Development.Shake.Progress:decay from shake-0.15.5

Percentage Accurate: 66.7% → 88.8%

Time: 14.7s

Alternatives: 14

Speedup: 0.9×

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: 66.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 88.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -1.75 \cdot 10^{+68}:\\ \;\;\;\;t_1 - \frac{x}{z}\\ \mathbf{elif}\;z \leq 8:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y - z \cdot \left(y - b\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1 + \frac{\frac{y}{\frac{b - y}{x}} + \frac{a - t}{\frac{{\left(b - y\right)}^{2}}{y}}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -1.75e+68)
     (- t_1 (/ x z))
     (if (<= z 8.0)
       (/ (+ (* z (- t a)) (* x y)) (- y (* z (- y b))))
       (+
        t_1
        (/ (+ (/ y (/ (- b y) x)) (/ (- a t) (/ (pow (- b y) 2.0) y))) z))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -1.75e+68) {
		tmp = t_1 - (x / z);
	} else if (z <= 8.0) {
		tmp = ((z * (t - a)) + (x * y)) / (y - (z * (y - b)));
	} else {
		tmp = t_1 + (((y / ((b - y) / x)) + ((a - t) / (pow((b - y), 2.0) / y))) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    if (z <= (-1.75d+68)) then
        tmp = t_1 - (x / z)
    else if (z <= 8.0d0) then
        tmp = ((z * (t - a)) + (x * y)) / (y - (z * (y - b)))
    else
        tmp = t_1 + (((y / ((b - y) / x)) + ((a - t) / (((b - y) ** 2.0d0) / y))) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -1.75e+68) {
		tmp = t_1 - (x / z);
	} else if (z <= 8.0) {
		tmp = ((z * (t - a)) + (x * y)) / (y - (z * (y - b)));
	} else {
		tmp = t_1 + (((y / ((b - y) / x)) + ((a - t) / (Math.pow((b - y), 2.0) / y))) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	tmp = 0
	if z <= -1.75e+68:
		tmp = t_1 - (x / z)
	elif z <= 8.0:
		tmp = ((z * (t - a)) + (x * y)) / (y - (z * (y - b)))
	else:
		tmp = t_1 + (((y / ((b - y) / x)) + ((a - t) / (math.pow((b - y), 2.0) / y))) / z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -1.75e+68)
		tmp = Float64(t_1 - Float64(x / z));
	elseif (z <= 8.0)
		tmp = Float64(Float64(Float64(z * Float64(t - a)) + Float64(x * y)) / Float64(y - Float64(z * Float64(y - b))));
	else
		tmp = Float64(t_1 + Float64(Float64(Float64(y / Float64(Float64(b - y) / x)) + Float64(Float64(a - t) / Float64((Float64(b - y) ^ 2.0) / y))) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -1.75e+68)
		tmp = t_1 - (x / z);
	elseif (z <= 8.0)
		tmp = ((z * (t - a)) + (x * y)) / (y - (z * (y - b)));
	else
		tmp = t_1 + (((y / ((b - y) / x)) + ((a - t) / (((b - y) ^ 2.0) / y))) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.75e+68], N[(t$95$1 - N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.0], N[(N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] / N[(y - N[(z * N[(y - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(N[(N[(y / N[(N[(b - y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] + N[(N[(a - t), $MachinePrecision] / N[(N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.74999999999999989e68

   1. Initial program 26.3%

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

   2. Taylor expanded in z around -inf 57.1%

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

      1. +-commutative 57.1%

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

      2. associate--l+ 57.1%

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

   4. Simplified 91.3%

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

   5. Taylor expanded in y around inf 95.0%

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

      1. associate-*r/ 95.0%

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

      2. mul-1-neg 95.0%

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

   7. Simplified 95.0%

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

   if -1.74999999999999989e68 < z < 8

   1. Initial program 86.9%

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

   if 8 < z

   1. Initial program 41.1%

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

   2. Taylor expanded in z around -inf 71.9%

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

      1. +-commutative 71.9%

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

      2. associate--l+ 71.9%

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

   4. Simplified 96.1%

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

4. Final simplification 91.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+68}:\\ \;\;\;\;\frac{t - a}{b - y} - \frac{x}{z}\\ \mathbf{elif}\;z \leq 8:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y - z \cdot \left(y - b\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y} + \frac{\frac{y}{\frac{b - y}{x}} + \frac{a - t}{\frac{{\left(b - y\right)}^{2}}{y}}}{z}\\ \end{array} \]

