Development.Shake.Progress:decay from shake-0.15.5

Percentage Accurate: 66.4% → 92.4%

Time: 18.7s

Alternatives: 18

Speedup: 0.6×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 66.4% 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: 65.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y}{z \cdot \left(b + \left(\frac{y}{z} - y\right)\right)}\\ t_2 := x \cdot y + z \cdot \left(t - a\right)\\ t_3 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -1.2 \cdot 10^{+107}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{+94}:\\ \;\;\;\;\frac{t\_2}{z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq -130:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-77}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-228}:\\ \;\;\;\;\frac{t\_2}{y}\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-37}:\\ \;\;\;\;\frac{t\_2}{z \cdot b}\\ \mathbf{elif}\;z \leq 980:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

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 -1.2e+107)
     t_3
     (if (<= z -1.35e+94)
       (/ t_2 (* z (- b y)))
       (if (<= z -130.0)
         t_3
         (if (<= z -3e-77)
           t_1
           (if (<= z 4.8e-228)
             (/ t_2 y)
             (if (<= z 9.2e-37)
               (/ t_2 (* z b))
               (if (<= z 980.0) 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 <= -1.2e+107) {
		tmp = t_3;
	} else if (z <= -1.35e+94) {
		tmp = t_2 / (z * (b - y));
	} else if (z <= -130.0) {
		tmp = t_3;
	} else if (z <= -3e-77) {
		tmp = t_1;
	} else if (z <= 4.8e-228) {
		tmp = t_2 / y;
	} else if (z <= 9.2e-37) {
		tmp = t_2 / (z * b);
	} else if (z <= 980.0) {
		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 <= (-1.2d+107)) then
        tmp = t_3
    else if (z <= (-1.35d+94)) then
        tmp = t_2 / (z * (b - y))
    else if (z <= (-130.0d0)) then
        tmp = t_3
    else if (z <= (-3d-77)) then
        tmp = t_1
    else if (z <= 4.8d-228) then
        tmp = t_2 / y
    else if (z <= 9.2d-37) then
        tmp = t_2 / (z * b)
    else if (z <= 980.0d0) 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 <= -1.2e+107) {
		tmp = t_3;
	} else if (z <= -1.35e+94) {
		tmp = t_2 / (z * (b - y));
	} else if (z <= -130.0) {
		tmp = t_3;
	} else if (z <= -3e-77) {
		tmp = t_1;
	} else if (z <= 4.8e-228) {
		tmp = t_2 / y;
	} else if (z <= 9.2e-37) {
		tmp = t_2 / (z * b);
	} else if (z <= 980.0) {
		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 <= -1.2e+107:
		tmp = t_3
	elif z <= -1.35e+94:
		tmp = t_2 / (z * (b - y))
	elif z <= -130.0:
		tmp = t_3
	elif z <= -3e-77:
		tmp = t_1
	elif z <= 4.8e-228:
		tmp = t_2 / y
	elif z <= 9.2e-37:
		tmp = t_2 / (z * b)
	elif z <= 980.0:
		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 <= -1.2e+107)
		tmp = t_3;
	elseif (z <= -1.35e+94)
		tmp = Float64(t_2 / Float64(z * Float64(b - y)));
	elseif (z <= -130.0)
		tmp = t_3;
	elseif (z <= -3e-77)
		tmp = t_1;
	elseif (z <= 4.8e-228)
		tmp = Float64(t_2 / y);
	elseif (z <= 9.2e-37)
		tmp = Float64(t_2 / Float64(z * b));
	elseif (z <= 980.0)
		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 <= -1.2e+107)
		tmp = t_3;
	elseif (z <= -1.35e+94)
		tmp = t_2 / (z * (b - y));
	elseif (z <= -130.0)
		tmp = t_3;
	elseif (z <= -3e-77)
		tmp = t_1;
	elseif (z <= 4.8e-228)
		tmp = t_2 / y;
	elseif (z <= 9.2e-37)
		tmp = t_2 / (z * b);
	elseif (z <= 980.0)
		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, -1.2e+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, -130.0], t$95$3, If[LessEqual[z, -3e-77], t$95$1, If[LessEqual[z, 4.8e-228], N[(t$95$2 / y), $MachinePrecision], If[LessEqual[z, 9.2e-37], N[(t$95$2 / N[(z * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 980.0], t$95$1, t$95$3]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.2e107 or -1.3500000000000001e94 < z < -130 or 980 < 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 -1.2e107 < 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 -130 < z < -3.00000000000000016e-77 or 9.1999999999999999e-37 < z < 980

