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

Percentage Accurate: 59.9% → 92.2%

Time: 10.7s

Alternatives: 13

Speedup: 2.4×

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: 59.9% 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: 92.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + y\right) + t\\ t_2 := \frac{y}{t\_1}\\ t_3 := \left(\frac{t + y}{t\_1} \cdot \frac{a}{z} - \mathsf{fma}\left(\frac{b}{z}, t\_2, \frac{-\left(x + y\right)}{t\_1}\right)\right) \cdot z\\ \mathbf{if}\;z \leq -3 \cdot 10^{-72}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-81}:\\ \;\;\;\;\left(\frac{\frac{\left(x + y\right) \cdot z}{a}}{t\_1} - \mathsf{fma}\left(\frac{b}{a}, t\_2, \frac{-\left(t + y\right)}{t\_1}\right)\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ x y) t))
        (t_2 (/ y t_1))
        (t_3
         (*
          (- (* (/ (+ t y) t_1) (/ a z)) (fma (/ b z) t_2 (/ (- (+ x y)) t_1)))
          z)))
   (if (<= z -3e-72)
     t_3
     (if (<= z 3.2e-81)
       (*
        (- (/ (/ (* (+ x y) z) a) t_1) (fma (/ b a) t_2 (/ (- (+ t y)) t_1)))
        a)
       t_3))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + y) + t;
	double t_2 = y / t_1;
	double t_3 = ((((t + y) / t_1) * (a / z)) - fma((b / z), t_2, (-(x + y) / t_1))) * z;
	double tmp;
	if (z <= -3e-72) {
		tmp = t_3;
	} else if (z <= 3.2e-81) {
		tmp = (((((x + y) * z) / a) / t_1) - fma((b / a), t_2, (-(t + y) / t_1))) * a;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + y) + t)
	t_2 = Float64(y / t_1)
	t_3 = Float64(Float64(Float64(Float64(Float64(t + y) / t_1) * Float64(a / z)) - fma(Float64(b / z), t_2, Float64(Float64(-Float64(x + y)) / t_1))) * z)
	tmp = 0.0
	if (z <= -3e-72)
		tmp = t_3;
	elseif (z <= 3.2e-81)
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(x + y) * z) / a) / t_1) - fma(Float64(b / a), t_2, Float64(Float64(-Float64(t + y)) / t_1))) * a);
	else
		tmp = t_3;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + y), $MachinePrecision] + t), $MachinePrecision]}, Block[{t$95$2 = N[(y / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(N[(N[(t + y), $MachinePrecision] / t$95$1), $MachinePrecision] * N[(a / z), $MachinePrecision]), $MachinePrecision] - N[(N[(b / z), $MachinePrecision] * t$95$2 + N[((-N[(x + y), $MachinePrecision]) / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[z, -3e-72], t$95$3, If[LessEqual[z, 3.2e-81], N[(N[(N[(N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] / a), $MachinePrecision] / t$95$1), $MachinePrecision] - N[(N[(b / a), $MachinePrecision] * t$95$2 + N[((-N[(t + y), $MachinePrecision]) / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision], t$95$3]]]]]

