Development.Shake.Progress:decay from shake-0.15.5

Percentage Accurate: 66.5% → 93.5%

Time: 23.9s

Alternatives: 17

Speedup: 0.5×

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: 66.5% 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: 93.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -3.1 \cdot 10^{+99}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -6000000000000 \lor \neg \left(z \leq 850\right):\\ \;\;\;\;t\_1 + \frac{x \cdot \frac{y}{b - y} + y \cdot \frac{a - t}{{\left(b - y\right)}^{2}}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z \cdot \left(b + y\right)}{y} + 1} + \frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -3.1e+99)
     t_1
     (if (or (<= z -6000000000000.0) (not (<= z 850.0)))
       (+
        t_1
        (/ (+ (* x (/ y (- b y))) (* y (/ (- a t) (pow (- b y) 2.0)))) z))
       (+
        (/ x (+ (/ (* z (+ b y)) y) 1.0))
        (/ (* z (- t a)) (+ y (* z (- b y)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -3.1e+99) {
		tmp = t_1;
	} else if ((z <= -6000000000000.0) || !(z <= 850.0)) {
		tmp = t_1 + (((x * (y / (b - y))) + (y * ((a - t) / pow((b - y), 2.0)))) / z);
	} else {
		tmp = (x / (((z * (b + y)) / y) + 1.0)) + ((z * (t - a)) / (y + (z * (b - y))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    if (z <= (-3.1d+99)) then
        tmp = t_1
    else if ((z <= (-6000000000000.0d0)) .or. (.not. (z <= 850.0d0))) then
        tmp = t_1 + (((x * (y / (b - y))) + (y * ((a - t) / ((b - y) ** 2.0d0)))) / z)
    else
        tmp = (x / (((z * (b + y)) / y) + 1.0d0)) + ((z * (t - a)) / (y + (z * (b - y))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -3.1e+99) {
		tmp = t_1;
	} else if ((z <= -6000000000000.0) || !(z <= 850.0)) {
		tmp = t_1 + (((x * (y / (b - y))) + (y * ((a - t) / Math.pow((b - y), 2.0)))) / z);
	} else {
		tmp = (x / (((z * (b + y)) / y) + 1.0)) + ((z * (t - a)) / (y + (z * (b - y))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	tmp = 0
	if z <= -3.1e+99:
		tmp = t_1
	elif (z <= -6000000000000.0) or not (z <= 850.0):
		tmp = t_1 + (((x * (y / (b - y))) + (y * ((a - t) / math.pow((b - y), 2.0)))) / z)
	else:
		tmp = (x / (((z * (b + y)) / y) + 1.0)) + ((z * (t - a)) / (y + (z * (b - y))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -3.1e+99)
		tmp = t_1;
	elseif ((z <= -6000000000000.0) || !(z <= 850.0))
		tmp = Float64(t_1 + Float64(Float64(Float64(x * Float64(y / Float64(b - y))) + Float64(y * Float64(Float64(a - t) / (Float64(b - y) ^ 2.0)))) / z));
	else
		tmp = Float64(Float64(x / Float64(Float64(Float64(z * Float64(b + y)) / y) + 1.0)) + Float64(Float64(z * Float64(t - a)) / Float64(y + Float64(z * Float64(b - y)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -3.1e+99)
		tmp = t_1;
	elseif ((z <= -6000000000000.0) || ~((z <= 850.0)))
		tmp = t_1 + (((x * (y / (b - y))) + (y * ((a - t) / ((b - y) ^ 2.0)))) / z);
	else
		tmp = (x / (((z * (b + y)) / y) + 1.0)) + ((z * (t - a)) / (y + (z * (b - y))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.1e+99], t$95$1, If[Or[LessEqual[z, -6000000000000.0], N[Not[LessEqual[z, 850.0]], $MachinePrecision]], N[(t$95$1 + 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]), $MachinePrecision], N[(N[(x / N[(N[(N[(z * N[(b + y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.1000000000000001e99

   1. Initial program 37.1%

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

   3. Taylor expanded in z around inf 92.2%

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

   if -3.1000000000000001e99 < z < -6e12 or 850 < z

   1. Initial program 46.5%

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

   3. Taylor expanded in z around -inf 66.0%

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

      1. associate--l+ 66.0%

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

      2. mul-1-neg 66.0%

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

      3. distribute-lft-out-- 66.0%

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

      4. associate-/l* 76.2%

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

      5. associate-/l* 90.9%

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

      6. div-sub 90.9%

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

   5. Simplified 90.9%

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

   if -6e12 < z < 850

   1. Initial program 82.4%

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

   3. Taylor expanded in x around 0 82.4%

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

      1. associate-/l* 99.7%

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

      2. sub-neg 99.7%

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

      3. distribute-lft-out 99.7%

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

      4. +-commutative 99.7%

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

      5. distribute-lft-out 99.7%

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

      6. sub-neg 99.7%

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

      7. fma-define 99.7%

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

      8. sub-neg 99.7%

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

      9. add-sqr-sqrt 42.5%

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

      10. sqrt-unprod 73.2%

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

      11. sqr-neg 73.2%

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

      12. sqrt-unprod 56.5%

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

      13. add-sqr-sqrt 98.8%

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

   5. Applied egg-rr 98.8%

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

      1. clear-num 98.7%

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

      2. un-div-inv 98.8%

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

      3. +-commutative 98.8%

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

   7. Applied egg-rr 98.8%

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

   8. Taylor expanded in z around inf 98.8%

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

4. Final simplification 95.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+99}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -6000000000000 \lor \neg \left(z \leq 850\right):\\ \;\;\;\;\frac{t - a}{b - y} + \frac{x \cdot \frac{y}{b - y} + y \cdot \frac{a - t}{{\left(b - y\right)}^{2}}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z \cdot \left(b + y\right)}{y} + 1} + \frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 86.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := z \cdot \left(t - a\right)\\ t_3 := \frac{t\_2 + y \cdot x}{t\_1}\\ \mathbf{if}\;t\_3 \leq -\infty:\\ \;\;\;\;x + \frac{t\_2}{t\_1}\\ \mathbf{elif}\;t\_3 \leq -2 \cdot 10^{-278} \lor \neg \left(t\_3 \leq 0\right) \land t\_3 \leq 10^{+308}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y))))
        (t_2 (* z (- t a)))
        (t_3 (/ (+ t_2 (* y x)) t_1)))
   (if (<= t_3 (- INFINITY))
     (+ x (/ t_2 t_1))
     (if (or (<= t_3 -2e-278) (and (not (<= t_3 0.0)) (<= t_3 1e+308)))
       t_3
       (/ (- t a) (- b y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double t_2 = z * (t - a);
	double t_3 = (t_2 + (y * x)) / t_1;
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = x + (t_2 / t_1);
	} else if ((t_3 <= -2e-278) || (!(t_3 <= 0.0) && (t_3 <= 1e+308))) {
		tmp = t_3;
	} else {
		tmp = (t - a) / (b - y);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double t_2 = z * (t - a);
	double t_3 = (t_2 + (y * x)) / t_1;
	double tmp;
	if (t_3 <= -Double.POSITIVE_INFINITY) {
		tmp = x + (t_2 / t_1);
	} else if ((t_3 <= -2e-278) || (!(t_3 <= 0.0) && (t_3 <= 1e+308))) {
		tmp = t_3;
	} else {
		tmp = (t - a) / (b - y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z * (b - y))
	t_2 = z * (t - a)
	t_3 = (t_2 + (y * x)) / t_1
	tmp = 0
	if t_3 <= -math.inf:
		tmp = x + (t_2 / t_1)
	elif (t_3 <= -2e-278) or (not (t_3 <= 0.0) and (t_3 <= 1e+308)):
		tmp = t_3
	else:
		tmp = (t - a) / (b - y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(z * Float64(b - y)))
	t_2 = Float64(z * Float64(t - a))
	t_3 = Float64(Float64(t_2 + Float64(y * x)) / t_1)
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = Float64(x + Float64(t_2 / t_1));
	elseif ((t_3 <= -2e-278) || (!(t_3 <= 0.0) && (t_3 <= 1e+308)))
		tmp = t_3;
	else
		tmp = Float64(Float64(t - a) / Float64(b - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (z * (b - y));
	t_2 = z * (t - a);
	t_3 = (t_2 + (y * x)) / t_1;
	tmp = 0.0;
	if (t_3 <= -Inf)
		tmp = x + (t_2 / t_1);
	elseif ((t_3 <= -2e-278) || (~((t_3 <= 0.0)) && (t_3 <= 1e+308)))
		tmp = t_3;
	else
		tmp = (t - a) / (b - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t$95$2 + N[(y * x), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], N[(x + N[(t$95$2 / t$95$1), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t$95$3, -2e-278], And[N[Not[LessEqual[t$95$3, 0.0]], $MachinePrecision], LessEqual[t$95$3, 1e+308]]], t$95$3, N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 24.1%

