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

Percentage Accurate: 59.8% → 89.8%

Time: 15.8s

Alternatives: 17

Speedup: 0.9×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 59.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 89.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y + t\right)\\ t_2 := y + \left(x + t\right)\\ t_3 := \frac{\left(z \cdot \left(x + y\right) + \left(y + t\right) \cdot a\right) - y \cdot b}{t\_2}\\ \mathbf{if}\;t\_3 \leq -\infty:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;t\_3 \leq 10^{+269}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_3 \leq \infty:\\ \;\;\;\;a \cdot \frac{y + t}{t\_1} + z \cdot \frac{x + y}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{a + \left(z - b\right)}{\frac{t\_2}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (+ y t)))
        (t_2 (+ y (+ x t)))
        (t_3 (/ (- (+ (* z (+ x y)) (* (+ y t) a)) (* y b)) t_2)))
   (if (<= t_3 (- INFINITY))
     (- (+ z a) b)
     (if (<= t_3 1e+269)
       t_3
       (if (<= t_3 INFINITY)
         (+ (* a (/ (+ y t) t_1)) (* z (/ (+ x y) t_1)))
         (/ (+ a (- z b)) (/ t_2 y)))))))

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 + (x + t);
	double t_3 = (((z * (x + y)) + ((y + t) * a)) - (y * b)) / t_2;
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = (z + a) - b;
	} else if (t_3 <= 1e+269) {
		tmp = t_3;
	} else if (t_3 <= ((double) INFINITY)) {
		tmp = (a * ((y + t) / t_1)) + (z * ((x + y) / t_1));
	} else {
		tmp = (a + (z - b)) / (t_2 / y);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y + t);
	double t_2 = y + (x + t);
	double t_3 = (((z * (x + y)) + ((y + t) * a)) - (y * b)) / t_2;
	double tmp;
	if (t_3 <= -Double.POSITIVE_INFINITY) {
		tmp = (z + a) - b;
	} else if (t_3 <= 1e+269) {
		tmp = t_3;
	} else if (t_3 <= Double.POSITIVE_INFINITY) {
		tmp = (a * ((y + t) / t_1)) + (z * ((x + y) / t_1));
	} else {
		tmp = (a + (z - b)) / (t_2 / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (y + t)
	t_2 = y + (x + t)
	t_3 = (((z * (x + y)) + ((y + t) * a)) - (y * b)) / t_2
	tmp = 0
	if t_3 <= -math.inf:
		tmp = (z + a) - b
	elif t_3 <= 1e+269:
		tmp = t_3
	elif t_3 <= math.inf:
		tmp = (a * ((y + t) / t_1)) + (z * ((x + y) / t_1))
	else:
		tmp = (a + (z - b)) / (t_2 / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(y + t))
	t_2 = Float64(y + Float64(x + t))
	t_3 = Float64(Float64(Float64(Float64(z * Float64(x + y)) + Float64(Float64(y + t) * a)) - Float64(y * b)) / t_2)
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = Float64(Float64(z + a) - b);
	elseif (t_3 <= 1e+269)
		tmp = t_3;
	elseif (t_3 <= Inf)
		tmp = Float64(Float64(a * Float64(Float64(y + t) / t_1)) + Float64(z * Float64(Float64(x + y) / t_1)));
	else
		tmp = Float64(Float64(a + Float64(z - b)) / Float64(t_2 / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (y + t);
	t_2 = y + (x + t);
	t_3 = (((z * (x + y)) + ((y + t) * a)) - (y * b)) / t_2;
	tmp = 0.0;
	if (t_3 <= -Inf)
		tmp = (z + a) - b;
	elseif (t_3 <= 1e+269)
		tmp = t_3;
	elseif (t_3 <= Inf)
		tmp = (a * ((y + t) / t_1)) + (z * ((x + y) / t_1));
	else
		tmp = (a + (z - b)) / (t_2 / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision] + N[(N[(y + t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], If[LessEqual[t$95$3, 1e+269], t$95$3, If[LessEqual[t$95$3, Infinity], N[(N[(a * N[(N[(y + t), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(x + y), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a + N[(z - b), $MachinePrecision]), $MachinePrecision] / N[(t$95$2 / y), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 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 6.5%

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

   3. Taylor expanded in y around inf 83.9%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1e269

   1. Initial program 99.1%

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

   if 1e269 < (/.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 7.7%

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

   3. Taylor expanded in b around inf 17.6%

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

      1. +-commutative 17.6%

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

      2. mul-1-neg 17.6%

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

      3. unsub-neg 17.6%

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

   5. Simplified 60.7%

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

   6. Taylor expanded in b around 0 7.1%

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

      1. associate-/l* 47.8%

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

      2. +-commutative 47.8%

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

      3. associate-+r+ 47.8%

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

      4. +-commutative 47.8%

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

      5. associate-+r+ 47.8%

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

      6. associate-/l* 84.5%

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

      7. +-commutative 84.5%

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

      8. associate-+r+ 84.5%

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

      9. +-commutative 84.5%

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

      10. associate-+r+ 84.5%

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

   8. Simplified 84.5%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in y around inf 6.0%

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

      1. clear-num 6.0%

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

      2. inv-pow 6.0%

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

      3. +-commutative 6.0%

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

      4. +-commutative 6.0%

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

      5. associate--l+ 6.0%

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

   5. Applied egg-rr 6.0%

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

      1. unpow-1 6.0%

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

      2. associate-+r- 6.0%

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

      3. associate-/r* 83.5%

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

      4. associate-+r+ 83.5%

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

      5. associate-+r- 83.5%

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

   7. Simplified 83.5%

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

      1. clear-num 83.6%

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

      2. add-cube-cbrt 81.6%

         \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{a + \left(z - b\right)} \cdot \sqrt[3]{a + \left(z - b\right)}\right) \cdot \sqrt[3]{a + \left(z - b\right)}}}{\frac{\left(y + t\right) + x}{y}} \]

      3. *-un-lft-identity 81.6%

         \[\leadsto \frac{\left(\sqrt[3]{a + \left(z - b\right)} \cdot \sqrt[3]{a + \left(z - b\right)}\right) \cdot \sqrt[3]{a + \left(z - b\right)}}{\color{blue}{1 \cdot \frac{\left(y + t\right) + x}{y}}} \]

      4. times-frac 81.6%

         \[\leadsto \color{blue}{\frac{\sqrt[3]{a + \left(z - b\right)} \cdot \sqrt[3]{a + \left(z - b\right)}}{1} \cdot \frac{\sqrt[3]{a + \left(z - b\right)}}{\frac{\left(y + t\right) + x}{y}}} \]

      5. pow2 81.6%

         \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{a + \left(z - b\right)}\right)}^{2}}}{1} \cdot \frac{\sqrt[3]{a + \left(z - b\right)}}{\frac{\left(y + t\right) + x}{y}} \]

      6. +-commutative 81.6%

         \[\leadsto \frac{{\left(\sqrt[3]{\color{blue}{\left(z - b\right) + a}}\right)}^{2}}{1} \cdot \frac{\sqrt[3]{a + \left(z - b\right)}}{\frac{\left(y + t\right) + x}{y}} \]

      7. associate-+l- 81.6%

         \[\leadsto \frac{{\left(\sqrt[3]{\color{blue}{z - \left(b - a\right)}}\right)}^{2}}{1} \cdot \frac{\sqrt[3]{a + \left(z - b\right)}}{\frac{\left(y + t\right) + x}{y}} \]

      8. +-commutative 81.6%

         \[\leadsto \frac{{\left(\sqrt[3]{z - \left(b - a\right)}\right)}^{2}}{1} \cdot \frac{\sqrt[3]{\color{blue}{\left(z - b\right) + a}}}{\frac{\left(y + t\right) + x}{y}} \]

      9. associate-+l- 81.6%

         \[\leadsto \frac{{\left(\sqrt[3]{z - \left(b - a\right)}\right)}^{2}}{1} \cdot \frac{\sqrt[3]{\color{blue}{z - \left(b - a\right)}}}{\frac{\left(y + t\right) + x}{y}} \]

      10. associate-+l+ 81.6%

          \[\leadsto \frac{{\left(\sqrt[3]{z - \left(b - a\right)}\right)}^{2}}{1} \cdot \frac{\sqrt[3]{z - \left(b - a\right)}}{\frac{\color{blue}{y + \left(t + x\right)}}{y}} \]

   9. Applied egg-rr 81.6%

      \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{z - \left(b - a\right)}\right)}^{2}}{1} \cdot \frac{\sqrt[3]{z - \left(b - a\right)}}{\frac{y + \left(t + x\right)}{y}}} \]
   10. Step-by-step derivation

       1. /-rgt-identity 81.6%

          \[\leadsto \color{blue}{{\left(\sqrt[3]{z - \left(b - a\right)}\right)}^{2}} \cdot \frac{\sqrt[3]{z - \left(b - a\right)}}{\frac{y + \left(t + x\right)}{y}} \]

       2. associate-*r/ 81.6%

          \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{z - \left(b - a\right)}\right)}^{2} \cdot \sqrt[3]{z - \left(b - a\right)}}{\frac{y + \left(t + x\right)}{y}}} \]

       3. unpow2 81.6%

          \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{z - \left(b - a\right)} \cdot \sqrt[3]{z - \left(b - a\right)}\right)} \cdot \sqrt[3]{z - \left(b - a\right)}}{\frac{y + \left(t + x\right)}{y}} \]

       4. rem-3cbrt-lft 83.6%

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

       5. associate--r- 83.6%

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

   11. Simplified 83.6%

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

4. Final simplification 92.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z \cdot \left(x + y\right) + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;\frac{\left(z \cdot \left(x + y\right) + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)} \leq 10^{+269}:\\ \;\;\;\;\frac{\left(z \cdot \left(x + y\right) + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{elif}\;\frac{\left(z \cdot \left(x + y\right) + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)} \leq \infty:\\ \;\;\;\;a \cdot \frac{y + t}{x + \left(y + t\right)} + z \cdot \frac{x + y}{x + \left(y + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{a + \left(z - b\right)}{\frac{y + \left(x + t\right)}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 88.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \frac{\left(z \cdot \left(x + y\right) + \left(y + t\right) \cdot a\right) - y \cdot b}{t\_1}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+277}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;z + a \cdot \frac{y + t}{x + \left(y + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{a + \left(z - b\right)}{\frac{t\_1}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t)))
        (t_2 (/ (- (+ (* z (+ x y)) (* (+ y t) a)) (* y b)) t_1)))
   (if (<= t_2 (- INFINITY))
     (- (+ z a) b)
     (if (<= t_2 5e+277)
       t_2
       (if (<= t_2 INFINITY)
         (+ z (* a (/ (+ y t) (+ x (+ y t)))))
         (/ (+ a (- z b)) (/ t_1 y)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = (((z * (x + y)) + ((y + t) * a)) - (y * b)) / t_1;
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = (z + a) - b;
	} else if (t_2 <= 5e+277) {
		tmp = t_2;
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = z + (a * ((y + t) / (x + (y + t))));
	} else {
		tmp = (a + (z - b)) / (t_1 / y);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = (((z * (x + y)) + ((y + t) * a)) - (y * b)) / t_1;
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = (z + a) - b;
	} else if (t_2 <= 5e+277) {
		tmp = t_2;
	} else if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = z + (a * ((y + t) / (x + (y + t))));
	} else {
		tmp = (a + (z - b)) / (t_1 / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = (((z * (x + y)) + ((y + t) * a)) - (y * b)) / t_1
	tmp = 0
	if t_2 <= -math.inf:
		tmp = (z + a) - b
	elif t_2 <= 5e+277:
		tmp = t_2
	elif t_2 <= math.inf:
		tmp = z + (a * ((y + t) / (x + (y + t))))
	else:
		tmp = (a + (z - b)) / (t_1 / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(Float64(Float64(Float64(z * Float64(x + y)) + Float64(Float64(y + t) * a)) - Float64(y * b)) / t_1)
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(Float64(z + a) - b);
	elseif (t_2 <= 5e+277)
		tmp = t_2;
	elseif (t_2 <= Inf)
		tmp = Float64(z + Float64(a * Float64(Float64(y + t) / Float64(x + Float64(y + t)))));
	else
		tmp = Float64(Float64(a + Float64(z - b)) / Float64(t_1 / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	t_2 = (((z * (x + y)) + ((y + t) * a)) - (y * b)) / t_1;
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = (z + a) - b;
	elseif (t_2 <= 5e+277)
		tmp = t_2;
	elseif (t_2 <= Inf)
		tmp = z + (a * ((y + t) / (x + (y + t))));
	else
		tmp = (a + (z - b)) / (t_1 / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision] + N[(N[(y + t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], If[LessEqual[t$95$2, 5e+277], t$95$2, If[LessEqual[t$95$2, Infinity], N[(z + N[(a * N[(N[(y + t), $MachinePrecision] / N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a + N[(z - b), $MachinePrecision]), $MachinePrecision] / N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 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 6.5%

