Development.Shake.Progress:decay from shake-0.15.5

Percentage Accurate: 66.2% → 90.4%

Time: 16.1s

Alternatives: 16

Speedup: 0.7×

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: 66.2% 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: 90.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ \mathbf{if}\;z \leq -0.00023 \lor \neg \left(z \leq 250000000\right):\\ \;\;\;\;\frac{x \cdot \frac{y}{b - y} - y \cdot \frac{t - a}{{\left(b - y\right)}^{2}}}{z} + \frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{t\_1} + \frac{z \cdot \left(t - a\right)}{x \cdot t\_1}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y)))))
   (if (or (<= z -0.00023) (not (<= z 250000000.0)))
     (+
      (/ (- (* x (/ y (- b y))) (* y (/ (- t a) (pow (- b y) 2.0)))) z)
      (/ (- t a) (- b y)))
     (* x (+ (/ y t_1) (/ (* z (- t a)) (* x t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double tmp;
	if ((z <= -0.00023) || !(z <= 250000000.0)) {
		tmp = (((x * (y / (b - y))) - (y * ((t - a) / pow((b - y), 2.0)))) / z) + ((t - a) / (b - y));
	} else {
		tmp = x * ((y / t_1) + ((z * (t - a)) / (x * t_1)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y + (z * (b - y))
    if ((z <= (-0.00023d0)) .or. (.not. (z <= 250000000.0d0))) then
        tmp = (((x * (y / (b - y))) - (y * ((t - a) / ((b - y) ** 2.0d0)))) / z) + ((t - a) / (b - y))
    else
        tmp = x * ((y / t_1) + ((z * (t - a)) / (x * t_1)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double tmp;
	if ((z <= -0.00023) || !(z <= 250000000.0)) {
		tmp = (((x * (y / (b - y))) - (y * ((t - a) / Math.pow((b - y), 2.0)))) / z) + ((t - a) / (b - y));
	} else {
		tmp = x * ((y / t_1) + ((z * (t - a)) / (x * t_1)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z * (b - y))
	tmp = 0
	if (z <= -0.00023) or not (z <= 250000000.0):
		tmp = (((x * (y / (b - y))) - (y * ((t - a) / math.pow((b - y), 2.0)))) / z) + ((t - a) / (b - y))
	else:
		tmp = x * ((y / t_1) + ((z * (t - a)) / (x * t_1)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(z * Float64(b - y)))
	tmp = 0.0
	if ((z <= -0.00023) || !(z <= 250000000.0))
		tmp = Float64(Float64(Float64(Float64(x * Float64(y / Float64(b - y))) - Float64(y * Float64(Float64(t - a) / (Float64(b - y) ^ 2.0)))) / z) + Float64(Float64(t - a) / Float64(b - y)));
	else
		tmp = Float64(x * Float64(Float64(y / t_1) + Float64(Float64(z * Float64(t - a)) / Float64(x * t_1))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (z * (b - y));
	tmp = 0.0;
	if ((z <= -0.00023) || ~((z <= 250000000.0)))
		tmp = (((x * (y / (b - y))) - (y * ((t - a) / ((b - y) ^ 2.0)))) / z) + ((t - a) / (b - y));
	else
		tmp = x * ((y / t_1) + ((z * (t - a)) / (x * t_1)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[z, -0.00023], N[Not[LessEqual[z, 250000000.0]], $MachinePrecision]], N[(N[(N[(N[(x * N[(y / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * N[(N[(t - a), $MachinePrecision] / N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] + N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y / t$95$1), $MachinePrecision] + N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / N[(x * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.3000000000000001e-4 or 2.5e8 < z

