Development.Shake.Progress:decay from shake-0.15.5

Percentage Accurate: 66.6% → 89.8%

Time: 14.5s

Alternatives: 14

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: 66.6% 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: 89.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ \mathbf{if}\;z \leq -1.46 \cdot 10^{+37} \lor \neg \left(z \leq 1.02 \cdot 10^{+65}\right):\\ \;\;\;\;\left(\frac{\frac{x}{z} \cdot y}{b - y} + \frac{t - a}{b - y}\right) - \left(t - a\right) \cdot \frac{y}{z \cdot {\left(b - y\right)}^{2}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{t\_1} + \frac{z \cdot \left(t - a\right)}{x \cdot t\_1}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y)))))
   (if (or (<= z -1.46e+37) (not (<= z 1.02e+65)))
     (-
      (+ (/ (* (/ x z) y) (- b y)) (/ (- t a) (- b y)))
      (* (- t a) (/ y (* z (pow (- b y) 2.0)))))
     (* x (+ (/ y t_1) (/ (* z (- t a)) (* x t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double tmp;
	if ((z <= -1.46e+37) || !(z <= 1.02e+65)) {
		tmp = ((((x / z) * y) / (b - y)) + ((t - a) / (b - y))) - ((t - a) * (y / (z * pow((b - y), 2.0))));
	} else {
		tmp = x * ((y / t_1) + ((z * (t - a)) / (x * t_1)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y + (z * (b - y))
    if ((z <= (-1.46d+37)) .or. (.not. (z <= 1.02d+65))) then
        tmp = ((((x / z) * y) / (b - y)) + ((t - a) / (b - y))) - ((t - a) * (y / (z * ((b - y) ** 2.0d0))))
    else
        tmp = x * ((y / t_1) + ((z * (t - a)) / (x * t_1)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double tmp;
	if ((z <= -1.46e+37) || !(z <= 1.02e+65)) {
		tmp = ((((x / z) * y) / (b - y)) + ((t - a) / (b - y))) - ((t - a) * (y / (z * Math.pow((b - y), 2.0))));
	} else {
		tmp = x * ((y / t_1) + ((z * (t - a)) / (x * t_1)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z * (b - y))
	tmp = 0
	if (z <= -1.46e+37) or not (z <= 1.02e+65):
		tmp = ((((x / z) * y) / (b - y)) + ((t - a) / (b - y))) - ((t - a) * (y / (z * math.pow((b - y), 2.0))))
	else:
		tmp = x * ((y / t_1) + ((z * (t - a)) / (x * t_1)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(z * Float64(b - y)))
	tmp = 0.0
	if ((z <= -1.46e+37) || !(z <= 1.02e+65))
		tmp = Float64(Float64(Float64(Float64(Float64(x / z) * y) / Float64(b - y)) + Float64(Float64(t - a) / Float64(b - y))) - Float64(Float64(t - a) * Float64(y / Float64(z * (Float64(b - y) ^ 2.0)))));
	else
		tmp = Float64(x * Float64(Float64(y / t_1) + Float64(Float64(z * Float64(t - a)) / Float64(x * t_1))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (z * (b - y));
	tmp = 0.0;
	if ((z <= -1.46e+37) || ~((z <= 1.02e+65)))
		tmp = ((((x / z) * y) / (b - y)) + ((t - a) / (b - y))) - ((t - a) * (y / (z * ((b - y) ^ 2.0))));
	else
		tmp = x * ((y / t_1) + ((z * (t - a)) / (x * t_1)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[z, -1.46e+37], N[Not[LessEqual[z, 1.02e+65]], $MachinePrecision]], N[(N[(N[(N[(N[(x / z), $MachinePrecision] * y), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision] + N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(t - a), $MachinePrecision] * N[(y / N[(z * N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $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 < -1.4599999999999999e37 or 1.02000000000000005e65 < z

