AI.Clustering.Hierarchical.Internal:ward from clustering-0.2.1

Percentage Accurate: 61.0% → 88.5%

Time: 13.0s

Alternatives: 14

Speedup: 0.3×

Specification

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 61.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 88.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y + t\right) \cdot \left(y + t\right)\\ t_2 := \frac{z}{y + t}\\ t_3 := \frac{\left(z \cdot \left(x + y\right) + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)}\\ t_4 := \left(x + y\right) \cdot \left(x + y\right)\\ \mathbf{if}\;t\_3 \leq -\infty:\\ \;\;\;\;\mathsf{fma}\left(t, \mathsf{fma}\left(y, \frac{b}{t\_4}, \frac{a}{x + y}\right) - \mathsf{fma}\left(a, \frac{y}{t\_4}, \frac{z}{x + y}\right), \mathsf{fma}\left(a, \frac{y}{x + y}, z\right)\right) - y \cdot \frac{b}{x + y}\\ \mathbf{elif}\;t\_3 \leq 5 \cdot 10^{+266}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, \mathsf{fma}\left(y, \frac{b}{t\_1}, t\_2\right) - \mathsf{fma}\left(y, \frac{z}{t\_1}, \frac{a}{y + t}\right), \mathsf{fma}\left(y, t\_2, a\right)\right) - y \cdot \frac{b}{y + t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (+ y t) (+ y t)))
        (t_2 (/ z (+ y t)))
        (t_3 (/ (- (+ (* z (+ x y)) (* (+ y t) a)) (* y b)) (+ y (+ x t))))
        (t_4 (* (+ x y) (+ x y))))
   (if (<= t_3 (- INFINITY))
     (-
      (fma
       t
       (- (fma y (/ b t_4) (/ a (+ x y))) (fma a (/ y t_4) (/ z (+ x y))))
       (fma a (/ y (+ x y)) z))
      (* y (/ b (+ x y))))
     (if (<= t_3 5e+266)
       t_3
       (-
        (fma
         x
         (- (fma y (/ b t_1) t_2) (fma y (/ z t_1) (/ a (+ y t))))
         (fma y t_2 a))
        (* y (/ b (+ y t))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y + t) * (y + t);
	double t_2 = z / (y + t);
	double t_3 = (((z * (x + y)) + ((y + t) * a)) - (y * b)) / (y + (x + t));
	double t_4 = (x + y) * (x + y);
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = fma(t, (fma(y, (b / t_4), (a / (x + y))) - fma(a, (y / t_4), (z / (x + y)))), fma(a, (y / (x + y)), z)) - (y * (b / (x + y)));
	} else if (t_3 <= 5e+266) {
		tmp = t_3;
	} else {
		tmp = fma(x, (fma(y, (b / t_1), t_2) - fma(y, (z / t_1), (a / (y + t)))), fma(y, t_2, a)) - (y * (b / (y + t)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y + t) * Float64(y + t))
	t_2 = Float64(z / Float64(y + t))
	t_3 = Float64(Float64(Float64(Float64(z * Float64(x + y)) + Float64(Float64(y + t) * a)) - Float64(y * b)) / Float64(y + Float64(x + t)))
	t_4 = Float64(Float64(x + y) * Float64(x + y))
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = Float64(fma(t, Float64(fma(y, Float64(b / t_4), Float64(a / Float64(x + y))) - fma(a, Float64(y / t_4), Float64(z / Float64(x + y)))), fma(a, Float64(y / Float64(x + y)), z)) - Float64(y * Float64(b / Float64(x + y))));
	elseif (t_3 <= 5e+266)
		tmp = t_3;
	else
		tmp = Float64(fma(x, Float64(fma(y, Float64(b / t_1), t_2) - fma(y, Float64(z / t_1), Float64(a / Float64(y + t)))), fma(y, t_2, a)) - Float64(y * Float64(b / Float64(y + t))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y + t), $MachinePrecision] * N[(y + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z / N[(y + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision] + N[(N[(y + t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(x + y), $MachinePrecision] * N[(x + y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], N[(N[(t * N[(N[(y * N[(b / t$95$4), $MachinePrecision] + N[(a / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * N[(y / t$95$4), $MachinePrecision] + N[(z / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(y / N[(x + y), $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] - N[(y * N[(b / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 5e+266], t$95$3, N[(N[(x * N[(N[(y * N[(b / t$95$1), $MachinePrecision] + t$95$2), $MachinePrecision] - N[(y * N[(z / t$95$1), $MachinePrecision] + N[(a / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * t$95$2 + a), $MachinePrecision]), $MachinePrecision] - N[(y * N[(b / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 6.4%

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

   3. Taylor expanded in t around 0

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

      1. lower--.f64 N/A

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

   5. Simplified 77.8%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 4.9999999999999999e266

   1. Initial program 99.7%

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

   if 4.9999999999999999e266 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 6.7%

