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

Percentage Accurate: 59.8% → 93.0%

Time: 10.9s

Alternatives: 20

Speedup: 1.4×

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: 59.8% 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: 93.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y + x\right) + t\\ t_2 := \frac{y}{t\_1}\\ t_3 := \left(\frac{t}{t\_1} + \left(t\_2 + \mathsf{fma}\left(\frac{x}{a}, \frac{z}{t\_1}, t\_2 \cdot \frac{z - b}{a}\right)\right)\right) \cdot a\\ \mathbf{if}\;a \leq -5.5 \cdot 10^{-31}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;a \leq 4.9 \cdot 10^{-36}:\\ \;\;\;\;\left(\left(\frac{x}{t\_1} + \mathsf{fma}\left(\frac{a}{z}, \frac{t + y}{t\_1}, t\_2\right)\right) - \frac{y}{t\_1 \cdot z} \cdot b\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ y x) t))
        (t_2 (/ y t_1))
        (t_3
         (*
          (+ (/ t t_1) (+ t_2 (fma (/ x a) (/ z t_1) (* t_2 (/ (- z b) a)))))
          a)))
   (if (<= a -5.5e-31)
     t_3
     (if (<= a 4.9e-36)
       (*
        (-
         (+ (/ x t_1) (fma (/ a z) (/ (+ t y) t_1) t_2))
         (* (/ y (* t_1 z)) b))
        z)
       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 = ((t / t_1) + (t_2 + fma((x / a), (z / t_1), (t_2 * ((z - b) / a))))) * a;
	double tmp;
	if (a <= -5.5e-31) {
		tmp = t_3;
	} else if (a <= 4.9e-36) {
		tmp = (((x / t_1) + fma((a / z), ((t + y) / t_1), t_2)) - ((y / (t_1 * z)) * b)) * z;
	} 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(t / t_1) + Float64(t_2 + fma(Float64(x / a), Float64(z / t_1), Float64(t_2 * Float64(Float64(z - b) / a))))) * a)
	tmp = 0.0
	if (a <= -5.5e-31)
		tmp = t_3;
	elseif (a <= 4.9e-36)
		tmp = Float64(Float64(Float64(Float64(x / t_1) + fma(Float64(a / z), Float64(Float64(t + y) / t_1), t_2)) - Float64(Float64(y / Float64(t_1 * z)) * b)) * z);
	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[(t / t$95$1), $MachinePrecision] + N[(t$95$2 + N[(N[(x / a), $MachinePrecision] * N[(z / t$95$1), $MachinePrecision] + N[(t$95$2 * N[(N[(z - b), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision]}, If[LessEqual[a, -5.5e-31], t$95$3, If[LessEqual[a, 4.9e-36], N[(N[(N[(N[(x / t$95$1), $MachinePrecision] + N[(N[(a / z), $MachinePrecision] * N[(N[(t + y), $MachinePrecision] / t$95$1), $MachinePrecision] + t$95$2), $MachinePrecision]), $MachinePrecision] - N[(N[(y / N[(t$95$1 * z), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision], t$95$3]]]]]