   1. Initial program 32.5%

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

   3. Taylor expanded in z around inf 66.1%

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

      1. associate--r+ 66.1%

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

      2. +-commutative 66.1%

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

      3. associate--l+ 66.1%

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

      4. times-frac 79.8%

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

      5. associate-*r/ 81.4%

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

      6. div-sub 81.4%

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

      7. *-commutative 81.4%

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

      8. associate-/l* 98.0%

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

   5. Simplified 98.0%

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

   if -1.4599999999999999e37 < z < 1.02000000000000005e65

   1. Initial program 86.8%

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

   3. Taylor expanded in x around inf 92.9%

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

4. Final simplification 94.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.46 \cdot 10^{+37} \lor \neg \left(z \leq 1.02 \cdot 10^{+65}\right):\\ \;\;\;\;\left(\frac{\frac{x}{z} \cdot y}{b - y} + \frac{t - a}{b - y}\right) - \left(t - a\right) \cdot \frac{y}{z \cdot {\left(b - y\right)}^{2}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{y + z \cdot \left(b - y\right)} + \frac{z \cdot \left(t - a\right)}{x \cdot \left(y + z \cdot \left(b - y\right)\right)}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 84.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(t - a\right)\\ t_2 := y + z \cdot \left(b - y\right)\\ t_3 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -1.8 \cdot 10^{+37}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-60}:\\ \;\;\;\;\frac{t\_1 + x \cdot y}{t\_2}\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{-298}:\\ \;\;\;\;x + \frac{t\_1}{t\_2}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+65}:\\ \;\;\;\;x \cdot \left(\frac{y}{t\_2} + \frac{t\_1}{x \cdot t\_2}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- t a)))
        (t_2 (+ y (* z (- b y))))
        (t_3 (/ (- t a) (- b y))))
   (if (<= z -1.8e+37)
     t_3
     (if (<= z -1.15e-60)
       (/ (+ t_1 (* x y)) t_2)
       (if (<= z -6.8e-298)
         (+ x (/ t_1 t_2))
         (if (<= z 1.25e+65) (* x (+ (/ y t_2) (/ t_1 (* x t_2)))) t_3))))))

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 - y));
	double t_3 = (t - a) / (b - y);
	double tmp;
	if (z <= -1.8e+37) {
		tmp = t_3;
	} else if (z <= -1.15e-60) {
		tmp = (t_1 + (x * y)) / t_2;
	} else if (z <= -6.8e-298) {
		tmp = x + (t_1 / t_2);
	} else if (z <= 1.25e+65) {
		tmp = x * ((y / t_2) + (t_1 / (x * t_2)));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = z * (t - a)
    t_2 = y + (z * (b - y))
    t_3 = (t - a) / (b - y)
    if (z <= (-1.8d+37)) then
        tmp = t_3
    else if (z <= (-1.15d-60)) then
        tmp = (t_1 + (x * y)) / t_2
    else if (z <= (-6.8d-298)) then
        tmp = x + (t_1 / t_2)
    else if (z <= 1.25d+65) then
        tmp = x * ((y / t_2) + (t_1 / (x * t_2)))
    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 * (t - a);
	double t_2 = y + (z * (b - y));
	double t_3 = (t - a) / (b - y);
	double tmp;
	if (z <= -1.8e+37) {
		tmp = t_3;
	} else if (z <= -1.15e-60) {
		tmp = (t_1 + (x * y)) / t_2;
	} else if (z <= -6.8e-298) {
		tmp = x + (t_1 / t_2);
	} else if (z <= 1.25e+65) {
		tmp = x * ((y / t_2) + (t_1 / (x * t_2)));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (t - a)
	t_2 = y + (z * (b - y))
	t_3 = (t - a) / (b - y)
	tmp = 0
	if z <= -1.8e+37:
		tmp = t_3
	elif z <= -1.15e-60:
		tmp = (t_1 + (x * y)) / t_2
	elif z <= -6.8e-298:
		tmp = x + (t_1 / t_2)
	elif z <= 1.25e+65:
		tmp = x * ((y / t_2) + (t_1 / (x * t_2)))
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(t - a))
	t_2 = Float64(y + Float64(z * Float64(b - y)))
	t_3 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -1.8e+37)
		tmp = t_3;
	elseif (z <= -1.15e-60)
		tmp = Float64(Float64(t_1 + Float64(x * y)) / t_2);
	elseif (z <= -6.8e-298)
		tmp = Float64(x + Float64(t_1 / t_2));
	elseif (z <= 1.25e+65)
		tmp = Float64(x * Float64(Float64(y / t_2) + Float64(t_1 / Float64(x * t_2))));
	else
		tmp = t_3;
	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 - y));
	t_3 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -1.8e+37)
		tmp = t_3;
	elseif (z <= -1.15e-60)
		tmp = (t_1 + (x * y)) / t_2;
	elseif (z <= -6.8e-298)
		tmp = x + (t_1 / t_2);
	elseif (z <= 1.25e+65)
		tmp = x * ((y / t_2) + (t_1 / (x * t_2)));
	else
		tmp = t_3;
	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 * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.8e+37], t$95$3, If[LessEqual[z, -1.15e-60], N[(N[(t$95$1 + N[(x * y), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision], If[LessEqual[z, -6.8e-298], N[(x + N[(t$95$1 / t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.25e+65], N[(x * N[(N[(y / t$95$2), $MachinePrecision] + N[(t$95$1 / N[(x * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.79999999999999999e37 or 1.24999999999999993e65 < z

