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

Percentage Accurate: 61.0% → 88.8%

Time: 13.7s

Alternatives: 9

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: 61.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 88.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := z \cdot \left(x + y\right)\\ t_3 := \frac{\left(t\_2 + \left(y + t\right) \cdot a\right) - y \cdot b}{t\_1}\\ \mathbf{if}\;t\_3 \leq -\infty:\\ \;\;\;\;\mathsf{fma}\left(y + t, \frac{a}{t + \left(x + y\right)}, z\right)\\ \mathbf{elif}\;t\_3 \leq 10^{+271}:\\ \;\;\;\;\frac{\left(t\_2 + \mathsf{fma}\left(y, a, t \cdot a\right)\right) - y \cdot b}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z - b}{y + t}, a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t)))
        (t_2 (* z (+ x y)))
        (t_3 (/ (- (+ t_2 (* (+ y t) a)) (* y b)) t_1)))
   (if (<= t_3 (- INFINITY))
     (fma (+ y t) (/ a (+ t (+ x y))) z)
     (if (<= t_3 1e+271)
       (/ (- (+ t_2 (fma y a (* t a))) (* y b)) t_1)
       (fma y (/ (- z b) (+ y t)) a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = z * (x + y);
	double t_3 = ((t_2 + ((y + t) * a)) - (y * b)) / t_1;
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = fma((y + t), (a / (t + (x + y))), z);
	} else if (t_3 <= 1e+271) {
		tmp = ((t_2 + fma(y, a, (t * a))) - (y * b)) / t_1;
	} else {
		tmp = fma(y, ((z - b) / (y + t)), a);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(z * Float64(x + y))
	t_3 = Float64(Float64(Float64(t_2 + Float64(Float64(y + t) * a)) - Float64(y * b)) / t_1)
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = fma(Float64(y + t), Float64(a / Float64(t + Float64(x + y))), z);
	elseif (t_3 <= 1e+271)
		tmp = Float64(Float64(Float64(t_2 + fma(y, a, Float64(t * a))) - Float64(y * b)) / t_1);
	else
		tmp = fma(y, Float64(Float64(z - b) / Float64(y + t)), a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(t$95$2 + N[(N[(y + t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], N[(N[(y + t), $MachinePrecision] * N[(a / N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision], If[LessEqual[t$95$3, 1e+271], N[(N[(N[(t$95$2 + N[(y * a + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], N[(y * N[(N[(z - b), $MachinePrecision] / N[(y + t), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 6.4%

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

   3. Taylor expanded in b around 0

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

      1. mul-1-neg N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

      6. sub-neg N/A

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

      7. accelerator-lowering-fma.f64 N/A

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

      8. +-lowering-+.f64 N/A

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

      9. /-lowering-/.f64 N/A

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

      10. +-lowering-+.f64 N/A

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

      11. +-commutative N/A

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

      12. +-lowering-+.f64 N/A

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

   5. Simplified 40.6%

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

   6. Taylor expanded in x around inf

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

   8. Simplified 74.9%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 9.99999999999999953e270

   1. Initial program 99.6%

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

      1. *-commutative N/A

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

      2. +-commutative N/A

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

      3. distribute-rgt-in N/A

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

      4. accelerator-lowering-fma.f64 N/A

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

      5. *-lowering-*.f64 99.6

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

   4. Applied egg-rr 99.6%

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

   if 9.99999999999999953e270 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 4.8%

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

   3. Taylor expanded in b around 0

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

      1. mul-1-neg N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

      6. sub-neg N/A

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

      7. accelerator-lowering-fma.f64 N/A

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

      8. +-lowering-+.f64 N/A

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

      9. /-lowering-/.f64 N/A

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

      10. +-lowering-+.f64 N/A

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

      11. +-commutative N/A

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

      12. +-lowering-+.f64 N/A

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

   5. Simplified 21.6%

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

   6. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. accelerator-lowering-fma.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. --lowering--.f64 N/A