Alternative 2: 63.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y} - \frac{x}{z}\\ \mathbf{if}\;z \leq -7 \cdot 10^{-6}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-68}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-302}:\\ \;\;\;\;\frac{t - a}{\left(b + \frac{y}{z}\right) - y}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-14}:\\ \;\;\;\;\frac{x \cdot y - z \cdot a}{y - z \cdot y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (/ (- t a) (- b y)) (/ x z))))
   (if (<= z -7e-6)
     t_1
     (if (<= z -6.2e-68)
       (/ x (- 1.0 z))
       (if (<= z -8e-302)
         (/ (- t a) (- (+ b (/ y z)) y))
         (if (<= z 1.1e-14) (/ (- (* x y) (* z a)) (- y (* z y))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((t - a) / (b - y)) - (x / z);
	double tmp;
	if (z <= -7e-6) {
		tmp = t_1;
	} else if (z <= -6.2e-68) {
		tmp = x / (1.0 - z);
	} else if (z <= -8e-302) {
		tmp = (t - a) / ((b + (y / z)) - y);
	} else if (z <= 1.1e-14) {
		tmp = ((x * y) - (z * a)) / (y - (z * y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((t - a) / (b - y)) - (x / z)
    if (z <= (-7d-6)) then
        tmp = t_1
    else if (z <= (-6.2d-68)) then
        tmp = x / (1.0d0 - z)
    else if (z <= (-8d-302)) then
        tmp = (t - a) / ((b + (y / z)) - y)
    else if (z <= 1.1d-14) then
        tmp = ((x * y) - (z * a)) / (y - (z * y))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((t - a) / (b - y)) - (x / z);
	double tmp;
	if (z <= -7e-6) {
		tmp = t_1;
	} else if (z <= -6.2e-68) {
		tmp = x / (1.0 - z);
	} else if (z <= -8e-302) {
		tmp = (t - a) / ((b + (y / z)) - y);
	} else if (z <= 1.1e-14) {
		tmp = ((x * y) - (z * a)) / (y - (z * y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((t - a) / (b - y)) - (x / z)
	tmp = 0
	if z <= -7e-6:
		tmp = t_1
	elif z <= -6.2e-68:
		tmp = x / (1.0 - z)
	elif z <= -8e-302:
		tmp = (t - a) / ((b + (y / z)) - y)
	elif z <= 1.1e-14:
		tmp = ((x * y) - (z * a)) / (y - (z * y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(t - a) / Float64(b - y)) - Float64(x / z))
	tmp = 0.0
	if (z <= -7e-6)
		tmp = t_1;
	elseif (z <= -6.2e-68)
		tmp = Float64(x / Float64(1.0 - z));
	elseif (z <= -8e-302)
		tmp = Float64(Float64(t - a) / Float64(Float64(b + Float64(y / z)) - y));
	elseif (z <= 1.1e-14)
		tmp = Float64(Float64(Float64(x * y) - Float64(z * a)) / Float64(y - Float64(z * y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((t - a) / (b - y)) - (x / z);
	tmp = 0.0;
	if (z <= -7e-6)
		tmp = t_1;
	elseif (z <= -6.2e-68)
		tmp = x / (1.0 - z);
	elseif (z <= -8e-302)
		tmp = (t - a) / ((b + (y / z)) - y);
	elseif (z <= 1.1e-14)
		tmp = ((x * y) - (z * a)) / (y - (z * y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision] - N[(x / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7e-6], t$95$1, If[LessEqual[z, -6.2e-68], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -8e-302], N[(N[(t - a), $MachinePrecision] / N[(N[(b + N[(y / z), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.1e-14], N[(N[(N[(x * y), $MachinePrecision] - N[(z * a), $MachinePrecision]), $MachinePrecision] / N[(y - N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -6.99999999999999989e-6 or 1.1e-14 < z

   1. Initial program 40.1%

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

   2. Taylor expanded in z around -inf 64.4%

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

      1. +-commutative 64.4%

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

      2. associate--l+ 64.4%

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

   4. Simplified 92.3%

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

   5. Taylor expanded in y around inf 84.9%

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

      1. associate-*r/ 84.9%

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

      2. mul-1-neg 84.9%

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

   7. Simplified 84.9%

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

   if -6.99999999999999989e-6 < z < -6.1999999999999999e-68

   1. Initial program 60.5%

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

   2. Taylor expanded in y around inf 85.9%

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

      1. +-commutative 85.9%

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

      2. mul-1-neg 85.9%

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

      3. unsub-neg 85.9%

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

   4. Simplified 85.9%

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

   if -6.1999999999999999e-68 < z < -7.9999999999999997e-302

   1. Initial program 83.1%

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

   2. Taylor expanded in x around 0 49.6%

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

      1. associate-/l* 53.7%

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

      2. +-commutative 53.7%

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

      3. *-commutative 53.7%

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

      4. fma-udef 53.7%

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

   4. Simplified 53.7%

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

   5. Taylor expanded in z around 0 53.7%

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

   if -7.9999999999999997e-302 < z < 1.1e-14

   1. Initial program 91.8%

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

   2. Taylor expanded in b around 0 72.4%

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

      1. mul-1-neg 72.4%

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

      2. distribute-lft-neg-out 72.4%

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

      3. *-commutative 72.4%

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

   4. Simplified 72.4%

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

   5. Taylor expanded in t around 0 65.8%

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

      1. mul-1-neg 65.8%

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

      2. unsub-neg 65.8%

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

      3. mul-1-neg 65.8%

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

      4. unsub-neg 65.8%

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

   7. Simplified 65.8%

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

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{-6}:\\ \;\;\;\;\frac{t - a}{b - y} - \frac{x}{z}\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-68}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-302}:\\ \;\;\;\;\frac{t - a}{\left(b + \frac{y}{z}\right) - y}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-14}:\\ \;\;\;\;\frac{x \cdot y - z \cdot a}{y - z \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y} - \frac{x}{z}\\ \end{array} \]

Alternative 3: 86.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+72} \lor \neg \left(z \leq 21000000000000\right):\\ \;\;\;\;\frac{t - a}{b - y} - \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y - z \cdot \left(y - b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -4.2e+72) (not (<= z 21000000000000.0)))
   (- (/ (- t a) (- b y)) (/ x z))
   (/ (+ (* z (- t a)) (* x y)) (- y (* z (- y b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -4.2e+72) || !(z <= 21000000000000.0)) {
		tmp = ((t - a) / (b - y)) - (x / z);
	} else {
		tmp = ((z * (t - a)) + (x * y)) / (y - (z * (y - b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-4.2d+72)) .or. (.not. (z <= 21000000000000.0d0))) then
        tmp = ((t - a) / (b - y)) - (x / z)
    else
        tmp = ((z * (t - a)) + (x * y)) / (y - (z * (y - b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -4.2e+72) || !(z <= 21000000000000.0)) {
		tmp = ((t - a) / (b - y)) - (x / z);
	} else {
		tmp = ((z * (t - a)) + (x * y)) / (y - (z * (y - b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -4.2e+72) or not (z <= 21000000000000.0):
		tmp = ((t - a) / (b - y)) - (x / z)
	else:
		tmp = ((z * (t - a)) + (x * y)) / (y - (z * (y - b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -4.2e+72) || !(z <= 21000000000000.0))
		tmp = Float64(Float64(Float64(t - a) / Float64(b - y)) - Float64(x / z));
	else
		tmp = Float64(Float64(Float64(z * Float64(t - a)) + Float64(x * y)) / Float64(y - Float64(z * Float64(y - b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -4.2e+72) || ~((z <= 21000000000000.0)))
		tmp = ((t - a) / (b - y)) - (x / z);
	else
		tmp = ((z * (t - a)) + (x * y)) / (y - (z * (y - b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -4.2e+72], N[Not[LessEqual[z, 21000000000000.0]], $MachinePrecision]], N[(N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision] - N[(x / z), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] / N[(y - N[(z * N[(y - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.2000000000000003e72 or 2.1e13 < z

