Development.Shake.Progress:decay from shake-0.15.5

Percentage Accurate: 66.4% → 89.7%

Time: 15.8s

Alternatives: 20

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 66.4% 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: 89.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(t - a\right)\\ t_2 := y + z \cdot \left(b - y\right)\\ t_3 := \frac{x \cdot \frac{y}{b - y} + y \cdot \frac{a - t}{{\left(b - y\right)}^{2}}}{z} + \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -34000000000000:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-188}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, t\_1\right)}{\mathsf{fma}\left(z, b - y, y\right)}\\ \mathbf{elif}\;z \leq 13000:\\ \;\;\;\;x \cdot \left(\frac{y}{t\_2} + \frac{t\_1}{x \cdot t\_2}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- t a)))
        (t_2 (+ y (* z (- b y))))
        (t_3
         (+
          (/ (+ (* x (/ y (- b y))) (* y (/ (- a t) (pow (- b y) 2.0)))) z)
          (/ (- t a) (- b y)))))
   (if (<= z -34000000000000.0)
     t_3
     (if (<= z -2.5e-188)
       (/ (fma x y t_1) (fma z (- b y) y))
       (if (<= z 13000.0) (* 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 = (((x * (y / (b - y))) + (y * ((a - t) / pow((b - y), 2.0)))) / z) + ((t - a) / (b - y));
	double tmp;
	if (z <= -34000000000000.0) {
		tmp = t_3;
	} else if (z <= -2.5e-188) {
		tmp = fma(x, y, t_1) / fma(z, (b - y), y);
	} else if (z <= 13000.0) {
		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(Float64(Float64(x * Float64(y / Float64(b - y))) + Float64(y * Float64(Float64(a - t) / (Float64(b - y) ^ 2.0)))) / z) + Float64(Float64(t - a) / Float64(b - y)))
	tmp = 0.0
	if (z <= -34000000000000.0)
		tmp = t_3;
	elseif (z <= -2.5e-188)
		tmp = Float64(fma(x, y, t_1) / fma(z, Float64(b - y), y));
	elseif (z <= 13000.0)
		tmp = Float64(x * Float64(Float64(y / t_2) + Float64(t_1 / Float64(x * t_2))));
	else
		tmp = t_3;
	end
	return 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[(N[(N[(x * N[(y / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * N[(N[(a - t), $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]}, If[LessEqual[z, -34000000000000.0], t$95$3, If[LessEqual[z, -2.5e-188], N[(N[(x * y + t$95$1), $MachinePrecision] / N[(z * N[(b - y), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 13000.0], 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 3 regimes

2. if z < -3.4e13 or 13000 < z

   1. Initial program 41.0%

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

   3. Taylor expanded in z around -inf 70.6%

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

      1. associate--l+ 70.6%

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

      2. mul-1-neg 70.6%

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

      3. distribute-lft-out-- 70.6%

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

      4. associate-/l* 76.2%

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

      5. associate-/l* 97.2%

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

      6. div-sub 97.2%

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

   5. Simplified 97.2%

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

   if -3.4e13 < z < -2.5e-188

   1. Initial program 97.1%

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

      1. fma-define 97.1%

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

      2. +-commutative 97.1%

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

      3. fma-define 97.1%

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

   3. Simplified 97.1%

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

   if -2.5e-188 < z < 13000

   1. Initial program 85.0%

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

   3. Taylor expanded in 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 3 regimes into one program.

4. Final simplification 95.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -34000000000000:\\ \;\;\;\;\frac{x \cdot \frac{y}{b - y} + y \cdot \frac{a - t}{{\left(b - y\right)}^{2}}}{z} + \frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-188}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, z \cdot \left(t - a\right)\right)}{\mathsf{fma}\left(z, b - y, y\right)}\\ \mathbf{elif}\;z \leq 13000:\\ \;\;\;\;x \cdot \left(\frac{y}{y + z \cdot \left(b - y\right)} + \frac{z \cdot \left(t - a\right)}{x \cdot \left(y + z \cdot \left(b - y\right)\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{y}{b - y} + y \cdot \frac{a - t}{{\left(b - y\right)}^{2}}}{z} + \frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 89.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(t - a\right)\\ t_2 := y + z \cdot \left(b - y\right)\\ t_3 := \frac{x \cdot \frac{y}{b - y} + y \cdot \frac{a - t}{{\left(b - y\right)}^{2}}}{z} + \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -13500000000:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-188}:\\ \;\;\;\;\frac{t\_1 + x \cdot y}{t\_2}\\ \mathbf{elif}\;z \leq 1400000:\\ \;\;\;\;x \cdot \left(\frac{y}{t\_2} + \frac{t\_1}{x \cdot t\_2}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- t a)))
        (t_2 (+ y (* z (- b y))))
        (t_3
         (+
          (/ (+ (* x (/ y (- b y))) (* y (/ (- a t) (pow (- b y) 2.0)))) z)
          (/ (- t a) (- b y)))))
   (if (<= z -13500000000.0)
     t_3
     (if (<= z -2e-188)
       (/ (+ t_1 (* x y)) t_2)
       (if (<= z 1400000.0) (* 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 = (((x * (y / (b - y))) + (y * ((a - t) / pow((b - y), 2.0)))) / z) + ((t - a) / (b - y));
	double tmp;
	if (z <= -13500000000.0) {
		tmp = t_3;
	} else if (z <= -2e-188) {
		tmp = (t_1 + (x * y)) / t_2;
	} else if (z <= 1400000.0) {
		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 = (((x * (y / (b - y))) + (y * ((a - t) / ((b - y) ** 2.0d0)))) / z) + ((t - a) / (b - y))
    if (z <= (-13500000000.0d0)) then
        tmp = t_3
    else if (z <= (-2d-188)) then
        tmp = (t_1 + (x * y)) / t_2
    else if (z <= 1400000.0d0) 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 = (((x * (y / (b - y))) + (y * ((a - t) / Math.pow((b - y), 2.0)))) / z) + ((t - a) / (b - y));
	double tmp;
	if (z <= -13500000000.0) {
		tmp = t_3;
	} else if (z <= -2e-188) {
		tmp = (t_1 + (x * y)) / t_2;
	} else if (z <= 1400000.0) {
		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 = (((x * (y / (b - y))) + (y * ((a - t) / math.pow((b - y), 2.0)))) / z) + ((t - a) / (b - y))
	tmp = 0
	if z <= -13500000000.0:
		tmp = t_3
	elif z <= -2e-188:
		tmp = (t_1 + (x * y)) / t_2
	elif z <= 1400000.0:
		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(Float64(Float64(x * Float64(y / Float64(b - y))) + Float64(y * Float64(Float64(a - t) / (Float64(b - y) ^ 2.0)))) / z) + Float64(Float64(t - a) / Float64(b - y)))
	tmp = 0.0
	if (z <= -13500000000.0)
		tmp = t_3;
	elseif (z <= -2e-188)
		tmp = Float64(Float64(t_1 + Float64(x * y)) / t_2);
	elseif (z <= 1400000.0)
		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 = (((x * (y / (b - y))) + (y * ((a - t) / ((b - y) ^ 2.0)))) / z) + ((t - a) / (b - y));
	tmp = 0.0;
	if (z <= -13500000000.0)
		tmp = t_3;
	elseif (z <= -2e-188)
		tmp = (t_1 + (x * y)) / t_2;
	elseif (z <= 1400000.0)
		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[(N[(N[(x * N[(y / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * N[(N[(a - t), $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]}, If[LessEqual[z, -13500000000.0], t$95$3, If[LessEqual[z, -2e-188], N[(N[(t$95$1 + N[(x * y), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision], If[LessEqual[z, 1400000.0], 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 3 regimes

