Development.Shake.Progress:decay from shake-0.15.5

Percentage Accurate: 66.6% → 77.6%

Time: 21.0s

Alternatives: 24

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: 66.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 77.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+58}:\\ \;\;\;\;\left(\frac{y}{z} \cdot \frac{x}{b - y} + \frac{t - a}{b - y}\right) + y \cdot \frac{a - t}{z \cdot {\left(b - y\right)}^{2}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, z \cdot \left(t - a\right)\right)}{\mathsf{fma}\left(z, b - y, y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -2.4e+58)
   (+
    (+ (* (/ y z) (/ x (- b y))) (/ (- t a) (- b y)))
    (* y (/ (- a t) (* z (pow (- b y) 2.0)))))
   (/ (fma x y (* z (- t a))) (fma z (- b y) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2.4e+58) {
		tmp = (((y / z) * (x / (b - y))) + ((t - a) / (b - y))) + (y * ((a - t) / (z * pow((b - y), 2.0))));
	} else {
		tmp = fma(x, y, (z * (t - a))) / fma(z, (b - y), y);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -2.4e+58)
		tmp = Float64(Float64(Float64(Float64(y / z) * Float64(x / Float64(b - y))) + Float64(Float64(t - a) / Float64(b - y))) + Float64(y * Float64(Float64(a - t) / Float64(z * (Float64(b - y) ^ 2.0)))));
	else
		tmp = Float64(fma(x, y, Float64(z * Float64(t - a))) / fma(z, Float64(b - y), y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -2.4e+58], N[(N[(N[(N[(y / z), $MachinePrecision] * N[(x / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * N[(N[(a - t), $MachinePrecision] / N[(z * N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * y + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * N[(b - y), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.4e58

   1. Initial program 34.2%

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

   3. Taylor expanded in z around inf 60.2%

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

      1. associate--r+ 60.2%

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

      2. +-commutative 60.2%

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

      3. associate--l+ 60.2%

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

      4. *-commutative 60.2%

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

      5. times-frac 62.6%

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

      6. div-sub 62.6%

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

      7. associate-/l* 93.6%

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

   5. Simplified 93.6%

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

   if -2.4e58 < z

   1. Initial program 69.4%

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

      1. fma-define 69.4%

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

      2. +-commutative 69.4%

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

      3. fma-define 69.4%

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

   3. Simplified 69.4%

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

4. Final simplification 74.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+58}:\\ \;\;\;\;\left(\frac{y}{z} \cdot \frac{x}{b - y} + \frac{t - a}{b - y}\right) + y \cdot \frac{a - t}{z \cdot {\left(b - y\right)}^{2}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, z \cdot \left(t - a\right)\right)}{\mathsf{fma}\left(z, b - y, y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 77.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ \mathbf{if}\;z \leq 7.6 \cdot 10^{+30}:\\ \;\;\;\;\frac{z \cdot a}{z \cdot \left(y - b\right) - y} + \left(\frac{z \cdot t}{t\_1} + \frac{y \cdot x}{t\_1}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{y}{z} \cdot \frac{x}{b - y} + \frac{t - a}{b - y}\right) + y \cdot \frac{a - t}{z \cdot {\left(b - y\right)}^{2}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y)))))
   (if (<= z 7.6e+30)
     (+ (/ (* z a) (- (* z (- y b)) y)) (+ (/ (* z t) t_1) (/ (* y x) t_1)))
     (+
      (+ (* (/ y z) (/ x (- b y))) (/ (- t a) (- b y)))
      (* y (/ (- a t) (* z (pow (- b y) 2.0))))))))

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 <= 7.6e+30) {
		tmp = ((z * a) / ((z * (y - b)) - y)) + (((z * t) / t_1) + ((y * x) / t_1));
	} else {
		tmp = (((y / z) * (x / (b - y))) + ((t - a) / (b - y))) + (y * ((a - t) / (z * pow((b - y), 2.0))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y + (z * (b - y))
    if (z <= 7.6d+30) then
        tmp = ((z * a) / ((z * (y - b)) - y)) + (((z * t) / t_1) + ((y * x) / t_1))
    else
        tmp = (((y / z) * (x / (b - y))) + ((t - a) / (b - y))) + (y * ((a - t) / (z * ((b - y) ** 2.0d0))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double tmp;
	if (z <= 7.6e+30) {
		tmp = ((z * a) / ((z * (y - b)) - y)) + (((z * t) / t_1) + ((y * x) / t_1));
	} else {
		tmp = (((y / z) * (x / (b - y))) + ((t - a) / (b - y))) + (y * ((a - t) / (z * Math.pow((b - y), 2.0))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z * (b - y))
	tmp = 0
	if z <= 7.6e+30:
		tmp = ((z * a) / ((z * (y - b)) - y)) + (((z * t) / t_1) + ((y * x) / t_1))
	else:
		tmp = (((y / z) * (x / (b - y))) + ((t - a) / (b - y))) + (y * ((a - t) / (z * math.pow((b - y), 2.0))))
	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 <= 7.6e+30)
		tmp = Float64(Float64(Float64(z * a) / Float64(Float64(z * Float64(y - b)) - y)) + Float64(Float64(Float64(z * t) / t_1) + Float64(Float64(y * x) / t_1)));
	else
		tmp = Float64(Float64(Float64(Float64(y / z) * Float64(x / Float64(b - y))) + Float64(Float64(t - a) / Float64(b - y))) + Float64(y * Float64(Float64(a - t) / Float64(z * (Float64(b - y) ^ 2.0)))));
	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 <= 7.6e+30)
		tmp = ((z * a) / ((z * (y - b)) - y)) + (((z * t) / t_1) + ((y * x) / t_1));
	else
		tmp = (((y / z) * (x / (b - y))) + ((t - a) / (b - y))) + (y * ((a - t) / (z * ((b - y) ^ 2.0))));
	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[LessEqual[z, 7.6e+30], N[(N[(N[(z * a), $MachinePrecision] / N[(N[(z * N[(y - b), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(z * t), $MachinePrecision] / t$95$1), $MachinePrecision] + N[(N[(y * x), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(y / z), $MachinePrecision] * N[(x / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * N[(N[(a - t), $MachinePrecision] / N[(z * N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < 7.6000000000000003e30

