Development.Shake.Progress:decay from shake-0.15.5

Percentage Accurate: 65.4% → 89.2%

Time: 16.2s

Alternatives: 17

Speedup: 1.5×

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: 65.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 89.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ \mathbf{if}\;z \leq -4 \cdot 10^{+18} \lor \neg \left(z \leq 5.2 \cdot 10^{+17}\right):\\ \;\;\;\;\mathsf{fma}\left(-1, \frac{\mathsf{fma}\left(-1, \frac{y}{\frac{b - y}{x}}, \frac{y}{{\left(b - y\right)}^{2}} \cdot \left(t - a\right)\right)}{z}, \frac{t - a}{b - y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{t_1} + \frac{z \cdot \left(t - a\right)}{t_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y)))))
   (if (or (<= z -4e+18) (not (<= z 5.2e+17)))
     (fma
      -1.0
      (/ (fma -1.0 (/ y (/ (- b y) x)) (* (/ y (pow (- b y) 2.0)) (- t a))) z)
      (/ (- t a) (- b y)))
     (+ (/ (* y x) t_1) (/ (* z (- t a)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double tmp;
	if ((z <= -4e+18) || !(z <= 5.2e+17)) {
		tmp = fma(-1.0, (fma(-1.0, (y / ((b - y) / x)), ((y / pow((b - y), 2.0)) * (t - a))) / z), ((t - a) / (b - y)));
	} else {
		tmp = ((y * x) / t_1) + ((z * (t - a)) / 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 <= -4e+18) || !(z <= 5.2e+17))
		tmp = fma(-1.0, Float64(fma(-1.0, Float64(y / Float64(Float64(b - y) / x)), Float64(Float64(y / (Float64(b - y) ^ 2.0)) * Float64(t - a))) / z), Float64(Float64(t - a) / Float64(b - y)));
	else
		tmp = Float64(Float64(Float64(y * x) / t_1) + Float64(Float64(z * Float64(t - a)) / t_1));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[z, -4e+18], N[Not[LessEqual[z, 5.2e+17]], $MachinePrecision]], N[(-1.0 * N[(N[(-1.0 * N[(y / N[(N[(b - y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] + N[(N[(y / N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] + N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y * x), $MachinePrecision] / t$95$1), $MachinePrecision] + N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -4e18 or 5.2e17 < z

   1. Initial program 40.7%

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

   2. Taylor expanded in z around -inf 72.0%

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

      1. associate--l+ 72.0%

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

      2. div-sub 72.0%

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

      3. fma-def 72.0%

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

   4. Simplified 96.9%

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

   if -4e18 < z < 5.2e17

   1. Initial program 93.7%

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

   2. Taylor expanded in x around 0 93.8%

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

4. Final simplification 95.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+18} \lor \neg \left(z \leq 5.2 \cdot 10^{+17}\right):\\ \;\;\;\;\mathsf{fma}\left(-1, \frac{\mathsf{fma}\left(-1, \frac{y}{\frac{b - y}{x}}, \frac{y}{{\left(b - y\right)}^{2}} \cdot \left(t - a\right)\right)}{z}, \frac{t - a}{b - y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{y + z \cdot \left(b - y\right)} + \frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \end{array} \]