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

   3. Taylor expanded in x around 0 24.1%

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

   4. Taylor expanded in z around 0 64.0%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -1.99999999999999988e-278 or 0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 1e308

   1. Initial program 99.6%

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

   if -1.99999999999999988e-278 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 0.0 or 1e308 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 11.4%

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

   3. Taylor expanded in z around inf 67.1%

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

4. Final simplification 85.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y + z \cdot \left(b - y\right)} \leq -2 \cdot 10^{-278} \lor \neg \left(\frac{z \cdot \left(t - a\right) + y \cdot x}{y + z \cdot \left(b - y\right)} \leq 0\right) \land \frac{z \cdot \left(t - a\right) + y \cdot x}{y + z \cdot \left(b - y\right)} \leq 10^{+308}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 90.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ t_2 := y + z \cdot \left(b - y\right)\\ \mathbf{if}\;z \leq -4.5 \cdot 10^{+85}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{+62}:\\ \;\;\;\;\frac{y}{b - y} \cdot \frac{x}{z} + t \cdot \frac{z}{t\_2}\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{+15}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 470:\\ \;\;\;\;\frac{x}{\frac{z \cdot \left(b + y\right)}{y} + 1} + \frac{z \cdot \left(t - a\right)}{t\_2}\\ \mathbf{else}:\\ \;\;\;\;t\_1 + \frac{y \cdot x}{t\_2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))) (t_2 (+ y (* z (- b y)))))
   (if (<= z -4.5e+85)
     t_1
     (if (<= z -1.4e+62)
       (+ (* (/ y (- b y)) (/ x z)) (* t (/ z t_2)))
       (if (<= z -1.6e+15)
         t_1
         (if (<= z 470.0)
           (+ (/ x (+ (/ (* z (+ b y)) y) 1.0)) (/ (* z (- t a)) t_2))
           (+ t_1 (/ (* y x) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double t_2 = y + (z * (b - y));
	double tmp;
	if (z <= -4.5e+85) {
		tmp = t_1;
	} else if (z <= -1.4e+62) {
		tmp = ((y / (b - y)) * (x / z)) + (t * (z / t_2));
	} else if (z <= -1.6e+15) {
		tmp = t_1;
	} else if (z <= 470.0) {
		tmp = (x / (((z * (b + y)) / y) + 1.0)) + ((z * (t - a)) / t_2);
	} else {
		tmp = t_1 + ((y * x) / 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 = (t - a) / (b - y)
    t_2 = y + (z * (b - y))
    if (z <= (-4.5d+85)) then
        tmp = t_1
    else if (z <= (-1.4d+62)) then
        tmp = ((y / (b - y)) * (x / z)) + (t * (z / t_2))
    else if (z <= (-1.6d+15)) then
        tmp = t_1
    else if (z <= 470.0d0) then
        tmp = (x / (((z * (b + y)) / y) + 1.0d0)) + ((z * (t - a)) / t_2)
    else
        tmp = t_1 + ((y * x) / 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 = (t - a) / (b - y);
	double t_2 = y + (z * (b - y));
	double tmp;
	if (z <= -4.5e+85) {
		tmp = t_1;
	} else if (z <= -1.4e+62) {
		tmp = ((y / (b - y)) * (x / z)) + (t * (z / t_2));
	} else if (z <= -1.6e+15) {
		tmp = t_1;
	} else if (z <= 470.0) {
		tmp = (x / (((z * (b + y)) / y) + 1.0)) + ((z * (t - a)) / t_2);
	} else {
		tmp = t_1 + ((y * x) / t_2);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	t_2 = y + (z * (b - y))
	tmp = 0
	if z <= -4.5e+85:
		tmp = t_1
	elif z <= -1.4e+62:
		tmp = ((y / (b - y)) * (x / z)) + (t * (z / t_2))
	elif z <= -1.6e+15:
		tmp = t_1
	elif z <= 470.0:
		tmp = (x / (((z * (b + y)) / y) + 1.0)) + ((z * (t - a)) / t_2)
	else:
		tmp = t_1 + ((y * x) / t_2)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	t_2 = Float64(y + Float64(z * Float64(b - y)))
	tmp = 0.0
	if (z <= -4.5e+85)
		tmp = t_1;
	elseif (z <= -1.4e+62)
		tmp = Float64(Float64(Float64(y / Float64(b - y)) * Float64(x / z)) + Float64(t * Float64(z / t_2)));
	elseif (z <= -1.6e+15)
		tmp = t_1;
	elseif (z <= 470.0)
		tmp = Float64(Float64(x / Float64(Float64(Float64(z * Float64(b + y)) / y) + 1.0)) + Float64(Float64(z * Float64(t - a)) / t_2));
	else
		tmp = Float64(t_1 + Float64(Float64(y * x) / t_2));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	t_2 = y + (z * (b - y));
	tmp = 0.0;
	if (z <= -4.5e+85)
		tmp = t_1;
	elseif (z <= -1.4e+62)
		tmp = ((y / (b - y)) * (x / z)) + (t * (z / t_2));
	elseif (z <= -1.6e+15)
		tmp = t_1;
	elseif (z <= 470.0)
		tmp = (x / (((z * (b + y)) / y) + 1.0)) + ((z * (t - a)) / t_2);
	else
		tmp = t_1 + ((y * x) / t_2);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.5e+85], t$95$1, If[LessEqual[z, -1.4e+62], N[(N[(N[(y / N[(b - y), $MachinePrecision]), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision] + N[(t * N[(z / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.6e+15], t$95$1, If[LessEqual[z, 470.0], N[(N[(x / N[(N[(N[(z * N[(b + y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(N[(y * x), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.50000000000000007e85 or -1.40000000000000007e62 < z < -1.6e15

