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

Percentage Accurate: 61.0% → 91.5%

Time: 10.8s

Alternatives: 18

Speedup: 0.4×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 61.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 91.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y + x\right) + t\\ t_2 := \frac{y}{t\_1}\\ t_3 := t\_2 + \frac{x}{t\_1}\\ \mathbf{if}\;a \leq -8.6 \cdot 10^{-75}:\\ \;\;\;\;\left(\mathsf{fma}\left(z, \frac{t\_3}{a}, t\_2\right) + \mathsf{fma}\left(\frac{-b}{a}, t\_2, \frac{t}{t\_1}\right)\right) \cdot a\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-250}:\\ \;\;\;\;\mathsf{fma}\left(t\_3, z, \frac{\mathsf{fma}\left(-y, b, \left(t + y\right) \cdot a\right)}{t\_1}\right)\\ \mathbf{elif}\;a \leq 8.8 \cdot 10^{-94}:\\ \;\;\;\;\left(\frac{\mathsf{fma}\left(y + x, \frac{z}{t\_1}, \frac{a}{t\_1} \cdot \left(t + y\right)\right)}{b} - t\_2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t\_3, z, \mathsf{fma}\left(\frac{b}{t\_1}, \frac{y}{a}, \frac{\left(-y\right) - t}{t\_1}\right) \cdot \left(-a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ y x) t)) (t_2 (/ y t_1)) (t_3 (+ t_2 (/ x t_1))))
   (if (<= a -8.6e-75)
     (* (+ (fma z (/ t_3 a) t_2) (fma (/ (- b) a) t_2 (/ t t_1))) a)
     (if (<= a 2.2e-250)
       (fma t_3 z (/ (fma (- y) b (* (+ t y) a)) t_1))
       (if (<= a 8.8e-94)
         (* (- (/ (fma (+ y x) (/ z t_1) (* (/ a t_1) (+ t y))) b) t_2) b)
         (fma t_3 z (* (fma (/ b t_1) (/ y a) (/ (- (- y) t) t_1)) (- a))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y + x) + t;
	double t_2 = y / t_1;
	double t_3 = t_2 + (x / t_1);
	double tmp;
	if (a <= -8.6e-75) {
		tmp = (fma(z, (t_3 / a), t_2) + fma((-b / a), t_2, (t / t_1))) * a;
	} else if (a <= 2.2e-250) {
		tmp = fma(t_3, z, (fma(-y, b, ((t + y) * a)) / t_1));
	} else if (a <= 8.8e-94) {
		tmp = ((fma((y + x), (z / t_1), ((a / t_1) * (t + y))) / b) - t_2) * b;
	} else {
		tmp = fma(t_3, z, (fma((b / t_1), (y / a), ((-y - t) / t_1)) * -a));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y + x) + t)
	t_2 = Float64(y / t_1)
	t_3 = Float64(t_2 + Float64(x / t_1))
	tmp = 0.0
	if (a <= -8.6e-75)
		tmp = Float64(Float64(fma(z, Float64(t_3 / a), t_2) + fma(Float64(Float64(-b) / a), t_2, Float64(t / t_1))) * a);
	elseif (a <= 2.2e-250)
		tmp = fma(t_3, z, Float64(fma(Float64(-y), b, Float64(Float64(t + y) * a)) / t_1));
	elseif (a <= 8.8e-94)
		tmp = Float64(Float64(Float64(fma(Float64(y + x), Float64(z / t_1), Float64(Float64(a / t_1) * Float64(t + y))) / b) - t_2) * b);
	else
		tmp = fma(t_3, z, Float64(fma(Float64(b / t_1), Float64(y / a), Float64(Float64(Float64(-y) - t) / t_1)) * Float64(-a)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y + x), $MachinePrecision] + t), $MachinePrecision]}, Block[{t$95$2 = N[(y / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 + N[(x / t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -8.6e-75], N[(N[(N[(z * N[(t$95$3 / a), $MachinePrecision] + t$95$2), $MachinePrecision] + N[(N[((-b) / a), $MachinePrecision] * t$95$2 + N[(t / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision], If[LessEqual[a, 2.2e-250], N[(t$95$3 * z + N[(N[((-y) * b + N[(N[(t + y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8.8e-94], N[(N[(N[(N[(N[(y + x), $MachinePrecision] * N[(z / t$95$1), $MachinePrecision] + N[(N[(a / t$95$1), $MachinePrecision] * N[(t + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision] - t$95$2), $MachinePrecision] * b), $MachinePrecision], N[(t$95$3 * z + N[(N[(N[(b / t$95$1), $MachinePrecision] * N[(y / a), $MachinePrecision] + N[(N[((-y) - t), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] * (-a)), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -8.5999999999999998e-75

   1. Initial program 58.6%

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

   3. Taylor expanded in z around 0

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

      1. associate--l+ N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-+.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 N/A

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

      8. lower-+.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. +-commutative N/A

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

      11. lower-+.f64 N/A

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

      12. lower-+.f64 N/A

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

      13. div-sub N/A

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

   5. Applied rewrites 66.7%

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

   6. Taylor expanded in a around inf

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

   8. Applied rewrites 99.7%

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

   if -8.5999999999999998e-75 < a < 2.2e-250

   1. Initial program 76.3%

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

   3. Taylor expanded in z around 0

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

      1. associate--l+ N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-+.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 N/A

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

      8. lower-+.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. +-commutative N/A

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

      11. lower-+.f64 N/A

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

      12. lower-+.f64 N/A

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

      13. div-sub N/A

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

   5. Applied rewrites 94.8%

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

   if 2.2e-250 < a < 8.80000000000000004e-94

   1. Initial program 68.2%

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

   3. Taylor expanded in b around -inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. +-commutative N/A

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

      6. mul-1-neg N/A

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

      7. unsub-neg N/A

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

      8. lower--.f64 N/A

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

   5. Applied rewrites 91.2%

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

   if 8.80000000000000004e-94 < a

   1. Initial program 53.1%

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

   3. Taylor expanded in z around 0

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

      1. associate--l+ N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-+.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 N/A

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

      8. lower-+.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. +-commutative N/A

