Development.Shake.Progress:decay from shake-0.15.5

Percentage Accurate: 66.4% → 92.4%

Time: 23.2s

Alternatives: 22

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: 66.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 92.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := b + \left(\frac{y}{z} - y\right)\\ t_3 := x \cdot \left(\frac{\frac{t - a}{t\_2}}{x} + \frac{\frac{y}{z}}{t\_2}\right)\\ t_4 := z \cdot \left(t - a\right)\\ t_5 := \frac{x \cdot y + t\_4}{t\_1}\\ \mathbf{if}\;t\_5 \leq -1 \cdot 10^{+303}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_5 \leq -5 \cdot 10^{-287}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;t\_5 \leq 0:\\ \;\;\;\;\frac{x \cdot \frac{y}{b - y} - y \cdot \frac{t - a}{{\left(b - y\right)}^{2}}}{z} + \frac{t - a}{b - y}\\ \mathbf{elif}\;t\_5 \leq 2 \cdot 10^{+290}:\\ \;\;\;\;\frac{x \cdot y}{t\_1} + \frac{t\_4}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y))))
        (t_2 (+ b (- (/ y z) y)))
        (t_3 (* x (+ (/ (/ (- t a) t_2) x) (/ (/ y z) t_2))))
        (t_4 (* z (- t a)))
        (t_5 (/ (+ (* x y) t_4) t_1)))
   (if (<= t_5 -1e+303)
     t_3
     (if (<= t_5 -5e-287)
       t_5
       (if (<= t_5 0.0)
         (+
          (/ (- (* x (/ y (- b y))) (* y (/ (- t a) (pow (- b y) 2.0)))) z)
          (/ (- t a) (- b y)))
         (if (<= t_5 2e+290) (+ (/ (* x y) t_1) (/ t_4 t_1)) t_3))))))

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 = b + ((y / z) - y);
	double t_3 = x * ((((t - a) / t_2) / x) + ((y / z) / t_2));
	double t_4 = z * (t - a);
	double t_5 = ((x * y) + t_4) / t_1;
	double tmp;
	if (t_5 <= -1e+303) {
		tmp = t_3;
	} else if (t_5 <= -5e-287) {
		tmp = t_5;
	} else if (t_5 <= 0.0) {
		tmp = (((x * (y / (b - y))) - (y * ((t - a) / pow((b - y), 2.0)))) / z) + ((t - a) / (b - y));
	} else if (t_5 <= 2e+290) {
		tmp = ((x * y) / t_1) + (t_4 / t_1);
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_1 = y + (z * (b - y))
    t_2 = b + ((y / z) - y)
    t_3 = x * ((((t - a) / t_2) / x) + ((y / z) / t_2))
    t_4 = z * (t - a)
    t_5 = ((x * y) + t_4) / t_1
    if (t_5 <= (-1d+303)) then
        tmp = t_3
    else if (t_5 <= (-5d-287)) then
        tmp = t_5
    else if (t_5 <= 0.0d0) then
        tmp = (((x * (y / (b - y))) - (y * ((t - a) / ((b - y) ** 2.0d0)))) / z) + ((t - a) / (b - y))
    else if (t_5 <= 2d+290) then
        tmp = ((x * y) / t_1) + (t_4 / t_1)
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double t_2 = b + ((y / z) - y);
	double t_3 = x * ((((t - a) / t_2) / x) + ((y / z) / t_2));
	double t_4 = z * (t - a);
	double t_5 = ((x * y) + t_4) / t_1;
	double tmp;
	if (t_5 <= -1e+303) {
		tmp = t_3;
	} else if (t_5 <= -5e-287) {
		tmp = t_5;
	} else if (t_5 <= 0.0) {
		tmp = (((x * (y / (b - y))) - (y * ((t - a) / Math.pow((b - y), 2.0)))) / z) + ((t - a) / (b - y));
	} else if (t_5 <= 2e+290) {
		tmp = ((x * y) / t_1) + (t_4 / t_1);
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z * (b - y))
	t_2 = b + ((y / z) - y)
	t_3 = x * ((((t - a) / t_2) / x) + ((y / z) / t_2))
	t_4 = z * (t - a)
	t_5 = ((x * y) + t_4) / t_1
	tmp = 0
	if t_5 <= -1e+303:
		tmp = t_3
	elif t_5 <= -5e-287:
		tmp = t_5
	elif t_5 <= 0.0:
		tmp = (((x * (y / (b - y))) - (y * ((t - a) / math.pow((b - y), 2.0)))) / z) + ((t - a) / (b - y))
	elif t_5 <= 2e+290:
		tmp = ((x * y) / t_1) + (t_4 / t_1)
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(z * Float64(b - y)))
	t_2 = Float64(b + Float64(Float64(y / z) - y))
	t_3 = Float64(x * Float64(Float64(Float64(Float64(t - a) / t_2) / x) + Float64(Float64(y / z) / t_2)))
	t_4 = Float64(z * Float64(t - a))
	t_5 = Float64(Float64(Float64(x * y) + t_4) / t_1)
	tmp = 0.0
	if (t_5 <= -1e+303)
		tmp = t_3;
	elseif (t_5 <= -5e-287)
		tmp = t_5;
	elseif (t_5 <= 0.0)
		tmp = Float64(Float64(Float64(Float64(x * Float64(y / Float64(b - y))) - Float64(y * Float64(Float64(t - a) / (Float64(b - y) ^ 2.0)))) / z) + Float64(Float64(t - a) / Float64(b - y)));
	elseif (t_5 <= 2e+290)
		tmp = Float64(Float64(Float64(x * y) / t_1) + Float64(t_4 / t_1));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (z * (b - y));
	t_2 = b + ((y / z) - y);
	t_3 = x * ((((t - a) / t_2) / x) + ((y / z) / t_2));
	t_4 = z * (t - a);
	t_5 = ((x * y) + t_4) / t_1;
	tmp = 0.0;
	if (t_5 <= -1e+303)
		tmp = t_3;
	elseif (t_5 <= -5e-287)
		tmp = t_5;
	elseif (t_5 <= 0.0)
		tmp = (((x * (y / (b - y))) - (y * ((t - a) / ((b - y) ^ 2.0)))) / z) + ((t - a) / (b - y));
	elseif (t_5 <= 2e+290)
		tmp = ((x * y) / t_1) + (t_4 / t_1);
	else
		tmp = t_3;
	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[(b + N[(N[(y / z), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(N[(N[(N[(t - a), $MachinePrecision] / t$95$2), $MachinePrecision] / x), $MachinePrecision] + N[(N[(y / z), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(N[(x * y), $MachinePrecision] + t$95$4), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[t$95$5, -1e+303], t$95$3, If[LessEqual[t$95$5, -5e-287], t$95$5, If[LessEqual[t$95$5, 0.0], N[(N[(N[(N[(x * N[(y / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * N[(N[(t - a), $MachinePrecision] / N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] + N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$5, 2e+290], N[(N[(N[(x * y), $MachinePrecision] / t$95$1), $MachinePrecision] + N[(t$95$4 / t$95$1), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -1e303 or 2.00000000000000012e290 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 12.9%

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

   3. Taylor expanded in z around inf 12.6%

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

   4. Taylor expanded in x around -inf 80.1%

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

      1. mul-1-neg 80.1%

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

      2. *-commutative 80.1%

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

      3. distribute-rgt-neg-in 80.1%

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

   6. Simplified 86.3%

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

   if -1e303 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -5.00000000000000025e-287

   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 -5.00000000000000025e-287 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -0.0

   1. Initial program 40.7%

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

   3. Taylor expanded in z around -inf 99.8%

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

      1. associate--l+ 99.8%

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

      2. mul-1-neg 99.8%

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

      3. distribute-lft-out-- 99.8%

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

      4. associate-/l* 99.8%

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

      5. associate-/l* 99.8%

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

      6. div-sub 99.8%

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

   5. Simplified 99.8%

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

   if -0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 2.00000000000000012e290

   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

   3. Taylor expanded in x around 0 99.6%

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

4. Final simplification 95.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -1 \cdot 10^{+303}:\\ \;\;\;\;x \cdot \left(\frac{\frac{t - a}{b + \left(\frac{y}{z} - y\right)}}{x} + \frac{\frac{y}{z}}{b + \left(\frac{y}{z} - y\right)}\right)\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -5 \cdot 10^{-287}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 0:\\ \;\;\;\;\frac{x \cdot \frac{y}{b - y} - y \cdot \frac{t - a}{{\left(b - y\right)}^{2}}}{z} + \frac{t - a}{b - y}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 2 \cdot 10^{+290}:\\ \;\;\;\;\frac{x \cdot y}{y + z \cdot \left(b - y\right)} + \frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{\frac{t - a}{b + \left(\frac{y}{z} - y\right)}}{x} + \frac{\frac{y}{z}}{b + \left(\frac{y}{z} - y\right)}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 91.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := b + \left(\frac{y}{z} - y\right)\\ t_3 := x \cdot \left(\frac{\frac{t - a}{t\_2}}{x} + \frac{\frac{y}{z}}{t\_2}\right)\\ t_4 := z \cdot \left(t - a\right)\\ t_5 := \frac{x \cdot y + t\_4}{t\_1}\\ \mathbf{if}\;t\_5 \leq -1 \cdot 10^{+303}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_5 \leq -2 \cdot 10^{-270}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;t\_5 \leq 0 \lor \neg \left(t\_5 \leq 2 \cdot 10^{+290}\right):\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{t\_1} + \frac{t\_4}{t\_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y))))
        (t_2 (+ b (- (/ y z) y)))
        (t_3 (* x (+ (/ (/ (- t a) t_2) x) (/ (/ y z) t_2))))
        (t_4 (* z (- t a)))
        (t_5 (/ (+ (* x y) t_4) t_1)))
   (if (<= t_5 -1e+303)
     t_3
     (if (<= t_5 -2e-270)
       t_5
       (if (or (<= t_5 0.0) (not (<= t_5 2e+290)))
         t_3
         (+ (/ (* x y) t_1) (/ t_4 t_1)))))))