   1. Initial program 43.0%

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

   3. Taylor expanded in z around inf 92.3%

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

   if -4.50000000000000007e85 < z < -1.40000000000000007e62

   1. Initial program 26.8%

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

   3. Taylor expanded in x around 0 26.8%

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

   4. Taylor expanded in t around inf 26.8%

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

      1. associate-/l* 39.0%

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

   6. Simplified 39.0%

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

   7. Taylor expanded in z around inf 39.0%

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

      1. times-frac 100.0%

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

   9. Simplified 100.0%

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

   if -1.6e15 < z < 470

   1. Initial program 82.4%

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

   3. Taylor expanded in x around 0 82.4%

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

      1. associate-/l* 99.7%

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

      2. sub-neg 99.7%

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

      3. distribute-lft-out 99.7%

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

      4. +-commutative 99.7%

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

      5. distribute-lft-out 99.7%

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

      6. sub-neg 99.7%

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

      7. fma-define 99.7%

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

      8. sub-neg 99.7%

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

      9. add-sqr-sqrt 42.5%

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

      10. sqrt-unprod 73.2%

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

      11. sqr-neg 73.2%

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

      12. sqrt-unprod 56.5%

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

      13. add-sqr-sqrt 98.8%

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

   5. Applied egg-rr 98.8%

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

      1. clear-num 98.7%

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

      2. un-div-inv 98.8%

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

      3. +-commutative 98.8%

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

   7. Applied egg-rr 98.8%

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

   8. Taylor expanded in z around inf 98.8%

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

   if 470 < z

   1. Initial program 45.7%

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

   3. Taylor expanded in x around 0 45.7%

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

   4. Taylor expanded in z around inf 83.9%

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

4. Final simplification 93.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+85}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{+62}:\\ \;\;\;\;\frac{y}{b - y} \cdot \frac{x}{z} + t \cdot \frac{z}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{+15}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq 470:\\ \;\;\;\;\frac{x}{\frac{z \cdot \left(b + y\right)}{y} + 1} + \frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y} + \frac{y \cdot x}{y + z \cdot \left(b - y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 83.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(t - a\right)\\ t_2 := y + z \cdot \left(b - y\right)\\ t_3 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -3.8 \cdot 10^{+74}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{+62}:\\ \;\;\;\;\frac{-t}{y} - \frac{x + \frac{t}{y}}{z}\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{+15}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq -8.4 \cdot 10^{-91}:\\ \;\;\;\;\frac{t\_1 + y \cdot x}{t\_2}\\ \mathbf{elif}\;z \leq 0.022:\\ \;\;\;\;x + \frac{t\_1}{t\_2}\\ \mathbf{else}:\\ \;\;\;\;t\_3 + \frac{y \cdot x}{t\_2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- t a)))
        (t_2 (+ y (* z (- b y))))
        (t_3 (/ (- t a) (- b y))))
   (if (<= z -3.8e+74)
     t_3
     (if (<= z -1.7e+62)
       (- (/ (- t) y) (/ (+ x (/ t y)) z))
       (if (<= z -1.6e+15)
         t_3
         (if (<= z -8.4e-91)
           (/ (+ t_1 (* y x)) t_2)
           (if (<= z 0.022) (+ x (/ t_1 t_2)) (+ t_3 (/ (* y x) t_2)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (t - a);
	double t_2 = y + (z * (b - y));
	double t_3 = (t - a) / (b - y);
	double tmp;
	if (z <= -3.8e+74) {
		tmp = t_3;
	} else if (z <= -1.7e+62) {
		tmp = (-t / y) - ((x + (t / y)) / z);
	} else if (z <= -1.6e+15) {
		tmp = t_3;
	} else if (z <= -8.4e-91) {
		tmp = (t_1 + (y * x)) / t_2;
	} else if (z <= 0.022) {
		tmp = x + (t_1 / t_2);
	} else {
		tmp = t_3 + ((y * x) / 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) :: t_3
    real(8) :: tmp
    t_1 = z * (t - a)
    t_2 = y + (z * (b - y))
    t_3 = (t - a) / (b - y)
    if (z <= (-3.8d+74)) then
        tmp = t_3
    else if (z <= (-1.7d+62)) then
        tmp = (-t / y) - ((x + (t / y)) / z)
    else if (z <= (-1.6d+15)) then
        tmp = t_3
    else if (z <= (-8.4d-91)) then
        tmp = (t_1 + (y * x)) / t_2
    else if (z <= 0.022d0) then
        tmp = x + (t_1 / t_2)
    else
        tmp = t_3 + ((y * x) / t_2)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (t - a);
	double t_2 = y + (z * (b - y));
	double t_3 = (t - a) / (b - y);
	double tmp;
	if (z <= -3.8e+74) {
		tmp = t_3;
	} else if (z <= -1.7e+62) {
		tmp = (-t / y) - ((x + (t / y)) / z);
	} else if (z <= -1.6e+15) {
		tmp = t_3;
	} else if (z <= -8.4e-91) {
		tmp = (t_1 + (y * x)) / t_2;
	} else if (z <= 0.022) {
		tmp = x + (t_1 / t_2);
	} else {
		tmp = t_3 + ((y * x) / t_2);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (t - a)
	t_2 = y + (z * (b - y))
	t_3 = (t - a) / (b - y)
	tmp = 0
	if z <= -3.8e+74:
		tmp = t_3
	elif z <= -1.7e+62:
		tmp = (-t / y) - ((x + (t / y)) / z)
	elif z <= -1.6e+15:
		tmp = t_3
	elif z <= -8.4e-91:
		tmp = (t_1 + (y * x)) / t_2
	elif z <= 0.022:
		tmp = x + (t_1 / t_2)
	else:
		tmp = t_3 + ((y * x) / t_2)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(t - a))
	t_2 = Float64(y + Float64(z * Float64(b - y)))
	t_3 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -3.8e+74)
		tmp = t_3;
	elseif (z <= -1.7e+62)
		tmp = Float64(Float64(Float64(-t) / y) - Float64(Float64(x + Float64(t / y)) / z));
	elseif (z <= -1.6e+15)
		tmp = t_3;
	elseif (z <= -8.4e-91)
		tmp = Float64(Float64(t_1 + Float64(y * x)) / t_2);
	elseif (z <= 0.022)
		tmp = Float64(x + Float64(t_1 / t_2));
	else
		tmp = Float64(t_3 + Float64(Float64(y * x) / t_2));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (t - a);
	t_2 = y + (z * (b - y));
	t_3 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -3.8e+74)
		tmp = t_3;
	elseif (z <= -1.7e+62)
		tmp = (-t / y) - ((x + (t / y)) / z);
	elseif (z <= -1.6e+15)
		tmp = t_3;
	elseif (z <= -8.4e-91)
		tmp = (t_1 + (y * x)) / t_2;
	elseif (z <= 0.022)
		tmp = x + (t_1 / t_2);
	else
		tmp = t_3 + ((y * x) / t_2);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.8e+74], t$95$3, If[LessEqual[z, -1.7e+62], N[(N[((-t) / y), $MachinePrecision] - N[(N[(x + N[(t / y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.6e+15], t$95$3, If[LessEqual[z, -8.4e-91], N[(N[(t$95$1 + N[(y * x), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision], If[LessEqual[z, 0.022], N[(x + N[(t$95$1 / t$95$2), $MachinePrecision]), $MachinePrecision], N[(t$95$3 + N[(N[(y * x), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -3.7999999999999998e74 or -1.70000000000000007e62 < z < -1.6e15