   1. Initial program 68.8%

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

   3. Taylor expanded in t around 0 68.8%

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

   if 7.6000000000000003e30 < z

   1. Initial program 31.8%

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

   3. Taylor expanded in z around inf 63.3%

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

      1. associate--r+ 63.3%

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

      2. +-commutative 63.3%

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

      3. associate--l+ 63.3%

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

      4. *-commutative 63.3%

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

      5. times-frac 70.8%

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

      6. div-sub 70.8%

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

      7. associate-/l* 94.1%

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

   5. Simplified 94.1%

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

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 7.6 \cdot 10^{+30}:\\ \;\;\;\;\frac{z \cdot a}{z \cdot \left(y - b\right) - y} + \left(\frac{z \cdot t}{y + z \cdot \left(b - y\right)} + \frac{y \cdot x}{y + z \cdot \left(b - y\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{y}{z} \cdot \frac{x}{b - y} + \frac{t - a}{b - y}\right) + y \cdot \frac{a - t}{z \cdot {\left(b - y\right)}^{2}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 71.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 4.6 \cdot 10^{+24}:\\ \;\;\;\;\frac{y \cdot x - \left(z \cdot a - z \cdot t\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z} - \frac{z \cdot \frac{t - a}{z + -1} + \frac{z \cdot \left(x \cdot b\right)}{{\left(z + -1\right)}^{2}}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y 4.6e+24)
   (/ (- (* y x) (- (* z a) (* z t))) (+ y (* z (- b y))))
   (-
    (/ x (- 1.0 z))
    (/
     (+ (* z (/ (- t a) (+ z -1.0))) (/ (* z (* x b)) (pow (+ z -1.0) 2.0)))
     y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 4.6e+24) {
		tmp = ((y * x) - ((z * a) - (z * t))) / (y + (z * (b - y)));
	} else {
		tmp = (x / (1.0 - z)) - (((z * ((t - a) / (z + -1.0))) + ((z * (x * b)) / pow((z + -1.0), 2.0))) / 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 (y <= 4.6d+24) then
        tmp = ((y * x) - ((z * a) - (z * t))) / (y + (z * (b - y)))
    else
        tmp = (x / (1.0d0 - z)) - (((z * ((t - a) / (z + (-1.0d0)))) + ((z * (x * b)) / ((z + (-1.0d0)) ** 2.0d0))) / 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 (y <= 4.6e+24) {
		tmp = ((y * x) - ((z * a) - (z * t))) / (y + (z * (b - y)));
	} else {
		tmp = (x / (1.0 - z)) - (((z * ((t - a) / (z + -1.0))) + ((z * (x * b)) / Math.pow((z + -1.0), 2.0))) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= 4.6e+24:
		tmp = ((y * x) - ((z * a) - (z * t))) / (y + (z * (b - y)))
	else:
		tmp = (x / (1.0 - z)) - (((z * ((t - a) / (z + -1.0))) + ((z * (x * b)) / math.pow((z + -1.0), 2.0))) / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= 4.6e+24)
		tmp = Float64(Float64(Float64(y * x) - Float64(Float64(z * a) - Float64(z * t))) / Float64(y + Float64(z * Float64(b - y))));
	else
		tmp = Float64(Float64(x / Float64(1.0 - z)) - Float64(Float64(Float64(z * Float64(Float64(t - a) / Float64(z + -1.0))) + Float64(Float64(z * Float64(x * b)) / (Float64(z + -1.0) ^ 2.0))) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= 4.6e+24)
		tmp = ((y * x) - ((z * a) - (z * t))) / (y + (z * (b - y)));
	else
		tmp = (x / (1.0 - z)) - (((z * ((t - a) / (z + -1.0))) + ((z * (x * b)) / ((z + -1.0) ^ 2.0))) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, 4.6e+24], N[(N[(N[(y * x), $MachinePrecision] - N[(N[(z * a), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(z * N[(N[(t - a), $MachinePrecision] / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(z * N[(x * b), $MachinePrecision]), $MachinePrecision] / N[Power[N[(z + -1.0), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 4.5999999999999998e24

   1. Initial program 70.3%

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

      1. sub-neg 70.3%

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

      2. distribute-lft-in 70.3%

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

   4. Applied egg-rr 70.3%

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

   if 4.5999999999999998e24 < y

   1. Initial program 38.3%

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

   3. Taylor expanded in x around 0 38.3%

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

   4. Taylor expanded in y around -inf 52.6%

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

      1. mul-1-neg 52.6%

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

      2. unsub-neg 52.6%

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

      3. associate-*r/ 52.6%

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

      4. mul-1-neg 52.6%

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

      5. sub-neg 52.6%

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

      6. metadata-eval 52.6%

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

   6. Simplified 67.5%

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

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 4.6 \cdot 10^{+24}:\\ \;\;\;\;\frac{y \cdot x - \left(z \cdot a - z \cdot t\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z} - \frac{z \cdot \frac{t - a}{z + -1} + \frac{z \cdot \left(x \cdot b\right)}{{\left(z + -1\right)}^{2}}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 73.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ \mathbf{if}\;z \leq 135000000000:\\ \;\;\;\;\frac{z \cdot a}{z \cdot \left(y - b\right) - y} + \left(\frac{z \cdot t}{t\_1} + \frac{y \cdot x}{t\_1}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y} - \frac{x \cdot \frac{y}{y - b} + \frac{y \cdot \left(t - a\right)}{{\left(b - y\right)}^{2}}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y)))))
   (if (<= z 135000000000.0)
     (+ (/ (* z a) (- (* z (- y b)) y)) (+ (/ (* z t) t_1) (/ (* y x) t_1)))
     (-
      (/ (- t a) (- b y))
      (/ (+ (* x (/ y (- y b))) (/ (* y (- t a)) (pow (- b y) 2.0))) z)))))