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

   3. Taylor expanded in y around inf 83.9%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 4.99999999999999982e277

   1. Initial program 99.1%

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

   if 4.99999999999999982e277 < (/.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 5.6%

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

   3. Taylor expanded in b around inf 17.8%

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

      1. +-commutative 17.8%

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

      2. mul-1-neg 17.8%

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

      3. unsub-neg 17.8%

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

   5. Simplified 61.9%

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

   6. Taylor expanded in b around 0 5.0%

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

      1. associate-/l* 46.6%

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

      2. +-commutative 46.6%

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

      3. associate-+r+ 46.6%

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

      4. +-commutative 46.6%

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

      5. associate-+r+ 46.6%

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

      6. associate-/l* 84.1%

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

      7. +-commutative 84.1%

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

      8. associate-+r+ 84.1%

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

      9. +-commutative 84.1%

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

      10. associate-+r+ 84.1%

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

   8. Simplified 84.1%

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

   9. Taylor expanded in y around inf 72.1%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in y around inf 6.0%

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

      1. clear-num 6.0%

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

      2. inv-pow 6.0%

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

      3. +-commutative 6.0%

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

      4. +-commutative 6.0%

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

      5. associate--l+ 6.0%

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

   5. Applied egg-rr 6.0%

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

      1. unpow-1 6.0%

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

      2. associate-+r- 6.0%

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

      3. associate-/r* 83.5%

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

      4. associate-+r+ 83.5%

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

      5. associate-+r- 83.5%

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

   7. Simplified 83.5%

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

      1. clear-num 83.6%

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

      2. add-cube-cbrt 81.6%

         \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{a + \left(z - b\right)} \cdot \sqrt[3]{a + \left(z - b\right)}\right) \cdot \sqrt[3]{a + \left(z - b\right)}}}{\frac{\left(y + t\right) + x}{y}} \]

      3. *-un-lft-identity 81.6%

         \[\leadsto \frac{\left(\sqrt[3]{a + \left(z - b\right)} \cdot \sqrt[3]{a + \left(z - b\right)}\right) \cdot \sqrt[3]{a + \left(z - b\right)}}{\color{blue}{1 \cdot \frac{\left(y + t\right) + x}{y}}} \]

      4. times-frac 81.6%

         \[\leadsto \color{blue}{\frac{\sqrt[3]{a + \left(z - b\right)} \cdot \sqrt[3]{a + \left(z - b\right)}}{1} \cdot \frac{\sqrt[3]{a + \left(z - b\right)}}{\frac{\left(y + t\right) + x}{y}}} \]

      5. pow2 81.6%

         \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{a + \left(z - b\right)}\right)}^{2}}}{1} \cdot \frac{\sqrt[3]{a + \left(z - b\right)}}{\frac{\left(y + t\right) + x}{y}} \]

      6. +-commutative 81.6%

         \[\leadsto \frac{{\left(\sqrt[3]{\color{blue}{\left(z - b\right) + a}}\right)}^{2}}{1} \cdot \frac{\sqrt[3]{a + \left(z - b\right)}}{\frac{\left(y + t\right) + x}{y}} \]

      7. associate-+l- 81.6%

         \[\leadsto \frac{{\left(\sqrt[3]{\color{blue}{z - \left(b - a\right)}}\right)}^{2}}{1} \cdot \frac{\sqrt[3]{a + \left(z - b\right)}}{\frac{\left(y + t\right) + x}{y}} \]

      8. +-commutative 81.6%

         \[\leadsto \frac{{\left(\sqrt[3]{z - \left(b - a\right)}\right)}^{2}}{1} \cdot \frac{\sqrt[3]{\color{blue}{\left(z - b\right) + a}}}{\frac{\left(y + t\right) + x}{y}} \]

      9. associate-+l- 81.6%

         \[\leadsto \frac{{\left(\sqrt[3]{z - \left(b - a\right)}\right)}^{2}}{1} \cdot \frac{\sqrt[3]{\color{blue}{z - \left(b - a\right)}}}{\frac{\left(y + t\right) + x}{y}} \]

      10. associate-+l+ 81.6%

          \[\leadsto \frac{{\left(\sqrt[3]{z - \left(b - a\right)}\right)}^{2}}{1} \cdot \frac{\sqrt[3]{z - \left(b - a\right)}}{\frac{\color{blue}{y + \left(t + x\right)}}{y}} \]

   9. Applied egg-rr 81.6%

      \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{z - \left(b - a\right)}\right)}^{2}}{1} \cdot \frac{\sqrt[3]{z - \left(b - a\right)}}{\frac{y + \left(t + x\right)}{y}}} \]
   10. Step-by-step derivation

       1. /-rgt-identity 81.6%

          \[\leadsto \color{blue}{{\left(\sqrt[3]{z - \left(b - a\right)}\right)}^{2}} \cdot \frac{\sqrt[3]{z - \left(b - a\right)}}{\frac{y + \left(t + x\right)}{y}} \]

       2. associate-*r/ 81.6%

          \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{z - \left(b - a\right)}\right)}^{2} \cdot \sqrt[3]{z - \left(b - a\right)}}{\frac{y + \left(t + x\right)}{y}}} \]

       3. unpow2 81.6%

          \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{z - \left(b - a\right)} \cdot \sqrt[3]{z - \left(b - a\right)}\right)} \cdot \sqrt[3]{z - \left(b - a\right)}}{\frac{y + \left(t + x\right)}{y}} \]

       4. rem-3cbrt-lft 83.6%

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

       5. associate--r- 83.6%

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

   11. Simplified 83.6%

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

4. Final simplification 90.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z \cdot \left(x + y\right) + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;\frac{\left(z \cdot \left(x + y\right) + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)} \leq 5 \cdot 10^{+277}:\\ \;\;\;\;\frac{\left(z \cdot \left(x + y\right) + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{elif}\;\frac{\left(z \cdot \left(x + y\right) + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)} \leq \infty:\\ \;\;\;\;z + a \cdot \frac{y + t}{x + \left(y + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{a + \left(z - b\right)}{\frac{y + \left(x + t\right)}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 62.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \frac{y}{t\_1}\\ \mathbf{if}\;y \leq -1.82 \cdot 10^{-68}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -7.7 \cdot 10^{-137}:\\ \;\;\;\;z \cdot \frac{x + y}{t\_1}\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-162}:\\ \;\;\;\;\frac{a}{\frac{t\_1}{y + t}}\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{-125}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-46}:\\ \;\;\;\;b \cdot \left(\frac{z}{b} - t\_2\right)\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+53}:\\ \;\;\;\;b \cdot \left(\frac{a}{b} - t\_2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{a + \left(z - b\right)}{x + y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t))) (t_2 (/ y t_1)))
   (if (<= y -1.82e-68)
     (- (+ z a) b)
     (if (<= y -7.7e-137)
       (* z (/ (+ x y) t_1))
       (if (<= y -2.5e-162)
         (/ a (/ t_1 (+ y t)))
         (if (<= y 2.05e-125)
           (/ (+ (* t a) (* x z)) (+ x t))
           (if (<= y 2.9e-46)
             (* b (- (/ z b) t_2))
             (if (<= y 4.8e+53)
               (* b (- (/ a b) t_2))
               (* y (/ (+ a (- z b)) (+ x y)))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = y / t_1;
	double tmp;
	if (y <= -1.82e-68) {
		tmp = (z + a) - b;
	} else if (y <= -7.7e-137) {
		tmp = z * ((x + y) / t_1);
	} else if (y <= -2.5e-162) {
		tmp = a / (t_1 / (y + t));
	} else if (y <= 2.05e-125) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else if (y <= 2.9e-46) {
		tmp = b * ((z / b) - t_2);
	} else if (y <= 4.8e+53) {
		tmp = b * ((a / b) - t_2);
	} else {
		tmp = y * ((a + (z - b)) / (x + y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y + (x + t)
    t_2 = y / t_1
    if (y <= (-1.82d-68)) then
        tmp = (z + a) - b
    else if (y <= (-7.7d-137)) then
        tmp = z * ((x + y) / t_1)
    else if (y <= (-2.5d-162)) then
        tmp = a / (t_1 / (y + t))
    else if (y <= 2.05d-125) then
        tmp = ((t * a) + (x * z)) / (x + t)
    else if (y <= 2.9d-46) then
        tmp = b * ((z / b) - t_2)
    else if (y <= 4.8d+53) then
        tmp = b * ((a / b) - t_2)
    else
        tmp = y * ((a + (z - b)) / (x + y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = y / t_1;
	double tmp;
	if (y <= -1.82e-68) {
		tmp = (z + a) - b;
	} else if (y <= -7.7e-137) {
		tmp = z * ((x + y) / t_1);
	} else if (y <= -2.5e-162) {
		tmp = a / (t_1 / (y + t));
	} else if (y <= 2.05e-125) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else if (y <= 2.9e-46) {
		tmp = b * ((z / b) - t_2);
	} else if (y <= 4.8e+53) {
		tmp = b * ((a / b) - t_2);
	} else {
		tmp = y * ((a + (z - b)) / (x + y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = y / t_1
	tmp = 0
	if y <= -1.82e-68:
		tmp = (z + a) - b
	elif y <= -7.7e-137:
		tmp = z * ((x + y) / t_1)
	elif y <= -2.5e-162:
		tmp = a / (t_1 / (y + t))
	elif y <= 2.05e-125:
		tmp = ((t * a) + (x * z)) / (x + t)
	elif y <= 2.9e-46:
		tmp = b * ((z / b) - t_2)
	elif y <= 4.8e+53:
		tmp = b * ((a / b) - t_2)
	else:
		tmp = y * ((a + (z - b)) / (x + y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(y / t_1)
	tmp = 0.0
	if (y <= -1.82e-68)
		tmp = Float64(Float64(z + a) - b);
	elseif (y <= -7.7e-137)
		tmp = Float64(z * Float64(Float64(x + y) / t_1));
	elseif (y <= -2.5e-162)
		tmp = Float64(a / Float64(t_1 / Float64(y + t)));
	elseif (y <= 2.05e-125)
		tmp = Float64(Float64(Float64(t * a) + Float64(x * z)) / Float64(x + t));
	elseif (y <= 2.9e-46)
		tmp = Float64(b * Float64(Float64(z / b) - t_2));
	elseif (y <= 4.8e+53)
		tmp = Float64(b * Float64(Float64(a / b) - t_2));
	else
		tmp = Float64(y * Float64(Float64(a + Float64(z - b)) / Float64(x + y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	t_2 = y / t_1;
	tmp = 0.0;
	if (y <= -1.82e-68)
		tmp = (z + a) - b;
	elseif (y <= -7.7e-137)
		tmp = z * ((x + y) / t_1);
	elseif (y <= -2.5e-162)
		tmp = a / (t_1 / (y + t));
	elseif (y <= 2.05e-125)
		tmp = ((t * a) + (x * z)) / (x + t);
	elseif (y <= 2.9e-46)
		tmp = b * ((z / b) - t_2);
	elseif (y <= 4.8e+53)
		tmp = b * ((a / b) - t_2);
	else
		tmp = y * ((a + (z - b)) / (x + y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y / t$95$1), $MachinePrecision]}, If[LessEqual[y, -1.82e-68], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], If[LessEqual[y, -7.7e-137], N[(z * N[(N[(x + y), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.5e-162], N[(a / N[(t$95$1 / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.05e-125], N[(N[(N[(t * a), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.9e-46], N[(b * N[(N[(z / b), $MachinePrecision] - t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.8e+53], N[(b * N[(N[(a / b), $MachinePrecision] - t$95$2), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(a + N[(z - b), $MachinePrecision]), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y < -1.81999999999999994e-68