Alternative 2: 85.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ \mathbf{if}\;z \leq -7.2 \cdot 10^{+56} \lor \neg \left(z \leq 1.14 \cdot 10^{+55}\right):\\ \;\;\;\;\left(\frac{t - a}{b - y} + \frac{y}{z} \cdot \frac{x}{b - y}\right) + \frac{\frac{a - t}{\frac{z}{y}}}{{\left(b - y\right)}^{2}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{t_1} + \frac{z \cdot \left(t - a\right)}{t_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y)))))
   (if (or (<= z -7.2e+56) (not (<= z 1.14e+55)))
     (+
      (+ (/ (- t a) (- b y)) (* (/ y z) (/ x (- b y))))
      (/ (/ (- a t) (/ z y)) (pow (- b y) 2.0)))
     (+ (/ (* y x) t_1) (/ (* z (- t a)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double tmp;
	if ((z <= -7.2e+56) || !(z <= 1.14e+55)) {
		tmp = (((t - a) / (b - y)) + ((y / z) * (x / (b - y)))) + (((a - t) / (z / y)) / pow((b - y), 2.0));
	} else {
		tmp = ((y * x) / t_1) + ((z * (t - a)) / t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y + (z * (b - y))
    if ((z <= (-7.2d+56)) .or. (.not. (z <= 1.14d+55))) then
        tmp = (((t - a) / (b - y)) + ((y / z) * (x / (b - y)))) + (((a - t) / (z / y)) / ((b - y) ** 2.0d0))
    else
        tmp = ((y * x) / t_1) + ((z * (t - a)) / t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double tmp;
	if ((z <= -7.2e+56) || !(z <= 1.14e+55)) {
		tmp = (((t - a) / (b - y)) + ((y / z) * (x / (b - y)))) + (((a - t) / (z / y)) / Math.pow((b - y), 2.0));
	} else {
		tmp = ((y * x) / t_1) + ((z * (t - a)) / t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z * (b - y))
	tmp = 0
	if (z <= -7.2e+56) or not (z <= 1.14e+55):
		tmp = (((t - a) / (b - y)) + ((y / z) * (x / (b - y)))) + (((a - t) / (z / y)) / math.pow((b - y), 2.0))
	else:
		tmp = ((y * x) / t_1) + ((z * (t - a)) / 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 <= -7.2e+56) || !(z <= 1.14e+55))
		tmp = Float64(Float64(Float64(Float64(t - a) / Float64(b - y)) + Float64(Float64(y / z) * Float64(x / Float64(b - y)))) + Float64(Float64(Float64(a - t) / Float64(z / y)) / (Float64(b - y) ^ 2.0)));
	else
		tmp = Float64(Float64(Float64(y * x) / t_1) + Float64(Float64(z * Float64(t - a)) / 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 <= -7.2e+56) || ~((z <= 1.14e+55)))
		tmp = (((t - a) / (b - y)) + ((y / z) * (x / (b - y)))) + (((a - t) / (z / y)) / ((b - y) ^ 2.0));
	else
		tmp = ((y * x) / t_1) + ((z * (t - a)) / t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[z, -7.2e+56], N[Not[LessEqual[z, 1.14e+55]], $MachinePrecision]], N[(N[(N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision] + N[(N[(y / z), $MachinePrecision] * N[(x / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(a - t), $MachinePrecision] / N[(z / y), $MachinePrecision]), $MachinePrecision] / N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y * x), $MachinePrecision] / t$95$1), $MachinePrecision] + N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -7.19999999999999996e56 or 1.1399999999999999e55 < z

   1. Initial program 36.7%

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

   2. Taylor expanded in z around inf 70.6%

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

      1. associate--r+ 70.6%

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

      2. +-commutative 70.6%

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

      3. associate--l+ 70.6%

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

      4. *-commutative 70.6%

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

      5. times-frac 78.1%

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

      6. div-sub 78.1%

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

      7. associate-/r* 78.3%

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

      8. *-commutative 78.3%

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

      9. associate-/l* 94.2%

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

   4. Simplified 94.2%

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

   if -7.19999999999999996e56 < z < 1.1399999999999999e55

   1. Initial program 89.9%

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

   2. Taylor expanded in x around 0 90.0%

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

4. Final simplification 91.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+56} \lor \neg \left(z \leq 1.14 \cdot 10^{+55}\right):\\ \;\;\;\;\left(\frac{t - a}{b - y} + \frac{y}{z} \cdot \frac{x}{b - y}\right) + \frac{\frac{a - t}{\frac{z}{y}}}{{\left(b - y\right)}^{2}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{y + z \cdot \left(b - y\right)} + \frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \end{array} \]

Alternative 3: 84.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ \mathbf{if}\;z \leq -6.8 \cdot 10^{+54} \lor \neg \left(z \leq 6.5 \cdot 10^{+18}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{t_1} + \frac{z \cdot \left(t - a\right)}{t_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y)))))
   (if (or (<= z -6.8e+54) (not (<= z 6.5e+18)))
     (/ (- t a) (- b y))
     (+ (/ (* y x) t_1) (/ (* z (- t a)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double tmp;
	if ((z <= -6.8e+54) || !(z <= 6.5e+18)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((y * x) / t_1) + ((z * (t - a)) / t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y + (z * (b - y))
    if ((z <= (-6.8d+54)) .or. (.not. (z <= 6.5d+18))) then
        tmp = (t - a) / (b - y)
    else
        tmp = ((y * x) / t_1) + ((z * (t - a)) / t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double tmp;
	if ((z <= -6.8e+54) || !(z <= 6.5e+18)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((y * x) / t_1) + ((z * (t - a)) / t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z * (b - y))
	tmp = 0
	if (z <= -6.8e+54) or not (z <= 6.5e+18):
		tmp = (t - a) / (b - y)
	else:
		tmp = ((y * x) / t_1) + ((z * (t - a)) / 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 <= -6.8e+54) || !(z <= 6.5e+18))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(Float64(Float64(y * x) / t_1) + Float64(Float64(z * Float64(t - a)) / 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 <= -6.8e+54) || ~((z <= 6.5e+18)))
		tmp = (t - a) / (b - y);
	else
		tmp = ((y * x) / t_1) + ((z * (t - a)) / t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[z, -6.8e+54], N[Not[LessEqual[z, 6.5e+18]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y * x), $MachinePrecision] / t$95$1), $MachinePrecision] + N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -6.8000000000000001e54 or 6.5e18 < z

