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

Percentage Accurate: 61.2% → 97.6%

Time: 16.1s

Alternatives: 15

Speedup: 0.7×

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: 61.2% 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: 97.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ \mathsf{fma}\left(z, \frac{y + x}{t\_1}, a \cdot \frac{y + t}{t\_1}\right) - y \cdot \frac{b}{t\_1} \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t))))
   (- (fma z (/ (+ y x) t_1) (* a (/ (+ y t) t_1))) (* y (/ b t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	return fma(z, ((y + x) / t_1), (a * ((y + t) / t_1))) - (y * (b / t_1));
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	return Float64(fma(z, Float64(Float64(y + x) / t_1), Float64(a * Float64(Float64(y + t) / t_1))) - Float64(y * Float64(b / t_1)))
end

Wolfram

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

Derivation

1. Initial program 61.9%

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

3. Taylor expanded in b around 0 61.9%

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

   1. mul-1-neg 61.9%

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

   2. +-commutative 61.9%

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

   3. unsub-neg 61.9%

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

   4. +-commutative 61.9%

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

   5. associate-/l* 74.0%

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

   6. fma-define 74.0%

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

   7. +-commutative 74.0%

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

   8. associate-+r+ 74.0%

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

   9. associate-/l* 86.6%

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

   10. associate-+r+ 86.6%

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

5. Simplified 97.1%

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

6. Final simplification 97.1%

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

Alternative 2: 90.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y + t\right)\\ t_2 := y + \left(x + t\right)\\ t_3 := \frac{\left(z \cdot \left(y + x\right) + t\_1\right) - y \cdot b}{t\_2}\\ t_4 := y \cdot \frac{b}{t\_2}\\ \mathbf{if}\;t\_3 \leq -\infty:\\ \;\;\;\;\left(a + y \cdot \frac{z}{y + t}\right) - t\_4\\ \mathbf{elif}\;t\_3 \leq 10^{+299}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y + x, z, t\_1\right) - y \cdot b}{x + \left(y + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a \cdot \frac{y}{y + x}\right) - t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (+ y t)))
        (t_2 (+ y (+ x t)))
        (t_3 (/ (- (+ (* z (+ y x)) t_1) (* y b)) t_2))
        (t_4 (* y (/ b t_2))))
   (if (<= t_3 (- INFINITY))
     (- (+ a (* y (/ z (+ y t)))) t_4)
     (if (<= t_3 1e+299)
       (/ (- (fma (+ y x) z t_1) (* y b)) (+ x (+ y t)))
       (- (+ z (* a (/ y (+ y x)))) t_4)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (y + t);
	double t_2 = y + (x + t);
	double t_3 = (((z * (y + x)) + t_1) - (y * b)) / t_2;
	double t_4 = y * (b / t_2);
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = (a + (y * (z / (y + t)))) - t_4;
	} else if (t_3 <= 1e+299) {
		tmp = (fma((y + x), z, t_1) - (y * b)) / (x + (y + t));
	} else {
		tmp = (z + (a * (y / (y + x)))) - t_4;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(y + t))
	t_2 = Float64(y + Float64(x + t))
	t_3 = Float64(Float64(Float64(Float64(z * Float64(y + x)) + t_1) - Float64(y * b)) / t_2)
	t_4 = Float64(y * Float64(b / t_2))
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = Float64(Float64(a + Float64(y * Float64(z / Float64(y + t)))) - t_4);
	elseif (t_3 <= 1e+299)
		tmp = Float64(Float64(fma(Float64(y + x), z, t_1) - Float64(y * b)) / Float64(x + Float64(y + t)));
	else
		tmp = Float64(Float64(z + Float64(a * Float64(y / Float64(y + x)))) - t_4);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(N[(z * N[(y + x), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(y * N[(b / t$95$2), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], N[(N[(a + N[(y * N[(z / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$4), $MachinePrecision], If[LessEqual[t$95$3, 1e+299], N[(N[(N[(N[(y + x), $MachinePrecision] * z + t$95$1), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z + N[(a * N[(y / N[(y + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$4), $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 6.3%

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

   3. Taylor expanded in b around 0 6.3%

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

      1. mul-1-neg 6.3%

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

      2. +-commutative 6.3%

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

      3. unsub-neg 6.3%

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

      4. +-commutative 6.3%

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

      5. associate-/l* 45.0%

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

      6. fma-define 45.0%

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

      7. +-commutative 45.0%

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

      8. associate-+r+ 45.0%

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

      9. associate-/l* 70.5%

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

      10. associate-+r+ 70.5%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in x around 0 46.4%

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

      1. associate-/l* 83.3%

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

      2. +-commutative 83.3%

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

   8. Simplified 83.3%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1.0000000000000001e299

   1. Initial program 99.8%

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

      1. fma-define 99.8%

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

      2. +-commutative 99.8%

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

      3. associate-+l+ 99.8%

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

      4. +-commutative 99.8%

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

   3. Simplified 99.8%

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

   if 1.0000000000000001e299 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 5.0%

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

   3. Taylor expanded in b around 0 5.0%

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

      1. mul-1-neg 5.0%

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

      2. +-commutative 5.0%

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

      3. unsub-neg 5.0%

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

      4. +-commutative 5.0%

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

      5. associate-/l* 26.6%

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

      6. fma-define 26.6%

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

      7. +-commutative 26.6%

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

      8. associate-+r+ 26.6%

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

      9. associate-/l* 63.2%

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

      10. associate-+r+ 63.2%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in t around 0 50.2%