   1. Initial program 32.5%

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

   3. Taylor expanded in z around inf 78.3%

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

   if -1.79999999999999999e37 < z < -1.1500000000000001e-60

   1. Initial program 92.4%

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

   if -1.1500000000000001e-60 < z < -6.8e-298

   1. Initial program 83.9%

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

   3. Taylor expanded in x around 0 83.9%

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

   4. Taylor expanded in z around 0 96.6%

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

   if -6.8e-298 < z < 1.24999999999999993e65

   1. Initial program 87.0%

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

   3. Taylor expanded in x around inf 95.9%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+37}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-60}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{-298}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+65}:\\ \;\;\;\;x \cdot \left(\frac{y}{y + z \cdot \left(b - y\right)} + \frac{z \cdot \left(t - a\right)}{x \cdot \left(y + z \cdot \left(b - y\right)\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 84.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(t - a\right)\\ t_2 := y + z \cdot \left(b - y\right)\\ t_3 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -2 \cdot 10^{+37}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-65}:\\ \;\;\;\;\frac{t\_1 + x \cdot y}{t\_2}\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-78}:\\ \;\;\;\;x + \frac{t\_1}{t\_2}\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{+49}:\\ \;\;\;\;\frac{z \cdot \left(\left(t + \frac{x \cdot y}{z}\right) - a\right)}{t\_2}\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- t a)))
        (t_2 (+ y (* z (- b y))))
        (t_3 (/ (- t a) (- b y))))
   (if (<= z -2e+37)
     t_3
     (if (<= z -2.6e-65)
       (/ (+ t_1 (* x y)) t_2)
       (if (<= z 4.6e-78)
         (+ x (/ t_1 t_2))
         (if (<= z 1.95e+49) (/ (* z (- (+ t (/ (* x y) z)) a)) t_2) t_3))))))

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 - y));
	double t_3 = (t - a) / (b - y);
	double tmp;
	if (z <= -2e+37) {
		tmp = t_3;
	} else if (z <= -2.6e-65) {
		tmp = (t_1 + (x * y)) / t_2;
	} else if (z <= 4.6e-78) {
		tmp = x + (t_1 / t_2);
	} else if (z <= 1.95e+49) {
		tmp = (z * ((t + ((x * y) / z)) - a)) / t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = z * (t - a)
    t_2 = y + (z * (b - y))
    t_3 = (t - a) / (b - y)
    if (z <= (-2d+37)) then
        tmp = t_3
    else if (z <= (-2.6d-65)) then
        tmp = (t_1 + (x * y)) / t_2
    else if (z <= 4.6d-78) then
        tmp = x + (t_1 / t_2)
    else if (z <= 1.95d+49) then
        tmp = (z * ((t + ((x * y) / z)) - a)) / t_2
    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 * (t - a);
	double t_2 = y + (z * (b - y));
	double t_3 = (t - a) / (b - y);
	double tmp;
	if (z <= -2e+37) {
		tmp = t_3;
	} else if (z <= -2.6e-65) {
		tmp = (t_1 + (x * y)) / t_2;
	} else if (z <= 4.6e-78) {
		tmp = x + (t_1 / t_2);
	} else if (z <= 1.95e+49) {
		tmp = (z * ((t + ((x * y) / z)) - a)) / t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (t - a)
	t_2 = y + (z * (b - y))
	t_3 = (t - a) / (b - y)
	tmp = 0
	if z <= -2e+37:
		tmp = t_3
	elif z <= -2.6e-65:
		tmp = (t_1 + (x * y)) / t_2
	elif z <= 4.6e-78:
		tmp = x + (t_1 / t_2)
	elif z <= 1.95e+49:
		tmp = (z * ((t + ((x * y) / z)) - a)) / t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(t - a))
	t_2 = Float64(y + Float64(z * Float64(b - y)))
	t_3 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -2e+37)
		tmp = t_3;
	elseif (z <= -2.6e-65)
		tmp = Float64(Float64(t_1 + Float64(x * y)) / t_2);
	elseif (z <= 4.6e-78)
		tmp = Float64(x + Float64(t_1 / t_2));
	elseif (z <= 1.95e+49)
		tmp = Float64(Float64(z * Float64(Float64(t + Float64(Float64(x * y) / z)) - a)) / t_2);
	else
		tmp = t_3;
	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 - y));
	t_3 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -2e+37)
		tmp = t_3;
	elseif (z <= -2.6e-65)
		tmp = (t_1 + (x * y)) / t_2;
	elseif (z <= 4.6e-78)
		tmp = x + (t_1 / t_2);
	elseif (z <= 1.95e+49)
		tmp = (z * ((t + ((x * y) / z)) - a)) / t_2;
	else
		tmp = t_3;
	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 * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2e+37], t$95$3, If[LessEqual[z, -2.6e-65], N[(N[(t$95$1 + N[(x * y), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision], If[LessEqual[z, 4.6e-78], N[(x + N[(t$95$1 / t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.95e+49], N[(N[(z * N[(N[(t + N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision], t$95$3]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.99999999999999991e37 or 1.95e49 < z