   1. Initial program 39.0%

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

   2. Taylor expanded in z around inf 87.1%

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

   if -6.8000000000000001e54 < z < 6.5e18

   1. Initial program 91.4%

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

   2. Taylor expanded in x around 0 91.4%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+54} \lor \neg \left(z \leq 6.5 \cdot 10^{+18}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{y + z \cdot \left(b - y\right)} + \frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \end{array} \]

Alternative 4: 84.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+54} \lor \neg \left(z \leq 4.4 \cdot 10^{+18}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -6.2e+54) (not (<= z 4.4e+18)))
   (/ (- t a) (- b y))
   (/ (+ (* y x) (* z (- t a))) (+ y (* z (- b y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -6.2e+54) || !(z <= 4.4e+18)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((y * x) + (z * (t - a))) / (y + (z * (b - y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-6.2d+54)) .or. (.not. (z <= 4.4d+18))) then
        tmp = (t - a) / (b - y)
    else
        tmp = ((y * x) + (z * (t - a))) / (y + (z * (b - y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -6.2e+54) || !(z <= 4.4e+18)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((y * x) + (z * (t - a))) / (y + (z * (b - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -6.2e+54) or not (z <= 4.4e+18):
		tmp = (t - a) / (b - y)
	else:
		tmp = ((y * x) + (z * (t - a))) / (y + (z * (b - y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -6.2e+54) || !(z <= 4.4e+18))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(Float64(Float64(y * x) + Float64(z * Float64(t - a))) / Float64(y + Float64(z * Float64(b - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -6.2e+54) || ~((z <= 4.4e+18)))
		tmp = (t - a) / (b - y);
	else
		tmp = ((y * x) + (z * (t - a))) / (y + (z * (b - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -6.2e+54], N[Not[LessEqual[z, 4.4e+18]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y * x), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.1999999999999999e54 or 4.4e18 < z

   1. Initial program 39.0%

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

   2. Taylor expanded in z around inf 87.1%

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

   if -6.1999999999999999e54 < z < 4.4e18

   1. Initial program 91.4%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+54} \lor \neg \left(z \leq 4.4 \cdot 10^{+18}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \end{array} \]

Alternative 5: 80.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+26} \lor \neg \left(z \leq 4.2 \cdot 10^{+16}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.4e+26) (not (<= z 4.2e+16)))
   (/ (- t a) (- b y))
   (+ x (/ (* z (- t a)) (+ y (* z (- b y)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.4e+26) || !(z <= 4.2e+16)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x + ((z * (t - a)) / (y + (z * (b - y))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-1.4d+26)) .or. (.not. (z <= 4.2d+16))) then
        tmp = (t - a) / (b - y)
    else
        tmp = x + ((z * (t - a)) / (y + (z * (b - y))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.4e+26) || !(z <= 4.2e+16)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x + ((z * (t - a)) / (y + (z * (b - y))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.4e+26) or not (z <= 4.2e+16):
		tmp = (t - a) / (b - y)
	else:
		tmp = x + ((z * (t - a)) / (y + (z * (b - y))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.4e+26) || !(z <= 4.2e+16))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(x + Float64(Float64(z * Float64(t - a)) / Float64(y + Float64(z * Float64(b - y)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1.4e+26) || ~((z <= 4.2e+16)))
		tmp = (t - a) / (b - y);
	else
		tmp = x + ((z * (t - a)) / (y + (z * (b - y))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.4e+26], N[Not[LessEqual[z, 4.2e+16]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.4e26 or 4.2e16 < z