Derivation

1. Split input into 2 regimes

2. if a < -5.49999999999999958e-31 or 4.8999999999999997e-36 < a

   1. Initial program 51.6%

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

   3. Taylor expanded in a around 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 74.6%

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

   6. Taylor expanded in a around inf

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

   8. Applied rewrites 96.4%

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

   if -5.49999999999999958e-31 < a < 4.8999999999999997e-36

   1. Initial program 72.5%

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

   3. Taylor expanded in 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 72.6%

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

   6. Taylor expanded in a around inf

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

   8. Applied rewrites 35.6%

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

   9. Taylor expanded in z around inf

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

       1. lower-*.f64 N/A

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

       2. lower--.f64 N/A

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

   11. Applied rewrites 89.1%

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

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.5 \cdot 10^{-31}:\\ \;\;\;\;\left(\frac{t}{\left(y + x\right) + t} + \left(\frac{y}{\left(y + x\right) + t} + \mathsf{fma}\left(\frac{x}{a}, \frac{z}{\left(y + x\right) + t}, \frac{y}{\left(y + x\right) + t} \cdot \frac{z - b}{a}\right)\right)\right) \cdot a\\ \mathbf{elif}\;a \leq 4.9 \cdot 10^{-36}:\\ \;\;\;\;\left(\left(\frac{x}{\left(y + x\right) + t} + \mathsf{fma}\left(\frac{a}{z}, \frac{t + y}{\left(y + x\right) + t}, \frac{y}{\left(y + x\right) + t}\right)\right) - \frac{y}{\left(\left(y + x\right) + t\right) \cdot z} \cdot b\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{t}{\left(y + x\right) + t} + \left(\frac{y}{\left(y + x\right) + t} + \mathsf{fma}\left(\frac{x}{a}, \frac{z}{\left(y + x\right) + t}, \frac{y}{\left(y + x\right) + t} \cdot \frac{z - b}{a}\right)\right)\right) \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 87.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(\left(t + y\right) \cdot a + \left(y + x\right) \cdot z\right) - b \cdot y}{\left(t + x\right) + y}\\ t_2 := \left(y + x\right) + t\\ t_3 := \frac{y}{t\_2}\\ t_4 := \left(\frac{\mathsf{fma}\left(y + x, \frac{z}{t\_2}, \frac{a}{t\_2} \cdot \left(t + y\right)\right)}{b} - t\_3\right) \cdot b\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+293}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t}{t\_2} + t\_3, a, \frac{\mathsf{fma}\left(x, z, \left(z - b\right) \cdot y\right)}{t\_2}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* (+ t y) a) (* (+ y x) z)) (* b y)) (+ (+ t x) y)))
        (t_2 (+ (+ y x) t))
        (t_3 (/ y t_2))
        (t_4
         (* (- (/ (fma (+ y x) (/ z t_2) (* (/ a t_2) (+ t y))) b) t_3) b)))
   (if (<= t_1 (- INFINITY))
     t_4
     (if (<= t_1 2e+293)
       (fma (+ (/ t t_2) t_3) a (/ (fma x z (* (- z b) y)) 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) + ((y + x) * z)) - (b * y)) / ((t + x) + y);
	double t_2 = (y + x) + t;
	double t_3 = y / t_2;
	double t_4 = ((fma((y + x), (z / t_2), ((a / t_2) * (t + y))) / b) - t_3) * b;
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = t_4;
	} else if (t_1 <= 2e+293) {
		tmp = fma(((t / t_2) + t_3), a, (fma(x, z, ((z - b) * y)) / t_2));
	} else {
		tmp = t_4;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(Float64(Float64(t + y) * a) + Float64(Float64(y + x) * z)) - Float64(b * y)) / Float64(Float64(t + x) + y))
	t_2 = Float64(Float64(y + x) + t)
	t_3 = Float64(y / t_2)
	t_4 = Float64(Float64(Float64(fma(Float64(y + x), Float64(z / t_2), Float64(Float64(a / t_2) * Float64(t + y))) / b) - t_3) * b)
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = t_4;
	elseif (t_1 <= 2e+293)
		tmp = fma(Float64(Float64(t / t_2) + t_3), a, Float64(fma(x, z, Float64(Float64(z - b) * y)) / t_2));
	else
		tmp = t_4;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(N[(N[(t + y), $MachinePrecision] * a), $MachinePrecision] + N[(N[(y + x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] - N[(b * y), $MachinePrecision]), $MachinePrecision] / N[(N[(t + x), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y + x), $MachinePrecision] + t), $MachinePrecision]}, Block[{t$95$3 = N[(y / t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(N[(N[(y + x), $MachinePrecision] * N[(z / t$95$2), $MachinePrecision] + N[(N[(a / t$95$2), $MachinePrecision] * N[(t + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision] - t$95$3), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], t$95$4, If[LessEqual[t$95$1, 2e+293], N[(N[(N[(t / t$95$2), $MachinePrecision] + t$95$3), $MachinePrecision] * a + N[(N[(x * z + N[(N[(z - b), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]), $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)) < -inf.0 or 1.9999999999999998e293 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 5.0%

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

   3. Taylor expanded in b around -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 72.9%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1.9999999999999998e293

   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 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(t + y\right) \cdot a + \left(y + x\right) \cdot z\right) - b \cdot y}{\left(t + x\right) + y} \leq -\infty:\\ \;\;\;\;\left(\frac{\mathsf{fma}\left(y + x, \frac{z}{\left(y + x\right) + t}, \frac{a}{\left(y + x\right) + t} \cdot \left(t + y\right)\right)}{b} - \frac{y}{\left(y + x\right) + t}\right) \cdot b\\ \mathbf{elif}\;\frac{\left(\left(t + y\right) \cdot a + \left(y + x\right) \cdot z\right) - b \cdot y}{\left(t + x\right) + y} \leq 2 \cdot 10^{+293}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t}{\left(y + x\right) + t} + \frac{y}{\left(y + x\right) + t}, a, \frac{\mathsf{fma}\left(x, z, \left(z - b\right) \cdot y\right)}{\left(y + x\right) + t}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{\mathsf{fma}\left(y + x, \frac{z}{\left(y + x\right) + t}, \frac{a}{\left(y + x\right) + t} \cdot \left(t + y\right)\right)}{b} - \frac{y}{\left(y + x\right) + t}\right) \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 66.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(\left(t + y\right) \cdot a + \left(y + x\right) \cdot z\right) - b \cdot y}{\left(t + x\right) + y}\\ t_2 := \left(z + a\right) - b\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+292}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+35}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, z, t \cdot a\right)}{t + x}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+209}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t, a, t\_2 \cdot y\right)}{t + y}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* (+ t y) a) (* (+ y x) z)) (* b y)) (+ (+ t x) y)))
        (t_2 (- (+ z a) b)))
   (if (<= t_1 -1e+292)
     t_2
     (if (<= t_1 5e+35)
       (/ (fma x z (* t a)) (+ t x))
       (if (<= t_1 2e+209) (/ (fma t a (* t_2 y)) (+ t y)) t_2)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((((t + y) * a) + ((y + x) * z)) - (b * y)) / ((t + x) + y);
	double t_2 = (z + a) - b;
	double tmp;
	if (t_1 <= -1e+292) {
		tmp = t_2;
	} else if (t_1 <= 5e+35) {
		tmp = fma(x, z, (t * a)) / (t + x);
	} else if (t_1 <= 2e+209) {
		tmp = fma(t, a, (t_2 * y)) / (t + y);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(Float64(Float64(t + y) * a) + Float64(Float64(y + x) * z)) - Float64(b * y)) / Float64(Float64(t + x) + y))
	t_2 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (t_1 <= -1e+292)
		tmp = t_2;
	elseif (t_1 <= 5e+35)
		tmp = Float64(fma(x, z, Float64(t * a)) / Float64(t + x));
	elseif (t_1 <= 2e+209)
		tmp = Float64(fma(t, a, Float64(t_2 * y)) / Float64(t + y));
	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[(t + y), $MachinePrecision] * a), $MachinePrecision] + N[(N[(y + x), $MachinePrecision] * z), $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, -1e+292], t$95$2, If[LessEqual[t$95$1, 5e+35], N[(N[(x * z + N[(t * a), $MachinePrecision]), $MachinePrecision] / N[(t + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+209], N[(N[(t * a + N[(t$95$2 * y), $MachinePrecision]), $MachinePrecision] / N[(t + y), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