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

      1. +-commutative 50.2%

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

      2. associate-/l* 78.2%

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

      3. +-commutative 78.2%

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

   8. Simplified 78.2%

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

4. Final simplification 92.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z \cdot \left(y + x\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty:\\ \;\;\;\;\left(a + y \cdot \frac{z}{y + t}\right) - y \cdot \frac{b}{y + \left(x + t\right)}\\ \mathbf{elif}\;\frac{\left(z \cdot \left(y + x\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 10^{+299}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y + x, z, a \cdot \left(y + t\right)\right) - y \cdot b}{x + \left(y + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a \cdot \frac{y}{y + x}\right) - y \cdot \frac{b}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 90.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \frac{\left(z \cdot \left(y + x\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{t\_1}\\ t_3 := y \cdot \frac{b}{t\_1}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;\left(a + y \cdot \frac{z}{y + t}\right) - t\_3\\ \mathbf{elif}\;t\_2 \leq 10^{+299}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\left(z + a \cdot \frac{y}{y + x}\right) - t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t)))
        (t_2 (/ (- (+ (* z (+ y x)) (* a (+ y t))) (* y b)) t_1))
        (t_3 (* y (/ b t_1))))
   (if (<= t_2 (- INFINITY))
     (- (+ a (* y (/ z (+ y t)))) t_3)
     (if (<= t_2 1e+299) t_2 (- (+ z (* a (/ y (+ y x)))) t_3)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = (((z * (y + x)) + (a * (y + t))) - (y * b)) / t_1;
	double t_3 = y * (b / t_1);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = (a + (y * (z / (y + t)))) - t_3;
	} else if (t_2 <= 1e+299) {
		tmp = t_2;
	} else {
		tmp = (z + (a * (y / (y + x)))) - t_3;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = (((z * (y + x)) + (a * (y + t))) - (y * b)) / t_1;
	double t_3 = y * (b / t_1);
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = (a + (y * (z / (y + t)))) - t_3;
	} else if (t_2 <= 1e+299) {
		tmp = t_2;
	} else {
		tmp = (z + (a * (y / (y + x)))) - t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = (((z * (y + x)) + (a * (y + t))) - (y * b)) / t_1
	t_3 = y * (b / t_1)
	tmp = 0
	if t_2 <= -math.inf:
		tmp = (a + (y * (z / (y + t)))) - t_3
	elif t_2 <= 1e+299:
		tmp = t_2
	else:
		tmp = (z + (a * (y / (y + x)))) - t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(Float64(Float64(Float64(z * Float64(y + x)) + Float64(a * Float64(y + t))) - Float64(y * b)) / t_1)
	t_3 = Float64(y * Float64(b / t_1))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(Float64(a + Float64(y * Float64(z / Float64(y + t)))) - t_3);
	elseif (t_2 <= 1e+299)
		tmp = t_2;
	else
		tmp = Float64(Float64(z + Float64(a * Float64(y / Float64(y + x)))) - t_3);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	t_2 = (((z * (y + x)) + (a * (y + t))) - (y * b)) / t_1;
	t_3 = y * (b / t_1);
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = (a + (y * (z / (y + t)))) - t_3;
	elseif (t_2 <= 1e+299)
		tmp = t_2;
	else
		tmp = (z + (a * (y / (y + x)))) - t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(z * N[(y + x), $MachinePrecision]), $MachinePrecision] + N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(y * N[(b / t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(N[(a + N[(y * N[(z / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$3), $MachinePrecision], If[LessEqual[t$95$2, 1e+299], t$95$2, N[(N[(z + N[(a * N[(y / N[(y + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$3), $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 6.3%

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

   3. Taylor expanded in b around 0 6.3%

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

      1. mul-1-neg 6.3%

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

      2. +-commutative 6.3%

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

      3. unsub-neg 6.3%

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

      4. +-commutative 6.3%

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

      5. associate-/l* 45.0%

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

      6. fma-define 45.0%

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

      7. +-commutative 45.0%

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

      8. associate-+r+ 45.0%

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

      9. associate-/l* 70.5%

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

      10. associate-+r+ 70.5%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in x around 0 46.4%

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

      1. associate-/l* 83.3%

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

      2. +-commutative 83.3%

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

   8. Simplified 83.3%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1.0000000000000001e299

   1. Initial program 99.8%

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

   if 1.0000000000000001e299 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 5.0%

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

   3. Taylor expanded in b around 0 5.0%

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

      1. mul-1-neg 5.0%

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

      2. +-commutative 5.0%

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

      3. unsub-neg 5.0%

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

      4. +-commutative 5.0%

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

      5. associate-/l* 26.6%

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

      6. fma-define 26.6%

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

      7. +-commutative 26.6%

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

      8. associate-+r+ 26.6%

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

      9. associate-/l* 63.2%

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

      10. associate-+r+ 63.2%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in t around 0 50.2%

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

      1. +-commutative 50.2%

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

      2. associate-/l* 78.2%

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

      3. +-commutative 78.2%

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

   8. Simplified 78.2%

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

4. Final simplification 92.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z \cdot \left(y + x\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty:\\ \;\;\;\;\left(a + y \cdot \frac{z}{y + t}\right) - y \cdot \frac{b}{y + \left(x + t\right)}\\ \mathbf{elif}\;\frac{\left(z \cdot \left(y + x\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 10^{+299}:\\ \;\;\;\;\frac{\left(z \cdot \left(y + x\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a \cdot \frac{y}{y + x}\right) - y \cdot \frac{b}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 72.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ \mathbf{if}\;x \leq -8.2 \cdot 10^{+173}:\\ \;\;\;\;z \cdot \frac{y + x}{t\_1}\\ \mathbf{elif}\;x \leq -1.1 \cdot 10^{+76} \lor \neg \left(x \leq -6.5 \cdot 10^{+38}\right) \land x \leq 1.5 \cdot 10^{+65}:\\ \;\;\;\;\left(a + y \cdot \frac{z}{y + t}\right) - b \cdot \frac{y}{y + t}\\ \mathbf{else}:\\ \;\;\;\;z - y \cdot \frac{b}{t\_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t))))
   (if (<= x -8.2e+173)
     (* z (/ (+ y x) t_1))
     (if (or (<= x -1.1e+76) (and (not (<= x -6.5e+38)) (<= x 1.5e+65)))
       (- (+ a (* y (/ z (+ y t)))) (* b (/ y (+ y t))))
       (- z (* y (/ b t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double tmp;
	if (x <= -8.2e+173) {
		tmp = z * ((y + x) / t_1);
	} else if ((x <= -1.1e+76) || (!(x <= -6.5e+38) && (x <= 1.5e+65))) {
		tmp = (a + (y * (z / (y + t)))) - (b * (y / (y + t)));
	} else {
		tmp = z - (y * (b / t_1));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y + (x + t)
    if (x <= (-8.2d+173)) then
        tmp = z * ((y + x) / t_1)
    else if ((x <= (-1.1d+76)) .or. (.not. (x <= (-6.5d+38))) .and. (x <= 1.5d+65)) then
        tmp = (a + (y * (z / (y + t)))) - (b * (y / (y + t)))
    else
        tmp = z - (y * (b / t_1))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double tmp;
	if (x <= -8.2e+173) {
		tmp = z * ((y + x) / t_1);
	} else if ((x <= -1.1e+76) || (!(x <= -6.5e+38) && (x <= 1.5e+65))) {
		tmp = (a + (y * (z / (y + t)))) - (b * (y / (y + t)));
	} else {
		tmp = z - (y * (b / t_1));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	tmp = 0
	if x <= -8.2e+173:
		tmp = z * ((y + x) / t_1)
	elif (x <= -1.1e+76) or (not (x <= -6.5e+38) and (x <= 1.5e+65)):
		tmp = (a + (y * (z / (y + t)))) - (b * (y / (y + t)))
	else:
		tmp = z - (y * (b / t_1))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	tmp = 0.0
	if (x <= -8.2e+173)
		tmp = Float64(z * Float64(Float64(y + x) / t_1));
	elseif ((x <= -1.1e+76) || (!(x <= -6.5e+38) && (x <= 1.5e+65)))
		tmp = Float64(Float64(a + Float64(y * Float64(z / Float64(y + t)))) - Float64(b * Float64(y / Float64(y + t))));
	else
		tmp = Float64(z - Float64(y * Float64(b / t_1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	tmp = 0.0;
	if (x <= -8.2e+173)
		tmp = z * ((y + x) / t_1);
	elseif ((x <= -1.1e+76) || (~((x <= -6.5e+38)) && (x <= 1.5e+65)))
		tmp = (a + (y * (z / (y + t)))) - (b * (y / (y + t)));
	else
		tmp = z - (y * (b / t_1));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -8.2e+173], N[(z * N[(N[(y + x), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, -1.1e+76], And[N[Not[LessEqual[x, -6.5e+38]], $MachinePrecision], LessEqual[x, 1.5e+65]]], N[(N[(a + N[(y * N[(z / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(y / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z - N[(y * N[(b / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -8.19999999999999951e173