   1. Initial program 43.4%

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

   3. Taylor expanded in z around inf 90.9%

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

   if -3.7999999999999998e74 < z < -1.70000000000000007e62

   1. Initial program 18.1%

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

   3. Taylor expanded in a around 0 18.1%

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

   4. Taylor expanded in b around 0 18.1%

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

      1. mul-1-neg 18.1%

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

      2. distribute-lft-neg-out 18.1%

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

      3. *-commutative 18.1%

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

   6. Simplified 18.1%

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

   7. Taylor expanded in z around -inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. unsub-neg 100.0%

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

      3. associate-*r/ 100.0%

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

      4. neg-mul-1 100.0%

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

      5. cancel-sign-sub-inv 100.0%

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

      6. metadata-eval 100.0%

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

      7. *-lft-identity 100.0%

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

   9. Simplified 100.0%

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

   if -1.6e15 < z < -8.3999999999999997e-91

   1. Initial program 84.1%

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

   if -8.3999999999999997e-91 < z < 0.021999999999999999

   1. Initial program 82.0%

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

   3. Taylor expanded in x around 0 82.0%

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

   4. Taylor expanded in z around 0 89.8%

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

   if 0.021999999999999999 < z

   1. Initial program 45.7%

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

   3. Taylor expanded in x around 0 45.7%

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

   4. Taylor expanded in z around inf 83.9%

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

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+74}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{+62}:\\ \;\;\;\;\frac{-t}{y} - \frac{x + \frac{t}{y}}{z}\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{+15}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -8.4 \cdot 10^{-91}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 0.022:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y} + \frac{y \cdot x}{y + z \cdot \left(b - y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 83.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(t - a\right)\\ t_2 := \frac{t - a}{b - y}\\ t_3 := y + z \cdot \left(b - y\right)\\ \mathbf{if}\;z \leq -5.2 \cdot 10^{+85}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{+60}:\\ \;\;\;\;\frac{y}{b - y} \cdot \frac{x}{z} + t \cdot \frac{z}{t\_3}\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{+15}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{-91}:\\ \;\;\;\;\frac{t\_1 + y \cdot x}{t\_3}\\ \mathbf{elif}\;z \leq 0.09:\\ \;\;\;\;x + \frac{t\_1}{t\_3}\\ \mathbf{else}:\\ \;\;\;\;t\_2 + \frac{y \cdot x}{t\_3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- t a)))
        (t_2 (/ (- t a) (- b y)))
        (t_3 (+ y (* z (- b y)))))
   (if (<= z -5.2e+85)
     t_2
     (if (<= z -6.2e+60)
       (+ (* (/ y (- b y)) (/ x z)) (* t (/ z t_3)))
       (if (<= z -1.6e+15)
         t_2
         (if (<= z -7.8e-91)
           (/ (+ t_1 (* y x)) t_3)
           (if (<= z 0.09) (+ x (/ t_1 t_3)) (+ t_2 (/ (* y x) t_3)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (t - a);
	double t_2 = (t - a) / (b - y);
	double t_3 = y + (z * (b - y));
	double tmp;
	if (z <= -5.2e+85) {
		tmp = t_2;
	} else if (z <= -6.2e+60) {
		tmp = ((y / (b - y)) * (x / z)) + (t * (z / t_3));
	} else if (z <= -1.6e+15) {
		tmp = t_2;
	} else if (z <= -7.8e-91) {
		tmp = (t_1 + (y * x)) / t_3;
	} else if (z <= 0.09) {
		tmp = x + (t_1 / t_3);
	} else {
		tmp = t_2 + ((y * x) / 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 = z * (t - a)
    t_2 = (t - a) / (b - y)
    t_3 = y + (z * (b - y))
    if (z <= (-5.2d+85)) then
        tmp = t_2
    else if (z <= (-6.2d+60)) then
        tmp = ((y / (b - y)) * (x / z)) + (t * (z / t_3))
    else if (z <= (-1.6d+15)) then
        tmp = t_2
    else if (z <= (-7.8d-91)) then
        tmp = (t_1 + (y * x)) / t_3
    else if (z <= 0.09d0) then
        tmp = x + (t_1 / t_3)
    else
        tmp = t_2 + ((y * x) / 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 * (t - a);
	double t_2 = (t - a) / (b - y);
	double t_3 = y + (z * (b - y));
	double tmp;
	if (z <= -5.2e+85) {
		tmp = t_2;
	} else if (z <= -6.2e+60) {
		tmp = ((y / (b - y)) * (x / z)) + (t * (z / t_3));
	} else if (z <= -1.6e+15) {
		tmp = t_2;
	} else if (z <= -7.8e-91) {
		tmp = (t_1 + (y * x)) / t_3;
	} else if (z <= 0.09) {
		tmp = x + (t_1 / t_3);
	} else {
		tmp = t_2 + ((y * x) / t_3);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (t - a)
	t_2 = (t - a) / (b - y)
	t_3 = y + (z * (b - y))
	tmp = 0
	if z <= -5.2e+85:
		tmp = t_2
	elif z <= -6.2e+60:
		tmp = ((y / (b - y)) * (x / z)) + (t * (z / t_3))
	elif z <= -1.6e+15:
		tmp = t_2
	elif z <= -7.8e-91:
		tmp = (t_1 + (y * x)) / t_3
	elif z <= 0.09:
		tmp = x + (t_1 / t_3)
	else:
		tmp = t_2 + ((y * x) / t_3)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(t - a))
	t_2 = Float64(Float64(t - a) / Float64(b - y))
	t_3 = Float64(y + Float64(z * Float64(b - y)))
	tmp = 0.0
	if (z <= -5.2e+85)
		tmp = t_2;
	elseif (z <= -6.2e+60)
		tmp = Float64(Float64(Float64(y / Float64(b - y)) * Float64(x / z)) + Float64(t * Float64(z / t_3)));
	elseif (z <= -1.6e+15)
		tmp = t_2;
	elseif (z <= -7.8e-91)
		tmp = Float64(Float64(t_1 + Float64(y * x)) / t_3);
	elseif (z <= 0.09)
		tmp = Float64(x + Float64(t_1 / t_3));
	else
		tmp = Float64(t_2 + Float64(Float64(y * x) / t_3));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (t - a);
	t_2 = (t - a) / (b - y);
	t_3 = y + (z * (b - y));
	tmp = 0.0;
	if (z <= -5.2e+85)
		tmp = t_2;
	elseif (z <= -6.2e+60)
		tmp = ((y / (b - y)) * (x / z)) + (t * (z / t_3));
	elseif (z <= -1.6e+15)
		tmp = t_2;
	elseif (z <= -7.8e-91)
		tmp = (t_1 + (y * x)) / t_3;
	elseif (z <= 0.09)
		tmp = x + (t_1 / t_3);
	else
		tmp = t_2 + ((y * x) / t_3);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.2e+85], t$95$2, If[LessEqual[z, -6.2e+60], N[(N[(N[(y / N[(b - y), $MachinePrecision]), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision] + N[(t * N[(z / t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.6e+15], t$95$2, If[LessEqual[z, -7.8e-91], N[(N[(t$95$1 + N[(y * x), $MachinePrecision]), $MachinePrecision] / t$95$3), $MachinePrecision], If[LessEqual[z, 0.09], N[(x + N[(t$95$1 / t$95$3), $MachinePrecision]), $MachinePrecision], N[(t$95$2 + N[(N[(y * x), $MachinePrecision] / t$95$3), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -5.20000000000000021e85 or -6.2000000000000001e60 < z < -1.6e15

   1. Initial program 43.0%

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

   3. Taylor expanded in z around inf 92.3%

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

   if -5.20000000000000021e85 < z < -6.2000000000000001e60

   1. Initial program 26.8%

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

   3. Taylor expanded in x around 0 26.8%

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

   4. Taylor expanded in t around inf 26.8%

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

      1. associate-/l* 39.0%

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

   6. Simplified 39.0%

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

   7. Taylor expanded in z around inf 39.0%

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

      1. times-frac 100.0%

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

   9. Simplified 100.0%

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

   if -1.6e15 < z < -7.79999999999999987e-91

   1. Initial program 84.1%

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

   if -7.79999999999999987e-91 < z < 0.089999999999999997

   1. Initial program 82.0%

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

   3. Taylor expanded in x around 0 82.0%

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

   4. Taylor expanded in z around 0 89.8%

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

   if 0.089999999999999997 < z

   1. Initial program 45.7%

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

   3. Taylor expanded in x around 0 45.7%

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

   4. Taylor expanded in z around inf 83.9%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+85}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{+60}:\\ \;\;\;\;\frac{y}{b - y} \cdot \frac{x}{z} + t \cdot \frac{z}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{+15}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{-91}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 0.09:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y} + \frac{y \cdot x}{y + z \cdot \left(b - y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 71.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{t - a}{y + z \cdot \left(b - y\right)}\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -3.8 \cdot 10^{+74}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{+62}:\\ \;\;\;\;\frac{-t}{y} - \frac{x + \frac{t}{y}}{z}\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{+15}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-88}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-101}:\\ \;\;\;\;\frac{y \cdot x + z \cdot t}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+15}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (/ (- t a) (+ y (* z (- b y)))))) (t_2 (/ (- t a) (- b y))))
   (if (<= z -3.8e+74)
     t_2
     (if (<= z -1.7e+62)
       (- (/ (- t) y) (/ (+ x (/ t y)) z))
       (if (<= z -1.05e+15)
         t_2
         (if (<= z -1.7e-88)
           t_1
           (if (<= z 7e-101)
             (/ (+ (* y x) (* z t)) (+ y (* z b)))
             (if (<= z 2.7e+15) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * ((t - a) / (y + (z * (b - y))));
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -3.8e+74) {
		tmp = t_2;
	} else if (z <= -1.7e+62) {
		tmp = (-t / y) - ((x + (t / y)) / z);
	} else if (z <= -1.05e+15) {
		tmp = t_2;
	} else if (z <= -1.7e-88) {
		tmp = t_1;
	} else if (z <= 7e-101) {
		tmp = ((y * x) + (z * t)) / (y + (z * b));
	} else if (z <= 2.7e+15) {
		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 = z * ((t - a) / (y + (z * (b - y))))
    t_2 = (t - a) / (b - y)
    if (z <= (-3.8d+74)) then
        tmp = t_2
    else if (z <= (-1.7d+62)) then
        tmp = (-t / y) - ((x + (t / y)) / z)
    else if (z <= (-1.05d+15)) then
        tmp = t_2
    else if (z <= (-1.7d-88)) then
        tmp = t_1
    else if (z <= 7d-101) then
        tmp = ((y * x) + (z * t)) / (y + (z * b))
    else if (z <= 2.7d+15) 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 = z * ((t - a) / (y + (z * (b - y))));
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -3.8e+74) {
		tmp = t_2;
	} else if (z <= -1.7e+62) {
		tmp = (-t / y) - ((x + (t / y)) / z);
	} else if (z <= -1.05e+15) {
		tmp = t_2;
	} else if (z <= -1.7e-88) {
		tmp = t_1;
	} else if (z <= 7e-101) {
		tmp = ((y * x) + (z * t)) / (y + (z * b));
	} else if (z <= 2.7e+15) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * ((t - a) / (y + (z * (b - y))))
	t_2 = (t - a) / (b - y)
	tmp = 0
	if z <= -3.8e+74:
		tmp = t_2
	elif z <= -1.7e+62:
		tmp = (-t / y) - ((x + (t / y)) / z)
	elif z <= -1.05e+15:
		tmp = t_2
	elif z <= -1.7e-88:
		tmp = t_1
	elif z <= 7e-101:
		tmp = ((y * x) + (z * t)) / (y + (z * b))
	elif z <= 2.7e+15:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(Float64(t - a) / Float64(y + Float64(z * Float64(b - y)))))
	t_2 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -3.8e+74)
		tmp = t_2;
	elseif (z <= -1.7e+62)
		tmp = Float64(Float64(Float64(-t) / y) - Float64(Float64(x + Float64(t / y)) / z));
	elseif (z <= -1.05e+15)
		tmp = t_2;
	elseif (z <= -1.7e-88)
		tmp = t_1;
	elseif (z <= 7e-101)
		tmp = Float64(Float64(Float64(y * x) + Float64(z * t)) / Float64(y + Float64(z * b)));
	elseif (z <= 2.7e+15)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * ((t - a) / (y + (z * (b - y))));
	t_2 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -3.8e+74)
		tmp = t_2;
	elseif (z <= -1.7e+62)
		tmp = (-t / y) - ((x + (t / y)) / z);
	elseif (z <= -1.05e+15)
		tmp = t_2;
	elseif (z <= -1.7e-88)
		tmp = t_1;
	elseif (z <= 7e-101)
		tmp = ((y * x) + (z * t)) / (y + (z * b));
	elseif (z <= 2.7e+15)
		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[(z * N[(N[(t - a), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.8e+74], t$95$2, If[LessEqual[z, -1.7e+62], N[(N[((-t) / y), $MachinePrecision] - N[(N[(x + N[(t / y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.05e+15], t$95$2, If[LessEqual[z, -1.7e-88], t$95$1, If[LessEqual[z, 7e-101], N[(N[(N[(y * x), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.7e+15], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.7999999999999998e74 or -1.70000000000000007e62 < z < -1.05e15 or 2.7e15 < z