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

   3. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

   5. Simplified 78.5%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z \cdot \left(x + y\right) + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty:\\ \;\;\;\;\mathsf{fma}\left(t, \mathsf{fma}\left(y, \frac{b}{\left(x + y\right) \cdot \left(x + y\right)}, \frac{a}{x + y}\right) - \mathsf{fma}\left(a, \frac{y}{\left(x + y\right) \cdot \left(x + y\right)}, \frac{z}{x + y}\right), \mathsf{fma}\left(a, \frac{y}{x + y}, z\right)\right) - y \cdot \frac{b}{x + y}\\ \mathbf{elif}\;\frac{\left(z \cdot \left(x + y\right) + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)} \leq 5 \cdot 10^{+266}:\\ \;\;\;\;\frac{\left(z \cdot \left(x + y\right) + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, \mathsf{fma}\left(y, \frac{b}{\left(y + t\right) \cdot \left(y + t\right)}, \frac{z}{y + t}\right) - \mathsf{fma}\left(y, \frac{z}{\left(y + t\right) \cdot \left(y + t\right)}, \frac{a}{y + t}\right), \mathsf{fma}\left(y, \frac{z}{y + t}, a\right)\right) - y \cdot \frac{b}{y + t}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 88.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(z \cdot \left(x + y\right) + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)}\\ t_2 := \left(x + y\right) \cdot \left(x + y\right)\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\mathsf{fma}\left(t, \mathsf{fma}\left(y, \frac{b}{t\_2}, \frac{a}{x + y}\right) - \mathsf{fma}\left(a, \frac{y}{t\_2}, \frac{z}{x + y}\right), \mathsf{fma}\left(a, \frac{y}{x + y}, z\right)\right) - y \cdot \frac{b}{x + y}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+248}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;a + \left(z - b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* z (+ x y)) (* (+ y t) a)) (* y b)) (+ y (+ x t))))
        (t_2 (* (+ x y) (+ x y))))
   (if (<= t_1 (- INFINITY))
     (-
      (fma
       t
       (- (fma y (/ b t_2) (/ a (+ x y))) (fma a (/ y t_2) (/ z (+ x y))))
       (fma a (/ y (+ x y)) z))
      (* y (/ b (+ x y))))
     (if (<= t_1 5e+248) t_1 (+ a (- z b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (((z * (x + y)) + ((y + t) * a)) - (y * b)) / (y + (x + t));
	double t_2 = (x + y) * (x + y);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = fma(t, (fma(y, (b / t_2), (a / (x + y))) - fma(a, (y / t_2), (z / (x + y)))), fma(a, (y / (x + y)), z)) - (y * (b / (x + y)));
	} else if (t_1 <= 5e+248) {
		tmp = t_1;
	} else {
		tmp = a + (z - b);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(Float64(z * Float64(x + y)) + Float64(Float64(y + t) * a)) - Float64(y * b)) / Float64(y + Float64(x + t)))
	t_2 = Float64(Float64(x + y) * Float64(x + y))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(fma(t, Float64(fma(y, Float64(b / t_2), Float64(a / Float64(x + y))) - fma(a, Float64(y / t_2), Float64(z / Float64(x + y)))), fma(a, Float64(y / Float64(x + y)), z)) - Float64(y * Float64(b / Float64(x + y))));
	elseif (t_1 <= 5e+248)
		tmp = t_1;
	else
		tmp = Float64(a + Float64(z - b));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision] + N[(N[(y + t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + y), $MachinePrecision] * N[(x + y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(t * N[(N[(y * N[(b / t$95$2), $MachinePrecision] + N[(a / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * N[(y / t$95$2), $MachinePrecision] + N[(z / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(y / N[(x + y), $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] - N[(y * N[(b / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+248], t$95$1, N[(a + N[(z - b), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 6.4%

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

   3. Taylor expanded in t around 0

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

      1. lower--.f64 N/A

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

   5. Simplified 77.8%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 4.9999999999999996e248

   1. Initial program 99.7%

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

   if 4.9999999999999996e248 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 8.2%

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

   3. Taylor expanded in y around inf

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

      1. associate--l+ N/A

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

      2. lower-+.f64 N/A

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

      3. lower--.f64 70.6

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

   5. Simplified 70.6%

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

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z \cdot \left(x + y\right) + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty:\\ \;\;\;\;\mathsf{fma}\left(t, \mathsf{fma}\left(y, \frac{b}{\left(x + y\right) \cdot \left(x + y\right)}, \frac{a}{x + y}\right) - \mathsf{fma}\left(a, \frac{y}{\left(x + y\right) \cdot \left(x + y\right)}, \frac{z}{x + y}\right), \mathsf{fma}\left(a, \frac{y}{x + y}, z\right)\right) - y \cdot \frac{b}{x + y}\\ \mathbf{elif}\;\frac{\left(z \cdot \left(x + y\right) + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)} \leq 5 \cdot 10^{+248}:\\ \;\;\;\;\frac{\left(z \cdot \left(x + y\right) + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;a + \left(z - b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 88.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(z \cdot \left(x + y\right) + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)}\\ t_2 := a + \left(z - b\right)\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+248}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* z (+ x y)) (* (+ y t) a)) (* y b)) (+ y (+ x t))))
        (t_2 (+ a (- z b))))
   (if (<= t_1 (- INFINITY)) t_2 (if (<= t_1 5e+248) t_1 t_2))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (((z * (x + y)) + ((y + t) * a)) - (y * b)) / (y + (x + t));
	double t_2 = a + (z - b);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = t_2;
	} else if (t_1 <= 5e+248) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (((z * (x + y)) + ((y + t) * a)) - (y * b)) / (y + (x + t));
	double t_2 = a + (z - b);
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else if (t_1 <= 5e+248) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (((z * (x + y)) + ((y + t) * a)) - (y * b)) / (y + (x + t))
	t_2 = a + (z - b)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = t_2
	elif t_1 <= 5e+248:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(Float64(z * Float64(x + y)) + Float64(Float64(y + t) * a)) - Float64(y * b)) / Float64(y + Float64(x + t)))
	t_2 = Float64(a + Float64(z - b))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = t_2;
	elseif (t_1 <= 5e+248)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (((z * (x + y)) + ((y + t) * a)) - (y * b)) / (y + (x + t));
	t_2 = a + (z - b);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = t_2;
	elseif (t_1 <= 5e+248)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision] + N[(N[(y + t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a + N[(z - b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], t$95$2, If[LessEqual[t$95$1, 5e+248], t$95$1, t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -inf.0 or 4.9999999999999996e248 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 7.4%