2. if z < -1.35e10 or 1.4e6 < z

   1. Initial program 41.0%

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

   3. Taylor expanded in z around -inf 70.6%

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

      1. associate--l+ 70.6%

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

      2. mul-1-neg 70.6%

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

      3. distribute-lft-out-- 70.6%

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

      4. associate-/l* 76.2%

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

      5. associate-/l* 97.2%

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

      6. div-sub 97.2%

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

   5. Simplified 97.2%

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

   if -1.35e10 < z < -1.9999999999999999e-188

   1. Initial program 97.1%

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

   if -1.9999999999999999e-188 < z < 1.4e6

   1. Initial program 85.0%

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

   3. Taylor expanded in 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 3 regimes into one program.

4. Final simplification 95.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -13500000000:\\ \;\;\;\;\frac{x \cdot \frac{y}{b - y} + y \cdot \frac{a - t}{{\left(b - y\right)}^{2}}}{z} + \frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-188}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 1400000:\\ \;\;\;\;x \cdot \left(\frac{y}{y + z \cdot \left(b - y\right)} + \frac{z \cdot \left(t - a\right)}{x \cdot \left(y + z \cdot \left(b - y\right)\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{y}{b - y} + y \cdot \frac{a - t}{{\left(b - y\right)}^{2}}}{z} + \frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 90.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ \mathbf{if}\;z \leq -1.2 \cdot 10^{+16} \lor \neg \left(z \leq 14600000000\right):\\ \;\;\;\;\left(\frac{t - a}{b - y} + \frac{y \cdot \frac{x}{z}}{b - y}\right) - \frac{t - a}{z} \cdot \frac{y}{{\left(b - y\right)}^{2}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{t\_1} + \frac{z \cdot \left(t - a\right)}{x \cdot t\_1}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y)))))
   (if (or (<= z -1.2e+16) (not (<= z 14600000000.0)))
     (-
      (+ (/ (- t a) (- b y)) (/ (* y (/ x z)) (- b y)))
      (* (/ (- t a) z) (/ y (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 <= -1.2e+16) || !(z <= 14600000000.0)) {
		tmp = (((t - a) / (b - y)) + ((y * (x / z)) / (b - y))) - (((t - a) / z) * (y / 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 <= (-1.2d+16)) .or. (.not. (z <= 14600000000.0d0))) then
        tmp = (((t - a) / (b - y)) + ((y * (x / z)) / (b - y))) - (((t - a) / z) * (y / ((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 <= -1.2e+16) || !(z <= 14600000000.0)) {
		tmp = (((t - a) / (b - y)) + ((y * (x / z)) / (b - y))) - (((t - a) / z) * (y / 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 <= -1.2e+16) or not (z <= 14600000000.0):
		tmp = (((t - a) / (b - y)) + ((y * (x / z)) / (b - y))) - (((t - a) / z) * (y / 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 <= -1.2e+16) || !(z <= 14600000000.0))
		tmp = Float64(Float64(Float64(Float64(t - a) / Float64(b - y)) + Float64(Float64(y * Float64(x / z)) / Float64(b - y))) - Float64(Float64(Float64(t - a) / z) * Float64(y / (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 <= -1.2e+16) || ~((z <= 14600000000.0)))
		tmp = (((t - a) / (b - y)) + ((y * (x / z)) / (b - y))) - (((t - a) / z) * (y / ((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, -1.2e+16], N[Not[LessEqual[z, 14600000000.0]], $MachinePrecision]], N[(N[(N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision] + N[(N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(t - a), $MachinePrecision] / z), $MachinePrecision] * N[(y / N[Power[N[(b - y), $MachinePrecision], 2.0], $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 < -1.2e16 or 1.46e10 < z

   1. Initial program 41.2%

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

   3. Taylor expanded in z around inf 68.4%

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

      1. associate--r+ 68.4%

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

      2. +-commutative 68.4%

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

      3. associate--l+ 68.4%

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

      4. times-frac 78.2%

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

      5. associate-*r/ 77.5%

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

      6. div-sub 77.5%

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

      7. *-commutative 77.5%

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

      8. times-frac 96.6%

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

   5. Simplified 96.6%

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

   if -1.2e16 < z < 1.46e10

   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 x around inf 91.0%

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

4. Final simplification 93.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+16} \lor \neg \left(z \leq 14600000000\right):\\ \;\;\;\;\left(\frac{t - a}{b - y} + \frac{y \cdot \frac{x}{z}}{b - y}\right) - \frac{t - a}{z} \cdot \frac{y}{{\left(b - y\right)}^{2}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{y + z \cdot \left(b - y\right)} + \frac{z \cdot \left(t - a\right)}{x \cdot \left(y + z \cdot \left(b - y\right)\right)}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 92.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := \frac{t - a}{b - y} + \frac{x}{1 - z}\\ t_3 := \frac{z \cdot \left(t - a\right) + x \cdot y}{t\_1}\\ \mathbf{if}\;t\_3 \leq -1 \cdot 10^{+284}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_3 \leq -1 \cdot 10^{-320}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_3 \leq 0 \lor \neg \left(t\_3 \leq 5 \cdot 10^{+233}\right):\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y + \left(z \cdot t - z \cdot a\right)}{t\_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y))))
        (t_2 (+ (/ (- t a) (- b y)) (/ x (- 1.0 z))))
        (t_3 (/ (+ (* z (- t a)) (* x y)) t_1)))
   (if (<= t_3 -1e+284)
     t_2
     (if (<= t_3 -1e-320)
       t_3
       (if (or (<= t_3 0.0) (not (<= t_3 5e+233)))
         t_2
         (/ (+ (* x y) (- (* z t) (* z a))) 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 t_2 = ((t - a) / (b - y)) + (x / (1.0 - z));
	double t_3 = ((z * (t - a)) + (x * y)) / t_1;
	double tmp;
	if (t_3 <= -1e+284) {
		tmp = t_2;
	} else if (t_3 <= -1e-320) {
		tmp = t_3;
	} else if ((t_3 <= 0.0) || !(t_3 <= 5e+233)) {
		tmp = t_2;
	} else {
		tmp = ((x * y) + ((z * t) - (z * a))) / 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) :: t_3
    real(8) :: tmp
    t_1 = y + (z * (b - y))
    t_2 = ((t - a) / (b - y)) + (x / (1.0d0 - z))
    t_3 = ((z * (t - a)) + (x * y)) / t_1
    if (t_3 <= (-1d+284)) then
        tmp = t_2
    else if (t_3 <= (-1d-320)) then
        tmp = t_3
    else if ((t_3 <= 0.0d0) .or. (.not. (t_3 <= 5d+233))) then
        tmp = t_2
    else
        tmp = ((x * y) + ((z * t) - (z * a))) / 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 t_2 = ((t - a) / (b - y)) + (x / (1.0 - z));
	double t_3 = ((z * (t - a)) + (x * y)) / t_1;
	double tmp;
	if (t_3 <= -1e+284) {
		tmp = t_2;
	} else if (t_3 <= -1e-320) {
		tmp = t_3;
	} else if ((t_3 <= 0.0) || !(t_3 <= 5e+233)) {
		tmp = t_2;
	} else {
		tmp = ((x * y) + ((z * t) - (z * a))) / t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z * (b - y))
	t_2 = ((t - a) / (b - y)) + (x / (1.0 - z))
	t_3 = ((z * (t - a)) + (x * y)) / t_1
	tmp = 0
	if t_3 <= -1e+284:
		tmp = t_2
	elif t_3 <= -1e-320:
		tmp = t_3
	elif (t_3 <= 0.0) or not (t_3 <= 5e+233):
		tmp = t_2
	else:
		tmp = ((x * y) + ((z * t) - (z * a))) / t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(z * Float64(b - y)))
	t_2 = Float64(Float64(Float64(t - a) / Float64(b - y)) + Float64(x / Float64(1.0 - z)))
	t_3 = Float64(Float64(Float64(z * Float64(t - a)) + Float64(x * y)) / t_1)
	tmp = 0.0
	if (t_3 <= -1e+284)
		tmp = t_2;
	elseif (t_3 <= -1e-320)
		tmp = t_3;
	elseif ((t_3 <= 0.0) || !(t_3 <= 5e+233))
		tmp = t_2;
	else
		tmp = Float64(Float64(Float64(x * y) + Float64(Float64(z * t) - Float64(z * a))) / t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (z * (b - y));
	t_2 = ((t - a) / (b - y)) + (x / (1.0 - z));
	t_3 = ((z * (t - a)) + (x * y)) / t_1;
	tmp = 0.0;
	if (t_3 <= -1e+284)
		tmp = t_2;
	elseif (t_3 <= -1e-320)
		tmp = t_3;
	elseif ((t_3 <= 0.0) || ~((t_3 <= 5e+233)))
		tmp = t_2;
	else
		tmp = ((x * y) + ((z * t) - (z * a))) / 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]}, Block[{t$95$2 = N[(N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision] + N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[t$95$3, -1e+284], t$95$2, If[LessEqual[t$95$3, -1e-320], t$95$3, If[Or[LessEqual[t$95$3, 0.0], N[Not[LessEqual[t$95$3, 5e+233]], $MachinePrecision]], t$95$2, N[(N[(N[(x * y), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -1.00000000000000008e284 or -9.99989e-321 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -0.0 or 5.00000000000000009e233 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 23.3%

