999999999e-48 < z < 5.10000000000000001e-8

   1. Initial program 99.5%

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

   3. Taylor expanded in z around 0 68.7%

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

   if 3.0500000000000002e71 < z < 1.0000000000000001e128

   1. Initial program 40.8%

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

   3. Taylor expanded in y around inf 74.0%

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

      1. mul-1-neg 74.0%

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

      2. unsub-neg 74.0%

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

   5. Simplified 74.0%

      \[\leadsto \color{blue}{\frac{x}{1 - z}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 75.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{-10}:\\ \;\;\;\;\frac{a - t}{y - b}\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{-65}:\\ \;\;\;\;x - \frac{z \cdot \left(a - t\right)}{y}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-48}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{z \cdot b}\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{-8}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;z \leq 3.05 \cdot 10^{+71} \lor \neg \left(z \leq 10^{+128}\right):\\ \;\;\;\;\frac{a - t}{y - b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 72.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a - t}{y - b}\\ t_2 := y + z \cdot \left(b - y\right)\\ \mathbf{if}\;z \leq -5.6 \cdot 10^{-10}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 6.7 \cdot 10^{-167}:\\ \;\;\;\;x - \frac{z \cdot \left(a - t\right)}{y}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-39}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{t\_2}\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-5}:\\ \;\;\;\;\frac{x \cdot y}{t\_2}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- a t) (- y b))) (t_2 (+ y (* z (- b y)))))
   (if (<= z -5.6e-10)
     t_1
     (if (<= z 6.7e-167)
       (- x (/ (* z (- a t)) y))
       (if (<= z 2.2e-39)
         (/ (* z (- t a)) t_2)
         (if (<= z 1.95e-5) (/ (* x y) t_2) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a - t) / (y - b);
	double t_2 = y + (z * (b - y));
	double tmp;
	if (z <= -5.6e-10) {
		tmp = t_1;
	} else if (z <= 6.7e-167) {
		tmp = x - ((z * (a - t)) / y);
	} else if (z <= 2.2e-39) {
		tmp = (z * (t - a)) / t_2;
	} else if (z <= 1.95e-5) {
		tmp = (x * y) / 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) :: tmp
    t_1 = (a - t) / (y - b)
    t_2 = y + (z * (b - y))
    if (z <= (-5.6d-10)) then
        tmp = t_1
    else if (z <= 6.7d-167) then
        tmp = x - ((z * (a - t)) / y)
    else if (z <= 2.2d-39) then
        tmp = (z * (t - a)) / t_2
    else if (z <= 1.95d-5) then
        tmp = (x * y) / 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 - t) / (y - b);
	double t_2 = y + (z * (b - y));
	double tmp;
	if (z <= -5.6e-10) {
		tmp = t_1;
	} else if (z <= 6.7e-167) {
		tmp = x - ((z * (a - t)) / y);
	} else if (z <= 2.2e-39) {
		tmp = (z * (t - a)) / t_2;
	} else if (z <= 1.95e-5) {
		tmp = (x * y) / t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a - t) / (y - b)
	t_2 = y + (z * (b - y))
	tmp = 0
	if z <= -5.6e-10:
		tmp = t_1
	elif z <= 6.7e-167:
		tmp = x - ((z * (a - t)) / y)
	elif z <= 2.2e-39:
		tmp = (z * (t - a)) / t_2
	elif z <= 1.95e-5:
		tmp = (x * y) / t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a - t) / Float64(y - b))
	t_2 = Float64(y + Float64(z * Float64(b - y)))
	tmp = 0.0
	if (z <= -5.6e-10)
		tmp = t_1;
	elseif (z <= 6.7e-167)
		tmp = Float64(x - Float64(Float64(z * Float64(a - t)) / y));
	elseif (z <= 2.2e-39)
		tmp = Float64(Float64(z * Float64(t - a)) / t_2);
	elseif (z <= 1.95e-5)
		tmp = Float64(Float64(x * y) / t_2);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a - t) / (y - b);
	t_2 = y + (z * (b - y));
	tmp = 0.0;
	if (z <= -5.6e-10)
		tmp = t_1;
	elseif (z <= 6.7e-167)
		tmp = x - ((z * (a - t)) / y);
	elseif (z <= 2.2e-39)
		tmp = (z * (t - a)) / t_2;
	elseif (z <= 1.95e-5)
		tmp = (x * y) / 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 - t), $MachinePrecision] / N[(y - b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.6e-10], t$95$1, If[LessEqual[z, 6.7e-167], N[(x - N[(N[(z * N[(a - t), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.2e-39], N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision], If[LessEqual[z, 1.95e-5], N[(N[(x * y), $MachinePrecision] / t$95$2), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.60000000000000031e-10 or 1.95e-5 < z