   1. Initial program 46.6%

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

   3. Taylor expanded in y around inf 80.2%

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

   if -1.81999999999999994e-68 < y < -7.7000000000000004e-137

   1. Initial program 68.1%

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

   3. Taylor expanded in z around inf 39.8%

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

      1. associate-/l* 63.6%

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

      2. +-commutative 63.6%

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

      3. +-commutative 63.6%

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

      4. associate-+r+ 63.6%

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

      5. +-commutative 63.6%

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

      6. associate-+l+ 63.6%

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

   5. Simplified 63.6%

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

   if -7.7000000000000004e-137 < y < -2.50000000000000007e-162

   1. Initial program 68.3%

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

   3. Taylor expanded in b around inf 67.1%

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

      1. +-commutative 67.1%

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

      2. mul-1-neg 67.1%

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

      3. unsub-neg 67.1%

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

   5. Simplified 78.1%

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

   6. Taylor expanded in a around -inf 68.3%

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

      1. associate-/l* 99.5%

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

      2. +-commutative 99.5%

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

      3. associate-+r+ 99.5%

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

      4. +-commutative 99.5%

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

      5. associate-+r+ 99.5%

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

   8. Simplified 99.5%

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

      1. clear-num 99.7%

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

      2. un-div-inv 99.8%

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

      3. associate-+l+ 99.8%

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

   10. Applied egg-rr 99.8%

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

   if -2.50000000000000007e-162 < y < 2.0499999999999999e-125

   1. Initial program 83.4%

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

   3. Taylor expanded in y around 0 68.6%

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

   if 2.0499999999999999e-125 < y < 2.90000000000000005e-46

   1. Initial program 94.3%

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

   3. Taylor expanded in b around inf 82.4%

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

      1. +-commutative 82.4%

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

      2. mul-1-neg 82.4%

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

      3. unsub-neg 82.4%

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

   5. Simplified 82.5%

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

   6. Taylor expanded in x around inf 68.5%

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

   if 2.90000000000000005e-46 < y < 4.8e53

   1. Initial program 75.5%

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

   3. Taylor expanded in b around inf 66.4%

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

      1. +-commutative 66.4%

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

      2. mul-1-neg 66.4%

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

      3. unsub-neg 66.4%

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

   5. Simplified 70.9%

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

   6. Taylor expanded in t around inf 75.4%

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

   if 4.8e53 < y

   1. Initial program 27.9%

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

   3. Taylor expanded in y around inf 24.9%

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

      1. clear-num 24.8%

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

      2. inv-pow 24.8%

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

      3. +-commutative 24.8%

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

      4. +-commutative 24.8%

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

      5. associate--l+ 24.8%

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

   5. Applied egg-rr 24.8%

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

      1. unpow-1 24.8%

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

      2. associate-+r- 24.8%

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

      3. associate-/r* 90.2%

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

      4. associate-+r+ 90.2%

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

      5. associate-+r- 90.2%

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

   7. Simplified 90.2%

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

   8. Taylor expanded in t around 0 21.8%

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

      1. associate-/l* 78.7%

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

      2. associate--l+ 78.7%

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

      3. +-commutative 78.7%

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

   10. Simplified 78.7%

       \[\leadsto \color{blue}{y \cdot \frac{a + \left(z - b\right)}{y + x}} \]
3. Recombined 7 regimes into one program.

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.82 \cdot 10^{-68}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -7.7 \cdot 10^{-137}:\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-162}:\\ \;\;\;\;\frac{a}{\frac{y + \left(x + t\right)}{y + t}}\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{-125}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-46}:\\ \;\;\;\;b \cdot \left(\frac{z}{b} - \frac{y}{y + \left(x + t\right)}\right)\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+53}:\\ \;\;\;\;b \cdot \left(\frac{a}{b} - \frac{y}{y + \left(x + t\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{a + \left(z - b\right)}{x + y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 63.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \frac{y}{t\_1}\\ \mathbf{if}\;y \leq -7.8 \cdot 10^{-69}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-138}:\\ \;\;\;\;z \cdot \frac{x + y}{t\_1}\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-162}:\\ \;\;\;\;\frac{a}{\frac{t\_1}{y + t}}\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-123}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{elif}\;y \leq 5.9 \cdot 10^{-49}:\\ \;\;\;\;b \cdot \left(\frac{z}{b} - t\_2\right)\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+54}:\\ \;\;\;\;b \cdot \left(\frac{a}{b} - t\_2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{a + \left(z - b\right)}{x + \left(y + t\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t))) (t_2 (/ y t_1)))
   (if (<= y -7.8e-69)
     (- (+ z a) b)
     (if (<= y -4.2e-138)
       (* z (/ (+ x y) t_1))
       (if (<= y -1.9e-162)
         (/ a (/ t_1 (+ y t)))
         (if (<= y 8.5e-123)
           (/ (+ (* t a) (* x z)) (+ x t))
           (if (<= y 5.9e-49)
             (* b (- (/ z b) t_2))
             (if (<= y 1.1e+54)
               (* b (- (/ a b) t_2))
               (* y (/ (+ a (- z b)) (+ x (+ y t))))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = y / t_1;
	double tmp;
	if (y <= -7.8e-69) {
		tmp = (z + a) - b;
	} else if (y <= -4.2e-138) {
		tmp = z * ((x + y) / t_1);
	} else if (y <= -1.9e-162) {
		tmp = a / (t_1 / (y + t));
	} else if (y <= 8.5e-123) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else if (y <= 5.9e-49) {
		tmp = b * ((z / b) - t_2);
	} else if (y <= 1.1e+54) {
		tmp = b * ((a / b) - t_2);
	} else {
		tmp = y * ((a + (z - b)) / (x + (y + t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y + (x + t)
    t_2 = y / t_1
    if (y <= (-7.8d-69)) then
        tmp = (z + a) - b
    else if (y <= (-4.2d-138)) then
        tmp = z * ((x + y) / t_1)
    else if (y <= (-1.9d-162)) then
        tmp = a / (t_1 / (y + t))
    else if (y <= 8.5d-123) then
        tmp = ((t * a) + (x * z)) / (x + t)
    else if (y <= 5.9d-49) then
        tmp = b * ((z / b) - t_2)
    else if (y <= 1.1d+54) then
        tmp = b * ((a / b) - t_2)
    else
        tmp = y * ((a + (z - b)) / (x + (y + t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = y / t_1;
	double tmp;
	if (y <= -7.8e-69) {
		tmp = (z + a) - b;
	} else if (y <= -4.2e-138) {
		tmp = z * ((x + y) / t_1);
	} else if (y <= -1.9e-162) {
		tmp = a / (t_1 / (y + t));
	} else if (y <= 8.5e-123) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else if (y <= 5.9e-49) {
		tmp = b * ((z / b) - t_2);
	} else if (y <= 1.1e+54) {
		tmp = b * ((a / b) - t_2);
	} else {
		tmp = y * ((a + (z - b)) / (x + (y + t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = y / t_1
	tmp = 0
	if y <= -7.8e-69:
		tmp = (z + a) - b
	elif y <= -4.2e-138:
		tmp = z * ((x + y) / t_1)
	elif y <= -1.9e-162:
		tmp = a / (t_1 / (y + t))
	elif y <= 8.5e-123:
		tmp = ((t * a) + (x * z)) / (x + t)
	elif y <= 5.9e-49:
		tmp = b * ((z / b) - t_2)
	elif y <= 1.1e+54:
		tmp = b * ((a / b) - t_2)
	else:
		tmp = y * ((a + (z - b)) / (x + (y + t)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(y / t_1)
	tmp = 0.0
	if (y <= -7.8e-69)
		tmp = Float64(Float64(z + a) - b);
	elseif (y <= -4.2e-138)
		tmp = Float64(z * Float64(Float64(x + y) / t_1));
	elseif (y <= -1.9e-162)
		tmp = Float64(a / Float64(t_1 / Float64(y + t)));
	elseif (y <= 8.5e-123)
		tmp = Float64(Float64(Float64(t * a) + Float64(x * z)) / Float64(x + t));
	elseif (y <= 5.9e-49)
		tmp = Float64(b * Float64(Float64(z / b) - t_2));
	elseif (y <= 1.1e+54)
		tmp = Float64(b * Float64(Float64(a / b) - t_2));
	else
		tmp = Float64(y * Float64(Float64(a + Float64(z - b)) / Float64(x + Float64(y + t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	t_2 = y / t_1;
	tmp = 0.0;
	if (y <= -7.8e-69)
		tmp = (z + a) - b;
	elseif (y <= -4.2e-138)
		tmp = z * ((x + y) / t_1);
	elseif (y <= -1.9e-162)
		tmp = a / (t_1 / (y + t));
	elseif (y <= 8.5e-123)
		tmp = ((t * a) + (x * z)) / (x + t);
	elseif (y <= 5.9e-49)
		tmp = b * ((z / b) - t_2);
	elseif (y <= 1.1e+54)
		tmp = b * ((a / b) - t_2);
	else
		tmp = y * ((a + (z - b)) / (x + (y + t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y / t$95$1), $MachinePrecision]}, If[LessEqual[y, -7.8e-69], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], If[LessEqual[y, -4.2e-138], N[(z * N[(N[(x + y), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.9e-162], N[(a / N[(t$95$1 / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.5e-123], N[(N[(N[(t * a), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.9e-49], N[(b * N[(N[(z / b), $MachinePrecision] - t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.1e+54], N[(b * N[(N[(a / b), $MachinePrecision] - t$95$2), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(a + N[(z - b), $MachinePrecision]), $MachinePrecision] / N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y < -7.79999999999999961e-69

   1. Initial program 46.6%

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

   3. Taylor expanded in y around inf 80.2%

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

   if -7.79999999999999961e-69 < y < -4.19999999999999972e-138

   1. Initial program 68.1%

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

   3. Taylor expanded in z around inf 39.8%

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

      1. associate-/l* 63.6%

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

      2. +-commutative 63.6%

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

      3. +-commutative 63.6%

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

      4. associate-+r+ 63.6%

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

      5. +-commutative 63.6%

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

      6. associate-+l+ 63.6%

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

   5. Simplified 63.6%

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

   if -4.19999999999999972e-138 < y < -1.90000000000000002e-162

   1. Initial program 68.3%

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

   3. Taylor expanded in b around inf 67.1%

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

      1. +-commutative 67.1%

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

      2. mul-1-neg 67.1%

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

      3. unsub-neg 67.1%

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

   5. Simplified 78.1%

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

   6. Taylor expanded in a around -inf 68.3%

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

      1. associate-/l* 99.5%

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

      2. +-commutative 99.5%

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

      3. associate-+r+ 99.5%

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

      4. +-commutative 99.5%

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

      5. associate-+r+ 99.5%

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

   8. Simplified 99.5%

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

      1. clear-num 99.7%

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

      2. un-div-inv 99.8%

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

      3. associate-+l+ 99.8%

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

   10. Applied egg-rr 99.8%

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

   if -1.90000000000000002e-162 < y < 8.4999999999999995e-123

   1. Initial program 83.4%

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

   3. Taylor expanded in y around 0 68.6%

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

   if 8.4999999999999995e-123 < y < 5.90000000000000037e-49

   1. Initial program 94.3%

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

   3. Taylor expanded in b around inf 82.4%

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

      1. +-commutative 82.4%

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

      2. mul-1-neg 82.4%

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

      3. unsub-neg 82.4%

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

   5. Simplified 82.5%

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

   6. Taylor expanded in x around inf 68.5%

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

   if 5.90000000000000037e-49 < y < 1.09999999999999995e54

   1. Initial program 75.5%

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

   3. Taylor expanded in b around inf 66.4%

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

      1. +-commutative 66.4%

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

      2. mul-1-neg 66.4%

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

      3. unsub-neg 66.4%

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

   5. Simplified 70.9%

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

   6. Taylor expanded in t around inf 75.4%

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

   if 1.09999999999999995e54 < y

   1. Initial program 27.9%

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

   3. Taylor expanded in y around inf 24.9%

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

      1. associate-/l* 90.3%

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

      2. associate--l+ 90.3%

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

      3. +-commutative 90.3%

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

      4. +-commutative 90.3%

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

   5. Applied egg-rr 90.3%

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

      1. associate-+r+ 90.3%

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

   7. Simplified 90.3%

      \[\leadsto \color{blue}{y \cdot \frac{a + \left(z - b\right)}{\left(y + t\right) + x}} \]
3. Recombined 7 regimes into one program.