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

   3. Taylor expanded in x around inf 35.0%

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

   4. Taylor expanded in y around -inf 41.6%

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

   5. Taylor expanded in z around inf 75.0%

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

      1. *-commutative 75.0%

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

   7. Simplified 75.0%

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

   8. Taylor expanded in x around 0 86.0%

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

      1. associate--l+ 86.0%

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

      2. mul-1-neg 86.0%

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

      3. sub-neg 86.0%

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

      4. metadata-eval 86.0%

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

      5. distribute-frac-neg 86.0%

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

      6. +-commutative 86.0%

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

      7. div-sub 86.0%

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

   10. Simplified 86.0%

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

   if -1.00000000000000008e284 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -9.99989e-321

   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

   if -0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 5.00000000000000009e233

   1. Initial program 99.4%

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

      1. sub-neg 99.4%

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

      2. distribute-lft-in 99.4%

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

   4. Applied egg-rr 99.4%

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

4. Final simplification 93.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)} \leq -1 \cdot 10^{+284}:\\ \;\;\;\;\frac{t - a}{b - y} + \frac{x}{1 - z}\\ \mathbf{elif}\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)} \leq -1 \cdot 10^{-320}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)} \leq 0 \lor \neg \left(\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)} \leq 5 \cdot 10^{+233}\right):\\ \;\;\;\;\frac{t - a}{b - y} + \frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y + \left(z \cdot t - z \cdot a\right)}{y + z \cdot \left(b - y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 92.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+284} \lor \neg \left(t\_1 \leq -1 \cdot 10^{-320} \lor \neg \left(t\_1 \leq 0\right) \land t\_1 \leq 5 \cdot 10^{+233}\right):\\ \;\;\;\;\frac{t - a}{b - y} + \frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ (* z (- t a)) (* x y)) (+ y (* z (- b y))))))
   (if (or (<= t_1 -1e+284)
           (not
            (or (<= t_1 -1e-320) (and (not (<= t_1 0.0)) (<= t_1 5e+233)))))
     (+ (/ (- t a) (- b y)) (/ x (- 1.0 z)))
     t_1)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((z * (t - a)) + (x * y)) / (y + (z * (b - y)));
	double tmp;
	if ((t_1 <= -1e+284) || !((t_1 <= -1e-320) || (!(t_1 <= 0.0) && (t_1 <= 5e+233)))) {
		tmp = ((t - a) / (b - y)) + (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 = ((z * (t - a)) + (x * y)) / (y + (z * (b - y)))
    if ((t_1 <= (-1d+284)) .or. (.not. (t_1 <= (-1d-320)) .or. (.not. (t_1 <= 0.0d0)) .and. (t_1 <= 5d+233))) then
        tmp = ((t - a) / (b - y)) + (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 = ((z * (t - a)) + (x * y)) / (y + (z * (b - y)));
	double tmp;
	if ((t_1 <= -1e+284) || !((t_1 <= -1e-320) || (!(t_1 <= 0.0) && (t_1 <= 5e+233)))) {
		tmp = ((t - a) / (b - y)) + (x / (1.0 - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((z * (t - a)) + (x * y)) / (y + (z * (b - y)))
	tmp = 0
	if (t_1 <= -1e+284) or not ((t_1 <= -1e-320) or (not (t_1 <= 0.0) and (t_1 <= 5e+233))):
		tmp = ((t - a) / (b - y)) + (x / (1.0 - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(z * Float64(t - a)) + Float64(x * y)) / Float64(y + Float64(z * Float64(b - y))))
	tmp = 0.0
	if ((t_1 <= -1e+284) || !((t_1 <= -1e-320) || (!(t_1 <= 0.0) && (t_1 <= 5e+233))))
		tmp = Float64(Float64(Float64(t - a) / Float64(b - y)) + 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 = ((z * (t - a)) + (x * y)) / (y + (z * (b - y)));
	tmp = 0.0;
	if ((t_1 <= -1e+284) || ~(((t_1 <= -1e-320) || (~((t_1 <= 0.0)) && (t_1 <= 5e+233)))))
		tmp = ((t - a) / (b - y)) + (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[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e+284], N[Not[Or[LessEqual[t$95$1, -1e-320], And[N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision], LessEqual[t$95$1, 5e+233]]]], $MachinePrecision]], N[(N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision] + N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -1.00000000000000008e284 or -9.99989e-321 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -0.0 or 5.00000000000000009e233 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 23.3%

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

   3. Taylor expanded in x around inf 35.0%

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

   4. Taylor expanded in y around -inf 41.6%

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

   5. Taylor expanded in z around inf 75.0%

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

      1. *-commutative 75.0%

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

   7. Simplified 75.0%

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

   8. Taylor expanded in x around 0 86.0%

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

      1. associate--l+ 86.0%

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

      2. mul-1-neg 86.0%

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

      3. sub-neg 86.0%

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

      4. metadata-eval 86.0%

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

      5. distribute-frac-neg 86.0%

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

      6. +-commutative 86.0%

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

      7. div-sub 86.0%

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

   10. Simplified 86.0%

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

   if -1.00000000000000008e284 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -9.99989e-321 or -0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 5.00000000000000009e233

