Development.Shake.Progress:decay from shake-0.15.5

Percentage Accurate: 66.3% → 85.8%

Time: 24.8s

Alternatives: 17

Speedup: 0.8×

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: 66.3% 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: 85.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -1.35 \cdot 10^{+38}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.16 \cdot 10^{+51}:\\ \;\;\;\;\frac{y \cdot x + z \cdot \left(t - a\right)}{z \cdot b - y \cdot \left(z + -1\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(t\_1 + \frac{y \cdot \frac{x}{z}}{b - y}\right) + \frac{\frac{a - t}{\frac{z}{y}}}{{\left(b - y\right)}^{2}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -1.35e+38)
     t_1
     (if (<= z 1.16e+51)
       (/ (+ (* y x) (* z (- t a))) (- (* z b) (* y (+ z -1.0))))
       (+
        (+ t_1 (/ (* y (/ x z)) (- b y)))
        (/ (/ (- a t) (/ z y)) (pow (- b y) 2.0)))))))

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 <= -1.35e+38) {
		tmp = t_1;
	} else if (z <= 1.16e+51) {
		tmp = ((y * x) + (z * (t - a))) / ((z * b) - (y * (z + -1.0)));
	} else {
		tmp = (t_1 + ((y * (x / z)) / (b - y))) + (((a - t) / (z / y)) / pow((b - y), 2.0));
	}
	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 <= (-1.35d+38)) then
        tmp = t_1
    else if (z <= 1.16d+51) then
        tmp = ((y * x) + (z * (t - a))) / ((z * b) - (y * (z + (-1.0d0))))
    else
        tmp = (t_1 + ((y * (x / z)) / (b - y))) + (((a - t) / (z / y)) / ((b - y) ** 2.0d0))
    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 <= -1.35e+38) {
		tmp = t_1;
	} else if (z <= 1.16e+51) {
		tmp = ((y * x) + (z * (t - a))) / ((z * b) - (y * (z + -1.0)));
	} else {
		tmp = (t_1 + ((y * (x / z)) / (b - y))) + (((a - t) / (z / y)) / Math.pow((b - y), 2.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	tmp = 0
	if z <= -1.35e+38:
		tmp = t_1
	elif z <= 1.16e+51:
		tmp = ((y * x) + (z * (t - a))) / ((z * b) - (y * (z + -1.0)))
	else:
		tmp = (t_1 + ((y * (x / z)) / (b - y))) + (((a - t) / (z / y)) / math.pow((b - y), 2.0))
	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 <= -1.35e+38)
		tmp = t_1;
	elseif (z <= 1.16e+51)
		tmp = Float64(Float64(Float64(y * x) + Float64(z * Float64(t - a))) / Float64(Float64(z * b) - Float64(y * Float64(z + -1.0))));
	else
		tmp = Float64(Float64(t_1 + Float64(Float64(y * Float64(x / z)) / Float64(b - y))) + Float64(Float64(Float64(a - t) / Float64(z / y)) / (Float64(b - y) ^ 2.0)));
	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 <= -1.35e+38)
		tmp = t_1;
	elseif (z <= 1.16e+51)
		tmp = ((y * x) + (z * (t - a))) / ((z * b) - (y * (z + -1.0)));
	else
		tmp = (t_1 + ((y * (x / z)) / (b - y))) + (((a - t) / (z / y)) / ((b - y) ^ 2.0));
	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, -1.35e+38], t$95$1, If[LessEqual[z, 1.16e+51], N[(N[(N[(y * x), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(z * b), $MachinePrecision] - N[(y * N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t$95$1 + N[(N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(a - t), $MachinePrecision] / N[(z / y), $MachinePrecision]), $MachinePrecision] / N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.34999999999999998e38