   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 -3.00000000000000016e-77 < z < 4.80000000000000004e-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 4.80000000000000004e-228 < z < 9.1999999999999999e-37

   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. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+107}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{+94}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq -130:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-77}:\\ \;\;\;\;x \cdot \frac{y}{z \cdot \left(b + \left(\frac{y}{z} - y\right)\right)}\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-228}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-37}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{z \cdot b}\\ \mathbf{elif}\;z \leq 980:\\ \;\;\;\;x \cdot \frac{y}{z \cdot \left(b + \left(\frac{y}{z} - y\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 65.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y}{z \cdot \left(b + \left(\frac{y}{z} - y\right)\right)}\\ t_2 := \frac{t - a}{b - y}\\ t_3 := x \cdot y + z \cdot \left(t - a\right)\\ \mathbf{if}\;z \leq -40:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-77}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-228}:\\ \;\;\;\;\frac{t\_3}{y}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-33}:\\ \;\;\;\;\frac{t\_3}{z \cdot b}\\ \mathbf{elif}\;z \leq 1200:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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 -40.0)
     t_2
     (if (<= z -3.2e-77)
       t_1
       (if (<= z 5.8e-228)
         (/ t_3 y)
         (if (<= z 1.4e-33) (/ t_3 (* z b)) (if (<= z 1200.0) 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 <= -40.0) {
		tmp = t_2;
	} else if (z <= -3.2e-77) {
		tmp = t_1;
	} else if (z <= 5.8e-228) {
		tmp = t_3 / y;
	} else if (z <= 1.4e-33) {
		tmp = t_3 / (z * b);
	} else if (z <= 1200.0) {
		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 <= (-40.0d0)) then
        tmp = t_2
    else if (z <= (-3.2d-77)) then
        tmp = t_1
    else if (z <= 5.8d-228) then
        tmp = t_3 / y
    else if (z <= 1.4d-33) then
        tmp = t_3 / (z * b)
    else if (z <= 1200.0d0) 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 <= -40.0) {
		tmp = t_2;
	} else if (z <= -3.2e-77) {
		tmp = t_1;
	} else if (z <= 5.8e-228) {
		tmp = t_3 / y;
	} else if (z <= 1.4e-33) {
		tmp = t_3 / (z * b);
	} else if (z <= 1200.0) {
		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 <= -40.0:
		tmp = t_2
	elif z <= -3.2e-77:
		tmp = t_1
	elif z <= 5.8e-228:
		tmp = t_3 / y
	elif z <= 1.4e-33:
		tmp = t_3 / (z * b)
	elif z <= 1200.0:
		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 <= -40.0)
		tmp = t_2;
	elseif (z <= -3.2e-77)
		tmp = t_1;
	elseif (z <= 5.8e-228)
		tmp = Float64(t_3 / y);
	elseif (z <= 1.4e-33)
		tmp = Float64(t_3 / Float64(z * b));
	elseif (z <= 1200.0)
		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 <= -40.0)
		tmp = t_2;
	elseif (z <= -3.2e-77)
		tmp = t_1;
	elseif (z <= 5.8e-228)
		tmp = t_3 / y;
	elseif (z <= 1.4e-33)
		tmp = t_3 / (z * b);
	elseif (z <= 1200.0)
		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, -40.0], t$95$2, If[LessEqual[z, -3.2e-77], t$95$1, If[LessEqual[z, 5.8e-228], N[(t$95$3 / y), $MachinePrecision], If[LessEqual[z, 1.4e-33], N[(t$95$3 / N[(z * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1200.0], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -40 or 1200 < 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 -40 < z < -3.2e-77 or 1.4e-33 < z < 1200