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 = b + ((y / z) - y);
	double t_3 = x * ((((t - a) / t_2) / x) + ((y / z) / t_2));
	double t_4 = z * (t - a);
	double t_5 = ((x * y) + t_4) / t_1;
	double tmp;
	if (t_5 <= -1e+303) {
		tmp = t_3;
	} else if (t_5 <= -2e-270) {
		tmp = t_5;
	} else if ((t_5 <= 0.0) || !(t_5 <= 2e+290)) {
		tmp = t_3;
	} else {
		tmp = ((x * y) / t_1) + (t_4 / t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_1 = y + (z * (b - y))
    t_2 = b + ((y / z) - y)
    t_3 = x * ((((t - a) / t_2) / x) + ((y / z) / t_2))
    t_4 = z * (t - a)
    t_5 = ((x * y) + t_4) / t_1
    if (t_5 <= (-1d+303)) then
        tmp = t_3
    else if (t_5 <= (-2d-270)) then
        tmp = t_5
    else if ((t_5 <= 0.0d0) .or. (.not. (t_5 <= 2d+290))) then
        tmp = t_3
    else
        tmp = ((x * y) / t_1) + (t_4 / 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 = y + (z * (b - y));
	double t_2 = b + ((y / z) - y);
	double t_3 = x * ((((t - a) / t_2) / x) + ((y / z) / t_2));
	double t_4 = z * (t - a);
	double t_5 = ((x * y) + t_4) / t_1;
	double tmp;
	if (t_5 <= -1e+303) {
		tmp = t_3;
	} else if (t_5 <= -2e-270) {
		tmp = t_5;
	} else if ((t_5 <= 0.0) || !(t_5 <= 2e+290)) {
		tmp = t_3;
	} else {
		tmp = ((x * y) / t_1) + (t_4 / t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z * (b - y))
	t_2 = b + ((y / z) - y)
	t_3 = x * ((((t - a) / t_2) / x) + ((y / z) / t_2))
	t_4 = z * (t - a)
	t_5 = ((x * y) + t_4) / t_1
	tmp = 0
	if t_5 <= -1e+303:
		tmp = t_3
	elif t_5 <= -2e-270:
		tmp = t_5
	elif (t_5 <= 0.0) or not (t_5 <= 2e+290):
		tmp = t_3
	else:
		tmp = ((x * y) / t_1) + (t_4 / t_1)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(z * Float64(b - y)))
	t_2 = Float64(b + Float64(Float64(y / z) - y))
	t_3 = Float64(x * Float64(Float64(Float64(Float64(t - a) / t_2) / x) + Float64(Float64(y / z) / t_2)))
	t_4 = Float64(z * Float64(t - a))
	t_5 = Float64(Float64(Float64(x * y) + t_4) / t_1)
	tmp = 0.0
	if (t_5 <= -1e+303)
		tmp = t_3;
	elseif (t_5 <= -2e-270)
		tmp = t_5;
	elseif ((t_5 <= 0.0) || !(t_5 <= 2e+290))
		tmp = t_3;
	else
		tmp = Float64(Float64(Float64(x * y) / t_1) + Float64(t_4 / t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (z * (b - y));
	t_2 = b + ((y / z) - y);
	t_3 = x * ((((t - a) / t_2) / x) + ((y / z) / t_2));
	t_4 = z * (t - a);
	t_5 = ((x * y) + t_4) / t_1;
	tmp = 0.0;
	if (t_5 <= -1e+303)
		tmp = t_3;
	elseif (t_5 <= -2e-270)
		tmp = t_5;
	elseif ((t_5 <= 0.0) || ~((t_5 <= 2e+290)))
		tmp = t_3;
	else
		tmp = ((x * y) / t_1) + (t_4 / t_1);
	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[(b + N[(N[(y / z), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(N[(N[(N[(t - a), $MachinePrecision] / t$95$2), $MachinePrecision] / x), $MachinePrecision] + N[(N[(y / z), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(N[(x * y), $MachinePrecision] + t$95$4), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[t$95$5, -1e+303], t$95$3, If[LessEqual[t$95$5, -2e-270], t$95$5, If[Or[LessEqual[t$95$5, 0.0], N[Not[LessEqual[t$95$5, 2e+290]], $MachinePrecision]], t$95$3, N[(N[(N[(x * y), $MachinePrecision] / t$95$1), $MachinePrecision] + N[(t$95$4 / t$95$1), $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)))) < -1e303 or -2.0000000000000001e-270 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -0.0 or 2.00000000000000012e290 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 19.7%

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

   3. Taylor expanded in z around inf 19.4%

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

   4. Taylor expanded in x around -inf 81.0%

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

      1. mul-1-neg 81.0%

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

      2. *-commutative 81.0%

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

      3. distribute-rgt-neg-in 81.0%

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

   6. Simplified 87.1%

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

   if -1e303 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -2.0000000000000001e-270

   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 -0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 2.00000000000000012e290

   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

   3. Taylor expanded in x around 0 99.6%

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

4. Final simplification 94.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -1 \cdot 10^{+303}:\\ \;\;\;\;x \cdot \left(\frac{\frac{t - a}{b + \left(\frac{y}{z} - y\right)}}{x} + \frac{\frac{y}{z}}{b + \left(\frac{y}{z} - y\right)}\right)\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -2 \cdot 10^{-270}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 0 \lor \neg \left(\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 2 \cdot 10^{+290}\right):\\ \;\;\;\;x \cdot \left(\frac{\frac{t - a}{b + \left(\frac{y}{z} - y\right)}}{x} + \frac{\frac{y}{z}}{b + \left(\frac{y}{z} - y\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{y + z \cdot \left(b - y\right)} + \frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 84.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := z \cdot \left(t - a\right)\\ t_3 := \frac{x \cdot y + t\_2}{t\_1}\\ \mathbf{if}\;t\_3 \leq -5 \cdot 10^{+284}:\\ \;\;\;\;x \cdot \left(\frac{y}{t\_1} + \frac{t\_2}{x \cdot t\_1}\right)\\ \mathbf{elif}\;t\_3 \leq -5 \cdot 10^{-287}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_3 \leq 0:\\ \;\;\;\;\frac{x \cdot \left(\left(\frac{y}{z} - \frac{a}{x}\right) + \frac{t}{x}\right)}{b}\\ \mathbf{elif}\;t\_3 \leq 2 \cdot 10^{+290}:\\ \;\;\;\;\frac{x \cdot y}{t\_1} + \frac{t\_2}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y))))
        (t_2 (* z (- t a)))
        (t_3 (/ (+ (* x y) t_2) t_1)))
   (if (<= t_3 -5e+284)
     (* x (+ (/ y t_1) (/ t_2 (* x t_1))))
     (if (<= t_3 -5e-287)
       t_3
       (if (<= t_3 0.0)
         (/ (* x (+ (- (/ y z) (/ a x)) (/ t x))) b)
         (if (<= t_3 2e+290)
           (+ (/ (* x y) t_1) (/ t_2 t_1))
           (/ (- 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 = ((x * y) + t_2) / t_1;
	double tmp;
	if (t_3 <= -5e+284) {
		tmp = x * ((y / t_1) + (t_2 / (x * t_1)));
	} else if (t_3 <= -5e-287) {
		tmp = t_3;
	} else if (t_3 <= 0.0) {
		tmp = (x * (((y / z) - (a / x)) + (t / x))) / b;
	} else if (t_3 <= 2e+290) {
		tmp = ((x * y) / t_1) + (t_2 / t_1);
	} else {
		tmp = (t - a) / (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) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = y + (z * (b - y))
    t_2 = z * (t - a)
    t_3 = ((x * y) + t_2) / t_1
    if (t_3 <= (-5d+284)) then
        tmp = x * ((y / t_1) + (t_2 / (x * t_1)))
    else if (t_3 <= (-5d-287)) then
        tmp = t_3
    else if (t_3 <= 0.0d0) then
        tmp = (x * (((y / z) - (a / x)) + (t / x))) / b
    else if (t_3 <= 2d+290) then
        tmp = ((x * y) / t_1) + (t_2 / t_1)
    else
        tmp = (t - a) / (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 = y + (z * (b - y));
	double t_2 = z * (t - a);
	double t_3 = ((x * y) + t_2) / t_1;
	double tmp;
	if (t_3 <= -5e+284) {
		tmp = x * ((y / t_1) + (t_2 / (x * t_1)));
	} else if (t_3 <= -5e-287) {
		tmp = t_3;
	} else if (t_3 <= 0.0) {
		tmp = (x * (((y / z) - (a / x)) + (t / x))) / b;
	} else if (t_3 <= 2e+290) {
		tmp = ((x * y) / t_1) + (t_2 / t_1);
	} 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 = ((x * y) + t_2) / t_1
	tmp = 0
	if t_3 <= -5e+284:
		tmp = x * ((y / t_1) + (t_2 / (x * t_1)))
	elif t_3 <= -5e-287:
		tmp = t_3
	elif t_3 <= 0.0:
		tmp = (x * (((y / z) - (a / x)) + (t / x))) / b
	elif t_3 <= 2e+290:
		tmp = ((x * y) / t_1) + (t_2 / t_1)
	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(Float64(x * y) + t_2) / t_1)
	tmp = 0.0
	if (t_3 <= -5e+284)
		tmp = Float64(x * Float64(Float64(y / t_1) + Float64(t_2 / Float64(x * t_1))));
	elseif (t_3 <= -5e-287)
		tmp = t_3;
	elseif (t_3 <= 0.0)
		tmp = Float64(Float64(x * Float64(Float64(Float64(y / z) - Float64(a / x)) + Float64(t / x))) / b);
	elseif (t_3 <= 2e+290)
		tmp = Float64(Float64(Float64(x * y) / t_1) + Float64(t_2 / t_1));
	else
		tmp = Float64(Float64(t - a) / Float64(b - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (z * (b - y));
	t_2 = z * (t - a);
	t_3 = ((x * y) + t_2) / t_1;
	tmp = 0.0;
	if (t_3 <= -5e+284)
		tmp = x * ((y / t_1) + (t_2 / (x * t_1)));
	elseif (t_3 <= -5e-287)
		tmp = t_3;
	elseif (t_3 <= 0.0)
		tmp = (x * (((y / z) - (a / x)) + (t / x))) / b;
	elseif (t_3 <= 2e+290)
		tmp = ((x * y) / t_1) + (t_2 / t_1);
	else
		tmp = (t - a) / (b - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(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[(N[(x * y), $MachinePrecision] + t$95$2), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[t$95$3, -5e+284], N[(x * N[(N[(y / t$95$1), $MachinePrecision] + N[(t$95$2 / N[(x * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, -5e-287], t$95$3, If[LessEqual[t$95$3, 0.0], N[(N[(x * N[(N[(N[(y / z), $MachinePrecision] - N[(a / x), $MachinePrecision]), $MachinePrecision] + N[(t / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[t$95$3, 2e+290], N[(N[(N[(x * y), $MachinePrecision] / t$95$1), $MachinePrecision] + N[(t$95$2 / t$95$1), $MachinePrecision]), $MachinePrecision], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -4.9999999999999999e284

   1. Initial program 21.4%

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

   3. Taylor expanded in x around inf 58.1%

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

   if -4.9999999999999999e284 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -5.00000000000000025e-287

   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 -5.00000000000000025e-287 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -0.0