   1. Initial program 44.3%

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

   3. Taylor expanded in z around -inf 63.4%

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

      1. associate--l+ 63.4%

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

      2. mul-1-neg 63.4%

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

      3. distribute-lft-out-- 63.4%

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

      4. associate-/l* 70.7%

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

      5. associate-/l* 93.0%

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

      6. div-sub 93.0%

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

   5. Simplified 93.0%

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

   if -2.3000000000000001e-4 < z < 2.5e8

   1. Initial program 89.3%

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

   3. Taylor expanded in x around inf 90.5%

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

4. Final simplification 91.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.00023 \lor \neg \left(z \leq 250000000\right):\\ \;\;\;\;\frac{x \cdot \frac{y}{b - y} - y \cdot \frac{t - a}{{\left(b - y\right)}^{2}}}{z} + \frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{y + z \cdot \left(b - y\right)} + \frac{z \cdot \left(t - a\right)}{x \cdot \left(y + z \cdot \left(b - y\right)\right)}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 68.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(t - a\right)\\ t_2 := y + z \cdot b\\ t_3 := \frac{t\_1}{t\_2}\\ t_4 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -2.8 \cdot 10^{-5}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;z \leq -2.05 \cdot 10^{-100}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-140}:\\ \;\;\;\;\frac{x \cdot y}{t\_2}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-201}:\\ \;\;\;\;\frac{t\_1 + x \cdot y}{y}\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-75}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq 7000:\\ \;\;\;\;x \cdot \frac{y}{y \cdot \left(1 - z\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- t a)))
        (t_2 (+ y (* z b)))
        (t_3 (/ t_1 t_2))
        (t_4 (/ (- t a) (- b y))))
   (if (<= z -2.8e-5)
     t_4
     (if (<= z -2.05e-100)
       t_3
       (if (<= z -2.8e-140)
         (/ (* x y) t_2)
         (if (<= z 5e-201)
           (/ (+ t_1 (* x y)) y)
           (if (<= z 1.75e-75)
             t_3
             (if (<= z 7000.0) (* x (/ y (* y (- 1.0 z)))) t_4))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (t - a);
	double t_2 = y + (z * b);
	double t_3 = t_1 / t_2;
	double t_4 = (t - a) / (b - y);
	double tmp;
	if (z <= -2.8e-5) {
		tmp = t_4;
	} else if (z <= -2.05e-100) {
		tmp = t_3;
	} else if (z <= -2.8e-140) {
		tmp = (x * y) / t_2;
	} else if (z <= 5e-201) {
		tmp = (t_1 + (x * y)) / y;
	} else if (z <= 1.75e-75) {
		tmp = t_3;
	} else if (z <= 7000.0) {
		tmp = x * (y / (y * (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) :: tmp
    t_1 = z * (t - a)
    t_2 = y + (z * b)
    t_3 = t_1 / t_2
    t_4 = (t - a) / (b - y)
    if (z <= (-2.8d-5)) then
        tmp = t_4
    else if (z <= (-2.05d-100)) then
        tmp = t_3
    else if (z <= (-2.8d-140)) then
        tmp = (x * y) / t_2
    else if (z <= 5d-201) then
        tmp = (t_1 + (x * y)) / y
    else if (z <= 1.75d-75) then
        tmp = t_3
    else if (z <= 7000.0d0) then
        tmp = x * (y / (y * (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 * (t - a);
	double t_2 = y + (z * b);
	double t_3 = t_1 / t_2;
	double t_4 = (t - a) / (b - y);
	double tmp;
	if (z <= -2.8e-5) {
		tmp = t_4;
	} else if (z <= -2.05e-100) {
		tmp = t_3;
	} else if (z <= -2.8e-140) {
		tmp = (x * y) / t_2;
	} else if (z <= 5e-201) {
		tmp = (t_1 + (x * y)) / y;
	} else if (z <= 1.75e-75) {
		tmp = t_3;
	} else if (z <= 7000.0) {
		tmp = x * (y / (y * (1.0 - z)));
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (t - a)
	t_2 = y + (z * b)
	t_3 = t_1 / t_2
	t_4 = (t - a) / (b - y)
	tmp = 0
	if z <= -2.8e-5:
		tmp = t_4
	elif z <= -2.05e-100:
		tmp = t_3
	elif z <= -2.8e-140:
		tmp = (x * y) / t_2
	elif z <= 5e-201:
		tmp = (t_1 + (x * y)) / y
	elif z <= 1.75e-75:
		tmp = t_3
	elif z <= 7000.0:
		tmp = x * (y / (y * (1.0 - z)))
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(t - a))
	t_2 = Float64(y + Float64(z * b))
	t_3 = Float64(t_1 / t_2)
	t_4 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -2.8e-5)
		tmp = t_4;
	elseif (z <= -2.05e-100)
		tmp = t_3;
	elseif (z <= -2.8e-140)
		tmp = Float64(Float64(x * y) / t_2);
	elseif (z <= 5e-201)
		tmp = Float64(Float64(t_1 + Float64(x * y)) / y);
	elseif (z <= 1.75e-75)
		tmp = t_3;
	elseif (z <= 7000.0)
		tmp = Float64(x * Float64(y / Float64(y * 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 * (t - a);
	t_2 = y + (z * b);
	t_3 = t_1 / t_2;
	t_4 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -2.8e-5)
		tmp = t_4;
	elseif (z <= -2.05e-100)
		tmp = t_3;
	elseif (z <= -2.8e-140)
		tmp = (x * y) / t_2;
	elseif (z <= 5e-201)
		tmp = (t_1 + (x * y)) / y;
	elseif (z <= 1.75e-75)
		tmp = t_3;
	elseif (z <= 7000.0)
		tmp = x * (y / (y * (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[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(z * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$1 / t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.8e-5], t$95$4, If[LessEqual[z, -2.05e-100], t$95$3, If[LessEqual[z, -2.8e-140], N[(N[(x * y), $MachinePrecision] / t$95$2), $MachinePrecision], If[LessEqual[z, 5e-201], N[(N[(t$95$1 + N[(x * y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[z, 1.75e-75], t$95$3, If[LessEqual[z, 7000.0], N[(x * N[(y / N[(y * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$4]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.79999999999999996e-5 or 7e3 < z

   1. Initial program 44.7%

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

   3. Taylor expanded in z around inf 78.9%

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

   if -2.79999999999999996e-5 < z < -2.0499999999999999e-100 or 4.9999999999999999e-201 < z < 1.74999999999999993e-75