   1. Initial program 33.8%

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

   2. Taylor expanded in z around -inf 65.4%

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

      1. +-commutative 65.4%

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

      2. associate--l+ 65.4%

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

   4. Simplified 94.5%

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

   5. Taylor expanded in y around inf 88.8%

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

      1. associate-*r/ 88.8%

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

      2. mul-1-neg 88.8%

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

   7. Simplified 88.8%

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

   if -4.2000000000000003e72 < z < 2.1e13

   1. Initial program 86.5%

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

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+72} \lor \neg \left(z \leq 21000000000000\right):\\ \;\;\;\;\frac{t - a}{b - y} - \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y - z \cdot \left(y - b\right)}\\ \end{array} \]

Alternative 4: 62.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y} - \frac{x}{z}\\ \mathbf{if}\;z \leq -1.76 \cdot 10^{-13}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{-73}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-302}:\\ \;\;\;\;\frac{t - a}{\left(b + \frac{y}{z}\right) - y}\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-13}:\\ \;\;\;\;\frac{x \cdot y}{y - z \cdot \left(y - b\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (/ (- t a) (- b y)) (/ x z))))
   (if (<= z -1.76e-13)
     t_1
     (if (<= z -8.2e-73)
       (/ x (- 1.0 z))
       (if (<= z 1.55e-302)
         (/ (- t a) (- (+ b (/ y z)) y))
         (if (<= z 1.02e-13) (/ (* x y) (- y (* z (- y b)))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((t - a) / (b - y)) - (x / z);
	double tmp;
	if (z <= -1.76e-13) {
		tmp = t_1;
	} else if (z <= -8.2e-73) {
		tmp = x / (1.0 - z);
	} else if (z <= 1.55e-302) {
		tmp = (t - a) / ((b + (y / z)) - y);
	} else if (z <= 1.02e-13) {
		tmp = (x * y) / (y - (z * (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 = ((t - a) / (b - y)) - (x / z)
    if (z <= (-1.76d-13)) then
        tmp = t_1
    else if (z <= (-8.2d-73)) then
        tmp = x / (1.0d0 - z)
    else if (z <= 1.55d-302) then
        tmp = (t - a) / ((b + (y / z)) - y)
    else if (z <= 1.02d-13) then
        tmp = (x * y) / (y - (z * (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 = ((t - a) / (b - y)) - (x / z);
	double tmp;
	if (z <= -1.76e-13) {
		tmp = t_1;
	} else if (z <= -8.2e-73) {
		tmp = x / (1.0 - z);
	} else if (z <= 1.55e-302) {
		tmp = (t - a) / ((b + (y / z)) - y);
	} else if (z <= 1.02e-13) {
		tmp = (x * y) / (y - (z * (y - b)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((t - a) / (b - y)) - (x / z)
	tmp = 0
	if z <= -1.76e-13:
		tmp = t_1
	elif z <= -8.2e-73:
		tmp = x / (1.0 - z)
	elif z <= 1.55e-302:
		tmp = (t - a) / ((b + (y / z)) - y)
	elif z <= 1.02e-13:
		tmp = (x * y) / (y - (z * (y - b)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(t - a) / Float64(b - y)) - Float64(x / z))
	tmp = 0.0
	if (z <= -1.76e-13)
		tmp = t_1;
	elseif (z <= -8.2e-73)
		tmp = Float64(x / Float64(1.0 - z));
	elseif (z <= 1.55e-302)
		tmp = Float64(Float64(t - a) / Float64(Float64(b + Float64(y / z)) - y));
	elseif (z <= 1.02e-13)
		tmp = Float64(Float64(x * y) / Float64(y - Float64(z * Float64(y - b))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((t - a) / (b - y)) - (x / z);
	tmp = 0.0;
	if (z <= -1.76e-13)
		tmp = t_1;
	elseif (z <= -8.2e-73)
		tmp = x / (1.0 - z);
	elseif (z <= 1.55e-302)
		tmp = (t - a) / ((b + (y / z)) - y);
	elseif (z <= 1.02e-13)
		tmp = (x * y) / (y - (z * (y - b)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision] - N[(x / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.76e-13], t$95$1, If[LessEqual[z, -8.2e-73], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.55e-302], N[(N[(t - a), $MachinePrecision] / N[(N[(b + N[(y / z), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.02e-13], N[(N[(x * y), $MachinePrecision] / N[(y - N[(z * N[(y - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.7600000000000001e-13 or 1.0199999999999999e-13 < z

   1. Initial program 40.1%

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

   2. Taylor expanded in z around -inf 64.4%

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

      1. +-commutative 64.4%

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

      2. associate--l+ 64.4%

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

   4. Simplified 92.3%

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

   5. Taylor expanded in y around inf 84.9%

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

      1. associate-*r/ 84.9%

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

      2. mul-1-neg 84.9%

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

   7. Simplified 84.9%

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

   if -1.7600000000000001e-13 < z < -8.20000000000000032e-73

   1. Initial program 60.5%

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

   2. Taylor expanded in y around inf 85.9%

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

      1. +-commutative 85.9%

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

      2. mul-1-neg 85.9%

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

      3. unsub-neg 85.9%

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

   4. Simplified 85.9%

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

   if -8.20000000000000032e-73 < z < 1.54999999999999992e-302

   1. Initial program 83.5%

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

   2. Taylor expanded in x around 0 50.7%

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

      1. associate-/l* 54.7%

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

      2. +-commutative 54.7%

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

      3. *-commutative 54.7%

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

      4. fma-udef 54.7%

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

   4. Simplified 54.7%

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

   5. Taylor expanded in z around 0 54.7%

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

   if 1.54999999999999992e-302 < z < 1.0199999999999999e-13

   1. Initial program 91.7%

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

   2. Taylor expanded in x around inf 57.1%

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

4. Final simplification 73.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.76 \cdot 10^{-13}:\\ \;\;\;\;\frac{t - a}{b - y} - \frac{x}{z}\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{-73}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-302}:\\ \;\;\;\;\frac{t - a}{\left(b + \frac{y}{z}\right) - y}\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-13}:\\ \;\;\;\;\frac{x \cdot y}{y - z \cdot \left(y - b\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y} - \frac{x}{z}\\ \end{array} \]