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

      11. lower-+.f64 N/A

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

      12. lower-+.f64 N/A

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

      13. div-sub N/A

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

   5. Applied rewrites 67.7%

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

   6. Taylor expanded in a around -inf

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

   8. Applied rewrites 98.7%

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

4. Final simplification 96.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.6 \cdot 10^{-75}:\\ \;\;\;\;\left(\mathsf{fma}\left(z, \frac{\frac{y}{\left(y + x\right) + t} + \frac{x}{\left(y + x\right) + t}}{a}, \frac{y}{\left(y + x\right) + t}\right) + \mathsf{fma}\left(\frac{-b}{a}, \frac{y}{\left(y + x\right) + t}, \frac{t}{\left(y + x\right) + t}\right)\right) \cdot a\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-250}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{\left(y + x\right) + t} + \frac{x}{\left(y + x\right) + t}, z, \frac{\mathsf{fma}\left(-y, b, \left(t + y\right) \cdot a\right)}{\left(y + x\right) + t}\right)\\ \mathbf{elif}\;a \leq 8.8 \cdot 10^{-94}:\\ \;\;\;\;\left(\frac{\mathsf{fma}\left(y + x, \frac{z}{\left(y + x\right) + t}, \frac{a}{\left(y + x\right) + t} \cdot \left(t + y\right)\right)}{b} - \frac{y}{\left(y + x\right) + t}\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{\left(y + x\right) + t} + \frac{x}{\left(y + x\right) + t}, z, \mathsf{fma}\left(\frac{b}{\left(y + x\right) + t}, \frac{y}{a}, \frac{\left(-y\right) - t}{\left(y + x\right) + t}\right) \cdot \left(-a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 63.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t + x\right) + y\\ t_2 := \frac{\left(\left(y + x\right) \cdot z + \left(t + y\right) \cdot a\right) - b \cdot y}{t\_1}\\ t_3 := \left(z + a\right) - b\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+39}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq -2 \cdot 10^{-130}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t, a, z \cdot x\right)}{t + x}\\ \mathbf{elif}\;t\_2 \leq 1.6 \cdot 10^{+98}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, z, \left(z - b\right) \cdot y\right)}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ t x) y))
        (t_2 (/ (- (+ (* (+ y x) z) (* (+ t y) a)) (* b y)) t_1))
        (t_3 (- (+ z a) b)))
   (if (<= t_2 -2e+39)
     t_3
     (if (<= t_2 -2e-130)
       (/ (fma t a (* z x)) (+ t x))
       (if (<= t_2 1.6e+98) (/ (fma x z (* (- z b) y)) t_1) t_3)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t + x) + y;
	double t_2 = ((((y + x) * z) + ((t + y) * a)) - (b * y)) / t_1;
	double t_3 = (z + a) - b;
	double tmp;
	if (t_2 <= -2e+39) {
		tmp = t_3;
	} else if (t_2 <= -2e-130) {
		tmp = fma(t, a, (z * x)) / (t + x);
	} else if (t_2 <= 1.6e+98) {
		tmp = fma(x, z, ((z - b) * y)) / t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t + x) + y)
	t_2 = Float64(Float64(Float64(Float64(Float64(y + x) * z) + Float64(Float64(t + y) * a)) - Float64(b * y)) / t_1)
	t_3 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (t_2 <= -2e+39)
		tmp = t_3;
	elseif (t_2 <= -2e-130)
		tmp = Float64(fma(t, a, Float64(z * x)) / Float64(t + x));
	elseif (t_2 <= 1.6e+98)
		tmp = Float64(fma(x, z, Float64(Float64(z - b) * y)) / t_1);
	else
		tmp = t_3;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t + x), $MachinePrecision] + y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(N[(y + x), $MachinePrecision] * z), $MachinePrecision] + N[(N[(t + y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] - N[(b * y), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+39], t$95$3, If[LessEqual[t$95$2, -2e-130], N[(N[(t * a + N[(z * x), $MachinePrecision]), $MachinePrecision] / N[(t + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1.6e+98], N[(N[(x * z + N[(N[(z - b), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], t$95$3]]]]]]

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)) < -1.99999999999999988e39 or 1.6000000000000001e98 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 39.4%

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

   3. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 64.4

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

   5. Applied rewrites 64.4%

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

   if -1.99999999999999988e39 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -2.0000000000000002e-130

   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 y around 0

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 75.4

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

   5. Applied rewrites 75.4%

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

   7. Applied rewrites 75.4%

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

   if -2.0000000000000002e-130 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1.6000000000000001e98

   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 a around 0

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

      1. distribute-rgt-in N/A

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

      2. associate--l+ N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. distribute-lft-out-- N/A

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

      6. lower-*.f64 N/A

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

      7. lower--.f64 67.1

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

   5. Applied rewrites 67.1%

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

4. Final simplification 66.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(y + x\right) \cdot z + \left(t + y\right) \cdot a\right) - b \cdot y}{\left(t + x\right) + y} \leq -2 \cdot 10^{+39}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;\frac{\left(\left(y + x\right) \cdot z + \left(t + y\right) \cdot a\right) - b \cdot y}{\left(t + x\right) + y} \leq -2 \cdot 10^{-130}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t, a, z \cdot x\right)}{t + x}\\ \mathbf{elif}\;\frac{\left(\left(y + x\right) \cdot z + \left(t + y\right) \cdot a\right) - b \cdot y}{\left(t + x\right) + y} \leq 1.6 \cdot 10^{+98}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, z, \left(z - b\right) \cdot y\right)}{\left(t + x\right) + y}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 87.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y + x\right) + t\\ t_2 := \frac{\left(\left(y + x\right) \cdot z + \left(t + y\right) \cdot a\right) - b \cdot y}{\left(t + x\right) + y}\\ t_3 := \left(z + a\right) - b\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+283}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t}{t\_1} + \frac{y}{t\_1}, a, \frac{\mathsf{fma}\left(x, z, \left(z - b\right) \cdot y\right)}{t\_1}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ y x) t))
        (t_2 (/ (- (+ (* (+ y x) z) (* (+ t y) a)) (* b y)) (+ (+ t x) y)))
        (t_3 (- (+ z a) b)))
   (if (<= t_2 (- INFINITY))
     t_3
     (if (<= t_2 2e+283)
       (fma (+ (/ t t_1) (/ y t_1)) a (/ (fma x z (* (- z b) y)) t_1))
       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 = ((((y + x) * z) + ((t + y) * a)) - (b * y)) / ((t + x) + y);
	double t_3 = (z + a) - b;
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_3;
	} else if (t_2 <= 2e+283) {
		tmp = fma(((t / t_1) + (y / t_1)), a, (fma(x, z, ((z - b) * y)) / t_1));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y + x) + t)
	t_2 = Float64(Float64(Float64(Float64(Float64(y + x) * z) + Float64(Float64(t + y) * a)) - Float64(b * y)) / Float64(Float64(t + x) + y))
	t_3 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_3;
	elseif (t_2 <= 2e+283)
		tmp = fma(Float64(Float64(t / t_1) + Float64(y / t_1)), a, Float64(fma(x, z, Float64(Float64(z - b) * y)) / t_1));
	else
		tmp = t_3;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y + x), $MachinePrecision] + t), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(N[(y + x), $MachinePrecision] * z), $MachinePrecision] + N[(N[(t + y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] - N[(b * y), $MachinePrecision]), $MachinePrecision] / N[(N[(t + x), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$3, If[LessEqual[t$95$2, 2e+283], N[(N[(N[(t / t$95$1), $MachinePrecision] + N[(y / t$95$1), $MachinePrecision]), $MachinePrecision] * a + N[(N[(x * z + N[(N[(z - b), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -inf.0 or 1.99999999999999991e283 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 6.3%