   1. Initial program 40.7%

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

   3. Taylor expanded in z around inf 40.7%

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

   4. Taylor expanded in x around -inf 82.9%

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

      1. mul-1-neg 82.9%

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

      2. *-commutative 82.9%

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

      3. distribute-rgt-neg-in 82.9%

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

   6. Simplified 89.5%

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

   7. Taylor expanded in b around -inf 83.4%

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

   if -0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 2.00000000000000012e290

   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

   3. Taylor expanded in x around 0 99.6%

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

   if 2.00000000000000012e290 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 10.3%

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

   3. Taylor expanded in z around inf 78.4%

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

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -5 \cdot 10^{+284}:\\ \;\;\;\;x \cdot \left(\frac{y}{y + z \cdot \left(b - y\right)} + \frac{z \cdot \left(t - a\right)}{x \cdot \left(y + z \cdot \left(b - y\right)\right)}\right)\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -5 \cdot 10^{-287}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 0:\\ \;\;\;\;\frac{x \cdot \left(\left(\frac{y}{z} - \frac{a}{x}\right) + \frac{t}{x}\right)}{b}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 2 \cdot 10^{+290}:\\ \;\;\;\;\frac{x \cdot y}{y + z \cdot \left(b - y\right)} + \frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := \frac{t - a}{b - y}\\ t_3 := z \cdot \left(t - a\right)\\ t_4 := \frac{x \cdot y + t\_3}{t\_1}\\ \mathbf{if}\;t\_4 \leq -1 \cdot 10^{+303}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_4 \leq -5 \cdot 10^{-287}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t\_4 \leq 0:\\ \;\;\;\;\frac{x \cdot \left(\left(\frac{y}{z} - \frac{a}{x}\right) + \frac{t}{x}\right)}{b}\\ \mathbf{elif}\;t\_4 \leq 2 \cdot 10^{+290}:\\ \;\;\;\;\frac{x \cdot y}{t\_1} + \frac{t\_3}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y))))
        (t_2 (/ (- t a) (- b y)))
        (t_3 (* z (- t a)))
        (t_4 (/ (+ (* x y) t_3) t_1)))
   (if (<= t_4 -1e+303)
     t_2
     (if (<= t_4 -5e-287)
       t_4
       (if (<= t_4 0.0)
         (/ (* x (+ (- (/ y z) (/ a x)) (/ t x))) b)
         (if (<= t_4 2e+290) (+ (/ (* x y) t_1) (/ t_3 t_1)) t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double t_2 = (t - a) / (b - y);
	double t_3 = z * (t - a);
	double t_4 = ((x * y) + t_3) / t_1;
	double tmp;
	if (t_4 <= -1e+303) {
		tmp = t_2;
	} else if (t_4 <= -5e-287) {
		tmp = t_4;
	} else if (t_4 <= 0.0) {
		tmp = (x * (((y / z) - (a / x)) + (t / x))) / b;
	} else if (t_4 <= 2e+290) {
		tmp = ((x * y) / t_1) + (t_3 / 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) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = y + (z * (b - y))
    t_2 = (t - a) / (b - y)
    t_3 = z * (t - a)
    t_4 = ((x * y) + t_3) / t_1
    if (t_4 <= (-1d+303)) then
        tmp = t_2
    else if (t_4 <= (-5d-287)) then
        tmp = t_4
    else if (t_4 <= 0.0d0) then
        tmp = (x * (((y / z) - (a / x)) + (t / x))) / b
    else if (t_4 <= 2d+290) then
        tmp = ((x * y) / t_1) + (t_3 / t_1)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double t_2 = (t - a) / (b - y);
	double t_3 = z * (t - a);
	double t_4 = ((x * y) + t_3) / t_1;
	double tmp;
	if (t_4 <= -1e+303) {
		tmp = t_2;
	} else if (t_4 <= -5e-287) {
		tmp = t_4;
	} else if (t_4 <= 0.0) {
		tmp = (x * (((y / z) - (a / x)) + (t / x))) / b;
	} else if (t_4 <= 2e+290) {
		tmp = ((x * y) / t_1) + (t_3 / t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z * (b - y))
	t_2 = (t - a) / (b - y)
	t_3 = z * (t - a)
	t_4 = ((x * y) + t_3) / t_1
	tmp = 0
	if t_4 <= -1e+303:
		tmp = t_2
	elif t_4 <= -5e-287:
		tmp = t_4
	elif t_4 <= 0.0:
		tmp = (x * (((y / z) - (a / x)) + (t / x))) / b
	elif t_4 <= 2e+290:
		tmp = ((x * y) / t_1) + (t_3 / t_1)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(z * Float64(b - y)))
	t_2 = Float64(Float64(t - a) / Float64(b - y))
	t_3 = Float64(z * Float64(t - a))
	t_4 = Float64(Float64(Float64(x * y) + t_3) / t_1)
	tmp = 0.0
	if (t_4 <= -1e+303)
		tmp = t_2;
	elseif (t_4 <= -5e-287)
		tmp = t_4;
	elseif (t_4 <= 0.0)
		tmp = Float64(Float64(x * Float64(Float64(Float64(y / z) - Float64(a / x)) + Float64(t / x))) / b);
	elseif (t_4 <= 2e+290)
		tmp = Float64(Float64(Float64(x * y) / t_1) + Float64(t_3 / t_1));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (z * (b - y));
	t_2 = (t - a) / (b - y);
	t_3 = z * (t - a);
	t_4 = ((x * y) + t_3) / t_1;
	tmp = 0.0;
	if (t_4 <= -1e+303)
		tmp = t_2;
	elseif (t_4 <= -5e-287)
		tmp = t_4;
	elseif (t_4 <= 0.0)
		tmp = (x * (((y / z) - (a / x)) + (t / x))) / b;
	elseif (t_4 <= 2e+290)
		tmp = ((x * y) / t_1) + (t_3 / t_1);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(x * y), $MachinePrecision] + t$95$3), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[t$95$4, -1e+303], t$95$2, If[LessEqual[t$95$4, -5e-287], t$95$4, If[LessEqual[t$95$4, 0.0], N[(N[(x * N[(N[(N[(y / z), $MachinePrecision] - N[(a / x), $MachinePrecision]), $MachinePrecision] + N[(t / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[t$95$4, 2e+290], N[(N[(N[(x * y), $MachinePrecision] / t$95$1), $MachinePrecision] + N[(t$95$3 / t$95$1), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -1e303 or 2.00000000000000012e290 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 12.9%

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

   3. Taylor expanded in z around inf 69.0%

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

   if -1e303 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -5.00000000000000025e-287

   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 -5.00000000000000025e-287 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -0.0

   1. Initial program 40.7%

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

   3. Taylor expanded in z around inf 40.7%

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

   4. Taylor expanded in x around -inf 82.9%

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

      1. mul-1-neg 82.9%

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

      2. *-commutative 82.9%

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

      3. distribute-rgt-neg-in 82.9%

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

   6. Simplified 89.5%

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

   7. Taylor expanded in b around -inf 83.4%

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

   if -0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 2.00000000000000012e290

   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

   3. Taylor expanded in x around 0 99.6%

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

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -1 \cdot 10^{+303}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -5 \cdot 10^{-287}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 0:\\ \;\;\;\;\frac{x \cdot \left(\left(\frac{y}{z} - \frac{a}{x}\right) + \frac{t}{x}\right)}{b}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 2 \cdot 10^{+290}:\\ \;\;\;\;\frac{x \cdot y}{y + z \cdot \left(b - y\right)} + \frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 86.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+303} \lor \neg \left(t\_1 \leq -5 \cdot 10^{-287} \lor \neg \left(t\_1 \leq 0\right) \land t\_1 \leq 2 \cdot 10^{+290}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))))
   (if (or (<= t_1 -1e+303)
           (not
            (or (<= t_1 -5e-287) (and (not (<= t_1 0.0)) (<= t_1 2e+290)))))
     (/ (- t a) (- b y))
     t_1)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x * y) + (z * (t - a))) / (y + (z * (b - y)));
	double tmp;
	if ((t_1 <= -1e+303) || !((t_1 <= -5e-287) || (!(t_1 <= 0.0) && (t_1 <= 2e+290)))) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((x * y) + (z * (t - a))) / (y + (z * (b - y)))
    if ((t_1 <= (-1d+303)) .or. (.not. (t_1 <= (-5d-287)) .or. (.not. (t_1 <= 0.0d0)) .and. (t_1 <= 2d+290))) then
        tmp = (t - a) / (b - y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x * y) + (z * (t - a))) / (y + (z * (b - y)));
	double tmp;
	if ((t_1 <= -1e+303) || !((t_1 <= -5e-287) || (!(t_1 <= 0.0) && (t_1 <= 2e+290)))) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((x * y) + (z * (t - a))) / (y + (z * (b - y)))
	tmp = 0
	if (t_1 <= -1e+303) or not ((t_1 <= -5e-287) or (not (t_1 <= 0.0) and (t_1 <= 2e+290))):
		tmp = (t - a) / (b - y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(x * y) + Float64(z * Float64(t - a))) / Float64(y + Float64(z * Float64(b - y))))
	tmp = 0.0
	if ((t_1 <= -1e+303) || !((t_1 <= -5e-287) || (!(t_1 <= 0.0) && (t_1 <= 2e+290))))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((x * y) + (z * (t - a))) / (y + (z * (b - y)));
	tmp = 0.0;
	if ((t_1 <= -1e+303) || ~(((t_1 <= -5e-287) || (~((t_1 <= 0.0)) && (t_1 <= 2e+290)))))
		tmp = (t - a) / (b - y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(x * y), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e+303], N[Not[Or[LessEqual[t$95$1, -5e-287], And[N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision], LessEqual[t$95$1, 2e+290]]]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], t$95$1]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -1e303 or -5.00000000000000025e-287 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -0.0 or 2.00000000000000012e290 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 18.0%

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

   3. Taylor expanded in z around inf 71.5%

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

   if -1e303 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -5.00000000000000025e-287 or -0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 2.00000000000000012e290

   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
3. Recombined 2 regimes into one program.