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

      6. +-commutative N/A

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

      7. +-lowering-+.f64 79.7

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

   8. Simplified 79.7%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z \cdot \left(x + y\right) + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty:\\ \;\;\;\;\mathsf{fma}\left(y + t, \frac{a}{t + \left(x + y\right)}, z\right)\\ \mathbf{elif}\;\frac{\left(z \cdot \left(x + y\right) + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)} \leq 10^{+271}:\\ \;\;\;\;\frac{\left(z \cdot \left(x + y\right) + \mathsf{fma}\left(y, a, t \cdot a\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z - b}{y + t}, a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 88.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(z \cdot \left(x + y\right) + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\mathsf{fma}\left(y + t, \frac{a}{t + \left(x + y\right)}, z\right)\\ \mathbf{elif}\;t\_1 \leq 10^{+271}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z - b}{y + t}, a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* z (+ x y)) (* (+ y t) a)) (* y b)) (+ y (+ x t)))))
   (if (<= t_1 (- INFINITY))
     (fma (+ y t) (/ a (+ t (+ x y))) z)
     (if (<= t_1 1e+271) t_1 (fma y (/ (- z b) (+ y t)) a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (((z * (x + y)) + ((y + t) * a)) - (y * b)) / (y + (x + t));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = fma((y + t), (a / (t + (x + y))), z);
	} else if (t_1 <= 1e+271) {
		tmp = t_1;
	} else {
		tmp = fma(y, ((z - b) / (y + t)), a);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(Float64(z * Float64(x + y)) + Float64(Float64(y + t) * a)) - Float64(y * b)) / Float64(y + Float64(x + t)))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = fma(Float64(y + t), Float64(a / Float64(t + Float64(x + y))), z);
	elseif (t_1 <= 1e+271)
		tmp = t_1;
	else
		tmp = fma(y, Float64(Float64(z - b) / Float64(y + t)), a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision] + N[(N[(y + t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(y + t), $MachinePrecision] * N[(a / N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision], If[LessEqual[t$95$1, 1e+271], t$95$1, N[(y * N[(N[(z - b), $MachinePrecision] / N[(y + t), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 6.4%

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

   3. Taylor expanded in b around 0

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

      1. mul-1-neg N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

      6. sub-neg N/A

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

      7. accelerator-lowering-fma.f64 N/A

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

      8. +-lowering-+.f64 N/A

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

      9. /-lowering-/.f64 N/A

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

      10. +-lowering-+.f64 N/A

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

      11. +-commutative N/A

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

      12. +-lowering-+.f64 N/A

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

   5. Simplified 40.6%

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

   6. Taylor expanded in x around inf

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

   8. Simplified 74.9%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 9.99999999999999953e270

   1. Initial program 99.6%

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

   if 9.99999999999999953e270 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 4.8%

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

   3. Taylor expanded in b around 0

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

      1. mul-1-neg N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

      6. sub-neg N/A

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

      7. accelerator-lowering-fma.f64 N/A

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

      8. +-lowering-+.f64 N/A

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

      9. /-lowering-/.f64 N/A

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

      10. +-lowering-+.f64 N/A

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

      11. +-commutative N/A

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

      12. +-lowering-+.f64 N/A

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

   5. Simplified 21.6%

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

   6. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. accelerator-lowering-fma.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. --lowering--.f64 N/A

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

      6. +-commutative N/A

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

      7. +-lowering-+.f64 79.7

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

   8. Simplified 79.7%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z \cdot \left(x + y\right) + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty:\\ \;\;\;\;\mathsf{fma}\left(y + t, \frac{a}{t + \left(x + y\right)}, z\right)\\ \mathbf{elif}\;\frac{\left(z \cdot \left(x + y\right) + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)} \leq 10^{+271}:\\ \;\;\;\;\frac{\left(z \cdot \left(x + y\right) + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z - b}{y + t}, a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 77.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y + t, \frac{a}{t + \left(x + y\right)}, z\right)\\ \mathbf{if}\;x \leq -3.05 \cdot 10^{+69}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 6.4 \cdot 10^{+72}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z - b}{y + t}, a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (+ y t) (/ a (+ t (+ x y))) z)))
   (if (<= x -3.05e+69)
     t_1
     (if (<= x 6.4e+72) (fma y (/ (- z b) (+ y t)) a) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma((y + t), (a / (t + (x + y))), z);
	double tmp;
	if (x <= -3.05e+69) {
		tmp = t_1;
	} else if (x <= 6.4e+72) {
		tmp = fma(y, ((z - b) / (y + t)), a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(Float64(y + t), Float64(a / Float64(t + Float64(x + y))), z)
	tmp = 0.0
	if (x <= -3.05e+69)
		tmp = t_1;
	elseif (x <= 6.4e+72)
		tmp = fma(y, Float64(Float64(z - b) / Float64(y + t)), a);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y + t), $MachinePrecision] * N[(a / N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision]}, If[LessEqual[x, -3.05e+69], t$95$1, If[LessEqual[x, 6.4e+72], N[(y * N[(N[(z - b), $MachinePrecision] / N[(y + t), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -3.05e69 or 6.4000000000000003e72 < x