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

   3. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 61.8

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

   5. Applied rewrites 61.8%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1.99999999999999991e283

   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 a around 0

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

      1. associate--l+ N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-+.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 N/A

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

      8. lower-+.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. +-commutative N/A

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

      11. lower-+.f64 N/A

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

      12. lower-+.f64 N/A

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

      13. div-sub N/A

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

   5. Applied rewrites 99.8%

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

4. Final simplification 84.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(y + x\right) \cdot z + \left(t + y\right) \cdot a\right) - b \cdot y}{\left(t + x\right) + y} \leq -\infty:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;\frac{\left(\left(y + x\right) \cdot z + \left(t + y\right) \cdot a\right) - b \cdot y}{\left(t + x\right) + y} \leq 2 \cdot 10^{+283}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t}{\left(y + x\right) + t} + \frac{y}{\left(y + x\right) + t}, a, \frac{\mathsf{fma}\left(x, z, \left(z - b\right) \cdot y\right)}{\left(y + x\right) + t}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 87.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t + x\right) + y\\ t_2 := \frac{\left(\left(y + x\right) \cdot z + \left(t + y\right) \cdot a\right) - b \cdot y}{t\_1}\\ t_3 := \left(z + a\right) - b\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+283}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t + y, a, \mathsf{fma}\left(x, z, \left(z - b\right) \cdot y\right)\right)}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ t x) y))
        (t_2 (/ (- (+ (* (+ y x) z) (* (+ t y) a)) (* b y)) t_1))
        (t_3 (- (+ z a) b)))
   (if (<= t_2 (- INFINITY))
     t_3
     (if (<= t_2 2e+283)
       (/ (fma (+ t y) a (fma x z (* (- z b) y))) t_1)
       t_3))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t + x) + y;
	double t_2 = ((((y + x) * z) + ((t + y) * a)) - (b * y)) / t_1;
	double t_3 = (z + a) - b;
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_3;
	} else if (t_2 <= 2e+283) {
		tmp = fma((t + y), a, fma(x, z, ((z - b) * y))) / t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t + x) + y)
	t_2 = Float64(Float64(Float64(Float64(Float64(y + x) * z) + Float64(Float64(t + y) * a)) - Float64(b * y)) / t_1)
	t_3 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_3;
	elseif (t_2 <= 2e+283)
		tmp = Float64(fma(Float64(t + y), a, fma(x, z, Float64(Float64(z - b) * y))) / t_1);
	else
		tmp = t_3;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t + x), $MachinePrecision] + y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(N[(y + x), $MachinePrecision] * z), $MachinePrecision] + N[(N[(t + y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] - N[(b * y), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$3, If[LessEqual[t$95$2, 2e+283], N[(N[(N[(t + y), $MachinePrecision] * a + N[(x * z + N[(N[(z - b), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], t$95$3]]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -inf.0 or 1.99999999999999991e283 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 6.3%

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

   3. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 61.8

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

   5. Applied rewrites 61.8%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1.99999999999999991e283

   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 b around 0

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

      1. mul-1-neg N/A

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

      2. +-commutative N/A

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

      3. sub-neg N/A

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

      4. associate--l+ N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 N/A

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

      9. distribute-rgt-in N/A

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

      10. associate--l+ N/A

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

      11. lower-fma.f64 N/A

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

      12. *-commutative N/A

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

      13. distribute-lft-out-- N/A

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

      14. lower-*.f64 N/A

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

      15. lower--.f64 99.7

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

   5. Applied rewrites 99.7%

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

4. Final simplification 84.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(y + x\right) \cdot z + \left(t + y\right) \cdot a\right) - b \cdot y}{\left(t + x\right) + y} \leq -\infty:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;\frac{\left(\left(y + x\right) \cdot z + \left(t + y\right) \cdot a\right) - b \cdot y}{\left(t + x\right) + y} \leq 2 \cdot 10^{+283}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t + y, a, \mathsf{fma}\left(x, z, \left(z - b\right) \cdot y\right)\right)}{\left(t + x\right) + y}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t + y\right) \cdot a\\ t_2 := \left(t + x\right) + y\\ t_3 := \frac{\left(\left(y + x\right) \cdot z + t\_1\right) - b \cdot y}{t\_2}\\ t_4 := \left(z + a\right) - b\\ \mathbf{if}\;t\_3 \leq -1 \cdot 10^{+190}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t\_3 \leq 2 \cdot 10^{+152}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y + x, z, t\_1\right)}{t\_2}\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (+ t y) a))
        (t_2 (+ (+ t x) y))
        (t_3 (/ (- (+ (* (+ y x) z) t_1) (* b y)) t_2))
        (t_4 (- (+ z a) b)))
   (if (<= t_3 -1e+190)
     t_4
     (if (<= t_3 2e+152) (/ (fma (+ y x) z t_1) t_2) t_4))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t + y) * a;
	double t_2 = (t + x) + y;
	double t_3 = ((((y + x) * z) + t_1) - (b * y)) / t_2;
	double t_4 = (z + a) - b;
	double tmp;
	if (t_3 <= -1e+190) {
		tmp = t_4;
	} else if (t_3 <= 2e+152) {
		tmp = fma((y + x), z, t_1) / t_2;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t + y) * a)
	t_2 = Float64(Float64(t + x) + y)
	t_3 = Float64(Float64(Float64(Float64(Float64(y + x) * z) + t_1) - Float64(b * y)) / t_2)
	t_4 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (t_3 <= -1e+190)
		tmp = t_4;
	elseif (t_3 <= 2e+152)
		tmp = Float64(fma(Float64(y + x), z, t_1) / t_2);
	else
		tmp = t_4;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t + y), $MachinePrecision] * a), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t + x), $MachinePrecision] + y), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(N[(N[(y + x), $MachinePrecision] * z), $MachinePrecision] + t$95$1), $MachinePrecision] - N[(b * y), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[t$95$3, -1e+190], t$95$4, If[LessEqual[t$95$3, 2e+152], N[(N[(N[(y + x), $MachinePrecision] * z + t$95$1), $MachinePrecision] / t$95$2), $MachinePrecision], t$95$4]]]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -1.0000000000000001e190 or 2.0000000000000001e152 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 19.0%

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

   3. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 63.8

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

   5. Applied rewrites 63.8%

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

   if -1.0000000000000001e190 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 2.0000000000000001e152

   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 b around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-+.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 82.0