   1. Initial program 41.3%

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

   3. Taylor expanded in z around inf 84.1%

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

   if -3.7999999999999998e74 < z < -1.70000000000000007e62

   1. Initial program 18.1%

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

   3. Taylor expanded in a around 0 18.1%

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

   4. Taylor expanded in b around 0 18.1%

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

      1. mul-1-neg 18.1%

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

      2. distribute-lft-neg-out 18.1%

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

      3. *-commutative 18.1%

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

   6. Simplified 18.1%

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

   7. Taylor expanded in z around -inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. unsub-neg 100.0%

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

      3. associate-*r/ 100.0%

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

      4. neg-mul-1 100.0%

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

      5. cancel-sign-sub-inv 100.0%

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

      6. metadata-eval 100.0%

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

      7. *-lft-identity 100.0%

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

   9. Simplified 100.0%

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

   if -1.05e15 < z < -1.69999999999999987e-88 or 6.99999999999999989e-101 < z < 2.7e15

   1. Initial program 81.4%

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

      1. sub-neg 81.4%

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

      2. distribute-lft-in 81.4%

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

   4. Applied egg-rr 81.4%

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

   5. Taylor expanded in x around 0 63.6%

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

      1. associate-/l* 63.5%

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

      2. +-commutative 63.5%

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

      3. associate-*r* 63.5%

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

      4. distribute-rgt-in 63.5%

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

      5. mul-1-neg 63.5%

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

      6. sub-neg 63.5%

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

   7. Simplified 63.5%

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

   if -1.69999999999999987e-88 < z < 6.99999999999999989e-101

   1. Initial program 84.3%

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

   3. Taylor expanded in a around 0 72.1%

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

   4. Taylor expanded in b around inf 72.1%

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

      1. *-commutative 72.1%

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

   6. Simplified 72.1%

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

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+74}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{+62}:\\ \;\;\;\;\frac{-t}{y} - \frac{x + \frac{t}{y}}{z}\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{+15}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-88}:\\ \;\;\;\;z \cdot \frac{t - a}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-101}:\\ \;\;\;\;\frac{y \cdot x + z \cdot t}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+15}:\\ \;\;\;\;z \cdot \frac{t - a}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 81.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(t - a\right)\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -3.8 \cdot 10^{+74}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{+62}:\\ \;\;\;\;\frac{-t}{y} - \frac{x + \frac{t}{y}}{z}\\ \mathbf{elif}\;z \leq -8500:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{-91}:\\ \;\;\;\;\frac{t\_1 + y \cdot x}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 185000000:\\ \;\;\;\;x + \frac{t\_1}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- t a))) (t_2 (/ (- t a) (- b y))))
   (if (<= z -3.8e+74)
     t_2
     (if (<= z -1.55e+62)
       (- (/ (- t) y) (/ (+ x (/ t y)) z))
       (if (<= z -8500.0)
         t_2
         (if (<= z -7.8e-91)
           (/ (+ t_1 (* y x)) (+ y (* z b)))
           (if (<= z 185000000.0) (+ x (/ t_1 (+ y (* z (- b y))))) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (t - a);
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -3.8e+74) {
		tmp = t_2;
	} else if (z <= -1.55e+62) {
		tmp = (-t / y) - ((x + (t / y)) / z);
	} else if (z <= -8500.0) {
		tmp = t_2;
	} else if (z <= -7.8e-91) {
		tmp = (t_1 + (y * x)) / (y + (z * b));
	} else if (z <= 185000000.0) {
		tmp = x + (t_1 / (y + (z * (b - y))));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z * (t - a)
    t_2 = (t - a) / (b - y)
    if (z <= (-3.8d+74)) then
        tmp = t_2
    else if (z <= (-1.55d+62)) then
        tmp = (-t / y) - ((x + (t / y)) / z)
    else if (z <= (-8500.0d0)) then
        tmp = t_2
    else if (z <= (-7.8d-91)) then
        tmp = (t_1 + (y * x)) / (y + (z * b))
    else if (z <= 185000000.0d0) then
        tmp = x + (t_1 / (y + (z * (b - y))))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (t - a);
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -3.8e+74) {
		tmp = t_2;
	} else if (z <= -1.55e+62) {
		tmp = (-t / y) - ((x + (t / y)) / z);
	} else if (z <= -8500.0) {
		tmp = t_2;
	} else if (z <= -7.8e-91) {
		tmp = (t_1 + (y * x)) / (y + (z * b));
	} else if (z <= 185000000.0) {
		tmp = x + (t_1 / (y + (z * (b - y))));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (t - a)
	t_2 = (t - a) / (b - y)
	tmp = 0
	if z <= -3.8e+74:
		tmp = t_2
	elif z <= -1.55e+62:
		tmp = (-t / y) - ((x + (t / y)) / z)
	elif z <= -8500.0:
		tmp = t_2
	elif z <= -7.8e-91:
		tmp = (t_1 + (y * x)) / (y + (z * b))
	elif z <= 185000000.0:
		tmp = x + (t_1 / (y + (z * (b - y))))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(t - a))
	t_2 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -3.8e+74)
		tmp = t_2;
	elseif (z <= -1.55e+62)
		tmp = Float64(Float64(Float64(-t) / y) - Float64(Float64(x + Float64(t / y)) / z));
	elseif (z <= -8500.0)
		tmp = t_2;
	elseif (z <= -7.8e-91)
		tmp = Float64(Float64(t_1 + Float64(y * x)) / Float64(y + Float64(z * b)));
	elseif (z <= 185000000.0)
		tmp = Float64(x + Float64(t_1 / Float64(y + Float64(z * Float64(b - y)))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (t - a);
	t_2 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -3.8e+74)
		tmp = t_2;
	elseif (z <= -1.55e+62)
		tmp = (-t / y) - ((x + (t / y)) / z);
	elseif (z <= -8500.0)
		tmp = t_2;
	elseif (z <= -7.8e-91)
		tmp = (t_1 + (y * x)) / (y + (z * b));
	elseif (z <= 185000000.0)
		tmp = x + (t_1 / (y + (z * (b - y))));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.8e+74], t$95$2, If[LessEqual[z, -1.55e+62], N[(N[((-t) / y), $MachinePrecision] - N[(N[(x + N[(t / y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -8500.0], t$95$2, If[LessEqual[z, -7.8e-91], N[(N[(t$95$1 + N[(y * x), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 185000000.0], N[(x + N[(t$95$1 / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.7999999999999998e74 or -1.55000000000000007e62 < z < -8500 or 1.85e8 < z

