Development.Shake.Progress:decay from shake-0.15.5

Percentage Accurate: 65.9% → 87.1%

Time: 17.8s

Alternatives: 17

Speedup: 1.0×

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: 65.9% 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: 87.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y - z \cdot \left(y - b\right)\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -1.3 \cdot 10^{+41}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 320000:\\ \;\;\;\;x \cdot \left(\frac{y}{t\_1} + \frac{z \cdot \left(t - a\right)}{x \cdot t\_1}\right)\\ \mathbf{elif}\;z \leq 1.46 \cdot 10^{+141}:\\ \;\;\;\;t\_2 + \frac{\frac{y \cdot x}{b - y} - y \cdot \frac{t - a}{{\left(b - y\right)}^{2}}}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- y (* z (- y b)))) (t_2 (/ (- t a) (- b y))))
   (if (<= z -1.3e+41)
     t_2
     (if (<= z 320000.0)
       (* x (+ (/ y t_1) (/ (* z (- t a)) (* x t_1))))
       (if (<= z 1.46e+141)
         (+
          t_2
          (/ (- (/ (* y x) (- b y)) (* y (/ (- t a) (pow (- b y) 2.0)))) z))
         t_2)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y - (z * (y - b));
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -1.3e+41) {
		tmp = t_2;
	} else if (z <= 320000.0) {
		tmp = x * ((y / t_1) + ((z * (t - a)) / (x * t_1)));
	} else if (z <= 1.46e+141) {
		tmp = t_2 + ((((y * x) / (b - y)) - (y * ((t - a) / pow((b - y), 2.0)))) / z);
	} 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 = y - (z * (y - b))
    t_2 = (t - a) / (b - y)
    if (z <= (-1.3d+41)) then
        tmp = t_2
    else if (z <= 320000.0d0) then
        tmp = x * ((y / t_1) + ((z * (t - a)) / (x * t_1)))
    else if (z <= 1.46d+141) then
        tmp = t_2 + ((((y * x) / (b - y)) - (y * ((t - a) / ((b - y) ** 2.0d0)))) / z)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y - (z * (y - b));
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -1.3e+41) {
		tmp = t_2;
	} else if (z <= 320000.0) {
		tmp = x * ((y / t_1) + ((z * (t - a)) / (x * t_1)));
	} else if (z <= 1.46e+141) {
		tmp = t_2 + ((((y * x) / (b - y)) - (y * ((t - a) / Math.pow((b - y), 2.0)))) / z);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y - (z * (y - b))
	t_2 = (t - a) / (b - y)
	tmp = 0
	if z <= -1.3e+41:
		tmp = t_2
	elif z <= 320000.0:
		tmp = x * ((y / t_1) + ((z * (t - a)) / (x * t_1)))
	elif z <= 1.46e+141:
		tmp = t_2 + ((((y * x) / (b - y)) - (y * ((t - a) / math.pow((b - y), 2.0)))) / z)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y - Float64(z * Float64(y - b)))
	t_2 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -1.3e+41)
		tmp = t_2;
	elseif (z <= 320000.0)
		tmp = Float64(x * Float64(Float64(y / t_1) + Float64(Float64(z * Float64(t - a)) / Float64(x * t_1))));
	elseif (z <= 1.46e+141)
		tmp = Float64(t_2 + Float64(Float64(Float64(Float64(y * x) / Float64(b - y)) - Float64(y * Float64(Float64(t - a) / (Float64(b - y) ^ 2.0)))) / z));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y - (z * (y - b));
	t_2 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -1.3e+41)
		tmp = t_2;
	elseif (z <= 320000.0)
		tmp = x * ((y / t_1) + ((z * (t - a)) / (x * t_1)));
	elseif (z <= 1.46e+141)
		tmp = t_2 + ((((y * x) / (b - y)) - (y * ((t - a) / ((b - y) ^ 2.0)))) / z);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y - N[(z * N[(y - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.3e+41], t$95$2, If[LessEqual[z, 320000.0], 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], If[LessEqual[z, 1.46e+141], N[(t$95$2 + N[(N[(N[(N[(y * x), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision] - N[(y * N[(N[(t - a), $MachinePrecision] / N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.3e41 or 1.4600000000000001e141 < z