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

   3. Taylor expanded in y around inf

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

      1. associate--l+ N/A

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

      2. lower-+.f64 N/A

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

      3. lower--.f64 72.3

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

   5. Simplified 72.3%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 4.9999999999999996e248

   1. Initial program 99.7%

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

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z \cdot \left(x + y\right) + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty:\\ \;\;\;\;a + \left(z - b\right)\\ \mathbf{elif}\;\frac{\left(z \cdot \left(x + y\right) + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)} \leq 5 \cdot 10^{+248}:\\ \;\;\;\;\frac{\left(z \cdot \left(x + y\right) + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;a + \left(z - b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 55.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(x, \frac{z}{t}, a\right) - a \cdot \frac{x}{t}\\ \mathbf{if}\;t \leq -1.7 \cdot 10^{+224}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{-247}:\\ \;\;\;\;a + \left(z - b\right)\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-64}:\\ \;\;\;\;z - \frac{\mathsf{fma}\left(y + t, z, -\mathsf{fma}\left(y, z - b, \left(y + t\right) \cdot a\right)\right)}{x}\\ \mathbf{elif}\;t \leq 1.32 \cdot 10^{+221}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (fma x (/ z t) a) (* a (/ x t)))))
   (if (<= t -1.7e+224)
     t_1
     (if (<= t 1.02e-247)
       (+ a (- z b))
       (if (<= t 7e-64)
         (- z (/ (fma (+ y t) z (- (fma y (- z b) (* (+ y t) a)))) x))
         (if (<= t 1.32e+221) (+ z a) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(x, (z / t), a) - (a * (x / t));
	double tmp;
	if (t <= -1.7e+224) {
		tmp = t_1;
	} else if (t <= 1.02e-247) {
		tmp = a + (z - b);
	} else if (t <= 7e-64) {
		tmp = z - (fma((y + t), z, -fma(y, (z - b), ((y + t) * a))) / x);
	} else if (t <= 1.32e+221) {
		tmp = z + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(fma(x, Float64(z / t), a) - Float64(a * Float64(x / t)))
	tmp = 0.0
	if (t <= -1.7e+224)
		tmp = t_1;
	elseif (t <= 1.02e-247)
		tmp = Float64(a + Float64(z - b));
	elseif (t <= 7e-64)
		tmp = Float64(z - Float64(fma(Float64(y + t), z, Float64(-fma(y, Float64(z - b), Float64(Float64(y + t) * a)))) / x));
	elseif (t <= 1.32e+221)
		tmp = Float64(z + a);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x * N[(z / t), $MachinePrecision] + a), $MachinePrecision] - N[(a * N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.7e+224], t$95$1, If[LessEqual[t, 1.02e-247], N[(a + N[(z - b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7e-64], N[(z - N[(N[(N[(y + t), $MachinePrecision] * z + (-N[(y * N[(z - b), $MachinePrecision] + N[(N[(y + t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision])), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.32e+221], N[(z + a), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.7000000000000001e224 or 1.32000000000000009e221 < t

   1. Initial program 45.1%

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

   3. Taylor expanded in t around inf

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. associate-/l* N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. associate-/l* N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. +-commutative N/A

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

      11. lower-+.f64 N/A

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

      12. associate-/l* N/A

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

      13. lower-fma.f64 N/A

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

      14. lower-/.f64 N/A

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

      15. +-commutative N/A

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

      16. lower-+.f64 N/A

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

      17. lower-/.f64 N/A

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

      18. *-commutative N/A

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

      19. lower-*.f64 82.7

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

   5. Simplified 82.7%

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

   6. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. associate-/l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. associate-/l* N/A

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

      7. lower-*.f64 N/A

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

      8. lower-/.f64 74.4

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

   8. Simplified 74.4%

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

   if -1.7000000000000001e224 < t < 1.01999999999999994e-247

   1. Initial program 60.0%

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

   3. Taylor expanded in y around inf

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

      1. associate--l+ N/A

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

      2. lower-+.f64 N/A

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

      3. lower--.f64 65.9

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

   5. Simplified 65.9%

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

   if 1.01999999999999994e-247 < t < 7.0000000000000006e-64

   1. Initial program 87.6%

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

   3. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

   5. Simplified 75.5%

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

   if 7.0000000000000006e-64 < t < 1.32000000000000009e221

   1. Initial program 62.4%

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

   3. Taylor expanded in y around inf

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

      1. associate--l+ N/A

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

      2. lower-+.f64 N/A

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

      3. lower--.f64 70.8

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

   5. Simplified 70.8%

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

   6. Taylor expanded in b around 0

      \[\leadsto \color{blue}{a + z} \]
   7. Step-by-step derivation

      1. lower-+.f64 72.9

         \[\leadsto \color{blue}{a + z} \]

   8. Simplified 72.9%

      \[\leadsto \color{blue}{a + z} \]
3. Recombined 4 regimes into one program.