Derivation

1. Split input into 2 regimes

2. if z < -3e-72 or 3.2e-81 < z

   1. Initial program 52.2%

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

      1. lift-/.f64 N/A

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

      2. frac-2neg N/A

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

      3. div-inv N/A

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

      4. lower-*.f64 N/A

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

   4. Applied rewrites 52.5%

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

   5. Taylor expanded in z around -inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower--.f64 N/A

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

   7. Applied rewrites 98.2%

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

   if -3e-72 < z < 3.2e-81

   1. Initial program 75.7%

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

      1. lift-/.f64 N/A

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

      2. frac-2neg N/A

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

      3. div-inv N/A

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

      4. lower-*.f64 N/A

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

   4. Applied rewrites 75.5%

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

   5. Taylor expanded in a around -inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower--.f64 N/A

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

   7. Applied rewrites 82.0%

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

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{-72}:\\ \;\;\;\;\left(\frac{t + y}{\left(x + y\right) + t} \cdot \frac{a}{z} - \mathsf{fma}\left(\frac{b}{z}, \frac{y}{\left(x + y\right) + t}, \frac{-\left(x + y\right)}{\left(x + y\right) + t}\right)\right) \cdot z\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-81}:\\ \;\;\;\;\left(\frac{\frac{\left(x + y\right) \cdot z}{a}}{\left(x + y\right) + t} - \mathsf{fma}\left(\frac{b}{a}, \frac{y}{\left(x + y\right) + t}, \frac{-\left(t + y\right)}{\left(x + y\right) + t}\right)\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{t + y}{\left(x + y\right) + t} \cdot \frac{a}{z} - \mathsf{fma}\left(\frac{b}{z}, \frac{y}{\left(x + y\right) + t}, \frac{-\left(x + y\right)}{\left(x + y\right) + t}\right)\right) \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 88.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(\left(t + y\right) \cdot a + \left(x + y\right) \cdot z\right) - y \cdot b}{\left(x + t\right) + y}\\ t_2 := \left(x + y\right) + t\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\left(\frac{t + y}{t\_2} \cdot \frac{a}{z} - \mathsf{fma}\left(y, \frac{b}{t\_2 \cdot z}, \frac{-\left(x + y\right)}{t\_2}\right)\right) \cdot z\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+235}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* (+ t y) a) (* (+ x y) z)) (* y b)) (+ (+ x t) y)))
        (t_2 (+ (+ x y) t)))
   (if (<= t_1 (- INFINITY))
     (*
      (-
       (* (/ (+ t y) t_2) (/ a z))
       (fma y (/ b (* t_2 z)) (/ (- (+ x y)) t_2)))
      z)
     (if (<= t_1 5e+235) t_1 (- (+ a z) b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((((t + y) * a) + ((x + y) * z)) - (y * b)) / ((x + t) + y);
	double t_2 = (x + y) + t;
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = ((((t + y) / t_2) * (a / z)) - fma(y, (b / (t_2 * z)), (-(x + y) / t_2))) * z;
	} else if (t_1 <= 5e+235) {
		tmp = t_1;
	} else {
		tmp = (a + z) - b;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(Float64(Float64(t + y) * a) + Float64(Float64(x + y) * z)) - Float64(y * b)) / Float64(Float64(x + t) + y))
	t_2 = Float64(Float64(x + y) + t)
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(Float64(Float64(Float64(t + y) / t_2) * Float64(a / z)) - fma(y, Float64(b / Float64(t_2 * z)), Float64(Float64(-Float64(x + y)) / t_2))) * z);
	elseif (t_1 <= 5e+235)
		tmp = t_1;
	else
		tmp = Float64(Float64(a + z) - b);
	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[(x + y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(N[(x + t), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + y), $MachinePrecision] + t), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(N[(N[(N[(t + y), $MachinePrecision] / t$95$2), $MachinePrecision] * N[(a / z), $MachinePrecision]), $MachinePrecision] - N[(y * N[(b / N[(t$95$2 * z), $MachinePrecision]), $MachinePrecision] + N[((-N[(x + y), $MachinePrecision]) / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[t$95$1, 5e+235], t$95$1, N[(N[(a + z), $MachinePrecision] - b), $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 6.7%

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

      1. lift-/.f64 N/A

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

      2. frac-2neg N/A

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

      3. div-inv N/A

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

      4. lower-*.f64 N/A

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

   4. Applied rewrites 6.7%

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

   5. Taylor expanded in z around -inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower--.f64 N/A

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

   7. Applied rewrites 84.3%

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

   9. Applied rewrites 84.3%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 5.00000000000000027e235

   1. Initial program 99.5%

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

   if 5.00000000000000027e235 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 8.8%