   1. Initial program 40.6%

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

   2. Taylor expanded in z around inf 84.9%

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

   if -1.4e26 < z < 4.2e16

   1. Initial program 93.1%

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

   2. Taylor expanded in x around 0 93.1%

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

   3. Taylor expanded in z around 0 87.8%

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

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+26} \lor \neg \left(z \leq 4.2 \cdot 10^{+16}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \end{array} \]

Alternative 6: 82.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.48 \cdot 10^{+23} \lor \neg \left(z \leq 7.6 \cdot 10^{+16}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x + z \cdot \left(t - a\right)}{y + z \cdot b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.48e+23) (not (<= z 7.6e+16)))
   (/ (- t a) (- b y))
   (/ (+ (* y x) (* z (- t a))) (+ y (* z b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.48e+23) || !(z <= 7.6e+16)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((y * x) + (z * (t - a))) / (y + (z * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-1.48d+23)) .or. (.not. (z <= 7.6d+16))) then
        tmp = (t - a) / (b - y)
    else
        tmp = ((y * x) + (z * (t - a))) / (y + (z * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.48e+23) || !(z <= 7.6e+16)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((y * x) + (z * (t - a))) / (y + (z * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.48e+23) or not (z <= 7.6e+16):
		tmp = (t - a) / (b - y)
	else:
		tmp = ((y * x) + (z * (t - a))) / (y + (z * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.48e+23) || !(z <= 7.6e+16))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(Float64(Float64(y * x) + Float64(z * Float64(t - a))) / Float64(y + Float64(z * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1.48e+23) || ~((z <= 7.6e+16)))
		tmp = (t - a) / (b - y);
	else
		tmp = ((y * x) + (z * (t - a))) / (y + (z * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.48e+23], N[Not[LessEqual[z, 7.6e+16]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y * x), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.4799999999999999e23 or 7.6e16 < z

   1. Initial program 41.0%

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

   2. Taylor expanded in z around inf 85.0%

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

   if -1.4799999999999999e23 < z < 7.6e16

   1. Initial program 93.0%

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

   2. Taylor expanded in b around inf 92.4%

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

      1. *-commutative 92.4%

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

   4. Simplified 92.4%

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

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.48 \cdot 10^{+23} \lor \neg \left(z \leq 7.6 \cdot 10^{+16}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x + z \cdot \left(t - a\right)}{y + z \cdot b}\\ \end{array} \]

Alternative 7: 69.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -3.35 \cdot 10^{-34}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-166}:\\ \;\;\;\;x + t \cdot \frac{z}{y}\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-13}:\\ \;\;\;\;x + \frac{z}{\frac{-y}{a}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -3.35e-34)
     t_1
     (if (<= z 3.2e-166)
       (+ x (* t (/ z y)))
       (if (<= z 1.05e-13) (+ x (/ z (/ (- y) a))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -3.35e-34) {
		tmp = t_1;
	} else if (z <= 3.2e-166) {
		tmp = x + (t * (z / y));
	} else if (z <= 1.05e-13) {
		tmp = x + (z / (-y / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    if (z <= (-3.35d-34)) then
        tmp = t_1
    else if (z <= 3.2d-166) then
        tmp = x + (t * (z / y))
    else if (z <= 1.05d-13) then
        tmp = x + (z / (-y / a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -3.35e-34) {
		tmp = t_1;
	} else if (z <= 3.2e-166) {
		tmp = x + (t * (z / y));
	} else if (z <= 1.05e-13) {
		tmp = x + (z / (-y / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	tmp = 0
	if z <= -3.35e-34:
		tmp = t_1
	elif z <= 3.2e-166:
		tmp = x + (t * (z / y))
	elif z <= 1.05e-13:
		tmp = x + (z / (-y / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -3.35e-34)
		tmp = t_1;
	elseif (z <= 3.2e-166)
		tmp = Float64(x + Float64(t * Float64(z / y)));
	elseif (z <= 1.05e-13)
		tmp = Float64(x + Float64(z / Float64(Float64(-y) / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -3.35e-34)
		tmp = t_1;
	elseif (z <= 3.2e-166)
		tmp = x + (t * (z / y));
	elseif (z <= 1.05e-13)
		tmp = x + (z / (-y / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.35e-34], t$95$1, If[LessEqual[z, 3.2e-166], N[(x + N[(t * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.05e-13], N[(x + N[(z / N[((-y) / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.3500000000000002e-34 or 1.04999999999999994e-13 < z