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

   5. Applied rewrites 82.0%

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

4. Final simplification 73.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(y + x\right) \cdot z + \left(t + y\right) \cdot a\right) - b \cdot y}{\left(t + x\right) + y} \leq -1 \cdot 10^{+190}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;\frac{\left(\left(y + x\right) \cdot z + \left(t + y\right) \cdot a\right) - b \cdot y}{\left(t + x\right) + y} \leq 2 \cdot 10^{+152}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y + x, z, \left(t + y\right) \cdot a\right)}{\left(t + x\right) + y}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 64.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(\left(y + x\right) \cdot z + \left(t + y\right) \cdot a\right) - b \cdot y}{\left(t + x\right) + y}\\ t_2 := \left(z + a\right) - b\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+39}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 1.6 \cdot 10^{+98}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t, a, z \cdot x\right)}{t + x}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* (+ y x) z) (* (+ t y) a)) (* b y)) (+ (+ t x) y)))
        (t_2 (- (+ z a) b)))
   (if (<= t_1 -2e+39)
     t_2
     (if (<= t_1 1.6e+98) (/ (fma t a (* z x)) (+ t x)) t_2))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((((y + x) * z) + ((t + y) * a)) - (b * y)) / ((t + x) + y);
	double t_2 = (z + a) - b;
	double tmp;
	if (t_1 <= -2e+39) {
		tmp = t_2;
	} else if (t_1 <= 1.6e+98) {
		tmp = fma(t, a, (z * x)) / (t + x);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(Float64(Float64(y + x) * z) + Float64(Float64(t + y) * a)) - Float64(b * y)) / Float64(Float64(t + x) + y))
	t_2 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (t_1 <= -2e+39)
		tmp = t_2;
	elseif (t_1 <= 1.6e+98)
		tmp = Float64(fma(t, a, Float64(z * x)) / Float64(t + x));
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(N[(N[(y + x), $MachinePrecision] * z), $MachinePrecision] + N[(N[(t + y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] - N[(b * y), $MachinePrecision]), $MachinePrecision] / N[(N[(t + x), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+39], t$95$2, If[LessEqual[t$95$1, 1.6e+98], N[(N[(t * a + N[(z * x), $MachinePrecision]), $MachinePrecision] / N[(t + x), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -1.99999999999999988e39 or 1.6000000000000001e98 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 39.4%

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

   3. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 64.4

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

   5. Applied rewrites 64.4%

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

   if -1.99999999999999988e39 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1.6000000000000001e98

   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 y around 0

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 63.8

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

   5. Applied rewrites 63.8%

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

   7. Applied rewrites 63.8%

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

4. Final simplification 64.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(y + x\right) \cdot z + \left(t + y\right) \cdot a\right) - b \cdot y}{\left(t + x\right) + y} \leq -2 \cdot 10^{+39}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;\frac{\left(\left(y + x\right) \cdot z + \left(t + y\right) \cdot a\right) - b \cdot y}{\left(t + x\right) + y} \leq 1.6 \cdot 10^{+98}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t, a, z \cdot x\right)}{t + x}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 91.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y + x\right) + t\\ t_2 := \frac{y}{t\_1}\\ t_3 := t\_2 + \frac{x}{t\_1}\\ t_4 := \mathsf{fma}\left(t\_3, z, \mathsf{fma}\left(\frac{b}{t\_1}, \frac{y}{a}, \frac{\left(-y\right) - t}{t\_1}\right) \cdot \left(-a\right)\right)\\ \mathbf{if}\;a \leq -4.6 \cdot 10^{-108}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-250}:\\ \;\;\;\;\mathsf{fma}\left(t\_3, z, \frac{\mathsf{fma}\left(-y, b, \left(t + y\right) \cdot a\right)}{t\_1}\right)\\ \mathbf{elif}\;a \leq 8.8 \cdot 10^{-94}:\\ \;\;\;\;\left(\frac{\mathsf{fma}\left(y + x, \frac{z}{t\_1}, \frac{a}{t\_1} \cdot \left(t + y\right)\right)}{b} - t\_2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ y x) t))
        (t_2 (/ y t_1))
        (t_3 (+ t_2 (/ x t_1)))
        (t_4
         (fma t_3 z (* (fma (/ b t_1) (/ y a) (/ (- (- y) t) t_1)) (- a)))))
   (if (<= a -4.6e-108)
     t_4
     (if (<= a 2.2e-250)
       (fma t_3 z (/ (fma (- y) b (* (+ t y) a)) t_1))
       (if (<= a 8.8e-94)
         (* (- (/ (fma (+ y x) (/ z t_1) (* (/ a t_1) (+ t y))) b) t_2) b)
         t_4)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y + x) + t;
	double t_2 = y / t_1;
	double t_3 = t_2 + (x / t_1);
	double t_4 = fma(t_3, z, (fma((b / t_1), (y / a), ((-y - t) / t_1)) * -a));
	double tmp;
	if (a <= -4.6e-108) {
		tmp = t_4;
	} else if (a <= 2.2e-250) {
		tmp = fma(t_3, z, (fma(-y, b, ((t + y) * a)) / t_1));
	} else if (a <= 8.8e-94) {
		tmp = ((fma((y + x), (z / t_1), ((a / t_1) * (t + y))) / b) - t_2) * b;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y + x) + t)
	t_2 = Float64(y / t_1)
	t_3 = Float64(t_2 + Float64(x / t_1))
	t_4 = fma(t_3, z, Float64(fma(Float64(b / t_1), Float64(y / a), Float64(Float64(Float64(-y) - t) / t_1)) * Float64(-a)))
	tmp = 0.0
	if (a <= -4.6e-108)
		tmp = t_4;
	elseif (a <= 2.2e-250)
		tmp = fma(t_3, z, Float64(fma(Float64(-y), b, Float64(Float64(t + y) * a)) / t_1));
	elseif (a <= 8.8e-94)
		tmp = Float64(Float64(Float64(fma(Float64(y + x), Float64(z / t_1), Float64(Float64(a / t_1) * Float64(t + y))) / b) - t_2) * b);
	else
		tmp = t_4;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y + x), $MachinePrecision] + t), $MachinePrecision]}, Block[{t$95$2 = N[(y / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 + N[(x / t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$3 * z + N[(N[(N[(b / t$95$1), $MachinePrecision] * N[(y / a), $MachinePrecision] + N[(N[((-y) - t), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] * (-a)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.6e-108], t$95$4, If[LessEqual[a, 2.2e-250], N[(t$95$3 * z + N[(N[((-y) * b + N[(N[(t + y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8.8e-94], N[(N[(N[(N[(N[(y + x), $MachinePrecision] * N[(z / t$95$1), $MachinePrecision] + N[(N[(a / t$95$1), $MachinePrecision] * N[(t + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision] - t$95$2), $MachinePrecision] * b), $MachinePrecision], t$95$4]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.59999999999999992e-108 or 8.80000000000000004e-94 < a

   1. Initial program 57.3%

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

   3. Taylor expanded in z around 0

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

      1. associate--l+ N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-+.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 N/A

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

      8. lower-+.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. +-commutative N/A

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

      11. lower-+.f64 N/A

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

      12. lower-+.f64 N/A

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

      13. div-sub N/A

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

   5. Applied rewrites 68.5%

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

   6. Taylor expanded in a around -inf

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

   8. Applied rewrites 97.0%

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

   if -4.59999999999999992e-108 < a < 2.2e-250

   1. Initial program 74.9%

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

   3. Taylor expanded in z around 0

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

      1. associate--l+ N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-+.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 N/A