   1. Initial program 33.0%

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

   3. Taylor expanded in z around inf 82.9%

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

   if -1.34999999999999998e38 < z < 1.16e51

   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 y around -inf 83.6%

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

      1. +-commutative 83.6%

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

      2. mul-1-neg 83.6%

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

      3. unsub-neg 83.6%

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

      4. *-commutative 83.6%

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

      5. sub-neg 83.6%

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

      6. metadata-eval 83.6%

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

   5. Simplified 83.6%

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

   if 1.16e51 < z

   1. Initial program 36.9%

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

   3. Taylor expanded in z around inf 61.4%

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

      1. associate--r+ 61.4%

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

      2. +-commutative 61.4%

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

      3. associate--l+ 61.4%

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

      4. times-frac 69.8%

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

      5. associate-*r/ 71.4%

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

      6. div-sub 73.1%

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

      7. associate-/r* 73.1%

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

      8. *-commutative 73.1%

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

      9. associate-/l* 86.4%

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

   5. Simplified 86.4%

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

4. Final simplification 84.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+38}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq 1.16 \cdot 10^{+51}:\\ \;\;\;\;\frac{y \cdot x + z \cdot \left(t - a\right)}{z \cdot b - y \cdot \left(z + -1\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{t - a}{b - y} + \frac{y \cdot \frac{x}{z}}{b - y}\right) + \frac{\frac{a - t}{\frac{z}{y}}}{{\left(b - y\right)}^{2}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 68.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot b - y \cdot \left(z + -1\right)\\ t_2 := z \cdot \left(t - a\right)\\ t_3 := y \cdot x + t\_2\\ t_4 := \frac{t - a}{b - y}\\ t_5 := \frac{t\_3}{y}\\ \mathbf{if}\;z \leq -1.28 \cdot 10^{+39}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-92}:\\ \;\;\;\;\frac{t\_3}{z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq -7.6 \cdot 10^{-127}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{-141}:\\ \;\;\;\;\frac{z}{\frac{t\_1}{t - a}}\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-239}:\\ \;\;\;\;\frac{y \cdot x}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-82}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{-6}:\\ \;\;\;\;\frac{1}{\frac{t\_1}{t\_2}}\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{+40}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (* z b) (* y (+ z -1.0))))
        (t_2 (* z (- t a)))
        (t_3 (+ (* y x) t_2))
        (t_4 (/ (- t a) (- b y)))
        (t_5 (/ t_3 y)))
   (if (<= z -1.28e+39)
     t_4
     (if (<= z -2.5e-92)
       (/ t_3 (* z (- b y)))
       (if (<= z -7.6e-127)
         t_5
         (if (<= z -9.2e-141)
           (/ z (/ t_1 (- t a)))
           (if (<= z -1.2e-239)
             (/ (* y x) (+ y (* z b)))
             (if (<= z 1.02e-82)
               t_5
               (if (<= z 5.3e-6)
                 (/ 1.0 (/ t_1 t_2))
                 (if (<= z 2.15e+40) (/ x (- 1.0 z)) t_4))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z * b) - (y * (z + -1.0));
	double t_2 = z * (t - a);
	double t_3 = (y * x) + t_2;
	double t_4 = (t - a) / (b - y);
	double t_5 = t_3 / y;
	double tmp;
	if (z <= -1.28e+39) {
		tmp = t_4;
	} else if (z <= -2.5e-92) {
		tmp = t_3 / (z * (b - y));
	} else if (z <= -7.6e-127) {
		tmp = t_5;
	} else if (z <= -9.2e-141) {
		tmp = z / (t_1 / (t - a));
	} else if (z <= -1.2e-239) {
		tmp = (y * x) / (y + (z * b));
	} else if (z <= 1.02e-82) {
		tmp = t_5;
	} else if (z <= 5.3e-6) {
		tmp = 1.0 / (t_1 / t_2);
	} else if (z <= 2.15e+40) {
		tmp = x / (1.0 - z);
	} else {
		tmp = t_4;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_1 = (z * b) - (y * (z + (-1.0d0)))
    t_2 = z * (t - a)
    t_3 = (y * x) + t_2
    t_4 = (t - a) / (b - y)
    t_5 = t_3 / y
    if (z <= (-1.28d+39)) then
        tmp = t_4
    else if (z <= (-2.5d-92)) then
        tmp = t_3 / (z * (b - y))
    else if (z <= (-7.6d-127)) then
        tmp = t_5
    else if (z <= (-9.2d-141)) then
        tmp = z / (t_1 / (t - a))
    else if (z <= (-1.2d-239)) then
        tmp = (y * x) / (y + (z * b))
    else if (z <= 1.02d-82) then
        tmp = t_5
    else if (z <= 5.3d-6) then
        tmp = 1.0d0 / (t_1 / t_2)
    else if (z <= 2.15d+40) then
        tmp = x / (1.0d0 - z)
    else
        tmp = t_4
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z * b) - (y * (z + -1.0));
	double t_2 = z * (t - a);
	double t_3 = (y * x) + t_2;
	double t_4 = (t - a) / (b - y);
	double t_5 = t_3 / y;
	double tmp;
	if (z <= -1.28e+39) {
		tmp = t_4;
	} else if (z <= -2.5e-92) {
		tmp = t_3 / (z * (b - y));
	} else if (z <= -7.6e-127) {
		tmp = t_5;
	} else if (z <= -9.2e-141) {
		tmp = z / (t_1 / (t - a));
	} else if (z <= -1.2e-239) {
		tmp = (y * x) / (y + (z * b));
	} else if (z <= 1.02e-82) {
		tmp = t_5;
	} else if (z <= 5.3e-6) {
		tmp = 1.0 / (t_1 / t_2);
	} else if (z <= 2.15e+40) {
		tmp = x / (1.0 - z);
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z * b) - (y * (z + -1.0))
	t_2 = z * (t - a)
	t_3 = (y * x) + t_2
	t_4 = (t - a) / (b - y)
	t_5 = t_3 / y
	tmp = 0
	if z <= -1.28e+39:
		tmp = t_4
	elif z <= -2.5e-92:
		tmp = t_3 / (z * (b - y))
	elif z <= -7.6e-127:
		tmp = t_5
	elif z <= -9.2e-141:
		tmp = z / (t_1 / (t - a))
	elif z <= -1.2e-239:
		tmp = (y * x) / (y + (z * b))
	elif z <= 1.02e-82:
		tmp = t_5
	elif z <= 5.3e-6:
		tmp = 1.0 / (t_1 / t_2)
	elif z <= 2.15e+40:
		tmp = x / (1.0 - z)
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z * b) - Float64(y * Float64(z + -1.0)))
	t_2 = Float64(z * Float64(t - a))
	t_3 = Float64(Float64(y * x) + t_2)
	t_4 = Float64(Float64(t - a) / Float64(b - y))
	t_5 = Float64(t_3 / y)
	tmp = 0.0
	if (z <= -1.28e+39)
		tmp = t_4;
	elseif (z <= -2.5e-92)
		tmp = Float64(t_3 / Float64(z * Float64(b - y)));
	elseif (z <= -7.6e-127)
		tmp = t_5;
	elseif (z <= -9.2e-141)
		tmp = Float64(z / Float64(t_1 / Float64(t - a)));
	elseif (z <= -1.2e-239)
		tmp = Float64(Float64(y * x) / Float64(y + Float64(z * b)));
	elseif (z <= 1.02e-82)
		tmp = t_5;
	elseif (z <= 5.3e-6)
		tmp = Float64(1.0 / Float64(t_1 / t_2));
	elseif (z <= 2.15e+40)
		tmp = Float64(x / Float64(1.0 - z));
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z * b) - (y * (z + -1.0));
	t_2 = z * (t - a);
	t_3 = (y * x) + t_2;
	t_4 = (t - a) / (b - y);
	t_5 = t_3 / y;
	tmp = 0.0;
	if (z <= -1.28e+39)
		tmp = t_4;
	elseif (z <= -2.5e-92)
		tmp = t_3 / (z * (b - y));
	elseif (z <= -7.6e-127)
		tmp = t_5;
	elseif (z <= -9.2e-141)
		tmp = z / (t_1 / (t - a));
	elseif (z <= -1.2e-239)
		tmp = (y * x) / (y + (z * b));
	elseif (z <= 1.02e-82)
		tmp = t_5;
	elseif (z <= 5.3e-6)
		tmp = 1.0 / (t_1 / t_2);
	elseif (z <= 2.15e+40)
		tmp = x / (1.0 - z);
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z * b), $MachinePrecision] - N[(y * N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y * x), $MachinePrecision] + t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(t$95$3 / y), $MachinePrecision]}, If[LessEqual[z, -1.28e+39], t$95$4, If[LessEqual[z, -2.5e-92], N[(t$95$3 / N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -7.6e-127], t$95$5, If[LessEqual[z, -9.2e-141], N[(z / N[(t$95$1 / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.2e-239], N[(N[(y * x), $MachinePrecision] / N[(y + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.02e-82], t$95$5, If[LessEqual[z, 5.3e-6], N[(1.0 / N[(t$95$1 / t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.15e+40], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], t$95$4]]]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if z < -1.27999999999999994e39 or 2.1500000000000001e40 < z

   1. Initial program 35.5%

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

   3. Taylor expanded in z around inf 82.5%

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

   if -1.27999999999999994e39 < z < -2.50000000000000006e-92

   1. Initial program 88.6%

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

   3. Taylor expanded in y around -inf 88.6%

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

      1. +-commutative 88.6%

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

      2. mul-1-neg 88.6%

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

      3. unsub-neg 88.6%

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

      4. *-commutative 88.6%

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

      5. sub-neg 88.6%

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

      6. metadata-eval 88.6%

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

   5. Simplified 88.6%

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

   6. Taylor expanded in z around inf 72.5%

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

   if -2.50000000000000006e-92 < z < -7.60000000000000005e-127 or -1.19999999999999996e-239 < z < 1.02000000000000007e-82

   1. Initial program 84.0%

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

   3. Taylor expanded in z around 0 69.0%

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

   if -7.60000000000000005e-127 < z < -9.1999999999999998e-141

   1. Initial program 76.2%

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

   3. Taylor expanded in y around -inf 76.2%

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

      1. +-commutative 76.2%

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

      2. mul-1-neg 76.2%

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

      3. unsub-neg 76.2%

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

      4. *-commutative 76.2%

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

      5. sub-neg 76.2%

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

      6. metadata-eval 76.2%

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

   5. Simplified 76.2%

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

   6. Taylor expanded in x around 0 57.7%

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

      1. associate-/l* 57.7%

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

      2. *-commutative 57.7%

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

      3. sub-neg 57.7%

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

      4. metadata-eval 57.7%

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

   8. Simplified 57.7%

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

   if -9.1999999999999998e-141 < z < -1.19999999999999996e-239

   1. Initial program 87.4%

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

   3. Taylor expanded in x around inf 62.4%

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

      1. *-commutative 62.4%

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

   5. Simplified 62.4%

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

   6. Taylor expanded in b around inf 62.4%

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

      1. *-commutative 62.4%

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

   8. Simplified 62.4%

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

   if 1.02000000000000007e-82 < z < 5.3000000000000001e-6

   1. Initial program 84.4%

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

   3. Taylor expanded in y around -inf 84.5%

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

      1. +-commutative 84.5%

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

      2. mul-1-neg 84.5%

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

      3. unsub-neg 84.5%

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

      4. *-commutative 84.5%

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

      5. sub-neg 84.5%

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

      6. metadata-eval 84.5%

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

   5. Simplified 84.5%

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

      1. clear-num 84.5%

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

      2. inv-pow 84.5%

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

      3. fma-def 84.5%

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

   7. Applied egg-rr 84.5%

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

      1. unpow-1 84.5%

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

   9. Simplified 84.5%

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

   10. Taylor expanded in x around 0 73.2%

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

       1. *-commutative 73.2%

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

       2. sub-neg 73.2%

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

       3. metadata-eval 73.2%

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

   12. Simplified 73.2%

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

   if 5.3000000000000001e-6 < z < 2.1500000000000001e40

   1. Initial program 64.8%

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

   3. Taylor expanded in y around inf 65.9%

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

      1. mul-1-neg 65.9%

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

      2. unsub-neg 65.9%

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

   5. Simplified 65.9%

      \[\leadsto \color{blue}{\frac{x}{1 - z}} \]
3. Recombined 7 regimes into one program.