   1. Initial program 43.8%

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

   2. Taylor expanded in z around inf 83.7%

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

   if -3.3500000000000002e-34 < z < 3.20000000000000001e-166

   1. Initial program 95.6%

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

   2. Taylor expanded in x around 0 95.6%

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

   3. Taylor expanded in z around 0 89.3%

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

   4. Taylor expanded in z around 0 77.3%

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

      1. associate-/l* 66.9%

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

   6. Simplified 66.9%

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

   7. Taylor expanded in t around inf 70.5%

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

      1. associate-*r/ 70.5%

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

   9. Simplified 70.5%

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

   if 3.20000000000000001e-166 < z < 1.04999999999999994e-13

   1. Initial program 86.0%

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

   2. Taylor expanded in x around 0 86.0%

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

   3. Taylor expanded in z around 0 88.6%

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

   4. Taylor expanded in z around 0 76.8%

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

      1. associate-/l* 77.0%

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

   6. Simplified 77.0%

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

   7. Taylor expanded in t around 0 67.8%

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

      1. associate-*r/ 67.8%

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

      2. neg-mul-1 67.8%

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

   9. Simplified 67.8%

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

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.35 \cdot 10^{-34}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-166}:\\ \;\;\;\;x + t \cdot \frac{z}{y}\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-13}:\\ \;\;\;\;x + \frac{z}{\frac{-y}{a}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 8: 72.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.8 \cdot 10^{-24} \lor \neg \left(z \leq 5 \cdot 10^{-8}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{y}{t - a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -9.8e-24) (not (<= z 5e-8)))
   (/ (- t a) (- b y))
   (+ x (/ z (/ y (- t a))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -9.8e-24) || !(z <= 5e-8)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x + (z / (y / (t - a)));
	}
	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 <= (-9.8d-24)) .or. (.not. (z <= 5d-8))) then
        tmp = (t - a) / (b - y)
    else
        tmp = x + (z / (y / (t - a)))
    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 <= -9.8e-24) || !(z <= 5e-8)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x + (z / (y / (t - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -9.8e-24) or not (z <= 5e-8):
		tmp = (t - a) / (b - y)
	else:
		tmp = x + (z / (y / (t - a)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -9.8e-24) || !(z <= 5e-8))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(x + Float64(z / Float64(y / Float64(t - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -9.8e-24) || ~((z <= 5e-8)))
		tmp = (t - a) / (b - y);
	else
		tmp = x + (z / (y / (t - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -9.8e-24], N[Not[LessEqual[z, 5e-8]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x + N[(z / N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.8000000000000002e-24 or 4.9999999999999998e-8 < z

   1. Initial program 43.8%

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

   2. Taylor expanded in z around inf 83.7%

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

   if -9.8000000000000002e-24 < z < 4.9999999999999998e-8

   1. Initial program 93.4%

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

   2. Taylor expanded in x around 0 93.4%

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

   3. Taylor expanded in z around 0 89.1%

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

   4. Taylor expanded in z around 0 77.2%

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

      1. associate-/l* 69.2%

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

   6. Simplified 69.2%

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

4. Final simplification 76.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.8 \cdot 10^{-24} \lor \neg \left(z \leq 5 \cdot 10^{-8}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{y}{t - a}}\\ \end{array} \]

Alternative 9: 75.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{-30} \lor \neg \left(z \leq 0.00096\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -6.5e-30) (not (<= z 0.00096)))
   (/ (- t a) (- b y))
   (+ x (/ (* z (- t a)) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -6.5e-30) || !(z <= 0.00096)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x + ((z * (t - a)) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-6.5d-30)) .or. (.not. (z <= 0.00096d0))) then
        tmp = (t - a) / (b - y)
    else
        tmp = x + ((z * (t - a)) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -6.5e-30) || !(z <= 0.00096)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x + ((z * (t - a)) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -6.5e-30) or not (z <= 0.00096):
		tmp = (t - a) / (b - y)
	else:
		tmp = x + ((z * (t - a)) / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -6.5e-30) || !(z <= 0.00096))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(x + Float64(Float64(z * Float64(t - a)) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -6.5e-30) || ~((z <= 0.00096)))
		tmp = (t - a) / (b - y);
	else
		tmp = x + ((z * (t - a)) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -6.5e-30], N[Not[LessEqual[z, 0.00096]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.5000000000000005e-30 or 9.60000000000000024e-4 < z