   1. Initial program 50.6%

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

   3. Taylor expanded in z around inf 29.6%

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

      1. associate-/l* 70.6%

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

      2. +-commutative 70.6%

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

      3. associate-+r+ 70.6%

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

   5. Simplified 70.6%

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

   if -8.19999999999999951e173 < x < -1.1e76 or -6.5e38 < x < 1.5000000000000001e65

   1. Initial program 67.8%

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

   3. Taylor expanded in b around 0 67.8%

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

      1. mul-1-neg 67.8%

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

      2. +-commutative 67.8%

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

      3. unsub-neg 67.8%

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

      4. +-commutative 67.8%

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

      5. associate-/l* 74.7%

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

      6. fma-define 74.7%

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

      7. +-commutative 74.7%

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

      8. associate-+r+ 74.7%

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

      9. associate-/l* 86.1%

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

      10. associate-+r+ 86.1%

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

   5. Simplified 96.5%

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

   6. Taylor expanded in x around 0 74.2%

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

      1. associate-/l* 86.1%

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

      2. +-commutative 86.1%

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

   8. Simplified 86.1%

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

   9. Taylor expanded in x around 0 73.9%

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

       1. associate-/l* 87.8%

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

       2. +-commutative 87.8%

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

   11. Simplified 87.8%

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

   if -1.1e76 < x < -6.5e38 or 1.5000000000000001e65 < x

   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 b around 0 51.3%

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

      1. mul-1-neg 51.3%

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

      2. +-commutative 51.3%

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

      3. unsub-neg 51.3%

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

      4. +-commutative 51.3%

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

      5. associate-/l* 69.2%

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

      6. fma-define 69.2%

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

      7. +-commutative 69.2%

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

      8. associate-+r+ 69.2%

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

      9. associate-/l* 85.9%

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

      10. associate-+r+ 85.9%

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

   5. Simplified 98.4%

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

   6. Taylor expanded in x around inf 65.6%

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

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.2 \cdot 10^{+173}:\\ \;\;\;\;z \cdot \frac{y + x}{y + \left(x + t\right)}\\ \mathbf{elif}\;x \leq -1.1 \cdot 10^{+76} \lor \neg \left(x \leq -6.5 \cdot 10^{+38}\right) \land x \leq 1.5 \cdot 10^{+65}:\\ \;\;\;\;\left(a + y \cdot \frac{z}{y + t}\right) - b \cdot \frac{y}{y + t}\\ \mathbf{else}:\\ \;\;\;\;z - y \cdot \frac{b}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 72.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a + y \cdot \frac{z}{y + t}\right) - b \cdot \frac{y}{y + t}\\ t_2 := y + \left(x + t\right)\\ \mathbf{if}\;x \leq -4 \cdot 10^{+173}:\\ \;\;\;\;z \cdot \frac{y + x}{t\_2}\\ \mathbf{elif}\;x \leq -2.25 \cdot 10^{+74}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -6.5 \cdot 10^{+38}:\\ \;\;\;\;\frac{\left(z \cdot \left(y + x\right) + y \cdot a\right) - y \cdot b}{y + x}\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{+65}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;z - y \cdot \frac{b}{t\_2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ a (* y (/ z (+ y t)))) (* b (/ y (+ y t)))))
        (t_2 (+ y (+ x t))))
   (if (<= x -4e+173)
     (* z (/ (+ y x) t_2))
     (if (<= x -2.25e+74)
       t_1
       (if (<= x -6.5e+38)
         (/ (- (+ (* z (+ y x)) (* y a)) (* y b)) (+ y x))
         (if (<= x 1.35e+65) t_1 (- z (* y (/ b t_2)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a + (y * (z / (y + t)))) - (b * (y / (y + t)));
	double t_2 = y + (x + t);
	double tmp;
	if (x <= -4e+173) {
		tmp = z * ((y + x) / t_2);
	} else if (x <= -2.25e+74) {
		tmp = t_1;
	} else if (x <= -6.5e+38) {
		tmp = (((z * (y + x)) + (y * a)) - (y * b)) / (y + x);
	} else if (x <= 1.35e+65) {
		tmp = t_1;
	} else {
		tmp = z - (y * (b / t_2));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (a + (y * (z / (y + t)))) - (b * (y / (y + t)))
    t_2 = y + (x + t)
    if (x <= (-4d+173)) then
        tmp = z * ((y + x) / t_2)
    else if (x <= (-2.25d+74)) then
        tmp = t_1
    else if (x <= (-6.5d+38)) then
        tmp = (((z * (y + x)) + (y * a)) - (y * b)) / (y + x)
    else if (x <= 1.35d+65) then
        tmp = t_1
    else
        tmp = z - (y * (b / t_2))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a + (y * (z / (y + t)))) - (b * (y / (y + t)));
	double t_2 = y + (x + t);
	double tmp;
	if (x <= -4e+173) {
		tmp = z * ((y + x) / t_2);
	} else if (x <= -2.25e+74) {
		tmp = t_1;
	} else if (x <= -6.5e+38) {
		tmp = (((z * (y + x)) + (y * a)) - (y * b)) / (y + x);
	} else if (x <= 1.35e+65) {
		tmp = t_1;
	} else {
		tmp = z - (y * (b / t_2));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a + (y * (z / (y + t)))) - (b * (y / (y + t)))
	t_2 = y + (x + t)
	tmp = 0
	if x <= -4e+173:
		tmp = z * ((y + x) / t_2)
	elif x <= -2.25e+74:
		tmp = t_1
	elif x <= -6.5e+38:
		tmp = (((z * (y + x)) + (y * a)) - (y * b)) / (y + x)
	elif x <= 1.35e+65:
		tmp = t_1
	else:
		tmp = z - (y * (b / t_2))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a + Float64(y * Float64(z / Float64(y + t)))) - Float64(b * Float64(y / Float64(y + t))))
	t_2 = Float64(y + Float64(x + t))
	tmp = 0.0
	if (x <= -4e+173)
		tmp = Float64(z * Float64(Float64(y + x) / t_2));
	elseif (x <= -2.25e+74)
		tmp = t_1;
	elseif (x <= -6.5e+38)
		tmp = Float64(Float64(Float64(Float64(z * Float64(y + x)) + Float64(y * a)) - Float64(y * b)) / Float64(y + x));
	elseif (x <= 1.35e+65)
		tmp = t_1;
	else
		tmp = Float64(z - Float64(y * Float64(b / t_2)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a + (y * (z / (y + t)))) - (b * (y / (y + t)));
	t_2 = y + (x + t);
	tmp = 0.0;
	if (x <= -4e+173)
		tmp = z * ((y + x) / t_2);
	elseif (x <= -2.25e+74)
		tmp = t_1;
	elseif (x <= -6.5e+38)
		tmp = (((z * (y + x)) + (y * a)) - (y * b)) / (y + x);
	elseif (x <= 1.35e+65)
		tmp = t_1;
	else
		tmp = z - (y * (b / t_2));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a + N[(y * N[(z / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(y / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4e+173], N[(z * N[(N[(y + x), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.25e+74], t$95$1, If[LessEqual[x, -6.5e+38], N[(N[(N[(N[(z * N[(y + x), $MachinePrecision]), $MachinePrecision] + N[(y * a), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.35e+65], t$95$1, N[(z - N[(y * N[(b / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -4.0000000000000001e173