4. Final simplification 74.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.28 \cdot 10^{+39}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-92}:\\ \;\;\;\;\frac{y \cdot x + z \cdot \left(t - a\right)}{z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq -7.6 \cdot 10^{-127}:\\ \;\;\;\;\frac{y \cdot x + z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{-141}:\\ \;\;\;\;\frac{z}{\frac{z \cdot b - y \cdot \left(z + -1\right)}{t - a}}\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-239}:\\ \;\;\;\;\frac{y \cdot x}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-82}:\\ \;\;\;\;\frac{y \cdot x + z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{-6}:\\ \;\;\;\;\frac{1}{\frac{z \cdot b - y \cdot \left(z + -1\right)}{z \cdot \left(t - a\right)}}\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{+40}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 67.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{\frac{z \cdot b - y \cdot \left(z + -1\right)}{t - a}}\\ t_2 := y \cdot x + z \cdot \left(t - a\right)\\ t_3 := \frac{t - a}{b - y}\\ t_4 := \frac{t\_2}{y}\\ \mathbf{if}\;z \leq -2.2 \cdot 10^{+38}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq -1.82 \cdot 10^{-87}:\\ \;\;\;\;\frac{t\_2}{z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{-128}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-142}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-242}:\\ \;\;\;\;\frac{y \cdot x}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 1.26 \cdot 10^{-83}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{-6}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{+40}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ z (/ (- (* z b) (* y (+ z -1.0))) (- t a))))
        (t_2 (+ (* y x) (* z (- t a))))
        (t_3 (/ (- t a) (- b y)))
        (t_4 (/ t_2 y)))
   (if (<= z -2.2e+38)
     t_3
     (if (<= z -1.82e-87)
       (/ t_2 (* z (- b y)))
       (if (<= z -4.6e-128)
         t_4
         (if (<= z -4.8e-142)
           t_1
           (if (<= z -1.7e-242)
             (/ (* y x) (+ y (* z b)))
             (if (<= z 1.26e-83)
               t_4
               (if (<= z 5.3e-6)
                 t_1
                 (if (<= z 2.15e+40) (/ x (- 1.0 z)) t_3))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z / (((z * b) - (y * (z + -1.0))) / (t - a));
	double t_2 = (y * x) + (z * (t - a));
	double t_3 = (t - a) / (b - y);
	double t_4 = t_2 / y;
	double tmp;
	if (z <= -2.2e+38) {
		tmp = t_3;
	} else if (z <= -1.82e-87) {
		tmp = t_2 / (z * (b - y));
	} else if (z <= -4.6e-128) {
		tmp = t_4;
	} else if (z <= -4.8e-142) {
		tmp = t_1;
	} else if (z <= -1.7e-242) {
		tmp = (y * x) / (y + (z * b));
	} else if (z <= 1.26e-83) {
		tmp = t_4;
	} else if (z <= 5.3e-6) {
		tmp = t_1;
	} else if (z <= 2.15e+40) {
		tmp = x / (1.0 - z);
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = z / (((z * b) - (y * (z + (-1.0d0)))) / (t - a))
    t_2 = (y * x) + (z * (t - a))
    t_3 = (t - a) / (b - y)
    t_4 = t_2 / y
    if (z <= (-2.2d+38)) then
        tmp = t_3
    else if (z <= (-1.82d-87)) then
        tmp = t_2 / (z * (b - y))
    else if (z <= (-4.6d-128)) then
        tmp = t_4
    else if (z <= (-4.8d-142)) then
        tmp = t_1
    else if (z <= (-1.7d-242)) then
        tmp = (y * x) / (y + (z * b))
    else if (z <= 1.26d-83) then
        tmp = t_4
    else if (z <= 5.3d-6) then
        tmp = t_1
    else if (z <= 2.15d+40) then
        tmp = x / (1.0d0 - z)
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z / (((z * b) - (y * (z + -1.0))) / (t - a));
	double t_2 = (y * x) + (z * (t - a));
	double t_3 = (t - a) / (b - y);
	double t_4 = t_2 / y;
	double tmp;
	if (z <= -2.2e+38) {
		tmp = t_3;
	} else if (z <= -1.82e-87) {
		tmp = t_2 / (z * (b - y));
	} else if (z <= -4.6e-128) {
		tmp = t_4;
	} else if (z <= -4.8e-142) {
		tmp = t_1;
	} else if (z <= -1.7e-242) {
		tmp = (y * x) / (y + (z * b));
	} else if (z <= 1.26e-83) {
		tmp = t_4;
	} else if (z <= 5.3e-6) {
		tmp = t_1;
	} else if (z <= 2.15e+40) {
		tmp = x / (1.0 - z);
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z / (((z * b) - (y * (z + -1.0))) / (t - a))
	t_2 = (y * x) + (z * (t - a))
	t_3 = (t - a) / (b - y)
	t_4 = t_2 / y
	tmp = 0
	if z <= -2.2e+38:
		tmp = t_3
	elif z <= -1.82e-87:
		tmp = t_2 / (z * (b - y))
	elif z <= -4.6e-128:
		tmp = t_4
	elif z <= -4.8e-142:
		tmp = t_1
	elif z <= -1.7e-242:
		tmp = (y * x) / (y + (z * b))
	elif z <= 1.26e-83:
		tmp = t_4
	elif z <= 5.3e-6:
		tmp = t_1
	elif z <= 2.15e+40:
		tmp = x / (1.0 - z)
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z / Float64(Float64(Float64(z * b) - Float64(y * Float64(z + -1.0))) / Float64(t - a)))
	t_2 = Float64(Float64(y * x) + Float64(z * Float64(t - a)))
	t_3 = Float64(Float64(t - a) / Float64(b - y))
	t_4 = Float64(t_2 / y)
	tmp = 0.0
	if (z <= -2.2e+38)
		tmp = t_3;
	elseif (z <= -1.82e-87)
		tmp = Float64(t_2 / Float64(z * Float64(b - y)));
	elseif (z <= -4.6e-128)
		tmp = t_4;
	elseif (z <= -4.8e-142)
		tmp = t_1;
	elseif (z <= -1.7e-242)
		tmp = Float64(Float64(y * x) / Float64(y + Float64(z * b)));
	elseif (z <= 1.26e-83)
		tmp = t_4;
	elseif (z <= 5.3e-6)
		tmp = t_1;
	elseif (z <= 2.15e+40)
		tmp = Float64(x / Float64(1.0 - z));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z / (((z * b) - (y * (z + -1.0))) / (t - a));
	t_2 = (y * x) + (z * (t - a));
	t_3 = (t - a) / (b - y);
	t_4 = t_2 / y;
	tmp = 0.0;
	if (z <= -2.2e+38)
		tmp = t_3;
	elseif (z <= -1.82e-87)
		tmp = t_2 / (z * (b - y));
	elseif (z <= -4.6e-128)
		tmp = t_4;
	elseif (z <= -4.8e-142)
		tmp = t_1;
	elseif (z <= -1.7e-242)
		tmp = (y * x) / (y + (z * b));
	elseif (z <= 1.26e-83)
		tmp = t_4;
	elseif (z <= 5.3e-6)
		tmp = t_1;
	elseif (z <= 2.15e+40)
		tmp = x / (1.0 - z);
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z / N[(N[(N[(z * b), $MachinePrecision] - N[(y * N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * x), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$2 / y), $MachinePrecision]}, If[LessEqual[z, -2.2e+38], t$95$3, If[LessEqual[z, -1.82e-87], N[(t$95$2 / N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4.6e-128], t$95$4, If[LessEqual[z, -4.8e-142], t$95$1, If[LessEqual[z, -1.7e-242], N[(N[(y * x), $MachinePrecision] / N[(y + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.26e-83], t$95$4, If[LessEqual[z, 5.3e-6], t$95$1, If[LessEqual[z, 2.15e+40], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -2.20000000000000006e38 or 2.1500000000000001e40 < z

   1. Initial program 35.5%

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

   3. Taylor expanded in z around inf 82.5%

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

   if -2.20000000000000006e38 < z < -1.81999999999999993e-87

   1. Initial program 88.6%

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

   3. Taylor expanded in y around -inf 88.6%

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

      1. +-commutative 88.6%

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

      2. mul-1-neg 88.6%

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

      3. unsub-neg 88.6%

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

      4. *-commutative 88.6%

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

      5. sub-neg 88.6%

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

      6. metadata-eval 88.6%

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

   5. Simplified 88.6%

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

   6. Taylor expanded in z around inf 72.5%

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

   if -1.81999999999999993e-87 < z < -4.6000000000000002e-128 or -1.7e-242 < z < 1.2600000000000001e-83

   1. Initial program 84.0%

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

   3. Taylor expanded in z around 0 69.0%

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

   if -4.6000000000000002e-128 < z < -4.79999999999999976e-142 or 1.2600000000000001e-83 < z < 5.3000000000000001e-6