   1. Initial program 43.8%

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

   2. Taylor expanded in z around inf 83.7%

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

   if -6.5000000000000005e-30 < z < 9.60000000000000024e-4

   1. Initial program 93.4%

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

   2. Taylor expanded in x around 0 93.4%

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

   3. Taylor expanded in z around 0 89.1%

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

   4. Taylor expanded in z around 0 77.2%

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

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{-30} \lor \neg \left(z \leq 0.00096\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y}\\ \end{array} \]

Alternative 10: 52.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{-25} \lor \neg \left(z \leq 3.45 \cdot 10^{-59}\right):\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.9e-25) (not (<= z 3.45e-59)))
   (/ (- t a) b)
   (+ x (* t (/ z y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.9e-25) || !(z <= 3.45e-59)) {
		tmp = (t - a) / b;
	} else {
		tmp = x + (t * (z / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-1.9d-25)) .or. (.not. (z <= 3.45d-59))) then
        tmp = (t - a) / b
    else
        tmp = x + (t * (z / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.9e-25) || !(z <= 3.45e-59)) {
		tmp = (t - a) / b;
	} else {
		tmp = x + (t * (z / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.9e-25) or not (z <= 3.45e-59):
		tmp = (t - a) / b
	else:
		tmp = x + (t * (z / y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.9e-25) || !(z <= 3.45e-59))
		tmp = Float64(Float64(t - a) / b);
	else
		tmp = Float64(x + Float64(t * Float64(z / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1.9e-25) || ~((z <= 3.45e-59)))
		tmp = (t - a) / b;
	else
		tmp = x + (t * (z / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.9e-25], N[Not[LessEqual[z, 3.45e-59]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision], N[(x + N[(t * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.8999999999999999e-25 or 3.44999999999999991e-59 < z

   1. Initial program 46.9%

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

   2. Taylor expanded in y around 0 55.5%

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

   if -1.8999999999999999e-25 < z < 3.44999999999999991e-59

   1. Initial program 93.7%

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

   2. Taylor expanded in x around 0 93.7%

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

   3. Taylor expanded in z around 0 89.7%

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

   4. Taylor expanded in z around 0 78.7%

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

      1. associate-/l* 69.9%

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

   6. Simplified 69.9%

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

   7. Taylor expanded in t around inf 69.6%

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

      1. associate-*r/ 68.7%

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

   9. Simplified 68.7%

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

4. Final simplification 61.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{-25} \lor \neg \left(z \leq 3.45 \cdot 10^{-59}\right):\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{z}{y}\\ \end{array} \]

Alternative 11: 69.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{-26} \lor \neg \left(z \leq 2.65 \cdot 10^{-58}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.55e-26) (not (<= z 2.65e-58)))
   (/ (- t a) (- b y))
   (+ x (* t (/ z y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.55e-26) || !(z <= 2.65e-58)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x + (t * (z / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-1.55d-26)) .or. (.not. (z <= 2.65d-58))) then
        tmp = (t - a) / (b - y)
    else
        tmp = x + (t * (z / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.55e-26) || !(z <= 2.65e-58)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x + (t * (z / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.55e-26) or not (z <= 2.65e-58):
		tmp = (t - a) / (b - y)
	else:
		tmp = x + (t * (z / y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.55e-26) || !(z <= 2.65e-58))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(x + Float64(t * Float64(z / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1.55e-26) || ~((z <= 2.65e-58)))
		tmp = (t - a) / (b - y);
	else
		tmp = x + (t * (z / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.55e-26], N[Not[LessEqual[z, 2.65e-58]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.54999999999999992e-26 or 2.6500000000000002e-58 < z

   1. Initial program 46.9%

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

   2. Taylor expanded in z around inf 80.8%

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

   if -1.54999999999999992e-26 < z < 2.6500000000000002e-58

   1. Initial program 93.7%

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

   2. Taylor expanded in x around 0 93.7%

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

   3. Taylor expanded in z around 0 89.7%

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

   4. Taylor expanded in z around 0 78.7%

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

      1. associate-/l* 69.9%

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

   6. Simplified 69.9%

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

   7. Taylor expanded in t around inf 69.6%

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

      1. associate-*r/ 68.7%

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

   9. Simplified 68.7%

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

4. Final simplification 75.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{-26} \lor \neg \left(z \leq 2.65 \cdot 10^{-58}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{z}{y}\\ \end{array} \]