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)) < -1e292 or 2.0000000000000001e209 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 11.7%

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

   3. Taylor expanded in y around inf

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

      1. 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 70.5

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

   5. Applied rewrites 70.5%

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

   if -1e292 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 5.00000000000000021e35

   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 67.0

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

   5. Applied rewrites 67.0%

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

   if 5.00000000000000021e35 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 2.0000000000000001e209

   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 x around 0

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

      1. lower-/.f64 N/A

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

      2. associate--l+ N/A

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

      3. distribute-lft-in N/A

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

      4. associate-+l+ N/A

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

      5. *-commutative N/A

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

      6. *-commutative N/A

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

      7. *-commutative N/A

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

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

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

      9. distribute-lft-in N/A

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

      10. associate--l+ N/A

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

      11. lower-fma.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. lower--.f64 N/A

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

      15. +-commutative N/A

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

      16. lower-+.f64 N/A

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

      17. +-commutative N/A

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

      18. lower-+.f64 79.8

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

   5. Applied rewrites 79.8%

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

4. Final simplification 69.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(t + y\right) \cdot a + \left(y + x\right) \cdot z\right) - b \cdot y}{\left(t + x\right) + y} \leq -1 \cdot 10^{+292}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;\frac{\left(\left(t + y\right) \cdot a + \left(y + x\right) \cdot z\right) - b \cdot y}{\left(t + x\right) + y} \leq 5 \cdot 10^{+35}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, z, t \cdot a\right)}{t + x}\\ \mathbf{elif}\;\frac{\left(\left(t + y\right) \cdot a + \left(y + x\right) \cdot z\right) - b \cdot y}{\left(t + x\right) + y} \leq 2 \cdot 10^{+209}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t, a, \left(\left(z + a\right) - b\right) \cdot y\right)}{t + y}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 87.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y + x\right) + t\\ t_2 := \frac{\left(\left(t + y\right) \cdot a + \left(y + x\right) \cdot z\right) - b \cdot y}{\left(t + x\right) + y}\\ t_3 := \left(z + a\right) - b\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+234}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t}{t\_1} + \frac{y}{t\_1}, a, \frac{\mathsf{fma}\left(x, z, \left(z - b\right) \cdot y\right)}{t\_1}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ y x) t))
        (t_2 (/ (- (+ (* (+ t y) a) (* (+ y x) z)) (* b y)) (+ (+ t x) y)))
        (t_3 (- (+ z a) b)))
   (if (<= t_2 (- INFINITY))
     t_3
     (if (<= t_2 2e+234)
       (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 = ((((t + y) * a) + ((y + x) * z)) - (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+234) {
		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(t + y) * a) + Float64(Float64(y + x) * z)) - 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+234)
		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[(t + y), $MachinePrecision] * a), $MachinePrecision] + N[(N[(y + x), $MachinePrecision] * z), $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+234], 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 2.00000000000000004e234 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 7.7%

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

   3. Taylor expanded in y around inf

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

      1. 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 70.2

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

   5. Applied rewrites 70.2%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 2.00000000000000004e234

   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 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(t + y\right) \cdot a + \left(y + x\right) \cdot z\right) - b \cdot y}{\left(t + x\right) + y} \leq -\infty:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;\frac{\left(\left(t + y\right) \cdot a + \left(y + x\right) \cdot z\right) - b \cdot y}{\left(t + x\right) + y} \leq 2 \cdot 10^{+234}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t}{\left(y + x\right) + t} + \frac{y}{\left(y + x\right) + t}, a, \frac{\mathsf{fma}\left(x, z, \left(z - b\right) \cdot y\right)}{\left(y + x\right) + t}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 87.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(\left(t + y\right) \cdot a + \left(y + x\right) \cdot z\right) - b \cdot y}{\left(t + x\right) + y}\\ t_2 := \left(z + a\right) - b\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+292}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+234}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* (+ t y) a) (* (+ y x) z)) (* b y)) (+ (+ t x) y)))
        (t_2 (- (+ z a) b)))
   (if (<= t_1 -1e+292) t_2 (if (<= t_1 2e+234) t_1 t_2))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((((t + y) * a) + ((y + x) * z)) - (b * y)) / ((t + x) + y);
	double t_2 = (z + a) - b;
	double tmp;
	if (t_1 <= -1e+292) {
		tmp = t_2;
	} else if (t_1 <= 2e+234) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((((t + y) * a) + ((y + x) * z)) - (b * y)) / ((t + x) + y)
    t_2 = (z + a) - b
    if (t_1 <= (-1d+292)) then
        tmp = t_2
    else if (t_1 <= 2d+234) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((((t + y) * a) + ((y + x) * z)) - (b * y)) / ((t + x) + y);
	double t_2 = (z + a) - b;
	double tmp;
	if (t_1 <= -1e+292) {
		tmp = t_2;
	} else if (t_1 <= 2e+234) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((((t + y) * a) + ((y + x) * z)) - (b * y)) / ((t + x) + y)
	t_2 = (z + a) - b
	tmp = 0
	if t_1 <= -1e+292:
		tmp = t_2
	elif t_1 <= 2e+234:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(Float64(Float64(t + y) * a) + Float64(Float64(y + x) * z)) - Float64(b * y)) / Float64(Float64(t + x) + y))
	t_2 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (t_1 <= -1e+292)
		tmp = t_2;
	elseif (t_1 <= 2e+234)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((((t + y) * a) + ((y + x) * z)) - (b * y)) / ((t + x) + y);
	t_2 = (z + a) - b;
	tmp = 0.0;
	if (t_1 <= -1e+292)
		tmp = t_2;
	elseif (t_1 <= 2e+234)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(N[(N[(t + y), $MachinePrecision] * a), $MachinePrecision] + N[(N[(y + x), $MachinePrecision] * z), $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, -1e+292], t$95$2, If[LessEqual[t$95$1, 2e+234], t$95$1, t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -1e292 or 2.00000000000000004e234 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 8.5%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   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 70.5