   1. Initial program 82.9%

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

   3. Taylor expanded in y around -inf 83.0%

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

      1. +-commutative 83.0%

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

      2. mul-1-neg 83.0%

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

      3. unsub-neg 83.0%

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

      4. *-commutative 83.0%

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

      5. sub-neg 83.0%

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

      6. metadata-eval 83.0%

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

   5. Simplified 83.0%

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

   6. Taylor expanded in x around 0 70.4%

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

      1. associate-/l* 70.0%

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

      2. *-commutative 70.0%

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

      3. sub-neg 70.0%

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

      4. metadata-eval 70.0%

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

   8. Simplified 70.0%

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

   if -4.79999999999999976e-142 < z < -1.7e-242

   1. Initial program 87.4%

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

   3. Taylor expanded in x around inf 62.4%

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

      1. *-commutative 62.4%

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

   5. Simplified 62.4%

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

   6. Taylor expanded in b around inf 62.4%

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

      1. *-commutative 62.4%

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

   8. Simplified 62.4%

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

   if 5.3000000000000001e-6 < z < 2.1500000000000001e40

   1. Initial program 64.8%

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

   3. Taylor expanded in y around inf 65.9%

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

      1. mul-1-neg 65.9%

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

      2. unsub-neg 65.9%

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

   5. Simplified 65.9%

      \[\leadsto \color{blue}{\frac{x}{1 - z}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 74.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+38}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -1.82 \cdot 10^{-87}:\\ \;\;\;\;\frac{y \cdot x + z \cdot \left(t - a\right)}{z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{-128}:\\ \;\;\;\;\frac{y \cdot x + z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-142}:\\ \;\;\;\;\frac{z}{\frac{z \cdot b - y \cdot \left(z + -1\right)}{t - a}}\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-242}:\\ \;\;\;\;\frac{y \cdot x}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 1.26 \cdot 10^{-83}:\\ \;\;\;\;\frac{y \cdot x + z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{-6}:\\ \;\;\;\;\frac{z}{\frac{z \cdot b - y \cdot \left(z + -1\right)}{t - a}}\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{+40}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 41.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{b - y}\\ \mathbf{if}\;z \leq -2.4 \cdot 10^{+111}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{+60}:\\ \;\;\;\;\frac{a}{y}\\ \mathbf{elif}\;z \leq -3.9 \cdot 10^{-87}:\\ \;\;\;\;-\frac{a}{b}\\ \mathbf{elif}\;z \leq 0.03:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+250}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ t (- b y))))
   (if (<= z -2.4e+111)
     t_1
     (if (<= z -4.8e+60)
       (/ a y)
       (if (<= z -3.9e-87)
         (- (/ a b))
         (if (<= z 0.03) x (if (<= z 1.15e+250) t_1 (/ a y))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t / (b - y);
	double tmp;
	if (z <= -2.4e+111) {
		tmp = t_1;
	} else if (z <= -4.8e+60) {
		tmp = a / y;
	} else if (z <= -3.9e-87) {
		tmp = -(a / b);
	} else if (z <= 0.03) {
		tmp = x;
	} else if (z <= 1.15e+250) {
		tmp = t_1;
	} else {
		tmp = 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) :: t_1
    real(8) :: tmp
    t_1 = t / (b - y)
    if (z <= (-2.4d+111)) then
        tmp = t_1
    else if (z <= (-4.8d+60)) then
        tmp = a / y
    else if (z <= (-3.9d-87)) then
        tmp = -(a / b)
    else if (z <= 0.03d0) then
        tmp = x
    else if (z <= 1.15d+250) then
        tmp = t_1
    else
        tmp = 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 t_1 = t / (b - y);
	double tmp;
	if (z <= -2.4e+111) {
		tmp = t_1;
	} else if (z <= -4.8e+60) {
		tmp = a / y;
	} else if (z <= -3.9e-87) {
		tmp = -(a / b);
	} else if (z <= 0.03) {
		tmp = x;
	} else if (z <= 1.15e+250) {
		tmp = t_1;
	} else {
		tmp = a / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t / (b - y)
	tmp = 0
	if z <= -2.4e+111:
		tmp = t_1
	elif z <= -4.8e+60:
		tmp = a / y
	elif z <= -3.9e-87:
		tmp = -(a / b)
	elif z <= 0.03:
		tmp = x
	elif z <= 1.15e+250:
		tmp = t_1
	else:
		tmp = a / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t / Float64(b - y))
	tmp = 0.0
	if (z <= -2.4e+111)
		tmp = t_1;
	elseif (z <= -4.8e+60)
		tmp = Float64(a / y);
	elseif (z <= -3.9e-87)
		tmp = Float64(-Float64(a / b));
	elseif (z <= 0.03)
		tmp = x;
	elseif (z <= 1.15e+250)
		tmp = t_1;
	else
		tmp = Float64(a / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t / (b - y);
	tmp = 0.0;
	if (z <= -2.4e+111)
		tmp = t_1;
	elseif (z <= -4.8e+60)
		tmp = a / y;
	elseif (z <= -3.9e-87)
		tmp = -(a / b);
	elseif (z <= 0.03)
		tmp = x;
	elseif (z <= 1.15e+250)
		tmp = t_1;
	else
		tmp = a / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.4e+111], t$95$1, If[LessEqual[z, -4.8e+60], N[(a / y), $MachinePrecision], If[LessEqual[z, -3.9e-87], (-N[(a / b), $MachinePrecision]), If[LessEqual[z, 0.03], x, If[LessEqual[z, 1.15e+250], t$95$1, N[(a / y), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.40000000000000006e111 or 0.029999999999999999 < z < 1.1500000000000001e250