   1. Initial program 35.9%

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

   3. Taylor expanded in z around inf 70.7%

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

   if -5.60000000000000031e-10 < z < 6.70000000000000007e-167

   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 z around 0 68.0%

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

   4. Taylor expanded in x around 0 77.5%

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

   if 6.70000000000000007e-167 < z < 2.20000000000000001e-39

   1. Initial program 99.4%

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

   3. Taylor expanded in x around 0 69.2%

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

   if 2.20000000000000001e-39 < z < 1.95e-5

   1. Initial program 99.4%

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

   3. Taylor expanded in x around inf 71.7%

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

      1. *-commutative 71.7%

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

   5. Simplified 71.7%

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

4. Final simplification 73.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{-10}:\\ \;\;\;\;\frac{a - t}{y - b}\\ \mathbf{elif}\;z \leq 6.7 \cdot 10^{-167}:\\ \;\;\;\;x - \frac{z \cdot \left(a - t\right)}{y}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-39}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-5}:\\ \;\;\;\;\frac{x \cdot y}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{a - t}{y - b}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 73.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a - t}{y - b}\\ \mathbf{if}\;z \leq -2.25 \cdot 10^{-10}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-65}:\\ \;\;\;\;x - \frac{z \cdot \left(a - t\right)}{y}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-50}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-5}:\\ \;\;\;\;\frac{x \cdot y}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- a t) (- y b))))
   (if (<= z -2.25e-10)
     t_1
     (if (<= z 2.4e-65)
       (- x (/ (* z (- a t)) y))
       (if (<= z 5e-50)
         (/ (- t a) b)
         (if (<= z 9.2e-5) (/ (* x y) (+ y (* z (- b y)))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a - t) / (y - b);
	double tmp;
	if (z <= -2.25e-10) {
		tmp = t_1;
	} else if (z <= 2.4e-65) {
		tmp = x - ((z * (a - t)) / y);
	} else if (z <= 5e-50) {
		tmp = (t - a) / b;
	} else if (z <= 9.2e-5) {
		tmp = (x * y) / (y + (z * (b - y)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a - t) / (y - b)
    if (z <= (-2.25d-10)) then
        tmp = t_1
    else if (z <= 2.4d-65) then
        tmp = x - ((z * (a - t)) / y)
    else if (z <= 5d-50) then
        tmp = (t - a) / b
    else if (z <= 9.2d-5) then
        tmp = (x * y) / (y + (z * (b - y)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a - t) / (y - b);
	double tmp;
	if (z <= -2.25e-10) {
		tmp = t_1;
	} else if (z <= 2.4e-65) {
		tmp = x - ((z * (a - t)) / y);
	} else if (z <= 5e-50) {
		tmp = (t - a) / b;
	} else if (z <= 9.2e-5) {
		tmp = (x * y) / (y + (z * (b - y)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a - t) / (y - b)
	tmp = 0
	if z <= -2.25e-10:
		tmp = t_1
	elif z <= 2.4e-65:
		tmp = x - ((z * (a - t)) / y)
	elif z <= 5e-50:
		tmp = (t - a) / b
	elif z <= 9.2e-5:
		tmp = (x * y) / (y + (z * (b - y)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a - t) / Float64(y - b))
	tmp = 0.0
	if (z <= -2.25e-10)
		tmp = t_1;
	elseif (z <= 2.4e-65)
		tmp = Float64(x - Float64(Float64(z * Float64(a - t)) / y));
	elseif (z <= 5e-50)
		tmp = Float64(Float64(t - a) / b);
	elseif (z <= 9.2e-5)
		tmp = Float64(Float64(x * y) / Float64(y + Float64(z * Float64(b - y))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a - t) / (y - b);
	tmp = 0.0;
	if (z <= -2.25e-10)
		tmp = t_1;
	elseif (z <= 2.4e-65)
		tmp = x - ((z * (a - t)) / y);
	elseif (z <= 5e-50)
		tmp = (t - a) / b;
	elseif (z <= 9.2e-5)
		tmp = (x * y) / (y + (z * (b - y)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a - t), $MachinePrecision] / N[(y - b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.25e-10], t$95$1, If[LessEqual[z, 2.4e-65], N[(x - N[(N[(z * N[(a - t), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5e-50], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[z, 9.2e-5], N[(N[(x * y), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.25e-10 or 9.20000000000000001e-5 < z