Alternative 5: 64.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t - a \leq -1 \cdot 10^{-104} \lor \neg \left(t - a \leq 10^{+14}\right):\\ \;\;\;\;\frac{t - a}{\left(b + \frac{y}{z}\right) - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= (- t a) -1e-104) (not (<= (- t a) 1e+14)))
   (/ (- t a) (- (+ b (/ y z)) y))
   (/ x (- 1.0 z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((t - a) <= -1e-104) || !((t - a) <= 1e+14)) {
		tmp = (t - a) / ((b + (y / z)) - y);
	} else {
		tmp = x / (1.0 - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (((t - a) <= (-1d-104)) .or. (.not. ((t - a) <= 1d+14))) then
        tmp = (t - a) / ((b + (y / z)) - y)
    else
        tmp = x / (1.0d0 - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((t - a) <= -1e-104) || !((t - a) <= 1e+14)) {
		tmp = (t - a) / ((b + (y / z)) - y);
	} else {
		tmp = x / (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if ((t - a) <= -1e-104) or not ((t - a) <= 1e+14):
		tmp = (t - a) / ((b + (y / z)) - y)
	else:
		tmp = x / (1.0 - z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((Float64(t - a) <= -1e-104) || !(Float64(t - a) <= 1e+14))
		tmp = Float64(Float64(t - a) / Float64(Float64(b + Float64(y / z)) - y));
	else
		tmp = Float64(x / Float64(1.0 - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (((t - a) <= -1e-104) || ~(((t - a) <= 1e+14)))
		tmp = (t - a) / ((b + (y / z)) - y);
	else
		tmp = x / (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[N[(t - a), $MachinePrecision], -1e-104], N[Not[LessEqual[N[(t - a), $MachinePrecision], 1e+14]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(N[(b + N[(y / z), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 t a) < -9.99999999999999927e-105 or 1e14 < (-.f64 t a)

   1. Initial program 57.1%

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

   2. Taylor expanded in x around 0 40.6%

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

      1. associate-/l* 48.5%

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

      2. +-commutative 48.5%

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

      3. *-commutative 48.5%

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

      4. fma-udef 48.5%

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

   4. Simplified 48.5%

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

   5. Taylor expanded in z around 0 71.8%

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

   if -9.99999999999999927e-105 < (-.f64 t a) < 1e14

   1. Initial program 73.1%

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

   2. Taylor expanded in y around inf 58.6%

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

      1. +-commutative 58.6%

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

      2. mul-1-neg 58.6%

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

      3. unsub-neg 58.6%

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

   4. Simplified 58.6%

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

4. Final simplification 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t - a \leq -1 \cdot 10^{-104} \lor \neg \left(t - a \leq 10^{+14}\right):\\ \;\;\;\;\frac{t - a}{\left(b + \frac{y}{z}\right) - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]

Alternative 6: 85.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.7 \lor \neg \left(z \leq 6000000000000\right):\\ \;\;\;\;\frac{t - a}{b - y} - \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -3.7) (not (<= z 6000000000000.0)))
   (- (/ (- t a) (- b y)) (/ x z))
   (/ (+ (* z (- t a)) (* x y)) (+ y (* z b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -3.7) || !(z <= 6000000000000.0)) {
		tmp = ((t - a) / (b - y)) - (x / z);
	} else {
		tmp = ((z * (t - a)) + (x * y)) / (y + (z * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-3.7d0)) .or. (.not. (z <= 6000000000000.0d0))) then
        tmp = ((t - a) / (b - y)) - (x / z)
    else
        tmp = ((z * (t - a)) + (x * y)) / (y + (z * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -3.7) || !(z <= 6000000000000.0)) {
		tmp = ((t - a) / (b - y)) - (x / z);
	} else {
		tmp = ((z * (t - a)) + (x * y)) / (y + (z * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -3.7) or not (z <= 6000000000000.0):
		tmp = ((t - a) / (b - y)) - (x / z)
	else:
		tmp = ((z * (t - a)) + (x * y)) / (y + (z * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -3.7) || !(z <= 6000000000000.0))
		tmp = Float64(Float64(Float64(t - a) / Float64(b - y)) - Float64(x / z));
	else
		tmp = Float64(Float64(Float64(z * Float64(t - a)) + Float64(x * y)) / Float64(y + Float64(z * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -3.7) || ~((z <= 6000000000000.0)))
		tmp = ((t - a) / (b - y)) - (x / z);
	else
		tmp = ((z * (t - a)) + (x * y)) / (y + (z * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -3.7], N[Not[LessEqual[z, 6000000000000.0]], $MachinePrecision]], N[(N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision] - N[(x / z), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.7000000000000002 or 6e12 < z

   1. Initial program 36.9%

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

   2. Taylor expanded in z around -inf 64.8%

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

      1. +-commutative 64.8%

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

      2. associate--l+ 64.8%

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

   4. Simplified 94.5%

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

   5. Taylor expanded in y around inf 87.8%

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

      1. associate-*r/ 87.8%

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

      2. mul-1-neg 87.8%

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

   7. Simplified 87.8%

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

   if -3.7000000000000002 < z < 6e12

   1. Initial program 86.5%

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

   2. Taylor expanded in b around inf 84.9%

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

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.7 \lor \neg \left(z \leq 6000000000000\right):\\ \;\;\;\;\frac{t - a}{b - y} - \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot b}\\ \end{array} \]