4. Final simplification 78.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.8 \cdot 10^{-69}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-138}:\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-162}:\\ \;\;\;\;\frac{a}{\frac{y + \left(x + t\right)}{y + t}}\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-123}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{elif}\;y \leq 5.9 \cdot 10^{-49}:\\ \;\;\;\;b \cdot \left(\frac{z}{b} - \frac{y}{y + \left(x + t\right)}\right)\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+54}:\\ \;\;\;\;b \cdot \left(\frac{a}{b} - \frac{y}{y + \left(x + t\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{a + \left(z - b\right)}{x + \left(y + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 70.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y + t\right)\\ \mathbf{if}\;b \leq -1.65 \cdot 10^{+110}:\\ \;\;\;\;b \cdot \left(\frac{z}{b} - \frac{y}{y + \left(x + t\right)}\right)\\ \mathbf{elif}\;b \leq -660000000:\\ \;\;\;\;a + z \cdot \frac{x + y}{t\_1}\\ \mathbf{elif}\;b \leq 1.95 \cdot 10^{+43} \lor \neg \left(b \leq 2.95 \cdot 10^{+233}\right) \land b \leq 4.75 \cdot 10^{+247}:\\ \;\;\;\;z + a \cdot \frac{y + t}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{a + \left(z - b\right)}{t\_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (+ y t))))
   (if (<= b -1.65e+110)
     (* b (- (/ z b) (/ y (+ y (+ x t)))))
     (if (<= b -660000000.0)
       (+ a (* z (/ (+ x y) t_1)))
       (if (or (<= b 1.95e+43) (and (not (<= b 2.95e+233)) (<= b 4.75e+247)))
         (+ z (* a (/ (+ y t) t_1)))
         (* y (/ (+ a (- z b)) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y + t);
	double tmp;
	if (b <= -1.65e+110) {
		tmp = b * ((z / b) - (y / (y + (x + t))));
	} else if (b <= -660000000.0) {
		tmp = a + (z * ((x + y) / t_1));
	} else if ((b <= 1.95e+43) || (!(b <= 2.95e+233) && (b <= 4.75e+247))) {
		tmp = z + (a * ((y + t) / t_1));
	} else {
		tmp = y * ((a + (z - b)) / t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y + t)
    if (b <= (-1.65d+110)) then
        tmp = b * ((z / b) - (y / (y + (x + t))))
    else if (b <= (-660000000.0d0)) then
        tmp = a + (z * ((x + y) / t_1))
    else if ((b <= 1.95d+43) .or. (.not. (b <= 2.95d+233)) .and. (b <= 4.75d+247)) then
        tmp = z + (a * ((y + t) / t_1))
    else
        tmp = y * ((a + (z - b)) / t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y + t);
	double tmp;
	if (b <= -1.65e+110) {
		tmp = b * ((z / b) - (y / (y + (x + t))));
	} else if (b <= -660000000.0) {
		tmp = a + (z * ((x + y) / t_1));
	} else if ((b <= 1.95e+43) || (!(b <= 2.95e+233) && (b <= 4.75e+247))) {
		tmp = z + (a * ((y + t) / t_1));
	} else {
		tmp = y * ((a + (z - b)) / t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (y + t)
	tmp = 0
	if b <= -1.65e+110:
		tmp = b * ((z / b) - (y / (y + (x + t))))
	elif b <= -660000000.0:
		tmp = a + (z * ((x + y) / t_1))
	elif (b <= 1.95e+43) or (not (b <= 2.95e+233) and (b <= 4.75e+247)):
		tmp = z + (a * ((y + t) / t_1))
	else:
		tmp = y * ((a + (z - b)) / t_1)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(y + t))
	tmp = 0.0
	if (b <= -1.65e+110)
		tmp = Float64(b * Float64(Float64(z / b) - Float64(y / Float64(y + Float64(x + t)))));
	elseif (b <= -660000000.0)
		tmp = Float64(a + Float64(z * Float64(Float64(x + y) / t_1)));
	elseif ((b <= 1.95e+43) || (!(b <= 2.95e+233) && (b <= 4.75e+247)))
		tmp = Float64(z + Float64(a * Float64(Float64(y + t) / t_1)));
	else
		tmp = Float64(y * Float64(Float64(a + Float64(z - b)) / t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (y + t);
	tmp = 0.0;
	if (b <= -1.65e+110)
		tmp = b * ((z / b) - (y / (y + (x + t))));
	elseif (b <= -660000000.0)
		tmp = a + (z * ((x + y) / t_1));
	elseif ((b <= 1.95e+43) || (~((b <= 2.95e+233)) && (b <= 4.75e+247)))
		tmp = z + (a * ((y + t) / t_1));
	else
		tmp = y * ((a + (z - b)) / t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.65e+110], N[(b * N[(N[(z / b), $MachinePrecision] - N[(y / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -660000000.0], N[(a + N[(z * N[(N[(x + y), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[b, 1.95e+43], And[N[Not[LessEqual[b, 2.95e+233]], $MachinePrecision], LessEqual[b, 4.75e+247]]], N[(z + N[(a * N[(N[(y + t), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(a + N[(z - b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.64999999999999986e110

   1. Initial program 56.9%

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

   3. Taylor expanded in b around inf 71.1%

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

      1. +-commutative 71.1%

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

      2. mul-1-neg 71.1%

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

      3. unsub-neg 71.1%

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

   5. Simplified 82.2%

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

   6. Taylor expanded in x around inf 85.7%

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

   if -1.64999999999999986e110 < b < -6.6e8

   1. Initial program 64.5%

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

   3. Taylor expanded in b around inf 57.7%

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

      1. +-commutative 57.7%

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

      2. mul-1-neg 57.7%

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

      3. unsub-neg 57.7%

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

   5. Simplified 77.0%

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

   6. Taylor expanded in b around 0 55.0%

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

      1. associate-/l* 71.4%

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

      2. +-commutative 71.4%

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

      3. associate-+r+ 71.4%

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

      4. +-commutative 71.4%

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

      5. associate-+r+ 71.4%

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

      6. associate-/l* 90.1%

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

      7. +-commutative 90.1%

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

      8. associate-+r+ 90.1%

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

      9. +-commutative 90.1%

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

      10. associate-+r+ 90.1%

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

   8. Simplified 90.1%

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

   9. Taylor expanded in y around inf 80.5%

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

   if -6.6e8 < b < 1.95e43 or 2.95000000000000013e233 < b < 4.7500000000000001e247

   1. Initial program 60.0%

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

   3. Taylor expanded in b around inf 53.0%

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

      1. +-commutative 53.0%

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

      2. mul-1-neg 53.0%

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

      3. unsub-neg 53.0%

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

   5. Simplified 70.4%

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

   6. Taylor expanded in b around 0 56.2%

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

      1. associate-/l* 72.5%

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

      2. +-commutative 72.5%

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

      3. associate-+r+ 72.5%

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

      4. +-commutative 72.5%

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

      5. associate-+r+ 72.5%

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

      6. associate-/l* 94.2%

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

      7. +-commutative 94.2%

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

      8. associate-+r+ 94.2%

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

      9. +-commutative 94.2%

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

      10. associate-+r+ 94.2%

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

   8. Simplified 94.2%

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

   9. Taylor expanded in y around inf 82.7%

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

   if 1.95e43 < b < 2.95000000000000013e233 or 4.7500000000000001e247 < b

   1. Initial program 51.2%

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

   3. Taylor expanded in y around inf 41.1%

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

      1. associate-/l* 84.1%

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

      2. associate--l+ 84.1%

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

      3. +-commutative 84.1%

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

      4. +-commutative 84.1%

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

   5. Applied egg-rr 84.1%

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

      1. associate-+r+ 84.1%

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

   7. Simplified 84.1%

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

4. Final simplification 83.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.65 \cdot 10^{+110}:\\ \;\;\;\;b \cdot \left(\frac{z}{b} - \frac{y}{y + \left(x + t\right)}\right)\\ \mathbf{elif}\;b \leq -660000000:\\ \;\;\;\;a + z \cdot \frac{x + y}{x + \left(y + t\right)}\\ \mathbf{elif}\;b \leq 1.95 \cdot 10^{+43} \lor \neg \left(b \leq 2.95 \cdot 10^{+233}\right) \land b \leq 4.75 \cdot 10^{+247}:\\ \;\;\;\;z + a \cdot \frac{y + t}{x + \left(y + t\right)}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{a + \left(z - b\right)}{x + \left(y + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 62.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ \mathbf{if}\;y \leq -2 \cdot 10^{-71}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-138}:\\ \;\;\;\;z \cdot \frac{x + y}{t\_1}\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-163}:\\ \;\;\;\;\frac{a}{\frac{t\_1}{y + t}}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-133}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+53}:\\ \;\;\;\;b \cdot \left(\frac{a}{b} - \frac{y}{t\_1}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{a + \left(z - b\right)}{x + y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t))))
   (if (<= y -2e-71)
     (- (+ z a) b)
     (if (<= y -6e-138)
       (* z (/ (+ x y) t_1))
       (if (<= y -2.4e-163)
         (/ a (/ t_1 (+ y t)))
         (if (<= y 1.2e-133)
           (/ (+ (* t a) (* x z)) (+ x t))
           (if (<= y 4e+53)
             (* b (- (/ a b) (/ y t_1)))
             (* y (/ (+ a (- z b)) (+ x y))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double tmp;
	if (y <= -2e-71) {
		tmp = (z + a) - b;
	} else if (y <= -6e-138) {
		tmp = z * ((x + y) / t_1);
	} else if (y <= -2.4e-163) {
		tmp = a / (t_1 / (y + t));
	} else if (y <= 1.2e-133) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else if (y <= 4e+53) {
		tmp = b * ((a / b) - (y / t_1));
	} else {
		tmp = y * ((a + (z - b)) / (x + y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y + (x + t)
    if (y <= (-2d-71)) then
        tmp = (z + a) - b
    else if (y <= (-6d-138)) then
        tmp = z * ((x + y) / t_1)
    else if (y <= (-2.4d-163)) then
        tmp = a / (t_1 / (y + t))
    else if (y <= 1.2d-133) then
        tmp = ((t * a) + (x * z)) / (x + t)
    else if (y <= 4d+53) then
        tmp = b * ((a / b) - (y / t_1))
    else
        tmp = y * ((a + (z - b)) / (x + y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double tmp;
	if (y <= -2e-71) {
		tmp = (z + a) - b;
	} else if (y <= -6e-138) {
		tmp = z * ((x + y) / t_1);
	} else if (y <= -2.4e-163) {
		tmp = a / (t_1 / (y + t));
	} else if (y <= 1.2e-133) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else if (y <= 4e+53) {
		tmp = b * ((a / b) - (y / t_1));
	} else {
		tmp = y * ((a + (z - b)) / (x + y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	tmp = 0
	if y <= -2e-71:
		tmp = (z + a) - b
	elif y <= -6e-138:
		tmp = z * ((x + y) / t_1)
	elif y <= -2.4e-163:
		tmp = a / (t_1 / (y + t))
	elif y <= 1.2e-133:
		tmp = ((t * a) + (x * z)) / (x + t)
	elif y <= 4e+53:
		tmp = b * ((a / b) - (y / t_1))
	else:
		tmp = y * ((a + (z - b)) / (x + y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	tmp = 0.0
	if (y <= -2e-71)
		tmp = Float64(Float64(z + a) - b);
	elseif (y <= -6e-138)
		tmp = Float64(z * Float64(Float64(x + y) / t_1));
	elseif (y <= -2.4e-163)
		tmp = Float64(a / Float64(t_1 / Float64(y + t)));
	elseif (y <= 1.2e-133)
		tmp = Float64(Float64(Float64(t * a) + Float64(x * z)) / Float64(x + t));
	elseif (y <= 4e+53)
		tmp = Float64(b * Float64(Float64(a / b) - Float64(y / t_1)));
	else
		tmp = Float64(y * Float64(Float64(a + Float64(z - b)) / Float64(x + y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	tmp = 0.0;
	if (y <= -2e-71)
		tmp = (z + a) - b;
	elseif (y <= -6e-138)
		tmp = z * ((x + y) / t_1);
	elseif (y <= -2.4e-163)
		tmp = a / (t_1 / (y + t));
	elseif (y <= 1.2e-133)
		tmp = ((t * a) + (x * z)) / (x + t);
	elseif (y <= 4e+53)
		tmp = b * ((a / b) - (y / t_1));
	else
		tmp = y * ((a + (z - b)) / (x + y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2e-71], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], If[LessEqual[y, -6e-138], N[(z * N[(N[(x + y), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.4e-163], N[(a / N[(t$95$1 / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.2e-133], N[(N[(N[(t * a), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4e+53], N[(b * N[(N[(a / b), $MachinePrecision] - N[(y / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(a + N[(z - b), $MachinePrecision]), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -1.9999999999999998e-71