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -1 \cdot 10^{+303} \lor \neg \left(\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -5 \cdot 10^{-287} \lor \neg \left(\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 0\right) \land \frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 2 \cdot 10^{+290}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 84.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ t_2 := \frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+303}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{-287}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;\frac{x \cdot \left(\left(\frac{y}{z} - \frac{a}{x}\right) + \frac{t}{x}\right)}{b}\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+290}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y)))
        (t_2 (/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))))
   (if (<= t_2 -1e+303)
     t_1
     (if (<= t_2 -5e-287)
       t_2
       (if (<= t_2 0.0)
         (/ (* x (+ (- (/ y z) (/ a x)) (/ t x))) b)
         (if (<= t_2 2e+290) t_2 t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double t_2 = ((x * y) + (z * (t - a))) / (y + (z * (b - y)));
	double tmp;
	if (t_2 <= -1e+303) {
		tmp = t_1;
	} else if (t_2 <= -5e-287) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = (x * (((y / z) - (a / x)) + (t / x))) / b;
	} else if (t_2 <= 2e+290) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    t_2 = ((x * y) + (z * (t - a))) / (y + (z * (b - y)))
    if (t_2 <= (-1d+303)) then
        tmp = t_1
    else if (t_2 <= (-5d-287)) then
        tmp = t_2
    else if (t_2 <= 0.0d0) then
        tmp = (x * (((y / z) - (a / x)) + (t / x))) / b
    else if (t_2 <= 2d+290) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double t_2 = ((x * y) + (z * (t - a))) / (y + (z * (b - y)));
	double tmp;
	if (t_2 <= -1e+303) {
		tmp = t_1;
	} else if (t_2 <= -5e-287) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = (x * (((y / z) - (a / x)) + (t / x))) / b;
	} else if (t_2 <= 2e+290) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	t_2 = ((x * y) + (z * (t - a))) / (y + (z * (b - y)))
	tmp = 0
	if t_2 <= -1e+303:
		tmp = t_1
	elif t_2 <= -5e-287:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = (x * (((y / z) - (a / x)) + (t / x))) / b
	elif t_2 <= 2e+290:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	t_2 = Float64(Float64(Float64(x * y) + Float64(z * Float64(t - a))) / Float64(y + Float64(z * Float64(b - y))))
	tmp = 0.0
	if (t_2 <= -1e+303)
		tmp = t_1;
	elseif (t_2 <= -5e-287)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = Float64(Float64(x * Float64(Float64(Float64(y / z) - Float64(a / x)) + Float64(t / x))) / b);
	elseif (t_2 <= 2e+290)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	t_2 = ((x * y) + (z * (t - a))) / (y + (z * (b - y)));
	tmp = 0.0;
	if (t_2 <= -1e+303)
		tmp = t_1;
	elseif (t_2 <= -5e-287)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = (x * (((y / z) - (a / x)) + (t / x))) / b;
	elseif (t_2 <= 2e+290)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = 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]}, If[LessEqual[t$95$2, -1e+303], t$95$1, If[LessEqual[t$95$2, -5e-287], t$95$2, If[LessEqual[t$95$2, 0.0], N[(N[(x * N[(N[(N[(y / z), $MachinePrecision] - N[(a / x), $MachinePrecision]), $MachinePrecision] + N[(t / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[t$95$2, 2e+290], t$95$2, t$95$1]]]]]]

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)))) < -1e303 or 2.00000000000000012e290 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 12.9%

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

   3. Taylor expanded in z around inf 69.0%

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

   if -1e303 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -5.00000000000000025e-287 or -0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 2.00000000000000012e290

   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 -5.00000000000000025e-287 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -0.0

   1. Initial program 40.7%

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

   3. Taylor expanded in z around inf 40.7%

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

   4. Taylor expanded in x around -inf 82.9%

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

      1. mul-1-neg 82.9%

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

      2. *-commutative 82.9%

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

      3. distribute-rgt-neg-in 82.9%

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

   6. Simplified 89.5%

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

   7. Taylor expanded in b around -inf 83.4%

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

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -1 \cdot 10^{+303}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -5 \cdot 10^{-287}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 0:\\ \;\;\;\;\frac{x \cdot \left(\left(\frac{y}{z} - \frac{a}{x}\right) + \frac{t}{x}\right)}{b}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 2 \cdot 10^{+290}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 84.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ t_2 := \frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+303}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{-287}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;\frac{z \cdot \left(\frac{t}{b} - \frac{a}{b}\right) + \frac{x \cdot y}{b}}{z}\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+290}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y)))
        (t_2 (/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))))
   (if (<= t_2 -1e+303)
     t_1
     (if (<= t_2 -5e-287)
       t_2
       (if (<= t_2 0.0)
         (/ (+ (* z (- (/ t b) (/ a b))) (/ (* x y) b)) z)
         (if (<= t_2 2e+290) t_2 t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double t_2 = ((x * y) + (z * (t - a))) / (y + (z * (b - y)));
	double tmp;
	if (t_2 <= -1e+303) {
		tmp = t_1;
	} else if (t_2 <= -5e-287) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = ((z * ((t / b) - (a / b))) + ((x * y) / b)) / z;
	} else if (t_2 <= 2e+290) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    t_2 = ((x * y) + (z * (t - a))) / (y + (z * (b - y)))
    if (t_2 <= (-1d+303)) then
        tmp = t_1
    else if (t_2 <= (-5d-287)) then
        tmp = t_2
    else if (t_2 <= 0.0d0) then
        tmp = ((z * ((t / b) - (a / b))) + ((x * y) / b)) / z
    else if (t_2 <= 2d+290) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double t_2 = ((x * y) + (z * (t - a))) / (y + (z * (b - y)));
	double tmp;
	if (t_2 <= -1e+303) {
		tmp = t_1;
	} else if (t_2 <= -5e-287) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = ((z * ((t / b) - (a / b))) + ((x * y) / b)) / z;
	} else if (t_2 <= 2e+290) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	t_2 = ((x * y) + (z * (t - a))) / (y + (z * (b - y)))
	tmp = 0
	if t_2 <= -1e+303:
		tmp = t_1
	elif t_2 <= -5e-287:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = ((z * ((t / b) - (a / b))) + ((x * y) / b)) / z
	elif t_2 <= 2e+290:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	t_2 = Float64(Float64(Float64(x * y) + Float64(z * Float64(t - a))) / Float64(y + Float64(z * Float64(b - y))))
	tmp = 0.0
	if (t_2 <= -1e+303)
		tmp = t_1;
	elseif (t_2 <= -5e-287)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = Float64(Float64(Float64(z * Float64(Float64(t / b) - Float64(a / b))) + Float64(Float64(x * y) / b)) / z);
	elseif (t_2 <= 2e+290)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	t_2 = ((x * y) + (z * (t - a))) / (y + (z * (b - y)));
	tmp = 0.0;
	if (t_2 <= -1e+303)
		tmp = t_1;
	elseif (t_2 <= -5e-287)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = ((z * ((t / b) - (a / b))) + ((x * y) / b)) / z;
	elseif (t_2 <= 2e+290)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = 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]}, If[LessEqual[t$95$2, -1e+303], t$95$1, If[LessEqual[t$95$2, -5e-287], t$95$2, If[LessEqual[t$95$2, 0.0], N[(N[(N[(z * N[(N[(t / b), $MachinePrecision] - N[(a / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$2, 2e+290], t$95$2, t$95$1]]]]]]

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)))) < -1e303 or 2.00000000000000012e290 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 12.9%

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

   3. Taylor expanded in z around inf 69.0%

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

   if -1e303 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -5.00000000000000025e-287 or -0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 2.00000000000000012e290

   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 -5.00000000000000025e-287 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -0.0

   1. Initial program 40.7%

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

   3. Taylor expanded in y around 0 40.3%

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

      1. *-commutative 40.3%

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

   5. Simplified 40.3%

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

   6. Taylor expanded in z around 0 83.2%

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

Alternative 8: 65.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y}{z \cdot \left(b + \left(\frac{y}{z} - y\right)\right)}\\ t_2 := x \cdot y + z \cdot \left(t - a\right)\\ t_3 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -2.75 \cdot 10^{+107}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{+94}:\\ \;\;\;\;\frac{t\_2}{z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq -2.5:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-77}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-228}:\\ \;\;\;\;\frac{t\_2}{y}\\ \mathbf{elif}\;z \leq 5.7 \cdot 10^{-34}:\\ \;\;\;\;\frac{t\_2}{z \cdot b}\\ \mathbf{elif}\;z \leq 750:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (/ y (* z (+ b (- (/ y z) y))))))
        (t_2 (+ (* x y) (* z (- t a))))
        (t_3 (/ (- t a) (- b y))))
   (if (<= z -2.75e+107)
     t_3
     (if (<= z -1.35e+94)
       (/ t_2 (* z (- b y)))
       (if (<= z -2.5)
         t_3
         (if (<= z -1.7e-77)
           t_1
           (if (<= z 5.8e-228)
             (/ t_2 y)
             (if (<= z 5.7e-34)
               (/ t_2 (* z b))
               (if (<= z 750.0) t_1 t_3)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * (y / (z * (b + ((y / z) - y))));
	double t_2 = (x * y) + (z * (t - a));
	double t_3 = (t - a) / (b - y);
	double tmp;
	if (z <= -2.75e+107) {
		tmp = t_3;
	} else if (z <= -1.35e+94) {
		tmp = t_2 / (z * (b - y));
	} else if (z <= -2.5) {
		tmp = t_3;
	} else if (z <= -1.7e-77) {
		tmp = t_1;
	} else if (z <= 5.8e-228) {
		tmp = t_2 / y;
	} else if (z <= 5.7e-34) {
		tmp = t_2 / (z * b);
	} else if (z <= 750.0) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x * (y / (z * (b + ((y / z) - y))))
    t_2 = (x * y) + (z * (t - a))
    t_3 = (t - a) / (b - y)
    if (z <= (-2.75d+107)) then
        tmp = t_3
    else if (z <= (-1.35d+94)) then
        tmp = t_2 / (z * (b - y))
    else if (z <= (-2.5d0)) then
        tmp = t_3
    else if (z <= (-1.7d-77)) then
        tmp = t_1
    else if (z <= 5.8d-228) then
        tmp = t_2 / y
    else if (z <= 5.7d-34) then
        tmp = t_2 / (z * b)
    else if (z <= 750.0d0) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * (y / (z * (b + ((y / z) - y))));
	double t_2 = (x * y) + (z * (t - a));
	double t_3 = (t - a) / (b - y);
	double tmp;
	if (z <= -2.75e+107) {
		tmp = t_3;
	} else if (z <= -1.35e+94) {
		tmp = t_2 / (z * (b - y));
	} else if (z <= -2.5) {
		tmp = t_3;
	} else if (z <= -1.7e-77) {
		tmp = t_1;
	} else if (z <= 5.8e-228) {
		tmp = t_2 / y;
	} else if (z <= 5.7e-34) {
		tmp = t_2 / (z * b);
	} else if (z <= 750.0) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * (y / (z * (b + ((y / z) - y))))
	t_2 = (x * y) + (z * (t - a))
	t_3 = (t - a) / (b - y)
	tmp = 0
	if z <= -2.75e+107:
		tmp = t_3
	elif z <= -1.35e+94:
		tmp = t_2 / (z * (b - y))
	elif z <= -2.5:
		tmp = t_3
	elif z <= -1.7e-77:
		tmp = t_1
	elif z <= 5.8e-228:
		tmp = t_2 / y
	elif z <= 5.7e-34:
		tmp = t_2 / (z * b)
	elif z <= 750.0:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * Float64(y / Float64(z * Float64(b + Float64(Float64(y / z) - y)))))
	t_2 = Float64(Float64(x * y) + Float64(z * Float64(t - a)))
	t_3 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -2.75e+107)
		tmp = t_3;
	elseif (z <= -1.35e+94)
		tmp = Float64(t_2 / Float64(z * Float64(b - y)));
	elseif (z <= -2.5)
		tmp = t_3;
	elseif (z <= -1.7e-77)
		tmp = t_1;
	elseif (z <= 5.8e-228)
		tmp = Float64(t_2 / y);
	elseif (z <= 5.7e-34)
		tmp = Float64(t_2 / Float64(z * b));
	elseif (z <= 750.0)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x * (y / (z * (b + ((y / z) - y))));
	t_2 = (x * y) + (z * (t - a));
	t_3 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -2.75e+107)
		tmp = t_3;
	elseif (z <= -1.35e+94)
		tmp = t_2 / (z * (b - y));
	elseif (z <= -2.5)
		tmp = t_3;
	elseif (z <= -1.7e-77)
		tmp = t_1;
	elseif (z <= 5.8e-228)
		tmp = t_2 / y;
	elseif (z <= 5.7e-34)
		tmp = t_2 / (z * b);
	elseif (z <= 750.0)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x * N[(y / N[(z * N[(b + N[(N[(y / z), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.75e+107], t$95$3, If[LessEqual[z, -1.35e+94], N[(t$95$2 / N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.5], t$95$3, If[LessEqual[z, -1.7e-77], t$95$1, If[LessEqual[z, 5.8e-228], N[(t$95$2 / y), $MachinePrecision], If[LessEqual[z, 5.7e-34], N[(t$95$2 / N[(z * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 750.0], t$95$1, t$95$3]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.7500000000000002e107 or -1.3500000000000001e94 < z < -2.5 or 750 < z