   1. Initial program 99.4%

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

4. Final simplification 93.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)} \leq -1 \cdot 10^{+284} \lor \neg \left(\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)} \leq -1 \cdot 10^{-320} \lor \neg \left(\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)} \leq 0\right) \land \frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)} \leq 5 \cdot 10^{+233}\right):\\ \;\;\;\;\frac{t - a}{b - y} + \frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 73.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \frac{t - a}{y}\\ t_2 := \frac{t - a}{b - y} + \frac{x}{1 - z}\\ \mathbf{if}\;z \leq -1.85 \cdot 10^{-13}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-139}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-193}:\\ \;\;\;\;\frac{z \cdot \left(a - t\right)}{z \cdot \left(y - b\right) - y}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-72}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* z (/ (- t a) y))))
        (t_2 (+ (/ (- t a) (- b y)) (/ x (- 1.0 z)))))
   (if (<= z -1.85e-13)
     t_2
     (if (<= z -3.3e-139)
       t_1
       (if (<= z -1.8e-193)
         (/ (* z (- a t)) (- (* z (- y b)) y))
         (if (<= z 7.2e-72) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z * ((t - a) / y));
	double t_2 = ((t - a) / (b - y)) + (x / (1.0 - z));
	double tmp;
	if (z <= -1.85e-13) {
		tmp = t_2;
	} else if (z <= -3.3e-139) {
		tmp = t_1;
	} else if (z <= -1.8e-193) {
		tmp = (z * (a - t)) / ((z * (y - b)) - y);
	} else if (z <= 7.2e-72) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (z * ((t - a) / y))
    t_2 = ((t - a) / (b - y)) + (x / (1.0d0 - z))
    if (z <= (-1.85d-13)) then
        tmp = t_2
    else if (z <= (-3.3d-139)) then
        tmp = t_1
    else if (z <= (-1.8d-193)) then
        tmp = (z * (a - t)) / ((z * (y - b)) - y)
    else if (z <= 7.2d-72) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z * ((t - a) / y));
	double t_2 = ((t - a) / (b - y)) + (x / (1.0 - z));
	double tmp;
	if (z <= -1.85e-13) {
		tmp = t_2;
	} else if (z <= -3.3e-139) {
		tmp = t_1;
	} else if (z <= -1.8e-193) {
		tmp = (z * (a - t)) / ((z * (y - b)) - y);
	} else if (z <= 7.2e-72) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (z * ((t - a) / y))
	t_2 = ((t - a) / (b - y)) + (x / (1.0 - z))
	tmp = 0
	if z <= -1.85e-13:
		tmp = t_2
	elif z <= -3.3e-139:
		tmp = t_1
	elif z <= -1.8e-193:
		tmp = (z * (a - t)) / ((z * (y - b)) - y)
	elif z <= 7.2e-72:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(z * Float64(Float64(t - a) / y)))
	t_2 = Float64(Float64(Float64(t - a) / Float64(b - y)) + Float64(x / Float64(1.0 - z)))
	tmp = 0.0
	if (z <= -1.85e-13)
		tmp = t_2;
	elseif (z <= -3.3e-139)
		tmp = t_1;
	elseif (z <= -1.8e-193)
		tmp = Float64(Float64(z * Float64(a - t)) / Float64(Float64(z * Float64(y - b)) - y));
	elseif (z <= 7.2e-72)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (z * ((t - a) / y));
	t_2 = ((t - a) / (b - y)) + (x / (1.0 - z));
	tmp = 0.0;
	if (z <= -1.85e-13)
		tmp = t_2;
	elseif (z <= -3.3e-139)
		tmp = t_1;
	elseif (z <= -1.8e-193)
		tmp = (z * (a - t)) / ((z * (y - b)) - y);
	elseif (z <= 7.2e-72)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(z * N[(N[(t - a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision] + N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.85e-13], t$95$2, If[LessEqual[z, -3.3e-139], t$95$1, If[LessEqual[z, -1.8e-193], N[(N[(z * N[(a - t), $MachinePrecision]), $MachinePrecision] / N[(N[(z * N[(y - b), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.2e-72], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.84999999999999994e-13 or 7.2e-72 < z

   1. Initial program 47.9%

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

   3. Taylor expanded in x around inf 46.3%

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

   4. Taylor expanded in y around -inf 46.5%

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

   5. Taylor expanded in z around inf 72.9%

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

      1. *-commutative 72.9%

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

   7. Simplified 72.9%

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

   8. Taylor expanded in x around 0 81.2%

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

      1. associate--l+ 81.2%

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

      2. mul-1-neg 81.2%

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

      3. sub-neg 81.2%

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

      4. metadata-eval 81.2%

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

      5. distribute-frac-neg 81.2%

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

      6. +-commutative 81.2%

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

      7. div-sub 81.2%

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

   10. Simplified 81.2%

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

   if -1.84999999999999994e-13 < z < -3.3e-139 or -1.7999999999999999e-193 < z < 7.2e-72

   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 61.2%

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

   4. Taylor expanded in x around 0 76.6%

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

      1. div-sub 77.6%

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

   6. Simplified 77.6%

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

   if -3.3e-139 < z < -1.7999999999999999e-193

   1. Initial program 99.6%

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

   3. Taylor expanded in x around 0 86.0%

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

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{-13}:\\ \;\;\;\;\frac{t - a}{b - y} + \frac{x}{1 - z}\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-139}:\\ \;\;\;\;x + z \cdot \frac{t - a}{y}\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-193}:\\ \;\;\;\;\frac{z \cdot \left(a - t\right)}{z \cdot \left(y - b\right) - y}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-72}:\\ \;\;\;\;x + z \cdot \frac{t - a}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y} + \frac{x}{1 - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 71.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \frac{t - a}{y}\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -2.8 \cdot 10^{-11}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{-139}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-193}:\\ \;\;\;\;\frac{z \cdot \left(a - t\right)}{z \cdot \left(y - b\right) - y}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-12}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* z (/ (- t a) y)))) (t_2 (/ (- t a) (- b y))))
   (if (<= z -2.8e-11)
     t_2
     (if (<= z -1.35e-139)
       t_1
       (if (<= z -1.8e-193)
         (/ (* z (- a t)) (- (* z (- y b)) y))
         (if (<= z 7.5e-12) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z * ((t - a) / y));
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -2.8e-11) {
		tmp = t_2;
	} else if (z <= -1.35e-139) {
		tmp = t_1;
	} else if (z <= -1.8e-193) {
		tmp = (z * (a - t)) / ((z * (y - b)) - y);
	} else if (z <= 7.5e-12) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (z * ((t - a) / y))
    t_2 = (t - a) / (b - y)
    if (z <= (-2.8d-11)) then
        tmp = t_2
    else if (z <= (-1.35d-139)) then
        tmp = t_1
    else if (z <= (-1.8d-193)) then
        tmp = (z * (a - t)) / ((z * (y - b)) - y)
    else if (z <= 7.5d-12) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z * ((t - a) / y));
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -2.8e-11) {
		tmp = t_2;
	} else if (z <= -1.35e-139) {
		tmp = t_1;
	} else if (z <= -1.8e-193) {
		tmp = (z * (a - t)) / ((z * (y - b)) - y);
	} else if (z <= 7.5e-12) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (z * ((t - a) / y))
	t_2 = (t - a) / (b - y)
	tmp = 0
	if z <= -2.8e-11:
		tmp = t_2
	elif z <= -1.35e-139:
		tmp = t_1
	elif z <= -1.8e-193:
		tmp = (z * (a - t)) / ((z * (y - b)) - y)
	elif z <= 7.5e-12:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(z * Float64(Float64(t - a) / y)))
	t_2 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -2.8e-11)
		tmp = t_2;
	elseif (z <= -1.35e-139)
		tmp = t_1;
	elseif (z <= -1.8e-193)
		tmp = Float64(Float64(z * Float64(a - t)) / Float64(Float64(z * Float64(y - b)) - y));
	elseif (z <= 7.5e-12)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (z * ((t - a) / y));
	t_2 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -2.8e-11)
		tmp = t_2;
	elseif (z <= -1.35e-139)
		tmp = t_1;
	elseif (z <= -1.8e-193)
		tmp = (z * (a - t)) / ((z * (y - b)) - y);
	elseif (z <= 7.5e-12)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(z * N[(N[(t - a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.8e-11], t$95$2, If[LessEqual[z, -1.35e-139], t$95$1, If[LessEqual[z, -1.8e-193], N[(N[(z * N[(a - t), $MachinePrecision]), $MachinePrecision] / N[(N[(z * N[(y - b), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.5e-12], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.8e-11 or 7.5e-12 < 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 76.3%

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

   if -2.8e-11 < z < -1.3499999999999999e-139 or -1.7999999999999999e-193 < z < 7.5e-12

   1. Initial program 86.7%

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

   3. Taylor expanded in z around 0 60.1%

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

   4. Taylor expanded in x around 0 75.3%

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

      1. div-sub 76.2%

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

   6. Simplified 76.2%

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

   if -1.3499999999999999e-139 < z < -1.7999999999999999e-193

   1. Initial program 99.6%

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

   3. Taylor expanded in x around 0 86.0%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{-11}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{-139}:\\ \;\;\;\;x + z \cdot \frac{t - a}{y}\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-193}:\\ \;\;\;\;\frac{z \cdot \left(a - t\right)}{z \cdot \left(y - b\right) - y}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-12}:\\ \;\;\;\;x + z \cdot \frac{t - a}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 66.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -2.25 \cdot 10^{-11}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-139}:\\ \;\;\;\;x - z \cdot \frac{a}{y}\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{-180} \lor \neg \left(z \leq 1.2 \cdot 10^{-12}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{t}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -2.25e-11)
     t_1
     (if (<= z -1.3e-139)
       (- x (* z (/ a y)))
       (if (or (<= z -3.1e-180) (not (<= z 1.2e-12)))
         t_1
         (+ x (* z (/ t y))))))))