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

   5. Applied rewrites 70.5%

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

   if -1e292 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 2.00000000000000004e234

   1. Initial program 99.7%

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

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(t + y\right) \cdot a + \left(y + x\right) \cdot z\right) - b \cdot y}{\left(t + x\right) + y} \leq -1 \cdot 10^{+292}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;\frac{\left(\left(t + y\right) \cdot a + \left(y + x\right) \cdot z\right) - b \cdot y}{\left(t + x\right) + y} \leq 2 \cdot 10^{+234}:\\ \;\;\;\;\frac{\left(\left(t + y\right) \cdot a + \left(y + x\right) \cdot z\right) - b \cdot y}{\left(t + x\right) + y}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 87.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t + x\right) + y\\ t_2 := \frac{\left(\left(t + y\right) \cdot a + \left(y + x\right) \cdot z\right) - b \cdot y}{t\_1}\\ t_3 := \left(z + a\right) - b\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+292}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+234}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t + y, a, \mathsf{fma}\left(x, z, \left(z - b\right) \cdot y\right)\right)}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ t x) y))
        (t_2 (/ (- (+ (* (+ t y) a) (* (+ y x) z)) (* b y)) t_1))
        (t_3 (- (+ z a) b)))
   (if (<= t_2 -1e+292)
     t_3
     (if (<= t_2 2e+234)
       (/ (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 = ((((t + y) * a) + ((y + x) * z)) - (b * y)) / t_1;
	double t_3 = (z + a) - b;
	double tmp;
	if (t_2 <= -1e+292) {
		tmp = t_3;
	} else if (t_2 <= 2e+234) {
		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(t + y) * a) + Float64(Float64(y + x) * z)) - Float64(b * y)) / t_1)
	t_3 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (t_2 <= -1e+292)
		tmp = t_3;
	elseif (t_2 <= 2e+234)
		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[(t + y), $MachinePrecision] * a), $MachinePrecision] + N[(N[(y + x), $MachinePrecision] * z), $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, -1e+292], t$95$3, If[LessEqual[t$95$2, 2e+234], 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)) < -1e292 or 2.00000000000000004e234 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 8.5%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   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 70.5

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

   5. Applied rewrites 70.5%

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

   if -1e292 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 2.00000000000000004e234

   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 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(t + y\right) \cdot a + \left(y + x\right) \cdot z\right) - b \cdot y}{\left(t + x\right) + y} \leq -1 \cdot 10^{+292}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;\frac{\left(\left(t + y\right) \cdot a + \left(y + x\right) \cdot z\right) - b \cdot y}{\left(t + x\right) + y} \leq 2 \cdot 10^{+234}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t + y, a, \mathsf{fma}\left(x, z, \left(z - b\right) \cdot y\right)\right)}{\left(t + x\right) + y}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 74.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t + x\right) + y\\ t_2 := \frac{\left(\left(t + y\right) \cdot a + \left(y + x\right) \cdot z\right) - b \cdot y}{t\_1}\\ t_3 := \left(z + a\right) - b\\ \mathbf{if}\;t\_2 \leq -4 \cdot 10^{+230}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+234}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, z, t \cdot a\right) - b \cdot y}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ t x) y))
        (t_2 (/ (- (+ (* (+ t y) a) (* (+ y x) z)) (* b y)) t_1))
        (t_3 (- (+ z a) b)))
   (if (<= t_2 -4e+230)
     t_3
     (if (<= t_2 2e+234) (/ (- (fma x z (* t a)) (* 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 = ((((t + y) * a) + ((y + x) * z)) - (b * y)) / t_1;
	double t_3 = (z + a) - b;
	double tmp;
	if (t_2 <= -4e+230) {
		tmp = t_3;
	} else if (t_2 <= 2e+234) {
		tmp = (fma(x, z, (t * a)) - (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(t + y) * a) + Float64(Float64(y + x) * z)) - Float64(b * y)) / t_1)
	t_3 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (t_2 <= -4e+230)
		tmp = t_3;
	elseif (t_2 <= 2e+234)
		tmp = Float64(Float64(fma(x, z, Float64(t * a)) - Float64(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[(t + y), $MachinePrecision] * a), $MachinePrecision] + N[(N[(y + x), $MachinePrecision] * z), $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, -4e+230], t$95$3, If[LessEqual[t$95$2, 2e+234], N[(N[(N[(x * z + N[(t * a), $MachinePrecision]), $MachinePrecision] - N[(b * y), $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)) < -4.0000000000000004e230 or 2.00000000000000004e234 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 12.5%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   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 71.0