   1. Initial program 34.2%

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

   3. Taylor expanded in z around inf 78.2%

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

   if -1.99999999999999991e37 < z < -2.6000000000000001e-65

   1. Initial program 92.4%

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

   if -2.6000000000000001e-65 < z < 4.6000000000000004e-78

   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 x around 0 84.4%

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

   4. Taylor expanded in z around 0 95.4%

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

   if 4.6000000000000004e-78 < z < 1.95e49

   1. Initial program 94.5%

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

   3. Taylor expanded in z around inf 94.6%

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

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+37}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-65}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-78}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{+49}:\\ \;\;\;\;\frac{z \cdot \left(\left(t + \frac{x \cdot y}{z}\right) - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(t - a\right)\\ t_2 := y + z \cdot \left(b - y\right)\\ t_3 := \frac{t\_1 + x \cdot y}{t\_2}\\ t_4 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -4.3 \cdot 10^{+37}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-62}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-76}:\\ \;\;\;\;x + \frac{t\_1}{t\_2}\\ \mathbf{elif}\;z \leq 9.4 \cdot 10^{+48}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- t a)))
        (t_2 (+ y (* z (- b y))))
        (t_3 (/ (+ t_1 (* x y)) t_2))
        (t_4 (/ (- t a) (- b y))))
   (if (<= z -4.3e+37)
     t_4
     (if (<= z -1.4e-62)
       t_3
       (if (<= z 9e-76) (+ x (/ t_1 t_2)) (if (<= z 9.4e+48) t_3 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 - y));
	double t_3 = (t_1 + (x * y)) / t_2;
	double t_4 = (t - a) / (b - y);
	double tmp;
	if (z <= -4.3e+37) {
		tmp = t_4;
	} else if (z <= -1.4e-62) {
		tmp = t_3;
	} else if (z <= 9e-76) {
		tmp = x + (t_1 / t_2);
	} else if (z <= 9.4e+48) {
		tmp = t_3;
	} 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 - y))
    t_3 = (t_1 + (x * y)) / t_2
    t_4 = (t - a) / (b - y)
    if (z <= (-4.3d+37)) then
        tmp = t_4
    else if (z <= (-1.4d-62)) then
        tmp = t_3
    else if (z <= 9d-76) then
        tmp = x + (t_1 / t_2)
    else if (z <= 9.4d+48) then
        tmp = t_3
    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 - y));
	double t_3 = (t_1 + (x * y)) / t_2;
	double t_4 = (t - a) / (b - y);
	double tmp;
	if (z <= -4.3e+37) {
		tmp = t_4;
	} else if (z <= -1.4e-62) {
		tmp = t_3;
	} else if (z <= 9e-76) {
		tmp = x + (t_1 / t_2);
	} else if (z <= 9.4e+48) {
		tmp = t_3;
	} 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 - y))
	t_3 = (t_1 + (x * y)) / t_2
	t_4 = (t - a) / (b - y)
	tmp = 0
	if z <= -4.3e+37:
		tmp = t_4
	elif z <= -1.4e-62:
		tmp = t_3
	elif z <= 9e-76:
		tmp = x + (t_1 / t_2)
	elif z <= 9.4e+48:
		tmp = t_3
	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 * Float64(b - y)))
	t_3 = Float64(Float64(t_1 + Float64(x * y)) / t_2)
	t_4 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -4.3e+37)
		tmp = t_4;
	elseif (z <= -1.4e-62)
		tmp = t_3;
	elseif (z <= 9e-76)
		tmp = Float64(x + Float64(t_1 / t_2));
	elseif (z <= 9.4e+48)
		tmp = t_3;
	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 - y));
	t_3 = (t_1 + (x * y)) / t_2;
	t_4 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -4.3e+37)
		tmp = t_4;
	elseif (z <= -1.4e-62)
		tmp = t_3;
	elseif (z <= 9e-76)
		tmp = x + (t_1 / t_2);
	elseif (z <= 9.4e+48)
		tmp = t_3;
	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 * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t$95$1 + N[(x * y), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.3e+37], t$95$4, If[LessEqual[z, -1.4e-62], t$95$3, If[LessEqual[z, 9e-76], N[(x + N[(t$95$1 / t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.4e+48], t$95$3, t$95$4]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.2999999999999997e37 or 9.40000000000000025e48 < z

   1. Initial program 34.2%

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

   3. Taylor expanded in z around inf 78.2%

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

   if -4.2999999999999997e37 < z < -1.40000000000000001e-62 or 9.0000000000000001e-76 < z < 9.40000000000000025e48