   1. Initial program 46.6%

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

   3. Taylor expanded in y around inf 80.2%

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

   if -1.9999999999999998e-71 < y < -6.0000000000000001e-138

   1. Initial program 68.1%

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

   3. Taylor expanded in z around inf 39.8%

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

      1. associate-/l* 63.6%

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

      2. +-commutative 63.6%

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

      3. +-commutative 63.6%

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

      4. associate-+r+ 63.6%

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

      5. +-commutative 63.6%

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

      6. associate-+l+ 63.6%

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

   5. Simplified 63.6%

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

   if -6.0000000000000001e-138 < y < -2.4000000000000001e-163

   1. Initial program 68.3%

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

   3. Taylor expanded in b around inf 67.1%

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

      1. +-commutative 67.1%

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

      2. mul-1-neg 67.1%

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

      3. unsub-neg 67.1%

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

   5. Simplified 78.1%

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

   6. Taylor expanded in a around -inf 68.3%

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

      1. associate-/l* 99.5%

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

      2. +-commutative 99.5%

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

      3. associate-+r+ 99.5%

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

      4. +-commutative 99.5%

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

      5. associate-+r+ 99.5%

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

   8. Simplified 99.5%

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

      1. clear-num 99.7%

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

      2. un-div-inv 99.8%

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

      3. associate-+l+ 99.8%

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

   10. Applied egg-rr 99.8%

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

   if -2.4000000000000001e-163 < y < 1.2e-133

   1. Initial program 83.1%

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

   3. Taylor expanded in y around 0 69.6%

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

   if 1.2e-133 < y < 4e53

   1. Initial program 83.8%

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

   3. Taylor expanded in b around inf 73.9%

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

      1. +-commutative 73.9%

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

      2. mul-1-neg 73.9%

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

      3. unsub-neg 73.9%

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

   5. Simplified 76.4%

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

   6. Taylor expanded in t around inf 60.8%

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

   if 4e53 < y

   1. Initial program 27.9%

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

   3. Taylor expanded in y around inf 24.9%

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

      1. clear-num 24.8%

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

      2. inv-pow 24.8%

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

      3. +-commutative 24.8%

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

      4. +-commutative 24.8%

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

      5. associate--l+ 24.8%

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

   5. Applied egg-rr 24.8%

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

      1. unpow-1 24.8%

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

      2. associate-+r- 24.8%

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

      3. associate-/r* 90.2%

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

      4. associate-+r+ 90.2%

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

      5. associate-+r- 90.2%

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

   7. Simplified 90.2%

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

   8. Taylor expanded in t around 0 21.8%

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

      1. associate-/l* 78.7%

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

      2. associate--l+ 78.7%

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

      3. +-commutative 78.7%

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

   10. Simplified 78.7%

       \[\leadsto \color{blue}{y \cdot \frac{a + \left(z - b\right)}{y + x}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 74.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{-71}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-138}:\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-163}:\\ \;\;\;\;\frac{a}{\frac{y + \left(x + t\right)}{y + t}}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-133}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+53}:\\ \;\;\;\;b \cdot \left(\frac{a}{b} - \frac{y}{y + \left(x + t\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{a + \left(z - b\right)}{x + y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 70.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := a + \left(z - b\right)\\ t_3 := x + \left(y + t\right)\\ t_4 := z + a \cdot \frac{y + t}{t\_3}\\ \mathbf{if}\;b \leq -3.3 \cdot 10^{+110}:\\ \;\;\;\;b \cdot \left(\frac{z}{b} - \frac{y}{t\_1}\right)\\ \mathbf{elif}\;b \leq -102000000:\\ \;\;\;\;a + z \cdot \frac{x + y}{t\_3}\\ \mathbf{elif}\;b \leq 7 \cdot 10^{+41}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;b \leq 2.95 \cdot 10^{+233}:\\ \;\;\;\;y \cdot \frac{t\_2}{t\_3}\\ \mathbf{elif}\;b \leq 4.75 \cdot 10^{+247}:\\ \;\;\;\;t\_4\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_2}{\frac{t\_1}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t)))
        (t_2 (+ a (- z b)))
        (t_3 (+ x (+ y t)))
        (t_4 (+ z (* a (/ (+ y t) t_3)))))
   (if (<= b -3.3e+110)
     (* b (- (/ z b) (/ y t_1)))
     (if (<= b -102000000.0)
       (+ a (* z (/ (+ x y) t_3)))
       (if (<= b 7e+41)
         t_4
         (if (<= b 2.95e+233)
           (* y (/ t_2 t_3))
           (if (<= b 4.75e+247) t_4 (/ t_2 (/ t_1 y)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = a + (z - b);
	double t_3 = x + (y + t);
	double t_4 = z + (a * ((y + t) / t_3));
	double tmp;
	if (b <= -3.3e+110) {
		tmp = b * ((z / b) - (y / t_1));
	} else if (b <= -102000000.0) {
		tmp = a + (z * ((x + y) / t_3));
	} else if (b <= 7e+41) {
		tmp = t_4;
	} else if (b <= 2.95e+233) {
		tmp = y * (t_2 / t_3);
	} else if (b <= 4.75e+247) {
		tmp = t_4;
	} else {
		tmp = t_2 / (t_1 / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = y + (x + t)
    t_2 = a + (z - b)
    t_3 = x + (y + t)
    t_4 = z + (a * ((y + t) / t_3))
    if (b <= (-3.3d+110)) then
        tmp = b * ((z / b) - (y / t_1))
    else if (b <= (-102000000.0d0)) then
        tmp = a + (z * ((x + y) / t_3))
    else if (b <= 7d+41) then
        tmp = t_4
    else if (b <= 2.95d+233) then
        tmp = y * (t_2 / t_3)
    else if (b <= 4.75d+247) then
        tmp = t_4
    else
        tmp = t_2 / (t_1 / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = a + (z - b);
	double t_3 = x + (y + t);
	double t_4 = z + (a * ((y + t) / t_3));
	double tmp;
	if (b <= -3.3e+110) {
		tmp = b * ((z / b) - (y / t_1));
	} else if (b <= -102000000.0) {
		tmp = a + (z * ((x + y) / t_3));
	} else if (b <= 7e+41) {
		tmp = t_4;
	} else if (b <= 2.95e+233) {
		tmp = y * (t_2 / t_3);
	} else if (b <= 4.75e+247) {
		tmp = t_4;
	} else {
		tmp = t_2 / (t_1 / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = a + (z - b)
	t_3 = x + (y + t)
	t_4 = z + (a * ((y + t) / t_3))
	tmp = 0
	if b <= -3.3e+110:
		tmp = b * ((z / b) - (y / t_1))
	elif b <= -102000000.0:
		tmp = a + (z * ((x + y) / t_3))
	elif b <= 7e+41:
		tmp = t_4
	elif b <= 2.95e+233:
		tmp = y * (t_2 / t_3)
	elif b <= 4.75e+247:
		tmp = t_4
	else:
		tmp = t_2 / (t_1 / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(a + Float64(z - b))
	t_3 = Float64(x + Float64(y + t))
	t_4 = Float64(z + Float64(a * Float64(Float64(y + t) / t_3)))
	tmp = 0.0
	if (b <= -3.3e+110)
		tmp = Float64(b * Float64(Float64(z / b) - Float64(y / t_1)));
	elseif (b <= -102000000.0)
		tmp = Float64(a + Float64(z * Float64(Float64(x + y) / t_3)));
	elseif (b <= 7e+41)
		tmp = t_4;
	elseif (b <= 2.95e+233)
		tmp = Float64(y * Float64(t_2 / t_3));
	elseif (b <= 4.75e+247)
		tmp = t_4;
	else
		tmp = Float64(t_2 / Float64(t_1 / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	t_2 = a + (z - b);
	t_3 = x + (y + t);
	t_4 = z + (a * ((y + t) / t_3));
	tmp = 0.0;
	if (b <= -3.3e+110)
		tmp = b * ((z / b) - (y / t_1));
	elseif (b <= -102000000.0)
		tmp = a + (z * ((x + y) / t_3));
	elseif (b <= 7e+41)
		tmp = t_4;
	elseif (b <= 2.95e+233)
		tmp = y * (t_2 / t_3);
	elseif (b <= 4.75e+247)
		tmp = t_4;
	else
		tmp = t_2 / (t_1 / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a + N[(z - b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(z + N[(a * N[(N[(y + t), $MachinePrecision] / t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.3e+110], N[(b * N[(N[(z / b), $MachinePrecision] - N[(y / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -102000000.0], N[(a + N[(z * N[(N[(x + y), $MachinePrecision] / t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 7e+41], t$95$4, If[LessEqual[b, 2.95e+233], N[(y * N[(t$95$2 / t$95$3), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.75e+247], t$95$4, N[(t$95$2 / N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -3.29999999999999971e110

   1. Initial program 56.9%

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

   3. Taylor expanded in b around inf 71.1%

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

      1. +-commutative 71.1%

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

      2. mul-1-neg 71.1%

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

      3. unsub-neg 71.1%

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

   5. Simplified 82.2%

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

   6. Taylor expanded in x around inf 85.7%

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

   if -3.29999999999999971e110 < b < -1.02e8

   1. Initial program 64.5%

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

   3. Taylor expanded in b around inf 57.7%

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

      1. +-commutative 57.7%

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

      2. mul-1-neg 57.7%

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

      3. unsub-neg 57.7%

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

   5. Simplified 77.0%

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

   6. Taylor expanded in b around 0 55.0%

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

      1. associate-/l* 71.4%

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

      2. +-commutative 71.4%

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

      3. associate-+r+ 71.4%

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

      4. +-commutative 71.4%

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

      5. associate-+r+ 71.4%

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

      6. associate-/l* 90.1%

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

      7. +-commutative 90.1%

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

      8. associate-+r+ 90.1%

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

      9. +-commutative 90.1%

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

      10. associate-+r+ 90.1%

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

   8. Simplified 90.1%

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

   9. Taylor expanded in y around inf 80.5%

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

   if -1.02e8 < b < 6.9999999999999998e41 or 2.95000000000000013e233 < b < 4.7500000000000001e247