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

   5. Applied rewrites 71.0%

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

   if -4.0000000000000004e230 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 2.00000000000000004e234

   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

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 75.8

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

   5. Applied rewrites 75.8%

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

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(t + y\right) \cdot a + \left(y + x\right) \cdot z\right) - b \cdot y}{\left(t + x\right) + y} \leq -4 \cdot 10^{+230}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;\frac{\left(\left(t + y\right) \cdot a + \left(y + x\right) \cdot z\right) - b \cdot y}{\left(t + x\right) + y} \leq 2 \cdot 10^{+234}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, z, t \cdot a\right) - b \cdot y}{\left(t + x\right) + y}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 65.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(\left(t + y\right) \cdot a + \left(y + x\right) \cdot z\right) - b \cdot y}{\left(t + x\right) + y}\\ t_2 := \left(z + a\right) - b\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+292}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+37}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, z, t \cdot a\right)}{t + x}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* (+ t y) a) (* (+ y x) z)) (* b y)) (+ (+ t x) y)))
        (t_2 (- (+ z a) b)))
   (if (<= t_1 -1e+292)
     t_2
     (if (<= t_1 2e+37) (/ (fma x z (* t a)) (+ t x)) t_2))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((((t + y) * a) + ((y + x) * z)) - (b * y)) / ((t + x) + y);
	double t_2 = (z + a) - b;
	double tmp;
	if (t_1 <= -1e+292) {
		tmp = t_2;
	} else if (t_1 <= 2e+37) {
		tmp = fma(x, z, (t * a)) / (t + x);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(Float64(Float64(t + y) * a) + Float64(Float64(y + x) * z)) - Float64(b * y)) / Float64(Float64(t + x) + y))
	t_2 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (t_1 <= -1e+292)
		tmp = t_2;
	elseif (t_1 <= 2e+37)
		tmp = Float64(fma(x, z, Float64(t * a)) / 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[(t + y), $MachinePrecision] * a), $MachinePrecision] + N[(N[(y + x), $MachinePrecision] * z), $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, -1e+292], t$95$2, If[LessEqual[t$95$1, 2e+37], N[(N[(x * z + N[(t * a), $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)) < -1e292 or 1.99999999999999991e37 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 26.7%

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

   3. Taylor expanded in y around inf

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

      1. 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 69.1

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

   5. Applied rewrites 69.1%

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

   if -1e292 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1.99999999999999991e37

   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 66.5

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

   5. Applied rewrites 66.5%

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

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(t + y\right) \cdot a + \left(y + x\right) \cdot z\right) - b \cdot y}{\left(t + x\right) + y} \leq -1 \cdot 10^{+292}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;\frac{\left(\left(t + y\right) \cdot a + \left(y + x\right) \cdot z\right) - b \cdot y}{\left(t + x\right) + y} \leq 2 \cdot 10^{+37}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, z, t \cdot a\right)}{t + x}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 90.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y + x\right) + t\\ t_2 := \frac{y}{t\_1}\\ t_3 := \left(\left(\frac{x}{t\_1} + \mathsf{fma}\left(\frac{a}{z}, \frac{t + y}{t\_1}, t\_2\right)\right) - \frac{y}{t\_1 \cdot z} \cdot b\right) \cdot z\\ \mathbf{if}\;z \leq -190:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-88}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t}{t\_1} + t\_2, a, \frac{\mathsf{fma}\left(x, z, \left(z - b\right) \cdot y\right)}{t\_1}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ y x) t))
        (t_2 (/ y t_1))
        (t_3
         (*
          (-
           (+ (/ x t_1) (fma (/ a z) (/ (+ t y) t_1) t_2))
           (* (/ y (* t_1 z)) b))
          z)))
   (if (<= z -190.0)
     t_3
     (if (<= z 6e-88)
       (fma (+ (/ t t_1) t_2) 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 / t_1;
	double t_3 = (((x / t_1) + fma((a / z), ((t + y) / t_1), t_2)) - ((y / (t_1 * z)) * b)) * z;
	double tmp;
	if (z <= -190.0) {
		tmp = t_3;
	} else if (z <= 6e-88) {
		tmp = fma(((t / t_1) + t_2), 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(y / t_1)
	t_3 = Float64(Float64(Float64(Float64(x / t_1) + fma(Float64(a / z), Float64(Float64(t + y) / t_1), t_2)) - Float64(Float64(y / Float64(t_1 * z)) * b)) * z)
	tmp = 0.0
	if (z <= -190.0)
		tmp = t_3;
	elseif (z <= 6e-88)
		tmp = fma(Float64(Float64(t / t_1) + t_2), 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[(y / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(N[(x / t$95$1), $MachinePrecision] + N[(N[(a / z), $MachinePrecision] * N[(N[(t + y), $MachinePrecision] / t$95$1), $MachinePrecision] + t$95$2), $MachinePrecision]), $MachinePrecision] - N[(N[(y / N[(t$95$1 * z), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[z, -190.0], t$95$3, If[LessEqual[z, 6e-88], N[(N[(N[(t / t$95$1), $MachinePrecision] + t$95$2), $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 z < -190 or 5.9999999999999999e-88 < z