   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 -3.2e-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 < 1.4e-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. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -40:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-77}:\\ \;\;\;\;x \cdot \frac{y}{z \cdot \left(b + \left(\frac{y}{z} - y\right)\right)}\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-228}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-33}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{z \cdot b}\\ \mathbf{elif}\;z \leq 1200:\\ \;\;\;\;x \cdot \frac{y}{z \cdot \left(b + \left(\frac{y}{z} - y\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 83.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ \mathbf{if}\;z \leq -1.2 \cdot 10^{+107} \lor \neg \left(z \leq 2.15 \cdot 10^{+136}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{t\_1} + \frac{z \cdot \left(t - a\right)}{x \cdot t\_1}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y)))))
   (if (or (<= z -1.2e+107) (not (<= z 2.15e+136)))
     (/ (- t a) (- b y))
     (* x (+ (/ y t_1) (/ (* z (- t a)) (* x 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 tmp;
	if ((z <= -1.2e+107) || !(z <= 2.15e+136)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x * ((y / t_1) + ((z * (t - a)) / (x * 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 = y + (z * (b - y))
    if ((z <= (-1.2d+107)) .or. (.not. (z <= 2.15d+136))) then
        tmp = (t - a) / (b - y)
    else
        tmp = x * ((y / t_1) + ((z * (t - a)) / (x * 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 tmp;
	if ((z <= -1.2e+107) || !(z <= 2.15e+136)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x * ((y / t_1) + ((z * (t - a)) / (x * t_1)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z * (b - y))
	tmp = 0
	if (z <= -1.2e+107) or not (z <= 2.15e+136):
		tmp = (t - a) / (b - y)
	else:
		tmp = x * ((y / t_1) + ((z * (t - a)) / (x * t_1)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(z * Float64(b - y)))
	tmp = 0.0
	if ((z <= -1.2e+107) || !(z <= 2.15e+136))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(x * Float64(Float64(y / t_1) + Float64(Float64(z * Float64(t - a)) / Float64(x * t_1))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (z * (b - y));
	tmp = 0.0;
	if ((z <= -1.2e+107) || ~((z <= 2.15e+136)))
		tmp = (t - a) / (b - y);
	else
		tmp = x * ((y / t_1) + ((z * (t - a)) / (x * 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]}, If[Or[LessEqual[z, -1.2e+107], N[Not[LessEqual[z, 2.15e+136]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y / t$95$1), $MachinePrecision] + N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / N[(x * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.2e107 or 2.1499999999999999e136 < z

   1. Initial program 34.0%

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

   3. Taylor expanded in z around inf 91.6%

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

   if -1.2e107 < z < 2.1499999999999999e136

   1. Initial program 84.0%

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

   3. Taylor expanded in x around inf 85.9%

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

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+107} \lor \neg \left(z \leq 2.15 \cdot 10^{+136}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{y + z \cdot \left(b - y\right)} + \frac{z \cdot \left(t - a\right)}{x \cdot \left(y + z \cdot \left(b - y\right)\right)}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 67.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y}{z \cdot \left(b + \left(\frac{y}{z} - y\right)\right)}\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -1.85:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -1.06 \cdot 10^{-77}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-173}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;z \leq 1250:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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 -1.85)
     t_2
     (if (<= z -1.06e-77)
       t_1
       (if (<= z 4.8e-173)
         (/ (+ (* x y) (* z (- t a))) y)
         (if (<= z 1250.0) 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 <= -1.85) {
		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 <= 1250.0) {
		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 <= (-1.85d0)) 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 <= 1250.0d0) 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 <= -1.85) {
		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 <= 1250.0) {
		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 <= -1.85:
		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 <= 1250.0:
		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 <= -1.85)
		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 <= 1250.0)
		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 <= -1.85)
		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 <= 1250.0)
		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, -1.85], 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, 1250.0], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.8500000000000001 or 1250 < 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 -1.8500000000000001 < z < -1.05999999999999991e-77 or 4.80000000000000034e-173 < z < 1250