   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 0 82.5%

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

   4. Taylor expanded in b around inf 81.9%

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

      1. *-commutative 81.9%

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

   6. Simplified 81.9%

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

   if -2.0499999999999999e-100 < z < -2.8000000000000002e-140

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 86.2%

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

      1. *-commutative 86.2%

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

   5. Simplified 86.2%

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

   6. Taylor expanded in b around inf 86.2%

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

      1. *-commutative 17.9%

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

   8. Simplified 86.2%

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

   if -2.8000000000000002e-140 < z < 4.9999999999999999e-201

   1. Initial program 91.7%

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

   3. Taylor expanded in b around inf 91.7%

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

      1. *-commutative 36.8%

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

   5. Simplified 91.7%

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

   6. Taylor expanded in b around 0 79.4%

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

   if 1.74999999999999993e-75 < z < 7e3

   1. Initial program 68.2%

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

   3. Taylor expanded in x around inf 41.0%

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

      1. *-commutative 41.0%

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

   5. Simplified 41.0%

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

   6. Taylor expanded in b around 0 21.4%

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

      1. associate-/l* 52.7%

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

      2. mul-1-neg 52.7%

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

      3. *-rgt-identity 52.7%

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

      4. distribute-rgt-neg-in 52.7%

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

      5. distribute-lft-in 52.7%

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

      6. sub-neg 52.7%

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

   8. Simplified 52.7%

      \[\leadsto \color{blue}{x \cdot \frac{y}{y \cdot \left(1 - z\right)}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{-5}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -2.05 \cdot 10^{-100}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot b}\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-140}:\\ \;\;\;\;\frac{x \cdot y}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-201}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y}\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-75}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 7000:\\ \;\;\;\;x \cdot \frac{y}{y \cdot \left(1 - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 85.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ \mathbf{if}\;z \leq -0.00023 \lor \neg \left(z \leq 2.2 \cdot 10^{+88}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{t\_1} + \frac{z \cdot \left(t - a\right)}{x \cdot t\_1}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y)))))
   (if (or (<= z -0.00023) (not (<= z 2.2e+88)))
     (/ (- t a) (- b y))
     (* x (+ (/ y t_1) (/ (* z (- t a)) (* x t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double tmp;
	if ((z <= -0.00023) || !(z <= 2.2e+88)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x * ((y / t_1) + ((z * (t - a)) / (x * t_1)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y + (z * (b - y))
    if ((z <= (-0.00023d0)) .or. (.not. (z <= 2.2d+88))) then
        tmp = (t - a) / (b - y)
    else
        tmp = x * ((y / t_1) + ((z * (t - a)) / (x * t_1)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double tmp;
	if ((z <= -0.00023) || !(z <= 2.2e+88)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x * ((y / t_1) + ((z * (t - a)) / (x * t_1)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z * (b - y))
	tmp = 0
	if (z <= -0.00023) or not (z <= 2.2e+88):
		tmp = (t - a) / (b - y)
	else:
		tmp = x * ((y / t_1) + ((z * (t - a)) / (x * t_1)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(z * Float64(b - y)))
	tmp = 0.0
	if ((z <= -0.00023) || !(z <= 2.2e+88))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(x * Float64(Float64(y / t_1) + Float64(Float64(z * Float64(t - a)) / Float64(x * t_1))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (z * (b - y));
	tmp = 0.0;
	if ((z <= -0.00023) || ~((z <= 2.2e+88)))
		tmp = (t - a) / (b - y);
	else
		tmp = x * ((y / t_1) + ((z * (t - a)) / (x * t_1)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[z, -0.00023], N[Not[LessEqual[z, 2.2e+88]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y / t$95$1), $MachinePrecision] + N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / N[(x * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.3000000000000001e-4 or 2.20000000000000009e88 < z

   1. Initial program 38.5%

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

   3. Taylor expanded in z around inf 81.6%

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

   if -2.3000000000000001e-4 < z < 2.20000000000000009e88

   1. Initial program 88.5%

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

   3. Taylor expanded in x around inf 88.8%

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

4. Final simplification 85.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.00023 \lor \neg \left(z \leq 2.2 \cdot 10^{+88}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{y + z \cdot \left(b - y\right)} + \frac{z \cdot \left(t - a\right)}{x \cdot \left(y + z \cdot \left(b - y\right)\right)}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 41.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{b - y}\\ \mathbf{if}\;z \leq -2.55 \cdot 10^{-95}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-201}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-101}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 0.64:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{+179} \lor \neg \left(z \leq 2.8 \cdot 10^{+228}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{-b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ t (- b y))))
   (if (<= z -2.55e-95)
     t_1
     (if (<= z 5e-201)
       x
       (if (<= z 1.55e-101)
         t_1
         (if (<= z 0.64)
           x
           (if (or (<= z 2.25e+179) (not (<= z 2.8e+228)))
             t_1
             (/ a (- b)))))))))

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 <= -2.55e-95) {
		tmp = t_1;
	} else if (z <= 5e-201) {
		tmp = x;
	} else if (z <= 1.55e-101) {
		tmp = t_1;
	} else if (z <= 0.64) {
		tmp = x;
	} else if ((z <= 2.25e+179) || !(z <= 2.8e+228)) {
		tmp = t_1;
	} else {
		tmp = a / -b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t / (b - y)
    if (z <= (-2.55d-95)) then
        tmp = t_1
    else if (z <= 5d-201) then
        tmp = x
    else if (z <= 1.55d-101) then
        tmp = t_1
    else if (z <= 0.64d0) then
        tmp = x
    else if ((z <= 2.25d+179) .or. (.not. (z <= 2.8d+228))) then
        tmp = t_1
    else
        tmp = a / -b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t / (b - y);
	double tmp;
	if (z <= -2.55e-95) {
		tmp = t_1;
	} else if (z <= 5e-201) {
		tmp = x;
	} else if (z <= 1.55e-101) {
		tmp = t_1;
	} else if (z <= 0.64) {
		tmp = x;
	} else if ((z <= 2.25e+179) || !(z <= 2.8e+228)) {
		tmp = t_1;
	} else {
		tmp = a / -b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t / (b - y)
	tmp = 0
	if z <= -2.55e-95:
		tmp = t_1
	elif z <= 5e-201:
		tmp = x
	elif z <= 1.55e-101:
		tmp = t_1
	elif z <= 0.64:
		tmp = x
	elif (z <= 2.25e+179) or not (z <= 2.8e+228):
		tmp = t_1
	else:
		tmp = a / -b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t / Float64(b - y))
	tmp = 0.0
	if (z <= -2.55e-95)
		tmp = t_1;
	elseif (z <= 5e-201)
		tmp = x;
	elseif (z <= 1.55e-101)
		tmp = t_1;
	elseif (z <= 0.64)
		tmp = x;
	elseif ((z <= 2.25e+179) || !(z <= 2.8e+228))
		tmp = t_1;
	else
		tmp = Float64(a / Float64(-b));
	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 <= -2.55e-95)
		tmp = t_1;
	elseif (z <= 5e-201)
		tmp = x;
	elseif (z <= 1.55e-101)
		tmp = t_1;
	elseif (z <= 0.64)
		tmp = x;
	elseif ((z <= 2.25e+179) || ~((z <= 2.8e+228)))
		tmp = t_1;
	else
		tmp = a / -b;
	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, -2.55e-95], t$95$1, If[LessEqual[z, 5e-201], x, If[LessEqual[z, 1.55e-101], t$95$1, If[LessEqual[z, 0.64], x, If[Or[LessEqual[z, 2.25e+179], N[Not[LessEqual[z, 2.8e+228]], $MachinePrecision]], t$95$1, N[(a / (-b)), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.55e-95 or 4.9999999999999999e-201 < z < 1.54999999999999987e-101 or 0.640000000000000013 < z < 2.2500000000000001e179 or 2.7999999999999999e228 < z

   1. Initial program 56.9%

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

   3. Taylor expanded in z around inf 69.6%

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

   4. Taylor expanded in t around inf 47.0%

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

   if -2.55e-95 < z < 4.9999999999999999e-201 or 1.54999999999999987e-101 < z < 0.640000000000000013