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 <= 135000000000.0) {
		tmp = ((z * a) / ((z * (y - b)) - y)) + (((z * t) / t_1) + ((y * x) / t_1));
	} else {
		tmp = ((t - a) / (b - y)) - (((x * (y / (y - b))) + ((y * (t - a)) / pow((b - y), 2.0))) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y + (z * (b - y))
    if (z <= 135000000000.0d0) then
        tmp = ((z * a) / ((z * (y - b)) - y)) + (((z * t) / t_1) + ((y * x) / t_1))
    else
        tmp = ((t - a) / (b - y)) - (((x * (y / (y - b))) + ((y * (t - a)) / ((b - y) ** 2.0d0))) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double tmp;
	if (z <= 135000000000.0) {
		tmp = ((z * a) / ((z * (y - b)) - y)) + (((z * t) / t_1) + ((y * x) / t_1));
	} else {
		tmp = ((t - a) / (b - y)) - (((x * (y / (y - b))) + ((y * (t - a)) / Math.pow((b - y), 2.0))) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z * (b - y))
	tmp = 0
	if z <= 135000000000.0:
		tmp = ((z * a) / ((z * (y - b)) - y)) + (((z * t) / t_1) + ((y * x) / t_1))
	else:
		tmp = ((t - a) / (b - y)) - (((x * (y / (y - b))) + ((y * (t - a)) / math.pow((b - y), 2.0))) / z)
	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 <= 135000000000.0)
		tmp = Float64(Float64(Float64(z * a) / Float64(Float64(z * Float64(y - b)) - y)) + Float64(Float64(Float64(z * t) / t_1) + Float64(Float64(y * x) / t_1)));
	else
		tmp = Float64(Float64(Float64(t - a) / Float64(b - y)) - Float64(Float64(Float64(x * Float64(y / Float64(y - b))) + Float64(Float64(y * Float64(t - a)) / (Float64(b - y) ^ 2.0))) / z));
	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 <= 135000000000.0)
		tmp = ((z * a) / ((z * (y - b)) - y)) + (((z * t) / t_1) + ((y * x) / t_1));
	else
		tmp = ((t - a) / (b - y)) - (((x * (y / (y - b))) + ((y * (t - a)) / ((b - y) ^ 2.0))) / z);
	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[LessEqual[z, 135000000000.0], N[(N[(N[(z * a), $MachinePrecision] / N[(N[(z * N[(y - b), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(z * t), $MachinePrecision] / t$95$1), $MachinePrecision] + N[(N[(y * x), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(x * N[(y / N[(y - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y * N[(t - a), $MachinePrecision]), $MachinePrecision] / N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < 1.35e11

   1. Initial program 68.5%

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

   3. Taylor expanded in t around 0 68.5%

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

   if 1.35e11 < z

   1. Initial program 34.4%

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

      1. sub-neg 34.4%

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

      2. distribute-lft-in 34.4%

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

   4. Applied egg-rr 34.4%

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

   5. Taylor expanded in z around -inf 66.7%

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

      1. mul-1-neg 66.7%

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

      2. unsub-neg 66.7%

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

      3. associate-*r/ 66.7%

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

      4. mul-1-neg 66.7%

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

      5. mul-1-neg 66.7%

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

      6. unsub-neg 66.7%

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

   7. Simplified 73.9%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 135000000000:\\ \;\;\;\;\frac{z \cdot a}{z \cdot \left(y - b\right) - y} + \left(\frac{z \cdot t}{y + z \cdot \left(b - y\right)} + \frac{y \cdot x}{y + z \cdot \left(b - y\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y} - \frac{x \cdot \frac{y}{y - b} + \frac{y \cdot \left(t - a\right)}{{\left(b - y\right)}^{2}}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 67.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t - a \leq -4 \cdot 10^{+234}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, z \cdot \left(t - a\right)\right)}{y + z \cdot \left(b - y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (- t a) -4e+234)
   (/ (- t a) (- b y))
   (/ (fma x y (* z (- t a))) (+ y (* z (- b y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t - a) <= -4e+234) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = fma(x, y, (z * (t - a))) / (y + (z * (b - y)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(t - a) <= -4e+234)
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(fma(x, y, Float64(z * Float64(t - a))) / Float64(y + Float64(z * Float64(b - y))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(t - a), $MachinePrecision], -4e+234], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(N[(x * y + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 t a) < -4.00000000000000007e234

   1. Initial program 33.8%

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

   3. Taylor expanded in z around inf 70.1%

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

   if -4.00000000000000007e234 < (-.f64 t a)

   1. Initial program 65.4%

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

      1. fma-define 65.4%

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

   3. Simplified 65.4%

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

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t - a \leq -4 \cdot 10^{+234}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, z \cdot \left(t - a\right)\right)}{y + z \cdot \left(b - y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 69.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(y - b\right) - y\\ t_2 := z \cdot \left(a - t\right)\\ \mathbf{if}\;\frac{y \cdot x - t\_2}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_2}{t\_1} - \frac{y \cdot x}{t\_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (* z (- y b)) y)) (t_2 (* z (- a t))))
   (if (<= (/ (- (* y x) t_2) (+ y (* z (- b y)))) (- INFINITY))
     (/ (- t a) (- b y))
     (- (/ t_2 t_1) (/ (* y x) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z * (y - b)) - y;
	double t_2 = z * (a - t);
	double tmp;
	if ((((y * x) - t_2) / (y + (z * (b - y)))) <= -((double) INFINITY)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = (t_2 / t_1) - ((y * x) / t_1);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z * (y - b)) - y;
	double t_2 = z * (a - t);
	double tmp;
	if ((((y * x) - t_2) / (y + (z * (b - y)))) <= -Double.POSITIVE_INFINITY) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = (t_2 / t_1) - ((y * x) / t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z * (y - b)) - y
	t_2 = z * (a - t)
	tmp = 0
	if (((y * x) - t_2) / (y + (z * (b - y)))) <= -math.inf:
		tmp = (t - a) / (b - y)
	else:
		tmp = (t_2 / t_1) - ((y * x) / t_1)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z * Float64(y - b)) - y)
	t_2 = Float64(z * Float64(a - t))
	tmp = 0.0
	if (Float64(Float64(Float64(y * x) - t_2) / Float64(y + Float64(z * Float64(b - y)))) <= Float64(-Inf))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(Float64(t_2 / t_1) - Float64(Float64(y * x) / t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z * (y - b)) - y;
	t_2 = z * (a - t);
	tmp = 0.0;
	if ((((y * x) - t_2) / (y + (z * (b - y)))) <= -Inf)
		tmp = (t - a) / (b - y);
	else
		tmp = (t_2 / t_1) - ((y * x) / t_1);
	end
	tmp_2 = tmp;
end