   1. Initial program 45.9%

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

   3. Taylor expanded in z around inf 85.2%

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

   if -2.7500000000000002e107 < z < -1.3500000000000001e94

   1. Initial program 99.3%

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

   3. Taylor expanded in z around inf 99.3%

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

   if -2.5 < z < -1.69999999999999991e-77 or 5.69999999999999974e-34 < z < 750

   1. Initial program 73.0%

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

   3. Taylor expanded in z around inf 70.0%

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

   4. Taylor expanded in x around inf 50.9%

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

      1. associate-/l* 77.5%

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

      2. associate-+r- 77.5%

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

   6. Simplified 77.5%

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

   if -1.69999999999999991e-77 < z < 5.8000000000000002e-228

   1. Initial program 94.5%

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

   3. Taylor expanded in z around 0 67.9%

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

   if 5.8000000000000002e-228 < z < 5.69999999999999974e-34

   1. Initial program 88.6%

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

   3. Taylor expanded in y around 0 60.7%

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

      1. *-commutative 60.7%

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

   5. Simplified 60.7%

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

Alternative 9: 73.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + z \cdot \left(t - a\right)\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -1.2 \cdot 10^{+107}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{+93}:\\ \;\;\;\;\frac{t\_1}{z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq -0.6:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-119}:\\ \;\;\;\;\frac{x}{1 - z} + \frac{z \cdot \left(a - t\right)}{y \cdot \left(z + -1\right)}\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-35}:\\ \;\;\;\;\frac{t\_1}{z \cdot b}\\ \mathbf{elif}\;z \leq 750:\\ \;\;\;\;x \cdot \frac{y}{z \cdot \left(b + \left(\frac{y}{z} - y\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* z (- t a)))) (t_2 (/ (- t a) (- b y))))
   (if (<= z -1.2e+107)
     t_2
     (if (<= z -7.5e+93)
       (/ t_1 (* z (- b y)))
       (if (<= z -0.6)
         t_2
         (if (<= z 2.8e-119)
           (+ (/ x (- 1.0 z)) (/ (* z (- a t)) (* y (+ z -1.0))))
           (if (<= z 1.55e-35)
             (/ t_1 (* z b))
             (if (<= z 750.0) (* x (/ y (* z (+ b (- (/ y z) y))))) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * y) + (z * (t - a));
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -1.2e+107) {
		tmp = t_2;
	} else if (z <= -7.5e+93) {
		tmp = t_1 / (z * (b - y));
	} else if (z <= -0.6) {
		tmp = t_2;
	} else if (z <= 2.8e-119) {
		tmp = (x / (1.0 - z)) + ((z * (a - t)) / (y * (z + -1.0)));
	} else if (z <= 1.55e-35) {
		tmp = t_1 / (z * b);
	} else if (z <= 750.0) {
		tmp = x * (y / (z * (b + ((y / z) - 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 = (x * y) + (z * (t - a))
    t_2 = (t - a) / (b - y)
    if (z <= (-1.2d+107)) then
        tmp = t_2
    else if (z <= (-7.5d+93)) then
        tmp = t_1 / (z * (b - y))
    else if (z <= (-0.6d0)) then
        tmp = t_2
    else if (z <= 2.8d-119) then
        tmp = (x / (1.0d0 - z)) + ((z * (a - t)) / (y * (z + (-1.0d0))))
    else if (z <= 1.55d-35) then
        tmp = t_1 / (z * b)
    else if (z <= 750.0d0) then
        tmp = x * (y / (z * (b + ((y / z) - 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 = (x * y) + (z * (t - a));
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -1.2e+107) {
		tmp = t_2;
	} else if (z <= -7.5e+93) {
		tmp = t_1 / (z * (b - y));
	} else if (z <= -0.6) {
		tmp = t_2;
	} else if (z <= 2.8e-119) {
		tmp = (x / (1.0 - z)) + ((z * (a - t)) / (y * (z + -1.0)));
	} else if (z <= 1.55e-35) {
		tmp = t_1 / (z * b);
	} else if (z <= 750.0) {
		tmp = x * (y / (z * (b + ((y / z) - y))));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x * y) + (z * (t - a))
	t_2 = (t - a) / (b - y)
	tmp = 0
	if z <= -1.2e+107:
		tmp = t_2
	elif z <= -7.5e+93:
		tmp = t_1 / (z * (b - y))
	elif z <= -0.6:
		tmp = t_2
	elif z <= 2.8e-119:
		tmp = (x / (1.0 - z)) + ((z * (a - t)) / (y * (z + -1.0)))
	elif z <= 1.55e-35:
		tmp = t_1 / (z * b)
	elif z <= 750.0:
		tmp = x * (y / (z * (b + ((y / z) - y))))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * y) + Float64(z * Float64(t - a)))
	t_2 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -1.2e+107)
		tmp = t_2;
	elseif (z <= -7.5e+93)
		tmp = Float64(t_1 / Float64(z * Float64(b - y)));
	elseif (z <= -0.6)
		tmp = t_2;
	elseif (z <= 2.8e-119)
		tmp = Float64(Float64(x / Float64(1.0 - z)) + Float64(Float64(z * Float64(a - t)) / Float64(y * Float64(z + -1.0))));
	elseif (z <= 1.55e-35)
		tmp = Float64(t_1 / Float64(z * b));
	elseif (z <= 750.0)
		tmp = Float64(x * Float64(y / Float64(z * Float64(b + Float64(Float64(y / z) - y)))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x * y) + (z * (t - a));
	t_2 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -1.2e+107)
		tmp = t_2;
	elseif (z <= -7.5e+93)
		tmp = t_1 / (z * (b - y));
	elseif (z <= -0.6)
		tmp = t_2;
	elseif (z <= 2.8e-119)
		tmp = (x / (1.0 - z)) + ((z * (a - t)) / (y * (z + -1.0)));
	elseif (z <= 1.55e-35)
		tmp = t_1 / (z * b);
	elseif (z <= 750.0)
		tmp = x * (y / (z * (b + ((y / z) - y))));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.2e+107], t$95$2, If[LessEqual[z, -7.5e+93], N[(t$95$1 / N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -0.6], t$95$2, If[LessEqual[z, 2.8e-119], N[(N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision] + N[(N[(z * N[(a - t), $MachinePrecision]), $MachinePrecision] / N[(y * N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.55e-35], N[(t$95$1 / N[(z * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 750.0], N[(x * N[(y / N[(z * N[(b + N[(N[(y / z), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.2e107 or -7.5000000000000002e93 < z < -0.599999999999999978 or 750 < z