4. Final simplification 70.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{+224}:\\ \;\;\;\;\mathsf{fma}\left(x, \frac{z}{t}, a\right) - a \cdot \frac{x}{t}\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{-247}:\\ \;\;\;\;a + \left(z - b\right)\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-64}:\\ \;\;\;\;z - \frac{\mathsf{fma}\left(y + t, z, -\mathsf{fma}\left(y, z - b, \left(y + t\right) \cdot a\right)\right)}{x}\\ \mathbf{elif}\;t \leq 1.32 \cdot 10^{+221}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, \frac{z}{t}, a\right) - a \cdot \frac{x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 56.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \frac{y}{\left(\left(-y\right) - x\right) - t}\\ \mathbf{if}\;b \leq -3 \cdot 10^{+133}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{+135}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (/ y (- (- (- y) x) t)))))
   (if (<= b -3e+133) t_1 (if (<= b 1.5e+135) (+ z a) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (y / ((-y - x) - t));
	double tmp;
	if (b <= -3e+133) {
		tmp = t_1;
	} else if (b <= 1.5e+135) {
		tmp = z + 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 = b * (y / ((-y - x) - t))
    if (b <= (-3d+133)) then
        tmp = t_1
    else if (b <= 1.5d+135) then
        tmp = z + 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 = b * (y / ((-y - x) - t));
	double tmp;
	if (b <= -3e+133) {
		tmp = t_1;
	} else if (b <= 1.5e+135) {
		tmp = z + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (y / ((-y - x) - t))
	tmp = 0
	if b <= -3e+133:
		tmp = t_1
	elif b <= 1.5e+135:
		tmp = z + a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(y / Float64(Float64(Float64(-y) - x) - t)))
	tmp = 0.0
	if (b <= -3e+133)
		tmp = t_1;
	elseif (b <= 1.5e+135)
		tmp = Float64(z + a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (y / ((-y - x) - t));
	tmp = 0.0;
	if (b <= -3e+133)
		tmp = t_1;
	elseif (b <= 1.5e+135)
		tmp = z + a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(y / N[(N[((-y) - x), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3e+133], t$95$1, If[LessEqual[b, 1.5e+135], N[(z + a), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -3.00000000000000007e133 or 1.5e135 < b

   1. Initial program 52.1%

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

   3. Taylor expanded in z around -inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. mul-1-neg N/A

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

      6. unsub-neg N/A

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

      7. lower--.f64 N/A

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

   5. Simplified 47.5%

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

   6. Taylor expanded in a around -inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. +-commutative N/A

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

      6. associate-/l* N/A

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

      7. lower-fma.f64 N/A

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

   8. Simplified 39.4%

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

   9. Taylor expanded in b around -inf

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

       1. associate-*r* N/A

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

       2. mul-1-neg N/A

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

       3. lower-*.f64 N/A

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

       4. lower-neg.f64 N/A

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

       5. +-commutative N/A

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

   11. Simplified 76.5%

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

   12. Taylor expanded in b around inf

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

       1. lower-/.f64 N/A

          \[\leadsto \left(\mathsf{neg}\left(b\right)\right) \cdot \color{blue}{\frac{y}{t + \left(x + y\right)}} \]

       2. lower-+.f64 N/A

          \[\leadsto \left(\mathsf{neg}\left(b\right)\right) \cdot \frac{y}{\color{blue}{t + \left(x + y\right)}} \]

       3. lower-+.f64 60.6

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

   14. Simplified 60.6%

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

   if -3.00000000000000007e133 < b < 1.5e135

   1. Initial program 64.8%

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

   3. Taylor expanded in y around inf

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

      1. associate--l+ N/A

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

      2. lower-+.f64 N/A

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

      3. lower--.f64 68.1

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

   5. Simplified 68.1%

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

   6. Taylor expanded in b around 0

      \[\leadsto \color{blue}{a + z} \]
   7. Step-by-step derivation

      1. lower-+.f64 69.5

         \[\leadsto \color{blue}{a + z} \]

   8. Simplified 69.5%

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

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3 \cdot 10^{+133}:\\ \;\;\;\;b \cdot \frac{y}{\left(\left(-y\right) - x\right) - t}\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{+135}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;b \cdot \frac{y}{\left(\left(-y\right) - x\right) - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 59.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{+132}:\\ \;\;\;\;z + \frac{y \cdot \left(a - b\right)}{x}\\ \mathbf{elif}\;x \leq 1.68 \cdot 10^{+124}:\\ \;\;\;\;a + \left(z - b\right)\\ \mathbf{else}:\\ \;\;\;\;z - \frac{y \cdot b}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -3.8e+132)
   (+ z (/ (* y (- a b)) x))
   (if (<= x 1.68e+124) (+ a (- z b)) (- z (/ (* y b) x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -3.8e+132) {
		tmp = z + ((y * (a - b)) / x);
	} else if (x <= 1.68e+124) {
		tmp = a + (z - b);
	} else {
		tmp = z - ((y * b) / 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 (x <= (-3.8d+132)) then
        tmp = z + ((y * (a - b)) / x)
    else if (x <= 1.68d+124) then
        tmp = a + (z - b)
    else
        tmp = z - ((y * b) / 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 (x <= -3.8e+132) {
		tmp = z + ((y * (a - b)) / x);
	} else if (x <= 1.68e+124) {
		tmp = a + (z - b);
	} else {
		tmp = z - ((y * b) / x);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -3.8e+132:
		tmp = z + ((y * (a - b)) / x)
	elif x <= 1.68e+124:
		tmp = a + (z - b)
	else:
		tmp = z - ((y * b) / x)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -3.8e+132)
		tmp = Float64(z + Float64(Float64(y * Float64(a - b)) / x));
	elseif (x <= 1.68e+124)
		tmp = Float64(a + Float64(z - b));
	else
		tmp = Float64(z - Float64(Float64(y * b) / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -3.8e+132)
		tmp = z + ((y * (a - b)) / x);
	elseif (x <= 1.68e+124)
		tmp = a + (z - b);
	else
		tmp = z - ((y * b) / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -3.8e+132], N[(z + N[(N[(y * N[(a - b), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.68e+124], N[(a + N[(z - b), $MachinePrecision]), $MachinePrecision], N[(z - N[(N[(y * b), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.80000000000000006e132