   1. Initial program 60.0%

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

   3. Taylor expanded in b around inf 53.0%

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

      1. +-commutative 53.0%

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

      2. mul-1-neg 53.0%

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

      3. unsub-neg 53.0%

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

   5. Simplified 70.4%

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

   6. Taylor expanded in b around 0 56.2%

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

      1. associate-/l* 72.5%

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

      2. +-commutative 72.5%

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

      3. associate-+r+ 72.5%

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

      4. +-commutative 72.5%

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

      5. associate-+r+ 72.5%

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

      6. associate-/l* 94.2%

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

      7. +-commutative 94.2%

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

      8. associate-+r+ 94.2%

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

      9. +-commutative 94.2%

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

      10. associate-+r+ 94.2%

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

   8. Simplified 94.2%

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

   9. Taylor expanded in y around inf 82.7%

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

   if 6.9999999999999998e41 < b < 2.95000000000000013e233

   1. Initial program 58.0%

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

   3. Taylor expanded in y around inf 43.3%

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

      1. associate-/l* 78.0%

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

      2. associate--l+ 78.0%

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

      3. +-commutative 78.0%

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

      4. +-commutative 78.0%

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

   5. Applied egg-rr 78.0%

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

      1. associate-+r+ 78.0%

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

   7. Simplified 78.0%

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

   if 4.7500000000000001e247 < b

   1. Initial program 35.5%

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

   3. Taylor expanded in y around inf 36.1%

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

      1. clear-num 36.0%

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

      2. inv-pow 36.0%

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

      3. +-commutative 36.0%

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

      4. +-commutative 36.0%

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

      5. associate--l+ 36.0%

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

   5. Applied egg-rr 36.0%

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

      1. unpow-1 36.0%

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

      2. associate-+r- 36.0%

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

      3. associate-/r* 98.1%

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

      4. associate-+r+ 98.1%

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

      5. associate-+r- 98.1%

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

   7. Simplified 98.1%

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

      1. clear-num 98.6%

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

      2. add-cube-cbrt 96.2%

         \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{a + \left(z - b\right)} \cdot \sqrt[3]{a + \left(z - b\right)}\right) \cdot \sqrt[3]{a + \left(z - b\right)}}}{\frac{\left(y + t\right) + x}{y}} \]

      3. *-un-lft-identity 96.2%

         \[\leadsto \frac{\left(\sqrt[3]{a + \left(z - b\right)} \cdot \sqrt[3]{a + \left(z - b\right)}\right) \cdot \sqrt[3]{a + \left(z - b\right)}}{\color{blue}{1 \cdot \frac{\left(y + t\right) + x}{y}}} \]

      4. times-frac 96.1%

         \[\leadsto \color{blue}{\frac{\sqrt[3]{a + \left(z - b\right)} \cdot \sqrt[3]{a + \left(z - b\right)}}{1} \cdot \frac{\sqrt[3]{a + \left(z - b\right)}}{\frac{\left(y + t\right) + x}{y}}} \]

      5. pow2 96.1%

         \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{a + \left(z - b\right)}\right)}^{2}}}{1} \cdot \frac{\sqrt[3]{a + \left(z - b\right)}}{\frac{\left(y + t\right) + x}{y}} \]

      6. +-commutative 96.1%

         \[\leadsto \frac{{\left(\sqrt[3]{\color{blue}{\left(z - b\right) + a}}\right)}^{2}}{1} \cdot \frac{\sqrt[3]{a + \left(z - b\right)}}{\frac{\left(y + t\right) + x}{y}} \]

      7. associate-+l- 96.1%

         \[\leadsto \frac{{\left(\sqrt[3]{\color{blue}{z - \left(b - a\right)}}\right)}^{2}}{1} \cdot \frac{\sqrt[3]{a + \left(z - b\right)}}{\frac{\left(y + t\right) + x}{y}} \]

      8. +-commutative 96.1%

         \[\leadsto \frac{{\left(\sqrt[3]{z - \left(b - a\right)}\right)}^{2}}{1} \cdot \frac{\sqrt[3]{\color{blue}{\left(z - b\right) + a}}}{\frac{\left(y + t\right) + x}{y}} \]

      9. associate-+l- 96.1%

         \[\leadsto \frac{{\left(\sqrt[3]{z - \left(b - a\right)}\right)}^{2}}{1} \cdot \frac{\sqrt[3]{\color{blue}{z - \left(b - a\right)}}}{\frac{\left(y + t\right) + x}{y}} \]

      10. associate-+l+ 96.1%

          \[\leadsto \frac{{\left(\sqrt[3]{z - \left(b - a\right)}\right)}^{2}}{1} \cdot \frac{\sqrt[3]{z - \left(b - a\right)}}{\frac{\color{blue}{y + \left(t + x\right)}}{y}} \]

   9. Applied egg-rr 96.1%

      \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{z - \left(b - a\right)}\right)}^{2}}{1} \cdot \frac{\sqrt[3]{z - \left(b - a\right)}}{\frac{y + \left(t + x\right)}{y}}} \]
   10. Step-by-step derivation

       1. /-rgt-identity 96.1%

          \[\leadsto \color{blue}{{\left(\sqrt[3]{z - \left(b - a\right)}\right)}^{2}} \cdot \frac{\sqrt[3]{z - \left(b - a\right)}}{\frac{y + \left(t + x\right)}{y}} \]

       2. associate-*r/ 96.2%

          \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{z - \left(b - a\right)}\right)}^{2} \cdot \sqrt[3]{z - \left(b - a\right)}}{\frac{y + \left(t + x\right)}{y}}} \]

       3. unpow2 96.2%

          \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{z - \left(b - a\right)} \cdot \sqrt[3]{z - \left(b - a\right)}\right)} \cdot \sqrt[3]{z - \left(b - a\right)}}{\frac{y + \left(t + x\right)}{y}} \]

       4. rem-3cbrt-lft 98.6%

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

       5. associate--r- 98.6%

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

   11. Simplified 98.6%

       \[\leadsto \color{blue}{\frac{\left(z - b\right) + a}{\frac{y + \left(t + x\right)}{y}}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 83.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.3 \cdot 10^{+110}:\\ \;\;\;\;b \cdot \left(\frac{z}{b} - \frac{y}{y + \left(x + t\right)}\right)\\ \mathbf{elif}\;b \leq -102000000:\\ \;\;\;\;a + z \cdot \frac{x + y}{x + \left(y + t\right)}\\ \mathbf{elif}\;b \leq 7 \cdot 10^{+41}:\\ \;\;\;\;z + a \cdot \frac{y + t}{x + \left(y + t\right)}\\ \mathbf{elif}\;b \leq 2.95 \cdot 10^{+233}:\\ \;\;\;\;y \cdot \frac{a + \left(z - b\right)}{x + \left(y + t\right)}\\ \mathbf{elif}\;b \leq 4.75 \cdot 10^{+247}:\\ \;\;\;\;z + a \cdot \frac{y + t}{x + \left(y + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{a + \left(z - b\right)}{\frac{y + \left(x + t\right)}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 56.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := z \cdot \frac{x + y}{t\_1}\\ \mathbf{if}\;y \leq -2 \cdot 10^{-68}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-134}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -3.3 \cdot 10^{-172}:\\ \;\;\;\;\frac{a}{\frac{t\_1}{y + t}}\\ \mathbf{elif}\;y \leq 2.95 \cdot 10^{-261}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 1.48 \cdot 10^{-130}:\\ \;\;\;\;\frac{\left(y + t\right) \cdot a}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{a + \left(z - b\right)}{x + y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t))) (t_2 (* z (/ (+ x y) t_1))))
   (if (<= y -2e-68)
     (- (+ z a) b)
     (if (<= y -2.8e-134)
       t_2
       (if (<= y -3.3e-172)
         (/ a (/ t_1 (+ y t)))
         (if (<= y 2.95e-261)
           t_2
           (if (<= y 1.48e-130)
             (/ (* (+ y t) a) t_1)
             (* y (/ (+ a (- z b)) (+ x y))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = z * ((x + y) / t_1);
	double tmp;
	if (y <= -2e-68) {
		tmp = (z + a) - b;
	} else if (y <= -2.8e-134) {
		tmp = t_2;
	} else if (y <= -3.3e-172) {
		tmp = a / (t_1 / (y + t));
	} else if (y <= 2.95e-261) {
		tmp = t_2;
	} else if (y <= 1.48e-130) {
		tmp = ((y + t) * a) / t_1;
	} else {
		tmp = y * ((a + (z - b)) / (x + y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y + (x + t)
    t_2 = z * ((x + y) / t_1)
    if (y <= (-2d-68)) then
        tmp = (z + a) - b
    else if (y <= (-2.8d-134)) then
        tmp = t_2
    else if (y <= (-3.3d-172)) then
        tmp = a / (t_1 / (y + t))
    else if (y <= 2.95d-261) then
        tmp = t_2
    else if (y <= 1.48d-130) then
        tmp = ((y + t) * a) / t_1
    else
        tmp = y * ((a + (z - b)) / (x + y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = z * ((x + y) / t_1);
	double tmp;
	if (y <= -2e-68) {
		tmp = (z + a) - b;
	} else if (y <= -2.8e-134) {
		tmp = t_2;
	} else if (y <= -3.3e-172) {
		tmp = a / (t_1 / (y + t));
	} else if (y <= 2.95e-261) {
		tmp = t_2;
	} else if (y <= 1.48e-130) {
		tmp = ((y + t) * a) / t_1;
	} else {
		tmp = y * ((a + (z - b)) / (x + y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = z * ((x + y) / t_1)
	tmp = 0
	if y <= -2e-68:
		tmp = (z + a) - b
	elif y <= -2.8e-134:
		tmp = t_2
	elif y <= -3.3e-172:
		tmp = a / (t_1 / (y + t))
	elif y <= 2.95e-261:
		tmp = t_2
	elif y <= 1.48e-130:
		tmp = ((y + t) * a) / t_1
	else:
		tmp = y * ((a + (z - b)) / (x + y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(z * Float64(Float64(x + y) / t_1))
	tmp = 0.0
	if (y <= -2e-68)
		tmp = Float64(Float64(z + a) - b);
	elseif (y <= -2.8e-134)
		tmp = t_2;
	elseif (y <= -3.3e-172)
		tmp = Float64(a / Float64(t_1 / Float64(y + t)));
	elseif (y <= 2.95e-261)
		tmp = t_2;
	elseif (y <= 1.48e-130)
		tmp = Float64(Float64(Float64(y + t) * a) / t_1);
	else
		tmp = Float64(y * Float64(Float64(a + Float64(z - b)) / Float64(x + y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	t_2 = z * ((x + y) / t_1);
	tmp = 0.0;
	if (y <= -2e-68)
		tmp = (z + a) - b;
	elseif (y <= -2.8e-134)
		tmp = t_2;
	elseif (y <= -3.3e-172)
		tmp = a / (t_1 / (y + t));
	elseif (y <= 2.95e-261)
		tmp = t_2;
	elseif (y <= 1.48e-130)
		tmp = ((y + t) * a) / t_1;
	else
		tmp = y * ((a + (z - b)) / (x + y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(N[(x + y), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2e-68], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], If[LessEqual[y, -2.8e-134], t$95$2, If[LessEqual[y, -3.3e-172], N[(a / N[(t$95$1 / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.95e-261], t$95$2, If[LessEqual[y, 1.48e-130], N[(N[(N[(y + t), $MachinePrecision] * a), $MachinePrecision] / t$95$1), $MachinePrecision], N[(y * N[(N[(a + N[(z - b), $MachinePrecision]), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -2.00000000000000013e-68

   1. Initial program 46.6%

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

   3. Taylor expanded in y around inf 80.2%

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

   if -2.00000000000000013e-68 < y < -2.7999999999999999e-134 or -3.3e-172 < y < 2.9500000000000002e-261