   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. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.85:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -1.06 \cdot 10^{-77}:\\ \;\;\;\;x \cdot \frac{y}{z \cdot \left(b + \left(\frac{y}{z} - y\right)\right)}\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-173}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;z \leq 1250:\\ \;\;\;\;x \cdot \frac{y}{z \cdot \left(b + \left(\frac{y}{z} - y\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 83.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+107} \lor \neg \left(z \leq 2.15 \cdot 10^{+136}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.3e+107) (not (<= z 2.15e+136)))
   (/ (- t a) (- b y))
   (/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.3e+107) || !(z <= 2.15e+136)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((x * y) + (z * (t - a))) / (y + (z * (b - y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-1.3d+107)) .or. (.not. (z <= 2.15d+136))) then
        tmp = (t - a) / (b - y)
    else
        tmp = ((x * y) + (z * (t - a))) / (y + (z * (b - y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.3e+107) || !(z <= 2.15e+136)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((x * y) + (z * (t - a))) / (y + (z * (b - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.3e+107) or not (z <= 2.15e+136):
		tmp = (t - a) / (b - y)
	else:
		tmp = ((x * y) + (z * (t - a))) / (y + (z * (b - y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.3e+107) || !(z <= 2.15e+136))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(Float64(Float64(x * y) + Float64(z * Float64(t - a))) / Float64(y + Float64(z * Float64(b - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1.3e+107) || ~((z <= 2.15e+136)))
		tmp = (t - a) / (b - y);
	else
		tmp = ((x * y) + (z * (t - a))) / (y + (z * (b - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.3e+107], N[Not[LessEqual[z, 2.15e+136]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], 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]]

Derivation

1. Split input into 2 regimes

2. if z < -1.3000000000000001e107 or 2.1499999999999999e136 < z

   1. Initial program 34.0%

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

   3. Taylor expanded in z around inf 91.6%

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

   if -1.3000000000000001e107 < z < 2.1499999999999999e136

   1. Initial program 84.0%

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

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+107} \lor \neg \left(z \leq 2.15 \cdot 10^{+136}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 54.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b}\\ t_2 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -3 \cdot 10^{-16}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{-91}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 7200:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+56}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) b)) (t_2 (/ x (- 1.0 z))))
   (if (<= y -3e-16)
     t_2
     (if (<= y 1.85e-91)
       t_1
       (if (<= y 7200.0) (/ t (- b y)) (if (<= y 4e+56) 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 <= -3e-16) {
		tmp = t_2;
	} else if (y <= 1.85e-91) {
		tmp = t_1;
	} else if (y <= 7200.0) {
		tmp = t / (b - y);
	} else if (y <= 4e+56) {
		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 <= (-3d-16)) then
        tmp = t_2
    else if (y <= 1.85d-91) then
        tmp = t_1
    else if (y <= 7200.0d0) then
        tmp = t / (b - y)
    else if (y <= 4d+56) 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 <= -3e-16) {
		tmp = t_2;
	} else if (y <= 1.85e-91) {
		tmp = t_1;
	} else if (y <= 7200.0) {
		tmp = t / (b - y);
	} else if (y <= 4e+56) {
		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 <= -3e-16:
		tmp = t_2
	elif y <= 1.85e-91:
		tmp = t_1
	elif y <= 7200.0:
		tmp = t / (b - y)
	elif y <= 4e+56:
		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 <= -3e-16)
		tmp = t_2;
	elseif (y <= 1.85e-91)
		tmp = t_1;
	elseif (y <= 7200.0)
		tmp = Float64(t / Float64(b - y));
	elseif (y <= 4e+56)
		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 <= -3e-16)
		tmp = t_2;
	elseif (y <= 1.85e-91)
		tmp = t_1;
	elseif (y <= 7200.0)
		tmp = t / (b - y);
	elseif (y <= 4e+56)
		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, -3e-16], t$95$2, If[LessEqual[y, 1.85e-91], t$95$1, If[LessEqual[y, 7200.0], N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4e+56], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.99999999999999994e-16 or 4.00000000000000037e56 < 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 -2.99999999999999994e-16 < y < 1.8500000000000001e-91 or 7200 < y < 4.00000000000000037e56