   1. Initial program 51.3%

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

   3. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

   5. Simplified 65.1%

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

   6. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 65.4

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

   8. Simplified 65.4%

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

   if -3.80000000000000006e132 < x < 1.67999999999999995e124

   1. Initial program 66.5%

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

   3. Taylor expanded in y around inf

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

      1. associate--l+ N/A

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

      2. lower-+.f64 N/A

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

      3. lower--.f64 68.6

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

   5. Simplified 68.6%

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

   if 1.67999999999999995e124 < x

   1. Initial program 49.1%

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

   3. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

   5. Simplified 53.0%

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

   6. Taylor expanded in b around inf

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

      1. lower-*.f64 58.6

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

   8. Simplified 58.6%

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

4. Final simplification 66.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{+132}:\\ \;\;\;\;z + \frac{y \cdot \left(a - b\right)}{x}\\ \mathbf{elif}\;x \leq 1.68 \cdot 10^{+124}:\\ \;\;\;\;a + \left(z - b\right)\\ \mathbf{else}:\\ \;\;\;\;z - \frac{y \cdot b}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 59.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z - \frac{y \cdot b}{x}\\ \mathbf{if}\;x \leq -2.6 \cdot 10^{+131}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.68 \cdot 10^{+124}:\\ \;\;\;\;a + \left(z - b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- z (/ (* y b) x))))
   (if (<= x -2.6e+131) t_1 (if (<= x 1.68e+124) (+ a (- z b)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z - ((y * b) / x);
	double tmp;
	if (x <= -2.6e+131) {
		tmp = t_1;
	} else if (x <= 1.68e+124) {
		tmp = a + (z - b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z - ((y * b) / x)
    if (x <= (-2.6d+131)) then
        tmp = t_1
    else if (x <= 1.68d+124) then
        tmp = a + (z - b)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z - ((y * b) / x);
	double tmp;
	if (x <= -2.6e+131) {
		tmp = t_1;
	} else if (x <= 1.68e+124) {
		tmp = a + (z - b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z - ((y * b) / x)
	tmp = 0
	if x <= -2.6e+131:
		tmp = t_1
	elif x <= 1.68e+124:
		tmp = a + (z - b)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z - Float64(Float64(y * b) / x))
	tmp = 0.0
	if (x <= -2.6e+131)
		tmp = t_1;
	elseif (x <= 1.68e+124)
		tmp = Float64(a + Float64(z - b));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z - ((y * b) / x);
	tmp = 0.0;
	if (x <= -2.6e+131)
		tmp = t_1;
	elseif (x <= 1.68e+124)
		tmp = a + (z - b);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z - N[(N[(y * b), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.6e+131], t$95$1, If[LessEqual[x, 1.68e+124], N[(a + N[(z - b), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.6e131 or 1.67999999999999995e124 < x

   1. Initial program 50.2%

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

   3. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

   5. Simplified 59.2%

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

   6. Taylor expanded in b around inf

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

      1. lower-*.f64 58.7

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

   8. Simplified 58.7%

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

   if -2.6e131 < x < 1.67999999999999995e124

   1. Initial program 66.5%

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

   3. Taylor expanded in y around inf

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

      1. associate--l+ N/A

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

      2. lower-+.f64 N/A

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

      3. lower--.f64 68.6

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

   5. Simplified 68.6%

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

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{+131}:\\ \;\;\;\;z - \frac{y \cdot b}{x}\\ \mathbf{elif}\;x \leq 1.68 \cdot 10^{+124}:\\ \;\;\;\;a + \left(z - b\right)\\ \mathbf{else}:\\ \;\;\;\;z - \frac{y \cdot b}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 58.1% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.05 \cdot 10^{+165}:\\ \;\;\;\;z \cdot \left(1 - \frac{t}{x}\right)\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{+124}:\\ \;\;\;\;a + \left(z - b\right)\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -2.05e+165)
   (* z (- 1.0 (/ t x)))
   (if (<= x 5.2e+124) (+ a (- z b)) z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -2.05e+165) {
		tmp = z * (1.0 - (t / x));
	} else if (x <= 5.2e+124) {
		tmp = a + (z - b);
	} else {
		tmp = 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 <= (-2.05d+165)) then
        tmp = z * (1.0d0 - (t / x))
    else if (x <= 5.2d+124) then
        tmp = a + (z - b)
    else
        tmp = 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 <= -2.05e+165) {
		tmp = z * (1.0 - (t / x));
	} else if (x <= 5.2e+124) {
		tmp = a + (z - b);
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -2.05e+165:
		tmp = z * (1.0 - (t / x))
	elif x <= 5.2e+124:
		tmp = a + (z - b)
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -2.05e+165)
		tmp = Float64(z * Float64(1.0 - Float64(t / x)));
	elseif (x <= 5.2e+124)
		tmp = Float64(a + Float64(z - b));
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -2.05e+165)
		tmp = z * (1.0 - (t / x));
	elseif (x <= 5.2e+124)
		tmp = a + (z - b);
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -2.05e+165], N[(z * N[(1.0 - N[(t / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.2e+124], N[(a + N[(z - b), $MachinePrecision]), $MachinePrecision], z]]