   1. Initial program 35.9%

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

   3. Taylor expanded in z around inf 70.7%

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

   if -2.25e-10 < z < 2.4000000000000002e-65

   1. Initial program 91.6%

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

   3. Taylor expanded in z around 0 67.2%

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

   4. Taylor expanded in x around 0 75.1%

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

   if 2.4000000000000002e-65 < z < 4.99999999999999968e-50

   1. Initial program 98.8%

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

   3. Taylor expanded in y around 0 93.9%

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

   if 4.99999999999999968e-50 < z < 9.20000000000000001e-5

   1. Initial program 99.5%

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

   3. Taylor expanded in x around inf 68.5%

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

      1. *-commutative 68.5%

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

   5. Simplified 68.5%

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

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.25 \cdot 10^{-10}:\\ \;\;\;\;\frac{a - t}{y - b}\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-65}:\\ \;\;\;\;x - \frac{z \cdot \left(a - t\right)}{y}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-50}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-5}:\\ \;\;\;\;\frac{x \cdot y}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{a - t}{y - b}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 74.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{z \cdot \left(a - t\right)}{y}\\ t_2 := \frac{a - t}{y - b}\\ \mathbf{if}\;z \leq -9.2 \cdot 10^{-10}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-65}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-48}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{-8}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- x (/ (* z (- a t)) y))) (t_2 (/ (- a t) (- y b))))
   (if (<= z -9.2e-10)
     t_2
     (if (<= z 2.4e-65)
       t_1
       (if (<= z 1.85e-48) (/ (- t a) b) (if (<= z 4.9e-8) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - ((z * (a - t)) / y);
	double t_2 = (a - t) / (y - b);
	double tmp;
	if (z <= -9.2e-10) {
		tmp = t_2;
	} else if (z <= 2.4e-65) {
		tmp = t_1;
	} else if (z <= 1.85e-48) {
		tmp = (t - a) / b;
	} else if (z <= 4.9e-8) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x - ((z * (a - t)) / y)
    t_2 = (a - t) / (y - b)
    if (z <= (-9.2d-10)) then
        tmp = t_2
    else if (z <= 2.4d-65) then
        tmp = t_1
    else if (z <= 1.85d-48) then
        tmp = (t - a) / b
    else if (z <= 4.9d-8) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - ((z * (a - t)) / y);
	double t_2 = (a - t) / (y - b);
	double tmp;
	if (z <= -9.2e-10) {
		tmp = t_2;
	} else if (z <= 2.4e-65) {
		tmp = t_1;
	} else if (z <= 1.85e-48) {
		tmp = (t - a) / b;
	} else if (z <= 4.9e-8) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x - ((z * (a - t)) / y)
	t_2 = (a - t) / (y - b)
	tmp = 0
	if z <= -9.2e-10:
		tmp = t_2
	elif z <= 2.4e-65:
		tmp = t_1
	elif z <= 1.85e-48:
		tmp = (t - a) / b
	elif z <= 4.9e-8:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x - Float64(Float64(z * Float64(a - t)) / y))
	t_2 = Float64(Float64(a - t) / Float64(y - b))
	tmp = 0.0
	if (z <= -9.2e-10)
		tmp = t_2;
	elseif (z <= 2.4e-65)
		tmp = t_1;
	elseif (z <= 1.85e-48)
		tmp = Float64(Float64(t - a) / b);
	elseif (z <= 4.9e-8)
		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 - ((z * (a - t)) / y);
	t_2 = (a - t) / (y - b);
	tmp = 0.0;
	if (z <= -9.2e-10)
		tmp = t_2;
	elseif (z <= 2.4e-65)
		tmp = t_1;
	elseif (z <= 1.85e-48)
		tmp = (t - a) / b;
	elseif (z <= 4.9e-8)
		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[(x - N[(N[(z * N[(a - t), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a - t), $MachinePrecision] / N[(y - b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9.2e-10], t$95$2, If[LessEqual[z, 2.4e-65], t$95$1, If[LessEqual[z, 1.85e-48], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[z, 4.9e-8], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.20000000000000028e-10 or 4.9000000000000002e-8 < z