   1. Initial program 87.6%

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

   3. Taylor expanded in z around 0 58.7%

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

   if 2.2500000000000001e179 < z < 2.7999999999999999e228

   1. Initial program 25.1%

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

   3. Taylor expanded in b around inf 24.9%

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

   4. Taylor expanded in a around inf 56.8%

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

      1. mul-1-neg 56.8%

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

      2. distribute-neg-frac2 56.8%

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

   6. Simplified 56.8%

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

4. Final simplification 51.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.55 \cdot 10^{-95}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-201}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-101}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;z \leq 0.64:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{+179} \lor \neg \left(z \leq 2.8 \cdot 10^{+228}\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{-b}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 66.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z \cdot \left(t - a\right)}{y + z \cdot b}\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -0.00023:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{-103}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-201}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-75}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 0.76:\\ \;\;\;\;x \cdot \frac{y}{y \cdot \left(1 - z\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* z (- t a)) (+ y (* z b)))) (t_2 (/ (- t a) (- b y))))
   (if (<= z -0.00023)
     t_2
     (if (<= z -1.95e-103)
       t_1
       (if (<= z 4.8e-201)
         x
         (if (<= z 1.35e-75)
           t_1
           (if (<= z 0.76) (* x (/ y (* y (- 1.0 z)))) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z * (t - a)) / (y + (z * b));
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -0.00023) {
		tmp = t_2;
	} else if (z <= -1.95e-103) {
		tmp = t_1;
	} else if (z <= 4.8e-201) {
		tmp = x;
	} else if (z <= 1.35e-75) {
		tmp = t_1;
	} else if (z <= 0.76) {
		tmp = x * (y / (y * (1.0 - z)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (z * (t - a)) / (y + (z * b))
    t_2 = (t - a) / (b - y)
    if (z <= (-0.00023d0)) then
        tmp = t_2
    else if (z <= (-1.95d-103)) then
        tmp = t_1
    else if (z <= 4.8d-201) then
        tmp = x
    else if (z <= 1.35d-75) then
        tmp = t_1
    else if (z <= 0.76d0) then
        tmp = x * (y / (y * (1.0d0 - z)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z * (t - a)) / (y + (z * b));
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -0.00023) {
		tmp = t_2;
	} else if (z <= -1.95e-103) {
		tmp = t_1;
	} else if (z <= 4.8e-201) {
		tmp = x;
	} else if (z <= 1.35e-75) {
		tmp = t_1;
	} else if (z <= 0.76) {
		tmp = x * (y / (y * (1.0 - z)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z * (t - a)) / (y + (z * b))
	t_2 = (t - a) / (b - y)
	tmp = 0
	if z <= -0.00023:
		tmp = t_2
	elif z <= -1.95e-103:
		tmp = t_1
	elif z <= 4.8e-201:
		tmp = x
	elif z <= 1.35e-75:
		tmp = t_1
	elif z <= 0.76:
		tmp = x * (y / (y * (1.0 - z)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z * Float64(t - a)) / Float64(y + Float64(z * b)))
	t_2 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -0.00023)
		tmp = t_2;
	elseif (z <= -1.95e-103)
		tmp = t_1;
	elseif (z <= 4.8e-201)
		tmp = x;
	elseif (z <= 1.35e-75)
		tmp = t_1;
	elseif (z <= 0.76)
		tmp = Float64(x * Float64(y / Float64(y * Float64(1.0 - z))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z * (t - a)) / (y + (z * b));
	t_2 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -0.00023)
		tmp = t_2;
	elseif (z <= -1.95e-103)
		tmp = t_1;
	elseif (z <= 4.8e-201)
		tmp = x;
	elseif (z <= 1.35e-75)
		tmp = t_1;
	elseif (z <= 0.76)
		tmp = x * (y / (y * (1.0 - z)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.00023], t$95$2, If[LessEqual[z, -1.95e-103], t$95$1, If[LessEqual[z, 4.8e-201], x, If[LessEqual[z, 1.35e-75], t$95$1, If[LessEqual[z, 0.76], N[(x * N[(y / N[(y * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.3000000000000001e-4 or 0.76000000000000001 < z

   1. Initial program 44.7%

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

   3. Taylor expanded in z around inf 78.9%

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

   if -2.3000000000000001e-4 < z < -1.9500000000000001e-103 or 4.80000000000000018e-201 < z < 1.3499999999999999e-75