   1. Initial program 93.3%

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

   if -1.40000000000000001e-62 < z < 9.0000000000000001e-76

   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 x around 0 84.4%

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

   4. Taylor expanded in z around 0 95.4%

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

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{+37}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-62}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-76}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 9.4 \cdot 10^{+48}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 64.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z \cdot a}{z \cdot \left(y - b\right) - y}\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -13000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-32}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-53}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-76}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;z \leq 0.00013:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* z a) (- (* z (- y b)) y))) (t_2 (/ (- t a) (- b y))))
   (if (<= z -13000.0)
     t_2
     (if (<= z -3.2e-32)
       t_1
       (if (<= z -2.6e-53)
         t_2
         (if (<= z 1.75e-76) (/ x (- 1.0 z)) (if (<= z 0.00013) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z * a) / ((z * (y - b)) - y);
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -13000.0) {
		tmp = t_2;
	} else if (z <= -3.2e-32) {
		tmp = t_1;
	} else if (z <= -2.6e-53) {
		tmp = t_2;
	} else if (z <= 1.75e-76) {
		tmp = x / (1.0 - z);
	} else if (z <= 0.00013) {
		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 = (z * a) / ((z * (y - b)) - y)
    t_2 = (t - a) / (b - y)
    if (z <= (-13000.0d0)) then
        tmp = t_2
    else if (z <= (-3.2d-32)) then
        tmp = t_1
    else if (z <= (-2.6d-53)) then
        tmp = t_2
    else if (z <= 1.75d-76) then
        tmp = x / (1.0d0 - z)
    else if (z <= 0.00013d0) 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 = (z * a) / ((z * (y - b)) - y);
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -13000.0) {
		tmp = t_2;
	} else if (z <= -3.2e-32) {
		tmp = t_1;
	} else if (z <= -2.6e-53) {
		tmp = t_2;
	} else if (z <= 1.75e-76) {
		tmp = x / (1.0 - z);
	} else if (z <= 0.00013) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z * a) / ((z * (y - b)) - y)
	t_2 = (t - a) / (b - y)
	tmp = 0
	if z <= -13000.0:
		tmp = t_2
	elif z <= -3.2e-32:
		tmp = t_1
	elif z <= -2.6e-53:
		tmp = t_2
	elif z <= 1.75e-76:
		tmp = x / (1.0 - z)
	elif z <= 0.00013:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z * a) / Float64(Float64(z * Float64(y - b)) - y))
	t_2 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -13000.0)
		tmp = t_2;
	elseif (z <= -3.2e-32)
		tmp = t_1;
	elseif (z <= -2.6e-53)
		tmp = t_2;
	elseif (z <= 1.75e-76)
		tmp = Float64(x / Float64(1.0 - z));
	elseif (z <= 0.00013)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z * a) / ((z * (y - b)) - y);
	t_2 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -13000.0)
		tmp = t_2;
	elseif (z <= -3.2e-32)
		tmp = t_1;
	elseif (z <= -2.6e-53)
		tmp = t_2;
	elseif (z <= 1.75e-76)
		tmp = x / (1.0 - z);
	elseif (z <= 0.00013)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z * a), $MachinePrecision] / N[(N[(z * N[(y - b), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -13000.0], t$95$2, If[LessEqual[z, -3.2e-32], t$95$1, If[LessEqual[z, -2.6e-53], t$95$2, If[LessEqual[z, 1.75e-76], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.00013], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -13000 or -3.2000000000000002e-32 < z < -2.59999999999999996e-53 or 1.29999999999999989e-4 < 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 74.5%

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

   if -13000 < z < -3.2000000000000002e-32 or 1.74999999999999999e-76 < z < 1.29999999999999989e-4