   1. Initial program 39.6%

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

   3. Taylor expanded in z around inf 89.0%

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

   if -1.3e41 < z < 3.2e5

   1. Initial program 87.1%

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

   3. Taylor expanded in x around inf 93.6%

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

   if 3.2e5 < z < 1.4600000000000001e141

   1. Initial program 55.8%

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

   3. Taylor expanded in z around -inf 72.7%

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

      1. associate--l+ 72.7%

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

      2. mul-1-neg 72.7%

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

      3. distribute-lft-out-- 72.7%

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

      4. *-commutative 72.7%

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

      5. associate-/l* 91.1%

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

      6. div-sub 95.6%

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

   5. Simplified 95.6%

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

4. Final simplification 92.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+41}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq 320000:\\ \;\;\;\;x \cdot \left(\frac{y}{y - z \cdot \left(y - b\right)} + \frac{z \cdot \left(t - a\right)}{x \cdot \left(y - z \cdot \left(y - b\right)\right)}\right)\\ \mathbf{elif}\;z \leq 1.46 \cdot 10^{+141}:\\ \;\;\;\;\frac{t - a}{b - y} + \frac{\frac{y \cdot x}{b - y} - y \cdot \frac{t - a}{{\left(b - y\right)}^{2}}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 87.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 1 - \frac{b}{y}\\ t_2 := y - z \cdot \left(y - b\right)\\ \mathbf{if}\;z \leq -1.1 \cdot 10^{+41}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq 290000:\\ \;\;\;\;x \cdot \left(\frac{y}{t\_2} + \frac{z \cdot \left(t - a\right)}{x \cdot t\_2}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{a - t}{y \cdot t\_1} + \frac{\frac{a - t}{y \cdot {t\_1}^{2}} + \frac{x}{-1 + \frac{b}{y}}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- 1.0 (/ b y))) (t_2 (- y (* z (- y b)))))
   (if (<= z -1.1e+41)
     (/ (- t a) (- b y))
     (if (<= z 290000.0)
       (* x (+ (/ y t_2) (/ (* z (- t a)) (* x t_2))))
       (+
        (/ (- a t) (* y t_1))
        (/ (+ (/ (- a t) (* y (pow t_1 2.0))) (/ x (+ -1.0 (/ b y)))) z))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 1.0 - (b / y);
	double t_2 = y - (z * (y - b));
	double tmp;
	if (z <= -1.1e+41) {
		tmp = (t - a) / (b - y);
	} else if (z <= 290000.0) {
		tmp = x * ((y / t_2) + ((z * (t - a)) / (x * t_2)));
	} else {
		tmp = ((a - t) / (y * t_1)) + ((((a - t) / (y * pow(t_1, 2.0))) + (x / (-1.0 + (b / 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) :: t_2
    real(8) :: tmp
    t_1 = 1.0d0 - (b / y)
    t_2 = y - (z * (y - b))
    if (z <= (-1.1d+41)) then
        tmp = (t - a) / (b - y)
    else if (z <= 290000.0d0) then
        tmp = x * ((y / t_2) + ((z * (t - a)) / (x * t_2)))
    else
        tmp = ((a - t) / (y * t_1)) + ((((a - t) / (y * (t_1 ** 2.0d0))) + (x / ((-1.0d0) + (b / 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 = 1.0 - (b / y);
	double t_2 = y - (z * (y - b));
	double tmp;
	if (z <= -1.1e+41) {
		tmp = (t - a) / (b - y);
	} else if (z <= 290000.0) {
		tmp = x * ((y / t_2) + ((z * (t - a)) / (x * t_2)));
	} else {
		tmp = ((a - t) / (y * t_1)) + ((((a - t) / (y * Math.pow(t_1, 2.0))) + (x / (-1.0 + (b / y)))) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = 1.0 - (b / y)
	t_2 = y - (z * (y - b))
	tmp = 0
	if z <= -1.1e+41:
		tmp = (t - a) / (b - y)
	elif z <= 290000.0:
		tmp = x * ((y / t_2) + ((z * (t - a)) / (x * t_2)))
	else:
		tmp = ((a - t) / (y * t_1)) + ((((a - t) / (y * math.pow(t_1, 2.0))) + (x / (-1.0 + (b / y)))) / z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(1.0 - Float64(b / y))
	t_2 = Float64(y - Float64(z * Float64(y - b)))
	tmp = 0.0
	if (z <= -1.1e+41)
		tmp = Float64(Float64(t - a) / Float64(b - y));
	elseif (z <= 290000.0)
		tmp = Float64(x * Float64(Float64(y / t_2) + Float64(Float64(z * Float64(t - a)) / Float64(x * t_2))));
	else
		tmp = Float64(Float64(Float64(a - t) / Float64(y * t_1)) + Float64(Float64(Float64(Float64(a - t) / Float64(y * (t_1 ^ 2.0))) + Float64(x / Float64(-1.0 + Float64(b / y)))) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = 1.0 - (b / y);
	t_2 = y - (z * (y - b));
	tmp = 0.0;
	if (z <= -1.1e+41)
		tmp = (t - a) / (b - y);
	elseif (z <= 290000.0)
		tmp = x * ((y / t_2) + ((z * (t - a)) / (x * t_2)));
	else
		tmp = ((a - t) / (y * t_1)) + ((((a - t) / (y * (t_1 ^ 2.0))) + (x / (-1.0 + (b / y)))) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(1.0 - N[(b / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y - N[(z * N[(y - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.1e+41], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 290000.0], N[(x * N[(N[(y / t$95$2), $MachinePrecision] + N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / N[(x * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(a - t), $MachinePrecision] / N[(y * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(N[(a - t), $MachinePrecision] / N[(y * N[Power[t$95$1, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x / N[(-1.0 + N[(b / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.09999999999999995e41