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

      8. lower-+.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. +-commutative N/A

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

      11. lower-+.f64 N/A

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

      12. lower-+.f64 N/A

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

      13. div-sub N/A

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

   5. Applied rewrites 94.1%

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

   if 2.2e-250 < a < 8.80000000000000004e-94

   1. Initial program 68.2%

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

   3. Taylor expanded in b around -inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. +-commutative N/A

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

      6. mul-1-neg N/A

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

      7. unsub-neg N/A

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

      8. lower--.f64 N/A

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

   5. Applied rewrites 91.2%

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

4. Final simplification 95.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.6 \cdot 10^{-108}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{\left(y + x\right) + t} + \frac{x}{\left(y + x\right) + t}, z, \mathsf{fma}\left(\frac{b}{\left(y + x\right) + t}, \frac{y}{a}, \frac{\left(-y\right) - t}{\left(y + x\right) + t}\right) \cdot \left(-a\right)\right)\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-250}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{\left(y + x\right) + t} + \frac{x}{\left(y + x\right) + t}, z, \frac{\mathsf{fma}\left(-y, b, \left(t + y\right) \cdot a\right)}{\left(y + x\right) + t}\right)\\ \mathbf{elif}\;a \leq 8.8 \cdot 10^{-94}:\\ \;\;\;\;\left(\frac{\mathsf{fma}\left(y + x, \frac{z}{\left(y + x\right) + t}, \frac{a}{\left(y + x\right) + t} \cdot \left(t + y\right)\right)}{b} - \frac{y}{\left(y + x\right) + t}\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{\left(y + x\right) + t} + \frac{x}{\left(y + x\right) + t}, z, \mathsf{fma}\left(\frac{b}{\left(y + x\right) + t}, \frac{y}{a}, \frac{\left(-y\right) - t}{\left(y + x\right) + t}\right) \cdot \left(-a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 84.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y + x\right) + t\\ t_2 := \frac{y}{t\_1}\\ t_3 := \left(\frac{\mathsf{fma}\left(y + x, \frac{z}{t\_1}, \frac{a}{t\_1} \cdot \left(t + y\right)\right)}{b} - t\_2\right) \cdot b\\ \mathbf{if}\;b \leq -8.2 \cdot 10^{-144}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq 4.8 \cdot 10^{+58}:\\ \;\;\;\;\mathsf{fma}\left(t\_2 + \frac{x}{t\_1}, z, \frac{\mathsf{fma}\left(-y, b, \left(t + y\right) \cdot a\right)}{t\_1}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ y x) t))
        (t_2 (/ y t_1))
        (t_3
         (* (- (/ (fma (+ y x) (/ z t_1) (* (/ a t_1) (+ t y))) b) t_2) b)))
   (if (<= b -8.2e-144)
     t_3
     (if (<= b 4.8e+58)
       (fma (+ t_2 (/ x t_1)) z (/ (fma (- y) b (* (+ t y) a)) t_1))
       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 = y / t_1;
	double t_3 = ((fma((y + x), (z / t_1), ((a / t_1) * (t + y))) / b) - t_2) * b;
	double tmp;
	if (b <= -8.2e-144) {
		tmp = t_3;
	} else if (b <= 4.8e+58) {
		tmp = fma((t_2 + (x / t_1)), z, (fma(-y, b, ((t + y) * a)) / t_1));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y + x) + t)
	t_2 = Float64(y / t_1)
	t_3 = Float64(Float64(Float64(fma(Float64(y + x), Float64(z / t_1), Float64(Float64(a / t_1) * Float64(t + y))) / b) - t_2) * b)
	tmp = 0.0
	if (b <= -8.2e-144)
		tmp = t_3;
	elseif (b <= 4.8e+58)
		tmp = fma(Float64(t_2 + Float64(x / t_1)), z, Float64(fma(Float64(-y), b, Float64(Float64(t + y) * a)) / t_1));
	else
		tmp = t_3;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y + x), $MachinePrecision] + t), $MachinePrecision]}, Block[{t$95$2 = N[(y / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(N[(N[(y + x), $MachinePrecision] * N[(z / t$95$1), $MachinePrecision] + N[(N[(a / t$95$1), $MachinePrecision] * N[(t + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision] - t$95$2), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -8.2e-144], t$95$3, If[LessEqual[b, 4.8e+58], N[(N[(t$95$2 + N[(x / t$95$1), $MachinePrecision]), $MachinePrecision] * z + N[(N[((-y) * b + N[(N[(t + y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]

Derivation

1. Split input into 2 regimes

2. if b < -8.2e-144 or 4.8e58 < b

   1. Initial program 54.9%

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

   3. Taylor expanded in b around -inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. +-commutative N/A

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

      6. mul-1-neg N/A

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

      7. unsub-neg N/A

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

      8. lower--.f64 N/A

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

   5. Applied rewrites 94.0%

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

   if -8.2e-144 < b < 4.8e58

   1. Initial program 71.2%

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

   3. Taylor expanded in z around 0

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

      1. associate--l+ N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-+.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 N/A

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

      8. lower-+.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. +-commutative N/A

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

      11. lower-+.f64 N/A

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

      12. lower-+.f64 N/A

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

      13. div-sub N/A

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

   5. Applied rewrites 85.7%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8.2 \cdot 10^{-144}:\\ \;\;\;\;\left(\frac{\mathsf{fma}\left(y + x, \frac{z}{\left(y + x\right) + t}, \frac{a}{\left(y + x\right) + t} \cdot \left(t + y\right)\right)}{b} - \frac{y}{\left(y + x\right) + t}\right) \cdot b\\ \mathbf{elif}\;b \leq 4.8 \cdot 10^{+58}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{\left(y + x\right) + t} + \frac{x}{\left(y + x\right) + t}, z, \frac{\mathsf{fma}\left(-y, b, \left(t + y\right) \cdot a\right)}{\left(y + x\right) + t}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{\mathsf{fma}\left(y + x, \frac{z}{\left(y + x\right) + t}, \frac{a}{\left(y + x\right) + t} \cdot \left(t + y\right)\right)}{b} - \frac{y}{\left(y + x\right) + t}\right) \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 59.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t + y}{\frac{\left(y + x\right) + t}{a}}\\ t_2 := \left(t + x\right) + y\\ \mathbf{if}\;a \leq -4 \cdot 10^{+57}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -3.2 \cdot 10^{-132}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-y, b, \left(t + y\right) \cdot a\right)}{t\_2}\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{-116}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, z, \left(z - b\right) \cdot y\right)}{t\_2}\\ \mathbf{elif}\;a \leq 2.85 \cdot 10^{+110}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ t y) (/ (+ (+ y x) t) a))) (t_2 (+ (+ t x) y)))
   (if (<= a -4e+57)
     t_1
     (if (<= a -3.2e-132)
       (/ (fma (- y) b (* (+ t y) a)) t_2)
       (if (<= a 1.05e-116)
         (/ (fma x z (* (- z b) y)) t_2)
         (if (<= a 2.85e+110) (- (+ z a) b) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t + y) / (((y + x) + t) / a);
	double t_2 = (t + x) + y;
	double tmp;
	if (a <= -4e+57) {
		tmp = t_1;
	} else if (a <= -3.2e-132) {
		tmp = fma(-y, b, ((t + y) * a)) / t_2;
	} else if (a <= 1.05e-116) {
		tmp = fma(x, z, ((z - b) * y)) / t_2;
	} else if (a <= 2.85e+110) {
		tmp = (z + a) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t + y) / Float64(Float64(Float64(y + x) + t) / a))
	t_2 = Float64(Float64(t + x) + y)
	tmp = 0.0
	if (a <= -4e+57)
		tmp = t_1;
	elseif (a <= -3.2e-132)
		tmp = Float64(fma(Float64(-y), b, Float64(Float64(t + y) * a)) / t_2);
	elseif (a <= 1.05e-116)
		tmp = Float64(fma(x, z, Float64(Float64(z - b) * y)) / t_2);
	elseif (a <= 2.85e+110)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t + y), $MachinePrecision] / N[(N[(N[(y + x), $MachinePrecision] + t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t + x), $MachinePrecision] + y), $MachinePrecision]}, If[LessEqual[a, -4e+57], t$95$1, If[LessEqual[a, -3.2e-132], N[(N[((-y) * b + N[(N[(t + y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision], If[LessEqual[a, 1.05e-116], N[(N[(x * z + N[(N[(z - b), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision], If[LessEqual[a, 2.85e+110], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -4.00000000000000019e57 or 2.8500000000000001e110 < a