Wolfram

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

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)))) < -inf.0

   1. Initial program 27.3%

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

   3. Taylor expanded in z around inf 58.5%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 65.3%

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

   3. Taylor expanded in x around 0 65.3%

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

4. Final simplification 64.6%

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

Alternative 7: 66.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := z \cdot \left(y - b\right) - y\\ \mathbf{if}\;\frac{y \cdot x - z \cdot \left(a - t\right)}{t\_1} \leq 10^{+294}:\\ \;\;\;\;\frac{y \cdot x - \left(z \cdot a - z \cdot t\right)}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(\frac{z}{t\_2} - \frac{y \cdot x}{a \cdot t\_2}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y)))) (t_2 (- (* z (- y b)) y)))
   (if (<= (/ (- (* y x) (* z (- a t))) t_1) 1e+294)
     (/ (- (* y x) (- (* z a) (* z t))) t_1)
     (* a (- (/ z t_2) (/ (* y x) (* a t_2)))))))

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 = (z * (y - b)) - y;
	double tmp;
	if ((((y * x) - (z * (a - t))) / t_1) <= 1e+294) {
		tmp = ((y * x) - ((z * a) - (z * t))) / t_1;
	} else {
		tmp = a * ((z / t_2) - ((y * x) / (a * t_2)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y + (z * (b - y))
    t_2 = (z * (y - b)) - y
    if ((((y * x) - (z * (a - t))) / t_1) <= 1d+294) then
        tmp = ((y * x) - ((z * a) - (z * t))) / t_1
    else
        tmp = a * ((z / t_2) - ((y * x) / (a * t_2)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double t_2 = (z * (y - b)) - y;
	double tmp;
	if ((((y * x) - (z * (a - t))) / t_1) <= 1e+294) {
		tmp = ((y * x) - ((z * a) - (z * t))) / t_1;
	} else {
		tmp = a * ((z / t_2) - ((y * x) / (a * t_2)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z * (b - y))
	t_2 = (z * (y - b)) - y
	tmp = 0
	if (((y * x) - (z * (a - t))) / t_1) <= 1e+294:
		tmp = ((y * x) - ((z * a) - (z * t))) / t_1
	else:
		tmp = a * ((z / t_2) - ((y * x) / (a * t_2)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(z * Float64(b - y)))
	t_2 = Float64(Float64(z * Float64(y - b)) - y)
	tmp = 0.0
	if (Float64(Float64(Float64(y * x) - Float64(z * Float64(a - t))) / t_1) <= 1e+294)
		tmp = Float64(Float64(Float64(y * x) - Float64(Float64(z * a) - Float64(z * t))) / t_1);
	else
		tmp = Float64(a * Float64(Float64(z / t_2) - Float64(Float64(y * x) / Float64(a * t_2))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (z * (b - y));
	t_2 = (z * (y - b)) - y;
	tmp = 0.0;
	if ((((y * x) - (z * (a - t))) / t_1) <= 1e+294)
		tmp = ((y * x) - ((z * a) - (z * t))) / t_1;
	else
		tmp = a * ((z / t_2) - ((y * x) / (a * t_2)));
	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[(z * N[(y - b), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]}, If[LessEqual[N[(N[(N[(y * x), $MachinePrecision] - N[(z * N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], 1e+294], N[(N[(N[(y * x), $MachinePrecision] - N[(N[(z * a), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], N[(a * N[(N[(z / t$95$2), $MachinePrecision] - N[(N[(y * x), $MachinePrecision] / N[(a * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

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)))) < 1.00000000000000007e294

   1. Initial program 79.2%

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

      1. sub-neg 79.2%

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

      2. distribute-lft-in 79.2%

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

   4. Applied egg-rr 79.2%

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

   if 1.00000000000000007e294 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 11.3%

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

   3. Taylor expanded in a around inf 19.9%

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

   4. Taylor expanded in t around 0 20.6%

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

4. Final simplification 63.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot x - z \cdot \left(a - t\right)}{y + z \cdot \left(b - y\right)} \leq 10^{+294}:\\ \;\;\;\;\frac{y \cdot x - \left(z \cdot a - z \cdot t\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(\frac{z}{z \cdot \left(y - b\right) - y} - \frac{y \cdot x}{a \cdot \left(z \cdot \left(y - b\right) - y\right)}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 66.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ \mathbf{if}\;\frac{y \cdot x - z \cdot \left(a - t\right)}{t\_1} \leq 10^{+308}:\\ \;\;\;\;\frac{y \cdot x - \left(z \cdot a - z \cdot t\right)}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot \left(z \cdot \frac{\left(x + \frac{t}{y}\right) - \frac{a}{y}}{b} - x \cdot \frac{z}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y)))))
   (if (<= (/ (- (* y x) (* z (- a t))) t_1) 1e+308)
     (/ (- (* y x) (- (* z a) (* z t))) t_1)
     (+ x (* b (- (* z (/ (- (+ x (/ t y)) (/ a y)) b)) (* x (/ z y))))))))