   1. Initial program 39.2%

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

   3. Taylor expanded in z around inf 87.6%

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

   if -1.09999999999999995e41 < z < 2.9e5

   1. Initial program 87.1%

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

   3. Taylor expanded in x around inf 93.6%

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

   if 2.9e5 < z

   1. Initial program 45.6%

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

   3. Taylor expanded in y around inf 37.6%

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

      1. +-commutative 37.6%

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

      2. mul-1-neg 37.6%

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

      3. unsub-neg 37.6%

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

      4. *-commutative 37.6%

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

   5. Simplified 37.6%

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

   6. Taylor expanded in z around -inf 89.1%

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

      1. distribute-lft-out 89.1%

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

      2. mul-1-neg 89.1%

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

      3. sub-neg 89.1%

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

   8. Simplified 89.1%

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

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+41}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq 290000:\\ \;\;\;\;x \cdot \left(\frac{y}{y - z \cdot \left(y - b\right)} + \frac{z \cdot \left(t - a\right)}{x \cdot \left(y - z \cdot \left(y - b\right)\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{a - t}{y \cdot \left(1 - \frac{b}{y}\right)} + \frac{\frac{a - t}{y \cdot {\left(1 - \frac{b}{y}\right)}^{2}} + \frac{x}{-1 + \frac{b}{y}}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 86.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y - z \cdot \left(y - b\right)\\ \mathbf{if}\;z \leq -9.6 \cdot 10^{+41} \lor \neg \left(z \leq 5.5 \cdot 10^{+16}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{t\_1} + \frac{z \cdot \left(t - a\right)}{x \cdot t\_1}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- y (* z (- y b)))))
   (if (or (<= z -9.6e+41) (not (<= z 5.5e+16)))
     (/ (- 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 * (y - b));
	double tmp;
	if ((z <= -9.6e+41) || !(z <= 5.5e+16)) {
		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 * (y - b))
    if ((z <= (-9.6d+41)) .or. (.not. (z <= 5.5d+16))) 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 * (y - b));
	double tmp;
	if ((z <= -9.6e+41) || !(z <= 5.5e+16)) {
		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 * (y - b))
	tmp = 0
	if (z <= -9.6e+41) or not (z <= 5.5e+16):
		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(y - b)))
	tmp = 0.0
	if ((z <= -9.6e+41) || !(z <= 5.5e+16))
		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 * (y - b));
	tmp = 0.0;
	if ((z <= -9.6e+41) || ~((z <= 5.5e+16)))
		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[(y - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[z, -9.6e+41], N[Not[LessEqual[z, 5.5e+16]], $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 < -9.6000000000000007e41 or 5.5e16 < z

   1. Initial program 42.2%

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

   3. Taylor expanded in z around inf 85.3%

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

   if -9.6000000000000007e41 < z < 5.5e16

   1. Initial program 87.2%

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

   3. Taylor expanded in x around inf 93.6%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.6 \cdot 10^{+41} \lor \neg \left(z \leq 5.5 \cdot 10^{+16}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{y - z \cdot \left(y - b\right)} + \frac{z \cdot \left(t - a\right)}{x \cdot \left(y - z \cdot \left(y - b\right)\right)}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 69.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{z \cdot a}{y}\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -0.0001:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-119}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-160}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + y \cdot x}{z \cdot b}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-96}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- x (/ (* z a) y))) (t_2 (/ (- t a) (- b y))))
   (if (<= z -0.0001)
     t_2
     (if (<= z -3.6e-119)
       t_1
       (if (<= z -3.3e-160)
         (/ (+ (* z (- t a)) (* y x)) (* z b))
         (if (<= z 2.2e-96) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - ((z * a) / y);
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -0.0001) {
		tmp = t_2;
	} else if (z <= -3.6e-119) {
		tmp = t_1;
	} else if (z <= -3.3e-160) {
		tmp = ((z * (t - a)) + (y * x)) / (z * b);
	} else if (z <= 2.2e-96) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x - ((z * a) / y)
    t_2 = (t - a) / (b - y)
    if (z <= (-0.0001d0)) then
        tmp = t_2
    else if (z <= (-3.6d-119)) then
        tmp = t_1
    else if (z <= (-3.3d-160)) then
        tmp = ((z * (t - a)) + (y * x)) / (z * b)
    else if (z <= 2.2d-96) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - ((z * a) / y);
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -0.0001) {
		tmp = t_2;
	} else if (z <= -3.6e-119) {
		tmp = t_1;
	} else if (z <= -3.3e-160) {
		tmp = ((z * (t - a)) + (y * x)) / (z * b);
	} else if (z <= 2.2e-96) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x - ((z * a) / y)
	t_2 = (t - a) / (b - y)
	tmp = 0
	if z <= -0.0001:
		tmp = t_2
	elif z <= -3.6e-119:
		tmp = t_1
	elif z <= -3.3e-160:
		tmp = ((z * (t - a)) + (y * x)) / (z * b)
	elif z <= 2.2e-96:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x - Float64(Float64(z * a) / y))
	t_2 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -0.0001)
		tmp = t_2;
	elseif (z <= -3.6e-119)
		tmp = t_1;
	elseif (z <= -3.3e-160)
		tmp = Float64(Float64(Float64(z * Float64(t - a)) + Float64(y * x)) / Float64(z * b));
	elseif (z <= 2.2e-96)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x - ((z * a) / y);
	t_2 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -0.0001)
		tmp = t_2;
	elseif (z <= -3.6e-119)
		tmp = t_1;
	elseif (z <= -3.3e-160)
		tmp = ((z * (t - a)) + (y * x)) / (z * b);
	elseif (z <= 2.2e-96)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x - N[(N[(z * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.0001], t$95$2, If[LessEqual[z, -3.6e-119], t$95$1, If[LessEqual[z, -3.3e-160], N[(N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] + N[(y * x), $MachinePrecision]), $MachinePrecision] / N[(z * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.2e-96], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.00000000000000005e-4 or 2.19999999999999979e-96 < z

   1. Initial program 52.5%

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

   3. Taylor expanded in z around inf 78.2%

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

   if -1.00000000000000005e-4 < z < -3.6e-119 or -3.3e-160 < z < 2.19999999999999979e-96