   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 1.8500000000000001e-91 < y < 7200

   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. Final simplification 55.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{-16}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{-91}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;y \leq 7200:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+56}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 54.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -1.3 \cdot 10^{-16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{-91}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;y \leq 1000000:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+66}:\\ \;\;\;\;\frac{a}{y - b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (- 1.0 z))))
   (if (<= y -1.3e-16)
     t_1
     (if (<= y 1.95e-91)
       (/ (- t a) b)
       (if (<= y 1000000.0)
         (/ t (- b y))
         (if (<= y 6.5e+66) (/ 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 <= -1.3e-16) {
		tmp = t_1;
	} else if (y <= 1.95e-91) {
		tmp = (t - a) / b;
	} else if (y <= 1000000.0) {
		tmp = t / (b - y);
	} else if (y <= 6.5e+66) {
		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 <= (-1.3d-16)) then
        tmp = t_1
    else if (y <= 1.95d-91) then
        tmp = (t - a) / b
    else if (y <= 1000000.0d0) then
        tmp = t / (b - y)
    else if (y <= 6.5d+66) 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 <= -1.3e-16) {
		tmp = t_1;
	} else if (y <= 1.95e-91) {
		tmp = (t - a) / b;
	} else if (y <= 1000000.0) {
		tmp = t / (b - y);
	} else if (y <= 6.5e+66) {
		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 <= -1.3e-16:
		tmp = t_1
	elif y <= 1.95e-91:
		tmp = (t - a) / b
	elif y <= 1000000.0:
		tmp = t / (b - y)
	elif y <= 6.5e+66:
		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 <= -1.3e-16)
		tmp = t_1;
	elseif (y <= 1.95e-91)
		tmp = Float64(Float64(t - a) / b);
	elseif (y <= 1000000.0)
		tmp = Float64(t / Float64(b - y));
	elseif (y <= 6.5e+66)
		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 <= -1.3e-16)
		tmp = t_1;
	elseif (y <= 1.95e-91)
		tmp = (t - a) / b;
	elseif (y <= 1000000.0)
		tmp = t / (b - y);
	elseif (y <= 6.5e+66)
		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, -1.3e-16], t$95$1, If[LessEqual[y, 1.95e-91], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[y, 1000000.0], N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.5e+66], N[(a / N[(y - b), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.2999999999999999e-16 or 6.5000000000000001e66 < 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 -1.2999999999999999e-16 < 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 < 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%

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

   if 1e6 < y < 6.5000000000000001e66

   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%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{-16}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{-91}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;y \leq 1000000:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+66}:\\ \;\;\;\;\frac{a}{y - b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 62.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.92 \lor \neg \left(z \leq 1700\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{y + z \cdot \left(b - y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -0.92) (not (<= z 1700.0)))
   (/ (- 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 <= -0.92) || !(z <= 1700.0)) {
		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 <= (-0.92d0)) .or. (.not. (z <= 1700.0d0))) 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 <= -0.92) || !(z <= 1700.0)) {
		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 <= -0.92) or not (z <= 1700.0):
		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 <= -0.92) || !(z <= 1700.0))
		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 <= -0.92) || ~((z <= 1700.0)))
		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, -0.92], N[Not[LessEqual[z, 1700.0]], $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 < -0.92000000000000004 or 1700 < 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 -0.92000000000000004 < z < 1700