   1. Initial program 46.0%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. +-commutative N/A

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

      5. lower-+.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 N/A

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

      9. lower-+.f64 73.2

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

   5. Applied rewrites 73.2%

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

   7. Applied rewrites 74.4%

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

   if -4.00000000000000019e57 < a < -3.2000000000000002e-132

   1. Initial program 77.7%

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

   3. Taylor expanded in z around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. distribute-lft-neg-in N/A

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

      5. mul-1-neg N/A

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

      6. lower-fma.f64 N/A

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

      7. mul-1-neg N/A

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

      8. lower-neg.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. +-commutative N/A

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

      12. lower-+.f64 59.4

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

   5. Applied rewrites 59.4%

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

   if -3.2000000000000002e-132 < a < 1.05e-116

   1. Initial program 71.9%

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

   3. Taylor expanded in a around 0

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

      1. distribute-rgt-in N/A

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

      2. associate--l+ N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. distribute-lft-out-- N/A

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

      6. lower-*.f64 N/A

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

      7. lower--.f64 67.1

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

   5. Applied rewrites 67.1%

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

   if 1.05e-116 < a < 2.8500000000000001e110

   1. Initial program 63.2%

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

   3. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 68.4

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

   5. Applied rewrites 68.4%

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

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4 \cdot 10^{+57}:\\ \;\;\;\;\frac{t + y}{\frac{\left(y + x\right) + t}{a}}\\ \mathbf{elif}\;a \leq -3.2 \cdot 10^{-132}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-y, b, \left(t + y\right) \cdot a\right)}{\left(t + x\right) + y}\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{-116}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, z, \left(z - b\right) \cdot y\right)}{\left(t + x\right) + y}\\ \mathbf{elif}\;a \leq 2.85 \cdot 10^{+110}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y}{\frac{\left(y + x\right) + t}{a}}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 56.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{t + x} \cdot a\\ \mathbf{if}\;t \leq -1.3 \cdot 10^{+136}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.9 \cdot 10^{+40}:\\ \;\;\;\;\frac{z}{\left(y + x\right) + t} \cdot \left(y + x\right)\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{+132}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (/ t (+ t x)) a)))
   (if (<= t -1.3e+136)
     t_1
     (if (<= t -1.9e+40)
       (* (/ z (+ (+ y x) t)) (+ y x))
       (if (<= t 7.2e+132) (- (+ z a) b) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t / (t + x)) * a;
	double tmp;
	if (t <= -1.3e+136) {
		tmp = t_1;
	} else if (t <= -1.9e+40) {
		tmp = (z / ((y + x) + t)) * (y + x);
	} else if (t <= 7.2e+132) {
		tmp = (z + a) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t / (t + x)) * a
    if (t <= (-1.3d+136)) then
        tmp = t_1
    else if (t <= (-1.9d+40)) then
        tmp = (z / ((y + x) + t)) * (y + x)
    else if (t <= 7.2d+132) then
        tmp = (z + a) - b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t / (t + x)) * a;
	double tmp;
	if (t <= -1.3e+136) {
		tmp = t_1;
	} else if (t <= -1.9e+40) {
		tmp = (z / ((y + x) + t)) * (y + x);
	} else if (t <= 7.2e+132) {
		tmp = (z + a) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t / (t + x)) * a
	tmp = 0
	if t <= -1.3e+136:
		tmp = t_1
	elif t <= -1.9e+40:
		tmp = (z / ((y + x) + t)) * (y + x)
	elif t <= 7.2e+132:
		tmp = (z + a) - b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t / Float64(t + x)) * a)
	tmp = 0.0
	if (t <= -1.3e+136)
		tmp = t_1;
	elseif (t <= -1.9e+40)
		tmp = Float64(Float64(z / Float64(Float64(y + x) + t)) * Float64(y + x));
	elseif (t <= 7.2e+132)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t / (t + x)) * a;
	tmp = 0.0;
	if (t <= -1.3e+136)
		tmp = t_1;
	elseif (t <= -1.9e+40)
		tmp = (z / ((y + x) + t)) * (y + x);
	elseif (t <= 7.2e+132)
		tmp = (z + a) - b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t / N[(t + x), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision]}, If[LessEqual[t, -1.3e+136], t$95$1, If[LessEqual[t, -1.9e+40], N[(N[(z / N[(N[(y + x), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision] * N[(y + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.2e+132], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.3000000000000001e136 or 7.20000000000000031e132 < t

   1. Initial program 49.5%

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

   3. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 37.3

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

   5. Applied rewrites 37.3%

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

   6. Taylor expanded in a around inf

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

   8. Applied rewrites 61.6%

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

   if -1.3000000000000001e136 < t < -1.90000000000000002e40

   1. Initial program 66.7%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-+.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 N/A