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 <= -2.25e-11) {
		tmp = t_1;
	} else if (z <= -1.3e-139) {
		tmp = x - (z * (a / y));
	} else if ((z <= -3.1e-180) || !(z <= 1.2e-12)) {
		tmp = t_1;
	} else {
		tmp = x + (z * (t / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    if (z <= (-2.25d-11)) then
        tmp = t_1
    else if (z <= (-1.3d-139)) then
        tmp = x - (z * (a / y))
    else if ((z <= (-3.1d-180)) .or. (.not. (z <= 1.2d-12))) then
        tmp = t_1
    else
        tmp = x + (z * (t / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -2.25e-11) {
		tmp = t_1;
	} else if (z <= -1.3e-139) {
		tmp = x - (z * (a / y));
	} else if ((z <= -3.1e-180) || !(z <= 1.2e-12)) {
		tmp = t_1;
	} else {
		tmp = x + (z * (t / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	tmp = 0
	if z <= -2.25e-11:
		tmp = t_1
	elif z <= -1.3e-139:
		tmp = x - (z * (a / y))
	elif (z <= -3.1e-180) or not (z <= 1.2e-12):
		tmp = t_1
	else:
		tmp = x + (z * (t / y))
	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 <= -2.25e-11)
		tmp = t_1;
	elseif (z <= -1.3e-139)
		tmp = Float64(x - Float64(z * Float64(a / y)));
	elseif ((z <= -3.1e-180) || !(z <= 1.2e-12))
		tmp = t_1;
	else
		tmp = Float64(x + Float64(z * Float64(t / y)));
	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 <= -2.25e-11)
		tmp = t_1;
	elseif (z <= -1.3e-139)
		tmp = x - (z * (a / y));
	elseif ((z <= -3.1e-180) || ~((z <= 1.2e-12)))
		tmp = t_1;
	else
		tmp = x + (z * (t / y));
	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, -2.25e-11], t$95$1, If[LessEqual[z, -1.3e-139], N[(x - N[(z * N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -3.1e-180], N[Not[LessEqual[z, 1.2e-12]], $MachinePrecision]], t$95$1, N[(x + N[(z * N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.25e-11 or -1.2999999999999999e-139 < z < -3.0999999999999999e-180 or 1.19999999999999994e-12 < z

   1. Initial program 48.8%

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

   3. Taylor expanded in z around inf 74.6%

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

   if -2.25e-11 < z < -1.2999999999999999e-139

   1. Initial program 95.6%

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

   3. Taylor expanded in z around 0 72.8%

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

   4. Taylor expanded in a around inf 65.3%

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

      1. associate-*r/ 65.3%

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

      2. neg-mul-1 65.3%

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

   6. Simplified 65.3%

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

   if -3.0999999999999999e-180 < z < 1.19999999999999994e-12

   1. Initial program 84.7%

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

   3. Taylor expanded in z around 0 57.9%

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

   4. Taylor expanded in t around inf 73.4%

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

4. Final simplification 73.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.25 \cdot 10^{-11}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-139}:\\ \;\;\;\;x - z \cdot \frac{a}{y}\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{-180} \lor \neg \left(z \leq 1.2 \cdot 10^{-12}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{t}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 43.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{b - y}\\ \mathbf{if}\;z \leq -2.26 \cdot 10^{-10}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-142}:\\ \;\;\;\;x + z \cdot x\\ \mathbf{elif}\;z \leq -6.4 \cdot 10^{-191}:\\ \;\;\;\;t \cdot \frac{z}{y}\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{-23}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ t (- b y))))
   (if (<= z -2.26e-10)
     t_1
     (if (<= z -6e-142)
       (+ x (* z x))
       (if (<= z -6.4e-191) (* t (/ z y)) (if (<= z 7.6e-23) x t_1))))))

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 <= -2.26e-10) {
		tmp = t_1;
	} else if (z <= -6e-142) {
		tmp = x + (z * x);
	} else if (z <= -6.4e-191) {
		tmp = t * (z / y);
	} else if (z <= 7.6e-23) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t / (b - y)
    if (z <= (-2.26d-10)) then
        tmp = t_1
    else if (z <= (-6d-142)) then
        tmp = x + (z * x)
    else if (z <= (-6.4d-191)) then
        tmp = t * (z / y)
    else if (z <= 7.6d-23) then
        tmp = x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t / (b - y);
	double tmp;
	if (z <= -2.26e-10) {
		tmp = t_1;
	} else if (z <= -6e-142) {
		tmp = x + (z * x);
	} else if (z <= -6.4e-191) {
		tmp = t * (z / y);
	} else if (z <= 7.6e-23) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t / (b - y)
	tmp = 0
	if z <= -2.26e-10:
		tmp = t_1
	elif z <= -6e-142:
		tmp = x + (z * x)
	elif z <= -6.4e-191:
		tmp = t * (z / y)
	elif z <= 7.6e-23:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t / Float64(b - y))
	tmp = 0.0
	if (z <= -2.26e-10)
		tmp = t_1;
	elseif (z <= -6e-142)
		tmp = Float64(x + Float64(z * x));
	elseif (z <= -6.4e-191)
		tmp = Float64(t * Float64(z / y));
	elseif (z <= 7.6e-23)
		tmp = x;
	else
		tmp = t_1;
	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 <= -2.26e-10)
		tmp = t_1;
	elseif (z <= -6e-142)
		tmp = x + (z * x);
	elseif (z <= -6.4e-191)
		tmp = t * (z / y);
	elseif (z <= 7.6e-23)
		tmp = x;
	else
		tmp = t_1;
	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, -2.26e-10], t$95$1, If[LessEqual[z, -6e-142], N[(x + N[(z * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -6.4e-191], N[(t * N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.6e-23], x, t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.26e-10 or 7.60000000000000023e-23 < z

   1. Initial program 44.8%

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

   3. Taylor expanded in t around inf 24.3%

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

      1. *-commutative 24.3%

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

   5. Simplified 24.3%

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

   6. Taylor expanded in z around inf 39.1%

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

   if -2.26e-10 < z < -6.0000000000000002e-142

   1. Initial program 95.8%

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

   3. Taylor expanded in z around 0 70.2%

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

   4. Taylor expanded in y around inf 50.7%

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

      1. *-commutative 50.7%

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

   6. Simplified 50.7%

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

   if -6.0000000000000002e-142 < z < -6.4000000000000006e-191

   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 t around inf 60.0%

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

      1. *-commutative 60.0%

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

   5. Simplified 60.0%

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

   6. Taylor expanded in z around 0 44.8%

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

      1. associate-/l* 39.8%

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

   8. Simplified 39.8%

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

   if -6.4000000000000006e-191 < z < 7.60000000000000023e-23

   1. Initial program 84.2%

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

   3. Taylor expanded in z around 0 66.1%

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

Alternative 10: 85.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{-12} \lor \neg \left(z \leq 55000000\right):\\ \;\;\;\;\frac{t - a}{b - y} + \frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -2.8e-12) (not (<= z 55000000.0)))
   (+ (/ (- t a) (- b y)) (/ x (- 1.0 z)))
   (/ (+ (* z (- t a)) (* x y)) (+ y (* z b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.8e-12) || !(z <= 55000000.0)) {
		tmp = ((t - a) / (b - y)) + (x / (1.0 - z));
	} else {
		tmp = ((z * (t - a)) + (x * y)) / (y + (z * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-2.8d-12)) .or. (.not. (z <= 55000000.0d0))) then
        tmp = ((t - a) / (b - y)) + (x / (1.0d0 - z))
    else
        tmp = ((z * (t - a)) + (x * y)) / (y + (z * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.8e-12) || !(z <= 55000000.0)) {
		tmp = ((t - a) / (b - y)) + (x / (1.0 - z));
	} else {
		tmp = ((z * (t - a)) + (x * y)) / (y + (z * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -2.8e-12) or not (z <= 55000000.0):
		tmp = ((t - a) / (b - y)) + (x / (1.0 - z))
	else:
		tmp = ((z * (t - a)) + (x * y)) / (y + (z * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -2.8e-12) || !(z <= 55000000.0))
		tmp = Float64(Float64(Float64(t - a) / Float64(b - y)) + Float64(x / Float64(1.0 - z)));
	else
		tmp = Float64(Float64(Float64(z * Float64(t - a)) + Float64(x * y)) / Float64(y + Float64(z * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -2.8e-12) || ~((z <= 55000000.0)))
		tmp = ((t - a) / (b - y)) + (x / (1.0 - z));
	else
		tmp = ((z * (t - a)) + (x * y)) / (y + (z * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -2.8e-12], N[Not[LessEqual[z, 55000000.0]], $MachinePrecision]], N[(N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision] + N[(x / N[(1.0 - z), $MachinePrecision]), $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 < -2.8000000000000002e-12 or 5.5e7 < z