   1. Initial program 45.5%

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

   3. Taylor expanded in z around inf 84.5%

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

   if -1.2e107 < z < -7.5000000000000002e93

   1. Initial program 99.3%

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

   3. Taylor expanded in z around inf 99.3%

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

   if -0.599999999999999978 < z < 2.8e-119

   1. Initial program 89.8%

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

   3. Taylor expanded in x around inf 86.4%

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

   4. Taylor expanded in b around 0 53.8%

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

      1. associate-/l* 62.7%

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

      2. associate-/l* 54.7%

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

      3. mul-1-neg 54.7%

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

      4. unsub-neg 54.7%

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

      5. *-commutative 54.7%

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

   6. Simplified 54.7%

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

   7. Taylor expanded in y around inf 67.0%

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

   if 2.8e-119 < z < 1.55000000000000006e-35

   1. Initial program 95.9%

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

   3. Taylor expanded in y around 0 69.7%

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

      1. *-commutative 69.7%

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

   5. Simplified 69.7%

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

   if 1.55000000000000006e-35 < z < 750

   1. Initial program 66.3%

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

   3. Taylor expanded in z around inf 66.3%

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

   4. Taylor expanded in x around inf 44.1%

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

      1. associate-/l* 77.5%

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

      2. associate-+r- 77.5%

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

   6. Simplified 77.5%

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

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+107}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{+93}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq -0.6:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-119}:\\ \;\;\;\;\frac{x}{1 - z} + \frac{z \cdot \left(a - t\right)}{y \cdot \left(z + -1\right)}\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-35}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{z \cdot b}\\ \mathbf{elif}\;z \leq 750:\\ \;\;\;\;x \cdot \frac{y}{z \cdot \left(b + \left(\frac{y}{z} - y\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 65.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y}{z \cdot \left(b + \left(\frac{y}{z} - y\right)\right)}\\ t_2 := \frac{t - a}{b - y}\\ t_3 := x \cdot y + z \cdot \left(t - a\right)\\ \mathbf{if}\;z \leq -2.2:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-77}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-228}:\\ \;\;\;\;\frac{t\_3}{y}\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{-33}:\\ \;\;\;\;\frac{t\_3}{z \cdot b}\\ \mathbf{elif}\;z \leq 2050:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (/ y (* z (+ b (- (/ y z) y))))))
        (t_2 (/ (- t a) (- b y)))
        (t_3 (+ (* x y) (* z (- t a)))))
   (if (<= z -2.2)
     t_2
     (if (<= z -2.5e-77)
       t_1
       (if (<= z 5.8e-228)
         (/ t_3 y)
         (if (<= z 9.8e-33) (/ t_3 (* z b)) (if (<= z 2050.0) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * (y / (z * (b + ((y / z) - y))));
	double t_2 = (t - a) / (b - y);
	double t_3 = (x * y) + (z * (t - a));
	double tmp;
	if (z <= -2.2) {
		tmp = t_2;
	} else if (z <= -2.5e-77) {
		tmp = t_1;
	} else if (z <= 5.8e-228) {
		tmp = t_3 / y;
	} else if (z <= 9.8e-33) {
		tmp = t_3 / (z * b);
	} else if (z <= 2050.0) {
		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) :: t_3
    real(8) :: tmp
    t_1 = x * (y / (z * (b + ((y / z) - y))))
    t_2 = (t - a) / (b - y)
    t_3 = (x * y) + (z * (t - a))
    if (z <= (-2.2d0)) then
        tmp = t_2
    else if (z <= (-2.5d-77)) then
        tmp = t_1
    else if (z <= 5.8d-228) then
        tmp = t_3 / y
    else if (z <= 9.8d-33) then
        tmp = t_3 / (z * b)
    else if (z <= 2050.0d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * (y / (z * (b + ((y / z) - y))));
	double t_2 = (t - a) / (b - y);
	double t_3 = (x * y) + (z * (t - a));
	double tmp;
	if (z <= -2.2) {
		tmp = t_2;
	} else if (z <= -2.5e-77) {
		tmp = t_1;
	} else if (z <= 5.8e-228) {
		tmp = t_3 / y;
	} else if (z <= 9.8e-33) {
		tmp = t_3 / (z * b);
	} else if (z <= 2050.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * (y / (z * (b + ((y / z) - y))))
	t_2 = (t - a) / (b - y)
	t_3 = (x * y) + (z * (t - a))
	tmp = 0
	if z <= -2.2:
		tmp = t_2
	elif z <= -2.5e-77:
		tmp = t_1
	elif z <= 5.8e-228:
		tmp = t_3 / y
	elif z <= 9.8e-33:
		tmp = t_3 / (z * b)
	elif z <= 2050.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * Float64(y / Float64(z * Float64(b + Float64(Float64(y / z) - y)))))
	t_2 = Float64(Float64(t - a) / Float64(b - y))
	t_3 = Float64(Float64(x * y) + Float64(z * Float64(t - a)))
	tmp = 0.0
	if (z <= -2.2)
		tmp = t_2;
	elseif (z <= -2.5e-77)
		tmp = t_1;
	elseif (z <= 5.8e-228)
		tmp = Float64(t_3 / y);
	elseif (z <= 9.8e-33)
		tmp = Float64(t_3 / Float64(z * b));
	elseif (z <= 2050.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x * (y / (z * (b + ((y / z) - y))));
	t_2 = (t - a) / (b - y);
	t_3 = (x * y) + (z * (t - a));
	tmp = 0.0;
	if (z <= -2.2)
		tmp = t_2;
	elseif (z <= -2.5e-77)
		tmp = t_1;
	elseif (z <= 5.8e-228)
		tmp = t_3 / y;
	elseif (z <= 9.8e-33)
		tmp = t_3 / (z * b);
	elseif (z <= 2050.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x * N[(y / N[(z * N[(b + N[(N[(y / z), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * y), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.2], t$95$2, If[LessEqual[z, -2.5e-77], t$95$1, If[LessEqual[z, 5.8e-228], N[(t$95$3 / y), $MachinePrecision], If[LessEqual[z, 9.8e-33], N[(t$95$3 / N[(z * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2050.0], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.2000000000000002 or 2050 < z

   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 z around inf 82.3%

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

   if -2.2000000000000002 < z < -2.49999999999999982e-77 or 9.7999999999999996e-33 < z < 2050

   1. Initial program 73.0%

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

   3. Taylor expanded in z around inf 70.0%

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

   4. Taylor expanded in x around inf 50.9%

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

      1. associate-/l* 77.5%

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

      2. associate-+r- 77.5%

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

   6. Simplified 77.5%

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

   if -2.49999999999999982e-77 < z < 5.8000000000000002e-228

   1. Initial program 94.5%

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

   3. Taylor expanded in z around 0 67.9%

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

   if 5.8000000000000002e-228 < z < 9.7999999999999996e-33

   1. Initial program 88.6%

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

   3. Taylor expanded in y around 0 60.7%

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

      1. *-commutative 60.7%

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

   5. Simplified 60.7%

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

Alternative 11: 67.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y}{z \cdot \left(b + \left(\frac{y}{z} - y\right)\right)}\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -5800:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -1.06 \cdot 10^{-77}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-173}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;z \leq 1360:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (/ y (* z (+ b (- (/ y z) y)))))) (t_2 (/ (- t a) (- b y))))
   (if (<= z -5800.0)
     t_2
     (if (<= z -1.06e-77)
       t_1
       (if (<= z 4.8e-173)
         (/ (+ (* x y) (* z (- t a))) y)
         (if (<= z 1360.0) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * (y / (z * (b + ((y / z) - y))));
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -5800.0) {
		tmp = t_2;
	} else if (z <= -1.06e-77) {
		tmp = t_1;
	} else if (z <= 4.8e-173) {
		tmp = ((x * y) + (z * (t - a))) / y;
	} else if (z <= 1360.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (y / (z * (b + ((y / z) - y))))
    t_2 = (t - a) / (b - y)
    if (z <= (-5800.0d0)) then
        tmp = t_2
    else if (z <= (-1.06d-77)) then
        tmp = t_1
    else if (z <= 4.8d-173) then
        tmp = ((x * y) + (z * (t - a))) / y
    else if (z <= 1360.0d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * (y / (z * (b + ((y / z) - y))));
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -5800.0) {
		tmp = t_2;
	} else if (z <= -1.06e-77) {
		tmp = t_1;
	} else if (z <= 4.8e-173) {
		tmp = ((x * y) + (z * (t - a))) / y;
	} else if (z <= 1360.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * (y / (z * (b + ((y / z) - y))))
	t_2 = (t - a) / (b - y)
	tmp = 0
	if z <= -5800.0:
		tmp = t_2
	elif z <= -1.06e-77:
		tmp = t_1
	elif z <= 4.8e-173:
		tmp = ((x * y) + (z * (t - a))) / y
	elif z <= 1360.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * Float64(y / Float64(z * Float64(b + Float64(Float64(y / z) - y)))))
	t_2 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -5800.0)
		tmp = t_2;
	elseif (z <= -1.06e-77)
		tmp = t_1;
	elseif (z <= 4.8e-173)
		tmp = Float64(Float64(Float64(x * y) + Float64(z * Float64(t - a))) / y);
	elseif (z <= 1360.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x * (y / (z * (b + ((y / z) - y))));
	t_2 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -5800.0)
		tmp = t_2;
	elseif (z <= -1.06e-77)
		tmp = t_1;
	elseif (z <= 4.8e-173)
		tmp = ((x * y) + (z * (t - a))) / y;
	elseif (z <= 1360.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x * N[(y / N[(z * N[(b + N[(N[(y / z), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5800.0], t$95$2, If[LessEqual[z, -1.06e-77], t$95$1, If[LessEqual[z, 4.8e-173], N[(N[(N[(x * y), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[z, 1360.0], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5800 or 1360 < z

   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 z around inf 82.3%

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

   if -5800 < z < -1.05999999999999991e-77 or 4.80000000000000034e-173 < z < 1360

   1. Initial program 80.7%

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

   3. Taylor expanded in z around inf 76.2%

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

   4. Taylor expanded in x around inf 44.5%

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

      1. associate-/l* 59.2%

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

      2. associate-+r- 59.2%

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

   6. Simplified 59.2%

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

   if -1.05999999999999991e-77 < z < 4.80000000000000034e-173

   1. Initial program 93.9%

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

   3. Taylor expanded in z around 0 62.5%

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

Alternative 12: 54.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -1 \cdot 10^{-18}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{-91}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;y \leq 440000:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;y \leq 1.32 \cdot 10^{+64}:\\ \;\;\;\;\frac{a}{y - b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (- 1.0 z))))
   (if (<= y -1e-18)
     t_1
     (if (<= y 1.95e-91)
       (/ (- t a) b)
       (if (<= y 440000.0)
         (/ t (- b y))
         (if (<= y 1.32e+64) (/ a (- y b)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 - z);
	double tmp;
	if (y <= -1e-18) {
		tmp = t_1;
	} else if (y <= 1.95e-91) {
		tmp = (t - a) / b;
	} else if (y <= 440000.0) {
		tmp = t / (b - y);
	} else if (y <= 1.32e+64) {
		tmp = a / (y - b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (1.0d0 - z)
    if (y <= (-1d-18)) then
        tmp = t_1
    else if (y <= 1.95d-91) then
        tmp = (t - a) / b
    else if (y <= 440000.0d0) then
        tmp = t / (b - y)
    else if (y <= 1.32d+64) then
        tmp = a / (y - b)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 - z);
	double tmp;
	if (y <= -1e-18) {
		tmp = t_1;
	} else if (y <= 1.95e-91) {
		tmp = (t - a) / b;
	} else if (y <= 440000.0) {
		tmp = t / (b - y);
	} else if (y <= 1.32e+64) {
		tmp = a / (y - b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (1.0 - z)
	tmp = 0
	if y <= -1e-18:
		tmp = t_1
	elif y <= 1.95e-91:
		tmp = (t - a) / b
	elif y <= 440000.0:
		tmp = t / (b - y)
	elif y <= 1.32e+64:
		tmp = a / (y - b)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(1.0 - z))
	tmp = 0.0
	if (y <= -1e-18)
		tmp = t_1;
	elseif (y <= 1.95e-91)
		tmp = Float64(Float64(t - a) / b);
	elseif (y <= 440000.0)
		tmp = Float64(t / Float64(b - y));
	elseif (y <= 1.32e+64)
		tmp = Float64(a / Float64(y - b));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (1.0 - z);
	tmp = 0.0;
	if (y <= -1e-18)
		tmp = t_1;
	elseif (y <= 1.95e-91)
		tmp = (t - a) / b;
	elseif (y <= 440000.0)
		tmp = t / (b - y);
	elseif (y <= 1.32e+64)
		tmp = a / (y - b);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1e-18], t$95$1, If[LessEqual[y, 1.95e-91], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[y, 440000.0], N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.32e+64], N[(a / N[(y - b), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.0000000000000001e-18 or 1.3200000000000001e64 < y