Alternative 12: 44.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.42 \cdot 10^{+23} \lor \neg \left(z \leq 5.4 \cdot 10^{-11}\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.42e+23) (not (<= z 5.4e-11))) (/ t (- b y)) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.42e+23) || !(z <= 5.4e-11)) {
		tmp = t / (b - y);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-1.42d+23)) .or. (.not. (z <= 5.4d-11))) then
        tmp = t / (b - y)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.42e+23) || !(z <= 5.4e-11)) {
		tmp = t / (b - y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.42e+23) or not (z <= 5.4e-11):
		tmp = t / (b - y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.42e+23) || !(z <= 5.4e-11))
		tmp = Float64(t / Float64(b - y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1.42e+23) || ~((z <= 5.4e-11)))
		tmp = t / (b - y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.42e+23], N[Not[LessEqual[z, 5.4e-11]], $MachinePrecision]], N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.42000000000000004e23 or 5.40000000000000009e-11 < z

   1. Initial program 42.8%

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

   2. Taylor expanded in t around inf 23.9%

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

      1. *-commutative 23.9%

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

   4. Simplified 23.9%

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

   5. Taylor expanded in z around inf 47.5%

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

   if -1.42000000000000004e23 < z < 5.40000000000000009e-11

   1. Initial program 92.8%

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

   2. Taylor expanded in z around 0 51.4%

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

4. Final simplification 49.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.42 \cdot 10^{+23} \lor \neg \left(z \leq 5.4 \cdot 10^{-11}\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 13: 45.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+23} \lor \neg \left(z \leq 0.049\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.7e+23) (not (<= z 0.049))) (/ t (- b y)) (/ x (- 1.0 z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.7e+23) || !(z <= 0.049)) {
		tmp = t / (b - y);
	} else {
		tmp = x / (1.0 - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-1.7d+23)) .or. (.not. (z <= 0.049d0))) then
        tmp = t / (b - y)
    else
        tmp = x / (1.0d0 - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.7e+23) || !(z <= 0.049)) {
		tmp = t / (b - y);
	} else {
		tmp = x / (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.7e+23) or not (z <= 0.049):
		tmp = t / (b - y)
	else:
		tmp = x / (1.0 - z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.7e+23) || !(z <= 0.049))
		tmp = Float64(t / Float64(b - y));
	else
		tmp = Float64(x / Float64(1.0 - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1.7e+23) || ~((z <= 0.049)))
		tmp = t / (b - y);
	else
		tmp = x / (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.7e+23], N[Not[LessEqual[z, 0.049]], $MachinePrecision]], N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.69999999999999996e23 or 0.049000000000000002 < z

   1. Initial program 42.8%

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

   2. Taylor expanded in t around inf 23.9%

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

      1. *-commutative 23.9%

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

   4. Simplified 23.9%

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

   5. Taylor expanded in z around inf 47.5%

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

   if -1.69999999999999996e23 < z < 0.049000000000000002

   1. Initial program 92.8%

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

   2. Taylor expanded in y around inf 52.9%

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

      1. mul-1-neg 52.9%

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

      2. unsub-neg 52.9%

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

   4. Simplified 52.9%

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

4. Final simplification 50.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+23} \lor \neg \left(z \leq 0.049\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]

Alternative 14: 53.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{-39} \lor \neg \left(y \leq 5.2 \cdot 10^{+128}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -2.7e-39) (not (<= y 5.2e+128))) (/ x (- 1.0 z)) (/ (- t a) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.7e-39) || !(y <= 5.2e+128)) {
		tmp = x / (1.0 - z);
	} else {
		tmp = (t - a) / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-2.7d-39)) .or. (.not. (y <= 5.2d+128))) then
        tmp = x / (1.0d0 - z)
    else
        tmp = (t - a) / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.7e-39) || !(y <= 5.2e+128)) {
		tmp = x / (1.0 - z);
	} else {
		tmp = (t - a) / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -2.7e-39) or not (y <= 5.2e+128):
		tmp = x / (1.0 - z)
	else:
		tmp = (t - a) / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -2.7e-39) || !(y <= 5.2e+128))
		tmp = Float64(x / Float64(1.0 - z));
	else
		tmp = Float64(Float64(t - a) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -2.7e-39) || ~((y <= 5.2e+128)))
		tmp = x / (1.0 - z);
	else
		tmp = (t - a) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -2.7e-39], N[Not[LessEqual[y, 5.2e+128]], $MachinePrecision]], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.7000000000000001e-39 or 5.2e128 < y