   1. Initial program 47.0%

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

   3. Taylor expanded in b around 0

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

      1. mul-1-neg N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

      6. sub-neg N/A

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

      7. accelerator-lowering-fma.f64 N/A

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

      8. +-lowering-+.f64 N/A

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

      9. /-lowering-/.f64 N/A

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

      10. +-lowering-+.f64 N/A

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

      11. +-commutative N/A

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

      12. +-lowering-+.f64 N/A

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

   5. Simplified 57.2%

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

   6. Taylor expanded in x around inf

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

   8. Simplified 79.7%

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

   if -3.05e69 < x < 6.4000000000000003e72

   1. Initial program 67.0%

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

   3. Taylor expanded in b around 0

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

      1. mul-1-neg N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

      6. sub-neg N/A

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

      7. accelerator-lowering-fma.f64 N/A

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

      8. +-lowering-+.f64 N/A

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

      9. /-lowering-/.f64 N/A

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

      10. +-lowering-+.f64 N/A

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

      11. +-commutative N/A

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

      12. +-lowering-+.f64 N/A

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

   5. Simplified 72.7%

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

   6. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. accelerator-lowering-fma.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. --lowering--.f64 N/A

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

      6. +-commutative N/A

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

      7. +-lowering-+.f64 83.8

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

   8. Simplified 83.8%

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

4. Final simplification 82.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.05 \cdot 10^{+69}:\\ \;\;\;\;\mathsf{fma}\left(y + t, \frac{a}{t + \left(x + y\right)}, z\right)\\ \mathbf{elif}\;x \leq 6.4 \cdot 10^{+72}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z - b}{y + t}, a\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y + t, \frac{a}{t + \left(x + y\right)}, z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(a, \frac{t}{x + t}, z\right)\\ \mathbf{if}\;x \leq -6.2 \cdot 10^{+74}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.02 \cdot 10^{+157}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z - b}{y + t}, a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma a (/ t (+ x t)) z)))
   (if (<= x -6.2e+74)
     t_1
     (if (<= x 1.02e+157) (fma y (/ (- z b) (+ y t)) a) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(a, (t / (x + t)), z);
	double tmp;
	if (x <= -6.2e+74) {
		tmp = t_1;
	} else if (x <= 1.02e+157) {
		tmp = fma(y, ((z - b) / (y + t)), a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(a, Float64(t / Float64(x + t)), z)
	tmp = 0.0
	if (x <= -6.2e+74)
		tmp = t_1;
	elseif (x <= 1.02e+157)
		tmp = fma(y, Float64(Float64(z - b) / Float64(y + t)), a);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(t / N[(x + t), $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision]}, If[LessEqual[x, -6.2e+74], t$95$1, If[LessEqual[x, 1.02e+157], N[(y * N[(N[(z - b), $MachinePrecision] / N[(y + t), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -6.20000000000000043e74 or 1.02000000000000003e157 < x