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

      8. lower-+.f64 57.9

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

   5. Applied rewrites 57.9%

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

   if -1.90000000000000002e40 < t < 7.20000000000000031e132

   1. Initial program 69.0%

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

   3. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 59.9

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

   5. Applied rewrites 59.9%

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

4. Final simplification 60.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{+136}:\\ \;\;\;\;\frac{t}{t + x} \cdot a\\ \mathbf{elif}\;t \leq -1.9 \cdot 10^{+40}:\\ \;\;\;\;\frac{z}{\left(y + x\right) + t} \cdot \left(y + x\right)\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{+132}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{t + x} \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 56.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a}{\left(y + x\right) + t} \cdot \left(t + y\right)\\ \mathbf{if}\;a \leq -1.45 \cdot 10^{+14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{+115}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (/ a (+ (+ y x) t)) (+ t y))))
   (if (<= a -1.45e+14) t_1 (if (<= a 1.6e+115) (- (+ z a) b) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a / ((y + x) + t)) * (t + y);
	double tmp;
	if (a <= -1.45e+14) {
		tmp = t_1;
	} else if (a <= 1.6e+115) {
		tmp = (z + a) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a / ((y + x) + t)) * (t + y)
    if (a <= (-1.45d+14)) then
        tmp = t_1
    else if (a <= 1.6d+115) then
        tmp = (z + a) - b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a / ((y + x) + t)) * (t + y);
	double tmp;
	if (a <= -1.45e+14) {
		tmp = t_1;
	} else if (a <= 1.6e+115) {
		tmp = (z + a) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a / ((y + x) + t)) * (t + y)
	tmp = 0
	if a <= -1.45e+14:
		tmp = t_1
	elif a <= 1.6e+115:
		tmp = (z + a) - b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a / Float64(Float64(y + x) + t)) * Float64(t + y))
	tmp = 0.0
	if (a <= -1.45e+14)
		tmp = t_1;
	elseif (a <= 1.6e+115)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a / ((y + x) + t)) * (t + y);
	tmp = 0.0;
	if (a <= -1.45e+14)
		tmp = t_1;
	elseif (a <= 1.6e+115)
		tmp = (z + a) - b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a / N[(N[(y + x), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision] * N[(t + y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.45e+14], t$95$1, If[LessEqual[a, 1.6e+115], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.45e14 or 1.6e115 < a

   1. Initial program 49.6%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. +-commutative N/A

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

      5. lower-+.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 N/A

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

      9. lower-+.f64 69.6

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

   5. Applied rewrites 69.6%

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

   if -1.45e14 < a < 1.6e115

   1. Initial program 70.8%

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

   3. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 56.5

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

   5. Applied rewrites 56.5%

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

4. Final simplification 61.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.45 \cdot 10^{+14}:\\ \;\;\;\;\frac{a}{\left(y + x\right) + t} \cdot \left(t + y\right)\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{+115}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{\left(y + x\right) + t} \cdot \left(t + y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 58.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{t + x} \cdot a\\ \mathbf{if}\;t \leq -1.52 \cdot 10^{+150}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{+132}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (/ t (+ t x)) a)))
   (if (<= t -1.52e+150) t_1 (if (<= t 7.2e+132) (- (+ z a) b) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t / (t + x)) * a;
	double tmp;
	if (t <= -1.52e+150) {
		tmp = t_1;
	} else if (t <= 7.2e+132) {
		tmp = (z + a) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t / (t + x)) * a
    if (t <= (-1.52d+150)) then
        tmp = t_1
    else if (t <= 7.2d+132) then
        tmp = (z + a) - b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t / (t + x)) * a;
	double tmp;
	if (t <= -1.52e+150) {
		tmp = t_1;
	} else if (t <= 7.2e+132) {
		tmp = (z + a) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t / (t + x)) * a
	tmp = 0
	if t <= -1.52e+150:
		tmp = t_1
	elif t <= 7.2e+132:
		tmp = (z + a) - b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t / Float64(t + x)) * a)
	tmp = 0.0
	if (t <= -1.52e+150)
		tmp = t_1;
	elseif (t <= 7.2e+132)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t / (t + x)) * a;
	tmp = 0.0;
	if (t <= -1.52e+150)
		tmp = t_1;
	elseif (t <= 7.2e+132)
		tmp = (z + a) - b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t / N[(t + x), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision]}, If[LessEqual[t, -1.52e+150], t$95$1, If[LessEqual[t, 7.2e+132], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.52e150 or 7.20000000000000031e132 < t

   1. Initial program 48.1%

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

   3. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 36.6

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

   5. Applied rewrites 36.6%

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

   6. Taylor expanded in a around inf

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

   8. Applied rewrites 62.1%

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

   if -1.52e150 < t < 7.20000000000000031e132

   1. Initial program 68.9%

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

   3. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 57.2

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

   5. Applied rewrites 57.2%

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

4. Final simplification 58.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.52 \cdot 10^{+150}:\\ \;\;\;\;\frac{t}{t + x} \cdot a\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{+132}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{t + x} \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 57.5% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.15 \cdot 10^{+150}:\\ \;\;\;\;1 \cdot a\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+133}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;1 \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -3.15e+150) (* 1.0 a) (if (<= t 3.2e+133) (- (+ z a) b) (* 1.0 a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -3.15e+150) {
		tmp = 1.0 * a;
	} else if (t <= 3.2e+133) {
		tmp = (z + a) - b;
	} else {
		tmp = 1.0 * a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-3.15d+150)) then
        tmp = 1.0d0 * a
    else if (t <= 3.2d+133) then
        tmp = (z + a) - b
    else
        tmp = 1.0d0 * a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -3.15e+150) {
		tmp = 1.0 * a;
	} else if (t <= 3.2e+133) {
		tmp = (z + a) - b;
	} else {
		tmp = 1.0 * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -3.15e+150:
		tmp = 1.0 * a
	elif t <= 3.2e+133:
		tmp = (z + a) - b
	else:
		tmp = 1.0 * a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -3.15e+150)
		tmp = Float64(1.0 * a);
	elseif (t <= 3.2e+133)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(1.0 * a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -3.15e+150)
		tmp = 1.0 * a;
	elseif (t <= 3.2e+133)
		tmp = (z + a) - b;
	else
		tmp = 1.0 * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -3.15e+150], N[(1.0 * a), $MachinePrecision], If[LessEqual[t, 3.2e+133], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(1.0 * a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -3.15000000000000015e150 or 3.19999999999999997e133 < t

   1. Initial program 48.1%

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

   3. Taylor expanded in z around 0

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

      1. associate--l+ N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-+.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 N/A

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

      8. lower-+.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. +-commutative N/A