Alternative 7: 41.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 - z}\\ t_2 := \frac{-a}{b}\\ \mathbf{if}\;y \leq -1.95 \cdot 10^{+37}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -9 \cdot 10^{-66}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{-94}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-305}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 6.7 \cdot 10^{-103}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;y \leq 1.55:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (- 1.0 z))) (t_2 (/ (- a) b)))
   (if (<= y -1.95e+37)
     t_1
     (if (<= y -9e-66)
       (/ t b)
       (if (<= y -7.5e-94)
         t_1
         (if (<= y -1.8e-305)
           t_2
           (if (<= y 6.7e-103) (/ t b) (if (<= y 1.55) t_2 t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 - z);
	double t_2 = -a / b;
	double tmp;
	if (y <= -1.95e+37) {
		tmp = t_1;
	} else if (y <= -9e-66) {
		tmp = t / b;
	} else if (y <= -7.5e-94) {
		tmp = t_1;
	} else if (y <= -1.8e-305) {
		tmp = t_2;
	} else if (y <= 6.7e-103) {
		tmp = t / b;
	} else if (y <= 1.55) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x / (1.0d0 - z)
    t_2 = -a / b
    if (y <= (-1.95d+37)) then
        tmp = t_1
    else if (y <= (-9d-66)) then
        tmp = t / b
    else if (y <= (-7.5d-94)) then
        tmp = t_1
    else if (y <= (-1.8d-305)) then
        tmp = t_2
    else if (y <= 6.7d-103) then
        tmp = t / b
    else if (y <= 1.55d0) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 - z);
	double t_2 = -a / b;
	double tmp;
	if (y <= -1.95e+37) {
		tmp = t_1;
	} else if (y <= -9e-66) {
		tmp = t / b;
	} else if (y <= -7.5e-94) {
		tmp = t_1;
	} else if (y <= -1.8e-305) {
		tmp = t_2;
	} else if (y <= 6.7e-103) {
		tmp = t / b;
	} else if (y <= 1.55) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (1.0 - z)
	t_2 = -a / b
	tmp = 0
	if y <= -1.95e+37:
		tmp = t_1
	elif y <= -9e-66:
		tmp = t / b
	elif y <= -7.5e-94:
		tmp = t_1
	elif y <= -1.8e-305:
		tmp = t_2
	elif y <= 6.7e-103:
		tmp = t / b
	elif y <= 1.55:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(1.0 - z))
	t_2 = Float64(Float64(-a) / b)
	tmp = 0.0
	if (y <= -1.95e+37)
		tmp = t_1;
	elseif (y <= -9e-66)
		tmp = Float64(t / b);
	elseif (y <= -7.5e-94)
		tmp = t_1;
	elseif (y <= -1.8e-305)
		tmp = t_2;
	elseif (y <= 6.7e-103)
		tmp = Float64(t / b);
	elseif (y <= 1.55)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (1.0 - z);
	t_2 = -a / b;
	tmp = 0.0;
	if (y <= -1.95e+37)
		tmp = t_1;
	elseif (y <= -9e-66)
		tmp = t / b;
	elseif (y <= -7.5e-94)
		tmp = t_1;
	elseif (y <= -1.8e-305)
		tmp = t_2;
	elseif (y <= 6.7e-103)
		tmp = t / b;
	elseif (y <= 1.55)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[((-a) / b), $MachinePrecision]}, If[LessEqual[y, -1.95e+37], t$95$1, If[LessEqual[y, -9e-66], N[(t / b), $MachinePrecision], If[LessEqual[y, -7.5e-94], t$95$1, If[LessEqual[y, -1.8e-305], t$95$2, If[LessEqual[y, 6.7e-103], N[(t / b), $MachinePrecision], If[LessEqual[y, 1.55], t$95$2, t$95$1]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.9499999999999999e37 or -8.9999999999999995e-66 < y < -7.5000000000000003e-94 or 1.55000000000000004 < y

   1. Initial program 44.2%

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

   2. Taylor expanded in y around inf 50.2%

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

      1. +-commutative 50.2%

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

      2. mul-1-neg 50.2%

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

      3. unsub-neg 50.2%

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

   4. Simplified 50.2%

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

   if -1.9499999999999999e37 < y < -8.9999999999999995e-66 or -1.80000000000000002e-305 < y < 6.69999999999999993e-103

   1. Initial program 78.5%

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

   2. Taylor expanded in b around inf 48.4%

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

   3. Taylor expanded in t around inf 42.4%

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

   if -7.5000000000000003e-94 < y < -1.80000000000000002e-305 or 6.69999999999999993e-103 < y < 1.55000000000000004

   1. Initial program 73.1%

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

   2. Taylor expanded in a around inf 39.7%

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

      1. mul-1-neg 39.7%

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

      2. distribute-lft-neg-out 39.7%

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

      3. *-commutative 39.7%

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

   4. Simplified 39.7%

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

   5. Taylor expanded in y around 0 49.9%

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

      1. associate-*r/ 49.9%

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

      2. neg-mul-1 49.9%

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

   7. Simplified 49.9%

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

4. Final simplification 48.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.95 \cdot 10^{+37}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq -9 \cdot 10^{-66}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{-94}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-305}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;y \leq 6.7 \cdot 10^{-103}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;y \leq 1.55:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]