   1. Initial program 55.3%

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

   2. Taylor expanded in y around inf 56.6%

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

      1. mul-1-neg 56.6%

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

      2. unsub-neg 56.6%

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

   4. Simplified 56.6%

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

   if -2.7000000000000001e-39 < y < 5.2e128

   1. Initial program 74.5%

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

   2. Taylor expanded in y around 0 56.0%

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

4. Final simplification 56.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{-39} \lor \neg \left(y \leq 5.2 \cdot 10^{+128}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \]

Alternative 15: 36.9% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+26} \lor \neg \left(z \leq 2.6 \cdot 10^{-6}\right):\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.4e+26) (not (<= z 2.6e-6))) (/ t b) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.4e+26) || !(z <= 2.6e-6)) {
		tmp = t / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-1.4d+26)) .or. (.not. (z <= 2.6d-6))) then
        tmp = t / b
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.4e+26) || !(z <= 2.6e-6)) {
		tmp = t / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.4e+26) or not (z <= 2.6e-6):
		tmp = t / b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.4e+26) || !(z <= 2.6e-6))
		tmp = Float64(t / b);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1.4e+26) || ~((z <= 2.6e-6)))
		tmp = t / b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.4e+26], N[Not[LessEqual[z, 2.6e-6]], $MachinePrecision]], N[(t / b), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.4e26 or 2.60000000000000009e-6 < z

   1. Initial program 42.4%

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

   2. Taylor expanded in t around inf 24.1%

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

      1. *-commutative 24.1%

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

   4. Simplified 24.1%

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

   5. Taylor expanded in y around 0 31.5%

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

   if -1.4e26 < z < 2.60000000000000009e-6

   1. Initial program 92.9%

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

   2. Taylor expanded in z around 0 51.0%

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

4. Final simplification 41.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+26} \lor \neg \left(z \leq 2.6 \cdot 10^{-6}\right):\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 16: 37.3% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.1 \cdot 10^{-16}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -6.1e-16) (/ (- a) b) (if (<= z 1.6e-13) x (/ t b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -6.1e-16) {
		tmp = -a / b;
	} else if (z <= 1.6e-13) {
		tmp = x;
	} else {
		tmp = t / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-6.1d-16)) then
        tmp = -a / b
    else if (z <= 1.6d-13) then
        tmp = x
    else
        tmp = t / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -6.1e-16) {
		tmp = -a / b;
	} else if (z <= 1.6e-13) {
		tmp = x;
	} else {
		tmp = t / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -6.1e-16:
		tmp = -a / b
	elif z <= 1.6e-13:
		tmp = x
	else:
		tmp = t / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -6.1e-16)
		tmp = Float64(Float64(-a) / b);
	elseif (z <= 1.6e-13)
		tmp = x;
	else
		tmp = Float64(t / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -6.1e-16)
		tmp = -a / b;
	elseif (z <= 1.6e-13)
		tmp = x;
	else
		tmp = t / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -6.1e-16], N[((-a) / b), $MachinePrecision], If[LessEqual[z, 1.6e-13], x, N[(t / b), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.09999999999999953e-16

   1. Initial program 40.0%

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

   2. Taylor expanded in a around inf 23.5%

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

      1. mul-1-neg 23.5%

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

      2. distribute-lft-neg-out 23.5%

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

      3. *-commutative 23.5%

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

   4. Simplified 23.5%

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

   5. Taylor expanded in y around 0 37.8%

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

      1. associate-*r/ 37.8%

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

      2. neg-mul-1 37.8%

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

   7. Simplified 37.8%

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

   if -6.09999999999999953e-16 < z < 1.6e-13

   1. Initial program 93.4%

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

   2. Taylor expanded in z around 0 52.9%

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

   if 1.6e-13 < z

   1. Initial program 47.7%

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

   2. Taylor expanded in t around inf 28.7%

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

      1. *-commutative 28.7%

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

   4. Simplified 28.7%

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

   5. Taylor expanded in y around 0 33.7%

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

4. Final simplification 43.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.1 \cdot 10^{-16}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \]

Alternative 17: 25.5% accurate, 17.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := x

Derivation

1. Initial program 66.8%

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

2. Taylor expanded in z around 0 26.5%

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

3. Final simplification 26.5%

   \[\leadsto x \]

Developer target: 73.0% 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 2023318 
(FPCore (x y z t a b)
  :name "Development.Shake.Progress:decay from shake-0.15.5"
  :precision binary64

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

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