   1. Initial program 95.0%

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

   3. Taylor expanded in a around inf 71.0%

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

      1. mul-1-neg 71.0%

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

      2. distribute-lft-neg-out 71.0%

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

      3. *-commutative 71.0%

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

   5. Simplified 71.0%

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

   if -2.59999999999999996e-53 < z < 1.74999999999999999e-76

   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 y around inf 67.5%

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

      1. mul-1-neg 67.5%

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

      2. unsub-neg 67.5%

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

   5. Simplified 67.5%

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

4. Final simplification 71.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -13000:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-32}:\\ \;\;\;\;\frac{z \cdot a}{z \cdot \left(y - b\right) - y}\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-53}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-76}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;z \leq 0.00013:\\ \;\;\;\;\frac{z \cdot a}{z \cdot \left(y - b\right) - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 64.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -2.4 \cdot 10^{-9}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-32}:\\ \;\;\;\;a \cdot \frac{z}{y \cdot \left(z + -1\right)}\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-53} \lor \neg \left(z \leq 6 \cdot 10^{-37}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -2.4e-9)
     t_1
     (if (<= z -3.4e-32)
       (* a (/ z (* y (+ z -1.0))))
       (if (or (<= z -3e-53) (not (<= z 6e-37))) t_1 x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -2.4e-9) {
		tmp = t_1;
	} else if (z <= -3.4e-32) {
		tmp = a * (z / (y * (z + -1.0)));
	} else if ((z <= -3e-53) || !(z <= 6e-37)) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    if (z <= (-2.4d-9)) then
        tmp = t_1
    else if (z <= (-3.4d-32)) then
        tmp = a * (z / (y * (z + (-1.0d0))))
    else if ((z <= (-3d-53)) .or. (.not. (z <= 6d-37))) then
        tmp = t_1
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -2.4e-9) {
		tmp = t_1;
	} else if (z <= -3.4e-32) {
		tmp = a * (z / (y * (z + -1.0)));
	} else if ((z <= -3e-53) || !(z <= 6e-37)) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	tmp = 0
	if z <= -2.4e-9:
		tmp = t_1
	elif z <= -3.4e-32:
		tmp = a * (z / (y * (z + -1.0)))
	elif (z <= -3e-53) or not (z <= 6e-37):
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -2.4e-9)
		tmp = t_1;
	elseif (z <= -3.4e-32)
		tmp = Float64(a * Float64(z / Float64(y * Float64(z + -1.0))));
	elseif ((z <= -3e-53) || !(z <= 6e-37))
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -2.4e-9)
		tmp = t_1;
	elseif (z <= -3.4e-32)
		tmp = a * (z / (y * (z + -1.0)));
	elseif ((z <= -3e-53) || ~((z <= 6e-37)))
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.4e-9], t$95$1, If[LessEqual[z, -3.4e-32], N[(a * N[(z / N[(y * N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -3e-53], N[Not[LessEqual[z, 6e-37]], $MachinePrecision]], t$95$1, x]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.4e-9 or -3.39999999999999978e-32 < z < -3.0000000000000002e-53 or 6e-37 < z

   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 z around inf 72.1%

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

   if -2.4e-9 < z < -3.39999999999999978e-32

   1. Initial program 99.5%

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

   3. Taylor expanded in a around inf 83.6%

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

      1. mul-1-neg 83.6%

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

      2. distribute-lft-neg-out 83.6%

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

      3. *-commutative 83.6%

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

   5. Simplified 83.6%

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

   6. Taylor expanded in y around -inf 83.3%

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

      1. associate-/l* 83.8%

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

      2. sub-neg 83.8%

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

      3. metadata-eval 83.8%

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

   8. Simplified 83.8%

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

   if -3.0000000000000002e-53 < z < 6e-37

   1. Initial program 85.6%

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

   3. Taylor expanded in z around 0 65.3%

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

4. Final simplification 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{-9}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-32}:\\ \;\;\;\;a \cdot \frac{z}{y \cdot \left(z + -1\right)}\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-53} \lor \neg \left(z \leq 6 \cdot 10^{-37}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 81.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6 \lor \neg \left(z \leq 1.52 \cdot 10^{+21}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -6.0) (not (<= z 1.52e+21)))
   (/ (- t a) (- b 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 <= -6.0) || !(z <= 1.52e+21)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = 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 <= (-6.0d0)) .or. (.not. (z <= 1.52d+21))) then
        tmp = (t - a) / (b - y)
    else
        tmp = 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 <= -6.0) || !(z <= 1.52e+21)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x + ((z * (t - a)) / (y + (z * (b - y))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -6.0) or not (z <= 1.52e+21):
		tmp = (t - a) / (b - y)
	else:
		tmp = x + ((z * (t - a)) / (y + (z * (b - y))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -6.0) || !(z <= 1.52e+21))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(x + Float64(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 <= -6.0) || ~((z <= 1.52e+21)))
		tmp = (t - a) / (b - y);
	else
		tmp = 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, -6.0], N[Not[LessEqual[z, 1.52e+21]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6 or 1.52e21 < z