   1. Initial program 48.2%

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

   3. Taylor expanded in b around 0

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

      1. mul-1-neg N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

      6. sub-neg N/A

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

      7. accelerator-lowering-fma.f64 N/A

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

      8. +-lowering-+.f64 N/A

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

      9. /-lowering-/.f64 N/A

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

      10. +-lowering-+.f64 N/A

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

      11. +-commutative N/A

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

      12. +-lowering-+.f64 N/A

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

   5. Simplified 57.8%

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

   6. Taylor expanded in x around inf

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

   8. Simplified 85.4%

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

   9. Taylor expanded in y around 0

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

       1. +-commutative N/A

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

       2. associate-/l* N/A

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

       3. accelerator-lowering-fma.f64 N/A

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

       4. /-lowering-/.f64 N/A

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

       5. +-lowering-+.f64 78.5

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

   11. Simplified 78.5%

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

   if -6.20000000000000043e74 < x < 1.02000000000000003e157

   1. Initial program 64.6%

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

   3. Taylor expanded in b around 0

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

      1. mul-1-neg N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

      6. sub-neg N/A

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

      7. accelerator-lowering-fma.f64 N/A

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

      8. +-lowering-+.f64 N/A

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

      9. /-lowering-/.f64 N/A

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

      10. +-lowering-+.f64 N/A

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

      11. +-commutative N/A

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

      12. +-lowering-+.f64 N/A

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

   5. Simplified 71.0%

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

   6. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. accelerator-lowering-fma.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. --lowering--.f64 N/A

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

      6. +-commutative N/A

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

      7. +-lowering-+.f64 80.8

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

   8. Simplified 80.8%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.2 \cdot 10^{+74}:\\ \;\;\;\;\mathsf{fma}\left(a, \frac{t}{x + t}, z\right)\\ \mathbf{elif}\;x \leq 1.02 \cdot 10^{+157}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z - b}{y + t}, a\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, \frac{t}{x + t}, z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 66.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + \left(z - b\right)\\ \mathbf{if}\;y \leq -4.4 \cdot 10^{+16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.04 \cdot 10^{+127}:\\ \;\;\;\;\mathsf{fma}\left(a, \frac{t}{x + t}, z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ a (- z b))))
   (if (<= y -4.4e+16) t_1 (if (<= y 1.04e+127) (fma a (/ t (+ x t)) z) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a + (z - b);
	double tmp;
	if (y <= -4.4e+16) {
		tmp = t_1;
	} else if (y <= 1.04e+127) {
		tmp = fma(a, (t / (x + t)), z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a + Float64(z - b))
	tmp = 0.0
	if (y <= -4.4e+16)
		tmp = t_1;
	elseif (y <= 1.04e+127)
		tmp = fma(a, Float64(t / Float64(x + t)), z);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a + N[(z - b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.4e+16], t$95$1, If[LessEqual[y, 1.04e+127], N[(a * N[(t / N[(x + t), $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -4.4e16 or 1.04e127 < y