   1. Initial program 54.4%

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

   3. Taylor expanded in a around 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 62.5%

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

   6. Taylor expanded in a around inf

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

   8. Applied rewrites 63.6%

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

   9. Taylor expanded in z around inf

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

       1. lower-*.f64 N/A

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

       2. lower--.f64 N/A

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

   11. Applied rewrites 93.0%

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

   if -190 < z < 5.9999999999999999e-88

   1. Initial program 70.4%

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

   3. Taylor expanded in a around 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 88.5%

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

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -190:\\ \;\;\;\;\left(\left(\frac{x}{\left(y + x\right) + t} + \mathsf{fma}\left(\frac{a}{z}, \frac{t + y}{\left(y + x\right) + t}, \frac{y}{\left(y + x\right) + t}\right)\right) - \frac{y}{\left(\left(y + x\right) + t\right) \cdot z} \cdot b\right) \cdot z\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-88}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t}{\left(y + x\right) + t} + \frac{y}{\left(y + x\right) + t}, a, \frac{\mathsf{fma}\left(x, z, \left(z - b\right) \cdot y\right)}{\left(y + x\right) + t}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\frac{x}{\left(y + x\right) + t} + \mathsf{fma}\left(\frac{a}{z}, \frac{t + y}{\left(y + x\right) + t}, \frac{y}{\left(y + x\right) + t}\right)\right) - \frac{y}{\left(\left(y + x\right) + t\right) \cdot z} \cdot b\right) \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 60.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+261}:\\ \;\;\;\;a - \left(-z\right) \cdot \frac{y + x}{t}\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{+46}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z - b}{t}, y, a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.05e+261)
   (- a (* (- z) (/ (+ y x) t)))
   (if (<= t 1.5e+46) (- (+ z a) b) (fma (/ (- z b) t) y a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.05e+261) {
		tmp = a - (-z * ((y + x) / t));
	} else if (t <= 1.5e+46) {
		tmp = (z + a) - b;
	} else {
		tmp = fma(((z - b) / t), y, a);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.05e+261)
		tmp = Float64(a - Float64(Float64(-z) * Float64(Float64(y + x) / t)));
	elseif (t <= 1.5e+46)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = fma(Float64(Float64(z - b) / t), y, a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.05e+261], N[(a - N[((-z) * N[(N[(y + x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.5e+46], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(N[(N[(z - b), $MachinePrecision] / t), $MachinePrecision] * y + a), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.05e261

   1. Initial program 67.9%

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

   3. Taylor expanded in t around -inf

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

   5. Applied rewrites 78.1%

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

   6. Taylor expanded in z around -inf

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

   8. Applied rewrites 99.8%

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

   if -1.05e261 < t < 1.50000000000000012e46

   1. Initial program 61.9%

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

   3. Taylor expanded in 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 61.2

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

   5. Applied rewrites 61.2%

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

   if 1.50000000000000012e46 < t

   1. Initial program 57.6%

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

   3. Taylor expanded in t around -inf

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

   5. Applied rewrites 56.9%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 65.0%

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

4. Final simplification 63.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+261}:\\ \;\;\;\;a - \left(-z\right) \cdot \frac{y + x}{t}\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{+46}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z - b}{t}, y, a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 62.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{z - b}{t}, y, a\right)\\ \mathbf{if}\;t \leq -5 \cdot 10^{+99}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{+46}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (/ (- z b) t) y a)))
   (if (<= t -5e+99) t_1 (if (<= t 1.5e+46) (- (+ z a) b) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(((z - b) / t), y, a);
	double tmp;
	if (t <= -5e+99) {
		tmp = t_1;
	} else if (t <= 1.5e+46) {
		tmp = (z + a) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(Float64(Float64(z - b) / t), y, a)
	tmp = 0.0
	if (t <= -5e+99)
		tmp = t_1;
	elseif (t <= 1.5e+46)
		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[(N[(z - b), $MachinePrecision] / t), $MachinePrecision] * y + a), $MachinePrecision]}, If[LessEqual[t, -5e+99], t$95$1, If[LessEqual[t, 1.5e+46], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -5.00000000000000008e99 or 1.50000000000000012e46 < t

   1. Initial program 57.0%

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

   3. Taylor expanded in t around -inf

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

   5. Applied rewrites 57.9%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 63.8%

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

   if -5.00000000000000008e99 < t < 1.50000000000000012e46

   1. Initial program 63.5%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   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 63.0

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

   5. Applied rewrites 63.0%

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

Alternative 12: 58.2% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 1.25 \cdot 10^{+126}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{t + x} \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t 1.25e+126) (- (+ z a) b) (* (/ t (+ t x)) a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= 1.25e+126) {
		tmp = (z + a) - b;
	} else {
		tmp = (t / (t + x)) * 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 <= 1.25d+126) then
        tmp = (z + a) - b
    else
        tmp = (t / (t + x)) * 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 <= 1.25e+126) {
		tmp = (z + a) - b;
	} else {
		tmp = (t / (t + x)) * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= 1.25e+126:
		tmp = (z + a) - b
	else:
		tmp = (t / (t + x)) * a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= 1.25e+126)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(Float64(t / Float64(t + x)) * a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= 1.25e+126)
		tmp = (z + a) - b;
	else
		tmp = (t / (t + x)) * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, 1.25e+126], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(N[(t / N[(t + x), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 1.24999999999999994e126