   1. Initial program 72.3%

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

   3. Taylor expanded in z around inf 42.2%

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

      1. associate-/l* 61.2%

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

      2. +-commutative 61.2%

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

      3. +-commutative 61.2%

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

      4. associate-+r+ 61.2%

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

      5. +-commutative 61.2%

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

      6. associate-+l+ 61.2%

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

   5. Simplified 61.2%

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

   if -2.7999999999999999e-134 < y < -3.3e-172

   1. Initial program 74.1%

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

   3. Taylor expanded in b around inf 73.1%

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

      1. +-commutative 73.1%

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

      2. mul-1-neg 73.1%

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

      3. unsub-neg 73.1%

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

   5. Simplified 82.0%

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

   6. Taylor expanded in a around -inf 74.1%

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

      1. associate-/l* 99.4%

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

      2. +-commutative 99.4%

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

      3. associate-+r+ 99.4%

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

      4. +-commutative 99.4%

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

      5. associate-+r+ 99.4%

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

   8. Simplified 99.4%

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

      1. clear-num 99.6%

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

      2. un-div-inv 99.7%

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

      3. associate-+l+ 99.7%

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

   10. Applied egg-rr 99.7%

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

   if 2.9500000000000002e-261 < y < 1.4800000000000001e-130

   1. Initial program 95.6%

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

   3. Taylor expanded in a around inf 61.8%

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

   if 1.4800000000000001e-130 < y

   1. Initial program 51.8%

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

   3. Taylor expanded in y around inf 36.0%

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

      1. clear-num 35.9%

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

      2. inv-pow 35.9%

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

      3. +-commutative 35.9%

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

      4. +-commutative 35.9%

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

      5. associate--l+ 35.9%

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

   5. Applied egg-rr 35.9%

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

      1. unpow-1 35.9%

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

      2. associate-+r- 35.9%

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

      3. associate-/r* 73.1%

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

      4. associate-+r+ 73.1%

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

      5. associate-+r- 73.1%

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

   7. Simplified 73.1%

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

   8. Taylor expanded in t around 0 31.3%

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

      1. associate-/l* 63.8%

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

      2. associate--l+ 63.8%

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

      3. +-commutative 63.8%

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

   10. Simplified 63.8%

       \[\leadsto \color{blue}{y \cdot \frac{a + \left(z - b\right)}{y + x}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 70.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{-68}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-134}:\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq -3.3 \cdot 10^{-172}:\\ \;\;\;\;\frac{a}{\frac{y + \left(x + t\right)}{y + t}}\\ \mathbf{elif}\;y \leq 2.95 \cdot 10^{-261}:\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq 1.48 \cdot 10^{-130}:\\ \;\;\;\;\frac{\left(y + t\right) \cdot a}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{a + \left(z - b\right)}{x + y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 62.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ \mathbf{if}\;y \leq -2.75 \cdot 10^{-70}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-133}:\\ \;\;\;\;z \cdot \frac{x + y}{t\_1}\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{-162}:\\ \;\;\;\;\frac{a}{\frac{t\_1}{y + t}}\\ \mathbf{elif}\;y \leq 9.4 \cdot 10^{-123}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{a + \left(z - b\right)}{x + y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t))))
   (if (<= y -2.75e-70)
     (- (+ z a) b)
     (if (<= y -3e-133)
       (* z (/ (+ x y) t_1))
       (if (<= y -2.3e-162)
         (/ a (/ t_1 (+ y t)))
         (if (<= y 9.4e-123)
           (/ (+ (* t a) (* x z)) (+ x t))
           (* y (/ (+ a (- z b)) (+ x y)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double tmp;
	if (y <= -2.75e-70) {
		tmp = (z + a) - b;
	} else if (y <= -3e-133) {
		tmp = z * ((x + y) / t_1);
	} else if (y <= -2.3e-162) {
		tmp = a / (t_1 / (y + t));
	} else if (y <= 9.4e-123) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else {
		tmp = y * ((a + (z - b)) / (x + y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y + (x + t)
    if (y <= (-2.75d-70)) then
        tmp = (z + a) - b
    else if (y <= (-3d-133)) then
        tmp = z * ((x + y) / t_1)
    else if (y <= (-2.3d-162)) then
        tmp = a / (t_1 / (y + t))
    else if (y <= 9.4d-123) then
        tmp = ((t * a) + (x * z)) / (x + t)
    else
        tmp = y * ((a + (z - b)) / (x + y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double tmp;
	if (y <= -2.75e-70) {
		tmp = (z + a) - b;
	} else if (y <= -3e-133) {
		tmp = z * ((x + y) / t_1);
	} else if (y <= -2.3e-162) {
		tmp = a / (t_1 / (y + t));
	} else if (y <= 9.4e-123) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else {
		tmp = y * ((a + (z - b)) / (x + y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	tmp = 0
	if y <= -2.75e-70:
		tmp = (z + a) - b
	elif y <= -3e-133:
		tmp = z * ((x + y) / t_1)
	elif y <= -2.3e-162:
		tmp = a / (t_1 / (y + t))
	elif y <= 9.4e-123:
		tmp = ((t * a) + (x * z)) / (x + t)
	else:
		tmp = y * ((a + (z - b)) / (x + y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	tmp = 0.0
	if (y <= -2.75e-70)
		tmp = Float64(Float64(z + a) - b);
	elseif (y <= -3e-133)
		tmp = Float64(z * Float64(Float64(x + y) / t_1));
	elseif (y <= -2.3e-162)
		tmp = Float64(a / Float64(t_1 / Float64(y + t)));
	elseif (y <= 9.4e-123)
		tmp = Float64(Float64(Float64(t * a) + Float64(x * z)) / Float64(x + t));
	else
		tmp = Float64(y * Float64(Float64(a + Float64(z - b)) / Float64(x + y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	tmp = 0.0;
	if (y <= -2.75e-70)
		tmp = (z + a) - b;
	elseif (y <= -3e-133)
		tmp = z * ((x + y) / t_1);
	elseif (y <= -2.3e-162)
		tmp = a / (t_1 / (y + t));
	elseif (y <= 9.4e-123)
		tmp = ((t * a) + (x * z)) / (x + t);
	else
		tmp = y * ((a + (z - b)) / (x + y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.75e-70], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], If[LessEqual[y, -3e-133], N[(z * N[(N[(x + y), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.3e-162], N[(a / N[(t$95$1 / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.4e-123], N[(N[(N[(t * a), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(a + N[(z - b), $MachinePrecision]), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -2.75e-70

   1. Initial program 46.6%

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

   3. Taylor expanded in y around inf 80.2%

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

   if -2.75e-70 < y < -3.00000000000000019e-133

   1. Initial program 68.1%

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

   3. Taylor expanded in z around inf 39.8%

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

      1. associate-/l* 63.6%

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

      2. +-commutative 63.6%

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

      3. +-commutative 63.6%

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

      4. associate-+r+ 63.6%

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

      5. +-commutative 63.6%

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

      6. associate-+l+ 63.6%

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

   5. Simplified 63.6%

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

   if -3.00000000000000019e-133 < y < -2.2999999999999998e-162

   1. Initial program 68.3%

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

   3. Taylor expanded in b around inf 67.1%

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

      1. +-commutative 67.1%

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

      2. mul-1-neg 67.1%

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

      3. unsub-neg 67.1%

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

   5. Simplified 78.1%

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

   6. Taylor expanded in a around -inf 68.3%

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

      1. associate-/l* 99.5%

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

      2. +-commutative 99.5%

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

      3. associate-+r+ 99.5%

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

      4. +-commutative 99.5%

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

      5. associate-+r+ 99.5%

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

   8. Simplified 99.5%

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

      1. clear-num 99.7%

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

      2. un-div-inv 99.8%

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

      3. associate-+l+ 99.8%

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

   10. Applied egg-rr 99.8%

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

   if -2.2999999999999998e-162 < y < 9.4000000000000004e-123

   1. Initial program 83.4%

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

   3. Taylor expanded in y around 0 68.6%

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

   if 9.4000000000000004e-123 < y

   1. Initial program 51.8%

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

   3. Taylor expanded in y around inf 36.0%

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

      1. clear-num 35.9%

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

      2. inv-pow 35.9%

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

      3. +-commutative 35.9%

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

      4. +-commutative 35.9%

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

      5. associate--l+ 35.9%

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

   5. Applied egg-rr 35.9%

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

      1. unpow-1 35.9%

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

      2. associate-+r- 35.9%

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

      3. associate-/r* 73.1%

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

      4. associate-+r+ 73.1%

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

      5. associate-+r- 73.1%

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

   7. Simplified 73.1%

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

   8. Taylor expanded in t around 0 31.3%

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

      1. associate-/l* 63.8%

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

      2. associate--l+ 63.8%

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

      3. +-commutative 63.8%

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

   10. Simplified 63.8%

       \[\leadsto \color{blue}{y \cdot \frac{a + \left(z - b\right)}{y + x}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 71.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.75 \cdot 10^{-70}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-133}:\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{-162}:\\ \;\;\;\;\frac{a}{\frac{y + \left(x + t\right)}{y + t}}\\ \mathbf{elif}\;y \leq 9.4 \cdot 10^{-123}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{a + \left(z - b\right)}{x + y}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 70.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y + t\right)\\ \mathbf{if}\;b \leq -2.2 \cdot 10^{+112}:\\ \;\;\;\;b \cdot \left(\frac{z}{b} - \frac{y}{y + \left(x + t\right)}\right)\\ \mathbf{elif}\;b \leq 8.2 \cdot 10^{+27}:\\ \;\;\;\;a + z \cdot \frac{x + y}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{a + \left(z - b\right)}{t\_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (+ y t))))
   (if (<= b -2.2e+112)
     (* b (- (/ z b) (/ y (+ y (+ x t)))))
     (if (<= b 8.2e+27)
       (+ a (* z (/ (+ x y) t_1)))
       (* y (/ (+ a (- z b)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y + t);
	double tmp;
	if (b <= -2.2e+112) {
		tmp = b * ((z / b) - (y / (y + (x + t))));
	} else if (b <= 8.2e+27) {
		tmp = a + (z * ((x + y) / t_1));
	} else {
		tmp = y * ((a + (z - b)) / t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y + t)
    if (b <= (-2.2d+112)) then
        tmp = b * ((z / b) - (y / (y + (x + t))))
    else if (b <= 8.2d+27) then
        tmp = a + (z * ((x + y) / t_1))
    else
        tmp = y * ((a + (z - b)) / t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y + t);
	double tmp;
	if (b <= -2.2e+112) {
		tmp = b * ((z / b) - (y / (y + (x + t))));
	} else if (b <= 8.2e+27) {
		tmp = a + (z * ((x + y) / t_1));
	} else {
		tmp = y * ((a + (z - b)) / t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (y + t)
	tmp = 0
	if b <= -2.2e+112:
		tmp = b * ((z / b) - (y / (y + (x + t))))
	elif b <= 8.2e+27:
		tmp = a + (z * ((x + y) / t_1))
	else:
		tmp = y * ((a + (z - b)) / t_1)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(y + t))
	tmp = 0.0
	if (b <= -2.2e+112)
		tmp = Float64(b * Float64(Float64(z / b) - Float64(y / Float64(y + Float64(x + t)))));
	elseif (b <= 8.2e+27)
		tmp = Float64(a + Float64(z * Float64(Float64(x + y) / t_1)));
	else
		tmp = Float64(y * Float64(Float64(a + Float64(z - b)) / t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (y + t);
	tmp = 0.0;
	if (b <= -2.2e+112)
		tmp = b * ((z / b) - (y / (y + (x + t))));
	elseif (b <= 8.2e+27)
		tmp = a + (z * ((x + y) / t_1));
	else
		tmp = y * ((a + (z - b)) / t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.2e+112], N[(b * N[(N[(z / b), $MachinePrecision] - N[(y / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 8.2e+27], N[(a + N[(z * N[(N[(x + y), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(a + N[(z - b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.1999999999999999e112