   1. Initial program 43.7%

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

   3. Taylor expanded in z around inf 83.1%

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

   if -3.7999999999999998e74 < z < -1.55000000000000007e62

   1. Initial program 18.1%

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

   3. Taylor expanded in a around 0 18.1%

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

   4. Taylor expanded in b around 0 18.1%

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

      1. mul-1-neg 18.1%

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

      2. distribute-lft-neg-out 18.1%

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

      3. *-commutative 18.1%

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

   6. Simplified 18.1%

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

   7. Taylor expanded in z around -inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. unsub-neg 100.0%

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

      3. associate-*r/ 100.0%

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

      4. neg-mul-1 100.0%

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

      5. cancel-sign-sub-inv 100.0%

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

      6. metadata-eval 100.0%

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

      7. *-lft-identity 100.0%

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

   9. Simplified 100.0%

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

   if -8500 < z < -7.79999999999999987e-91

   1. Initial program 82.7%

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

   3. Taylor expanded in b around inf 81.3%

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

      1. *-commutative 48.1%

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

   5. Simplified 81.3%

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

   if -7.79999999999999987e-91 < z < 1.85e8

   1. Initial program 82.6%

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

   3. Taylor expanded in x around 0 82.6%

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

   4. Taylor expanded in z around 0 88.4%

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

4. Final simplification 85.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+74}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{+62}:\\ \;\;\;\;\frac{-t}{y} - \frac{x + \frac{t}{y}}{z}\\ \mathbf{elif}\;z \leq -8500:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{-91}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 185000000:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 80.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -3.8 \cdot 10^{+74}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{+62}:\\ \;\;\;\;\frac{-t}{y} - \frac{x + \frac{t}{y}}{z}\\ \mathbf{elif}\;z \leq -1150000000 \lor \neg \left(z \leq 160000000\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -3.8e+74)
     t_1
     (if (<= z -1.7e+62)
       (- (/ (- t) y) (/ (+ x (/ t y)) z))
       (if (or (<= z -1150000000.0) (not (<= z 160000000.0)))
         t_1
         (+ x (/ (* z (- t a)) (+ y (* z (- b y))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -3.8e+74) {
		tmp = t_1;
	} else if (z <= -1.7e+62) {
		tmp = (-t / y) - ((x + (t / y)) / z);
	} else if ((z <= -1150000000.0) || !(z <= 160000000.0)) {
		tmp = t_1;
	} else {
		tmp = x + ((z * (t - a)) / (y + (z * (b - y))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    if (z <= (-3.8d+74)) then
        tmp = t_1
    else if (z <= (-1.7d+62)) then
        tmp = (-t / y) - ((x + (t / y)) / z)
    else if ((z <= (-1150000000.0d0)) .or. (.not. (z <= 160000000.0d0))) then
        tmp = t_1
    else
        tmp = x + ((z * (t - a)) / (y + (z * (b - y))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -3.8e+74) {
		tmp = t_1;
	} else if (z <= -1.7e+62) {
		tmp = (-t / y) - ((x + (t / y)) / z);
	} else if ((z <= -1150000000.0) || !(z <= 160000000.0)) {
		tmp = t_1;
	} else {
		tmp = x + ((z * (t - a)) / (y + (z * (b - y))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	tmp = 0
	if z <= -3.8e+74:
		tmp = t_1
	elif z <= -1.7e+62:
		tmp = (-t / y) - ((x + (t / y)) / z)
	elif (z <= -1150000000.0) or not (z <= 160000000.0):
		tmp = t_1
	else:
		tmp = x + ((z * (t - a)) / (y + (z * (b - y))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -3.8e+74)
		tmp = t_1;
	elseif (z <= -1.7e+62)
		tmp = Float64(Float64(Float64(-t) / y) - Float64(Float64(x + Float64(t / y)) / z));
	elseif ((z <= -1150000000.0) || !(z <= 160000000.0))
		tmp = t_1;
	else
		tmp = Float64(x + Float64(Float64(z * Float64(t - a)) / Float64(y + Float64(z * Float64(b - y)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -3.8e+74)
		tmp = t_1;
	elseif (z <= -1.7e+62)
		tmp = (-t / y) - ((x + (t / y)) / z);
	elseif ((z <= -1150000000.0) || ~((z <= 160000000.0)))
		tmp = t_1;
	else
		tmp = x + ((z * (t - a)) / (y + (z * (b - y))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.8e+74], t$95$1, If[LessEqual[z, -1.7e+62], N[(N[((-t) / y), $MachinePrecision] - N[(N[(x + N[(t / y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -1150000000.0], N[Not[LessEqual[z, 160000000.0]], $MachinePrecision]], t$95$1, N[(x + N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.7999999999999998e74 or -1.70000000000000007e62 < z < -1.15e9 or 1.6e8 < z

   1. Initial program 42.7%

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

   3. Taylor expanded in z around inf 83.7%

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

   if -3.7999999999999998e74 < z < -1.70000000000000007e62

   1. Initial program 18.1%

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

   3. Taylor expanded in a around 0 18.1%

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

   4. Taylor expanded in b around 0 18.1%

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

      1. mul-1-neg 18.1%

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

      2. distribute-lft-neg-out 18.1%

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

      3. *-commutative 18.1%

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

   6. Simplified 18.1%

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

   7. Taylor expanded in z around -inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. unsub-neg 100.0%

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

      3. associate-*r/ 100.0%

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

      4. neg-mul-1 100.0%

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

      5. cancel-sign-sub-inv 100.0%

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

      6. metadata-eval 100.0%

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

      7. *-lft-identity 100.0%

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

   9. Simplified 100.0%

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

   if -1.15e9 < z < 1.6e8

   1. Initial program 82.9%

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

   3. Taylor expanded in x around 0 82.9%

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

   4. Taylor expanded in z around 0 83.2%

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

4. Final simplification 83.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+74}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{+62}:\\ \;\;\;\;\frac{-t}{y} - \frac{x + \frac{t}{y}}{z}\\ \mathbf{elif}\;z \leq -1150000000 \lor \neg \left(z \leq 160000000\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 67.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{t}{y}\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -3.9 \cdot 10^{+74}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{+62}:\\ \;\;\;\;\frac{-t}{y} - \frac{t\_1}{z}\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{+15}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-153}:\\ \;\;\;\;z \cdot \frac{t - a}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 0.0005:\\ \;\;\;\;x + z \cdot t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (/ t y))) (t_2 (/ (- t a) (- b y))))
   (if (<= z -3.9e+74)
     t_2
     (if (<= z -1.7e+62)
       (- (/ (- t) y) (/ t_1 z))
       (if (<= z -1.3e+15)
         t_2
         (if (<= z -1e-153)
           (* z (/ (- t a) (+ y (* z (- b y)))))
           (if (<= z 0.0005) (+ x (* z t_1)) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (t / y);
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -3.9e+74) {
		tmp = t_2;
	} else if (z <= -1.7e+62) {
		tmp = (-t / y) - (t_1 / z);
	} else if (z <= -1.3e+15) {
		tmp = t_2;
	} else if (z <= -1e-153) {
		tmp = z * ((t - a) / (y + (z * (b - y))));
	} else if (z <= 0.0005) {
		tmp = x + (z * 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 + (t / y)
    t_2 = (t - a) / (b - y)
    if (z <= (-3.9d+74)) then
        tmp = t_2
    else if (z <= (-1.7d+62)) then
        tmp = (-t / y) - (t_1 / z)
    else if (z <= (-1.3d+15)) then
        tmp = t_2
    else if (z <= (-1d-153)) then
        tmp = z * ((t - a) / (y + (z * (b - y))))
    else if (z <= 0.0005d0) then
        tmp = x + (z * 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 + (t / y);
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -3.9e+74) {
		tmp = t_2;
	} else if (z <= -1.7e+62) {
		tmp = (-t / y) - (t_1 / z);
	} else if (z <= -1.3e+15) {
		tmp = t_2;
	} else if (z <= -1e-153) {
		tmp = z * ((t - a) / (y + (z * (b - y))));
	} else if (z <= 0.0005) {
		tmp = x + (z * t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (t / y)
	t_2 = (t - a) / (b - y)
	tmp = 0
	if z <= -3.9e+74:
		tmp = t_2
	elif z <= -1.7e+62:
		tmp = (-t / y) - (t_1 / z)
	elif z <= -1.3e+15:
		tmp = t_2
	elif z <= -1e-153:
		tmp = z * ((t - a) / (y + (z * (b - y))))
	elif z <= 0.0005:
		tmp = x + (z * t_1)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(t / y))
	t_2 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -3.9e+74)
		tmp = t_2;
	elseif (z <= -1.7e+62)
		tmp = Float64(Float64(Float64(-t) / y) - Float64(t_1 / z));
	elseif (z <= -1.3e+15)
		tmp = t_2;
	elseif (z <= -1e-153)
		tmp = Float64(z * Float64(Float64(t - a) / Float64(y + Float64(z * Float64(b - y)))));
	elseif (z <= 0.0005)
		tmp = Float64(x + Float64(z * t_1));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (t / y);
	t_2 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -3.9e+74)
		tmp = t_2;
	elseif (z <= -1.7e+62)
		tmp = (-t / y) - (t_1 / z);
	elseif (z <= -1.3e+15)
		tmp = t_2;
	elseif (z <= -1e-153)
		tmp = z * ((t - a) / (y + (z * (b - y))));
	elseif (z <= 0.0005)
		tmp = x + (z * 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[(t / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.9e+74], t$95$2, If[LessEqual[z, -1.7e+62], N[(N[((-t) / y), $MachinePrecision] - N[(t$95$1 / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.3e+15], t$95$2, If[LessEqual[z, -1e-153], N[(z * N[(N[(t - a), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.0005], N[(x + N[(z * t$95$1), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.90000000000000008e74 or -1.70000000000000007e62 < z < -1.3e15 or 5.0000000000000001e-4 < z