   1. Initial program 63.0%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   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 59.2

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

   5. Applied rewrites 59.2%

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

   if 1.24999999999999994e126 < t

   1. Initial program 51.3%

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

   3. Taylor expanded in 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 61.2

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

   5. Applied rewrites 61.2%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 68.5%

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

4. Final simplification 60.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 1.25 \cdot 10^{+126}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{t + x} \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 50.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{+156}:\\ \;\;\;\;1 \cdot z\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{-98}:\\ \;\;\;\;a - b\\ \mathbf{elif}\;x \leq 2.05 \cdot 10^{+144}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;1 \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -4e+156)
   (* 1.0 z)
   (if (<= x 4.8e-98) (- a b) (if (<= x 2.05e+144) (+ z a) (* 1.0 z)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -4e+156) {
		tmp = 1.0 * z;
	} else if (x <= 4.8e-98) {
		tmp = a - b;
	} else if (x <= 2.05e+144) {
		tmp = z + a;
	} else {
		tmp = 1.0 * z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-4d+156)) then
        tmp = 1.0d0 * z
    else if (x <= 4.8d-98) then
        tmp = a - b
    else if (x <= 2.05d+144) then
        tmp = z + a
    else
        tmp = 1.0d0 * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -4e+156) {
		tmp = 1.0 * z;
	} else if (x <= 4.8e-98) {
		tmp = a - b;
	} else if (x <= 2.05e+144) {
		tmp = z + a;
	} else {
		tmp = 1.0 * z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -4e+156:
		tmp = 1.0 * z
	elif x <= 4.8e-98:
		tmp = a - b
	elif x <= 2.05e+144:
		tmp = z + a
	else:
		tmp = 1.0 * z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -4e+156)
		tmp = Float64(1.0 * z);
	elseif (x <= 4.8e-98)
		tmp = Float64(a - b);
	elseif (x <= 2.05e+144)
		tmp = Float64(z + a);
	else
		tmp = Float64(1.0 * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -4e+156)
		tmp = 1.0 * z;
	elseif (x <= 4.8e-98)
		tmp = a - b;
	elseif (x <= 2.05e+144)
		tmp = z + a;
	else
		tmp = 1.0 * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -4e+156], N[(1.0 * z), $MachinePrecision], If[LessEqual[x, 4.8e-98], N[(a - b), $MachinePrecision], If[LessEqual[x, 2.05e+144], N[(z + a), $MachinePrecision], N[(1.0 * z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.9999999999999999e156 or 2.05000000000000001e144 < x

   1. Initial program 49.2%

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

   3. Taylor expanded in 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 56.6%

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

   6. Taylor expanded in a around inf

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

   8. Applied rewrites 50.3%

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

   9. Taylor expanded in z around inf

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

       1. lower-*.f64 N/A

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

       2. lower--.f64 N/A

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

   11. Applied rewrites 88.6%

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

   12. Taylor expanded in x around inf

       \[\leadsto z \cdot 1 \]
   13. Step-by-step derivation

   14. Applied rewrites 58.4%

       \[\leadsto z \cdot 1 \]

   if -3.9999999999999999e156 < x < 4.8000000000000001e-98

   1. Initial program 66.0%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   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 65.1

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

   5. Applied rewrites 65.1%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 55.4%

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

   if 4.8000000000000001e-98 < x < 2.05000000000000001e144

   1. Initial program 67.3%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   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 53.7

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

   5. Applied rewrites 53.7%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 62.5%

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

4. Final simplification 57.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{+156}:\\ \;\;\;\;1 \cdot z\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{-98}:\\ \;\;\;\;a - b\\ \mathbf{elif}\;x \leq 2.05 \cdot 10^{+144}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;1 \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 58.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 2.7 \cdot 10^{+127}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{t}, y, a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t 2.7e+127) (- (+ z a) b) (fma (/ z t) y a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= 2.7e+127) {
		tmp = (z + a) - b;
	} else {
		tmp = fma((z / t), y, a);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= 2.7e+127)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = fma(Float64(z / t), y, a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, 2.7e+127], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(N[(z / t), $MachinePrecision] * y + a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 2.7000000000000002e127

   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 59.0

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

   5. Applied rewrites 59.0%

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

   if 2.7000000000000002e127 < t

   1. Initial program 50.0%

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

   3. Taylor expanded in t around -inf

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

   5. Applied rewrites 61.5%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 75.2%

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

   9. Taylor expanded in b around 0

      \[\leadsto \mathsf{fma}\left(\frac{z}{t}, y, a\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 65.2%

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

Alternative 15: 58.5% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.4 \cdot 10^{+156}:\\ \;\;\;\;1 \cdot z\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{+97}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;1 \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -8.4e+156) (* 1.0 z) (if (<= x 9.5e+97) (- (+ z a) b) (* 1.0 z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -8.4e+156) {
		tmp = 1.0 * z;
	} else if (x <= 9.5e+97) {
		tmp = (z + a) - b;
	} else {
		tmp = 1.0 * z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-8.4d+156)) then
        tmp = 1.0d0 * z
    else if (x <= 9.5d+97) then
        tmp = (z + a) - b
    else
        tmp = 1.0d0 * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -8.4e+156) {
		tmp = 1.0 * z;
	} else if (x <= 9.5e+97) {
		tmp = (z + a) - b;
	} else {
		tmp = 1.0 * z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -8.4e+156:
		tmp = 1.0 * z
	elif x <= 9.5e+97:
		tmp = (z + a) - b
	else:
		tmp = 1.0 * z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -8.4e+156)
		tmp = Float64(1.0 * z);
	elseif (x <= 9.5e+97)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(1.0 * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -8.4e+156)
		tmp = 1.0 * z;
	elseif (x <= 9.5e+97)
		tmp = (z + a) - b;
	else
		tmp = 1.0 * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -8.4e+156], N[(1.0 * z), $MachinePrecision], If[LessEqual[x, 9.5e+97], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(1.0 * z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -8.39999999999999925e156 or 9.49999999999999975e97 < x