   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 0 82.5%

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

   4. Taylor expanded in b around inf 81.9%

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

      1. *-commutative 81.9%

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

   6. Simplified 81.9%

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

   if -1.9500000000000001e-103 < z < 4.80000000000000018e-201

   1. Initial program 92.6%

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

   3. Taylor expanded in z around 0 66.7%

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

   if 1.3499999999999999e-75 < z < 0.76000000000000001

   1. Initial program 68.2%

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

   3. Taylor expanded in x around inf 41.0%

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

      1. *-commutative 41.0%

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

   5. Simplified 41.0%

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

   6. Taylor expanded in b around 0 21.4%

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

      1. associate-/l* 52.7%

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

      2. mul-1-neg 52.7%

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

      3. *-rgt-identity 52.7%

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

      4. distribute-rgt-neg-in 52.7%

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

      5. distribute-lft-in 52.7%

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

      6. sub-neg 52.7%

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

   8. Simplified 52.7%

      \[\leadsto \color{blue}{x \cdot \frac{y}{y \cdot \left(1 - z\right)}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 74.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.00023:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{-103}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-201}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-75}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 0.76:\\ \;\;\;\;x \cdot \frac{y}{y \cdot \left(1 - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 69.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ t_2 := z \cdot \left(t - a\right)\\ \mathbf{if}\;z \leq -1.2 \cdot 10^{+16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{-84}:\\ \;\;\;\;z \cdot \frac{t - a}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-201}:\\ \;\;\;\;\frac{t\_2 + x \cdot y}{y}\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-78}:\\ \;\;\;\;\frac{t\_2}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 0.65:\\ \;\;\;\;x \cdot \frac{y}{y \cdot \left(1 - z\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))) (t_2 (* z (- t a))))
   (if (<= z -1.2e+16)
     t_1
     (if (<= z -1.65e-84)
       (* z (/ (- t a) (+ y (* z (- b y)))))
       (if (<= z 5e-201)
         (/ (+ t_2 (* x y)) y)
         (if (<= z 3.7e-78)
           (/ t_2 (+ y (* z b)))
           (if (<= z 0.65) (* x (/ y (* y (- 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 t_2 = z * (t - a);
	double tmp;
	if (z <= -1.2e+16) {
		tmp = t_1;
	} else if (z <= -1.65e-84) {
		tmp = z * ((t - a) / (y + (z * (b - y))));
	} else if (z <= 5e-201) {
		tmp = (t_2 + (x * y)) / y;
	} else if (z <= 3.7e-78) {
		tmp = t_2 / (y + (z * b));
	} else if (z <= 0.65) {
		tmp = x * (y / (y * (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) :: t_2
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    t_2 = z * (t - a)
    if (z <= (-1.2d+16)) then
        tmp = t_1
    else if (z <= (-1.65d-84)) then
        tmp = z * ((t - a) / (y + (z * (b - y))))
    else if (z <= 5d-201) then
        tmp = (t_2 + (x * y)) / y
    else if (z <= 3.7d-78) then
        tmp = t_2 / (y + (z * b))
    else if (z <= 0.65d0) then
        tmp = x * (y / (y * (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 t_2 = z * (t - a);
	double tmp;
	if (z <= -1.2e+16) {
		tmp = t_1;
	} else if (z <= -1.65e-84) {
		tmp = z * ((t - a) / (y + (z * (b - y))));
	} else if (z <= 5e-201) {
		tmp = (t_2 + (x * y)) / y;
	} else if (z <= 3.7e-78) {
		tmp = t_2 / (y + (z * b));
	} else if (z <= 0.65) {
		tmp = x * (y / (y * (1.0 - z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	t_2 = z * (t - a)
	tmp = 0
	if z <= -1.2e+16:
		tmp = t_1
	elif z <= -1.65e-84:
		tmp = z * ((t - a) / (y + (z * (b - y))))
	elif z <= 5e-201:
		tmp = (t_2 + (x * y)) / y
	elif z <= 3.7e-78:
		tmp = t_2 / (y + (z * b))
	elif z <= 0.65:
		tmp = x * (y / (y * (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))
	t_2 = Float64(z * Float64(t - a))
	tmp = 0.0
	if (z <= -1.2e+16)
		tmp = t_1;
	elseif (z <= -1.65e-84)
		tmp = Float64(z * Float64(Float64(t - a) / Float64(y + Float64(z * Float64(b - y)))));
	elseif (z <= 5e-201)
		tmp = Float64(Float64(t_2 + Float64(x * y)) / y);
	elseif (z <= 3.7e-78)
		tmp = Float64(t_2 / Float64(y + Float64(z * b)));
	elseif (z <= 0.65)
		tmp = Float64(x * Float64(y / Float64(y * 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);
	t_2 = z * (t - a);
	tmp = 0.0;
	if (z <= -1.2e+16)
		tmp = t_1;
	elseif (z <= -1.65e-84)
		tmp = z * ((t - a) / (y + (z * (b - y))));
	elseif (z <= 5e-201)
		tmp = (t_2 + (x * y)) / y;
	elseif (z <= 3.7e-78)
		tmp = t_2 / (y + (z * b));
	elseif (z <= 0.65)
		tmp = x * (y / (y * (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]}, Block[{t$95$2 = N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.2e+16], t$95$1, If[LessEqual[z, -1.65e-84], N[(z * N[(N[(t - a), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5e-201], N[(N[(t$95$2 + N[(x * y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[z, 3.7e-78], N[(t$95$2 / N[(y + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.65], N[(x * N[(y / N[(y * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.2e16 or 0.650000000000000022 < z