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

   3. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 75.1

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

   5. Applied rewrites 75.1%

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

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(t + y\right) \cdot a + \left(x + y\right) \cdot z\right) - y \cdot b}{\left(x + t\right) + y} \leq -\infty:\\ \;\;\;\;\left(\frac{t + y}{\left(x + y\right) + t} \cdot \frac{a}{z} - \mathsf{fma}\left(y, \frac{b}{\left(\left(x + y\right) + t\right) \cdot z}, \frac{-\left(x + y\right)}{\left(x + y\right) + t}\right)\right) \cdot z\\ \mathbf{elif}\;\frac{\left(\left(t + y\right) \cdot a + \left(x + y\right) \cdot z\right) - y \cdot b}{\left(x + t\right) + y} \leq 5 \cdot 10^{+235}:\\ \;\;\;\;\frac{\left(\left(t + y\right) \cdot a + \left(x + y\right) \cdot z\right) - y \cdot b}{\left(x + t\right) + y}\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 88.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(\left(t + y\right) \cdot a + \left(x + y\right) \cdot z\right) - y \cdot b}{\left(x + t\right) + y}\\ t_2 := \left(a + z\right) - b\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+235}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* (+ t y) a) (* (+ x y) z)) (* y b)) (+ (+ x t) y)))
        (t_2 (- (+ a z) b)))
   (if (<= t_1 (- INFINITY)) t_2 (if (<= t_1 5e+235) 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) + ((x + y) * z)) - (y * b)) / ((x + t) + y);
	double t_2 = (a + z) - b;
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = t_2;
	} else if (t_1 <= 5e+235) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((((t + y) * a) + ((x + y) * z)) - (y * b)) / ((x + t) + y);
	double t_2 = (a + z) - b;
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else if (t_1 <= 5e+235) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((((t + y) * a) + ((x + y) * z)) - (y * b)) / ((x + t) + y)
	t_2 = (a + z) - b
	tmp = 0
	if t_1 <= -math.inf:
		tmp = t_2
	elif t_1 <= 5e+235:
		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(x + y) * z)) - Float64(y * b)) / Float64(Float64(x + t) + y))
	t_2 = Float64(Float64(a + z) - b)
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = t_2;
	elseif (t_1 <= 5e+235)
		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) + ((x + y) * z)) - (y * b)) / ((x + t) + y);
	t_2 = (a + z) - b;
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = t_2;
	elseif (t_1 <= 5e+235)
		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[(x + y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(N[(x + t), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], t$95$2, If[LessEqual[t$95$1, 5e+235], t$95$1, t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -inf.0 or 5.00000000000000027e235 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 8.1%

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

   3. Taylor expanded in y around inf

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

      1. 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 75.6

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

   5. Applied rewrites 75.6%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 5.00000000000000027e235

   1. Initial program 99.5%

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

4. Final simplification 89.2%

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

Alternative 4: 74.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + t\right) + y\\ t_2 := \left(a + z\right) - b\\ t_3 := \left(t + y\right) \cdot a\\ t_4 := \frac{\left(t\_3 + \left(x + y\right) \cdot z\right) - y \cdot b}{t\_1}\\ \mathbf{if}\;t\_4 \leq -\infty:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_4 \leq 4 \cdot 10^{+139}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x + y, z, t\_3\right)}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ x t) y))
        (t_2 (- (+ a z) b))
        (t_3 (* (+ t y) a))
        (t_4 (/ (- (+ t_3 (* (+ x y) z)) (* y b)) t_1)))
   (if (<= t_4 (- INFINITY))
     t_2
     (if (<= t_4 4e+139) (/ (fma (+ x y) z t_3) t_1) t_2))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + t) + y;
	double t_2 = (a + z) - b;
	double t_3 = (t + y) * a;
	double t_4 = ((t_3 + ((x + y) * z)) - (y * b)) / t_1;
	double tmp;
	if (t_4 <= -((double) INFINITY)) {
		tmp = t_2;
	} else if (t_4 <= 4e+139) {
		tmp = fma((x + y), z, t_3) / t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + t) + y)
	t_2 = Float64(Float64(a + z) - b)
	t_3 = Float64(Float64(t + y) * a)
	t_4 = Float64(Float64(Float64(t_3 + Float64(Float64(x + y) * z)) - Float64(y * b)) / t_1)
	tmp = 0.0
	if (t_4 <= Float64(-Inf))
		tmp = t_2;
	elseif (t_4 <= 4e+139)
		tmp = Float64(fma(Float64(x + y), z, t_3) / t_1);
	else
		tmp = t_2;
	end
	return 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[(a + z), $MachinePrecision] - b), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t + y), $MachinePrecision] * a), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(t$95$3 + N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[t$95$4, (-Infinity)], t$95$2, If[LessEqual[t$95$4, 4e+139], N[(N[(N[(x + y), $MachinePrecision] * z + t$95$3), $MachinePrecision] / t$95$1), $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)) < -inf.0 or 4.00000000000000013e139 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 13.6%