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 ((((y * x) - (z * (a - t))) / t_1) <= 1e+308) {
		tmp = ((y * x) - ((z * a) - (z * t))) / t_1;
	} else {
		tmp = x + (b * ((z * (((x + (t / y)) - (a / y)) / b)) - (x * (z / y))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y + (z * (b - y))
    if ((((y * x) - (z * (a - t))) / t_1) <= 1d+308) then
        tmp = ((y * x) - ((z * a) - (z * t))) / t_1
    else
        tmp = x + (b * ((z * (((x + (t / y)) - (a / y)) / b)) - (x * (z / y))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double tmp;
	if ((((y * x) - (z * (a - t))) / t_1) <= 1e+308) {
		tmp = ((y * x) - ((z * a) - (z * t))) / t_1;
	} else {
		tmp = x + (b * ((z * (((x + (t / y)) - (a / y)) / b)) - (x * (z / y))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z * (b - y))
	tmp = 0
	if (((y * x) - (z * (a - t))) / t_1) <= 1e+308:
		tmp = ((y * x) - ((z * a) - (z * t))) / t_1
	else:
		tmp = x + (b * ((z * (((x + (t / y)) - (a / y)) / b)) - (x * (z / y))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(z * Float64(b - y)))
	tmp = 0.0
	if (Float64(Float64(Float64(y * x) - Float64(z * Float64(a - t))) / t_1) <= 1e+308)
		tmp = Float64(Float64(Float64(y * x) - Float64(Float64(z * a) - Float64(z * t))) / t_1);
	else
		tmp = Float64(x + Float64(b * Float64(Float64(z * Float64(Float64(Float64(x + Float64(t / y)) - Float64(a / y)) / b)) - Float64(x * Float64(z / y)))));
	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 ((((y * x) - (z * (a - t))) / t_1) <= 1e+308)
		tmp = ((y * x) - ((z * a) - (z * t))) / t_1;
	else
		tmp = x + (b * ((z * (((x + (t / y)) - (a / y)) / b)) - (x * (z / y))));
	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[LessEqual[N[(N[(N[(y * x), $MachinePrecision] - N[(z * N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], 1e+308], N[(N[(N[(y * x), $MachinePrecision] - N[(N[(z * a), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], N[(x + N[(b * N[(N[(z * N[(N[(N[(x + N[(t / y), $MachinePrecision]), $MachinePrecision] - N[(a / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision] - N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

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)))) < 1e308

   1. Initial program 79.3%

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

      1. sub-neg 79.3%

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

      2. distribute-lft-in 79.3%

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

   4. Applied egg-rr 79.3%

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

   if 1e308 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 9.9%

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

   3. Taylor expanded in z around 0 8.5%

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

      1. *-commutative 8.5%

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

   5. Simplified 8.5%

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

   6. Taylor expanded in b around inf 28.5%

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

      1. +-commutative 28.5%

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

      2. mul-1-neg 28.5%

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

      3. unsub-neg 28.5%

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

      4. associate-/l* 25.7%

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

      5. associate--r+ 25.7%

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

      6. sub-neg 25.7%

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

      7. mul-1-neg 25.7%

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

      8. remove-double-neg 25.7%

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

      9. associate-/l* 25.8%

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

   8. Simplified 25.8%

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

4. Final simplification 65.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot x - z \cdot \left(a - t\right)}{y + z \cdot \left(b - y\right)} \leq 10^{+308}:\\ \;\;\;\;\frac{y \cdot x - \left(z \cdot a - z \cdot t\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot \left(z \cdot \frac{\left(x + \frac{t}{y}\right) - \frac{a}{y}}{b} - x \cdot \frac{z}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 65.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y + z \cdot \left(b - y\right)\right)\\ \mathbf{if}\;z \leq -1.4 \cdot 10^{+60}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(\frac{z}{z \cdot \left(y - b\right) - y} + \left(\frac{z \cdot t}{t\_1} + \frac{y \cdot x}{t\_1}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (+ y (* z (- b y))))))
   (if (<= z -1.4e+60)
     (/ (- t a) (- b y))
     (* a (+ (/ z (- (* z (- y b)) y)) (+ (/ (* z t) t_1) (/ (* y x) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (y + (z * (b - y)));
	double tmp;
	if (z <= -1.4e+60) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = a * ((z / ((z * (y - b)) - y)) + (((z * t) / t_1) + ((y * 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 = a * (y + (z * (b - y)))
    if (z <= (-1.4d+60)) then
        tmp = (t - a) / (b - y)
    else
        tmp = a * ((z / ((z * (y - b)) - y)) + (((z * t) / t_1) + ((y * 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 = a * (y + (z * (b - y)));
	double tmp;
	if (z <= -1.4e+60) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = a * ((z / ((z * (y - b)) - y)) + (((z * t) / t_1) + ((y * x) / t_1)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (y + (z * (b - y)))
	tmp = 0
	if z <= -1.4e+60:
		tmp = (t - a) / (b - y)
	else:
		tmp = a * ((z / ((z * (y - b)) - y)) + (((z * t) / t_1) + ((y * x) / t_1)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(y + Float64(z * Float64(b - y))))
	tmp = 0.0
	if (z <= -1.4e+60)
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(a * Float64(Float64(z / Float64(Float64(z * Float64(y - b)) - y)) + Float64(Float64(Float64(z * t) / t_1) + Float64(Float64(y * x) / t_1))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (y + (z * (b - y)));
	tmp = 0.0;
	if (z <= -1.4e+60)
		tmp = (t - a) / (b - y);
	else
		tmp = a * ((z / ((z * (y - b)) - y)) + (((z * t) / t_1) + ((y * x) / t_1)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.4e+60], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(a * N[(N[(z / N[(N[(z * N[(y - b), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(z * t), $MachinePrecision] / t$95$1), $MachinePrecision] + N[(N[(y * x), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.4e60