   1. Initial program 85.0%

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

   3. Taylor expanded in z around 0 60.1%

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

   4. Taylor expanded in a around inf 73.9%

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

      1. associate-*r/ 73.9%

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

      2. associate-*r* 73.9%

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

      3. mul-1-neg 73.9%

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

   6. Simplified 73.9%

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

   if -3.6e-119 < z < -3.3e-160

   1. Initial program 99.7%

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

   3. Taylor expanded in b around inf 97.6%

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

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.0001:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-119}:\\ \;\;\;\;x - \frac{z \cdot a}{y}\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-160}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + y \cdot x}{z \cdot b}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-96}:\\ \;\;\;\;x - \frac{z \cdot a}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+41} \lor \neg \left(z \leq 1.05 \cdot 10^{+78}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y - z \cdot \left(y - b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -2.6e+41) (not (<= z 1.05e+78)))
   (/ (- t a) (- b y))
   (/ (+ (* z (- t a)) (* y x)) (- y (* z (- y b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.6e+41) || !(z <= 1.05e+78)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((z * (t - a)) + (y * x)) / (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 <= (-2.6d+41)) .or. (.not. (z <= 1.05d+78))) then
        tmp = (t - a) / (b - y)
    else
        tmp = ((z * (t - a)) + (y * x)) / (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 <= -2.6e+41) || !(z <= 1.05e+78)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((z * (t - a)) + (y * x)) / (y - (z * (y - b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -2.6e+41) or not (z <= 1.05e+78):
		tmp = (t - a) / (b - y)
	else:
		tmp = ((z * (t - a)) + (y * x)) / (y - (z * (y - b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -2.6e+41) || !(z <= 1.05e+78))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(Float64(Float64(z * Float64(t - a)) + Float64(y * x)) / 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 <= -2.6e+41) || ~((z <= 1.05e+78)))
		tmp = (t - a) / (b - y);
	else
		tmp = ((z * (t - a)) + (y * x)) / (y - (z * (y - b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -2.6e+41], N[Not[LessEqual[z, 1.05e+78]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] + N[(y * x), $MachinePrecision]), $MachinePrecision] / N[(y - N[(z * N[(y - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.6000000000000001e41 or 1.05e78 < z

   1. Initial program 38.6%

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

   3. Taylor expanded in z around inf 87.4%

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

   if -2.6000000000000001e41 < z < 1.05e78

   1. Initial program 86.8%

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

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+41} \lor \neg \left(z \leq 1.05 \cdot 10^{+78}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y - z \cdot \left(y - b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 71.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -9.5 \cdot 10^{+40}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-270}:\\ \;\;\;\;\frac{y \cdot x - z \cdot a}{y - z \cdot \left(y - b\right)}\\ \mathbf{elif}\;z \leq 5.7 \cdot 10^{-95}:\\ \;\;\;\;x - \frac{z \cdot a}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -9.5e+40)
     t_1
     (if (<= z -1.3e-270)
       (/ (- (* y x) (* z a)) (- y (* z (- y b))))
       (if (<= z 5.7e-95) (- x (/ (* z a) 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);
	double tmp;
	if (z <= -9.5e+40) {
		tmp = t_1;
	} else if (z <= -1.3e-270) {
		tmp = ((y * x) - (z * a)) / (y - (z * (y - b)));
	} else if (z <= 5.7e-95) {
		tmp = x - ((z * a) / 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)
    if (z <= (-9.5d+40)) then
        tmp = t_1
    else if (z <= (-1.3d-270)) then
        tmp = ((y * x) - (z * a)) / (y - (z * (y - b)))
    else if (z <= 5.7d-95) then
        tmp = x - ((z * a) / 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);
	double tmp;
	if (z <= -9.5e+40) {
		tmp = t_1;
	} else if (z <= -1.3e-270) {
		tmp = ((y * x) - (z * a)) / (y - (z * (y - b)));
	} else if (z <= 5.7e-95) {
		tmp = x - ((z * a) / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	tmp = 0
	if z <= -9.5e+40:
		tmp = t_1
	elif z <= -1.3e-270:
		tmp = ((y * x) - (z * a)) / (y - (z * (y - b)))
	elif z <= 5.7e-95:
		tmp = x - ((z * a) / y)
	else:
		tmp = t_1
	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 <= -9.5e+40)
		tmp = t_1;
	elseif (z <= -1.3e-270)
		tmp = Float64(Float64(Float64(y * x) - Float64(z * a)) / Float64(y - Float64(z * Float64(y - b))));
	elseif (z <= 5.7e-95)
		tmp = Float64(x - Float64(Float64(z * a) / 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);
	tmp = 0.0;
	if (z <= -9.5e+40)
		tmp = t_1;
	elseif (z <= -1.3e-270)
		tmp = ((y * x) - (z * a)) / (y - (z * (y - b)));
	elseif (z <= 5.7e-95)
		tmp = x - ((z * a) / y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9.5e+40], t$95$1, If[LessEqual[z, -1.3e-270], N[(N[(N[(y * x), $MachinePrecision] - N[(z * a), $MachinePrecision]), $MachinePrecision] / N[(y - N[(z * N[(y - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.7e-95], N[(x - N[(N[(z * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.5000000000000003e40 or 5.7e-95 < z