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

   3. Taylor expanded in y around inf

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

      1. 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 74.7

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

   5. Applied rewrites 74.7%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 4.00000000000000013e139

   1. Initial program 99.5%

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

   3. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-+.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 81.4

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

   5. Applied rewrites 81.4%

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

4. Final simplification 78.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(t + y\right) \cdot a + \left(x + y\right) \cdot z\right) - y \cdot b}{\left(x + t\right) + y} \leq -\infty:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{elif}\;\frac{\left(\left(t + y\right) \cdot a + \left(x + y\right) \cdot z\right) - y \cdot b}{\left(x + t\right) + y} \leq 4 \cdot 10^{+139}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x + y, z, \left(t + y\right) \cdot a\right)}{\left(x + t\right) + y}\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 88.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + y\right) + t\\ t_2 := \left(\frac{t + y}{t\_1} \cdot \frac{a}{z} - \mathsf{fma}\left(y, \frac{b}{t\_1 \cdot z}, \frac{-\left(x + y\right)}{t\_1}\right)\right) \cdot z\\ \mathbf{if}\;z \leq -4.8 \cdot 10^{-211}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-83}:\\ \;\;\;\;\left(\frac{\frac{\left(x + y\right) \cdot z}{a}}{t\_1} - \mathsf{fma}\left(\frac{b}{a}, \frac{y}{t\_1}, \frac{-\left(t + y\right)}{t\_1}\right)\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ x y) t))
        (t_2
         (*
          (-
           (* (/ (+ t y) t_1) (/ a z))
           (fma y (/ b (* t_1 z)) (/ (- (+ x y)) t_1)))
          z)))
   (if (<= z -4.8e-211)
     t_2
     (if (<= z 1.45e-83)
       (*
        (-
         (/ (/ (* (+ x y) z) a) t_1)
         (fma (/ b a) (/ y t_1) (/ (- (+ t y)) t_1)))
        a)
       t_2))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + y) + t;
	double t_2 = ((((t + y) / t_1) * (a / z)) - fma(y, (b / (t_1 * z)), (-(x + y) / t_1))) * z;
	double tmp;
	if (z <= -4.8e-211) {
		tmp = t_2;
	} else if (z <= 1.45e-83) {
		tmp = (((((x + y) * z) / a) / t_1) - fma((b / a), (y / t_1), (-(t + y) / t_1))) * a;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + y) + t)
	t_2 = Float64(Float64(Float64(Float64(Float64(t + y) / t_1) * Float64(a / z)) - fma(y, Float64(b / Float64(t_1 * z)), Float64(Float64(-Float64(x + y)) / t_1))) * z)
	tmp = 0.0
	if (z <= -4.8e-211)
		tmp = t_2;
	elseif (z <= 1.45e-83)
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(x + y) * z) / a) / t_1) - fma(Float64(b / a), Float64(y / t_1), Float64(Float64(-Float64(t + y)) / t_1))) * a);
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + y), $MachinePrecision] + t), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(N[(t + y), $MachinePrecision] / t$95$1), $MachinePrecision] * N[(a / z), $MachinePrecision]), $MachinePrecision] - N[(y * N[(b / N[(t$95$1 * z), $MachinePrecision]), $MachinePrecision] + N[((-N[(x + y), $MachinePrecision]) / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[z, -4.8e-211], t$95$2, If[LessEqual[z, 1.45e-83], N[(N[(N[(N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] / a), $MachinePrecision] / t$95$1), $MachinePrecision] - N[(N[(b / a), $MachinePrecision] * N[(y / t$95$1), $MachinePrecision] + N[((-N[(t + y), $MachinePrecision]) / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if z < -4.8000000000000004e-211 or 1.45e-83 < z