Derivation

1. Split input into 3 regimes

2. if x < -2.0500000000000001e165

   1. Initial program 48.1%

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

   3. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

   5. Simplified 66.2%

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

   6. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 55.0

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

   8. Simplified 55.0%

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

   if -2.0500000000000001e165 < x < 5.2000000000000001e124

   1. Initial program 66.2%

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

   3. Taylor expanded in y around inf

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

      1. associate--l+ N/A

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

      2. lower-+.f64 N/A

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

      3. lower--.f64 67.2

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

   5. Simplified 67.2%

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

   if 5.2000000000000001e124 < x

   1. Initial program 49.1%

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

   3. Taylor expanded in z around -inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. mul-1-neg N/A

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

      6. unsub-neg N/A

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

      7. lower--.f64 N/A

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

   5. Simplified 74.0%

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

   6. Taylor expanded in x around inf

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

   8. Simplified 54.3%

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

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.05 \cdot 10^{+165}:\\ \;\;\;\;z \cdot \left(1 - \frac{t}{x}\right)\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{+124}:\\ \;\;\;\;a + \left(z - b\right)\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 58.1% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.05 \cdot 10^{+165}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{+124}:\\ \;\;\;\;a + \left(z - b\right)\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -2.05e+165) z (if (<= x 5.2e+124) (+ a (- z b)) z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -2.05e+165) {
		tmp = z;
	} else if (x <= 5.2e+124) {
		tmp = a + (z - b);
	} else {
		tmp = 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 <= (-2.05d+165)) then
        tmp = z
    else if (x <= 5.2d+124) then
        tmp = a + (z - b)
    else
        tmp = 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 <= -2.05e+165) {
		tmp = z;
	} else if (x <= 5.2e+124) {
		tmp = a + (z - b);
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -2.05e+165:
		tmp = z
	elif x <= 5.2e+124:
		tmp = a + (z - b)
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -2.05e+165)
		tmp = z;
	elseif (x <= 5.2e+124)
		tmp = Float64(a + Float64(z - b));
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -2.05e+165)
		tmp = z;
	elseif (x <= 5.2e+124)
		tmp = a + (z - b);
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -2.05e+165], z, If[LessEqual[x, 5.2e+124], N[(a + N[(z - b), $MachinePrecision]), $MachinePrecision], z]]

Derivation

1. Split input into 2 regimes

2. if x < -2.0500000000000001e165 or 5.2000000000000001e124 < x

   1. Initial program 48.7%

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

   3. Taylor expanded in z around -inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. mul-1-neg N/A

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

      6. unsub-neg N/A

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

      7. lower--.f64 N/A

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

   5. Simplified 76.3%

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

   6. Taylor expanded in x around inf

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

   8. Simplified 54.6%

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

   if -2.0500000000000001e165 < x < 5.2000000000000001e124

   1. Initial program 66.2%

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

   3. Taylor expanded in y around inf

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

      1. associate--l+ N/A

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

      2. lower-+.f64 N/A

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

      3. lower--.f64 67.2

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

   5. Simplified 67.2%

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

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.05 \cdot 10^{+165}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{+124}:\\ \;\;\;\;a + \left(z - b\right)\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 55.2% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{+237}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-251}:\\ \;\;\;\;a + \left(z - b\right)\\ \mathbf{else}:\\ \;\;\;\;z + a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -4.2e+237) a (if (<= t 9.5e-251) (+ a (- z b)) (+ z a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -4.2e+237) {
		tmp = a;
	} else if (t <= 9.5e-251) {
		tmp = a + (z - b);
	} else {
		tmp = z + 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 (t <= (-4.2d+237)) then
        tmp = a
    else if (t <= 9.5d-251) then
        tmp = a + (z - b)
    else
        tmp = z + 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 (t <= -4.2e+237) {
		tmp = a;
	} else if (t <= 9.5e-251) {
		tmp = a + (z - b);
	} else {
		tmp = z + a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -4.2e+237:
		tmp = a
	elif t <= 9.5e-251:
		tmp = a + (z - b)
	else:
		tmp = z + a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -4.2e+237)
		tmp = a;
	elseif (t <= 9.5e-251)
		tmp = Float64(a + Float64(z - b));
	else
		tmp = Float64(z + a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -4.2e+237)
		tmp = a;
	elseif (t <= 9.5e-251)
		tmp = a + (z - b);
	else
		tmp = z + a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -4.2e+237], a, If[LessEqual[t, 9.5e-251], N[(a + N[(z - b), $MachinePrecision]), $MachinePrecision], N[(z + a), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.20000000000000029e237