   1. Initial program 40.7%

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

   3. Taylor expanded in z around inf 76.5%

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

   if -6 < z < 1.52e21

   1. Initial program 87.1%

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

   3. Taylor expanded in x around 0 87.1%

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

   4. Taylor expanded in z around 0 91.5%

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

4. Final simplification 84.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \lor \neg \left(z \leq 1.52 \cdot 10^{+21}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 37.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+78}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq -0.315 \lor \neg \left(z \leq 2.2 \cdot 10^{-33}\right):\\ \;\;\;\;-\frac{a}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.15e+78)
   (/ t b)
   (if (or (<= z -0.315) (not (<= z 2.2e-33))) (- (/ a b)) x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.15e+78) {
		tmp = t / b;
	} else if ((z <= -0.315) || !(z <= 2.2e-33)) {
		tmp = -(a / b);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-1.15d+78)) then
        tmp = t / b
    else if ((z <= (-0.315d0)) .or. (.not. (z <= 2.2d-33))) then
        tmp = -(a / b)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.15e+78) {
		tmp = t / b;
	} else if ((z <= -0.315) || !(z <= 2.2e-33)) {
		tmp = -(a / b);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1.15e+78:
		tmp = t / b
	elif (z <= -0.315) or not (z <= 2.2e-33):
		tmp = -(a / b)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.15e+78)
		tmp = Float64(t / b);
	elseif ((z <= -0.315) || !(z <= 2.2e-33))
		tmp = Float64(-Float64(a / b));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -1.15e+78)
		tmp = t / b;
	elseif ((z <= -0.315) || ~((z <= 2.2e-33)))
		tmp = -(a / b);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.15e+78], N[(t / b), $MachinePrecision], If[Or[LessEqual[z, -0.315], N[Not[LessEqual[z, 2.2e-33]], $MachinePrecision]], (-N[(a / b), $MachinePrecision]), x]]

Derivation

1. Split input into 3 regimes

2. if z < -1.1500000000000001e78

   1. Initial program 32.2%

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

   3. Taylor expanded in b around inf 14.3%

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

   4. Taylor expanded in t around inf 31.7%

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

   if -1.1500000000000001e78 < z < -0.315000000000000002 or 2.20000000000000005e-33 < z

   1. Initial program 51.5%

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

   3. Taylor expanded in a around inf 27.1%

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

      1. mul-1-neg 27.1%

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

      2. distribute-lft-neg-out 27.1%

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

      3. *-commutative 27.1%

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

   5. Simplified 27.1%

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

   6. Taylor expanded in y around 0 31.1%

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

      1. associate-*r/ 31.1%

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

      2. neg-mul-1 31.1%

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

   8. Simplified 31.1%

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

   if -0.315000000000000002 < z < 2.20000000000000005e-33

   1. Initial program 86.9%

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

   3. Taylor expanded in z around 0 60.3%

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

4. Final simplification 45.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+78}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq -0.315 \lor \neg \left(z \leq 2.2 \cdot 10^{-33}\right):\\ \;\;\;\;-\frac{a}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 64.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{-53} \lor \neg \left(z \leq 8.2 \cdot 10^{-38}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -3.9e-53) (not (<= z 8.2e-38))) (/ (- t a) (- b y)) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -3.9e-53) || !(z <= 8.2e-38)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-3.9d-53)) .or. (.not. (z <= 8.2d-38))) then
        tmp = (t - a) / (b - y)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -3.9e-53) || !(z <= 8.2e-38)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -3.9e-53) or not (z <= 8.2e-38):
		tmp = (t - a) / (b - y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -3.9e-53) || !(z <= 8.2e-38))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -3.9e-53) || ~((z <= 8.2e-38)))
		tmp = (t - a) / (b - y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -3.9e-53], N[Not[LessEqual[z, 8.2e-38]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -3.9000000000000002e-53 or 8.1999999999999996e-38 < z

   1. Initial program 49.1%

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

   3. Taylor expanded in z around inf 69.5%

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

   if -3.9000000000000002e-53 < z < 8.1999999999999996e-38

   1. Initial program 85.6%

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

   3. Taylor expanded in z around 0 65.3%

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

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{-53} \lor \neg \left(z \leq 8.2 \cdot 10^{-38}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 53.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{-19} \lor \neg \left(y \leq 300000000\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -5.5e-19) (not (<= y 300000000.0)))
   (/ 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 <= -5.5e-19) || !(y <= 300000000.0)) {
		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 <= (-5.5d-19)) .or. (.not. (y <= 300000000.0d0))) 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 <= -5.5e-19) || !(y <= 300000000.0)) {
		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 <= -5.5e-19) or not (y <= 300000000.0):
		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 <= -5.5e-19) || !(y <= 300000000.0))
		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 <= -5.5e-19) || ~((y <= 300000000.0)))
		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, -5.5e-19], N[Not[LessEqual[y, 300000000.0]], $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 < -5.4999999999999996e-19 or 3e8 < y