   1. Initial program 39.2%

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

   3. Taylor expanded in y around inf

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

      1. associate--l+ N/A

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

      2. +-lowering-+.f64 N/A

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

      3. --lowering--.f64 81.8

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

   5. Simplified 81.8%

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

   if -4.4e16 < y < 1.04e127

   1. Initial program 72.0%

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

   3. Taylor expanded in b around 0

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

      1. mul-1-neg N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

      6. sub-neg N/A

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

      7. accelerator-lowering-fma.f64 N/A

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

      8. +-lowering-+.f64 N/A

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

      9. /-lowering-/.f64 N/A

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

      10. +-lowering-+.f64 N/A

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

      11. +-commutative N/A

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

      12. +-lowering-+.f64 N/A

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

   5. Simplified 80.3%

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

   6. Taylor expanded in x around inf

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

   8. Simplified 64.9%

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

   9. Taylor expanded in y around 0

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

       1. +-commutative N/A

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

       2. associate-/l* N/A

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

       3. accelerator-lowering-fma.f64 N/A

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

       4. /-lowering-/.f64 N/A

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

       5. +-lowering-+.f64 62.2

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

   11. Simplified 62.2%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+16}:\\ \;\;\;\;a + \left(z - b\right)\\ \mathbf{elif}\;y \leq 1.04 \cdot 10^{+127}:\\ \;\;\;\;\mathsf{fma}\left(a, \frac{t}{x + t}, z\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(z - b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 58.4% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.85 \cdot 10^{+169}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{+157}:\\ \;\;\;\;a + \left(z - b\right)\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -1.85e+169) z (if (<= x 2.2e+157) (+ a (- z b)) z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.85e+169) {
		tmp = z;
	} else if (x <= 2.2e+157) {
		tmp = a + (z - b);
	} else {
		tmp = z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-1.85d+169)) then
        tmp = z
    else if (x <= 2.2d+157) then
        tmp = a + (z - b)
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.85e+169) {
		tmp = z;
	} else if (x <= 2.2e+157) {
		tmp = a + (z - b);
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -1.85e+169:
		tmp = z
	elif x <= 2.2e+157:
		tmp = a + (z - b)
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -1.85e+169)
		tmp = z;
	elseif (x <= 2.2e+157)
		tmp = Float64(a + Float64(z - b));
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -1.85e+169)
		tmp = z;
	elseif (x <= 2.2e+157)
		tmp = a + (z - b);
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -1.85e+169], z, If[LessEqual[x, 2.2e+157], N[(a + N[(z - b), $MachinePrecision]), $MachinePrecision], z]]

Derivation

1. Split input into 2 regimes

2. if x < -1.85e169 or 2.2000000000000001e157 < x

   1. Initial program 50.5%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 72.1%

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

   if -1.85e169 < x < 2.2000000000000001e157

   1. Initial program 62.3%

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

   3. Taylor expanded in y around inf

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

      1. associate--l+ N/A

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

      2. +-lowering-+.f64 N/A

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

      3. --lowering--.f64 62.3

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

   5. Simplified 62.3%

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

Alternative 7: 45.4% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{+39}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{+38}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -8.5e+39) z (if (<= x 5.8e+38) a z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -8.5e+39) {
		tmp = z;
	} else if (x <= 5.8e+38) {
		tmp = a;
	} else {
		tmp = z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-8.5d+39)) then
        tmp = z
    else if (x <= 5.8d+38) then
        tmp = a
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -8.5e+39) {
		tmp = z;
	} else if (x <= 5.8e+38) {
		tmp = a;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -8.5e+39:
		tmp = z
	elif x <= 5.8e+38:
		tmp = a
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -8.5e+39)
		tmp = z;
	elseif (x <= 5.8e+38)
		tmp = a;
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -8.5e+39)
		tmp = z;
	elseif (x <= 5.8e+38)
		tmp = a;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -8.5e+39], z, If[LessEqual[x, 5.8e+38], a, z]]

Derivation

1. Split input into 2 regimes

2. if x < -8.49999999999999971e39 or 5.80000000000000013e38 < x

   1. Initial program 47.9%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 56.9%

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

   if -8.49999999999999971e39 < x < 5.80000000000000013e38

   1. Initial program 68.5%

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

   3. Taylor expanded in t around inf

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

   5. Simplified 45.8%

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

Alternative 8: 52.6% accurate, 4.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.8 \cdot 10^{+173}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;z + a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (if (<= x -8.8e+173) z (+ z a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -8.8e+173) {
		tmp = z;
	} else {
		tmp = z + a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-8.8d+173)) then
        tmp = z
    else
        tmp = z + a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -8.8e+173) {
		tmp = z;
	} else {
		tmp = z + a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -8.8e+173:
		tmp = z
	else:
		tmp = z + a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -8.8e+173)
		tmp = z;
	else
		tmp = Float64(z + a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -8.8e+173)
		tmp = z;
	else
		tmp = z + a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -8.8e+173], z, N[(z + a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -8.7999999999999999e173

   1. Initial program 44.1%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 71.3%

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

   if -8.7999999999999999e173 < x

   1. Initial program 61.9%

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

   3. Taylor expanded in b around 0

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

      1. accelerator-lowering-fma.f64 N/A

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

      2. +-lowering-+.f64 N/A

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

      3. *-lowering-*.f64 N/A

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

      4. +-commutative N/A

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

      5. +-lowering-+.f64 47.2

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

   5. Simplified 47.2%

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

   6. Taylor expanded in y around inf

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

      1. +-lowering-+.f64 54.5

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

   8. Simplified 54.5%

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

4. Final simplification 56.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.8 \cdot 10^{+173}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;z + a\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 33.3% accurate, 45.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 59.6%

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

3. Taylor expanded in t around inf

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

5. Simplified 32.6%

   \[\leadsto \color{blue}{a} \]
6. Add Preprocessing

Developer Target 1: 82.0% 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 2024201 
(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)))