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

      11. lower-+.f64 N/A

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

      12. lower-+.f64 N/A

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

      13. div-sub N/A

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

   5. Applied rewrites 53.2%

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

   6. Taylor expanded in a around inf

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

   8. Applied rewrites 83.9%

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

   9. Taylor expanded in t around inf

      \[\leadsto 1 \cdot a \]
   10. Step-by-step derivation

   11. Applied rewrites 56.6%

       \[\leadsto 1 \cdot a \]

   if -3.15000000000000015e150 < t < 3.19999999999999997e133

   1. Initial program 68.9%

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

   3. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 57.2

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

   5. Applied rewrites 57.2%

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

Alternative 14: 49.3% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3300000000000:\\ \;\;\;\;1 \cdot a\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{-41}:\\ \;\;\;\;z - b\\ \mathbf{else}:\\ \;\;\;\;z + a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -3300000000000.0) (* 1.0 a) (if (<= a 7.5e-41) (- z b) (+ z a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -3300000000000.0) {
		tmp = 1.0 * a;
	} else if (a <= 7.5e-41) {
		tmp = z - b;
	} else {
		tmp = z + a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-3300000000000.0d0)) then
        tmp = 1.0d0 * a
    else if (a <= 7.5d-41) then
        tmp = z - b
    else
        tmp = z + a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -3300000000000.0) {
		tmp = 1.0 * a;
	} else if (a <= 7.5e-41) {
		tmp = z - b;
	} else {
		tmp = z + a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -3300000000000.0:
		tmp = 1.0 * a
	elif a <= 7.5e-41:
		tmp = z - b
	else:
		tmp = z + a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -3300000000000.0)
		tmp = Float64(1.0 * a);
	elseif (a <= 7.5e-41)
		tmp = Float64(z - b);
	else
		tmp = Float64(z + a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -3300000000000.0)
		tmp = 1.0 * a;
	elseif (a <= 7.5e-41)
		tmp = z - b;
	else
		tmp = z + a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -3300000000000.0], N[(1.0 * a), $MachinePrecision], If[LessEqual[a, 7.5e-41], N[(z - b), $MachinePrecision], N[(z + a), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.3e12

   1. Initial program 54.6%

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

   3. Taylor expanded in z around 0

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

      1. associate--l+ N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-+.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 N/A

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

      8. lower-+.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. +-commutative N/A

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

      11. lower-+.f64 N/A

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

      12. lower-+.f64 N/A

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

      13. div-sub N/A

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

   5. Applied rewrites 63.7%

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

   6. Taylor expanded in a around inf

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

   8. Applied rewrites 99.7%

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

   9. Taylor expanded in t around inf

      \[\leadsto 1 \cdot a \]
   10. Step-by-step derivation

   11. Applied rewrites 46.1%

       \[\leadsto 1 \cdot a \]

   if -3.3e12 < a < 7.50000000000000049e-41

   1. Initial program 72.2%

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

   3. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 54.0

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

   5. Applied rewrites 54.0%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 53.7%

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

   if 7.50000000000000049e-41 < a

   1. Initial program 52.4%

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

   3. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 54.3

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

   5. Applied rewrites 54.3%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 59.1%

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

4. Final simplification 53.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3300000000000:\\ \;\;\;\;1 \cdot a\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{-41}:\\ \;\;\;\;z - b\\ \mathbf{else}:\\ \;\;\;\;z + a\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 48.4% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -9 \cdot 10^{-86}:\\ \;\;\;\;a - b\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{-41}:\\ \;\;\;\;z - b\\ \mathbf{else}:\\ \;\;\;\;z + a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -9e-86) (- a b) (if (<= a 7.5e-41) (- z b) (+ z a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -9e-86) {
		tmp = a - b;
	} else if (a <= 7.5e-41) {
		tmp = z - b;
	} else {
		tmp = z + a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-9d-86)) then
        tmp = a - b
    else if (a <= 7.5d-41) then
        tmp = z - b
    else
        tmp = z + a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -9e-86) {
		tmp = a - b;
	} else if (a <= 7.5e-41) {
		tmp = z - b;
	} else {
		tmp = z + a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -9e-86:
		tmp = a - b
	elif a <= 7.5e-41:
		tmp = z - b
	else:
		tmp = z + a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -9e-86)
		tmp = Float64(a - b);
	elseif (a <= 7.5e-41)
		tmp = Float64(z - b);
	else
		tmp = Float64(z + a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -9e-86)
		tmp = a - b;
	elseif (a <= 7.5e-41)
		tmp = z - b;
	else
		tmp = z + a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -9e-86], N[(a - b), $MachinePrecision], If[LessEqual[a, 7.5e-41], N[(z - b), $MachinePrecision], N[(z + a), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -8.9999999999999995e-86

   1. Initial program 60.0%

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

   3. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 45.8

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

   5. Applied rewrites 45.8%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 47.1%

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

   if -8.9999999999999995e-86 < a < 7.50000000000000049e-41

   1. Initial program 71.5%

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

   3. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 52.8

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

   5. Applied rewrites 52.8%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 54.2%

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

   if 7.50000000000000049e-41 < a

   1. Initial program 52.4%

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

   3. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 54.3

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

   5. Applied rewrites 54.3%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 59.1%

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

4. Final simplification 53.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9 \cdot 10^{-86}:\\ \;\;\;\;a - b\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{-41}:\\ \;\;\;\;z - b\\ \mathbf{else}:\\ \;\;\;\;z + a\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 46.2% accurate, 4.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.5 \cdot 10^{-88}:\\ \;\;\;\;a - b\\ \mathbf{else}:\\ \;\;\;\;z + a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (if (<= a -5.5e-88) (- a b) (+ z a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -5.5e-88) {
		tmp = a - b;
	} else {
		tmp = z + a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-5.5d-88)) then
        tmp = a - b
    else
        tmp = z + a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -5.5e-88) {
		tmp = a - b;
	} else {
		tmp = z + a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -5.5e-88:
		tmp = a - b
	else:
		tmp = z + a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -5.5e-88)
		tmp = Float64(a - b);
	else
		tmp = Float64(z + a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -5.5e-88)
		tmp = a - b;
	else
		tmp = z + a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -5.5e-88], N[(a - b), $MachinePrecision], N[(z + a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -5.49999999999999971e-88

   1. Initial program 60.0%

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

   3. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 45.8

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

   5. Applied rewrites 45.8%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 47.1%

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

   if -5.49999999999999971e-88 < a

   1. Initial program 63.8%

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

   3. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 53.4

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

   5. Applied rewrites 53.4%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 52.3%

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

4. Final simplification 50.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.5 \cdot 10^{-88}:\\ \;\;\;\;a - b\\ \mathbf{else}:\\ \;\;\;\;z + a\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 50.1% accurate, 11.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 62.5%

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

3. Taylor expanded in y around inf

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

   1. lower--.f64 N/A

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

   2. +-commutative N/A

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

   3. lower-+.f64 50.8

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

5. Applied rewrites 50.8%

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

6. Taylor expanded in b around 0

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

8. Applied rewrites 48.3%

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

9. Final simplification 48.3%

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

Alternative 18: 13.5% accurate, 15.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 62.5%

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

3. Taylor expanded in y around inf

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

   1. lower--.f64 N/A

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

   2. +-commutative N/A

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

   3. lower-+.f64 50.8

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

5. Applied rewrites 50.8%

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

6. Taylor expanded in b around inf

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

8. Applied rewrites 11.7%

   \[\leadsto -b \]
9. Add Preprocessing

Developer Target 1: 81.6% 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 2024254 
(FPCore (x y z t a b)
  :name "AI.Clustering.Hierarchical.Internal:ward from clustering-0.2.1"
  :precision binary64

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

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