   1. Initial program 40.2%

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

   3. Taylor expanded in t around inf 20.6%

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

      1. associate-/l* 26.2%

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

      2. +-commutative 26.2%

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

      3. fma-def 26.2%

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

   5. Simplified 26.2%

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

   6. Taylor expanded in z around inf 39.6%

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

   if -2.40000000000000006e111 < z < -4.8e60 or 1.1500000000000001e250 < z

   1. Initial program 28.0%

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

   3. Taylor expanded in y around -inf 27.7%

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

      1. +-commutative 27.7%

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

      2. mul-1-neg 27.7%

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

      3. unsub-neg 27.7%

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

      4. *-commutative 27.7%

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

      5. sub-neg 27.7%

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

      6. metadata-eval 27.7%

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

   5. Simplified 27.7%

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

   6. Taylor expanded in a around inf 25.0%

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

      1. mul-1-neg 25.0%

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

      2. *-commutative 25.0%

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

      3. distribute-rgt-neg-in 25.0%

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

   8. Simplified 25.0%

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

   9. Taylor expanded in z around inf 72.2%

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

       1. associate-*r/ 72.2%

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

       2. neg-mul-1 72.2%

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

   11. Simplified 72.2%

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

   12. Taylor expanded in b around 0 58.0%

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

   if -4.8e60 < z < -3.8999999999999998e-87

   1. Initial program 70.5%

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

   3. Taylor expanded in b around inf 49.1%

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

   4. Taylor expanded in a around inf 33.0%

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

      1. associate-*r/ 33.0%

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

      2. neg-mul-1 33.0%

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

   6. Simplified 33.0%

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

   if -3.8999999999999998e-87 < z < 0.029999999999999999

   1. Initial program 84.9%

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

   3. Taylor expanded in z around 0 51.5%

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

4. Final simplification 46.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+111}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{+60}:\\ \;\;\;\;\frac{a}{y}\\ \mathbf{elif}\;z \leq -3.9 \cdot 10^{-87}:\\ \;\;\;\;-\frac{a}{b}\\ \mathbf{elif}\;z \leq 0.03:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+250}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 68.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -4 \cdot 10^{-87}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-82}:\\ \;\;\;\;\frac{y \cdot x + z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{-6}:\\ \;\;\;\;\frac{z}{\frac{z \cdot b - y \cdot \left(z + -1\right)}{t - a}}\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{+40}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -4e-87)
     t_1
     (if (<= z 1.8e-82)
       (/ (+ (* y x) (* z (- t a))) y)
       (if (<= z 5.3e-6)
         (/ z (/ (- (* z b) (* y (+ z -1.0))) (- t a)))
         (if (<= z 2.15e+40) (/ x (- 1.0 z)) 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 <= -4e-87) {
		tmp = t_1;
	} else if (z <= 1.8e-82) {
		tmp = ((y * x) + (z * (t - a))) / y;
	} else if (z <= 5.3e-6) {
		tmp = z / (((z * b) - (y * (z + -1.0))) / (t - a));
	} else if (z <= 2.15e+40) {
		tmp = x / (1.0 - z);
	} 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 <= (-4d-87)) then
        tmp = t_1
    else if (z <= 1.8d-82) then
        tmp = ((y * x) + (z * (t - a))) / y
    else if (z <= 5.3d-6) then
        tmp = z / (((z * b) - (y * (z + (-1.0d0)))) / (t - a))
    else if (z <= 2.15d+40) then
        tmp = x / (1.0d0 - z)
    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 <= -4e-87) {
		tmp = t_1;
	} else if (z <= 1.8e-82) {
		tmp = ((y * x) + (z * (t - a))) / y;
	} else if (z <= 5.3e-6) {
		tmp = z / (((z * b) - (y * (z + -1.0))) / (t - a));
	} else if (z <= 2.15e+40) {
		tmp = x / (1.0 - z);
	} 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 <= -4e-87:
		tmp = t_1
	elif z <= 1.8e-82:
		tmp = ((y * x) + (z * (t - a))) / y
	elif z <= 5.3e-6:
		tmp = z / (((z * b) - (y * (z + -1.0))) / (t - a))
	elif z <= 2.15e+40:
		tmp = x / (1.0 - z)
	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 <= -4e-87)
		tmp = t_1;
	elseif (z <= 1.8e-82)
		tmp = Float64(Float64(Float64(y * x) + Float64(z * Float64(t - a))) / y);
	elseif (z <= 5.3e-6)
		tmp = Float64(z / Float64(Float64(Float64(z * b) - Float64(y * Float64(z + -1.0))) / Float64(t - a)));
	elseif (z <= 2.15e+40)
		tmp = Float64(x / Float64(1.0 - z));
	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 <= -4e-87)
		tmp = t_1;
	elseif (z <= 1.8e-82)
		tmp = ((y * x) + (z * (t - a))) / y;
	elseif (z <= 5.3e-6)
		tmp = z / (((z * b) - (y * (z + -1.0))) / (t - a));
	elseif (z <= 2.15e+40)
		tmp = x / (1.0 - z);
	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, -4e-87], t$95$1, If[LessEqual[z, 1.8e-82], N[(N[(N[(y * x), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[z, 5.3e-6], N[(z / N[(N[(N[(z * b), $MachinePrecision] - N[(y * N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.15e+40], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.00000000000000007e-87 or 2.1500000000000001e40 < 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 78.1%

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

   if -4.00000000000000007e-87 < z < 1.79999999999999999e-82

   1. Initial program 84.5%

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

   3. Taylor expanded in z around 0 62.4%

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

   if 1.79999999999999999e-82 < z < 5.3000000000000001e-6

   1. Initial program 84.4%

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

   3. Taylor expanded in y around -inf 84.5%

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

      1. +-commutative 84.5%

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

      2. mul-1-neg 84.5%

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

      3. unsub-neg 84.5%

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

      4. *-commutative 84.5%

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

      5. sub-neg 84.5%

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

      6. metadata-eval 84.5%

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

   5. Simplified 84.5%

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

   6. Taylor expanded in x around 0 73.2%

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

      1. associate-/l* 72.8%

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

      2. *-commutative 72.8%

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

      3. sub-neg 72.8%

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

      4. metadata-eval 72.8%

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

   8. Simplified 72.8%

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

   if 5.3000000000000001e-6 < z < 2.1500000000000001e40

   1. Initial program 64.8%

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

   3. Taylor expanded in y around inf 65.9%

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

      1. mul-1-neg 65.9%

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

      2. unsub-neg 65.9%

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

   5. Simplified 65.9%

      \[\leadsto \color{blue}{\frac{x}{1 - z}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 71.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{-87}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-82}:\\ \;\;\;\;\frac{y \cdot x + z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{-6}:\\ \;\;\;\;\frac{z}{\frac{z \cdot b - y \cdot \left(z + -1\right)}{t - a}}\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{+40}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 36.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -\frac{a}{b}\\ \mathbf{if}\;z \leq -1.75 \cdot 10^{+109}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.15 \cdot 10^{+88}:\\ \;\;\;\;\frac{a}{y}\\ \mathbf{elif}\;z \leq -1.08 \cdot 10^{-88}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{-31}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+251}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (/ a b))))
   (if (<= z -1.75e+109)
     t_1
     (if (<= z -2.15e+88)
       (/ a y)
       (if (<= z -1.08e-88)
         t_1
         (if (<= z 1.22e-31) x (if (<= z 2e+251) t_1 (/ a y))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -(a / b);
	double tmp;
	if (z <= -1.75e+109) {
		tmp = t_1;
	} else if (z <= -2.15e+88) {
		tmp = a / y;
	} else if (z <= -1.08e-88) {
		tmp = t_1;
	} else if (z <= 1.22e-31) {
		tmp = x;
	} else if (z <= 2e+251) {
		tmp = t_1;
	} else {
		tmp = 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) :: t_1
    real(8) :: tmp
    t_1 = -(a / b)
    if (z <= (-1.75d+109)) then
        tmp = t_1
    else if (z <= (-2.15d+88)) then
        tmp = a / y
    else if (z <= (-1.08d-88)) then
        tmp = t_1
    else if (z <= 1.22d-31) then
        tmp = x
    else if (z <= 2d+251) then
        tmp = t_1
    else
        tmp = 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 t_1 = -(a / b);
	double tmp;
	if (z <= -1.75e+109) {
		tmp = t_1;
	} else if (z <= -2.15e+88) {
		tmp = a / y;
	} else if (z <= -1.08e-88) {
		tmp = t_1;
	} else if (z <= 1.22e-31) {
		tmp = x;
	} else if (z <= 2e+251) {
		tmp = t_1;
	} else {
		tmp = a / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = -(a / b)
	tmp = 0
	if z <= -1.75e+109:
		tmp = t_1
	elif z <= -2.15e+88:
		tmp = a / y
	elif z <= -1.08e-88:
		tmp = t_1
	elif z <= 1.22e-31:
		tmp = x
	elif z <= 2e+251:
		tmp = t_1
	else:
		tmp = a / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(-Float64(a / b))
	tmp = 0.0
	if (z <= -1.75e+109)
		tmp = t_1;
	elseif (z <= -2.15e+88)
		tmp = Float64(a / y);
	elseif (z <= -1.08e-88)
		tmp = t_1;
	elseif (z <= 1.22e-31)
		tmp = x;
	elseif (z <= 2e+251)
		tmp = t_1;
	else
		tmp = Float64(a / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = -(a / b);
	tmp = 0.0;
	if (z <= -1.75e+109)
		tmp = t_1;
	elseif (z <= -2.15e+88)
		tmp = a / y;
	elseif (z <= -1.08e-88)
		tmp = t_1;
	elseif (z <= 1.22e-31)
		tmp = x;
	elseif (z <= 2e+251)
		tmp = t_1;
	else
		tmp = a / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = (-N[(a / b), $MachinePrecision])}, If[LessEqual[z, -1.75e+109], t$95$1, If[LessEqual[z, -2.15e+88], N[(a / y), $MachinePrecision], If[LessEqual[z, -1.08e-88], t$95$1, If[LessEqual[z, 1.22e-31], x, If[LessEqual[z, 2e+251], t$95$1, N[(a / y), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.74999999999999992e109 or -2.14999999999999987e88 < z < -1.07999999999999995e-88 or 1.21999999999999992e-31 < z < 2.0000000000000001e251

   1. Initial program 50.4%

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

   3. Taylor expanded in b around inf 30.7%

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

   4. Taylor expanded in a around inf 32.1%

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

      1. associate-*r/ 32.1%

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

      2. neg-mul-1 32.1%

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

   6. Simplified 32.1%

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

   if -1.74999999999999992e109 < z < -2.14999999999999987e88 or 2.0000000000000001e251 < z