   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%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.92 \lor \neg \left(z \leq 1700\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{y + z \cdot \left(b - y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 54.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -2.4 \cdot 10^{-18}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-18}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+102}:\\ \;\;\;\;\frac{a - t}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (- 1.0 z))))
   (if (<= y -2.4e-18)
     t_1
     (if (<= y 8.2e-18)
       (/ (- t a) b)
       (if (<= y 2.7e+102) (/ (- 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 <= -2.4e-18) {
		tmp = t_1;
	} else if (y <= 8.2e-18) {
		tmp = (t - a) / b;
	} else if (y <= 2.7e+102) {
		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 <= (-2.4d-18)) then
        tmp = t_1
    else if (y <= 8.2d-18) then
        tmp = (t - a) / b
    else if (y <= 2.7d+102) 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 <= -2.4e-18) {
		tmp = t_1;
	} else if (y <= 8.2e-18) {
		tmp = (t - a) / b;
	} else if (y <= 2.7e+102) {
		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 <= -2.4e-18:
		tmp = t_1
	elif y <= 8.2e-18:
		tmp = (t - a) / b
	elif y <= 2.7e+102:
		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 <= -2.4e-18)
		tmp = t_1;
	elseif (y <= 8.2e-18)
		tmp = Float64(Float64(t - a) / b);
	elseif (y <= 2.7e+102)
		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 <= -2.4e-18)
		tmp = t_1;
	elseif (y <= 8.2e-18)
		tmp = (t - a) / b;
	elseif (y <= 2.7e+102)
		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, -2.4e-18], t$95$1, If[LessEqual[y, 8.2e-18], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[y, 2.7e+102], N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.39999999999999994e-18 or 2.7000000000000001e102 < 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 -2.39999999999999994e-18 < y < 8.1999999999999995e-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 8.1999999999999995e-18 < y < 2.7000000000000001e102

   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%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{-18}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-18}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+102}:\\ \;\;\;\;\frac{a - t}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 37.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.18 \cdot 10^{+148}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;z \leq -2.15 \cdot 10^{-6} \lor \neg \left(z \leq 580\right):\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.18e+148)
   (/ (- a) b)
   (if (or (<= z -2.15e-6) (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 <= -1.18e+148) {
		tmp = -a / b;
	} else if ((z <= -2.15e-6) || !(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 <= (-1.18d+148)) then
        tmp = -a / b
    else if ((z <= (-2.15d-6)) .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 <= -1.18e+148) {
		tmp = -a / b;
	} else if ((z <= -2.15e-6) || !(z <= 580.0)) {
		tmp = t / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1.18e+148:
		tmp = -a / b
	elif (z <= -2.15e-6) 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 <= -1.18e+148)
		tmp = Float64(Float64(-a) / b);
	elseif ((z <= -2.15e-6) || !(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 <= -1.18e+148)
		tmp = -a / b;
	elseif ((z <= -2.15e-6) || ~((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, -1.18e+148], N[((-a) / b), $MachinePrecision], If[Or[LessEqual[z, -2.15e-6], N[Not[LessEqual[z, 580.0]], $MachinePrecision]], N[(t / b), $MachinePrecision], x]]