   1. Initial program 55.1%

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

   3. Taylor expanded in y around inf 51.2%

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

      1. mul-1-neg 51.2%

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

      2. unsub-neg 51.2%

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

   5. Simplified 51.2%

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

   if -1.0000000000000001e-18 < y < 1.94999999999999997e-91

   1. Initial program 85.4%

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

   3. Taylor expanded in y around 0 64.6%

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

   if 1.94999999999999997e-91 < y < 4.4e5

   1. Initial program 66.4%

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

   3. Taylor expanded in t around inf 46.8%

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

      1. *-commutative 46.8%

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

   5. Simplified 46.8%

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

   6. Taylor expanded in z around inf 52.3%

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

   if 4.4e5 < y < 1.3200000000000001e64

   1. Initial program 51.4%

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

   3. Taylor expanded in x around inf 50.9%

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

   4. Taylor expanded in z around inf 36.1%

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

      1. associate-/l* 35.7%

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

      2. div-sub 36.0%

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

   6. Simplified 36.0%

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

   7. Taylor expanded in t around 0 41.7%

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

      1. mul-1-neg 41.7%

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

   9. Simplified 41.7%

      \[\leadsto \color{blue}{-\frac{a}{b - y}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 56.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{-18}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{-91}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;y \leq 440000:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;y \leq 1.32 \cdot 10^{+64}:\\ \;\;\;\;\frac{a}{y - b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 54.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b}\\ t_2 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -3.8 \cdot 10^{-18}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-91}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1000000:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+58}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) b)) (t_2 (/ x (- 1.0 z))))
   (if (<= y -3.8e-18)
     t_2
     (if (<= y 1.2e-91)
       t_1
       (if (<= y 1000000.0) (/ t (- b y)) (if (<= y 2.1e+58) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / b;
	double t_2 = x / (1.0 - z);
	double tmp;
	if (y <= -3.8e-18) {
		tmp = t_2;
	} else if (y <= 1.2e-91) {
		tmp = t_1;
	} else if (y <= 1000000.0) {
		tmp = t / (b - y);
	} else if (y <= 2.1e+58) {
		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 = (t - a) / b
    t_2 = x / (1.0d0 - z)
    if (y <= (-3.8d-18)) then
        tmp = t_2
    else if (y <= 1.2d-91) then
        tmp = t_1
    else if (y <= 1000000.0d0) then
        tmp = t / (b - y)
    else if (y <= 2.1d+58) 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 = (t - a) / b;
	double t_2 = x / (1.0 - z);
	double tmp;
	if (y <= -3.8e-18) {
		tmp = t_2;
	} else if (y <= 1.2e-91) {
		tmp = t_1;
	} else if (y <= 1000000.0) {
		tmp = t / (b - y);
	} else if (y <= 2.1e+58) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / b
	t_2 = x / (1.0 - z)
	tmp = 0
	if y <= -3.8e-18:
		tmp = t_2
	elif y <= 1.2e-91:
		tmp = t_1
	elif y <= 1000000.0:
		tmp = t / (b - y)
	elif y <= 2.1e+58:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / b)
	t_2 = Float64(x / Float64(1.0 - z))
	tmp = 0.0
	if (y <= -3.8e-18)
		tmp = t_2;
	elseif (y <= 1.2e-91)
		tmp = t_1;
	elseif (y <= 1000000.0)
		tmp = Float64(t / Float64(b - y));
	elseif (y <= 2.1e+58)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / b;
	t_2 = x / (1.0 - z);
	tmp = 0.0;
	if (y <= -3.8e-18)
		tmp = t_2;
	elseif (y <= 1.2e-91)
		tmp = t_1;
	elseif (y <= 1000000.0)
		tmp = t / (b - y);
	elseif (y <= 2.1e+58)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.8e-18], t$95$2, If[LessEqual[y, 1.2e-91], t$95$1, If[LessEqual[y, 1000000.0], N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.1e+58], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.7999999999999998e-18 or 2.10000000000000012e58 < y

   1. Initial program 54.5%

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

   3. Taylor expanded in y around inf 49.9%

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

      1. mul-1-neg 49.9%

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

      2. unsub-neg 49.9%

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

   5. Simplified 49.9%

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

   if -3.7999999999999998e-18 < y < 1.20000000000000005e-91 or 1e6 < y < 2.10000000000000012e58

   1. Initial program 81.6%

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

   3. Taylor expanded in y around 0 61.1%

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

   if 1.20000000000000005e-91 < y < 1e6

   1. Initial program 66.4%

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

   3. Taylor expanded in t around inf 46.8%

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

      1. *-commutative 46.8%

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

   5. Simplified 46.8%

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

   6. Taylor expanded in z around inf 52.3%

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

Alternative 14: 62.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.7 \lor \neg \left(z \leq 900\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{y + z \cdot \left(b - y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -0.7) (not (<= z 900.0)))
   (/ (- t a) (- b y))
   (/ (* x y) (+ y (* z (- b y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -0.7) || !(z <= 900.0)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = (x * y) / (y + (z * (b - y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-0.7d0)) .or. (.not. (z <= 900.0d0))) then
        tmp = (t - a) / (b - y)
    else
        tmp = (x * y) / (y + (z * (b - y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -0.7) || !(z <= 900.0)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = (x * y) / (y + (z * (b - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -0.7) or not (z <= 900.0):
		tmp = (t - a) / (b - y)
	else:
		tmp = (x * y) / (y + (z * (b - y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -0.7) || !(z <= 900.0))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(Float64(x * y) / Float64(y + Float64(z * Float64(b - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -0.7) || ~((z <= 900.0)))
		tmp = (t - a) / (b - y);
	else
		tmp = (x * y) / (y + (z * (b - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -0.7], N[Not[LessEqual[z, 900.0]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.69999999999999996 or 900 < z

   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 z around inf 82.3%

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

   if -0.69999999999999996 < z < 900

   1. Initial program 87.3%

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

   3. Taylor expanded in x around inf 52.3%

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

      1. *-commutative 52.3%

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

   5. Simplified 52.3%

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

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.7 \lor \neg \left(z \leq 900\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{y + z \cdot \left(b - y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 54.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -1.55 \cdot 10^{-15}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-18}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+109}:\\ \;\;\;\;\frac{a - t}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (- 1.0 z))))
   (if (<= y -1.55e-15)
     t_1
     (if (<= y 7.5e-18)
       (/ (- t a) b)
       (if (<= y 5.2e+109) (/ (- a t) y) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 - z);
	double tmp;
	if (y <= -1.55e-15) {
		tmp = t_1;
	} else if (y <= 7.5e-18) {
		tmp = (t - a) / b;
	} else if (y <= 5.2e+109) {
		tmp = (a - t) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (1.0d0 - z)
    if (y <= (-1.55d-15)) then
        tmp = t_1
    else if (y <= 7.5d-18) then
        tmp = (t - a) / b
    else if (y <= 5.2d+109) then
        tmp = (a - t) / y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 - z);
	double tmp;
	if (y <= -1.55e-15) {
		tmp = t_1;
	} else if (y <= 7.5e-18) {
		tmp = (t - a) / b;
	} else if (y <= 5.2e+109) {
		tmp = (a - t) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (1.0 - z)
	tmp = 0
	if y <= -1.55e-15:
		tmp = t_1
	elif y <= 7.5e-18:
		tmp = (t - a) / b
	elif y <= 5.2e+109:
		tmp = (a - t) / y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(1.0 - z))
	tmp = 0.0
	if (y <= -1.55e-15)
		tmp = t_1;
	elseif (y <= 7.5e-18)
		tmp = Float64(Float64(t - a) / b);
	elseif (y <= 5.2e+109)
		tmp = Float64(Float64(a - t) / y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (1.0 - z);
	tmp = 0.0;
	if (y <= -1.55e-15)
		tmp = t_1;
	elseif (y <= 7.5e-18)
		tmp = (t - a) / b;
	elseif (y <= 5.2e+109)
		tmp = (a - t) / y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.55e-15], t$95$1, If[LessEqual[y, 7.5e-18], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[y, 5.2e+109], N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.5499999999999999e-15 or 5.1999999999999997e109 < y

   1. Initial program 53.6%

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

   3. Taylor expanded in y around inf 53.9%

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

      1. mul-1-neg 53.9%

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

      2. unsub-neg 53.9%

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

   5. Simplified 53.9%

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

   if -1.5499999999999999e-15 < y < 7.50000000000000015e-18

   1. Initial program 85.1%

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

   3. Taylor expanded in y around 0 61.5%

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

   if 7.50000000000000015e-18 < y < 5.1999999999999997e109

   1. Initial program 54.6%

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

   3. Taylor expanded in x around inf 48.8%

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

   4. Taylor expanded in z around inf 46.8%

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

      1. associate-/l* 46.6%

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

      2. div-sub 46.7%

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

   6. Simplified 46.7%

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

   7. Taylor expanded in b around 0 40.0%

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

      1. associate-*r/ 40.0%

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

      2. mul-1-neg 40.0%

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

   9. Simplified 40.0%

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

4. Final simplification 55.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{-15}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-18}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+109}:\\ \;\;\;\;\frac{a - t}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 37.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.4 \cdot 10^{+146}:\\ \;\;\;\;\frac{a}{-b}\\ \mathbf{elif}\;z \leq -7.4 \cdot 10^{-14} \lor \neg \left(z \leq 580\right):\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -7.4e+146)
   (/ a (- b))
   (if (or (<= z -7.4e-14) (not (<= z 580.0))) (/ t b) x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -7.4e+146) {
		tmp = a / -b;
	} else if ((z <= -7.4e-14) || !(z <= 580.0)) {
		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 <= (-7.4d+146)) then
        tmp = a / -b
    else if ((z <= (-7.4d-14)) .or. (.not. (z <= 580.0d0))) 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 <= -7.4e+146) {
		tmp = a / -b;
	} else if ((z <= -7.4e-14) || !(z <= 580.0)) {
		tmp = t / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -7.4e+146:
		tmp = a / -b
	elif (z <= -7.4e-14) or not (z <= 580.0):
		tmp = t / b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -7.4e+146)
		tmp = Float64(a / Float64(-b));
	elseif ((z <= -7.4e-14) || !(z <= 580.0))
		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 <= -7.4e+146)
		tmp = a / -b;
	elseif ((z <= -7.4e-14) || ~((z <= 580.0)))
		tmp = t / b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -7.4e+146], N[(a / (-b)), $MachinePrecision], If[Or[LessEqual[z, -7.4e-14], N[Not[LessEqual[z, 580.0]], $MachinePrecision]], N[(t / b), $MachinePrecision], x]]