   1. Initial program 44.2%

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

   3. Taylor expanded in x around inf 39.3%

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

   4. Taylor expanded in y around -inf 43.0%

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

   5. Taylor expanded in z around inf 75.2%

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

      1. *-commutative 75.2%

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

   7. Simplified 75.2%

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

   8. Taylor expanded in x around 0 84.6%

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

      1. associate--l+ 84.6%

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

      2. mul-1-neg 84.6%

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

      3. sub-neg 84.6%

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

      4. metadata-eval 84.6%

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

      5. distribute-frac-neg 84.6%

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

      6. +-commutative 84.6%

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

      7. div-sub 84.6%

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

   10. Simplified 84.6%

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

   if -2.8000000000000002e-12 < z < 5.5e7

   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 b around inf 87.5%

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

      1. *-commutative 87.5%

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

   5. Simplified 87.5%

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

4. Final simplification 86.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{-12} \lor \neg \left(z \leq 55000000\right):\\ \;\;\;\;\frac{t - a}{b - y} + \frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot b}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 36.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.7:\\ \;\;\;\;\frac{a}{-b}\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-142}:\\ \;\;\;\;x + z \cdot x\\ \mathbf{elif}\;z \leq -6.4 \cdot 10^{-191}:\\ \;\;\;\;t \cdot \frac{z}{y}\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-20}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -0.7)
   (/ a (- b))
   (if (<= z -6e-142)
     (+ x (* z x))
     (if (<= z -6.4e-191) (* t (/ z y)) (if (<= z 3.4e-20) x (/ t b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -0.7) {
		tmp = a / -b;
	} else if (z <= -6e-142) {
		tmp = x + (z * x);
	} else if (z <= -6.4e-191) {
		tmp = t * (z / y);
	} else if (z <= 3.4e-20) {
		tmp = x;
	} else {
		tmp = t / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-0.7d0)) then
        tmp = a / -b
    else if (z <= (-6d-142)) then
        tmp = x + (z * x)
    else if (z <= (-6.4d-191)) then
        tmp = t * (z / y)
    else if (z <= 3.4d-20) then
        tmp = x
    else
        tmp = t / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -0.7) {
		tmp = a / -b;
	} else if (z <= -6e-142) {
		tmp = x + (z * x);
	} else if (z <= -6.4e-191) {
		tmp = t * (z / y);
	} else if (z <= 3.4e-20) {
		tmp = x;
	} else {
		tmp = t / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -0.7:
		tmp = a / -b
	elif z <= -6e-142:
		tmp = x + (z * x)
	elif z <= -6.4e-191:
		tmp = t * (z / y)
	elif z <= 3.4e-20:
		tmp = x
	else:
		tmp = t / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -0.7)
		tmp = Float64(a / Float64(-b));
	elseif (z <= -6e-142)
		tmp = Float64(x + Float64(z * x));
	elseif (z <= -6.4e-191)
		tmp = Float64(t * Float64(z / y));
	elseif (z <= 3.4e-20)
		tmp = x;
	else
		tmp = Float64(t / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -0.7)
		tmp = a / -b;
	elseif (z <= -6e-142)
		tmp = x + (z * x);
	elseif (z <= -6.4e-191)
		tmp = t * (z / y);
	elseif (z <= 3.4e-20)
		tmp = x;
	else
		tmp = t / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -0.7], N[(a / (-b)), $MachinePrecision], If[LessEqual[z, -6e-142], N[(x + N[(z * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -6.4e-191], N[(t * N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.4e-20], x, N[(t / b), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -0.69999999999999996

   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 x around inf 35.6%

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

   4. Taylor expanded in b around inf 44.6%

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

      1. associate-/l* 39.4%

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

      2. associate--l+ 39.4%

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

   6. Simplified 39.4%

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

   7. Taylor expanded in a around inf 30.9%

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

      1. associate-*r/ 30.9%

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

      2. mul-1-neg 30.9%

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

   9. Simplified 30.9%

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

   if -0.69999999999999996 < z < -6.0000000000000002e-142

   1. Initial program 96.1%

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

   3. Taylor expanded in z around 0 66.2%

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

   4. Taylor expanded in y around inf 47.6%

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

      1. *-commutative 47.6%

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

   6. Simplified 47.6%

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

   if -6.0000000000000002e-142 < z < -6.4000000000000006e-191

   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 t around inf 60.0%

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

      1. *-commutative 60.0%

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

   5. Simplified 60.0%

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

   6. Taylor expanded in z around 0 44.8%

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

      1. associate-/l* 39.8%

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

   8. Simplified 39.8%

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

   if -6.4000000000000006e-191 < z < 3.3999999999999997e-20

   1. Initial program 84.2%

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

   3. Taylor expanded in z around 0 66.1%

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

   if 3.3999999999999997e-20 < z

   1. Initial program 46.4%

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

   3. Taylor expanded in t around inf 22.4%

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

      1. *-commutative 22.4%

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

   5. Simplified 22.4%

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

   6. Taylor expanded in y around 0 32.8%

      \[\leadsto \color{blue}{\frac{t}{b}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 46.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.7:\\ \;\;\;\;\frac{a}{-b}\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-142}:\\ \;\;\;\;x + z \cdot x\\ \mathbf{elif}\;z \leq -6.4 \cdot 10^{-191}:\\ \;\;\;\;t \cdot \frac{z}{y}\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-20}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 35.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.65:\\ \;\;\;\;\frac{a}{-b}\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-142}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -6.4 \cdot 10^{-191}:\\ \;\;\;\;t \cdot \frac{z}{y}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-19}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -0.65)
   (/ a (- b))
   (if (<= z -6e-142)
     x
     (if (<= z -6.4e-191) (* t (/ z y)) (if (<= z 1.3e-19) x (/ t b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -0.65) {
		tmp = a / -b;
	} else if (z <= -6e-142) {
		tmp = x;
	} else if (z <= -6.4e-191) {
		tmp = t * (z / y);
	} else if (z <= 1.3e-19) {
		tmp = x;
	} else {
		tmp = t / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-0.65d0)) then
        tmp = a / -b
    else if (z <= (-6d-142)) then
        tmp = x
    else if (z <= (-6.4d-191)) then
        tmp = t * (z / y)
    else if (z <= 1.3d-19) then
        tmp = x
    else
        tmp = t / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -0.65) {
		tmp = a / -b;
	} else if (z <= -6e-142) {
		tmp = x;
	} else if (z <= -6.4e-191) {
		tmp = t * (z / y);
	} else if (z <= 1.3e-19) {
		tmp = x;
	} else {
		tmp = t / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -0.65:
		tmp = a / -b
	elif z <= -6e-142:
		tmp = x
	elif z <= -6.4e-191:
		tmp = t * (z / y)
	elif z <= 1.3e-19:
		tmp = x
	else:
		tmp = t / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -0.65)
		tmp = Float64(a / Float64(-b));
	elseif (z <= -6e-142)
		tmp = x;
	elseif (z <= -6.4e-191)
		tmp = Float64(t * Float64(z / y));
	elseif (z <= 1.3e-19)
		tmp = x;
	else
		tmp = Float64(t / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -0.65)
		tmp = a / -b;
	elseif (z <= -6e-142)
		tmp = x;
	elseif (z <= -6.4e-191)
		tmp = t * (z / y);
	elseif (z <= 1.3e-19)
		tmp = x;
	else
		tmp = t / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -0.65], N[(a / (-b)), $MachinePrecision], If[LessEqual[z, -6e-142], x, If[LessEqual[z, -6.4e-191], N[(t * N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.3e-19], x, N[(t / b), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -0.650000000000000022