   1. Initial program 50.5%

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

   3. Taylor expanded in z around inf 79.3%

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

   if -9.5000000000000003e40 < z < -1.3000000000000001e-270

   1. Initial program 90.9%

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

   3. Taylor expanded in t around 0 74.7%

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

      1. +-commutative 74.7%

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

      2. mul-1-neg 74.7%

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

      3. unsub-neg 74.7%

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

      4. *-commutative 74.7%

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

      5. *-commutative 74.7%

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

   5. Simplified 74.7%

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

   if -1.3000000000000001e-270 < z < 5.7e-95

   1. Initial program 81.9%

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

   3. Taylor expanded in z around 0 68.3%

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

   4. Taylor expanded in a around inf 83.2%

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

      1. associate-*r/ 83.2%

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

      2. associate-*r* 83.2%

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

      3. mul-1-neg 83.2%

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

   6. Simplified 83.2%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+40}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-270}:\\ \;\;\;\;\frac{y \cdot x - z \cdot a}{y - z \cdot \left(y - b\right)}\\ \mathbf{elif}\;z \leq 5.7 \cdot 10^{-95}:\\ \;\;\;\;x - \frac{z \cdot a}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 71.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -2.6 \cdot 10^{+39}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{-261}:\\ \;\;\;\;\frac{y \cdot x + z \cdot t}{y - z \cdot \left(y - b\right)}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-94}:\\ \;\;\;\;x - \frac{z \cdot a}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -2.6e+39)
     t_1
     (if (<= z -3.1e-261)
       (/ (+ (* y x) (* z t)) (- y (* z (- y b))))
       (if (<= z 1.25e-94) (- x (/ (* z a) 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);
	double tmp;
	if (z <= -2.6e+39) {
		tmp = t_1;
	} else if (z <= -3.1e-261) {
		tmp = ((y * x) + (z * t)) / (y - (z * (y - b)));
	} else if (z <= 1.25e-94) {
		tmp = x - ((z * a) / 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)
    if (z <= (-2.6d+39)) then
        tmp = t_1
    else if (z <= (-3.1d-261)) then
        tmp = ((y * x) + (z * t)) / (y - (z * (y - b)))
    else if (z <= 1.25d-94) then
        tmp = x - ((z * a) / 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);
	double tmp;
	if (z <= -2.6e+39) {
		tmp = t_1;
	} else if (z <= -3.1e-261) {
		tmp = ((y * x) + (z * t)) / (y - (z * (y - b)));
	} else if (z <= 1.25e-94) {
		tmp = x - ((z * a) / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	tmp = 0
	if z <= -2.6e+39:
		tmp = t_1
	elif z <= -3.1e-261:
		tmp = ((y * x) + (z * t)) / (y - (z * (y - b)))
	elif z <= 1.25e-94:
		tmp = x - ((z * a) / y)
	else:
		tmp = t_1
	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 <= -2.6e+39)
		tmp = t_1;
	elseif (z <= -3.1e-261)
		tmp = Float64(Float64(Float64(y * x) + Float64(z * t)) / Float64(y - Float64(z * Float64(y - b))));
	elseif (z <= 1.25e-94)
		tmp = Float64(x - Float64(Float64(z * a) / 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);
	tmp = 0.0;
	if (z <= -2.6e+39)
		tmp = t_1;
	elseif (z <= -3.1e-261)
		tmp = ((y * x) + (z * t)) / (y - (z * (y - b)));
	elseif (z <= 1.25e-94)
		tmp = x - ((z * a) / y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.6e+39], t$95$1, If[LessEqual[z, -3.1e-261], N[(N[(N[(y * x), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] / N[(y - N[(z * N[(y - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.25e-94], N[(x - N[(N[(z * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.6e39 or 1.2499999999999999e-94 < z

   1. Initial program 50.8%

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

   3. Taylor expanded in z around inf 79.5%

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

   if -2.6e39 < z < -3.0999999999999998e-261

   1. Initial program 90.0%

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

   3. Taylor expanded in t around inf 66.8%

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

   if -3.0999999999999998e-261 < z < 1.2499999999999999e-94

   1. Initial program 83.5%

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

   3. Taylor expanded in z around 0 67.7%

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

   4. Taylor expanded in a around inf 83.5%

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

      1. associate-*r/ 83.5%

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

      2. associate-*r* 83.5%

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

      3. mul-1-neg 83.5%

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

   6. Simplified 83.5%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+39}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{-261}:\\ \;\;\;\;\frac{y \cdot x + z \cdot t}{y - z \cdot \left(y - b\right)}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-94}:\\ \;\;\;\;x - \frac{z \cdot a}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 69.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{-5} \lor \neg \left(z \leq 1.26 \cdot 10^{-94}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z \cdot a}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -5.5e-5) (not (<= z 1.26e-94)))
   (/ (- t a) (- b y))
   (- x (/ (* z a) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -5.5e-5) || !(z <= 1.26e-94)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x - ((z * a) / 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 <= (-5.5d-5)) .or. (.not. (z <= 1.26d-94))) then
        tmp = (t - a) / (b - y)
    else
        tmp = x - ((z * a) / 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 <= -5.5e-5) || !(z <= 1.26e-94)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x - ((z * a) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -5.5e-5) or not (z <= 1.26e-94):
		tmp = (t - a) / (b - y)
	else:
		tmp = x - ((z * a) / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -5.5e-5) || !(z <= 1.26e-94))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(x - Float64(Float64(z * a) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -5.5e-5) || ~((z <= 1.26e-94)))
		tmp = (t - a) / (b - y);
	else
		tmp = x - ((z * a) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -5.5e-5], N[Not[LessEqual[z, 1.26e-94]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(z * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.5000000000000002e-5 or 1.2600000000000001e-94 < z