Derivation

1. Split input into 3 regimes

2. if z < -7.40000000000000009e146

   1. Initial program 22.9%

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

   3. Taylor expanded in y around 0 13.6%

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

      1. *-commutative 13.6%

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

   5. Simplified 13.6%

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

   6. Taylor expanded in a around inf 29.9%

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

      1. mul-1-neg 29.9%

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

      2. distribute-neg-frac2 29.9%

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

   8. Simplified 29.9%

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

   if -7.40000000000000009e146 < z < -7.40000000000000002e-14 or 580 < z

   1. Initial program 57.8%

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

   3. Taylor expanded in t around inf 28.7%

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

      1. *-commutative 28.7%

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

   5. Simplified 28.7%

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

   6. Taylor expanded in y around 0 30.6%

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

   if -7.40000000000000002e-14 < z < 580

   1. Initial program 87.9%

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

   3. Taylor expanded in z around 0 43.3%

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

4. Final simplification 36.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.4 \cdot 10^{+146}:\\ \;\;\;\;\frac{a}{-b}\\ \mathbf{elif}\;z \leq -7.4 \cdot 10^{-14} \lor \neg \left(z \leq 580\right):\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 36.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.3 \cdot 10^{+151}:\\ \;\;\;\;\frac{a}{-b}\\ \mathbf{elif}\;z \leq -2700000000:\\ \;\;\;\;\frac{t}{-y}\\ \mathbf{elif}\;z \leq 580:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -8.3e+151)
   (/ a (- b))
   (if (<= z -2700000000.0) (/ t (- y)) (if (<= z 580.0) x (/ t b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -8.3e+151) {
		tmp = a / -b;
	} else if (z <= -2700000000.0) {
		tmp = t / -y;
	} else if (z <= 580.0) {
		tmp = x;
	} else {
		tmp = t / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-8.3d+151)) then
        tmp = a / -b
    else if (z <= (-2700000000.0d0)) then
        tmp = t / -y
    else if (z <= 580.0d0) then
        tmp = x
    else
        tmp = t / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -8.3e+151) {
		tmp = a / -b;
	} else if (z <= -2700000000.0) {
		tmp = t / -y;
	} else if (z <= 580.0) {
		tmp = x;
	} else {
		tmp = t / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -8.3e+151:
		tmp = a / -b
	elif z <= -2700000000.0:
		tmp = t / -y
	elif z <= 580.0:
		tmp = x
	else:
		tmp = t / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -8.3e+151)
		tmp = Float64(a / Float64(-b));
	elseif (z <= -2700000000.0)
		tmp = Float64(t / Float64(-y));
	elseif (z <= 580.0)
		tmp = x;
	else
		tmp = Float64(t / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -8.3e+151)
		tmp = a / -b;
	elseif (z <= -2700000000.0)
		tmp = t / -y;
	elseif (z <= 580.0)
		tmp = x;
	else
		tmp = t / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -8.3e+151], N[(a / (-b)), $MachinePrecision], If[LessEqual[z, -2700000000.0], N[(t / (-y)), $MachinePrecision], If[LessEqual[z, 580.0], x, N[(t / b), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -8.2999999999999999e151

   1. Initial program 21.2%

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

   3. Taylor expanded in y around 0 14.4%

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

      1. *-commutative 14.4%

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

   5. Simplified 14.4%

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

   6. Taylor expanded in a around inf 31.5%

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

      1. mul-1-neg 31.5%

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

      2. distribute-neg-frac2 31.5%

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

   8. Simplified 31.5%

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

   if -8.2999999999999999e151 < z < -2.7e9

   1. Initial program 69.5%

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

   3. Taylor expanded in t around inf 30.5%

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

      1. *-commutative 30.5%

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

   5. Simplified 30.5%

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

   6. Taylor expanded in z around inf 29.9%

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

   7. Taylor expanded in b around 0 32.0%

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

      1. associate-*r/ 32.0%

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

      2. mul-1-neg 32.0%

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

   9. Simplified 32.0%

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

   if -2.7e9 < z < 580

   1. Initial program 87.5%

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

   3. Taylor expanded in z around 0 42.3%

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

   if 580 < z

   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 t around inf 28.0%

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

      1. *-commutative 28.0%

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

   5. Simplified 28.0%

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

   6. Taylor expanded in y around 0 32.3%

      \[\leadsto \color{blue}{\frac{t}{b}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 37.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.3 \cdot 10^{+151}:\\ \;\;\;\;\frac{a}{-b}\\ \mathbf{elif}\;z \leq -2700000000:\\ \;\;\;\;\frac{t}{-y}\\ \mathbf{elif}\;z \leq 580:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 61.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6200 \lor \neg \left(y \leq 6.6 \cdot 10^{+106}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -6200.0) (not (<= y 6.6e+106)))
   (/ x (- 1.0 z))
   (/ (- t a) (- b y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -6200.0) || !(y <= 6.6e+106)) {
		tmp = x / (1.0 - z);
	} else {
		tmp = (t - a) / (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 <= (-6200.0d0)) .or. (.not. (y <= 6.6d+106))) then
        tmp = x / (1.0d0 - z)
    else
        tmp = (t - a) / (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 <= -6200.0) || !(y <= 6.6e+106)) {
		tmp = x / (1.0 - z);
	} else {
		tmp = (t - a) / (b - y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -6200.0) or not (y <= 6.6e+106):
		tmp = x / (1.0 - z)
	else:
		tmp = (t - a) / (b - y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -6200.0) || !(y <= 6.6e+106))
		tmp = Float64(x / Float64(1.0 - z));
	else
		tmp = Float64(Float64(t - a) / Float64(b - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -6200.0) || ~((y <= 6.6e+106)))
		tmp = x / (1.0 - z);
	else
		tmp = (t - a) / (b - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -6200.0], N[Not[LessEqual[y, 6.6e+106]], $MachinePrecision]], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6200 or 6.60000000000000015e106 < y

   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 y around inf 55.1%

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

      1. mul-1-neg 55.1%

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

      2. unsub-neg 55.1%

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

   5. Simplified 55.1%

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

   if -6200 < y < 6.60000000000000015e106

   1. Initial program 77.6%

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

   3. Taylor expanded in z around inf 67.9%

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

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6200 \lor \neg \left(y \leq 6.6 \cdot 10^{+106}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 45.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.6 \cdot 10^{-10} \lor \neg \left(z \leq 1700\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -8.6e-10) (not (<= z 1700.0))) (/ t (- b y)) (/ x (- 1.0 z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -8.6e-10) || !(z <= 1700.0)) {
		tmp = t / (b - y);
	} else {
		tmp = x / (1.0 - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-8.6d-10)) .or. (.not. (z <= 1700.0d0))) then
        tmp = t / (b - y)
    else
        tmp = x / (1.0d0 - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -8.6e-10) || !(z <= 1700.0)) {
		tmp = t / (b - y);
	} else {
		tmp = x / (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -8.6e-10) or not (z <= 1700.0):
		tmp = t / (b - y)
	else:
		tmp = x / (1.0 - z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -8.6e-10) || !(z <= 1700.0))
		tmp = Float64(t / Float64(b - y));
	else
		tmp = Float64(x / Float64(1.0 - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -8.6e-10) || ~((z <= 1700.0)))
		tmp = t / (b - y);
	else
		tmp = x / (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -8.6e-10], N[Not[LessEqual[z, 1700.0]], $MachinePrecision]], N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.60000000000000029e-10 or 1700 < z

   1. Initial program 48.5%

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

   3. Taylor expanded in t around inf 24.1%

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

      1. *-commutative 24.1%

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

   5. Simplified 24.1%

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

   6. Taylor expanded in z around inf 44.8%

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

   if -8.60000000000000029e-10 < z < 1700

   1. Initial program 87.9%

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

   3. Taylor expanded in y around inf 45.4%

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

      1. mul-1-neg 45.4%

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

      2. unsub-neg 45.4%

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

   5. Simplified 45.4%

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

4. Final simplification 45.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.6 \cdot 10^{-10} \lor \neg \left(z \leq 1700\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 44.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{-10} \lor \neg \left(z \leq 0.37\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -3.2e-10) (not (<= z 0.37))) (/ t (- b y)) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -3.2e-10) || !(z <= 0.37)) {
		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 <= (-3.2d-10)) .or. (.not. (z <= 0.37d0))) 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 <= -3.2e-10) || !(z <= 0.37)) {
		tmp = t / (b - y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -3.2e-10) or not (z <= 0.37):
		tmp = t / (b - y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -3.2e-10) || !(z <= 0.37))
		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 <= -3.2e-10) || ~((z <= 0.37)))
		tmp = t / (b - y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -3.2e-10], N[Not[LessEqual[z, 0.37]], $MachinePrecision]], N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -3.19999999999999981e-10 or 0.37 < z

   1. Initial program 48.2%

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

   3. Taylor expanded in t around inf 23.9%

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

      1. *-commutative 23.9%

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

   5. Simplified 23.9%

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

   6. Taylor expanded in z around inf 44.5%

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

   if -3.19999999999999981e-10 < z < 0.37

   1. Initial program 88.5%

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

   3. Taylor expanded in z around 0 43.6%

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

4. Final simplification 44.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{-10} \lor \neg \left(z \leq 0.37\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 36.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{-7} \lor \neg \left(z \leq 580\right):\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1e-7) (not (<= z 580.0))) (/ t b) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1e-7) || !(z <= 580.0)) {
		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 <= (-1d-7)) .or. (.not. (z <= 580.0d0))) 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 <= -1e-7) || !(z <= 580.0)) {
		tmp = t / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1e-7) or not (z <= 580.0):
		tmp = t / b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1e-7) || !(z <= 580.0))
		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 <= -1e-7) || ~((z <= 580.0)))
		tmp = t / b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1e-7], N[Not[LessEqual[z, 580.0]], $MachinePrecision]], N[(t / b), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -9.9999999999999995e-8 or 580 < z

   1. Initial program 48.5%

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

   3. Taylor expanded in t around inf 24.1%

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

      1. *-commutative 24.1%

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

   5. Simplified 24.1%

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

   6. Taylor expanded in y around 0 26.6%

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

   if -9.9999999999999995e-8 < z < 580

   1. Initial program 87.9%

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

   3. Taylor expanded in z around 0 43.3%

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

4. Final simplification 35.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{-7} \lor \neg \left(z \leq 580\right):\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 24.9% accurate, 17.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 68.4%

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

3. Taylor expanded in z around 0 23.4%

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

Developer target: 73.9% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024095 
(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)))))