   1. Initial program 51.7%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   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 58.5%

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

   6. Taylor expanded in a around inf

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

   8. Applied rewrites 53.8%

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

   9. Taylor expanded in z around inf

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

       1. lower-*.f64 N/A

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

       2. lower--.f64 N/A

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

   11. Applied rewrites 89.6%

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

   12. Taylor expanded in x around inf

       \[\leadsto z \cdot 1 \]
   13. Step-by-step derivation

   14. Applied rewrites 58.8%

       \[\leadsto z \cdot 1 \]

   if -8.39999999999999925e156 < x < 9.49999999999999975e97

   1. Initial program 66.0%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   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 62.3

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

   5. Applied rewrites 62.3%

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

4. Final simplification 61.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.4 \cdot 10^{+156}:\\ \;\;\;\;1 \cdot z\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{+97}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;1 \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 53.3% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 1.35 \cdot 10^{+126}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;1 \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t 1.35e+126) (+ z a) (* 1.0 a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= 1.35e+126) {
		tmp = z + a;
	} 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 <= 1.35d+126) then
        tmp = z + a
    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 <= 1.35e+126) {
		tmp = z + a;
	} else {
		tmp = 1.0 * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= 1.35e+126:
		tmp = z + a
	else:
		tmp = 1.0 * a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= 1.35e+126)
		tmp = Float64(z + a);
	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 <= 1.35e+126)
		tmp = z + a;
	else
		tmp = 1.0 * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, 1.35e+126], N[(z + a), $MachinePrecision], N[(1.0 * a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 1.35000000000000001e126

   1. Initial program 63.0%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   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 59.2

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

   5. Applied rewrites 59.2%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 54.2%

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

   if 1.35000000000000001e126 < t

   1. Initial program 51.3%

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

   3. Taylor expanded in 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 80.5%

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

   6. Taylor expanded in a around inf

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

   8. Applied rewrites 79.8%

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

   9. Taylor expanded in t around inf

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

   11. Applied rewrites 56.1%

       \[\leadsto 1 \cdot a \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 17: 52.1% accurate, 4.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 5.6 \cdot 10^{+43}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;z - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (if (<= b 5.6e+43) (+ z a) (- z b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 5.6e+43) {
		tmp = z + a;
	} else {
		tmp = z - b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= 5.6d+43) then
        tmp = z + a
    else
        tmp = z - b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 5.6e+43) {
		tmp = z + a;
	} else {
		tmp = z - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 5.6e+43:
		tmp = z + a
	else:
		tmp = z - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 5.6e+43)
		tmp = Float64(z + a);
	else
		tmp = Float64(z - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 5.6e+43)
		tmp = z + a;
	else
		tmp = z - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 5.6e+43], N[(z + a), $MachinePrecision], N[(z - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 5.60000000000000038e43

   1. Initial program 61.5%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   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 57.0

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

   5. Applied rewrites 57.0%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 58.1%

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

   if 5.60000000000000038e43 < b

   1. Initial program 60.4%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   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 47.1

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

   5. Applied rewrites 47.1%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 38.7%

      \[\leadsto z - \color{blue}{b} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 18: 52.1% accurate, 4.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 6.5 \cdot 10^{+79}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;a - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (if (<= b 6.5e+79) (+ z a) (- a b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 6.5e+79) {
		tmp = z + a;
	} else {
		tmp = a - b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= 6.5d+79) then
        tmp = z + a
    else
        tmp = a - b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 6.5e+79) {
		tmp = z + a;
	} else {
		tmp = a - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 6.5e+79:
		tmp = z + a
	else:
		tmp = a - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 6.5e+79)
		tmp = Float64(z + a);
	else
		tmp = Float64(a - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 6.5e+79)
		tmp = z + a;
	else
		tmp = a - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 6.5e+79], N[(z + a), $MachinePrecision], N[(a - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 6.49999999999999954e79

   1. Initial program 62.4%

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

   3. Taylor expanded in y around inf

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

      1. 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 56.8

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

   5. Applied rewrites 56.8%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 56.9%

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

   if 6.49999999999999954e79 < b

   1. Initial program 56.0%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   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 45.9

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

   5. Applied rewrites 45.9%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 39.8%

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

Alternative 19: 52.6% accurate, 11.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 61.2%

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

3. Taylor expanded in y around inf

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

   1. 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 54.8

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

5. Applied rewrites 54.8%

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

6. Taylor expanded in b around 0

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

8. Applied rewrites 52.1%

   \[\leadsto z + \color{blue}{a} \]
9. Add Preprocessing

Alternative 20: 13.3% accurate, 15.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 61.2%

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

3. Taylor expanded in y around inf

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

   1. 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 54.8

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

5. Applied rewrites 54.8%

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

6. Taylor expanded in b around inf

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

8. Applied rewrites 11.8%

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

Developer Target 1: 82.5% 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 2024268 
(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)))