   1. Initial program 19.8%

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

   3. Taylor expanded in y around -inf 19.4%

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

      1. +-commutative 19.4%

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

      2. mul-1-neg 19.4%

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

      3. unsub-neg 19.4%

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

      4. *-commutative 19.4%

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

      5. sub-neg 19.4%

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

      6. metadata-eval 19.4%

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

   5. Simplified 19.4%

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

   6. Taylor expanded in a around inf 16.1%

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

      1. mul-1-neg 16.1%

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

      2. *-commutative 16.1%

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

      3. distribute-rgt-neg-in 16.1%

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

   8. Simplified 16.1%

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

   9. Taylor expanded in z around inf 67.4%

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

       1. associate-*r/ 67.4%

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

       2. neg-mul-1 67.4%

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

   11. Simplified 67.4%

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

   12. Taylor expanded in b around 0 59.3%

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

   if -1.07999999999999995e-88 < z < 1.21999999999999992e-31

   1. Initial program 83.8%

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

   3. Taylor expanded in z around 0 54.2%

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

4. Final simplification 43.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+109}:\\ \;\;\;\;-\frac{a}{b}\\ \mathbf{elif}\;z \leq -2.15 \cdot 10^{+88}:\\ \;\;\;\;\frac{a}{y}\\ \mathbf{elif}\;z \leq -1.08 \cdot 10^{-88}:\\ \;\;\;\;-\frac{a}{b}\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{-31}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+251}:\\ \;\;\;\;-\frac{a}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 84.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{+41} \lor \neg \left(z \leq 9.5 \cdot 10^{+40}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x + z \cdot \left(t - a\right)}{z \cdot b - y \cdot \left(z + -1\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -3.7e+41) (not (<= z 9.5e+40)))
   (/ (- t a) (- b y))
   (/ (+ (* y x) (* z (- t a))) (- (* z b) (* y (+ z -1.0))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -3.7e+41) || !(z <= 9.5e+40)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((y * x) + (z * (t - a))) / ((z * b) - (y * (z + -1.0)));
	}
	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 <= (-3.7d+41)) .or. (.not. (z <= 9.5d+40))) then
        tmp = (t - a) / (b - y)
    else
        tmp = ((y * x) + (z * (t - a))) / ((z * b) - (y * (z + (-1.0d0))))
    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 <= -3.7e+41) || !(z <= 9.5e+40)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((y * x) + (z * (t - a))) / ((z * b) - (y * (z + -1.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -3.7e+41) or not (z <= 9.5e+40):
		tmp = (t - a) / (b - y)
	else:
		tmp = ((y * x) + (z * (t - a))) / ((z * b) - (y * (z + -1.0)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -3.7e+41) || !(z <= 9.5e+40))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(Float64(Float64(y * x) + Float64(z * Float64(t - a))) / Float64(Float64(z * b) - Float64(y * Float64(z + -1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -3.7e+41) || ~((z <= 9.5e+40)))
		tmp = (t - a) / (b - y);
	else
		tmp = ((y * x) + (z * (t - a))) / ((z * b) - (y * (z + -1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -3.7e+41], N[Not[LessEqual[z, 9.5e+40]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y * x), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(z * b), $MachinePrecision] - N[(y * N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.69999999999999981e41 or 9.5000000000000003e40 < z

   1. Initial program 35.5%

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

   3. Taylor expanded in z around inf 82.5%

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

   if -3.69999999999999981e41 < z < 9.5000000000000003e40

   1. Initial program 83.4%

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

   3. Taylor expanded in y around -inf 83.4%

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

      1. +-commutative 83.4%

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

      2. mul-1-neg 83.4%

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

      3. unsub-neg 83.4%

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

      4. *-commutative 83.4%

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

      5. sub-neg 83.4%

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

      6. metadata-eval 83.4%

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

   5. Simplified 83.4%

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

4. Final simplification 83.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{+41} \lor \neg \left(z \leq 9.5 \cdot 10^{+40}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x + z \cdot \left(t - a\right)}{z \cdot b - y \cdot \left(z + -1\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 63.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -4.6 \cdot 10^{-90}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-169}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-244}:\\ \;\;\;\;\frac{y \cdot x}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{+40}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -4.6e-90)
     t_1
     (if (<= z -7.5e-169)
       x
       (if (<= z -1.3e-244)
         (/ (* y x) (+ y (* z b)))
         (if (<= z 2.15e+40) (/ x (- 1.0 z)) 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 <= -4.6e-90) {
		tmp = t_1;
	} else if (z <= -7.5e-169) {
		tmp = x;
	} else if (z <= -1.3e-244) {
		tmp = (y * x) / (y + (z * b));
	} else if (z <= 2.15e+40) {
		tmp = x / (1.0 - z);
	} 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 <= (-4.6d-90)) then
        tmp = t_1
    else if (z <= (-7.5d-169)) then
        tmp = x
    else if (z <= (-1.3d-244)) then
        tmp = (y * x) / (y + (z * b))
    else if (z <= 2.15d+40) then
        tmp = x / (1.0d0 - z)
    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 <= -4.6e-90) {
		tmp = t_1;
	} else if (z <= -7.5e-169) {
		tmp = x;
	} else if (z <= -1.3e-244) {
		tmp = (y * x) / (y + (z * b));
	} else if (z <= 2.15e+40) {
		tmp = x / (1.0 - z);
	} 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 <= -4.6e-90:
		tmp = t_1
	elif z <= -7.5e-169:
		tmp = x
	elif z <= -1.3e-244:
		tmp = (y * x) / (y + (z * b))
	elif z <= 2.15e+40:
		tmp = x / (1.0 - z)
	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 <= -4.6e-90)
		tmp = t_1;
	elseif (z <= -7.5e-169)
		tmp = x;
	elseif (z <= -1.3e-244)
		tmp = Float64(Float64(y * x) / Float64(y + Float64(z * b)));
	elseif (z <= 2.15e+40)
		tmp = Float64(x / Float64(1.0 - z));
	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 <= -4.6e-90)
		tmp = t_1;
	elseif (z <= -7.5e-169)
		tmp = x;
	elseif (z <= -1.3e-244)
		tmp = (y * x) / (y + (z * b));
	elseif (z <= 2.15e+40)
		tmp = x / (1.0 - z);
	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, -4.6e-90], t$95$1, If[LessEqual[z, -7.5e-169], x, If[LessEqual[z, -1.3e-244], N[(N[(y * x), $MachinePrecision] / N[(y + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.15e+40], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.5999999999999996e-90 or 2.1500000000000001e40 < 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 78.1%

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

   if -4.5999999999999996e-90 < z < -7.49999999999999978e-169

   1. Initial program 73.5%

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

   3. Taylor expanded in z around 0 57.7%

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

   if -7.49999999999999978e-169 < z < -1.3000000000000001e-244

   1. Initial program 94.9%

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

   3. Taylor expanded in x around inf 66.3%

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

      1. *-commutative 66.3%

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

   5. Simplified 66.3%

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

   6. Taylor expanded in b around inf 66.3%

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

      1. *-commutative 66.3%

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

   8. Simplified 66.3%

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

   if -1.3000000000000001e-244 < z < 2.1500000000000001e40

   1. Initial program 81.8%

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

   3. Taylor expanded in y around inf 55.9%

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

      1. mul-1-neg 55.9%

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

      2. unsub-neg 55.9%

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

   5. Simplified 55.9%

      \[\leadsto \color{blue}{\frac{x}{1 - z}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{-90}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-169}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-244}:\\ \;\;\;\;\frac{y \cdot x}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{+40}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 84.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+39} \lor \neg \left(z \leq 1.7 \cdot 10^{+47}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.85e+39) (not (<= z 1.7e+47)))
   (/ (- t a) (- b y))
   (/ (+ (* y x) (* z (- t a))) (+ y (* z (- b y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.85e+39) || !(z <= 1.7e+47)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((y * x) + (z * (t - a))) / (y + (z * (b - y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-1.85d+39)) .or. (.not. (z <= 1.7d+47))) then
        tmp = (t - a) / (b - y)
    else
        tmp = ((y * x) + (z * (t - a))) / (y + (z * (b - y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.85e+39) || !(z <= 1.7e+47)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((y * x) + (z * (t - a))) / (y + (z * (b - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.85e+39) or not (z <= 1.7e+47):
		tmp = (t - a) / (b - y)
	else:
		tmp = ((y * x) + (z * (t - a))) / (y + (z * (b - y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.85e+39) || !(z <= 1.7e+47))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(Float64(Float64(y * x) + Float64(z * Float64(t - a))) / Float64(y + Float64(z * Float64(b - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1.85e+39) || ~((z <= 1.7e+47)))
		tmp = (t - a) / (b - y);
	else
		tmp = ((y * x) + (z * (t - a))) / (y + (z * (b - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.85e+39], N[Not[LessEqual[z, 1.7e+47]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y * x), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.85000000000000006e39 or 1.6999999999999999e47 < z