   1. Initial program 35.9%

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

   3. Taylor expanded in z around inf 70.7%

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

   if -9.20000000000000028e-10 < z < 2.4000000000000002e-65 or 1.8499999999999999e-48 < z < 4.9000000000000002e-8

   1. Initial program 92.3%

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

   3. Taylor expanded in z around 0 67.3%

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

   4. Taylor expanded in x around 0 74.5%

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

   if 2.4000000000000002e-65 < z < 1.8499999999999999e-48

   1. Initial program 99.0%

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

   3. Taylor expanded in y around 0 79.8%

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

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{-10}:\\ \;\;\;\;\frac{a - t}{y - b}\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-65}:\\ \;\;\;\;x - \frac{z \cdot \left(a - t\right)}{y}\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-48}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{-8}:\\ \;\;\;\;x - \frac{z \cdot \left(a - t\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{a - t}{y - b}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 53.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -1.4 \cdot 10^{+88}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-65}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;y \leq 6.3 \cdot 10^{+50} \lor \neg \left(y \leq 1.2 \cdot 10^{+77}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (- 1.0 z))))
   (if (<= y -1.4e+88)
     t_1
     (if (<= y 1.5e-65)
       (/ (- t a) b)
       (if (or (<= y 6.3e+50) (not (<= y 1.2e+77))) 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 <= -1.4e+88) {
		tmp = t_1;
	} else if (y <= 1.5e-65) {
		tmp = (t - a) / b;
	} else if ((y <= 6.3e+50) || !(y <= 1.2e+77)) {
		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 <= (-1.4d+88)) then
        tmp = t_1
    else if (y <= 1.5d-65) then
        tmp = (t - a) / b
    else if ((y <= 6.3d+50) .or. (.not. (y <= 1.2d+77))) 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 <= -1.4e+88) {
		tmp = t_1;
	} else if (y <= 1.5e-65) {
		tmp = (t - a) / b;
	} else if ((y <= 6.3e+50) || !(y <= 1.2e+77)) {
		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 <= -1.4e+88:
		tmp = t_1
	elif y <= 1.5e-65:
		tmp = (t - a) / b
	elif (y <= 6.3e+50) or not (y <= 1.2e+77):
		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 <= -1.4e+88)
		tmp = t_1;
	elseif (y <= 1.5e-65)
		tmp = Float64(Float64(t - a) / b);
	elseif ((y <= 6.3e+50) || !(y <= 1.2e+77))
		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 <= -1.4e+88)
		tmp = t_1;
	elseif (y <= 1.5e-65)
		tmp = (t - a) / b;
	elseif ((y <= 6.3e+50) || ~((y <= 1.2e+77)))
		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, -1.4e+88], t$95$1, If[LessEqual[y, 1.5e-65], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision], If[Or[LessEqual[y, 6.3e+50], N[Not[LessEqual[y, 1.2e+77]], $MachinePrecision]], t$95$1, N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.39999999999999994e88 or 1.49999999999999999e-65 < y < 6.29999999999999986e50 or 1.1999999999999999e77 < y