   1. Initial program 43.7%

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

   3. Taylor expanded in z around -inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. mul-1-neg N/A

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

      6. unsub-neg N/A

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

      7. lower--.f64 N/A

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

   5. Simplified 46.9%

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

   6. Taylor expanded in a around -inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. +-commutative N/A

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

      6. associate-/l* N/A

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

      7. lower-fma.f64 N/A

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

   8. Simplified 91.0%

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

   9. Taylor expanded in t around inf

      \[\leadsto \left(\mathsf{neg}\left(a\right)\right) \cdot \color{blue}{-1} \]
   10. Step-by-step derivation

   11. Simplified 73.6%

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

   if -4.20000000000000029e237 < t < 9.49999999999999927e-251

   1. Initial program 59.0%

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

   3. Taylor expanded in y around inf

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

      1. associate--l+ N/A

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

      2. lower-+.f64 N/A

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

      3. lower--.f64 63.5

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

   5. Simplified 63.5%

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

   if 9.49999999999999927e-251 < t

   1. Initial program 67.1%

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

   3. Taylor expanded in y around inf

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

      1. associate--l+ N/A

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

      2. lower-+.f64 N/A

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

      3. lower--.f64 56.2

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

   5. Simplified 56.2%

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

   6. Taylor expanded in b around 0

      \[\leadsto \color{blue}{a + z} \]
   7. Step-by-step derivation

      1. lower-+.f64 61.4

         \[\leadsto \color{blue}{a + z} \]

   8. Simplified 61.4%

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

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{+237}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-251}:\\ \;\;\;\;a + \left(z - b\right)\\ \mathbf{else}:\\ \;\;\;\;z + a\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 53.6% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 9.5 \cdot 10^{-251}:\\ \;\;\;\;a + \left(z - b\right)\\ \mathbf{else}:\\ \;\;\;\;z + a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t 9.5e-251) (+ a (- z b)) (+ z a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= 9.5e-251) {
		tmp = a + (z - b);
	} else {
		tmp = z + 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 (t <= 9.5d-251) then
        tmp = a + (z - b)
    else
        tmp = z + 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 (t <= 9.5e-251) {
		tmp = a + (z - b);
	} else {
		tmp = z + a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= 9.5e-251:
		tmp = a + (z - b)
	else:
		tmp = z + a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= 9.5e-251)
		tmp = Float64(a + Float64(z - b));
	else
		tmp = Float64(z + a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= 9.5e-251)
		tmp = a + (z - b);
	else
		tmp = z + a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, 9.5e-251], N[(a + N[(z - b), $MachinePrecision]), $MachinePrecision], N[(z + a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 9.49999999999999927e-251

   1. Initial program 56.7%

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

   3. Taylor expanded in y around inf

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

      1. associate--l+ N/A

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

      2. lower-+.f64 N/A

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

      3. lower--.f64 61.2

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

   5. Simplified 61.2%

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

   if 9.49999999999999927e-251 < t

   1. Initial program 67.1%

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

   3. Taylor expanded in y around inf

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

      1. associate--l+ N/A

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

      2. lower-+.f64 N/A

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

      3. lower--.f64 56.2

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

   5. Simplified 56.2%

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

   6. Taylor expanded in b around 0

      \[\leadsto \color{blue}{a + z} \]
   7. Step-by-step derivation

      1. lower-+.f64 61.4

         \[\leadsto \color{blue}{a + z} \]

   8. Simplified 61.4%

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

4. Final simplification 61.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 9.5 \cdot 10^{-251}:\\ \;\;\;\;a + \left(z - b\right)\\ \mathbf{else}:\\ \;\;\;\;z + a\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 52.0% accurate, 4.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 5.8 \cdot 10^{+135}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;a - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (if (<= b 5.8e+135) (+ z a) (- a b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 5.8e+135) {
		tmp = z + a;
	} else {
		tmp = a - b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= 5.8d+135) then
        tmp = z + a
    else
        tmp = a - b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 5.8e+135) {
		tmp = z + a;
	} else {
		tmp = a - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 5.8e+135:
		tmp = z + a
	else:
		tmp = a - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 5.8e+135)
		tmp = Float64(z + a);
	else
		tmp = Float64(a - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 5.8e+135)
		tmp = z + a;
	else
		tmp = a - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 5.8e+135], N[(z + a), $MachinePrecision], N[(a - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 5.7999999999999997e135

   1. Initial program 62.6%

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

   3. Taylor expanded in y around inf

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

      1. associate--l+ N/A

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

      2. lower-+.f64 N/A

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

      3. lower--.f64 62.2

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

   5. Simplified 62.2%

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

   6. Taylor expanded in b around 0

      \[\leadsto \color{blue}{a + z} \]
   7. Step-by-step derivation

      1. lower-+.f64 62.1

         \[\leadsto \color{blue}{a + z} \]

   8. Simplified 62.1%

      \[\leadsto \color{blue}{a + z} \]

   if 5.7999999999999997e135 < b

   1. Initial program 53.4%

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

   3. Taylor expanded in y around inf

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

      1. associate--l+ N/A

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

      2. lower-+.f64 N/A

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

      3. lower--.f64 42.1

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

   5. Simplified 42.1%

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

   6. Taylor expanded in z around 0

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

      1. lower--.f64 40.7

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

   8. Simplified 40.7%

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

4. Final simplification 58.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 5.8 \cdot 10^{+135}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;a - b\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 51.5% accurate, 11.3× speedup

Math

\[\begin{array}{l} \\ z + a \end{array} \]

FPCore

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

C

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

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 + a
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(z + a), $MachinePrecision]