   1. Initial program 50.6%

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

   3. Taylor expanded in z around inf 29.6%

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

      1. associate-/l* 70.6%

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

      2. +-commutative 70.6%

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

      3. associate-+r+ 70.6%

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

   5. Simplified 70.6%

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

   if -4.0000000000000001e173 < x < -2.25e74 or -6.5e38 < x < 1.35000000000000009e65

   1. Initial program 67.8%

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

   3. Taylor expanded in b around 0 67.8%

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

      1. mul-1-neg 67.8%

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

      2. +-commutative 67.8%

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

      3. unsub-neg 67.8%

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

      4. +-commutative 67.8%

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

      5. associate-/l* 74.7%

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

      6. fma-define 74.7%

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

      7. +-commutative 74.7%

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

      8. associate-+r+ 74.7%

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

      9. associate-/l* 86.1%

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

      10. associate-+r+ 86.1%

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

   5. Simplified 96.5%

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

   6. Taylor expanded in x around 0 74.2%

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

      1. associate-/l* 86.1%

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

      2. +-commutative 86.1%

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

   8. Simplified 86.1%

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

   9. Taylor expanded in x around 0 73.9%

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

       1. associate-/l* 87.8%

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

       2. +-commutative 87.8%

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

   11. Simplified 87.8%

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

   if -2.25e74 < x < -6.5e38

   1. Initial program 92.6%

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

   3. Taylor expanded in t around 0 86.7%

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

   if 1.35000000000000009e65 < x

   1. Initial program 41.6%

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

   3. Taylor expanded in b around 0 41.6%

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

      1. mul-1-neg 41.6%

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

      2. +-commutative 41.6%

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

      3. unsub-neg 41.6%

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

      4. +-commutative 41.6%

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

      5. associate-/l* 62.0%

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

      6. fma-define 62.0%

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

      7. +-commutative 62.0%

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

      8. associate-+r+ 62.0%

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

      9. associate-/l* 82.6%

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

      10. associate-+r+ 82.6%

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

   5. Simplified 98.1%

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

   6. Taylor expanded in x around inf 64.5%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{+173}:\\ \;\;\;\;z \cdot \frac{y + x}{y + \left(x + t\right)}\\ \mathbf{elif}\;x \leq -2.25 \cdot 10^{+74}:\\ \;\;\;\;\left(a + y \cdot \frac{z}{y + t}\right) - b \cdot \frac{y}{y + t}\\ \mathbf{elif}\;x \leq -6.5 \cdot 10^{+38}:\\ \;\;\;\;\frac{\left(z \cdot \left(y + x\right) + y \cdot a\right) - y \cdot b}{y + x}\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{+65}:\\ \;\;\;\;\left(a + y \cdot \frac{z}{y + t}\right) - b \cdot \frac{y}{y + t}\\ \mathbf{else}:\\ \;\;\;\;z - y \cdot \frac{b}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 57.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := a \cdot \frac{y + t}{t\_1}\\ t_3 := \left(z + a\right) - b\\ t_4 := z \cdot \frac{y + x}{t\_1}\\ \mathbf{if}\;y \leq -1.15 \cdot 10^{-42}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-236}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-126}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;y \leq 9.4 \cdot 10^{+21}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{+70}:\\ \;\;\;\;t\_4\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t)))
        (t_2 (* a (/ (+ y t) t_1)))
        (t_3 (- (+ z a) b))
        (t_4 (* z (/ (+ y x) t_1))))
   (if (<= y -1.15e-42)
     t_3
     (if (<= y 1.4e-236)
       t_2
       (if (<= y 1.15e-126)
         t_4
         (if (<= y 9.4e+21) t_2 (if (<= y 4.6e+70) t_4 t_3)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = a * ((y + t) / t_1);
	double t_3 = (z + a) - b;
	double t_4 = z * ((y + x) / t_1);
	double tmp;
	if (y <= -1.15e-42) {
		tmp = t_3;
	} else if (y <= 1.4e-236) {
		tmp = t_2;
	} else if (y <= 1.15e-126) {
		tmp = t_4;
	} else if (y <= 9.4e+21) {
		tmp = t_2;
	} else if (y <= 4.6e+70) {
		tmp = t_4;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = y + (x + t)
    t_2 = a * ((y + t) / t_1)
    t_3 = (z + a) - b
    t_4 = z * ((y + x) / t_1)
    if (y <= (-1.15d-42)) then
        tmp = t_3
    else if (y <= 1.4d-236) then
        tmp = t_2
    else if (y <= 1.15d-126) then
        tmp = t_4
    else if (y <= 9.4d+21) then
        tmp = t_2
    else if (y <= 4.6d+70) then
        tmp = t_4
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = a * ((y + t) / t_1);
	double t_3 = (z + a) - b;
	double t_4 = z * ((y + x) / t_1);
	double tmp;
	if (y <= -1.15e-42) {
		tmp = t_3;
	} else if (y <= 1.4e-236) {
		tmp = t_2;
	} else if (y <= 1.15e-126) {
		tmp = t_4;
	} else if (y <= 9.4e+21) {
		tmp = t_2;
	} else if (y <= 4.6e+70) {
		tmp = t_4;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = a * ((y + t) / t_1)
	t_3 = (z + a) - b
	t_4 = z * ((y + x) / t_1)
	tmp = 0
	if y <= -1.15e-42:
		tmp = t_3
	elif y <= 1.4e-236:
		tmp = t_2
	elif y <= 1.15e-126:
		tmp = t_4
	elif y <= 9.4e+21:
		tmp = t_2
	elif y <= 4.6e+70:
		tmp = t_4
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(a * Float64(Float64(y + t) / t_1))
	t_3 = Float64(Float64(z + a) - b)
	t_4 = Float64(z * Float64(Float64(y + x) / t_1))
	tmp = 0.0
	if (y <= -1.15e-42)
		tmp = t_3;
	elseif (y <= 1.4e-236)
		tmp = t_2;
	elseif (y <= 1.15e-126)
		tmp = t_4;
	elseif (y <= 9.4e+21)
		tmp = t_2;
	elseif (y <= 4.6e+70)
		tmp = t_4;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	t_2 = a * ((y + t) / t_1);
	t_3 = (z + a) - b;
	t_4 = z * ((y + x) / t_1);
	tmp = 0.0;
	if (y <= -1.15e-42)
		tmp = t_3;
	elseif (y <= 1.4e-236)
		tmp = t_2;
	elseif (y <= 1.15e-126)
		tmp = t_4;
	elseif (y <= 9.4e+21)
		tmp = t_2;
	elseif (y <= 4.6e+70)
		tmp = t_4;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(y + t), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, Block[{t$95$4 = N[(z * N[(N[(y + x), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.15e-42], t$95$3, If[LessEqual[y, 1.4e-236], t$95$2, If[LessEqual[y, 1.15e-126], t$95$4, If[LessEqual[y, 9.4e+21], t$95$2, If[LessEqual[y, 4.6e+70], t$95$4, t$95$3]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.15000000000000002e-42 or 4.59999999999999987e70 < y