   1. Initial program 35.5%

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

   3. Taylor expanded in z around inf 82.5%

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

   if -1.85000000000000006e39 < z < 1.6999999999999999e47

   1. Initial program 83.4%

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

4. Final simplification 83.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+39} \lor \neg \left(z \leq 1.7 \cdot 10^{+47}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 51.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -2.7 \cdot 10^{+194}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{+94}:\\ \;\;\;\;\frac{-a}{b - y}\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{-40} \lor \neg \left(y \leq 6.5 \cdot 10^{+73}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (- 1.0 z))))
   (if (<= y -2.7e+194)
     t_1
     (if (<= y -3.2e+94)
       (/ (- a) (- b y))
       (if (or (<= y -1.15e-40) (not (<= y 6.5e+73))) t_1 (/ (- t a) b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 - z);
	double tmp;
	if (y <= -2.7e+194) {
		tmp = t_1;
	} else if (y <= -3.2e+94) {
		tmp = -a / (b - y);
	} else if ((y <= -1.15e-40) || !(y <= 6.5e+73)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x / (1.0d0 - z)
    if (y <= (-2.7d+194)) then
        tmp = t_1
    else if (y <= (-3.2d+94)) then
        tmp = -a / (b - y)
    else if ((y <= (-1.15d-40)) .or. (.not. (y <= 6.5d+73))) then
        tmp = t_1
    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 t_1 = x / (1.0 - z);
	double tmp;
	if (y <= -2.7e+194) {
		tmp = t_1;
	} else if (y <= -3.2e+94) {
		tmp = -a / (b - y);
	} else if ((y <= -1.15e-40) || !(y <= 6.5e+73)) {
		tmp = t_1;
	} else {
		tmp = (t - a) / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (1.0 - z)
	tmp = 0
	if y <= -2.7e+194:
		tmp = t_1
	elif y <= -3.2e+94:
		tmp = -a / (b - y)
	elif (y <= -1.15e-40) or not (y <= 6.5e+73):
		tmp = t_1
	else:
		tmp = (t - a) / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(1.0 - z))
	tmp = 0.0
	if (y <= -2.7e+194)
		tmp = t_1;
	elseif (y <= -3.2e+94)
		tmp = Float64(Float64(-a) / Float64(b - y));
	elseif ((y <= -1.15e-40) || !(y <= 6.5e+73))
		tmp = t_1;
	else
		tmp = Float64(Float64(t - a) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (1.0 - z);
	tmp = 0.0;
	if (y <= -2.7e+194)
		tmp = t_1;
	elseif (y <= -3.2e+94)
		tmp = -a / (b - y);
	elseif ((y <= -1.15e-40) || ~((y <= 6.5e+73)))
		tmp = t_1;
	else
		tmp = (t - a) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.7e+194], t$95$1, If[LessEqual[y, -3.2e+94], N[((-a) / N[(b - y), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -1.15e-40], N[Not[LessEqual[y, 6.5e+73]], $MachinePrecision]], t$95$1, N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.7000000000000002e194 or -3.20000000000000014e94 < y < -1.15e-40 or 6.5000000000000001e73 < y

   1. Initial program 46.3%

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

   3. Taylor expanded in y around inf 60.9%

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

      1. mul-1-neg 60.9%

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

      2. unsub-neg 60.9%

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

   5. Simplified 60.9%

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

   if -2.7000000000000002e194 < y < -3.20000000000000014e94

   1. Initial program 49.5%

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

   3. Taylor expanded in y around -inf 49.5%

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

      1. +-commutative 49.5%

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

      2. mul-1-neg 49.5%

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

      3. unsub-neg 49.5%

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

      4. *-commutative 49.5%

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

      5. sub-neg 49.5%

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

      6. metadata-eval 49.5%

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

   5. Simplified 49.5%

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

   6. Taylor expanded in a around inf 12.5%

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

      1. mul-1-neg 12.5%

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

      2. *-commutative 12.5%

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

      3. distribute-rgt-neg-in 12.5%

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

   8. Simplified 12.5%

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

   9. Taylor expanded in z around inf 37.2%

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

       1. associate-*r/ 37.2%

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

       2. neg-mul-1 37.2%

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

   11. Simplified 37.2%

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

   if -1.15e-40 < y < 6.5000000000000001e73

   1. Initial program 76.5%

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

   3. Taylor expanded in y around 0 55.0%

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

4. Final simplification 55.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+194}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{+94}:\\ \;\;\;\;\frac{-a}{b - y}\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{-40} \lor \neg \left(y \leq 6.5 \cdot 10^{+73}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 43.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{b - y}\\ t_2 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -2.7 \cdot 10^{-38}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{-121}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-209}:\\ \;\;\;\;-\frac{a}{b}\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-27}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ t (- b y))) (t_2 (/ x (- 1.0 z))))
   (if (<= y -2.7e-38)
     t_2
     (if (<= y -8.5e-121)
       t_1
       (if (<= y 5e-209) (- (/ a b)) (if (<= y 1.45e-27) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t / (b - y);
	double t_2 = x / (1.0 - z);
	double tmp;
	if (y <= -2.7e-38) {
		tmp = t_2;
	} else if (y <= -8.5e-121) {
		tmp = t_1;
	} else if (y <= 5e-209) {
		tmp = -(a / b);
	} else if (y <= 1.45e-27) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t / (b - y)
    t_2 = x / (1.0d0 - z)
    if (y <= (-2.7d-38)) then
        tmp = t_2
    else if (y <= (-8.5d-121)) then
        tmp = t_1
    else if (y <= 5d-209) then
        tmp = -(a / b)
    else if (y <= 1.45d-27) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t / (b - y);
	double t_2 = x / (1.0 - z);
	double tmp;
	if (y <= -2.7e-38) {
		tmp = t_2;
	} else if (y <= -8.5e-121) {
		tmp = t_1;
	} else if (y <= 5e-209) {
		tmp = -(a / b);
	} else if (y <= 1.45e-27) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t / (b - y)
	t_2 = x / (1.0 - z)
	tmp = 0
	if y <= -2.7e-38:
		tmp = t_2
	elif y <= -8.5e-121:
		tmp = t_1
	elif y <= 5e-209:
		tmp = -(a / b)
	elif y <= 1.45e-27:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t / Float64(b - y))
	t_2 = Float64(x / Float64(1.0 - z))
	tmp = 0.0
	if (y <= -2.7e-38)
		tmp = t_2;
	elseif (y <= -8.5e-121)
		tmp = t_1;
	elseif (y <= 5e-209)
		tmp = Float64(-Float64(a / b));
	elseif (y <= 1.45e-27)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t / (b - y);
	t_2 = x / (1.0 - z);
	tmp = 0.0;
	if (y <= -2.7e-38)
		tmp = t_2;
	elseif (y <= -8.5e-121)
		tmp = t_1;
	elseif (y <= 5e-209)
		tmp = -(a / b);
	elseif (y <= 1.45e-27)
		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[(t / N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.7e-38], t$95$2, If[LessEqual[y, -8.5e-121], t$95$1, If[LessEqual[y, 5e-209], (-N[(a / b), $MachinePrecision]), If[LessEqual[y, 1.45e-27], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.70000000000000005e-38 or 1.45000000000000002e-27 < y

   1. Initial program 47.8%

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

   3. Taylor expanded in y around inf 50.6%

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

      1. mul-1-neg 50.6%

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

      2. unsub-neg 50.6%

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

   5. Simplified 50.6%

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

   if -2.70000000000000005e-38 < y < -8.50000000000000025e-121 or 5.0000000000000005e-209 < y < 1.45000000000000002e-27