   1. Initial program 54.6%

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

      1. lift-/.f64 N/A

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

      2. frac-2neg N/A

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

      3. div-inv N/A

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

      4. lower-*.f64 N/A

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

   4. Applied rewrites 54.8%

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

   5. Taylor expanded in z around -inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower--.f64 N/A

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

   7. Applied rewrites 94.8%

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

   9. Applied rewrites 93.8%

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

   if -4.8000000000000004e-211 < z < 1.45e-83

   1. Initial program 75.2%

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

      1. lift-/.f64 N/A

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

      2. frac-2neg N/A

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

      3. div-inv N/A

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

      4. lower-*.f64 N/A

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

   4. Applied rewrites 74.9%

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

   5. Taylor expanded in a around -inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower--.f64 N/A

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

   7. Applied rewrites 83.2%

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

4. Final simplification 90.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{-211}:\\ \;\;\;\;\left(\frac{t + y}{\left(x + y\right) + t} \cdot \frac{a}{z} - \mathsf{fma}\left(y, \frac{b}{\left(\left(x + y\right) + t\right) \cdot z}, \frac{-\left(x + y\right)}{\left(x + y\right) + t}\right)\right) \cdot z\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-83}:\\ \;\;\;\;\left(\frac{\frac{\left(x + y\right) \cdot z}{a}}{\left(x + y\right) + t} - \mathsf{fma}\left(\frac{b}{a}, \frac{y}{\left(x + y\right) + t}, \frac{-\left(t + y\right)}{\left(x + y\right) + t}\right)\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{t + y}{\left(x + y\right) + t} \cdot \frac{a}{z} - \mathsf{fma}\left(y, \frac{b}{\left(\left(x + y\right) + t\right) \cdot z}, \frac{-\left(x + y\right)}{\left(x + y\right) + t}\right)\right) \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 72.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.02 \cdot 10^{+129}:\\ \;\;\;\;\mathsf{fma}\left(t, \frac{a - z}{x}, z\right)\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{+140}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z - b}{t + y}, a\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y}{\left(x + y\right) + t} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -1.02e+129)
   (fma t (/ (- a z) x) z)
   (if (<= x 4.4e+140)
     (fma y (/ (- z b) (+ t y)) a)
     (* (/ (+ x y) (+ (+ x y) t)) z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.02e+129) {
		tmp = fma(t, ((a - z) / x), z);
	} else if (x <= 4.4e+140) {
		tmp = fma(y, ((z - b) / (t + y)), a);
	} else {
		tmp = ((x + y) / ((x + y) + t)) * z;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -1.02e+129)
		tmp = fma(t, Float64(Float64(a - z) / x), z);
	elseif (x <= 4.4e+140)
		tmp = fma(y, Float64(Float64(z - b) / Float64(t + y)), a);
	else
		tmp = Float64(Float64(Float64(x + y) / Float64(Float64(x + y) + t)) * z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -1.02e+129], N[(t * N[(N[(a - z), $MachinePrecision] / x), $MachinePrecision] + z), $MachinePrecision], If[LessEqual[x, 4.4e+140], N[(y * N[(N[(z - b), $MachinePrecision] / N[(t + y), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision], N[(N[(N[(x + y), $MachinePrecision] / N[(N[(x + y), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.01999999999999996e129

   1. Initial program 43.7%

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

   3. Taylor expanded in t around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. associate-/l* N/A

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

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

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

      5. mul-1-neg N/A

         \[\leadsto \color{blue}{\left(-1 \cdot b\right)} \cdot \frac{y}{x + y} + \left(z + \left(t \cdot \left(\left(\frac{a}{x + y} + \frac{b \cdot y}{{\left(x + y\right)}^{2}}\right) - \left(\frac{z}{x + y} + \frac{a \cdot y}{{\left(x + y\right)}^{2}}\right)\right) + \frac{a \cdot y}{x + y}\right)\right) \]

      6. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(-1 \cdot b, \frac{y}{x + y}, z + \left(t \cdot \left(\left(\frac{a}{x + y} + \frac{b \cdot y}{{\left(x + y\right)}^{2}}\right) - \left(\frac{z}{x + y} + \frac{a \cdot y}{{\left(x + y\right)}^{2}}\right)\right) + \frac{a \cdot y}{x + y}\right)\right)} \]