   1. Initial program 58.1%

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

   3. Taylor expanded in y around inf 58.7%

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

      1. mul-1-neg 58.7%

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

      2. unsub-neg 58.7%

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

   5. Simplified 58.7%

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

   if -5.4999999999999996e-19 < y < 3e8

   1. Initial program 74.0%

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

   3. Taylor expanded in y around 0 56.7%

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

4. Final simplification 57.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{-19} \lor \neg \left(y \leq 300000000\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 41.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{-115} \lor \neg \left(y \leq 4.5 \cdot 10^{-43}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;-\frac{a}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -3e-115) (not (<= y 4.5e-43))) (/ x (- 1.0 z)) (- (/ a b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -3e-115) || !(y <= 4.5e-43)) {
		tmp = x / (1.0 - z);
	} 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 ((y <= (-3d-115)) .or. (.not. (y <= 4.5d-43))) then
        tmp = x / (1.0d0 - z)
    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 ((y <= -3e-115) || !(y <= 4.5e-43)) {
		tmp = x / (1.0 - z);
	} else {
		tmp = -(a / b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -3e-115) or not (y <= 4.5e-43):
		tmp = x / (1.0 - z)
	else:
		tmp = -(a / b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -3e-115) || !(y <= 4.5e-43))
		tmp = Float64(x / Float64(1.0 - z));
	else
		tmp = Float64(-Float64(a / b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -3e-115) || ~((y <= 4.5e-43)))
		tmp = x / (1.0 - z);
	else
		tmp = -(a / b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -3e-115], N[Not[LessEqual[y, 4.5e-43]], $MachinePrecision]], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], (-N[(a / b), $MachinePrecision])]

Derivation

1. Split input into 2 regimes

2. if y < -3.0000000000000002e-115 or 4.50000000000000025e-43 < y

   1. Initial program 59.4%

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

   3. Taylor expanded in y around inf 52.3%

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

      1. mul-1-neg 52.3%

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

      2. unsub-neg 52.3%

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

   5. Simplified 52.3%

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

   if -3.0000000000000002e-115 < y < 4.50000000000000025e-43

   1. Initial program 77.4%

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

   3. Taylor expanded in a around inf 28.6%

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

      1. mul-1-neg 28.6%

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

      2. distribute-lft-neg-out 28.6%

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

      3. *-commutative 28.6%

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

   5. Simplified 28.6%

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

   6. Taylor expanded in y around 0 35.1%

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

      1. associate-*r/ 35.1%

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

      2. neg-mul-1 35.1%

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

   8. Simplified 35.1%

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

4. Final simplification 46.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{-115} \lor \neg \left(y \leq 4.5 \cdot 10^{-43}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;-\frac{a}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 36.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{-52} \lor \neg \left(z \leq 1.45 \cdot 10^{-38}\right):\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -2.5e-52) (not (<= z 1.45e-38))) (/ t b) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.5e-52) || !(z <= 1.45e-38)) {
		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 <= (-2.5d-52)) .or. (.not. (z <= 1.45d-38))) 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 <= -2.5e-52) || !(z <= 1.45e-38)) {
		tmp = t / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -2.5e-52) or not (z <= 1.45e-38):
		tmp = t / b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -2.5e-52) || !(z <= 1.45e-38))
		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 <= -2.5e-52) || ~((z <= 1.45e-38)))
		tmp = t / b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -2.5e-52], N[Not[LessEqual[z, 1.45e-38]], $MachinePrecision]], N[(t / b), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -2.5e-52 or 1.44999999999999997e-38 < z

   1. Initial program 48.7%

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

   3. Taylor expanded in b around inf 24.3%

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

   4. Taylor expanded in t around inf 25.6%

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

   if -2.5e-52 < z < 1.44999999999999997e-38

   1. Initial program 85.7%

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

   3. Taylor expanded in z around 0 64.8%

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

4. Final simplification 43.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{-52} \lor \neg \left(z \leq 1.45 \cdot 10^{-38}\right):\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 34.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.8 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;\frac{a}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -5.8) (not (<= z 1.0))) (/ a y) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -5.8) || !(z <= 1.0)) {
		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 <= (-5.8d0)) .or. (.not. (z <= 1.0d0))) 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 <= -5.8) || !(z <= 1.0)) {
		tmp = a / y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -5.8) or not (z <= 1.0):
		tmp = a / y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -5.8) || !(z <= 1.0))
		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 <= -5.8) || ~((z <= 1.0)))
		tmp = a / y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -5.8], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(a / y), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -5.79999999999999982 or 1 < z

   1. Initial program 42.6%

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

   3. Taylor expanded in a around inf 20.4%

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

      1. mul-1-neg 20.4%

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

      2. distribute-lft-neg-out 20.4%

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

      3. *-commutative 20.4%

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

   5. Simplified 20.4%

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

   6. Taylor expanded in y around -inf 9.5%

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

      1. associate-/l* 11.3%

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

      2. sub-neg 11.3%

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

      3. metadata-eval 11.3%

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

   8. Simplified 11.3%

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

   9. Taylor expanded in z around inf 13.7%

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

   if -5.79999999999999982 < z < 1

   1. Initial program 86.8%

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

   3. Taylor expanded in z around 0 57.7%

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

4. Final simplification 36.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;\frac{a}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 25.4% 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 65.2%

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

3. Taylor expanded in z around 0 31.1%

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

Developer target: 73.9% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024091 
(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)))))