   1. Initial program 44.6%

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

   3. Taylor expanded in z around inf 82.3%

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

   if -3.90000000000000008e74 < z < -1.70000000000000007e62

   1. Initial program 18.1%

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

   3. Taylor expanded in a around 0 18.1%

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

   4. Taylor expanded in b around 0 18.1%

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

      1. mul-1-neg 18.1%

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

      2. distribute-lft-neg-out 18.1%

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

      3. *-commutative 18.1%

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

   6. Simplified 18.1%

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

   7. Taylor expanded in z around -inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. unsub-neg 100.0%

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

      3. associate-*r/ 100.0%

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

      4. neg-mul-1 100.0%

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

      5. cancel-sign-sub-inv 100.0%

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

      6. metadata-eval 100.0%

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

      7. *-lft-identity 100.0%

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

   9. Simplified 100.0%

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

   if -1.3e15 < z < -1.00000000000000004e-153

   1. Initial program 84.5%

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

      1. sub-neg 84.5%

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

      2. distribute-lft-in 84.5%

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

   4. Applied egg-rr 84.5%

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

   5. Taylor expanded in x around 0 66.8%

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

      1. associate-/l* 59.2%

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

      2. +-commutative 59.2%

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

      3. associate-*r* 59.2%

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

      4. distribute-rgt-in 59.2%

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

      5. mul-1-neg 59.2%

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

      6. sub-neg 59.2%

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

   7. Simplified 59.2%

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

   if -1.00000000000000004e-153 < z < 5.0000000000000001e-4

   1. Initial program 81.5%

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

   3. Taylor expanded in a around 0 64.0%

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

   4. Taylor expanded in b around 0 56.1%

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

      1. mul-1-neg 56.1%

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

      2. distribute-lft-neg-out 56.1%

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

      3. *-commutative 56.1%

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

   6. Simplified 56.1%

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

   7. Taylor expanded in z around 0 63.6%

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

      1. mul-1-neg 63.6%

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

   9. Simplified 63.6%

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

4. Final simplification 72.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{+74}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{+62}:\\ \;\;\;\;\frac{-t}{y} - \frac{x + \frac{t}{y}}{z}\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{+15}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-153}:\\ \;\;\;\;z \cdot \frac{t - a}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 0.0005:\\ \;\;\;\;x + z \cdot \left(x + \frac{t}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 65.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{t}{y}\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -3.8 \cdot 10^{+74}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{+62}:\\ \;\;\;\;\frac{-t}{y} - \frac{t\_1}{z}\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-153} \lor \neg \left(z \leq 0.0005\right):\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (/ t y))) (t_2 (/ (- t a) (- b y))))
   (if (<= z -3.8e+74)
     t_2
     (if (<= z -1.7e+62)
       (- (/ (- t) y) (/ t_1 z))
       (if (or (<= z -9.5e-153) (not (<= z 0.0005))) t_2 (+ x (* z t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (t / y);
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -3.8e+74) {
		tmp = t_2;
	} else if (z <= -1.7e+62) {
		tmp = (-t / y) - (t_1 / z);
	} else if ((z <= -9.5e-153) || !(z <= 0.0005)) {
		tmp = t_2;
	} else {
		tmp = x + (z * t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (t / y)
    t_2 = (t - a) / (b - y)
    if (z <= (-3.8d+74)) then
        tmp = t_2
    else if (z <= (-1.7d+62)) then
        tmp = (-t / y) - (t_1 / z)
    else if ((z <= (-9.5d-153)) .or. (.not. (z <= 0.0005d0))) then
        tmp = t_2
    else
        tmp = x + (z * t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (t / y);
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -3.8e+74) {
		tmp = t_2;
	} else if (z <= -1.7e+62) {
		tmp = (-t / y) - (t_1 / z);
	} else if ((z <= -9.5e-153) || !(z <= 0.0005)) {
		tmp = t_2;
	} else {
		tmp = x + (z * t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (t / y)
	t_2 = (t - a) / (b - y)
	tmp = 0
	if z <= -3.8e+74:
		tmp = t_2
	elif z <= -1.7e+62:
		tmp = (-t / y) - (t_1 / z)
	elif (z <= -9.5e-153) or not (z <= 0.0005):
		tmp = t_2
	else:
		tmp = x + (z * t_1)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(t / y))
	t_2 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -3.8e+74)
		tmp = t_2;
	elseif (z <= -1.7e+62)
		tmp = Float64(Float64(Float64(-t) / y) - Float64(t_1 / z));
	elseif ((z <= -9.5e-153) || !(z <= 0.0005))
		tmp = t_2;
	else
		tmp = Float64(x + Float64(z * t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (t / y);
	t_2 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -3.8e+74)
		tmp = t_2;
	elseif (z <= -1.7e+62)
		tmp = (-t / y) - (t_1 / z);
	elseif ((z <= -9.5e-153) || ~((z <= 0.0005)))
		tmp = t_2;
	else
		tmp = x + (z * t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(t / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.8e+74], t$95$2, If[LessEqual[z, -1.7e+62], N[(N[((-t) / y), $MachinePrecision] - N[(t$95$1 / z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -9.5e-153], N[Not[LessEqual[z, 0.0005]], $MachinePrecision]], t$95$2, N[(x + N[(z * t$95$1), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.7999999999999998e74 or -1.70000000000000007e62 < z < -9.50000000000000031e-153 or 5.0000000000000001e-4 < z

   1. Initial program 54.0%

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

   3. Taylor expanded in z around inf 74.1%

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

   if -3.7999999999999998e74 < z < -1.70000000000000007e62

   1. Initial program 18.1%

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

   3. Taylor expanded in a around 0 18.1%

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

   4. Taylor expanded in b around 0 18.1%

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

      1. mul-1-neg 18.1%

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

      2. distribute-lft-neg-out 18.1%

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

      3. *-commutative 18.1%

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

   6. Simplified 18.1%

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

   7. Taylor expanded in z around -inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. unsub-neg 100.0%

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

      3. associate-*r/ 100.0%

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

      4. neg-mul-1 100.0%

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

      5. cancel-sign-sub-inv 100.0%

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

      6. metadata-eval 100.0%

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

      7. *-lft-identity 100.0%

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

   9. Simplified 100.0%

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

   if -9.50000000000000031e-153 < z < 5.0000000000000001e-4

   1. Initial program 81.5%

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

   3. Taylor expanded in a around 0 64.0%

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

   4. Taylor expanded in b around 0 56.1%

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

      1. mul-1-neg 56.1%

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

      2. distribute-lft-neg-out 56.1%

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

      3. *-commutative 56.1%

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

   6. Simplified 56.1%

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

   7. Taylor expanded in z around 0 63.6%

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

      1. mul-1-neg 63.6%

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

   9. Simplified 63.6%

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

4. Final simplification 70.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+74}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{+62}:\\ \;\;\;\;\frac{-t}{y} - \frac{x + \frac{t}{y}}{z}\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-153} \lor \neg \left(z \leq 0.0005\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(x + \frac{t}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 66.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{-153} \lor \neg \left(z \leq 6.2 \cdot 10^{-5}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(x + \frac{t}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -9.5e-153) (not (<= z 6.2e-5)))
   (/ (- t a) (- b y))
   (+ x (* z (+ x (/ t y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -9.5e-153) || !(z <= 6.2e-5)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x + (z * (x + (t / y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-9.5d-153)) .or. (.not. (z <= 6.2d-5))) then
        tmp = (t - a) / (b - y)
    else
        tmp = x + (z * (x + (t / y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -9.5e-153) || !(z <= 6.2e-5)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x + (z * (x + (t / y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -9.5e-153) or not (z <= 6.2e-5):
		tmp = (t - a) / (b - y)
	else:
		tmp = x + (z * (x + (t / y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -9.5e-153) || !(z <= 6.2e-5))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(x + Float64(z * Float64(x + Float64(t / y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -9.5e-153) || ~((z <= 6.2e-5)))
		tmp = (t - a) / (b - y);
	else
		tmp = x + (z * (x + (t / y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -9.5e-153], N[Not[LessEqual[z, 6.2e-5]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(x + N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.50000000000000031e-153 or 6.20000000000000027e-5 < z