   1. Initial program 52.5%

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

   3. Taylor expanded in z around inf 78.2%

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

   if -5.5000000000000002e-5 < z < 1.2600000000000001e-94

   1. Initial program 86.2%

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

   3. Taylor expanded in z around 0 55.4%

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

   4. Taylor expanded in a around inf 68.2%

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

      1. associate-*r/ 68.2%

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

      2. associate-*r* 68.2%

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

      3. mul-1-neg 68.2%

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

   6. Simplified 68.2%

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

4. Final simplification 73.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{-5} \lor \neg \left(z \leq 1.26 \cdot 10^{-94}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z \cdot a}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 69.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.000185 \lor \neg \left(z \leq 5.7 \cdot 10^{-95}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -0.000185) (not (<= z 5.7e-95)))
   (/ (- t a) (- b y))
   (- x (* a (/ z y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -0.000185) || !(z <= 5.7e-95)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x - (a * (z / 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 <= (-0.000185d0)) .or. (.not. (z <= 5.7d-95))) then
        tmp = (t - a) / (b - y)
    else
        tmp = x - (a * (z / 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 <= -0.000185) || !(z <= 5.7e-95)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x - (a * (z / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -0.000185) or not (z <= 5.7e-95):
		tmp = (t - a) / (b - y)
	else:
		tmp = x - (a * (z / y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -0.000185) || !(z <= 5.7e-95))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(x - Float64(a * Float64(z / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -0.000185) || ~((z <= 5.7e-95)))
		tmp = (t - a) / (b - y);
	else
		tmp = x - (a * (z / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -0.000185], N[Not[LessEqual[z, 5.7e-95]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x - N[(a * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.85e-4 or 5.7e-95 < z

   1. Initial program 52.5%

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

   3. Taylor expanded in z around inf 78.2%

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

   if -1.85e-4 < z < 5.7e-95

   1. Initial program 86.2%

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

   3. Taylor expanded in z around 0 55.4%

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

   4. Taylor expanded in a around inf 63.0%

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

      1. associate-*r/ 63.0%

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

      2. mul-1-neg 63.0%

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

   6. Simplified 63.0%

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

   7. Taylor expanded in x around 0 68.2%

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

      1. mul-1-neg 68.2%

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

      2. associate-/l* 66.4%

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

      3. distribute-lft-neg-in 66.4%

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

      4. cancel-sign-sub-inv 66.4%

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

   9. Simplified 66.4%

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

4. Final simplification 73.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.000185 \lor \neg \left(z \leq 5.7 \cdot 10^{-95}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 51.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.00036:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-94}:\\ \;\;\;\;x - a \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -0.00036)
   (/ t (- b y))
   (if (<= z 1.05e-94) (- x (* a (/ z y))) (/ (- t a) b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -0.00036) {
		tmp = t / (b - y);
	} else if (z <= 1.05e-94) {
		tmp = x - (a * (z / y));
	} 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 (z <= (-0.00036d0)) then
        tmp = t / (b - y)
    else if (z <= 1.05d-94) then
        tmp = x - (a * (z / y))
    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 (z <= -0.00036) {
		tmp = t / (b - y);
	} else if (z <= 1.05e-94) {
		tmp = x - (a * (z / y));
	} else {
		tmp = (t - a) / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -0.00036:
		tmp = t / (b - y)
	elif z <= 1.05e-94:
		tmp = x - (a * (z / y))
	else:
		tmp = (t - a) / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -0.00036)
		tmp = Float64(t / Float64(b - y));
	elseif (z <= 1.05e-94)
		tmp = Float64(x - Float64(a * Float64(z / y)));
	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 (z <= -0.00036)
		tmp = t / (b - y);
	elseif (z <= 1.05e-94)
		tmp = x - (a * (z / y));
	else
		tmp = (t - a) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -0.00036], N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.05e-94], N[(x - N[(a * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.60000000000000023e-4

   1. Initial program 45.3%

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

   3. Taylor expanded in t around inf 24.2%

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

      1. *-commutative 24.2%

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

   5. Simplified 24.2%

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

   6. Taylor expanded in z around inf 49.4%

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

   if -3.60000000000000023e-4 < z < 1.05e-94

   1. Initial program 86.2%

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

   3. Taylor expanded in z around 0 55.4%

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

   4. Taylor expanded in a around inf 63.0%

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

      1. associate-*r/ 63.0%

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

      2. mul-1-neg 63.0%

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

   6. Simplified 63.0%

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

   7. Taylor expanded in x around 0 68.2%

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

      1. mul-1-neg 68.2%

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

      2. associate-/l* 66.4%

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

      3. distribute-lft-neg-in 66.4%

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

      4. cancel-sign-sub-inv 66.4%

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

   9. Simplified 66.4%

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

   if 1.05e-94 < z

   1. Initial program 57.4%

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

   3. Taylor expanded in y around 0 51.0%

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

Alternative 11: 54.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{-37} \lor \neg \left(y \leq 1.05 \cdot 10^{+19}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -9.5e-37) (not (<= y 1.05e+19))) (/ 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 <= -9.5e-37) || !(y <= 1.05e+19)) {
		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 <= (-9.5d-37)) .or. (.not. (y <= 1.05d+19))) 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 <= -9.5e-37) || !(y <= 1.05e+19)) {
		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 <= -9.5e-37) or not (y <= 1.05e+19):
		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 <= -9.5e-37) || !(y <= 1.05e+19))
		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 <= -9.5e-37) || ~((y <= 1.05e+19)))
		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, -9.5e-37], N[Not[LessEqual[y, 1.05e+19]], $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 < -9.49999999999999927e-37 or 1.05e19 < y