   5. Applied rewrites 83.2%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 69.0%

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

   if -1.01999999999999996e129 < x < 4.3999999999999997e140

   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 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 45.9

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

   5. Applied rewrites 45.9%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 76.1%

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

   if 4.3999999999999997e140 < x

   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 z around inf

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-+.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 N/A

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

      8. lower-+.f64 44.3

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

   5. Applied rewrites 44.3%

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

   7. Applied rewrites 66.5%

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

4. Final simplification 73.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.02 \cdot 10^{+129}:\\ \;\;\;\;\mathsf{fma}\left(t, \frac{a - z}{x}, z\right)\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{+140}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z - b}{t + y}, a\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y}{\left(x + y\right) + t} \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 72.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(t, \frac{a - z}{x}, z\right)\\ \mathbf{if}\;x \leq -1.02 \cdot 10^{+129}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.34 \cdot 10^{+132}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z - b}{t + y}, a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma t (/ (- a z) x) z)))
   (if (<= x -1.02e+129)
     t_1
     (if (<= x 1.34e+132) (fma y (/ (- z b) (+ t y)) a) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(t, ((a - z) / x), z);
	double tmp;
	if (x <= -1.02e+129) {
		tmp = t_1;
	} else if (x <= 1.34e+132) {
		tmp = fma(y, ((z - b) / (t + y)), a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(t, Float64(Float64(a - z) / x), z)
	tmp = 0.0
	if (x <= -1.02e+129)
		tmp = t_1;
	elseif (x <= 1.34e+132)
		tmp = fma(y, Float64(Float64(z - b) / Float64(t + y)), a);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(N[(a - z), $MachinePrecision] / x), $MachinePrecision] + z), $MachinePrecision]}, If[LessEqual[x, -1.02e+129], t$95$1, If[LessEqual[x, 1.34e+132], N[(y * N[(N[(z - b), $MachinePrecision] / N[(t + y), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.01999999999999996e129 or 1.34000000000000002e132 < 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 t around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. associate-/l* N/A

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

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

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

      5. mul-1-neg N/A

         \[\leadsto \color{blue}{\left(-1 \cdot b\right)} \cdot \frac{y}{x + y} + \left(z + \left(t \cdot \left(\left(\frac{a}{x + y} + \frac{b \cdot y}{{\left(x + y\right)}^{2}}\right) - \left(\frac{z}{x + y} + \frac{a \cdot y}{{\left(x + y\right)}^{2}}\right)\right) + \frac{a \cdot y}{x + y}\right)\right) \]

      6. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(-1 \cdot b, \frac{y}{x + y}, z + \left(t \cdot \left(\left(\frac{a}{x + y} + \frac{b \cdot y}{{\left(x + y\right)}^{2}}\right) - \left(\frac{z}{x + y} + \frac{a \cdot y}{{\left(x + y\right)}^{2}}\right)\right) + \frac{a \cdot y}{x + y}\right)\right)} \]

   5. Applied rewrites 85.4%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 63.3%

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

   if -1.01999999999999996e129 < x < 1.34000000000000002e132

   1. Initial program 64.9%

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

   3. Taylor expanded in x around 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 46.2

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

   5. Applied rewrites 46.2%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 76.5%

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

Alternative 8: 61.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(t, \frac{a - z}{x}, z\right)\\ \mathbf{if}\;x \leq -1.02 \cdot 10^{+129}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 9.2 \cdot 10^{+135}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma t (/ (- a z) x) z)))
   (if (<= x -1.02e+129) t_1 (if (<= x 9.2e+135) (- (+ a z) b) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(t, ((a - z) / x), z);
	double tmp;
	if (x <= -1.02e+129) {
		tmp = t_1;
	} else if (x <= 9.2e+135) {
		tmp = (a + z) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(t, Float64(Float64(a - z) / x), z)
	tmp = 0.0
	if (x <= -1.02e+129)
		tmp = t_1;
	elseif (x <= 9.2e+135)
		tmp = Float64(Float64(a + z) - b);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(N[(a - z), $MachinePrecision] / x), $MachinePrecision] + z), $MachinePrecision]}, If[LessEqual[x, -1.02e+129], t$95$1, If[LessEqual[x, 9.2e+135], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.01999999999999996e129 or 9.2000000000000005e135 < 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 t around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. associate-/l* N/A