   1. Initial program 55.8%

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

   3. Taylor expanded in y around inf 60.9%

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

      1. mul-1-neg 60.9%

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

      2. unsub-neg 60.9%

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

   5. Simplified 60.9%

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

   if -1.39999999999999994e88 < y < 1.49999999999999999e-65

   1. Initial program 75.9%

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

   3. Taylor expanded in y around 0 53.7%

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

   if 6.29999999999999986e50 < y < 1.1999999999999999e77

   1. Initial program 50.6%

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

   3. Taylor expanded in x around inf 38.3%

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

   4. Taylor expanded in z around inf 76.0%

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

   5. Taylor expanded in t around inf 70.0%

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

4. Final simplification 57.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+88}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-65}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;y \leq 6.3 \cdot 10^{+50} \lor \neg \left(y \leq 1.2 \cdot 10^{+77}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 37.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+204}:\\ \;\;\;\;\frac{a}{-b}\\ \mathbf{elif}\;z \leq -1.46 \cdot 10^{-11} \lor \neg \left(z \leq 1.08 \cdot 10^{-7}\right):\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.65e+204)
   (/ a (- b))
   (if (or (<= z -1.46e-11) (not (<= z 1.08e-7))) (/ t b) x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.65e+204) {
		tmp = a / -b;
	} else if ((z <= -1.46e-11) || !(z <= 1.08e-7)) {
		tmp = t / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-1.65d+204)) then
        tmp = a / -b
    else if ((z <= (-1.46d-11)) .or. (.not. (z <= 1.08d-7))) then
        tmp = t / b
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.65e+204) {
		tmp = a / -b;
	} else if ((z <= -1.46e-11) || !(z <= 1.08e-7)) {
		tmp = t / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1.65e+204:
		tmp = a / -b
	elif (z <= -1.46e-11) or not (z <= 1.08e-7):
		tmp = t / b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.65e+204)
		tmp = Float64(a / Float64(-b));
	elseif ((z <= -1.46e-11) || !(z <= 1.08e-7))
		tmp = Float64(t / b);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -1.65e+204)
		tmp = a / -b;
	elseif ((z <= -1.46e-11) || ~((z <= 1.08e-7)))
		tmp = t / b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.65e+204], N[(a / (-b)), $MachinePrecision], If[Or[LessEqual[z, -1.46e-11], N[Not[LessEqual[z, 1.08e-7]], $MachinePrecision]], N[(t / b), $MachinePrecision], x]]