   1. Initial program 54.2%

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

   3. Taylor expanded in y around inf 56.7%

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

      1. mul-1-neg 56.7%

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

      2. unsub-neg 56.7%

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

   5. Simplified 56.7%

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

   if -9.49999999999999927e-37 < y < 1.05e19

   1. Initial program 78.7%

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

   3. Taylor expanded in y around 0 57.4%

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

4. Final simplification 57.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{-37} \lor \neg \left(y \leq 1.05 \cdot 10^{+19}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 44.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.4 \cdot 10^{+32} \lor \neg \left(z \leq 1.26 \cdot 10^{-94}\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -7.4e+32) (not (<= z 1.26e-94))) (/ 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 <= -7.4e+32) || !(z <= 1.26e-94)) {
		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 <= (-7.4d+32)) .or. (.not. (z <= 1.26d-94))) 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 <= -7.4e+32) || !(z <= 1.26e-94)) {
		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 <= -7.4e+32) or not (z <= 1.26e-94):
		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 <= -7.4e+32) || !(z <= 1.26e-94))
		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 <= -7.4e+32) || ~((z <= 1.26e-94)))
		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, -7.4e+32], N[Not[LessEqual[z, 1.26e-94]], $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 < -7.4e32 or 1.2600000000000001e-94 < z

   1. Initial program 51.5%

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

   3. Taylor expanded in t around inf 24.6%

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

      1. *-commutative 24.6%

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

   5. Simplified 24.6%

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

   6. Taylor expanded in z around inf 44.1%

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

   if -7.4e32 < z < 1.2600000000000001e-94

   1. Initial program 86.6%

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

   3. Taylor expanded in y around inf 56.8%

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

      1. mul-1-neg 56.8%

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

      2. unsub-neg 56.8%

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

   5. Simplified 56.8%

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

4. Final simplification 49.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.4 \cdot 10^{+32} \lor \neg \left(z \leq 1.26 \cdot 10^{-94}\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 44.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.0003 \lor \neg \left(z \leq 2.55 \cdot 10^{-95}\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -0.0003) (not (<= z 2.55e-95))) (/ t (- b y)) (+ x (* z x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -0.0003) || !(z <= 2.55e-95)) {
		tmp = t / (b - y);
	} else {
		tmp = x + (z * 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 <= (-0.0003d0)) .or. (.not. (z <= 2.55d-95))) then
        tmp = t / (b - y)
    else
        tmp = x + (z * 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 <= -0.0003) || !(z <= 2.55e-95)) {
		tmp = t / (b - y);
	} else {
		tmp = x + (z * x);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -0.0003) or not (z <= 2.55e-95):
		tmp = t / (b - y)
	else:
		tmp = x + (z * x)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -0.0003) || !(z <= 2.55e-95))
		tmp = Float64(t / Float64(b - y));
	else
		tmp = Float64(x + Float64(z * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -0.0003) || ~((z <= 2.55e-95)))
		tmp = t / (b - y);
	else
		tmp = x + (z * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -0.0003], N[Not[LessEqual[z, 2.55e-95]], $MachinePrecision]], N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.99999999999999974e-4 or 2.55e-95 < z

   1. Initial program 52.5%

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

   3. Taylor expanded in t around inf 24.8%

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

      1. *-commutative 24.8%

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

   5. Simplified 24.8%

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

   6. Taylor expanded in z around inf 43.9%

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

   if -2.99999999999999974e-4 < z < 2.55e-95

   1. Initial program 86.2%

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

   3. Taylor expanded in z around 0 55.4%

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

   4. Taylor expanded in y around inf 56.1%

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

      1. *-commutative 56.1%

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

   6. Simplified 56.1%

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

4. Final simplification 49.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.0003 \lor \neg \left(z \leq 2.55 \cdot 10^{-95}\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 37.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.00016:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 1.26 \cdot 10^{-94}:\\ \;\;\;\;x + z \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{-b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -0.00016) (/ t b) (if (<= z 1.26e-94) (+ x (* z x)) (/ a (- b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -0.00016) {
		tmp = t / b;
	} else if (z <= 1.26e-94) {
		tmp = x + (z * x);
	} else {
		tmp = 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 (z <= (-0.00016d0)) then
        tmp = t / b
    else if (z <= 1.26d-94) then
        tmp = x + (z * x)
    else
        tmp = 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 (z <= -0.00016) {
		tmp = t / b;
	} else if (z <= 1.26e-94) {
		tmp = x + (z * x);
	} else {
		tmp = a / -b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -0.00016:
		tmp = t / b
	elif z <= 1.26e-94:
		tmp = x + (z * x)
	else:
		tmp = a / -b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -0.00016)
		tmp = Float64(t / b);
	elseif (z <= 1.26e-94)
		tmp = Float64(x + Float64(z * x));
	else
		tmp = Float64(a / Float64(-b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -0.00016)
		tmp = t / b;
	elseif (z <= 1.26e-94)
		tmp = x + (z * x);
	else
		tmp = a / -b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -0.00016], N[(t / b), $MachinePrecision], If[LessEqual[z, 1.26e-94], N[(x + N[(z * x), $MachinePrecision]), $MachinePrecision], N[(a / (-b)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.60000000000000013e-4