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

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

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

      5. mul-1-neg N/A

         \[\leadsto \color{blue}{\left(-1 \cdot b\right)} \cdot \frac{y}{x + y} + \left(z + \left(t \cdot \left(\left(\frac{a}{x + y} + \frac{b \cdot y}{{\left(x + y\right)}^{2}}\right) - \left(\frac{z}{x + y} + \frac{a \cdot y}{{\left(x + y\right)}^{2}}\right)\right) + \frac{a \cdot y}{x + y}\right)\right) \]

      6. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(-1 \cdot b, \frac{y}{x + y}, z + \left(t \cdot \left(\left(\frac{a}{x + y} + \frac{b \cdot y}{{\left(x + y\right)}^{2}}\right) - \left(\frac{z}{x + y} + \frac{a \cdot y}{{\left(x + y\right)}^{2}}\right)\right) + \frac{a \cdot y}{x + y}\right)\right)} \]

   5. Applied rewrites 85.4%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 63.3%

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

   if -1.01999999999999996e129 < x < 9.2000000000000005e135

   1. Initial program 64.9%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   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 70.2

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

   5. Applied rewrites 70.2%

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

4. Final simplification 67.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.02 \cdot 10^{+129}:\\ \;\;\;\;\mathsf{fma}\left(t, \frac{a - z}{x}, z\right)\\ \mathbf{elif}\;x \leq 9.2 \cdot 10^{+135}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t, \frac{a - z}{x}, z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 59.4% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -1 \cdot \left(-z\right)\\ \mathbf{if}\;x \leq -8.5 \cdot 10^{+227}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.06 \cdot 10^{+142}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* -1.0 (- z))))
   (if (<= x -8.5e+227) t_1 (if (<= x 1.06e+142) (- (+ a z) b) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -1.0 * -z;
	double tmp;
	if (x <= -8.5e+227) {
		tmp = t_1;
	} else if (x <= 1.06e+142) {
		tmp = (a + z) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (-1.0d0) * -z
    if (x <= (-8.5d+227)) then
        tmp = t_1
    else if (x <= 1.06d+142) then
        tmp = (a + z) - b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -1.0 * -z;
	double tmp;
	if (x <= -8.5e+227) {
		tmp = t_1;
	} else if (x <= 1.06e+142) {
		tmp = (a + z) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = -1.0 * -z
	tmp = 0
	if x <= -8.5e+227:
		tmp = t_1
	elif x <= 1.06e+142:
		tmp = (a + z) - b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(-1.0 * Float64(-z))
	tmp = 0.0
	if (x <= -8.5e+227)
		tmp = t_1;
	elseif (x <= 1.06e+142)
		tmp = Float64(Float64(a + z) - b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = -1.0 * -z;
	tmp = 0.0;
	if (x <= -8.5e+227)
		tmp = t_1;
	elseif (x <= 1.06e+142)
		tmp = (a + z) - b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(-1.0 * (-z)), $MachinePrecision]}, If[LessEqual[x, -8.5e+227], t$95$1, If[LessEqual[x, 1.06e+142], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -8.4999999999999995e227 or 1.06e142 < x

   1. Initial program 54.3%

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

      1. lift-/.f64 N/A

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

      2. frac-2neg N/A

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

      3. div-inv N/A

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

      4. lower-*.f64 N/A

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

   4. Applied rewrites 54.5%

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

   5. Taylor expanded in z around -inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower--.f64 N/A

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

   7. Applied rewrites 79.3%

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

   8. Taylor expanded in x around inf

      \[\leadsto \left(-z\right) \cdot -1 \]
   9. Step-by-step derivation

   10. Applied rewrites 61.4%

       \[\leadsto \left(-z\right) \cdot -1 \]

   if -8.4999999999999995e227 < x < 1.06e142

   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. 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 66.8