   1. Initial program 31.9%

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

   3. Taylor expanded in z around inf 90.4%

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

   if -1.4e60 < z

   1. Initial program 69.7%

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

   3. Taylor expanded in a around inf 60.6%

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

4. Final simplification 67.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+60}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(\frac{z}{z \cdot \left(y - b\right) - y} + \left(\frac{z \cdot t}{a \cdot \left(y + z \cdot \left(b - y\right)\right)} + \frac{y \cdot x}{a \cdot \left(y + z \cdot \left(b - y\right)\right)}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 66.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ \mathbf{if}\;z \leq -2.4 \cdot 10^{+58}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\frac{z \cdot a}{t \cdot \left(z \cdot \left(y - b\right) - y\right)} + \left(\frac{z}{t\_1} + \frac{y \cdot x}{t \cdot t\_1}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y)))))
   (if (<= z -2.4e+58)
     (/ (- t a) (- b y))
     (*
      t
      (+
       (/ (* z a) (* t (- (* z (- y b)) y)))
       (+ (/ z t_1) (/ (* y x) (* t 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 <= -2.4e+58) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = t * (((z * a) / (t * ((z * (y - b)) - y))) + ((z / t_1) + ((y * x) / (t * 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 <= (-2.4d+58)) then
        tmp = (t - a) / (b - y)
    else
        tmp = t * (((z * a) / (t * ((z * (y - b)) - y))) + ((z / t_1) + ((y * x) / (t * 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 <= -2.4e+58) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = t * (((z * a) / (t * ((z * (y - b)) - y))) + ((z / t_1) + ((y * x) / (t * t_1))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z * (b - y))
	tmp = 0
	if z <= -2.4e+58:
		tmp = (t - a) / (b - y)
	else:
		tmp = t * (((z * a) / (t * ((z * (y - b)) - y))) + ((z / t_1) + ((y * x) / (t * 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 <= -2.4e+58)
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(t * Float64(Float64(Float64(z * a) / Float64(t * Float64(Float64(z * Float64(y - b)) - y))) + Float64(Float64(z / t_1) + Float64(Float64(y * x) / Float64(t * 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 <= -2.4e+58)
		tmp = (t - a) / (b - y);
	else
		tmp = t * (((z * a) / (t * ((z * (y - b)) - y))) + ((z / t_1) + ((y * x) / (t * 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[LessEqual[z, -2.4e+58], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(N[(z * a), $MachinePrecision] / N[(t * N[(N[(z * N[(y - b), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(z / t$95$1), $MachinePrecision] + N[(N[(y * x), $MachinePrecision] / N[(t * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.4e58

   1. Initial program 34.2%

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

   3. Taylor expanded in z around inf 90.8%

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

   if -2.4e58 < z

   1. Initial program 69.4%

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

   3. Taylor expanded in t around inf 61.8%

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

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+58}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\frac{z \cdot a}{t \cdot \left(z \cdot \left(y - b\right) - y\right)} + \left(\frac{z}{y + z \cdot \left(b - y\right)} + \frac{y \cdot x}{t \cdot \left(y + z \cdot \left(b - y\right)\right)}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 75.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ \mathbf{if}\;z \leq -7.4 \cdot 10^{+58}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot a}{z \cdot \left(y - b\right) - y} + \left(\frac{z \cdot t}{t\_1} + \frac{y \cdot x}{t\_1}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y)))))
   (if (<= z -7.4e+58)
     (/ (- t a) (- b y))
     (+ (/ (* z a) (- (* z (- y b)) y)) (+ (/ (* z t) t_1) (/ (* y 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 <= -7.4e+58) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((z * a) / ((z * (y - b)) - y)) + (((z * t) / t_1) + ((y * 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 <= (-7.4d+58)) then
        tmp = (t - a) / (b - y)
    else
        tmp = ((z * a) / ((z * (y - b)) - y)) + (((z * t) / t_1) + ((y * 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 <= -7.4e+58) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((z * a) / ((z * (y - b)) - y)) + (((z * t) / t_1) + ((y * x) / t_1));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z * (b - y))
	tmp = 0
	if z <= -7.4e+58:
		tmp = (t - a) / (b - y)
	else:
		tmp = ((z * a) / ((z * (y - b)) - y)) + (((z * t) / t_1) + ((y * 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 <= -7.4e+58)
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(Float64(Float64(z * a) / Float64(Float64(z * Float64(y - b)) - y)) + Float64(Float64(Float64(z * t) / t_1) + Float64(Float64(y * 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 <= -7.4e+58)
		tmp = (t - a) / (b - y);
	else
		tmp = ((z * a) / ((z * (y - b)) - y)) + (((z * t) / t_1) + ((y * 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[LessEqual[z, -7.4e+58], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z * a), $MachinePrecision] / N[(N[(z * N[(y - b), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(z * t), $MachinePrecision] / t$95$1), $MachinePrecision] + N[(N[(y * x), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -7.4000000000000004e58

   1. Initial program 34.2%

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

   3. Taylor expanded in z around inf 90.8%

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

   if -7.4000000000000004e58 < z

   1. Initial program 69.4%

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

   3. Taylor expanded in t around 0 68.9%

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

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.4 \cdot 10^{+58}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot a}{z \cdot \left(y - b\right) - y} + \left(\frac{z \cdot t}{y + z \cdot \left(b - y\right)} + \frac{y \cdot x}{y + z \cdot \left(b - y\right)}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 63.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+59}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y + z \cdot \frac{t - a}{x}\right)}{y + z \cdot \left(b - y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -6e+59)
   (/ (- t a) (- b y))
   (/ (* x (+ y (* z (/ (- t a) x)))) (+ y (* z (- b y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -6e+59) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = (x * (y + (z * ((t - a) / x)))) / (y + (z * (b - y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-6d+59)) then
        tmp = (t - a) / (b - y)
    else
        tmp = (x * (y + (z * ((t - a) / x)))) / (y + (z * (b - y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -6e+59) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = (x * (y + (z * ((t - a) / x)))) / (y + (z * (b - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -6e+59:
		tmp = (t - a) / (b - y)
	else:
		tmp = (x * (y + (z * ((t - a) / x)))) / (y + (z * (b - y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -6e+59)
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(Float64(x * Float64(y + Float64(z * Float64(Float64(t - a) / x)))) / Float64(y + Float64(z * Float64(b - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -6e+59)
		tmp = (t - a) / (b - y);
	else
		tmp = (x * (y + (z * ((t - a) / x)))) / (y + (z * (b - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -6e+59], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(y + N[(z * N[(N[(t - a), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.0000000000000001e59