   1. Initial program 45.3%

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

   3. Taylor expanded in t around inf 24.2%

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

      1. *-commutative 24.2%

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

   5. Simplified 24.2%

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

   6. Taylor expanded in y around 0 31.5%

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

   if -1.60000000000000013e-4 < z < 1.2600000000000001e-94

   1. Initial program 86.2%

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

   3. Taylor expanded in z around 0 55.4%

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

   4. Taylor expanded in y around inf 56.1%

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

      1. *-commutative 56.1%

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

   6. Simplified 56.1%

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

   if 1.2600000000000001e-94 < z

   1. Initial program 57.4%

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

   3. Taylor expanded in x around inf 51.5%

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

   4. Taylor expanded in b around inf 43.0%

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

   5. Taylor expanded in a around inf 29.0%

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

      1. mul-1-neg 29.0%

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

   7. Simplified 29.0%

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

4. Final simplification 41.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.00016:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 1.26 \cdot 10^{-94}:\\ \;\;\;\;x + z \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{-b}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 37.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{-5}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-94}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{-b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -5.5e-5) (/ t b) (if (<= z 1.02e-94) x (/ a (- b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -5.5e-5) {
		tmp = t / b;
	} else if (z <= 1.02e-94) {
		tmp = x;
	} else {
		tmp = 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 (z <= (-5.5d-5)) then
        tmp = t / b
    else if (z <= 1.02d-94) then
        tmp = x
    else
        tmp = 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 (z <= -5.5e-5) {
		tmp = t / b;
	} else if (z <= 1.02e-94) {
		tmp = x;
	} else {
		tmp = a / -b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -5.5e-5:
		tmp = t / b
	elif z <= 1.02e-94:
		tmp = x
	else:
		tmp = a / -b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -5.5e-5)
		tmp = Float64(t / b);
	elseif (z <= 1.02e-94)
		tmp = x;
	else
		tmp = Float64(a / Float64(-b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -5.5e-5)
		tmp = t / b;
	elseif (z <= 1.02e-94)
		tmp = x;
	else
		tmp = a / -b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -5.5e-5], N[(t / b), $MachinePrecision], If[LessEqual[z, 1.02e-94], x, N[(a / (-b)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.5000000000000002e-5

   1. Initial program 45.3%

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

   3. Taylor expanded in t around inf 24.2%

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

      1. *-commutative 24.2%

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

   5. Simplified 24.2%

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

   6. Taylor expanded in y around 0 31.5%

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

   if -5.5000000000000002e-5 < z < 1.02e-94

   1. Initial program 86.2%

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

   3. Taylor expanded in z around 0 55.3%

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

   if 1.02e-94 < z

   1. Initial program 57.4%

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

   3. Taylor expanded in x around inf 51.5%

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

   4. Taylor expanded in b around inf 43.0%

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

   5. Taylor expanded in a around inf 29.0%

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

      1. mul-1-neg 29.0%

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

   7. Simplified 29.0%

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

4. Final simplification 40.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{-5}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-94}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{-b}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 36.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{-5} \lor \neg \left(z \leq 1.06 \cdot 10^{-94}\right):\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -7.5e-5) (not (<= z 1.06e-94))) (/ t b) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -7.5e-5) || !(z <= 1.06e-94)) {
		tmp = t / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-7.5d-5)) .or. (.not. (z <= 1.06d-94))) then
        tmp = t / b
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -7.5e-5) || !(z <= 1.06e-94)) {
		tmp = t / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -7.5e-5) or not (z <= 1.06e-94):
		tmp = t / b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -7.5e-5) || !(z <= 1.06e-94))
		tmp = Float64(t / b);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -7.5e-5) || ~((z <= 1.06e-94)))
		tmp = t / b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -7.5e-5], N[Not[LessEqual[z, 1.06e-94]], $MachinePrecision]], N[(t / b), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -7.49999999999999934e-5 or 1.06e-94 < z

   1. Initial program 52.5%

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

   3. Taylor expanded in t around inf 24.8%

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

      1. *-commutative 24.8%

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

   5. Simplified 24.8%

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

   6. Taylor expanded in y around 0 29.8%

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

   if -7.49999999999999934e-5 < z < 1.06e-94

   1. Initial program 86.2%

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

   3. Taylor expanded in z around 0 55.3%

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

4. Final simplification 40.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{-5} \lor \neg \left(z \leq 1.06 \cdot 10^{-94}\right):\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 26.2% accurate, 17.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 67.0%

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

3. Taylor expanded in z around 0 27.2%

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

Developer Target 1: 74.0% 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 2024128 
(FPCore (x y z t a b)
  :name "Development.Shake.Progress:decay from shake-0.15.5"
  :precision binary64

  :alt
  (! :herbie-platform default (- (/ (+ (* z t) (* y x)) (+ y (* z (- b y)))) (/ a (+ (- b y) (/ y z)))))

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