   1. Initial program 45.9%

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

   3. Taylor expanded in y around inf 72.6%

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

   if -1.15000000000000002e-42 < y < 1.39999999999999993e-236 or 1.15000000000000005e-126 < y < 9.4e21

   1. Initial program 79.4%

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

   3. Taylor expanded in a around inf 45.4%

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

      1. associate-/l* 57.6%

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

      2. associate-+r+ 57.6%

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

   5. Simplified 57.6%

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

   if 1.39999999999999993e-236 < y < 1.15000000000000005e-126 or 9.4e21 < y < 4.59999999999999987e70

   1. Initial program 78.7%

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

   3. Taylor expanded in z around inf 49.1%

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

      1. associate-/l* 70.1%

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

      2. +-commutative 70.1%

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

      3. associate-+r+ 70.1%

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

   5. Simplified 70.1%

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

4. Final simplification 66.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{-42}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-236}:\\ \;\;\;\;a \cdot \frac{y + t}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-126}:\\ \;\;\;\;z \cdot \frac{y + x}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq 9.4 \cdot 10^{+21}:\\ \;\;\;\;a \cdot \frac{y + t}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{+70}:\\ \;\;\;\;z \cdot \frac{y + x}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 63.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -3.1 \cdot 10^{-41}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-115}:\\ \;\;\;\;\frac{t \cdot a + z \cdot x}{x + t}\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-55} \lor \neg \left(y \leq 1.9 \cdot 10^{-6}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot a - y \cdot b}{y + \left(x + t\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= y -3.1e-41)
     t_1
     (if (<= y 2.5e-115)
       (/ (+ (* t a) (* z x)) (+ x t))
       (if (or (<= y 8.2e-55) (not (<= y 1.9e-6)))
         t_1
         (/ (- (* t a) (* y b)) (+ y (+ x t))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -3.1e-41) {
		tmp = t_1;
	} else if (y <= 2.5e-115) {
		tmp = ((t * a) + (z * x)) / (x + t);
	} else if ((y <= 8.2e-55) || !(y <= 1.9e-6)) {
		tmp = t_1;
	} else {
		tmp = ((t * a) - (y * b)) / (y + (x + t));
	}
	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 + a) - b
    if (y <= (-3.1d-41)) then
        tmp = t_1
    else if (y <= 2.5d-115) then
        tmp = ((t * a) + (z * x)) / (x + t)
    else if ((y <= 8.2d-55) .or. (.not. (y <= 1.9d-6))) then
        tmp = t_1
    else
        tmp = ((t * a) - (y * b)) / (y + (x + t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -3.1e-41) {
		tmp = t_1;
	} else if (y <= 2.5e-115) {
		tmp = ((t * a) + (z * x)) / (x + t);
	} else if ((y <= 8.2e-55) || !(y <= 1.9e-6)) {
		tmp = t_1;
	} else {
		tmp = ((t * a) - (y * b)) / (y + (x + t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	tmp = 0
	if y <= -3.1e-41:
		tmp = t_1
	elif y <= 2.5e-115:
		tmp = ((t * a) + (z * x)) / (x + t)
	elif (y <= 8.2e-55) or not (y <= 1.9e-6):
		tmp = t_1
	else:
		tmp = ((t * a) - (y * b)) / (y + (x + t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -3.1e-41)
		tmp = t_1;
	elseif (y <= 2.5e-115)
		tmp = Float64(Float64(Float64(t * a) + Float64(z * x)) / Float64(x + t));
	elseif ((y <= 8.2e-55) || !(y <= 1.9e-6))
		tmp = t_1;
	else
		tmp = Float64(Float64(Float64(t * a) - Float64(y * b)) / Float64(y + Float64(x + t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	tmp = 0.0;
	if (y <= -3.1e-41)
		tmp = t_1;
	elseif (y <= 2.5e-115)
		tmp = ((t * a) + (z * x)) / (x + t);
	elseif ((y <= 8.2e-55) || ~((y <= 1.9e-6)))
		tmp = t_1;
	else
		tmp = ((t * a) - (y * b)) / (y + (x + t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -3.1e-41], t$95$1, If[LessEqual[y, 2.5e-115], N[(N[(N[(t * a), $MachinePrecision] + N[(z * x), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 8.2e-55], N[Not[LessEqual[y, 1.9e-6]], $MachinePrecision]], t$95$1, N[(N[(N[(t * a), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.10000000000000001e-41 or 2.5000000000000001e-115 < y < 8.1999999999999996e-55 or 1.9e-6 < y

   1. Initial program 47.1%

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

   3. Taylor expanded in y around inf 70.9%

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

   if -3.10000000000000001e-41 < y < 2.5000000000000001e-115

   1. Initial program 85.6%

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

   3. Taylor expanded in y around 0 71.0%

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

   if 8.1999999999999996e-55 < y < 1.9e-6

   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. Taylor expanded in t around inf 81.0%

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

4. Final simplification 71.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{-41}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-115}:\\ \;\;\;\;\frac{t \cdot a + z \cdot x}{x + t}\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-55} \lor \neg \left(y \leq 1.9 \cdot 10^{-6}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot a - y \cdot b}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 63.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{-42} \lor \neg \left(y \leq 2.5 \cdot 10^{-119} \lor \neg \left(y \leq 2.7 \cdot 10^{-65}\right) \land y \leq 1900\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot a + z \cdot x}{x + t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -8e-42)
         (not (or (<= y 2.5e-119) (and (not (<= y 2.7e-65)) (<= y 1900.0)))))
   (- (+ z a) b)
   (/ (+ (* t a) (* z x)) (+ x t))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -8e-42) || !((y <= 2.5e-119) || (!(y <= 2.7e-65) && (y <= 1900.0)))) {
		tmp = (z + a) - b;
	} else {
		tmp = ((t * a) + (z * x)) / (x + t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-8d-42)) .or. (.not. (y <= 2.5d-119) .or. (.not. (y <= 2.7d-65)) .and. (y <= 1900.0d0))) then
        tmp = (z + a) - b
    else
        tmp = ((t * a) + (z * x)) / (x + t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -8e-42) || !((y <= 2.5e-119) || (!(y <= 2.7e-65) && (y <= 1900.0)))) {
		tmp = (z + a) - b;
	} else {
		tmp = ((t * a) + (z * x)) / (x + t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -8e-42) or not ((y <= 2.5e-119) or (not (y <= 2.7e-65) and (y <= 1900.0))):
		tmp = (z + a) - b
	else:
		tmp = ((t * a) + (z * x)) / (x + t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -8e-42) || !((y <= 2.5e-119) || (!(y <= 2.7e-65) && (y <= 1900.0))))
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(Float64(Float64(t * a) + Float64(z * x)) / Float64(x + t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -8e-42) || ~(((y <= 2.5e-119) || (~((y <= 2.7e-65)) && (y <= 1900.0)))))
		tmp = (z + a) - b;
	else
		tmp = ((t * a) + (z * x)) / (x + t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -8e-42], N[Not[Or[LessEqual[y, 2.5e-119], And[N[Not[LessEqual[y, 2.7e-65]], $MachinePrecision], LessEqual[y, 1900.0]]]], $MachinePrecision]], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(N[(N[(t * a), $MachinePrecision] + N[(z * x), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.0000000000000003e-42 or 2.49999999999999996e-119 < y < 2.6999999999999999e-65 or 1900 < y