   1. Initial program 33.1%

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

   3. Taylor expanded in z around inf 90.6%

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

   if -6.0000000000000001e59 < z

   1. Initial program 69.5%

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

   3. Taylor expanded in x around inf 65.0%

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

      1. associate-/l* 56.7%

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

   5. Simplified 56.7%

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

4. Final simplification 64.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+59}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y + z \cdot \frac{t - a}{x}\right)}{y + z \cdot \left(b - y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 63.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+58}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(t + \left(\frac{y}{z} \cdot x - a\right)\right)}{y + z \cdot \left(b - y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -2.5e+58)
   (/ (- t a) (- b y))
   (/ (* z (+ t (- (* (/ y z) x) a))) (+ y (* z (- b y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2.5e+58) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = (z * (t + (((y / z) * x) - a))) / (y + (z * (b - y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-2.5d+58)) then
        tmp = (t - a) / (b - y)
    else
        tmp = (z * (t + (((y / z) * x) - a))) / (y + (z * (b - y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2.5e+58) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = (z * (t + (((y / z) * x) - a))) / (y + (z * (b - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -2.5e+58:
		tmp = (t - a) / (b - y)
	else:
		tmp = (z * (t + (((y / z) * x) - a))) / (y + (z * (b - y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -2.5e+58)
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(Float64(z * Float64(t + Float64(Float64(Float64(y / z) * x) - a))) / Float64(y + Float64(z * Float64(b - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -2.5e+58)
		tmp = (t - a) / (b - y);
	else
		tmp = (z * (t + (((y / z) * x) - a))) / (y + (z * (b - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -2.5e+58], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(N[(z * N[(t + N[(N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.49999999999999993e58

   1. Initial program 34.2%

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

   3. Taylor expanded in z around inf 90.8%

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

   if -2.49999999999999993e58 < z

   1. Initial program 69.4%

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

   3. Taylor expanded in z around inf 57.8%

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

      1. associate--l+ 57.8%

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

      2. associate-/l* 55.3%

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

   5. Simplified 55.3%

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

4. Final simplification 63.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+58}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(t + \left(\frac{y}{z} \cdot x - a\right)\right)}{y + z \cdot \left(b - y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 67.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.22 \cdot 10^{+59}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x - z \cdot \left(a - t\right)}{z \cdot \left(\left(\frac{y}{z} + b\right) - y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.22e+59)
   (/ (- t a) (- b y))
   (/ (- (* y x) (* z (- a t))) (* z (- (+ (/ y z) b) y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.22e+59) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((y * x) - (z * (a - t))) / (z * (((y / z) + b) - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-1.22d+59)) then
        tmp = (t - a) / (b - y)
    else
        tmp = ((y * x) - (z * (a - t))) / (z * (((y / z) + b) - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.22e+59) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((y * x) - (z * (a - t))) / (z * (((y / z) + b) - y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1.22e+59:
		tmp = (t - a) / (b - y)
	else:
		tmp = ((y * x) - (z * (a - t))) / (z * (((y / z) + b) - y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.22e+59)
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(Float64(Float64(y * x) - Float64(z * Float64(a - t))) / Float64(z * Float64(Float64(Float64(y / z) + b) - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -1.22e+59)
		tmp = (t - a) / (b - y);
	else
		tmp = ((y * x) - (z * (a - t))) / (z * (((y / z) + b) - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.22e+59], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y * x), $MachinePrecision] - N[(z * N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * N[(N[(N[(y / z), $MachinePrecision] + b), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.22e59

   1. Initial program 34.2%

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

   3. Taylor expanded in z around inf 90.8%

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

   if -1.22e59 < z

   1. Initial program 69.4%

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

   3. Taylor expanded in z around inf 60.5%

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

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.22 \cdot 10^{+59}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x - z \cdot \left(a - t\right)}{z \cdot \left(\left(\frac{y}{z} + b\right) - y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 53.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 6 \cdot 10^{+59}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{y + z \cdot \left(b - y\right)} + \frac{t - a}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x 6e+59)
   (/ (- t a) (- b y))
   (+ (/ (* y x) (+ y (* z (- b y)))) (/ (- t a) b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= 6e+59) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((y * x) / (y + (z * (b - y)))) + ((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 (x <= 6d+59) then
        tmp = (t - a) / (b - y)
    else
        tmp = ((y * x) / (y + (z * (b - y)))) + ((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 (x <= 6e+59) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((y * x) / (y + (z * (b - y)))) + ((t - a) / b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= 6e+59:
		tmp = (t - a) / (b - y)
	else:
		tmp = ((y * x) / (y + (z * (b - y)))) + ((t - a) / b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= 6e+59)
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(Float64(Float64(y * x) / Float64(y + Float64(z * Float64(b - y)))) + Float64(Float64(t - a) / b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= 6e+59)
		tmp = (t - a) / (b - y);
	else
		tmp = ((y * x) / (y + (z * (b - y)))) + ((t - a) / b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, 6e+59], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y * x), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 6.0000000000000001e59

   1. Initial program 61.4%

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

   3. Taylor expanded in z around inf 58.3%

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

   if 6.0000000000000001e59 < x

   1. Initial program 61.3%

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

   3. Taylor expanded in x around 0 61.2%

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

   4. Taylor expanded in y around 0 56.4%

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

4. Final simplification 57.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 6 \cdot 10^{+59}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{y + z \cdot \left(b - y\right)} + \frac{t - a}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 50.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 9 \cdot 10^{+115}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{y + y \cdot \left(b \cdot \frac{z}{y} - z\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x 9e+115)
   (/ (- t a) (- b y))
   (/ (* y x) (+ y (* y (- (* b (/ z y)) z))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= 9e+115) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = (y * x) / (y + (y * ((b * (z / y)) - z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= 9d+115) then
        tmp = (t - a) / (b - y)
    else
        tmp = (y * x) / (y + (y * ((b * (z / y)) - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= 9e+115) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = (y * x) / (y + (y * ((b * (z / y)) - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= 9e+115:
		tmp = (t - a) / (b - y)
	else:
		tmp = (y * x) / (y + (y * ((b * (z / y)) - z)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= 9e+115)
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(Float64(y * x) / Float64(y + Float64(y * Float64(Float64(b * Float64(z / y)) - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= 9e+115)
		tmp = (t - a) / (b - y);
	else
		tmp = (y * x) / (y + (y * ((b * (z / y)) - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, 9e+115], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(N[(y * x), $MachinePrecision] / N[(y + N[(y * N[(N[(b * N[(z / y), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 8.99999999999999927e115