   1. Initial program 43.0%

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

   3. Taylor expanded in z around inf 78.6%

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

   if -1.2e16 < z < -1.64999999999999992e-84

   1. Initial program 88.2%

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

      1. sub-neg 88.2%

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

      2. distribute-lft-in 88.3%

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

   4. Applied egg-rr 88.3%

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

   5. Taylor expanded in x around 0 82.2%

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

      1. associate-/l* 82.4%

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

      2. +-commutative 82.4%

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

      3. associate-*r* 82.4%

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

      4. distribute-rgt-in 82.4%

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

      5. mul-1-neg 82.4%

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

      6. sub-neg 82.4%

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

   7. Simplified 82.4%

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

   if -1.64999999999999992e-84 < z < 4.9999999999999999e-201

   1. Initial program 92.8%

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

   3. Taylor expanded in b around inf 92.8%

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

      1. *-commutative 36.7%

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

   5. Simplified 92.8%

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

   6. Taylor expanded in b around 0 79.3%

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

   if 4.9999999999999999e-201 < z < 3.70000000000000006e-78

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 84.1%

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

   4. Taylor expanded in b around inf 84.1%

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

      1. *-commutative 84.1%

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

   6. Simplified 84.1%

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

   if 3.70000000000000006e-78 < z < 0.650000000000000022

   1. Initial program 68.2%

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

   3. Taylor expanded in x around inf 41.0%

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

      1. *-commutative 41.0%

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

   5. Simplified 41.0%

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

   6. Taylor expanded in b around 0 21.4%

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

      1. associate-/l* 52.7%

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

      2. mul-1-neg 52.7%

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

      3. *-rgt-identity 52.7%

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

      4. distribute-rgt-neg-in 52.7%

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

      5. distribute-lft-in 52.7%

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

      6. sub-neg 52.7%

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

   8. Simplified 52.7%

      \[\leadsto \color{blue}{x \cdot \frac{y}{y \cdot \left(1 - z\right)}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+16}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{-84}:\\ \;\;\;\;z \cdot \frac{t - a}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-201}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y}\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-78}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 0.65:\\ \;\;\;\;x \cdot \frac{y}{y \cdot \left(1 - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 63.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -3.65 \cdot 10^{-96}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-201}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-87}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;z \leq 0.85:\\ \;\;\;\;x \cdot \frac{y}{y \cdot \left(1 - z\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -3.65e-96)
     t_1
     (if (<= z 5e-201)
       x
       (if (<= z 1.02e-87)
         (/ (* z (- t a)) y)
         (if (<= z 0.85) (* x (/ y (* y (- 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 <= -3.65e-96) {
		tmp = t_1;
	} else if (z <= 5e-201) {
		tmp = x;
	} else if (z <= 1.02e-87) {
		tmp = (z * (t - a)) / y;
	} else if (z <= 0.85) {
		tmp = x * (y / (y * (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 <= (-3.65d-96)) then
        tmp = t_1
    else if (z <= 5d-201) then
        tmp = x
    else if (z <= 1.02d-87) then
        tmp = (z * (t - a)) / y
    else if (z <= 0.85d0) then
        tmp = x * (y / (y * (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 <= -3.65e-96) {
		tmp = t_1;
	} else if (z <= 5e-201) {
		tmp = x;
	} else if (z <= 1.02e-87) {
		tmp = (z * (t - a)) / y;
	} else if (z <= 0.85) {
		tmp = x * (y / (y * (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 <= -3.65e-96:
		tmp = t_1
	elif z <= 5e-201:
		tmp = x
	elif z <= 1.02e-87:
		tmp = (z * (t - a)) / y
	elif z <= 0.85:
		tmp = x * (y / (y * (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 <= -3.65e-96)
		tmp = t_1;
	elseif (z <= 5e-201)
		tmp = x;
	elseif (z <= 1.02e-87)
		tmp = Float64(Float64(z * Float64(t - a)) / y);
	elseif (z <= 0.85)
		tmp = Float64(x * Float64(y / Float64(y * 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 <= -3.65e-96)
		tmp = t_1;
	elseif (z <= 5e-201)
		tmp = x;
	elseif (z <= 1.02e-87)
		tmp = (z * (t - a)) / y;
	elseif (z <= 0.85)
		tmp = x * (y / (y * (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, -3.65e-96], t$95$1, If[LessEqual[z, 5e-201], x, If[LessEqual[z, 1.02e-87], N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[z, 0.85], N[(x * N[(y / N[(y * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.64999999999999997e-96 or 0.849999999999999978 < z

   1. Initial program 49.0%

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

   3. Taylor expanded in z around inf 74.6%

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

   if -3.64999999999999997e-96 < z < 4.9999999999999999e-201

   1. Initial program 92.6%

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

   3. Taylor expanded in z around 0 66.7%

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

   if 4.9999999999999999e-201 < z < 1.02000000000000009e-87

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 86.8%

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

   4. Taylor expanded in z around 0 54.1%

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

   if 1.02000000000000009e-87 < z < 0.849999999999999978

   1. Initial program 70.9%

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

   3. Taylor expanded in x around inf 42.0%

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

      1. *-commutative 42.0%

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

   5. Simplified 42.0%

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

   6. Taylor expanded in b around 0 24.1%

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

      1. associate-/l* 52.7%

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

      2. mul-1-neg 52.7%

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

      3. *-rgt-identity 52.7%

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

      4. distribute-rgt-neg-in 52.7%

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

      5. distribute-lft-in 52.7%

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

      6. sub-neg 52.7%

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

   8. Simplified 52.7%

      \[\leadsto \color{blue}{x \cdot \frac{y}{y \cdot \left(1 - z\right)}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.65 \cdot 10^{-96}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-201}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-87}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;z \leq 0.85:\\ \;\;\;\;x \cdot \frac{y}{y \cdot \left(1 - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 84.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.05 \cdot 10^{+38} \lor \neg \left(z \leq 1.8 \cdot 10^{+88}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + \left(z \cdot b - z \cdot y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -3.05e+38) (not (<= z 1.8e+88)))
   (/ (- t a) (- b y))
   (/ (+ (* z (- t a)) (* x y)) (+ y (- (* z b) (* z y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -3.05e+38) || !(z <= 1.8e+88)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((z * (t - a)) + (x * y)) / (y + ((z * b) - (z * y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-3.05d+38)) .or. (.not. (z <= 1.8d+88))) then
        tmp = (t - a) / (b - y)
    else
        tmp = ((z * (t - a)) + (x * y)) / (y + ((z * b) - (z * y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -3.05e+38) || !(z <= 1.8e+88)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((z * (t - a)) + (x * y)) / (y + ((z * b) - (z * y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -3.05e+38) or not (z <= 1.8e+88):
		tmp = (t - a) / (b - y)
	else:
		tmp = ((z * (t - a)) + (x * y)) / (y + ((z * b) - (z * y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -3.05e+38) || !(z <= 1.8e+88))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(Float64(Float64(z * Float64(t - a)) + Float64(x * y)) / Float64(y + Float64(Float64(z * b) - Float64(z * y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -3.05e+38) || ~((z <= 1.8e+88)))
		tmp = (t - a) / (b - y);
	else
		tmp = ((z * (t - a)) + (x * y)) / (y + ((z * b) - (z * y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -3.05e+38], N[Not[LessEqual[z, 1.8e+88]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] / N[(y + N[(N[(z * b), $MachinePrecision] - N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.05e38 or 1.8000000000000001e88 < z