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

   5. Applied rewrites 66.8%

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

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{+227}:\\ \;\;\;\;-1 \cdot \left(-z\right)\\ \mathbf{elif}\;x \leq 1.06 \cdot 10^{+142}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;-1 \cdot \left(-z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 60.5% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a + z\right) - b\\ \mathbf{if}\;y \leq -1 \cdot 10^{-38}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-34}:\\ \;\;\;\;a + z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ a z) b)))
   (if (<= y -1e-38) t_1 (if (<= y 4e-34) (+ a 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 <= -1e-38) {
		tmp = t_1;
	} else if (y <= 4e-34) {
		tmp = a + z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a + z) - b
    if (y <= (-1d-38)) then
        tmp = t_1
    else if (y <= 4d-34) then
        tmp = a + z
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a + z) - b;
	double tmp;
	if (y <= -1e-38) {
		tmp = t_1;
	} else if (y <= 4e-34) {
		tmp = a + z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a + z) - b
	tmp = 0
	if y <= -1e-38:
		tmp = t_1
	elif y <= 4e-34:
		tmp = a + z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a + z) - b)
	tmp = 0.0
	if (y <= -1e-38)
		tmp = t_1;
	elseif (y <= 4e-34)
		tmp = Float64(a + z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a + z) - b;
	tmp = 0.0;
	if (y <= -1e-38)
		tmp = t_1;
	elseif (y <= 4e-34)
		tmp = a + z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -1e-38], t$95$1, If[LessEqual[y, 4e-34], N[(a + z), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -9.9999999999999996e-39 or 3.99999999999999971e-34 < y

   1. Initial program 52.2%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   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 69.3

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

   5. Applied rewrites 69.3%

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

   if -9.9999999999999996e-39 < y < 3.99999999999999971e-34

   1. Initial program 71.8%

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

   3. Taylor expanded in 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 39.6

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

   5. Applied rewrites 39.6%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 48.5%

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

4. Final simplification 60.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{-38}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-34}:\\ \;\;\;\;a + z\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 53.5% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{-19}:\\ \;\;\;\;a + z\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-66}:\\ \;\;\;\;a - b\\ \mathbf{else}:\\ \;\;\;\;a + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -2.3e-19) (+ a z) (if (<= z 1.02e-66) (- a b) (+ a z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2.3e-19) {
		tmp = a + z;
	} else if (z <= 1.02e-66) {
		tmp = a - b;
	} else {
		tmp = a + z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-2.3d-19)) then
        tmp = a + z
    else if (z <= 1.02d-66) then
        tmp = a - b
    else
        tmp = a + z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2.3e-19) {
		tmp = a + z;
	} else if (z <= 1.02e-66) {
		tmp = a - b;
	} else {
		tmp = a + z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -2.3e-19:
		tmp = a + z
	elif z <= 1.02e-66:
		tmp = a - b
	else:
		tmp = a + z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -2.3e-19)
		tmp = Float64(a + z);
	elseif (z <= 1.02e-66)
		tmp = Float64(a - b);
	else
		tmp = Float64(a + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -2.3e-19)
		tmp = a + z;
	elseif (z <= 1.02e-66)
		tmp = a - b;
	else
		tmp = a + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -2.3e-19], N[(a + z), $MachinePrecision], If[LessEqual[z, 1.02e-66], N[(a - b), $MachinePrecision], N[(a + z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.2999999999999998e-19 or 1.01999999999999996e-66 < z

   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 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 62.4

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

   5. Applied rewrites 62.4%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 62.2%

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

   if -2.2999999999999998e-19 < z < 1.01999999999999996e-66

   1. Initial program 75.2%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   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 49.5

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

   5. Applied rewrites 49.5%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 48.6%

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

4. Final simplification 56.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{-19}:\\ \;\;\;\;a + z\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-66}:\\ \;\;\;\;a - b\\ \mathbf{else}:\\ \;\;\;\;a + z\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 51.3% accurate, 11.3× speedup

Math

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

FPCore

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

C

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

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 + z
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 60.2%

   \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
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 57.1

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

5. Applied rewrites 57.1%

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

6. Taylor expanded in b around 0

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

8. Applied rewrites 53.0%

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

9. Final simplification 53.0%

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

Alternative 13: 14.3% 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 60.2%

   \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
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 57.1

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

5. Applied rewrites 57.1%

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

6. Taylor expanded in b around inf

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

8. Applied rewrites 12.5%

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

Developer Target 1: 82.3% accurate, 0.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024273 
(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)))