Derivation

1. Split input into 3 regimes

2. if z < -1.18e148

   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 -1.18e148 < z < -2.15000000000000017e-6 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 -2.15000000000000017e-6 < 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%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.18 \cdot 10^{+148}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;z \leq -2.15 \cdot 10^{-6} \lor \neg \left(z \leq 580\right):\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 36.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+150}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;z \leq -2700000000:\\ \;\;\;\;\frac{t}{-y}\\ \mathbf{elif}\;z \leq 580:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -8e+150)
   (/ (- 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 <= -8e+150) {
		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 <= (-8d+150)) 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 <= -8e+150) {
		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 <= -8e+150:
		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 <= -8e+150)
		tmp = Float64(Float64(-a) / 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 <= -8e+150)
		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, -8e+150], 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 < -7.99999999999999985e150

   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 -7.99999999999999985e150 < 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%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+150}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;z \leq -2700000000:\\ \;\;\;\;\frac{t}{-y}\\ \mathbf{elif}\;z \leq 580:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 61.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -15200 \lor \neg \left(y \leq 2.05 \cdot 10^{+104}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -15200.0) (not (<= y 2.05e+104)))
   (/ 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 <= -15200.0) || !(y <= 2.05e+104)) {
		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 <= (-15200.0d0)) .or. (.not. (y <= 2.05d+104))) 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 <= -15200.0) || !(y <= 2.05e+104)) {
		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 <= -15200.0) or not (y <= 2.05e+104):
		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 <= -15200.0) || !(y <= 2.05e+104))
		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 <= -15200.0) || ~((y <= 2.05e+104)))
		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, -15200.0], N[Not[LessEqual[y, 2.05e+104]], $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 < -15200 or 2.04999999999999992e104 < 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 -15200 < y < 2.04999999999999992e104

   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%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -15200 \lor \neg \left(y \leq 2.05 \cdot 10^{+104}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 44.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{-14} \lor \neg \left(z \leq 0.29\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -6.8e-14) (not (<= z 0.29))) (/ t (- b y)) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -6.8e-14) || !(z <= 0.29)) {
		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 <= (-6.8d-14)) .or. (.not. (z <= 0.29d0))) 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 <= -6.8e-14) || !(z <= 0.29)) {
		tmp = t / (b - y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -6.8e-14) or not (z <= 0.29):
		tmp = t / (b - y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -6.8e-14) || !(z <= 0.29))
		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 <= -6.8e-14) || ~((z <= 0.29)))
		tmp = t / (b - y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -6.8e-14], N[Not[LessEqual[z, 0.29]], $MachinePrecision]], N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -6.80000000000000006e-14 or 0.28999999999999998 < 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 -6.80000000000000006e-14 < z < 0.28999999999999998

   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%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{-14} \lor \neg \left(z \leq 0.29\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 45.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{-8} \lor \neg \left(z \leq 650\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -6e-8) (not (<= z 650.0))) (/ 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 <= -6e-8) || !(z <= 650.0)) {
		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 <= (-6d-8)) .or. (.not. (z <= 650.0d0))) 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 <= -6e-8) || !(z <= 650.0)) {
		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 <= -6e-8) or not (z <= 650.0):
		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 <= -6e-8) || !(z <= 650.0))
		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 <= -6e-8) || ~((z <= 650.0)))
		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, -6e-8], N[Not[LessEqual[z, 650.0]], $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 < -5.99999999999999946e-8 or 650 < 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 -5.99999999999999946e-8 < z < 650

   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%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{-8} \lor \neg \left(z \leq 650\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 36.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{-14} \lor \neg \left(z \leq 580\right):\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -3.1e-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 <= -3.1e-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 <= (-3.1d-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 <= -3.1e-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 <= -3.1e-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 <= -3.1e-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 <= -3.1e-14) || ~((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, -3.1e-14], N[Not[LessEqual[z, 580.0]], $MachinePrecision]], N[(t / b), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -3.10000000000000004e-14 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 -3.10000000000000004e-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 2 regimes into one program.

4. Final simplification 35.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{-14} \lor \neg \left(z \leq 580\right):\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 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. Final simplification 23.4%

   \[\leadsto x \]
5. 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)))))