   1. Initial program 34.5%

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

   3. Taylor expanded in z around inf 80.8%

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

   if -3.05e38 < z < 1.8000000000000001e88

   1. Initial program 89.0%

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

      1. sub-neg 89.0%

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

      2. distribute-lft-in 89.0%

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

   4. Applied egg-rr 89.0%

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

4. Final simplification 85.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.05 \cdot 10^{+38} \lor \neg \left(z \leq 1.8 \cdot 10^{+88}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + \left(z \cdot b - z \cdot y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 63.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -1.08 \cdot 10^{-95}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-201}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-87}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;z \leq 1.25:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -1.08e-95)
     t_1
     (if (<= z 3e-201)
       x
       (if (<= z 1.02e-87)
         (/ (* z (- t a)) y)
         (if (<= z 1.25) (/ 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 <= -1.08e-95) {
		tmp = t_1;
	} else if (z <= 3e-201) {
		tmp = x;
	} else if (z <= 1.02e-87) {
		tmp = (z * (t - a)) / y;
	} else if (z <= 1.25) {
		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 <= (-1.08d-95)) then
        tmp = t_1
    else if (z <= 3d-201) then
        tmp = x
    else if (z <= 1.02d-87) then
        tmp = (z * (t - a)) / y
    else if (z <= 1.25d0) 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 <= -1.08e-95) {
		tmp = t_1;
	} else if (z <= 3e-201) {
		tmp = x;
	} else if (z <= 1.02e-87) {
		tmp = (z * (t - a)) / y;
	} else if (z <= 1.25) {
		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 <= -1.08e-95:
		tmp = t_1
	elif z <= 3e-201:
		tmp = x
	elif z <= 1.02e-87:
		tmp = (z * (t - a)) / y
	elif z <= 1.25:
		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 <= -1.08e-95)
		tmp = t_1;
	elseif (z <= 3e-201)
		tmp = x;
	elseif (z <= 1.02e-87)
		tmp = Float64(Float64(z * Float64(t - a)) / y);
	elseif (z <= 1.25)
		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 <= -1.08e-95)
		tmp = t_1;
	elseif (z <= 3e-201)
		tmp = x;
	elseif (z <= 1.02e-87)
		tmp = (z * (t - a)) / y;
	elseif (z <= 1.25)
		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, -1.08e-95], t$95$1, If[LessEqual[z, 3e-201], x, If[LessEqual[z, 1.02e-87], N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[z, 1.25], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.08e-95 or 1.25 < z

   1. Initial program 49.0%

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

   3. Taylor expanded in z around inf 74.6%

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

   if -1.08e-95 < z < 3.00000000000000002e-201

   1. Initial program 92.6%

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

   3. Taylor expanded in z around 0 66.7%

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

   if 3.00000000000000002e-201 < z < 1.02000000000000009e-87

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 86.8%

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

   4. Taylor expanded in z around 0 54.1%

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

   if 1.02000000000000009e-87 < z < 1.25

   1. Initial program 70.9%

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

   3. Taylor expanded in y around inf 52.7%

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

      1. mul-1-neg 52.7%

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

      2. unsub-neg 52.7%

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

   5. Simplified 52.7%

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

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.08 \cdot 10^{-95}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-201}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-87}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;z \leq 1.25:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 84.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.52 \cdot 10^{+38} \lor \neg \left(z \leq 2.05 \cdot 10^{+88}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.52e+38) (not (<= z 2.05e+88)))
   (/ (- t a) (- b y))
   (/ (+ (* z (- t a)) (* x y)) (+ y (* z (- b y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.52e+38) || !(z <= 2.05e+88)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((z * (t - a)) + (x * y)) / (y + (z * (b - y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-1.52d+38)) .or. (.not. (z <= 2.05d+88))) then
        tmp = (t - a) / (b - y)
    else
        tmp = ((z * (t - a)) + (x * y)) / (y + (z * (b - y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.52e+38) || !(z <= 2.05e+88)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((z * (t - a)) + (x * y)) / (y + (z * (b - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.52e+38) or not (z <= 2.05e+88):
		tmp = (t - a) / (b - y)
	else:
		tmp = ((z * (t - a)) + (x * y)) / (y + (z * (b - y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.52e+38) || !(z <= 2.05e+88))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(Float64(Float64(z * Float64(t - a)) + Float64(x * y)) / Float64(y + Float64(z * Float64(b - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1.52e+38) || ~((z <= 2.05e+88)))
		tmp = (t - a) / (b - y);
	else
		tmp = ((z * (t - a)) + (x * y)) / (y + (z * (b - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.52e+38], N[Not[LessEqual[z, 2.05e+88]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.51999999999999996e38 or 2.05000000000000014e88 < z

   1. Initial program 34.5%

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

   3. Taylor expanded in z around inf 80.8%

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

   if -1.51999999999999996e38 < z < 2.05000000000000014e88

   1. Initial program 89.0%

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

4. Final simplification 85.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.52 \cdot 10^{+38} \lor \neg \left(z \leq 2.05 \cdot 10^{+88}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 83.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.00023 \lor \neg \left(z \leq 800000000\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -0.00023) (not (<= z 800000000.0)))
   (/ (- t a) (- b y))
   (/ (+ (* z (- t a)) (* x y)) (+ y (* z b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -0.00023) || !(z <= 800000000.0)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((z * (t - a)) + (x * y)) / (y + (z * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-0.00023d0)) .or. (.not. (z <= 800000000.0d0))) then
        tmp = (t - a) / (b - y)
    else
        tmp = ((z * (t - a)) + (x * y)) / (y + (z * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -0.00023) || !(z <= 800000000.0)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((z * (t - a)) + (x * y)) / (y + (z * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -0.00023) or not (z <= 800000000.0):
		tmp = (t - a) / (b - y)
	else:
		tmp = ((z * (t - a)) + (x * y)) / (y + (z * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -0.00023) || !(z <= 800000000.0))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(Float64(Float64(z * Float64(t - a)) + Float64(x * y)) / Float64(y + Float64(z * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -0.00023) || ~((z <= 800000000.0)))
		tmp = (t - a) / (b - y);
	else
		tmp = ((z * (t - a)) + (x * y)) / (y + (z * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -0.00023], N[Not[LessEqual[z, 800000000.0]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.3000000000000001e-4 or 8e8 < z

   1. Initial program 43.4%

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

   3. Taylor expanded in z around inf 79.9%

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

   if -2.3000000000000001e-4 < z < 8e8

   1. Initial program 89.5%

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

   3. Taylor expanded in b around inf 88.1%

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

      1. *-commutative 47.8%

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

   5. Simplified 88.1%

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

4. Final simplification 84.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.00023 \lor \neg \left(z \leq 800000000\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot b}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 42.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1600 \lor \neg \left(t \leq 4.7 \cdot 10^{+27}\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -1600.0) (not (<= t 4.7e+27))) (/ t (- b y)) (/ x (- 1.0 z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1600.0) || !(t <= 4.7e+27)) {
		tmp = t / (b - y);
	} else {
		tmp = x / (1.0 - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-1600.0d0)) .or. (.not. (t <= 4.7d+27))) then
        tmp = t / (b - y)
    else
        tmp = x / (1.0d0 - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1600.0) || !(t <= 4.7e+27)) {
		tmp = t / (b - y);
	} else {
		tmp = x / (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -1600.0) or not (t <= 4.7e+27):
		tmp = t / (b - y)
	else:
		tmp = x / (1.0 - z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -1600.0) || !(t <= 4.7e+27))
		tmp = Float64(t / Float64(b - y));
	else
		tmp = Float64(x / Float64(1.0 - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -1600.0) || ~((t <= 4.7e+27)))
		tmp = t / (b - y);
	else
		tmp = x / (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -1600.0], N[Not[LessEqual[t, 4.7e+27]], $MachinePrecision]], N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1600 or 4.69999999999999976e27 < t