Alternative 8: 62.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 - z}\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -4.8 \cdot 10^{-12}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{-69}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-118}:\\ \;\;\;\;\frac{-a}{\left(b - y\right) + \frac{y}{z}}\\ \mathbf{elif}\;z \leq -2.25 \cdot 10^{-128}:\\ \;\;\;\;\frac{x \cdot y}{z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+28}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (- 1.0 z))) (t_2 (/ (- t a) (- b y))))
   (if (<= z -4.8e-12)
     t_2
     (if (<= z -6.8e-69)
       t_1
       (if (<= z -7e-118)
         (/ (- a) (+ (- b y) (/ y z)))
         (if (<= z -2.25e-128)
           (/ (* x y) (* z (- b y)))
           (if (<= z 4.2e+28) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 - z);
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -4.8e-12) {
		tmp = t_2;
	} else if (z <= -6.8e-69) {
		tmp = t_1;
	} else if (z <= -7e-118) {
		tmp = -a / ((b - y) + (y / z));
	} else if (z <= -2.25e-128) {
		tmp = (x * y) / (z * (b - y));
	} else if (z <= 4.2e+28) {
		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 / (1.0d0 - z)
    t_2 = (t - a) / (b - y)
    if (z <= (-4.8d-12)) then
        tmp = t_2
    else if (z <= (-6.8d-69)) then
        tmp = t_1
    else if (z <= (-7d-118)) then
        tmp = -a / ((b - y) + (y / z))
    else if (z <= (-2.25d-128)) then
        tmp = (x * y) / (z * (b - y))
    else if (z <= 4.2d+28) 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 / (1.0 - z);
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -4.8e-12) {
		tmp = t_2;
	} else if (z <= -6.8e-69) {
		tmp = t_1;
	} else if (z <= -7e-118) {
		tmp = -a / ((b - y) + (y / z));
	} else if (z <= -2.25e-128) {
		tmp = (x * y) / (z * (b - y));
	} else if (z <= 4.2e+28) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (1.0 - z)
	t_2 = (t - a) / (b - y)
	tmp = 0
	if z <= -4.8e-12:
		tmp = t_2
	elif z <= -6.8e-69:
		tmp = t_1
	elif z <= -7e-118:
		tmp = -a / ((b - y) + (y / z))
	elif z <= -2.25e-128:
		tmp = (x * y) / (z * (b - y))
	elif z <= 4.2e+28:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(1.0 - z))
	t_2 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -4.8e-12)
		tmp = t_2;
	elseif (z <= -6.8e-69)
		tmp = t_1;
	elseif (z <= -7e-118)
		tmp = Float64(Float64(-a) / Float64(Float64(b - y) + Float64(y / z)));
	elseif (z <= -2.25e-128)
		tmp = Float64(Float64(x * y) / Float64(z * Float64(b - y)));
	elseif (z <= 4.2e+28)
		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 / (1.0 - z);
	t_2 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -4.8e-12)
		tmp = t_2;
	elseif (z <= -6.8e-69)
		tmp = t_1;
	elseif (z <= -7e-118)
		tmp = -a / ((b - y) + (y / z));
	elseif (z <= -2.25e-128)
		tmp = (x * y) / (z * (b - y));
	elseif (z <= 4.2e+28)
		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[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.8e-12], t$95$2, If[LessEqual[z, -6.8e-69], t$95$1, If[LessEqual[z, -7e-118], N[((-a) / N[(N[(b - y), $MachinePrecision] + N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.25e-128], N[(N[(x * y), $MachinePrecision] / N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.2e+28], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.79999999999999974e-12 or 4.19999999999999978e28 < z

   1. Initial program 36.9%

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

   2. Taylor expanded in z around inf 84.9%

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

   if -4.79999999999999974e-12 < z < -6.80000000000000016e-69 or -2.25e-128 < z < 4.19999999999999978e28

   1. Initial program 84.1%

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

   2. Taylor expanded in y around inf 54.0%

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

      1. +-commutative 54.0%

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

      2. mul-1-neg 54.0%

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

      3. unsub-neg 54.0%

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

   4. Simplified 54.0%

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

   if -6.80000000000000016e-69 < z < -7e-118

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 80.8%

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

      1. associate-/l* 80.8%

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

      2. +-commutative 80.8%

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

      3. *-commutative 80.8%

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

      4. fma-udef 80.8%

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

   4. Simplified 80.8%

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

   5. Taylor expanded in z around 0 80.8%

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

   6. Taylor expanded in t around 0 80.8%

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

      1. associate-*r/ 80.8%

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

      2. neg-mul-1 80.8%

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

      3. +-commutative 80.8%

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

      4. associate--l+ 80.8%

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

   8. Simplified 80.8%

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

   if -7e-118 < z < -2.25e-128

   1. Initial program 99.6%

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

   2. Taylor expanded in x around inf 75.8%

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

   3. Taylor expanded in z around inf 77.0%

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

4. Final simplification 71.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{-12}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{-69}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-118}:\\ \;\;\;\;\frac{-a}{\left(b - y\right) + \frac{y}{z}}\\ \mathbf{elif}\;z \leq -2.25 \cdot 10^{-128}:\\ \;\;\;\;\frac{x \cdot y}{z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+28}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 9: 37.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-a}{b}\\ \mathbf{if}\;z \leq -1.5 \cdot 10^{+222}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{+65}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq -0.00285 \lor \neg \left(z \leq 2.25 \cdot 10^{-12}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- a) b)))
   (if (<= z -1.5e+222)
     t_1
     (if (<= z -3.1e+65)
       (/ t b)
       (if (or (<= z -0.00285) (not (<= z 2.25e-12))) t_1 x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -a / b;
	double tmp;
	if (z <= -1.5e+222) {
		tmp = t_1;
	} else if (z <= -3.1e+65) {
		tmp = t / b;
	} else if ((z <= -0.00285) || !(z <= 2.25e-12)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = -a / b
    if (z <= (-1.5d+222)) then
        tmp = t_1
    else if (z <= (-3.1d+65)) then
        tmp = t / b
    else if ((z <= (-0.00285d0)) .or. (.not. (z <= 2.25d-12))) then
        tmp = t_1
    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 t_1 = -a / b;
	double tmp;
	if (z <= -1.5e+222) {
		tmp = t_1;
	} else if (z <= -3.1e+65) {
		tmp = t / b;
	} else if ((z <= -0.00285) || !(z <= 2.25e-12)) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = -a / b
	tmp = 0
	if z <= -1.5e+222:
		tmp = t_1
	elif z <= -3.1e+65:
		tmp = t / b
	elif (z <= -0.00285) or not (z <= 2.25e-12):
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(-a) / b)
	tmp = 0.0
	if (z <= -1.5e+222)
		tmp = t_1;
	elseif (z <= -3.1e+65)
		tmp = Float64(t / b);
	elseif ((z <= -0.00285) || !(z <= 2.25e-12))
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = -a / b;
	tmp = 0.0;
	if (z <= -1.5e+222)
		tmp = t_1;
	elseif (z <= -3.1e+65)
		tmp = t / b;
	elseif ((z <= -0.00285) || ~((z <= 2.25e-12)))
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[((-a) / b), $MachinePrecision]}, If[LessEqual[z, -1.5e+222], t$95$1, If[LessEqual[z, -3.1e+65], N[(t / b), $MachinePrecision], If[Or[LessEqual[z, -0.00285], N[Not[LessEqual[z, 2.25e-12]], $MachinePrecision]], t$95$1, x]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.50000000000000007e222 or -3.09999999999999991e65 < z < -0.0028500000000000001 or 2.2499999999999999e-12 < z