Derivation

1. Initial program 61.2%

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

3. Taylor expanded in y around inf

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

   1. associate--l+ N/A

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

   2. lower-+.f64 N/A

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

   3. lower--.f64 59.0

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

5. Simplified 59.0%

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

6. Taylor expanded in b around 0

   \[\leadsto \color{blue}{a + z} \]
7. Step-by-step derivation

   1. lower-+.f64 56.3

      \[\leadsto \color{blue}{a + z} \]

8. Simplified 56.3%

   \[\leadsto \color{blue}{a + z} \]

9. Final simplification 56.3%

   \[\leadsto z + a \]
10. Add Preprocessing

Alternative 14: 13.2% accurate, 15.0× speedup

Math

\[\begin{array}{l} \\ -b \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := (-b)

Derivation

1. Initial program 61.2%

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

3. Taylor expanded in y around inf

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

   1. associate--l+ N/A

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

   2. lower-+.f64 N/A

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

   3. lower--.f64 59.0

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

5. Simplified 59.0%

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

6. Taylor expanded in b around inf

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

   1. mul-1-neg N/A

      \[\leadsto \color{blue}{\mathsf{neg}\left(b\right)} \]

   2. lower-neg.f64 10.7

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

8. Simplified 10.7%

   \[\leadsto \color{blue}{-b} \]
9. Add Preprocessing

Developer Target 1: 82.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + t\right) + y\\ t_2 := \left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b\\ t_3 := \frac{t\_2}{t\_1}\\ t_4 := \left(z + a\right) - b\\ \mathbf{if}\;t\_3 < -3.5813117084150564 \cdot 10^{+153}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t\_3 < 1.2285964308315609 \cdot 10^{+82}:\\ \;\;\;\;\frac{1}{\frac{t\_1}{t\_2}}\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ x t) y))
        (t_2 (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)))
        (t_3 (/ t_2 t_1))
        (t_4 (- (+ z a) b)))
   (if (< t_3 -3.5813117084150564e+153)
     t_4
     (if (< t_3 1.2285964308315609e+82) (/ 1.0 (/ t_1 t_2)) t_4))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + t) + y;
	double t_2 = (((x + y) * z) + ((t + y) * a)) - (y * b);
	double t_3 = t_2 / t_1;
	double t_4 = (z + a) - b;
	double tmp;
	if (t_3 < -3.5813117084150564e+153) {
		tmp = t_4;
	} else if (t_3 < 1.2285964308315609e+82) {
		tmp = 1.0 / (t_1 / t_2);
	} else {
		tmp = t_4;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = (x + t) + y
    t_2 = (((x + y) * z) + ((t + y) * a)) - (y * b)
    t_3 = t_2 / t_1
    t_4 = (z + a) - b
    if (t_3 < (-3.5813117084150564d+153)) then
        tmp = t_4
    else if (t_3 < 1.2285964308315609d+82) then
        tmp = 1.0d0 / (t_1 / t_2)
    else
        tmp = t_4
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + t) + y;
	double t_2 = (((x + y) * z) + ((t + y) * a)) - (y * b);
	double t_3 = t_2 / t_1;
	double t_4 = (z + a) - b;
	double tmp;
	if (t_3 < -3.5813117084150564e+153) {
		tmp = t_4;
	} else if (t_3 < 1.2285964308315609e+82) {
		tmp = 1.0 / (t_1 / t_2);
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + t) + y
	t_2 = (((x + y) * z) + ((t + y) * a)) - (y * b)
	t_3 = t_2 / t_1
	t_4 = (z + a) - b
	tmp = 0
	if t_3 < -3.5813117084150564e+153:
		tmp = t_4
	elif t_3 < 1.2285964308315609e+82:
		tmp = 1.0 / (t_1 / t_2)
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + t) + y)
	t_2 = Float64(Float64(Float64(Float64(x + y) * z) + Float64(Float64(t + y) * a)) - Float64(y * b))
	t_3 = Float64(t_2 / t_1)
	t_4 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (t_3 < -3.5813117084150564e+153)
		tmp = t_4;
	elseif (t_3 < 1.2285964308315609e+82)
		tmp = Float64(1.0 / Float64(t_1 / t_2));
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + t) + y;
	t_2 = (((x + y) * z) + ((t + y) * a)) - (y * b);
	t_3 = t_2 / t_1;
	t_4 = (z + a) - b;
	tmp = 0.0;
	if (t_3 < -3.5813117084150564e+153)
		tmp = t_4;
	elseif (t_3 < 1.2285964308315609e+82)
		tmp = 1.0 / (t_1 / t_2);
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + t), $MachinePrecision] + y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + N[(N[(t + y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 / t$95$1), $MachinePrecision]}, Block[{t$95$4 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[Less[t$95$3, -3.5813117084150564e+153], t$95$4, If[Less[t$95$3, 1.2285964308315609e+82], N[(1.0 / N[(t$95$1 / t$95$2), $MachinePrecision]), $MachinePrecision], t$95$4]]]]]]

Reproduce

herbie shell --seed 2024207 
(FPCore (x y z t a b)
  :name "AI.Clustering.Hierarchical.Internal:ward from clustering-0.2.1"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)) -3581311708415056400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (+ z a) b) (if (< (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)) 12285964308315609000000000000000000000000000000000000000000000000000000000000000000) (/ 1 (/ (+ (+ x t) y) (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)))) (- (+ z a) b))))

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