   1. Initial program 52.7%

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

   3. Taylor expanded in z around inf 72.1%

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

   if -9.50000000000000031e-153 < z < 6.20000000000000027e-5

   1. Initial program 81.5%

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

   3. Taylor expanded in a around 0 64.0%

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

   4. Taylor expanded in b around 0 56.1%

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

      1. mul-1-neg 56.1%

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

      2. distribute-lft-neg-out 56.1%

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

      3. *-commutative 56.1%

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

   6. Simplified 56.1%

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

   7. Taylor expanded in z around 0 63.6%

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

      1. mul-1-neg 63.6%

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

   9. Simplified 63.6%

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

4. Final simplification 69.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{-153} \lor \neg \left(z \leq 6.2 \cdot 10^{-5}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(x + \frac{t}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 63.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{-153} \lor \neg \left(z \leq 41000\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1e-153) (not (<= z 41000.0)))
   (/ (- t a) (- b y))
   (/ x (- 1.0 z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1e-153) || !(z <= 41000.0)) {
		tmp = (t - a) / (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 ((z <= (-1d-153)) .or. (.not. (z <= 41000.0d0))) then
        tmp = (t - a) / (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 ((z <= -1e-153) || !(z <= 41000.0)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x / (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1e-153) or not (z <= 41000.0):
		tmp = (t - a) / (b - y)
	else:
		tmp = x / (1.0 - z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1e-153) || !(z <= 41000.0))
		tmp = Float64(Float64(t - a) / 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 ((z <= -1e-153) || ~((z <= 41000.0)))
		tmp = (t - a) / (b - y);
	else
		tmp = x / (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1e-153], N[Not[LessEqual[z, 41000.0]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.00000000000000004e-153 or 41000 < z

   1. Initial program 52.1%

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

   3. Taylor expanded in z around inf 72.9%

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

   if -1.00000000000000004e-153 < z < 41000

   1. Initial program 81.9%

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

   3. Taylor expanded in y around inf 56.8%

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

      1. mul-1-neg 56.8%

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

      2. unsub-neg 56.8%

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

   5. Simplified 56.8%

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

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{-153} \lor \neg \left(z \leq 41000\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 43.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{-154} \lor \neg \left(z \leq 0.000106\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1e-154) (not (<= z 0.000106))) (/ t (- b y)) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1e-154) || !(z <= 0.000106)) {
		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 <= (-1d-154)) .or. (.not. (z <= 0.000106d0))) 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 <= -1e-154) || !(z <= 0.000106)) {
		tmp = t / (b - y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1e-154) or not (z <= 0.000106):
		tmp = t / (b - y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1e-154) || !(z <= 0.000106))
		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 <= -1e-154) || ~((z <= 0.000106)))
		tmp = t / (b - y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1e-154], N[Not[LessEqual[z, 0.000106]], $MachinePrecision]], N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -9.9999999999999997e-155 or 1.06e-4 < z

   1. Initial program 52.7%

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

   3. Taylor expanded in a around 0 37.5%

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

   4. Taylor expanded in z around inf 42.9%

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

   if -9.9999999999999997e-155 < z < 1.06e-4

   1. Initial program 81.5%

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

   3. Taylor expanded in z around 0 56.8%

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

4. Final simplification 47.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{-154} \lor \neg \left(z \leq 0.000106\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 43.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{+58} \lor \neg \left(y \leq 5.5 \cdot 10^{-11}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.35e+58) (not (<= y 5.5e-11))) (/ x (- 1.0 z)) (/ t (- b y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.35e+58) || !(y <= 5.5e-11)) {
		tmp = x / (1.0 - z);
	} else {
		tmp = t / (b - y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-1.35d+58)) .or. (.not. (y <= 5.5d-11))) then
        tmp = x / (1.0d0 - z)
    else
        tmp = t / (b - y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.35e+58) || !(y <= 5.5e-11)) {
		tmp = x / (1.0 - z);
	} else {
		tmp = t / (b - y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.35e+58) or not (y <= 5.5e-11):
		tmp = x / (1.0 - z)
	else:
		tmp = t / (b - y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.35e+58) || !(y <= 5.5e-11))
		tmp = Float64(x / Float64(1.0 - z));
	else
		tmp = Float64(t / Float64(b - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.35e+58) || ~((y <= 5.5e-11)))
		tmp = x / (1.0 - z);
	else
		tmp = t / (b - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.35e+58], N[Not[LessEqual[y, 5.5e-11]], $MachinePrecision]], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.3500000000000001e58 or 5.49999999999999975e-11 < y

   1. Initial program 49.9%

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

   3. Taylor expanded in y around inf 56.3%

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

      1. mul-1-neg 56.3%

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

      2. unsub-neg 56.3%

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

   5. Simplified 56.3%

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

   if -1.3500000000000001e58 < y < 5.49999999999999975e-11

   1. Initial program 75.5%

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

   3. Taylor expanded in a around 0 51.7%

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

   4. Taylor expanded in z around inf 43.8%

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

4. Final simplification 49.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{+58} \lor \neg \left(y \leq 5.5 \cdot 10^{-11}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 53.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.4 \cdot 10^{+56} \lor \neg \left(y \leq 1.85 \cdot 10^{+64}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -7.4e+56) (not (<= y 1.85e+64))) (/ x (- 1.0 z)) (/ (- t a) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -7.4e+56) || !(y <= 1.85e+64)) {
		tmp = x / (1.0 - z);
	} else {
		tmp = (t - a) / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-7.4d+56)) .or. (.not. (y <= 1.85d+64))) then
        tmp = x / (1.0d0 - z)
    else
        tmp = (t - a) / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -7.4e+56) || !(y <= 1.85e+64)) {
		tmp = x / (1.0 - z);
	} else {
		tmp = (t - a) / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -7.4e+56) or not (y <= 1.85e+64):
		tmp = x / (1.0 - z)
	else:
		tmp = (t - a) / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -7.4e+56) || !(y <= 1.85e+64))
		tmp = Float64(x / Float64(1.0 - z));
	else
		tmp = Float64(Float64(t - a) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -7.4e+56) || ~((y <= 1.85e+64)))
		tmp = x / (1.0 - z);
	else
		tmp = (t - a) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -7.4e+56], N[Not[LessEqual[y, 1.85e+64]], $MachinePrecision]], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.39999999999999994e56 or 1.84999999999999992e64 < y

   1. Initial program 48.8%

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

   3. Taylor expanded in y around inf 59.4%

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

      1. mul-1-neg 59.4%

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

      2. unsub-neg 59.4%

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

   5. Simplified 59.4%

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

   if -7.39999999999999994e56 < y < 1.84999999999999992e64

   1. Initial program 73.6%

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

   3. Taylor expanded in y around 0 56.8%

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

4. Final simplification 57.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.4 \cdot 10^{+56} \lor \neg \left(y \leq 1.85 \cdot 10^{+64}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 34.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{-153} \lor \neg \left(z \leq 1.5 \cdot 10^{-7}\right):\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -9.5e-153) (not (<= z 1.5e-7))) (/ t b) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -9.5e-153) || !(z <= 1.5e-7)) {
		tmp = t / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-9.5d-153)) .or. (.not. (z <= 1.5d-7))) then
        tmp = t / b
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -9.5e-153) || !(z <= 1.5e-7)) {
		tmp = t / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -9.5e-153) or not (z <= 1.5e-7):
		tmp = t / b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -9.5e-153) || !(z <= 1.5e-7))
		tmp = Float64(t / b);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -9.5e-153) || ~((z <= 1.5e-7)))
		tmp = t / b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -9.5e-153], N[Not[LessEqual[z, 1.5e-7]], $MachinePrecision]], N[(t / b), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -9.50000000000000031e-153 or 1.4999999999999999e-7 < z

   1. Initial program 53.2%

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

   3. Taylor expanded in a around 0 37.7%

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

   4. Taylor expanded in y around 0 32.2%

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

   if -9.50000000000000031e-153 < z < 1.4999999999999999e-7

   1. Initial program 81.1%

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

   3. Taylor expanded in z around 0 58.0%

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

4. Final simplification 41.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{-153} \lor \neg \left(z \leq 1.5 \cdot 10^{-7}\right):\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 25.3% 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 63.0%

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

3. Taylor expanded in z around 0 25.1%

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

4. Final simplification 25.1%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 73.6% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024053 
(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)))))