Derivation

1. Split input into 3 regimes

2. if z < -1.6499999999999999e204

   1. Initial program 19.8%

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

   3. Taylor expanded in a around inf 7.6%

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

      1. mul-1-neg 7.6%

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

      2. distribute-lft-neg-out 7.6%

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

      3. *-commutative 7.6%

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

   5. Simplified 7.6%

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

   6. Taylor expanded in y around 0 48.6%

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

      1. associate-*r/ 48.6%

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

      2. mul-1-neg 48.6%

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

   8. Simplified 48.6%

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

   if -1.6499999999999999e204 < z < -1.46e-11 or 1.08000000000000001e-7 < z

   1. Initial program 38.4%

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

   3. Taylor expanded in x around inf 38.3%

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

   4. Taylor expanded in z around inf 66.7%

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

   5. Taylor expanded in b around -inf 38.0%

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

      1. mul-1-neg 38.0%

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

      2. associate-/l* 34.4%

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

      3. distribute-lft-neg-in 34.4%

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

      4. mul-1-neg 34.4%

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

      5. unsub-neg 34.4%

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

      6. associate-*r/ 34.4%

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

      7. neg-mul-1 34.4%

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

   7. Simplified 34.4%

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

   8. Taylor expanded in t around inf 27.3%

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

   if -1.46e-11 < z < 1.08000000000000001e-7

   1. Initial program 92.6%

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

   3. Taylor expanded in z around 0 44.5%

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

4. Final simplification 37.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+204}:\\ \;\;\;\;\frac{a}{-b}\\ \mathbf{elif}\;z \leq -1.46 \cdot 10^{-11} \lor \neg \left(z \leq 1.08 \cdot 10^{-7}\right):\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 60.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+89} \lor \neg \left(y \leq 6.4 \cdot 10^{+139}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{a - t}{y - b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -4.5e+89) (not (<= y 6.4e+139)))
   (/ x (- 1.0 z))
   (/ (- a t) (- y b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -4.5e+89) || !(y <= 6.4e+139)) {
		tmp = x / (1.0 - z);
	} else {
		tmp = (a - t) / (y - b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-4.5d+89)) .or. (.not. (y <= 6.4d+139))) then
        tmp = x / (1.0d0 - z)
    else
        tmp = (a - t) / (y - b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -4.5e+89) || !(y <= 6.4e+139)) {
		tmp = x / (1.0 - z);
	} else {
		tmp = (a - t) / (y - b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -4.5e+89) or not (y <= 6.4e+139):
		tmp = x / (1.0 - z)
	else:
		tmp = (a - t) / (y - b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -4.5e+89) || !(y <= 6.4e+139))
		tmp = Float64(x / Float64(1.0 - z));
	else
		tmp = Float64(Float64(a - t) / Float64(y - b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -4.5e+89) || ~((y <= 6.4e+139)))
		tmp = x / (1.0 - z);
	else
		tmp = (a - t) / (y - b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -4.5e+89], N[Not[LessEqual[y, 6.4e+139]], $MachinePrecision]], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(N[(a - t), $MachinePrecision] / N[(y - b), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.5e89 or 6.4000000000000002e139 < y

   1. Initial program 49.5%

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

   3. Taylor expanded in y around inf 71.3%

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

      1. mul-1-neg 71.3%

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

      2. unsub-neg 71.3%

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

   5. Simplified 71.3%

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

   if -4.5e89 < y < 6.4000000000000002e139

   1. Initial program 73.1%

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

   3. Taylor expanded in z around inf 56.5%

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

4. Final simplification 61.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+89} \lor \neg \left(y \leq 6.4 \cdot 10^{+139}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{a - t}{y - b}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 42.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.18 \cdot 10^{+61} \lor \neg \left(t \leq 6.5 \cdot 10^{+35}\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -1.18e+61) (not (<= t 6.5e+35))) (/ t (- b y)) (/ x (- 1.0 z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.18e+61) || !(t <= 6.5e+35)) {
		tmp = t / (b - y);
	} else {
		tmp = x / (1.0 - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-1.18d+61)) .or. (.not. (t <= 6.5d+35))) then
        tmp = t / (b - y)
    else
        tmp = x / (1.0d0 - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.18e+61) || !(t <= 6.5e+35)) {
		tmp = t / (b - y);
	} else {
		tmp = x / (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -1.18e+61) or not (t <= 6.5e+35):
		tmp = t / (b - y)
	else:
		tmp = x / (1.0 - z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -1.18e+61) || !(t <= 6.5e+35))
		tmp = Float64(t / Float64(b - y));
	else
		tmp = Float64(x / Float64(1.0 - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -1.18e+61) || ~((t <= 6.5e+35)))
		tmp = t / (b - y);
	else
		tmp = x / (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -1.18e+61], N[Not[LessEqual[t, 6.5e+35]], $MachinePrecision]], N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.18000000000000004e61 or 6.5000000000000003e35 < t

   1. Initial program 58.9%

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

   3. Taylor expanded in x around inf 51.9%

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

   4. Taylor expanded in z around inf 49.5%

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

   5. Taylor expanded in t around inf 47.3%

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

   if -1.18000000000000004e61 < t < 6.5000000000000003e35

   1. Initial program 69.8%

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

   3. Taylor expanded in y around inf 49.3%

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

      1. mul-1-neg 49.3%

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

      2. unsub-neg 49.3%

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

   5. Simplified 49.3%

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

4. Final simplification 48.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.18 \cdot 10^{+61} \lor \neg \left(t \leq 6.5 \cdot 10^{+35}\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 45.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.05 \cdot 10^{-11} \lor \neg \left(z \leq 4.3 \cdot 10^{-5}\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -2.05e-11) (not (<= z 4.3e-5))) (/ t (- b y)) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.05e-11) || !(z <= 4.3e-5)) {
		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 ((z <= (-2.05d-11)) .or. (.not. (z <= 4.3d-5))) 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 ((z <= -2.05e-11) || !(z <= 4.3e-5)) {
		tmp = t / (b - y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -2.05e-11) or not (z <= 4.3e-5):
		tmp = t / (b - y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -2.05e-11) || !(z <= 4.3e-5))
		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 ((z <= -2.05e-11) || ~((z <= 4.3e-5)))
		tmp = t / (b - y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -2.05e-11], N[Not[LessEqual[z, 4.3e-5]], $MachinePrecision]], N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -2.05e-11 or 4.3000000000000002e-5 < z