   1. Initial program 46.1%

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

   3. Taylor expanded in y around inf 70.9%

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

   if -8.0000000000000003e-42 < y < 2.49999999999999996e-119 or 2.6999999999999999e-65 < y < 1900

   1. Initial program 87.4%

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

   3. Taylor expanded in y around 0 71.1%

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

4. Final simplification 71.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{-42} \lor \neg \left(y \leq 2.5 \cdot 10^{-119} \lor \neg \left(y \leq 2.7 \cdot 10^{-65}\right) \land y \leq 1900\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot a + z \cdot x}{x + t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 56.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \frac{y + t}{y + \left(x + t\right)}\\ t_2 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -4.8 \cdot 10^{-42}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-235}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-128}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+21}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (/ (+ y t) (+ y (+ x t))))) (t_2 (- (+ z a) b)))
   (if (<= y -4.8e-42)
     t_2
     (if (<= y 3e-235) t_1 (if (<= y 5.5e-128) z (if (<= y 9e+21) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * ((y + t) / (y + (x + t)));
	double t_2 = (z + a) - b;
	double tmp;
	if (y <= -4.8e-42) {
		tmp = t_2;
	} else if (y <= 3e-235) {
		tmp = t_1;
	} else if (y <= 5.5e-128) {
		tmp = z;
	} else if (y <= 9e+21) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * ((y + t) / (y + (x + t)))
    t_2 = (z + a) - b
    if (y <= (-4.8d-42)) then
        tmp = t_2
    else if (y <= 3d-235) then
        tmp = t_1
    else if (y <= 5.5d-128) then
        tmp = z
    else if (y <= 9d+21) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * ((y + t) / (y + (x + t)));
	double t_2 = (z + a) - b;
	double tmp;
	if (y <= -4.8e-42) {
		tmp = t_2;
	} else if (y <= 3e-235) {
		tmp = t_1;
	} else if (y <= 5.5e-128) {
		tmp = z;
	} else if (y <= 9e+21) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * ((y + t) / (y + (x + t)))
	t_2 = (z + a) - b
	tmp = 0
	if y <= -4.8e-42:
		tmp = t_2
	elif y <= 3e-235:
		tmp = t_1
	elif y <= 5.5e-128:
		tmp = z
	elif y <= 9e+21:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(Float64(y + t) / Float64(y + Float64(x + t))))
	t_2 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -4.8e-42)
		tmp = t_2;
	elseif (y <= 3e-235)
		tmp = t_1;
	elseif (y <= 5.5e-128)
		tmp = z;
	elseif (y <= 9e+21)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * ((y + t) / (y + (x + t)));
	t_2 = (z + a) - b;
	tmp = 0.0;
	if (y <= -4.8e-42)
		tmp = t_2;
	elseif (y <= 3e-235)
		tmp = t_1;
	elseif (y <= 5.5e-128)
		tmp = z;
	elseif (y <= 9e+21)
		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[(a * N[(N[(y + t), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -4.8e-42], t$95$2, If[LessEqual[y, 3e-235], t$95$1, If[LessEqual[y, 5.5e-128], z, If[LessEqual[y, 9e+21], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.80000000000000005e-42 or 9e21 < y

   1. Initial program 47.0%

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

   3. Taylor expanded in y around inf 70.5%

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

   if -4.80000000000000005e-42 < y < 2.9999999999999999e-235 or 5.5000000000000004e-128 < y < 9e21

   1. Initial program 79.4%

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

   3. Taylor expanded in a around inf 45.4%

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

      1. associate-/l* 57.6%

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

      2. associate-+r+ 57.6%

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

   5. Simplified 57.6%

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

   if 2.9999999999999999e-235 < y < 5.5000000000000004e-128

   1. Initial program 86.7%

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

   3. Taylor expanded in x around inf 61.0%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{-42}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-235}:\\ \;\;\;\;a \cdot \frac{y + t}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-128}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+21}:\\ \;\;\;\;a \cdot \frac{y + t}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 62.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := a \cdot \frac{y + t}{t\_1}\\ \mathbf{if}\;a \leq -4.8 \cdot 10^{+217}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -7.2 \cdot 10^{-13}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;a \leq -5.6 \cdot 10^{-74}:\\ \;\;\;\;a - \frac{x \cdot a}{y + t}\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-33}:\\ \;\;\;\;z - y \cdot \frac{b}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t))) (t_2 (* a (/ (+ y t) t_1))))
   (if (<= a -4.8e+217)
     t_2
     (if (<= a -7.2e-13)
       (- (+ z a) b)
       (if (<= a -5.6e-74)
         (- a (/ (* x a) (+ y t)))
         (if (<= a 1.8e-33) (- z (* y (/ b t_1))) t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = a * ((y + t) / t_1);
	double tmp;
	if (a <= -4.8e+217) {
		tmp = t_2;
	} else if (a <= -7.2e-13) {
		tmp = (z + a) - b;
	} else if (a <= -5.6e-74) {
		tmp = a - ((x * a) / (y + t));
	} else if (a <= 1.8e-33) {
		tmp = z - (y * (b / t_1));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y + (x + t)
    t_2 = a * ((y + t) / t_1)
    if (a <= (-4.8d+217)) then
        tmp = t_2
    else if (a <= (-7.2d-13)) then
        tmp = (z + a) - b
    else if (a <= (-5.6d-74)) then
        tmp = a - ((x * a) / (y + t))
    else if (a <= 1.8d-33) then
        tmp = z - (y * (b / t_1))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = a * ((y + t) / t_1);
	double tmp;
	if (a <= -4.8e+217) {
		tmp = t_2;
	} else if (a <= -7.2e-13) {
		tmp = (z + a) - b;
	} else if (a <= -5.6e-74) {
		tmp = a - ((x * a) / (y + t));
	} else if (a <= 1.8e-33) {
		tmp = z - (y * (b / t_1));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = a * ((y + t) / t_1)
	tmp = 0
	if a <= -4.8e+217:
		tmp = t_2
	elif a <= -7.2e-13:
		tmp = (z + a) - b
	elif a <= -5.6e-74:
		tmp = a - ((x * a) / (y + t))
	elif a <= 1.8e-33:
		tmp = z - (y * (b / t_1))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(a * Float64(Float64(y + t) / t_1))
	tmp = 0.0
	if (a <= -4.8e+217)
		tmp = t_2;
	elseif (a <= -7.2e-13)
		tmp = Float64(Float64(z + a) - b);
	elseif (a <= -5.6e-74)
		tmp = Float64(a - Float64(Float64(x * a) / Float64(y + t)));
	elseif (a <= 1.8e-33)
		tmp = Float64(z - Float64(y * Float64(b / t_1)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	t_2 = a * ((y + t) / t_1);
	tmp = 0.0;
	if (a <= -4.8e+217)
		tmp = t_2;
	elseif (a <= -7.2e-13)
		tmp = (z + a) - b;
	elseif (a <= -5.6e-74)
		tmp = a - ((x * a) / (y + t));
	elseif (a <= 1.8e-33)
		tmp = z - (y * (b / t_1));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(y + t), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.8e+217], t$95$2, If[LessEqual[a, -7.2e-13], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], If[LessEqual[a, -5.6e-74], N[(a - N[(N[(x * a), $MachinePrecision] / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.8e-33], N[(z - N[(y * N[(b / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -4.7999999999999996e217 or 1.80000000000000017e-33 < a