   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 x around inf 35.6%

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

   4. Taylor expanded in b around inf 44.6%

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

      1. associate-/l* 39.4%

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

      2. associate--l+ 39.4%

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

   6. Simplified 39.4%

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

   7. Taylor expanded in a around inf 30.9%

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

      1. associate-*r/ 30.9%

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

      2. mul-1-neg 30.9%

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

   9. Simplified 30.9%

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

   if -0.650000000000000022 < z < -6.0000000000000002e-142 or -6.4000000000000006e-191 < z < 1.30000000000000006e-19

   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 z around 0 61.1%

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

   if -6.0000000000000002e-142 < z < -6.4000000000000006e-191

   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 t around inf 60.0%

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

      1. *-commutative 60.0%

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

   5. Simplified 60.0%

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

   6. Taylor expanded in z around 0 44.8%

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

      1. associate-/l* 39.8%

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

   8. Simplified 39.8%

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

   if 1.30000000000000006e-19 < z

   1. Initial program 46.4%

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

   3. Taylor expanded in t around inf 22.4%

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

      1. *-commutative 22.4%

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

   5. Simplified 22.4%

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

   6. Taylor expanded in y around 0 32.8%

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

4. Final simplification 46.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.65:\\ \;\;\;\;\frac{a}{-b}\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-142}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -6.4 \cdot 10^{-191}:\\ \;\;\;\;t \cdot \frac{z}{y}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-19}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 51.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+174}:\\ \;\;\;\;\frac{a}{y - b}\\ \mathbf{elif}\;z \leq -8.8 \cdot 10^{-11} \lor \neg \left(z \leq 4.2 \cdot 10^{-13}\right):\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{t}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.8e+174)
   (/ a (- y b))
   (if (or (<= z -8.8e-11) (not (<= z 4.2e-13)))
     (/ (- t a) b)
     (+ x (* z (/ t y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.8e+174) {
		tmp = a / (y - b);
	} else if ((z <= -8.8e-11) || !(z <= 4.2e-13)) {
		tmp = (t - a) / b;
	} else {
		tmp = x + (z * (t / 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 <= (-1.8d+174)) then
        tmp = a / (y - b)
    else if ((z <= (-8.8d-11)) .or. (.not. (z <= 4.2d-13))) then
        tmp = (t - a) / b
    else
        tmp = x + (z * (t / 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 <= -1.8e+174) {
		tmp = a / (y - b);
	} else if ((z <= -8.8e-11) || !(z <= 4.2e-13)) {
		tmp = (t - a) / b;
	} else {
		tmp = x + (z * (t / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1.8e+174:
		tmp = a / (y - b)
	elif (z <= -8.8e-11) or not (z <= 4.2e-13):
		tmp = (t - a) / b
	else:
		tmp = x + (z * (t / y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.8e+174)
		tmp = Float64(a / Float64(y - b));
	elseif ((z <= -8.8e-11) || !(z <= 4.2e-13))
		tmp = Float64(Float64(t - a) / b);
	else
		tmp = Float64(x + Float64(z * Float64(t / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -1.8e+174)
		tmp = a / (y - b);
	elseif ((z <= -8.8e-11) || ~((z <= 4.2e-13)))
		tmp = (t - a) / b;
	else
		tmp = x + (z * (t / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.8e+174], N[(a / N[(y - b), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -8.8e-11], N[Not[LessEqual[z, 4.2e-13]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision], N[(x + N[(z * N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.8000000000000001e174

   1. Initial program 11.8%

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

   3. Taylor expanded in x around inf 7.1%

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

   4. Taylor expanded in y around -inf 15.4%

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

   5. Taylor expanded in z around inf 75.3%

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

      1. *-commutative 75.3%

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

   7. Simplified 75.3%

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

   8. Taylor expanded in a around inf 57.4%

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

      1. associate-*r/ 57.4%

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

      2. mul-1-neg 57.4%

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

   10. Simplified 57.4%

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

   if -1.8000000000000001e174 < z < -8.8000000000000006e-11 or 4.19999999999999977e-13 < z

   1. Initial program 51.3%

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

   3. Taylor expanded in y around 0 52.9%

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

   if -8.8000000000000006e-11 < z < 4.19999999999999977e-13

   1. Initial program 88.1%

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

   3. Taylor expanded in z around 0 58.4%

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

   4. Taylor expanded in t around inf 66.5%

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

4. Final simplification 60.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+174}:\\ \;\;\;\;\frac{a}{y - b}\\ \mathbf{elif}\;z \leq -8.8 \cdot 10^{-11} \lor \neg \left(z \leq 4.2 \cdot 10^{-13}\right):\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{t}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 41.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -7.8 \cdot 10^{-70}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-279}:\\ \;\;\;\;\frac{a}{-b}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-87}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (- 1.0 z))))
   (if (<= y -7.8e-70)
     t_1
     (if (<= y 1.7e-279) (/ a (- b)) (if (<= y 3.5e-87) (/ t b) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 - z);
	double tmp;
	if (y <= -7.8e-70) {
		tmp = t_1;
	} else if (y <= 1.7e-279) {
		tmp = a / -b;
	} else if (y <= 3.5e-87) {
		tmp = t / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (1.0d0 - z)
    if (y <= (-7.8d-70)) then
        tmp = t_1
    else if (y <= 1.7d-279) then
        tmp = a / -b
    else if (y <= 3.5d-87) then
        tmp = t / b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 - z);
	double tmp;
	if (y <= -7.8e-70) {
		tmp = t_1;
	} else if (y <= 1.7e-279) {
		tmp = a / -b;
	} else if (y <= 3.5e-87) {
		tmp = t / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (1.0 - z)
	tmp = 0
	if y <= -7.8e-70:
		tmp = t_1
	elif y <= 1.7e-279:
		tmp = a / -b
	elif y <= 3.5e-87:
		tmp = t / b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(1.0 - z))
	tmp = 0.0
	if (y <= -7.8e-70)
		tmp = t_1;
	elseif (y <= 1.7e-279)
		tmp = Float64(a / Float64(-b));
	elseif (y <= 3.5e-87)
		tmp = Float64(t / b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (1.0 - z);
	tmp = 0.0;
	if (y <= -7.8e-70)
		tmp = t_1;
	elseif (y <= 1.7e-279)
		tmp = a / -b;
	elseif (y <= 3.5e-87)
		tmp = t / b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7.8e-70], t$95$1, If[LessEqual[y, 1.7e-279], N[(a / (-b)), $MachinePrecision], If[LessEqual[y, 3.5e-87], N[(t / b), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.80000000000000038e-70 or 3.50000000000000012e-87 < y