   1. Initial program 81.8%

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

   3. Taylor expanded in t around inf 34.0%

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

      1. associate-/l* 37.8%

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

      2. +-commutative 37.8%

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

      3. fma-def 37.8%

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

   5. Simplified 37.8%

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

   6. Taylor expanded in z around inf 41.5%

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

   if -8.50000000000000025e-121 < y < 5.0000000000000005e-209

   1. Initial program 79.2%

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

   3. Taylor expanded in b around inf 52.3%

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

   4. Taylor expanded in a around inf 53.5%

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

      1. associate-*r/ 53.5%

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

      2. neg-mul-1 53.5%

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

   6. Simplified 53.5%

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

4. Final simplification 49.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{-38}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{-121}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-209}:\\ \;\;\;\;-\frac{a}{b}\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-27}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 68.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{-87} \lor \neg \left(z \leq 0.024\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x + z \cdot \left(t - a\right)}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -2.9e-87) (not (<= z 0.024)))
   (/ (- t a) (- b y))
   (/ (+ (* y x) (* z (- t a))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.9e-87) || !(z <= 0.024)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((y * x) + (z * (t - 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 <= (-2.9d-87)) .or. (.not. (z <= 0.024d0))) then
        tmp = (t - a) / (b - y)
    else
        tmp = ((y * x) + (z * (t - 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 <= -2.9e-87) || !(z <= 0.024)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((y * x) + (z * (t - a))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -2.9e-87) or not (z <= 0.024):
		tmp = (t - a) / (b - y)
	else:
		tmp = ((y * x) + (z * (t - a))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -2.9e-87) || !(z <= 0.024))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(Float64(Float64(y * x) + Float64(z * Float64(t - a))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -2.9e-87) || ~((z <= 0.024)))
		tmp = (t - a) / (b - y);
	else
		tmp = ((y * x) + (z * (t - a))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -2.9e-87], N[Not[LessEqual[z, 0.024]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y * x), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.8999999999999999e-87 or 0.024 < z

   1. Initial program 42.7%

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

   3. Taylor expanded in z around inf 75.8%

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

   if -2.8999999999999999e-87 < z < 0.024

   1. Initial program 84.9%

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

   3. Taylor expanded in z around 0 58.8%

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

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{-87} \lor \neg \left(z \leq 0.024\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x + z \cdot \left(t - a\right)}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 63.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{-87} \lor \neg \left(z \leq 2.15 \cdot 10^{+40}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -3.9e-87) (not (<= z 2.15e+40)))
   (/ (- 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 <= -3.9e-87) || !(z <= 2.15e+40)) {
		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 <= (-3.9d-87)) .or. (.not. (z <= 2.15d+40))) 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 <= -3.9e-87) || !(z <= 2.15e+40)) {
		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 <= -3.9e-87) or not (z <= 2.15e+40):
		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 <= -3.9e-87) || !(z <= 2.15e+40))
		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 <= -3.9e-87) || ~((z <= 2.15e+40)))
		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, -3.9e-87], N[Not[LessEqual[z, 2.15e+40]], $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 < -3.8999999999999998e-87 or 2.1500000000000001e40 < 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 78.1%

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

   if -3.8999999999999998e-87 < z < 2.1500000000000001e40

   1. Initial program 82.7%

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

   3. Taylor expanded in y around inf 53.1%

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

      1. mul-1-neg 53.1%

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

      2. unsub-neg 53.1%

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

   5. Simplified 53.1%

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

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{-87} \lor \neg \left(z \leq 2.15 \cdot 10^{+40}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 54.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{-40} \lor \neg \left(y \leq 6 \cdot 10^{+73}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -4.4e-40) (not (<= y 6e+73))) (/ 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 <= -4.4e-40) || !(y <= 6e+73)) {
		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 <= (-4.4d-40)) .or. (.not. (y <= 6d+73))) 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 <= -4.4e-40) || !(y <= 6e+73)) {
		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 <= -4.4e-40) or not (y <= 6e+73):
		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 <= -4.4e-40) || !(y <= 6e+73))
		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 <= -4.4e-40) || ~((y <= 6e+73)))
		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, -4.4e-40], N[Not[LessEqual[y, 6e+73]], $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 < -4.40000000000000018e-40 or 6.00000000000000021e73 < y

   1. Initial program 46.9%

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

   3. Taylor expanded in y around inf 53.7%

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

      1. mul-1-neg 53.7%

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

      2. unsub-neg 53.7%

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

   5. Simplified 53.7%

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

   if -4.40000000000000018e-40 < y < 6.00000000000000021e73

   1. Initial program 76.5%

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

   3. Taylor expanded in y around 0 55.0%

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

4. Final simplification 54.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{-40} \lor \neg \left(y \leq 6 \cdot 10^{+73}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 33.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+58} \lor \neg \left(z \leq 0.96\right):\\ \;\;\;\;\frac{a}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -2.8e+58) (not (<= z 0.96))) (/ a y) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.8e+58) || !(z <= 0.96)) {
		tmp = a / y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-2.8d+58)) .or. (.not. (z <= 0.96d0))) then
        tmp = a / y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.8e+58) || !(z <= 0.96)) {
		tmp = a / y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -2.8e+58) or not (z <= 0.96):
		tmp = a / y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -2.8e+58) || !(z <= 0.96))
		tmp = Float64(a / y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -2.8e+58) || ~((z <= 0.96)))
		tmp = a / y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -2.8e+58], N[Not[LessEqual[z, 0.96]], $MachinePrecision]], N[(a / y), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -2.7999999999999998e58 or 0.95999999999999996 < z

   1. Initial program 37.4%

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

   3. Taylor expanded in y around -inf 37.4%

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

      1. +-commutative 37.4%

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

      2. mul-1-neg 37.4%

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

      3. unsub-neg 37.4%

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

      4. *-commutative 37.4%

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

      5. sub-neg 37.4%

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

      6. metadata-eval 37.4%

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

   5. Simplified 37.4%

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

   6. Taylor expanded in a around inf 23.3%

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

      1. mul-1-neg 23.3%

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

      2. *-commutative 23.3%

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

      3. distribute-rgt-neg-in 23.3%

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

   8. Simplified 23.3%

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

   9. Taylor expanded in z around inf 51.0%

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

       1. associate-*r/ 51.0%

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

       2. neg-mul-1 51.0%

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

   11. Simplified 51.0%

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

   12. Taylor expanded in b around 0 29.2%

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

   if -2.7999999999999998e58 < z < 0.95999999999999996

   1. Initial program 82.5%

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

   3. Taylor expanded in z around 0 44.9%

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

4. Final simplification 37.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+58} \lor \neg \left(z \leq 0.96\right):\\ \;\;\;\;\frac{a}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 35.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{-49}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 0.62:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -2.6e-49) (/ t b) (if (<= z 0.62) x (/ a y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2.6e-49) {
		tmp = t / b;
	} else if (z <= 0.62) {
		tmp = x;
	} else {
		tmp = 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 <= (-2.6d-49)) then
        tmp = t / b
    else if (z <= 0.62d0) then
        tmp = x
    else
        tmp = 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 <= -2.6e-49) {
		tmp = t / b;
	} else if (z <= 0.62) {
		tmp = x;
	} else {
		tmp = a / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -2.6e-49:
		tmp = t / b
	elif z <= 0.62:
		tmp = x
	else:
		tmp = a / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -2.6e-49)
		tmp = Float64(t / b);
	elseif (z <= 0.62)
		tmp = x;
	else
		tmp = Float64(a / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -2.6e-49)
		tmp = t / b;
	elseif (z <= 0.62)
		tmp = x;
	else
		tmp = a / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -2.6e-49], N[(t / b), $MachinePrecision], If[LessEqual[z, 0.62], x, N[(a / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.59999999999999995e-49

   1. Initial program 43.1%

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

   3. Taylor expanded in b around inf 26.3%

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

   4. Taylor expanded in t around inf 22.2%

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

   if -2.59999999999999995e-49 < z < 0.619999999999999996

   1. Initial program 84.7%

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

   3. Taylor expanded in z around 0 50.3%

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

   if 0.619999999999999996 < 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 y around -inf 39.5%

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

      1. +-commutative 39.5%

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

      2. mul-1-neg 39.5%

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

      3. unsub-neg 39.5%

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

      4. *-commutative 39.5%

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

      5. sub-neg 39.5%

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

      6. metadata-eval 39.5%

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

   5. Simplified 39.5%

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

   6. Taylor expanded in a around inf 25.4%

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

      1. mul-1-neg 25.4%

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

      2. *-commutative 25.4%

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

      3. distribute-rgt-neg-in 25.4%

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

   8. Simplified 25.4%

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

   9. Taylor expanded in z around inf 51.6%

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

       1. associate-*r/ 51.6%

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

       2. neg-mul-1 51.6%

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

   11. Simplified 51.6%

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

   12. Taylor expanded in b around 0 31.7%

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

4. Final simplification 37.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{-49}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 0.62:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 25.0% 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 61.4%

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

3. Taylor expanded in z around 0 25.6%

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

4. Final simplification 25.6%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 73.3% 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 2024027 
(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)))))