   1. Initial program 35.9%

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

   3. Taylor expanded in x around inf 35.2%

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

   4. Taylor expanded in z around inf 64.8%

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

   5. Taylor expanded in t around inf 41.6%

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

   if -2.05e-11 < z < 4.3000000000000002e-5

   1. Initial program 92.6%

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

   3. Taylor expanded in z around 0 44.5%

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

4. Final simplification 43.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.05 \cdot 10^{-11} \lor \neg \left(z \leq 4.3 \cdot 10^{-5}\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 37.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.28 \cdot 10^{-11} \lor \neg \left(z \leq 4 \cdot 10^{-8}\right):\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.28e-11) (not (<= z 4e-8))) (/ t b) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.28e-11) || !(z <= 4e-8)) {
		tmp = t / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-1.28d-11)) .or. (.not. (z <= 4d-8))) then
        tmp = t / b
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.28e-11) || !(z <= 4e-8)) {
		tmp = t / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.28e-11) or not (z <= 4e-8):
		tmp = t / b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.28e-11) || !(z <= 4e-8))
		tmp = Float64(t / b);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1.28e-11) || ~((z <= 4e-8)))
		tmp = t / b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.28e-11], N[Not[LessEqual[z, 4e-8]], $MachinePrecision]], N[(t / b), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.28e-11 or 4.0000000000000001e-8 < z

   1. Initial program 35.9%

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

   3. Taylor expanded in x around inf 35.2%

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

   4. Taylor expanded in z around inf 64.8%

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

   5. Taylor expanded in b around -inf 40.3%

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

      1. mul-1-neg 40.3%

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

      2. associate-/l* 36.1%

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

      3. distribute-lft-neg-in 36.1%

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

      4. mul-1-neg 36.1%

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

      5. unsub-neg 36.1%

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

      6. associate-*r/ 36.1%

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

      7. neg-mul-1 36.1%

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

   7. Simplified 36.1%

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

   8. Taylor expanded in t around inf 26.7%

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

   if -1.28e-11 < z < 4.0000000000000001e-8

   1. Initial program 92.6%

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

   3. Taylor expanded in z around 0 44.5%

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

4. Final simplification 36.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.28 \cdot 10^{-11} \lor \neg \left(z \leq 4 \cdot 10^{-8}\right):\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 33.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{+24} \lor \neg \left(z \leq 0.66\right):\\ \;\;\;\;\frac{a}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -5.6e+24) (not (<= z 0.66))) (/ a y) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -5.6e+24) || !(z <= 0.66)) {
		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 <= (-5.6d+24)) .or. (.not. (z <= 0.66d0))) 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 <= -5.6e+24) || !(z <= 0.66)) {
		tmp = a / y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -5.6e+24) or not (z <= 0.66):
		tmp = a / y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -5.6e+24) || !(z <= 0.66))
		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 <= -5.6e+24) || ~((z <= 0.66)))
		tmp = a / y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -5.6e+24], N[Not[LessEqual[z, 0.66]], $MachinePrecision]], N[(a / y), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -5.6000000000000003e24 or 0.660000000000000031 < z

   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 y around inf 20.3%

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

      1. mul-1-neg 20.3%

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

      2. unsub-neg 20.3%

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

   5. Simplified 20.3%

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

   6. Taylor expanded in z around inf 31.1%

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

      1. associate-*r/ 31.1%

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

      2. mul-1-neg 31.1%

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

   8. Simplified 31.1%

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

   9. Taylor expanded in t around 0 17.5%

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

   if -5.6000000000000003e24 < z < 0.660000000000000031

   1. Initial program 91.6%

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

   3. Taylor expanded in z around 0 42.7%

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

4. Final simplification 31.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{+24} \lor \neg \left(z \leq 0.66\right):\\ \;\;\;\;\frac{a}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 25.2% accurate, 17.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 65.6%

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

3. Taylor expanded in z around 0 25.0%

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

Developer target: 73.4% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024087 
(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)))))