   1. Initial program 52.3%

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

   3. Taylor expanded in a around inf 38.6%

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

      1. associate-/l* 70.7%

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

      2. associate-+r+ 70.7%

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

   5. Simplified 70.7%

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

   if -4.7999999999999996e217 < a < -7.1999999999999996e-13

   1. Initial program 64.3%

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

   3. Taylor expanded in y around inf 69.1%

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

   if -7.1999999999999996e-13 < a < -5.59999999999999976e-74

   1. Initial program 80.5%

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

   3. Taylor expanded in a around inf 58.7%

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

   4. Taylor expanded in x around 0 59.7%

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

      1. mul-1-neg 59.7%

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

      2. unsub-neg 59.7%

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

      3. *-commutative 59.7%

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

   6. Simplified 59.7%

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

   if -5.59999999999999976e-74 < a < 1.80000000000000017e-33

   1. Initial program 66.1%

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

   3. Taylor expanded in b around 0 66.1%

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

      1. mul-1-neg 66.1%

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

      2. +-commutative 66.1%

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

      3. unsub-neg 66.1%

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

      4. +-commutative 66.1%

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

      5. associate-/l* 85.2%

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

      6. fma-define 85.2%

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

      7. +-commutative 85.2%

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

      8. associate-+r+ 85.2%

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

      9. associate-/l* 85.2%

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

      10. associate-+r+ 85.2%

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

   5. Simplified 95.7%

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

   6. Taylor expanded in x around inf 67.2%

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

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.8 \cdot 10^{+217}:\\ \;\;\;\;a \cdot \frac{y + t}{y + \left(x + t\right)}\\ \mathbf{elif}\;a \leq -7.2 \cdot 10^{-13}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;a \leq -5.6 \cdot 10^{-74}:\\ \;\;\;\;a - \frac{x \cdot a}{y + t}\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-33}:\\ \;\;\;\;z - y \cdot \frac{b}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{y + t}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 80.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{b}{y + \left(x + t\right)}\\ \mathbf{if}\;t \leq -5 \cdot 10^{-33} \lor \neg \left(t \leq 14000000000000\right):\\ \;\;\;\;\left(a + y \cdot \frac{z}{y + t}\right) - t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(z + a \cdot \frac{y}{y + x}\right) - t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (/ b (+ y (+ x t))))))
   (if (or (<= t -5e-33) (not (<= t 14000000000000.0)))
     (- (+ a (* y (/ z (+ y t)))) t_1)
     (- (+ z (* a (/ y (+ y x)))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b / (y + (x + t)));
	double tmp;
	if ((t <= -5e-33) || !(t <= 14000000000000.0)) {
		tmp = (a + (y * (z / (y + t)))) - t_1;
	} else {
		tmp = (z + (a * (y / (y + x)))) - t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (b / (y + (x + t)))
    if ((t <= (-5d-33)) .or. (.not. (t <= 14000000000000.0d0))) then
        tmp = (a + (y * (z / (y + t)))) - t_1
    else
        tmp = (z + (a * (y / (y + x)))) - t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b / (y + (x + t)));
	double tmp;
	if ((t <= -5e-33) || !(t <= 14000000000000.0)) {
		tmp = (a + (y * (z / (y + t)))) - t_1;
	} else {
		tmp = (z + (a * (y / (y + x)))) - t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b / (y + (x + t)))
	tmp = 0
	if (t <= -5e-33) or not (t <= 14000000000000.0):
		tmp = (a + (y * (z / (y + t)))) - t_1
	else:
		tmp = (z + (a * (y / (y + x)))) - t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(b / Float64(y + Float64(x + t))))
	tmp = 0.0
	if ((t <= -5e-33) || !(t <= 14000000000000.0))
		tmp = Float64(Float64(a + Float64(y * Float64(z / Float64(y + t)))) - t_1);
	else
		tmp = Float64(Float64(z + Float64(a * Float64(y / Float64(y + x)))) - t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (b / (y + (x + t)));
	tmp = 0.0;
	if ((t <= -5e-33) || ~((t <= 14000000000000.0)))
		tmp = (a + (y * (z / (y + t)))) - t_1;
	else
		tmp = (z + (a * (y / (y + x)))) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(b / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t, -5e-33], N[Not[LessEqual[t, 14000000000000.0]], $MachinePrecision]], N[(N[(a + N[(y * N[(z / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[(z + N[(a * N[(y / N[(y + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -5.00000000000000028e-33 or 1.4e13 < t