   1. Initial program 62.1%

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

   3. Taylor expanded in z around inf 61.1%

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

   4. Taylor expanded in t around inf 51.5%

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

   if -1600 < t < 4.69999999999999976e27

   1. Initial program 71.1%

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

   3. Taylor expanded in y around inf 44.0%

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

      1. mul-1-neg 44.0%

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

      2. unsub-neg 44.0%

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

   5. Simplified 44.0%

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

4. Final simplification 47.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1600 \lor \neg \left(t \leq 4.7 \cdot 10^{+27}\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 53.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{-73} \lor \neg \left(y \leq 3.1 \cdot 10^{-46}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.35e-73) (not (<= y 3.1e-46))) (/ x (- 1.0 z)) (/ (- t a) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.35e-73) || !(y <= 3.1e-46)) {
		tmp = x / (1.0 - z);
	} else {
		tmp = (t - a) / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-1.35d-73)) .or. (.not. (y <= 3.1d-46))) then
        tmp = x / (1.0d0 - z)
    else
        tmp = (t - a) / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.35e-73) || !(y <= 3.1e-46)) {
		tmp = x / (1.0 - z);
	} else {
		tmp = (t - a) / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.35e-73) or not (y <= 3.1e-46):
		tmp = x / (1.0 - z)
	else:
		tmp = (t - a) / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.35e-73) || !(y <= 3.1e-46))
		tmp = Float64(x / Float64(1.0 - z));
	else
		tmp = Float64(Float64(t - a) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.35e-73) || ~((y <= 3.1e-46)))
		tmp = x / (1.0 - z);
	else
		tmp = (t - a) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.35e-73], N[Not[LessEqual[y, 3.1e-46]], $MachinePrecision]], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.34999999999999997e-73 or 3.1000000000000001e-46 < y

   1. Initial program 57.2%

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

   3. Taylor expanded in y around inf 45.6%

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

      1. mul-1-neg 45.6%

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

      2. unsub-neg 45.6%

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

   5. Simplified 45.6%

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

   if -1.34999999999999997e-73 < y < 3.1000000000000001e-46

   1. Initial program 80.6%

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

   3. Taylor expanded in y around 0 66.1%

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

4. Final simplification 53.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{-73} \lor \neg \left(y \leq 3.1 \cdot 10^{-46}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 35.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.55 \cdot 10^{-95}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 0.64:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{-b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -2.55e-95) (/ t b) (if (<= z 0.64) x (/ a (- b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2.55e-95) {
		tmp = t / b;
	} else if (z <= 0.64) {
		tmp = x;
	} else {
		tmp = a / -b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-2.55d-95)) then
        tmp = t / b
    else if (z <= 0.64d0) then
        tmp = x
    else
        tmp = a / -b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2.55e-95) {
		tmp = t / b;
	} else if (z <= 0.64) {
		tmp = x;
	} else {
		tmp = a / -b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -2.55e-95:
		tmp = t / b
	elif z <= 0.64:
		tmp = x
	else:
		tmp = a / -b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -2.55e-95)
		tmp = Float64(t / b);
	elseif (z <= 0.64)
		tmp = x;
	else
		tmp = Float64(a / Float64(-b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -2.55e-95)
		tmp = t / b;
	elseif (z <= 0.64)
		tmp = x;
	else
		tmp = a / -b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -2.55e-95], N[(t / b), $MachinePrecision], If[LessEqual[z, 0.64], x, N[(a / (-b)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.55e-95

   1. Initial program 53.5%

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

   3. Taylor expanded in b around inf 33.1%

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

   4. Taylor expanded in t around inf 38.7%

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

   if -2.55e-95 < z < 0.640000000000000013

   1. Initial program 89.5%

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

   3. Taylor expanded in z around 0 51.3%

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

   if 0.640000000000000013 < z

   1. Initial program 43.6%

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

   3. Taylor expanded in b around inf 29.1%

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

   4. Taylor expanded in a around inf 28.6%

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

      1. mul-1-neg 28.6%

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

      2. distribute-neg-frac2 28.6%

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

   6. Simplified 28.6%

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

4. Final simplification 41.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.55 \cdot 10^{-95}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 0.64:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{-b}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 35.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.55 \cdot 10^{-95} \lor \neg \left(z \leq 0.64\right):\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -2.55e-95) (not (<= z 0.64))) (/ t b) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.55e-95) || !(z <= 0.64)) {
		tmp = t / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-2.55d-95)) .or. (.not. (z <= 0.64d0))) then
        tmp = t / b
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.55e-95) || !(z <= 0.64)) {
		tmp = t / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -2.55e-95) or not (z <= 0.64):
		tmp = t / b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -2.55e-95) || !(z <= 0.64))
		tmp = Float64(t / b);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -2.55e-95) || ~((z <= 0.64)))
		tmp = t / b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -2.55e-95], N[Not[LessEqual[z, 0.64]], $MachinePrecision]], N[(t / b), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -2.55e-95 or 0.640000000000000013 < z

   1. Initial program 49.0%

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

   3. Taylor expanded in b around inf 31.3%

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

   4. Taylor expanded in t around inf 32.0%

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

   if -2.55e-95 < z < 0.640000000000000013

   1. Initial program 89.5%

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

   3. Taylor expanded in z around 0 51.3%

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

4. Final simplification 40.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.55 \cdot 10^{-95} \lor \neg \left(z \leq 0.64\right):\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 24.7% 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 66.4%

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

3. Taylor expanded in z around 0 24.7%

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

4. Final simplification 24.7%

   \[\leadsto x \]
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 2024075 
(FPCore (x y z t a b)
  :name "Development.Shake.Progress:decay from shake-0.15.5"
  :precision binary64

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

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