   1. Initial program 62.5%

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

   3. Taylor expanded in z around inf 58.7%

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

   if 8.99999999999999927e115 < x

   1. Initial program 55.6%

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

   3. Taylor expanded in x around inf 43.8%

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

      1. *-commutative 43.8%

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

   5. Simplified 43.8%

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

   6. Taylor expanded in y around inf 39.2%

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

      1. +-commutative 39.2%

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

      2. neg-mul-1 39.2%

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

      3. unsub-neg 39.2%

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

      4. associate-/l* 39.1%

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

   8. Simplified 39.1%

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

4. Final simplification 55.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 9 \cdot 10^{+115}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{y + y \cdot \left(b \cdot \frac{z}{y} - z\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 50.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 4.8 \cdot 10^{+187}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x + a \cdot \left(\frac{z \cdot t}{a} - z\right)}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x 4.8e+187)
   (/ (- t a) (- b y))
   (/ (+ (* y x) (* a (- (/ (* z t) a) z))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= 4.8e+187) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((y * x) + (a * (((z * t) / a) - z))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= 4.8d+187) then
        tmp = (t - a) / (b - y)
    else
        tmp = ((y * x) + (a * (((z * t) / a) - z))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= 4.8e+187) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((y * x) + (a * (((z * t) / a) - z))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= 4.8e+187:
		tmp = (t - a) / (b - y)
	else:
		tmp = ((y * x) + (a * (((z * t) / a) - z))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= 4.8e+187)
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(Float64(Float64(y * x) + Float64(a * Float64(Float64(Float64(z * t) / a) - z))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= 4.8e+187)
		tmp = (t - a) / (b - y);
	else
		tmp = ((y * x) + (a * (((z * t) / a) - z))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, 4.8e+187], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y * x), $MachinePrecision] + N[(a * N[(N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 4.79999999999999971e187

   1. Initial program 62.8%

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

   3. Taylor expanded in z around inf 56.8%

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

   if 4.79999999999999971e187 < x

   1. Initial program 48.7%

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

   3. Taylor expanded in a around inf 48.7%

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

      1. +-commutative 48.7%

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

      2. mul-1-neg 48.7%

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

      3. unsub-neg 48.7%

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

      4. *-commutative 48.7%

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

   5. Simplified 48.7%

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

   6. Taylor expanded in z around 0 25.8%

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

4. Final simplification 53.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 4.8 \cdot 10^{+187}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x + a \cdot \left(\frac{z \cdot t}{a} - z\right)}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 50.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 9 \cdot 10^{+115}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{y + y \cdot \left(\frac{z \cdot b}{y} - z\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x 9e+115)
   (/ (- t a) (- b y))
   (/ (* y x) (+ y (* y (- (/ (* z b) y) z))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= 9e+115) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = (y * x) / (y + (y * (((z * b) / y) - z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= 9d+115) then
        tmp = (t - a) / (b - y)
    else
        tmp = (y * x) / (y + (y * (((z * b) / y) - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= 9e+115) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = (y * x) / (y + (y * (((z * b) / y) - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= 9e+115:
		tmp = (t - a) / (b - y)
	else:
		tmp = (y * x) / (y + (y * (((z * b) / y) - z)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= 9e+115)
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(Float64(y * x) / Float64(y + Float64(y * Float64(Float64(Float64(z * b) / y) - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= 9e+115)
		tmp = (t - a) / (b - y);
	else
		tmp = (y * x) / (y + (y * (((z * b) / y) - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, 9e+115], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(N[(y * x), $MachinePrecision] / N[(y + N[(y * N[(N[(N[(z * b), $MachinePrecision] / y), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 8.99999999999999927e115

   1. Initial program 62.5%

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

   3. Taylor expanded in z around inf 58.7%

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

   if 8.99999999999999927e115 < x

   1. Initial program 55.6%

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

   3. Taylor expanded in x around inf 43.8%

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

      1. *-commutative 43.8%

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

   5. Simplified 43.8%

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

   6. Taylor expanded in y around inf 39.2%

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

4. Final simplification 55.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 9 \cdot 10^{+115}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{y + y \cdot \left(\frac{z \cdot b}{y} - z\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 66.3% accurate, 0.9× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 61.4%

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

   1. sub-neg 61.4%

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

   2. distribute-lft-in 61.4%

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

4. Applied egg-rr 61.4%

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

5. Final simplification 61.4%

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

Alternative 20: 66.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 61.4%

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

3. Final simplification 61.4%

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

Alternative 21: 51.4% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \frac{t - a}{b - y} \end{array} \]

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b) {
	return (t - a) / (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 = (t - a) / (b - y)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 61.4%

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

3. Taylor expanded in z around inf 52.1%

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

4. Final simplification 52.1%

   \[\leadsto \frac{t - a}{b - y} \]
5. Add Preprocessing

Alternative 22: 33.1% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \frac{x}{1 - z} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (/ x (- 1.0 z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return x / (1.0 - 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 = x / (1.0d0 - z)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return x / (1.0 - z);
}

Python

def code(x, y, z, t, a, b):
	return x / (1.0 - z)

Julia

function code(x, y, z, t, a, b)
	return Float64(x / Float64(1.0 - z))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = x / (1.0 - z);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 61.4%

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

3. Taylor expanded in y around inf 31.2%

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

   1. mul-1-neg 31.2%

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

   2. unsub-neg 31.2%

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

5. Simplified 31.2%

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

6. Final simplification 31.2%

   \[\leadsto \frac{x}{1 - z} \]
7. Add Preprocessing

Alternative 23: 35.6% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \frac{t - a}{b} \end{array} \]

FPCore

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

C

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

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 = (t - a) / b
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 61.4%

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

3. Taylor expanded in y around 0 34.1%

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

4. Final simplification 34.1%

   \[\leadsto \frac{t - a}{b} \]
5. Add Preprocessing

Alternative 24: 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 61.4%

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

3. Taylor expanded in z around 0 24.5%

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

4. Final simplification 24.5%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 73.8% 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 2024066 
(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)))))