   1. Initial program 55.1%

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

   3. Taylor expanded in b around 0 55.1%

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

      1. mul-1-neg 55.1%

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

      2. +-commutative 55.1%

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

      3. unsub-neg 55.1%

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

      4. +-commutative 55.1%

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

      5. associate-/l* 69.1%

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

      6. fma-define 69.1%

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

      7. +-commutative 69.1%

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

      8. associate-+r+ 69.1%

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

      9. associate-/l* 85.1%

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

      10. associate-+r+ 85.1%

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

   5. Simplified 98.8%

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

   6. Taylor expanded in x around 0 66.5%

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

      1. associate-/l* 83.1%

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

      2. +-commutative 83.1%

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

   8. Simplified 83.1%

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

   if -5.00000000000000028e-33 < t < 1.4e13

   1. Initial program 70.3%

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

   3. Taylor expanded in b around 0 70.3%

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

      1. mul-1-neg 70.3%

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

      2. +-commutative 70.3%

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

      3. unsub-neg 70.3%

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

      4. +-commutative 70.3%

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

      5. associate-/l* 80.1%

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

      6. fma-define 80.1%

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

      7. +-commutative 80.1%

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

      8. associate-+r+ 80.1%

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

      9. associate-/l* 88.4%

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

      10. associate-+r+ 88.4%

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

   5. Simplified 95.0%

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

   6. Taylor expanded in t around 0 79.1%

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

      1. +-commutative 79.1%

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

      2. associate-/l* 91.4%

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

      3. +-commutative 91.4%

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

   8. Simplified 91.4%

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

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{-33} \lor \neg \left(t \leq 14000000000000\right):\\ \;\;\;\;\left(a + y \cdot \frac{z}{y + t}\right) - y \cdot \frac{b}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a \cdot \frac{y}{y + x}\right) - y \cdot \frac{b}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 71.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ \mathbf{if}\;z \leq -5.6 \cdot 10^{+176}:\\ \;\;\;\;z \cdot \frac{y + x}{t\_1}\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+137}:\\ \;\;\;\;\left(a + y \cdot \frac{z}{y + t}\right) - y \cdot \frac{b}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{1}{\frac{t\_1}{y + x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t))))
   (if (<= z -5.6e+176)
     (* z (/ (+ y x) t_1))
     (if (<= z 2.4e+137)
       (- (+ a (* y (/ z (+ y t)))) (* y (/ b t_1)))
       (* z (/ 1.0 (/ t_1 (+ y x))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double tmp;
	if (z <= -5.6e+176) {
		tmp = z * ((y + x) / t_1);
	} else if (z <= 2.4e+137) {
		tmp = (a + (y * (z / (y + t)))) - (y * (b / t_1));
	} else {
		tmp = z * (1.0 / (t_1 / (y + x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y + (x + t)
    if (z <= (-5.6d+176)) then
        tmp = z * ((y + x) / t_1)
    else if (z <= 2.4d+137) then
        tmp = (a + (y * (z / (y + t)))) - (y * (b / t_1))
    else
        tmp = z * (1.0d0 / (t_1 / (y + x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double tmp;
	if (z <= -5.6e+176) {
		tmp = z * ((y + x) / t_1);
	} else if (z <= 2.4e+137) {
		tmp = (a + (y * (z / (y + t)))) - (y * (b / t_1));
	} else {
		tmp = z * (1.0 / (t_1 / (y + x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	tmp = 0
	if z <= -5.6e+176:
		tmp = z * ((y + x) / t_1)
	elif z <= 2.4e+137:
		tmp = (a + (y * (z / (y + t)))) - (y * (b / t_1))
	else:
		tmp = z * (1.0 / (t_1 / (y + x)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	tmp = 0.0
	if (z <= -5.6e+176)
		tmp = Float64(z * Float64(Float64(y + x) / t_1));
	elseif (z <= 2.4e+137)
		tmp = Float64(Float64(a + Float64(y * Float64(z / Float64(y + t)))) - Float64(y * Float64(b / t_1)));
	else
		tmp = Float64(z * Float64(1.0 / Float64(t_1 / Float64(y + x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	tmp = 0.0;
	if (z <= -5.6e+176)
		tmp = z * ((y + x) / t_1);
	elseif (z <= 2.4e+137)
		tmp = (a + (y * (z / (y + t)))) - (y * (b / t_1));
	else
		tmp = z * (1.0 / (t_1 / (y + x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.6e+176], N[(z * N[(N[(y + x), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.4e+137], N[(N[(a + N[(y * N[(z / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * N[(b / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(1.0 / N[(t$95$1 / N[(y + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.6000000000000005e176

   1. Initial program 25.7%

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

   3. Taylor expanded in z around inf 26.4%

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

      1. associate-/l* 93.5%

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

      2. +-commutative 93.5%

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

      3. associate-+r+ 93.5%

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

   5. Simplified 93.5%

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

   if -5.6000000000000005e176 < z < 2.39999999999999983e137

   1. Initial program 71.8%

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

   3. Taylor expanded in b around 0 71.8%

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

      1. mul-1-neg 71.8%

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

      2. +-commutative 71.8%

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

      3. unsub-neg 71.8%

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

      4. +-commutative 71.8%

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

      5. associate-/l* 75.3%

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

      6. fma-define 75.3%

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

      7. +-commutative 75.3%

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

      8. associate-+r+ 75.3%

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

      9. associate-/l* 87.8%

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

      10. associate-+r+ 87.8%

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

   5. Simplified 96.7%

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

   6. Taylor expanded in x around 0 74.7%

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

      1. associate-/l* 77.1%

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

      2. +-commutative 77.1%

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

   8. Simplified 77.1%

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

   if 2.39999999999999983e137 < z

   1. Initial program 34.4%

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

   3. Taylor expanded in z around inf 32.2%

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

      1. associate-/l* 83.2%

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

      2. +-commutative 83.2%

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

      3. associate-+r+ 83.2%

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

   5. Simplified 83.2%

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

      1. clear-num 83.3%

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

      2. inv-pow 83.3%

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

      3. +-commutative 83.3%

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

      4. +-commutative 83.3%

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

      5. +-commutative 83.3%

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

   7. Applied egg-rr 83.3%

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

      1. unpow-1 83.3%

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

   9. Simplified 83.3%

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

4. Final simplification 79.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{+176}:\\ \;\;\;\;z \cdot \frac{y + x}{y + \left(x + t\right)}\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+137}:\\ \;\;\;\;\left(a + y \cdot \frac{z}{y + t}\right) - y \cdot \frac{b}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{1}{\frac{y + \left(x + t\right)}{y + x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 54.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{-42} \lor \neg \left(y \leq 4.5 \cdot 10^{-221}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -4.5e-42) (not (<= y 4.5e-221))) (- (+ z a) b) a))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -4.5e-42) || !(y <= 4.5e-221)) {
		tmp = (z + a) - b;
	} else {
		tmp = 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 ((y <= (-4.5d-42)) .or. (.not. (y <= 4.5d-221))) then
        tmp = (z + a) - b
    else
        tmp = 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 ((y <= -4.5e-42) || !(y <= 4.5e-221)) {
		tmp = (z + a) - b;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -4.5e-42) or not (y <= 4.5e-221):
		tmp = (z + a) - b
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -4.5e-42) || !(y <= 4.5e-221))
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -4.5e-42) || ~((y <= 4.5e-221)))
		tmp = (z + a) - b;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -4.5e-42], N[Not[LessEqual[y, 4.5e-221]], $MachinePrecision]], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], a]

Derivation

1. Split input into 2 regimes

2. if y < -4.5e-42 or 4.50000000000000026e-221 < y

   1. Initial program 53.9%

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

   3. Taylor expanded in y around inf 66.7%

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

   if -4.5e-42 < y < 4.50000000000000026e-221

   1. Initial program 85.4%

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

   3. Taylor expanded in t around inf 50.6%

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

4. Final simplification 62.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{-42} \lor \neg \left(y \leq 4.5 \cdot 10^{-221}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 44.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{+55}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 7400:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -3.7e+55) z (if (<= z 7400.0) a z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -3.7e+55) {
		tmp = z;
	} else if (z <= 7400.0) {
		tmp = a;
	} 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 (z <= (-3.7d+55)) then
        tmp = z
    else if (z <= 7400.0d0) then
        tmp = a
    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 (z <= -3.7e+55) {
		tmp = z;
	} else if (z <= 7400.0) {
		tmp = a;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -3.7e+55:
		tmp = z
	elif z <= 7400.0:
		tmp = a
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -3.7e+55)
		tmp = z;
	elseif (z <= 7400.0)
		tmp = a;
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -3.7e+55)
		tmp = z;
	elseif (z <= 7400.0)
		tmp = a;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -3.7e+55], z, If[LessEqual[z, 7400.0], a, z]]

Derivation

1. Split input into 2 regimes

2. if z < -3.7000000000000002e55 or 7400 < z

   1. Initial program 48.3%

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

   3. Taylor expanded in x around inf 56.6%

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

   if -3.7000000000000002e55 < z < 7400

   1. Initial program 72.5%

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

   3. Taylor expanded in t around inf 51.2%

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

4. Final simplification 53.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{+55}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 7400:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 32.0% accurate, 21.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 61.9%

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

3. Taylor expanded in t around inf 36.9%

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

4. Final simplification 36.9%

   \[\leadsto a \]
5. Add Preprocessing

Developer target: 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 2024080 
(FPCore (x y z t a b)
  :name "AI.Clustering.Hierarchical.Internal:ward from clustering-0.2.1"
  :precision binary64

  :alt
  (if (< (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)) -3.5813117084150564e+153) (- (+ z a) b) (if (< (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)) 1.2285964308315609e+82) (/ 1.0 (/ (+ (+ 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)))