   1. Initial program 41.9%

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

   2. Taylor expanded in a around inf 22.4%

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

      1. mul-1-neg 22.4%

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

      2. distribute-lft-neg-out 22.4%

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

      3. *-commutative 22.4%

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

   4. Simplified 22.4%

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

   5. Taylor expanded in y around 0 32.5%

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

      1. associate-*r/ 32.5%

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

      2. neg-mul-1 32.5%

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

   7. Simplified 32.5%

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

   if -1.50000000000000007e222 < z < -3.09999999999999991e65

   1. Initial program 30.6%

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

   2. Taylor expanded in b around inf 19.9%

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

   3. Taylor expanded in t around inf 33.7%

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

   if -0.0028500000000000001 < z < 2.2499999999999999e-12

   1. Initial program 86.5%

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

   2. Taylor expanded in z around 0 50.0%

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

4. Final simplification 40.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+222}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{+65}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq -0.00285 \lor \neg \left(z \leq 2.25 \cdot 10^{-12}\right):\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 10: 36.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-a}{b}\\ \mathbf{if}\;z \leq -1.25 \cdot 10^{+260}:\\ \;\;\;\;\frac{-t}{y}\\ \mathbf{elif}\;z \leq -5 \cdot 10^{+223}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{+65}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-11}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- a) b)))
   (if (<= z -1.25e+260)
     (/ (- t) y)
     (if (<= z -5e+223)
       t_1
       (if (<= z -1.55e+65) (/ t b) (if (<= z 5.2e-11) x t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -a / b;
	double tmp;
	if (z <= -1.25e+260) {
		tmp = -t / y;
	} else if (z <= -5e+223) {
		tmp = t_1;
	} else if (z <= -1.55e+65) {
		tmp = t / b;
	} else if (z <= 5.2e-11) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = -a / b
    if (z <= (-1.25d+260)) then
        tmp = -t / y
    else if (z <= (-5d+223)) then
        tmp = t_1
    else if (z <= (-1.55d+65)) then
        tmp = t / b
    else if (z <= 5.2d-11) then
        tmp = x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -a / b;
	double tmp;
	if (z <= -1.25e+260) {
		tmp = -t / y;
	} else if (z <= -5e+223) {
		tmp = t_1;
	} else if (z <= -1.55e+65) {
		tmp = t / b;
	} else if (z <= 5.2e-11) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = -a / b
	tmp = 0
	if z <= -1.25e+260:
		tmp = -t / y
	elif z <= -5e+223:
		tmp = t_1
	elif z <= -1.55e+65:
		tmp = t / b
	elif z <= 5.2e-11:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(-a) / b)
	tmp = 0.0
	if (z <= -1.25e+260)
		tmp = Float64(Float64(-t) / y);
	elseif (z <= -5e+223)
		tmp = t_1;
	elseif (z <= -1.55e+65)
		tmp = Float64(t / b);
	elseif (z <= 5.2e-11)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = -a / b;
	tmp = 0.0;
	if (z <= -1.25e+260)
		tmp = -t / y;
	elseif (z <= -5e+223)
		tmp = t_1;
	elseif (z <= -1.55e+65)
		tmp = t / b;
	elseif (z <= 5.2e-11)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[((-a) / b), $MachinePrecision]}, If[LessEqual[z, -1.25e+260], N[((-t) / y), $MachinePrecision], If[LessEqual[z, -5e+223], t$95$1, If[LessEqual[z, -1.55e+65], N[(t / b), $MachinePrecision], If[LessEqual[z, 5.2e-11], x, t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.2499999999999999e260

   1. Initial program 18.3%

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

   2. Taylor expanded in b around 0 9.4%

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

      1. mul-1-neg 9.4%

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

      2. distribute-lft-neg-out 9.4%

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

      3. *-commutative 9.4%

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

   4. Simplified 9.4%

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

   5. Taylor expanded in t around inf 10.0%

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

      1. associate-/l* 12.2%

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

      2. +-commutative 12.2%

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

      3. mul-1-neg 12.2%

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

      4. distribute-rgt-neg-in 12.2%

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

      5. mul-1-neg 12.2%

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

      6. *-rgt-identity 12.2%

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

      7. distribute-lft-in 12.2%

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

      8. *-commutative 12.2%

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

      9. associate-/l* 43.3%

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

      10. +-commutative 43.3%

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

      11. mul-1-neg 43.3%

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

      12. unsub-neg 43.3%

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

   7. Simplified 43.3%

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

   8. Taylor expanded in z around inf 45.8%

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

      1. associate-*r/ 45.8%

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

      2. mul-1-neg 45.8%

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

   10. Simplified 45.8%

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

   if -1.2499999999999999e260 < z < -4.99999999999999985e223 or 5.2000000000000001e-11 < z