   1. Initial program 62.0%

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

   3. Taylor expanded in y around inf 54.3%

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

      1. mul-1-neg 54.3%

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

      2. unsub-neg 54.3%

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

   5. Simplified 54.3%

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

   if -7.80000000000000038e-70 < y < 1.70000000000000007e-279

   1. Initial program 77.6%

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

   3. Taylor expanded in x around inf 62.1%

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

   4. Taylor expanded in b around inf 52.0%

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

      1. associate-/l* 51.8%

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

      2. associate--l+ 51.8%

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

   6. Simplified 51.8%

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

   7. Taylor expanded in a around inf 39.9%

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

      1. associate-*r/ 39.9%

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

      2. mul-1-neg 39.9%

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

   9. Simplified 39.9%

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

   if 1.70000000000000007e-279 < y < 3.50000000000000012e-87

   1. Initial program 71.8%

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

   3. Taylor expanded in t around inf 38.6%

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

      1. *-commutative 38.6%

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

   5. Simplified 38.6%

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

   6. Taylor expanded in y around 0 48.2%

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

4. Final simplification 50.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.8 \cdot 10^{-70}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-279}:\\ \;\;\;\;\frac{a}{-b}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-87}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 71.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{-10} \lor \neg \left(z \leq 2.3 \cdot 10^{-15}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{t - a}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -6.2e-10) (not (<= z 2.3e-15)))
   (/ (- t a) (- b y))
   (+ x (* z (/ (- t a) y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -6.2e-10) || !(z <= 2.3e-15)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x + (z * ((t - a) / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-6.2d-10)) .or. (.not. (z <= 2.3d-15))) then
        tmp = (t - a) / (b - y)
    else
        tmp = x + (z * ((t - a) / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -6.2e-10) || !(z <= 2.3e-15)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x + (z * ((t - a) / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -6.2e-10) or not (z <= 2.3e-15):
		tmp = (t - a) / (b - y)
	else:
		tmp = x + (z * ((t - a) / y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -6.2e-10) || !(z <= 2.3e-15))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(x + Float64(z * Float64(Float64(t - a) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -6.2e-10) || ~((z <= 2.3e-15)))
		tmp = (t - a) / (b - y);
	else
		tmp = x + (z * ((t - a) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -6.2e-10], N[Not[LessEqual[z, 2.3e-15]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(N[(t - a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.2000000000000003e-10 or 2.2999999999999999e-15 < 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 76.3%

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

   if -6.2000000000000003e-10 < z < 2.2999999999999999e-15

   1. Initial program 88.1%

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

   3. Taylor expanded in z around 0 58.4%

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

   4. Taylor expanded in x around 0 72.0%

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

      1. div-sub 72.9%

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

   6. Simplified 72.9%

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

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{-10} \lor \neg \left(z \leq 2.3 \cdot 10^{-15}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{t - a}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 67.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{-11} \lor \neg \left(z \leq 2.5 \cdot 10^{-17}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{t}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -2.4e-11) (not (<= z 2.5e-17)))
   (/ (- t a) (- b y))
   (+ x (* z (/ t y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.4e-11) || !(z <= 2.5e-17)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x + (z * (t / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-2.4d-11)) .or. (.not. (z <= 2.5d-17))) then
        tmp = (t - a) / (b - y)
    else
        tmp = x + (z * (t / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.4e-11) || !(z <= 2.5e-17)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x + (z * (t / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -2.4e-11) or not (z <= 2.5e-17):
		tmp = (t - a) / (b - y)
	else:
		tmp = x + (z * (t / y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -2.4e-11) || !(z <= 2.5e-17))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(x + Float64(z * Float64(t / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -2.4e-11) || ~((z <= 2.5e-17)))
		tmp = (t - a) / (b - y);
	else
		tmp = x + (z * (t / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -2.4e-11], N[Not[LessEqual[z, 2.5e-17]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.4000000000000001e-11 or 2.4999999999999999e-17 < 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 76.3%

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

   if -2.4000000000000001e-11 < z < 2.4999999999999999e-17

   1. Initial program 88.1%

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

   3. Taylor expanded in z around 0 58.4%

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

   4. Taylor expanded in t around inf 66.5%

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

4. Final simplification 71.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{-11} \lor \neg \left(z \leq 2.5 \cdot 10^{-17}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{t}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 53.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{-25} \lor \neg \left(y \leq 700000000\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.25e-25) (not (<= y 700000000.0)))
   (/ 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 <= -1.25e-25) || !(y <= 700000000.0)) {
		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 <= (-1.25d-25)) .or. (.not. (y <= 700000000.0d0))) 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 <= -1.25e-25) || !(y <= 700000000.0)) {
		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 <= -1.25e-25) or not (y <= 700000000.0):
		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 <= -1.25e-25) || !(y <= 700000000.0))
		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 <= -1.25e-25) || ~((y <= 700000000.0)))
		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, -1.25e-25], N[Not[LessEqual[y, 700000000.0]], $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 < -1.2499999999999999e-25 or 7e8 < 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 58.5%

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

      1. mul-1-neg 58.5%

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

      2. unsub-neg 58.5%

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

   5. Simplified 58.5%

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

   if -1.2499999999999999e-25 < y < 7e8

   1. Initial program 75.7%

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

   3. Taylor expanded in y around 0 58.8%

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

4. Final simplification 58.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{-25} \lor \neg \left(y \leq 700000000\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 37.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-10} \lor \neg \left(z \leq 7 \cdot 10^{-21}\right):\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -2e-10) (not (<= z 7e-21))) (/ t b) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2e-10) || !(z <= 7e-21)) {
		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 <= (-2d-10)) .or. (.not. (z <= 7d-21))) 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 <= -2e-10) || !(z <= 7e-21)) {
		tmp = t / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -2e-10) or not (z <= 7e-21):
		tmp = t / b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -2e-10) || !(z <= 7e-21))
		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 <= -2e-10) || ~((z <= 7e-21)))
		tmp = t / b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -2e-10], N[Not[LessEqual[z, 7e-21]], $MachinePrecision]], N[(t / b), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -2.00000000000000007e-10 or 7.0000000000000007e-21 < z

   1. Initial program 44.8%

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

   3. Taylor expanded in t around inf 24.3%

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

      1. *-commutative 24.3%

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

   5. Simplified 24.3%

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

   6. Taylor expanded in y around 0 30.9%

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

   if -2.00000000000000007e-10 < z < 7.0000000000000007e-21

   1. Initial program 88.0%

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

   3. Taylor expanded in z around 0 56.5%

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

4. Final simplification 43.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-10} \lor \neg \left(z \leq 7 \cdot 10^{-21}\right):\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 37.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.85:\\ \;\;\;\;\frac{a}{-b}\\ \mathbf{elif}\;z \leq 9.4 \cdot 10^{-20}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -0.85) (/ a (- b)) (if (<= z 9.4e-20) x (/ t b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -0.85) {
		tmp = a / -b;
	} else if (z <= 9.4e-20) {
		tmp = x;
	} else {
		tmp = t / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-0.85d0)) then
        tmp = a / -b
    else if (z <= 9.4d-20) then
        tmp = x
    else
        tmp = t / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -0.85) {
		tmp = a / -b;
	} else if (z <= 9.4e-20) {
		tmp = x;
	} else {
		tmp = t / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -0.85:
		tmp = a / -b
	elif z <= 9.4e-20:
		tmp = x
	else:
		tmp = t / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -0.85)
		tmp = Float64(a / Float64(-b));
	elseif (z <= 9.4e-20)
		tmp = x;
	else
		tmp = Float64(t / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -0.85)
		tmp = a / -b;
	elseif (z <= 9.4e-20)
		tmp = x;
	else
		tmp = t / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -0.85], N[(a / (-b)), $MachinePrecision], If[LessEqual[z, 9.4e-20], x, N[(t / b), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.849999999999999978

   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 x around inf 35.6%

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

   4. Taylor expanded in b around inf 44.6%

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

      1. associate-/l* 39.4%

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

      2. associate--l+ 39.4%

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

   6. Simplified 39.4%

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

   7. Taylor expanded in a around inf 30.9%

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

      1. associate-*r/ 30.9%

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

      2. mul-1-neg 30.9%

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

   9. Simplified 30.9%

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

   if -0.849999999999999978 < z < 9.4000000000000003e-20

   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. Taylor expanded in z around 0 55.7%

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

   if 9.4000000000000003e-20 < z

   1. Initial program 46.4%

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

   3. Taylor expanded in t around inf 22.4%

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

      1. *-commutative 22.4%

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

   5. Simplified 22.4%

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

   6. Taylor expanded in y around 0 32.8%

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

4. Final simplification 44.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.85:\\ \;\;\;\;\frac{a}{-b}\\ \mathbf{elif}\;z \leq 9.4 \cdot 10^{-20}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 25.8% 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 66.7%

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

3. Taylor expanded in z around 0 30.5%

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

Developer target: 73.6% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024100 
(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)))))