   1. Initial program 43.5%

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

   2. Taylor expanded in a around inf 22.3%

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

      1. mul-1-neg 22.3%

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

      2. distribute-lft-neg-out 22.3%

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

      3. *-commutative 22.3%

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

   4. Simplified 22.3%

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

   5. Taylor expanded in y around 0 35.1%

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

      1. associate-*r/ 35.1%

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

      2. neg-mul-1 35.1%

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

   7. Simplified 35.1%

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

   if -4.99999999999999985e223 < z < -1.54999999999999995e65

   1. Initial program 29.7%

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

   2. Taylor expanded in b around inf 19.3%

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

   3. Taylor expanded in t around inf 32.8%

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

   if -1.54999999999999995e65 < z < 5.2000000000000001e-11

   1. Initial program 86.4%

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

   2. Taylor expanded in z around 0 47.5%

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

4. Final simplification 41.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+260}:\\ \;\;\;\;\frac{-t}{y}\\ \mathbf{elif}\;z \leq -5 \cdot 10^{+223}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{+65}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-11}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{-a}{b}\\ \end{array} \]

Alternative 11: 63.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.68 \cdot 10^{-12} \lor \neg \left(z \leq 7 \cdot 10^{+37}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.68e-12) (not (<= z 7e+37)))
   (/ (- t a) (- b y))
   (/ x (- 1.0 z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.68e-12) || !(z <= 7e+37)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x / (1.0 - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-1.68d-12)) .or. (.not. (z <= 7d+37))) then
        tmp = (t - a) / (b - y)
    else
        tmp = x / (1.0d0 - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.68e-12) || !(z <= 7e+37)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x / (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.68e-12) or not (z <= 7e+37):
		tmp = (t - a) / (b - y)
	else:
		tmp = x / (1.0 - z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.68e-12) || !(z <= 7e+37))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(x / Float64(1.0 - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1.68e-12) || ~((z <= 7e+37)))
		tmp = (t - a) / (b - y);
	else
		tmp = x / (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.68e-12], N[Not[LessEqual[z, 7e+37]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.67999999999999991e-12 or 7e37 < z

   1. Initial program 36.9%

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

   2. Taylor expanded in z around inf 84.9%

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

   if -1.67999999999999991e-12 < z < 7e37

   1. Initial program 85.2%

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

   2. Taylor expanded in y around inf 51.1%

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

      1. +-commutative 51.1%

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

      2. mul-1-neg 51.1%

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

      3. unsub-neg 51.1%

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

   4. Simplified 51.1%

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

4. Final simplification 68.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.68 \cdot 10^{-12} \lor \neg \left(z \leq 7 \cdot 10^{+37}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]

Alternative 12: 54.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+37} \lor \neg \left(y \leq 12.2\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.25e+37) (not (<= y 12.2))) (/ x (- 1.0 z)) (/ (- t a) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.25e+37) || !(y <= 12.2)) {
		tmp = x / (1.0 - z);
	} else {
		tmp = (t - a) / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-1.25d+37)) .or. (.not. (y <= 12.2d0))) then
        tmp = x / (1.0d0 - z)
    else
        tmp = (t - a) / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.25e+37) || !(y <= 12.2)) {
		tmp = x / (1.0 - z);
	} else {
		tmp = (t - a) / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.25e+37) or not (y <= 12.2):
		tmp = x / (1.0 - z)
	else:
		tmp = (t - a) / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.25e+37) || !(y <= 12.2))
		tmp = Float64(x / Float64(1.0 - z));
	else
		tmp = Float64(Float64(t - a) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.25e+37) || ~((y <= 12.2)))
		tmp = x / (1.0 - z);
	else
		tmp = (t - a) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.25e+37], N[Not[LessEqual[y, 12.2]], $MachinePrecision]], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.24999999999999997e37 or 12.199999999999999 < y

   1. Initial program 41.8%

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

   2. Taylor expanded in y around inf 51.3%

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

      1. +-commutative 51.3%

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

      2. mul-1-neg 51.3%

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

      3. unsub-neg 51.3%

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

   4. Simplified 51.3%

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

   if -1.24999999999999997e37 < y < 12.199999999999999

   1. Initial program 76.2%

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

   2. Taylor expanded in y around 0 58.2%

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

4. Final simplification 54.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+37} \lor \neg \left(y \leq 12.2\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \]

Alternative 13: 36.8% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+64}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-14}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -2.3e+64) (/ t b) (if (<= z 2e-14) x (/ t b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2.3e+64) {
		tmp = t / b;
	} else if (z <= 2e-14) {
		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 <= (-2.3d+64)) then
        tmp = t / b
    else if (z <= 2d-14) 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 <= -2.3e+64) {
		tmp = t / b;
	} else if (z <= 2e-14) {
		tmp = x;
	} else {
		tmp = t / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -2.3e+64:
		tmp = t / b
	elif z <= 2e-14:
		tmp = x
	else:
		tmp = t / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -2.3e+64)
		tmp = Float64(t / b);
	elseif (z <= 2e-14)
		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 <= -2.3e+64)
		tmp = t / b;
	elseif (z <= 2e-14)
		tmp = x;
	else
		tmp = t / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -2.3e+64], N[(t / b), $MachinePrecision], If[LessEqual[z, 2e-14], x, N[(t / b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.3e64 or 2e-14 < z

   1. Initial program 37.4%

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

   2. Taylor expanded in b around inf 26.2%

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

   3. Taylor expanded in t around inf 25.3%

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

   if -2.3e64 < z < 2e-14

   1. Initial program 86.3%

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

   2. Taylor expanded in z around 0 47.8%

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

4. Final simplification 35.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+64}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-14}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \]

Alternative 14: 25.3% accurate, 17.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 59.9%

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

2. Taylor expanded in z around 0 23.9%

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

3. Final simplification 23.9%

   \[\leadsto x \]

Developer target: 73.6% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023229 
(FPCore (x y z t a b)
  :name "Development.Shake.Progress:decay from shake-0.15.5"
  :precision binary64

  :herbie-target
  (- (/ (+ (* z t) (* y x)) (+ y (* z (- b y)))) (/ a (+ (- b y) (/ y z))))

  (/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y)))))