   1. Initial program 56.9%

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

   3. Taylor expanded in b around inf 71.1%

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

      1. +-commutative 71.1%

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

      2. mul-1-neg 71.1%

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

      3. unsub-neg 71.1%

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

   5. Simplified 82.2%

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

   6. Taylor expanded in x around inf 85.7%

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

   if -2.1999999999999999e112 < b < 8.2000000000000005e27

   1. Initial program 60.6%

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

   3. Taylor expanded in b around inf 54.6%

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

      1. +-commutative 54.6%

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

      2. mul-1-neg 54.6%

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

      3. unsub-neg 54.6%

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

   5. Simplified 73.7%

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

   6. Taylor expanded in b around 0 55.5%

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

      1. associate-/l* 72.7%

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

      2. +-commutative 72.7%

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

      3. associate-+r+ 72.7%

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

      4. +-commutative 72.7%

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

      5. associate-+r+ 72.7%

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

      6. associate-/l* 94.1%

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

      7. +-commutative 94.1%

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

      8. associate-+r+ 94.1%

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

      9. +-commutative 94.1%

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

      10. associate-+r+ 94.1%

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

   8. Simplified 94.1%

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

   9. Taylor expanded in y around inf 76.9%

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

   if 8.2000000000000005e27 < b

   1. Initial program 53.1%

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

   3. Taylor expanded in y around inf 38.9%

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

      1. associate-/l* 75.2%

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

      2. associate--l+ 75.2%

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

      3. +-commutative 75.2%

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

      4. +-commutative 75.2%

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

   5. Applied egg-rr 75.2%

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

      1. associate-+r+ 75.2%

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

   7. Simplified 75.2%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.2 \cdot 10^{+112}:\\ \;\;\;\;b \cdot \left(\frac{z}{b} - \frac{y}{y + \left(x + t\right)}\right)\\ \mathbf{elif}\;b \leq 8.2 \cdot 10^{+27}:\\ \;\;\;\;a + z \cdot \frac{x + y}{x + \left(y + t\right)}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{a + \left(z - b\right)}{x + \left(y + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 56.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ \mathbf{if}\;a \leq 1.2 \cdot 10^{-302}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;a \leq 170000000:\\ \;\;\;\;z \cdot \frac{x + y}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{y + t}{t\_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t))))
   (if (<= a 1.2e-302)
     (- (+ z a) b)
     (if (<= a 170000000.0) (* z (/ (+ x y) t_1)) (* a (/ (+ y t) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double tmp;
	if (a <= 1.2e-302) {
		tmp = (z + a) - b;
	} else if (a <= 170000000.0) {
		tmp = z * ((x + y) / t_1);
	} else {
		tmp = a * ((y + t) / t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y + (x + t)
    if (a <= 1.2d-302) then
        tmp = (z + a) - b
    else if (a <= 170000000.0d0) then
        tmp = z * ((x + y) / t_1)
    else
        tmp = a * ((y + t) / t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double tmp;
	if (a <= 1.2e-302) {
		tmp = (z + a) - b;
	} else if (a <= 170000000.0) {
		tmp = z * ((x + y) / t_1);
	} else {
		tmp = a * ((y + t) / t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	tmp = 0
	if a <= 1.2e-302:
		tmp = (z + a) - b
	elif a <= 170000000.0:
		tmp = z * ((x + y) / t_1)
	else:
		tmp = a * ((y + t) / t_1)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	tmp = 0.0
	if (a <= 1.2e-302)
		tmp = Float64(Float64(z + a) - b);
	elseif (a <= 170000000.0)
		tmp = Float64(z * Float64(Float64(x + y) / t_1));
	else
		tmp = Float64(a * Float64(Float64(y + t) / t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	tmp = 0.0;
	if (a <= 1.2e-302)
		tmp = (z + a) - b;
	elseif (a <= 170000000.0)
		tmp = z * ((x + y) / t_1);
	else
		tmp = a * ((y + t) / t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, 1.2e-302], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], If[LessEqual[a, 170000000.0], N[(z * N[(N[(x + y), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], N[(a * N[(N[(y + t), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < 1.20000000000000011e-302

   1. Initial program 58.4%

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

   3. Taylor expanded in y around inf 62.5%

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

   if 1.20000000000000011e-302 < a < 1.7e8

   1. Initial program 67.7%

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

   3. Taylor expanded in z around inf 36.7%

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

      1. associate-/l* 64.3%

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

      2. +-commutative 64.3%

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

      3. +-commutative 64.3%

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

      4. associate-+r+ 64.3%

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

      5. +-commutative 64.3%

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

      6. associate-+l+ 64.3%

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

   5. Simplified 64.3%

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

   if 1.7e8 < a

   1. Initial program 49.0%

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

   3. Taylor expanded in a around inf 39.9%

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

      1. associate-/l* 70.4%

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

      2. +-commutative 70.4%

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

      3. associate-+r+ 70.4%

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

      4. +-commutative 70.4%

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

      5. associate-+l+ 70.4%

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

   5. Simplified 70.4%

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

4. Final simplification 64.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 1.2 \cdot 10^{-302}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;a \leq 170000000:\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{y + t}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 55.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ \mathbf{if}\;a \leq 2.35 \cdot 10^{-303}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;a \leq 240000000:\\ \;\;\;\;z \cdot \frac{x + y}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;\left(y + t\right) \cdot \frac{a}{t\_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t))))
   (if (<= a 2.35e-303)
     (- (+ z a) b)
     (if (<= a 240000000.0) (* z (/ (+ x y) t_1)) (* (+ y t) (/ a t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double tmp;
	if (a <= 2.35e-303) {
		tmp = (z + a) - b;
	} else if (a <= 240000000.0) {
		tmp = z * ((x + y) / t_1);
	} else {
		tmp = (y + t) * (a / t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y + (x + t)
    if (a <= 2.35d-303) then
        tmp = (z + a) - b
    else if (a <= 240000000.0d0) then
        tmp = z * ((x + y) / t_1)
    else
        tmp = (y + t) * (a / t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double tmp;
	if (a <= 2.35e-303) {
		tmp = (z + a) - b;
	} else if (a <= 240000000.0) {
		tmp = z * ((x + y) / t_1);
	} else {
		tmp = (y + t) * (a / t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	tmp = 0
	if a <= 2.35e-303:
		tmp = (z + a) - b
	elif a <= 240000000.0:
		tmp = z * ((x + y) / t_1)
	else:
		tmp = (y + t) * (a / t_1)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	tmp = 0.0
	if (a <= 2.35e-303)
		tmp = Float64(Float64(z + a) - b);
	elseif (a <= 240000000.0)
		tmp = Float64(z * Float64(Float64(x + y) / t_1));
	else
		tmp = Float64(Float64(y + t) * Float64(a / t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	tmp = 0.0;
	if (a <= 2.35e-303)
		tmp = (z + a) - b;
	elseif (a <= 240000000.0)
		tmp = z * ((x + y) / t_1);
	else
		tmp = (y + t) * (a / t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, 2.35e-303], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], If[LessEqual[a, 240000000.0], N[(z * N[(N[(x + y), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], N[(N[(y + t), $MachinePrecision] * N[(a / t$95$1), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < 2.3499999999999999e-303

   1. Initial program 58.4%

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

   3. Taylor expanded in y around inf 62.5%

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

   if 2.3499999999999999e-303 < a < 2.4e8

   1. Initial program 67.7%

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

   3. Taylor expanded in z around inf 36.7%

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

      1. associate-/l* 64.3%

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

      2. +-commutative 64.3%

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

      3. +-commutative 64.3%

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

      4. associate-+r+ 64.3%

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

      5. +-commutative 64.3%

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

      6. associate-+l+ 64.3%

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

   5. Simplified 64.3%

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

   if 2.4e8 < a

   1. Initial program 49.0%

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

   3. Taylor expanded in b around inf 46.4%

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

      1. +-commutative 46.4%

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

      2. mul-1-neg 46.4%

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

      3. unsub-neg 46.4%

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

   5. Simplified 67.3%

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

   6. Taylor expanded in a around -inf 39.9%

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

      1. associate-/l* 70.4%

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

      2. +-commutative 70.4%

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

      3. associate-+r+ 70.4%

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

      4. +-commutative 70.4%

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

      5. associate-+r+ 70.4%

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

   8. Simplified 70.4%

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

      1. clear-num 70.4%

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

      2. un-div-inv 70.4%

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

      3. associate-+l+ 70.4%

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

   10. Applied egg-rr 70.4%

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

       1. associate-/r/ 72.0%

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

       2. +-commutative 72.0%

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

   12. Simplified 72.0%

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

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 2.35 \cdot 10^{-303}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;a \leq 240000000:\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(y + t\right) \cdot \frac{a}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 56.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 1.05 \cdot 10^{+98}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{y + t}{y + \left(x + t\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a 1.05e+98) (- (+ z a) b) (* a (/ (+ y t) (+ y (+ x t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= 1.05e+98) {
		tmp = (z + a) - b;
	} else {
		tmp = a * ((y + t) / (y + (x + t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= 1.05d+98) then
        tmp = (z + a) - b
    else
        tmp = a * ((y + t) / (y + (x + t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= 1.05e+98) {
		tmp = (z + a) - b;
	} else {
		tmp = a * ((y + t) / (y + (x + t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= 1.05e+98:
		tmp = (z + a) - b
	else:
		tmp = a * ((y + t) / (y + (x + t)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= 1.05e+98)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(a * Float64(Float64(y + t) / Float64(y + Float64(x + t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= 1.05e+98)
		tmp = (z + a) - b;
	else
		tmp = a * ((y + t) / (y + (x + t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, 1.05e+98], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(a * N[(N[(y + t), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 1.05000000000000002e98

   1. Initial program 61.4%

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

   3. Taylor expanded in y around inf 59.8%

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

   if 1.05000000000000002e98 < a

   1. Initial program 43.2%

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

   3. Taylor expanded in a around inf 37.9%

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

      1. associate-/l* 80.4%

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

      2. +-commutative 80.4%

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

      3. associate-+r+ 80.4%

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

      4. +-commutative 80.4%

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

      5. associate-+l+ 80.4%

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

   5. Simplified 80.4%

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

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 1.05 \cdot 10^{+98}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{y + t}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 55.3% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 1.15 \cdot 10^{+234}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t}{x + t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a 1.15e+234) (- (+ z a) b) (* a (/ t (+ x t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= 1.15e+234) {
		tmp = (z + a) - b;
	} else {
		tmp = a * (t / (x + t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= 1.15d+234) then
        tmp = (z + a) - b
    else
        tmp = a * (t / (x + t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= 1.15e+234) {
		tmp = (z + a) - b;
	} else {
		tmp = a * (t / (x + t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= 1.15e+234:
		tmp = (z + a) - b
	else:
		tmp = a * (t / (x + t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= 1.15e+234)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(a * Float64(t / Float64(x + t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= 1.15e+234)
		tmp = (z + a) - b;
	else
		tmp = a * (t / (x + t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, 1.15e+234], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(a * N[(t / N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 1.15e234

   1. Initial program 59.0%

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

   3. Taylor expanded in y around inf 61.9%

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

   if 1.15e234 < a

   1. Initial program 49.9%

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

   3. Taylor expanded in b around inf 41.6%

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

      1. +-commutative 41.6%

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

      2. mul-1-neg 41.6%

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

      3. unsub-neg 41.6%

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

   5. Simplified 41.8%

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

   6. Taylor expanded in a around -inf 44.1%

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

      1. associate-/l* 79.0%

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

      2. +-commutative 79.0%

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

      3. associate-+r+ 79.0%

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

      4. +-commutative 79.0%

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

      5. associate-+r+ 79.0%

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

   8. Simplified 79.0%

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

   9. Taylor expanded in y around 0 36.1%

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

       1. associate-/l* 56.7%

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

   11. Simplified 56.7%

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

4. Final simplification 61.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 1.15 \cdot 10^{+234}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t}{x + t}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 42.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.9 \cdot 10^{-68}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{+99}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -4.9e-68) a (if (<= t 1.6e+99) z a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -4.9e-68) {
		tmp = a;
	} else if (t <= 1.6e+99) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-4.9d-68)) then
        tmp = a
    else if (t <= 1.6d+99) then
        tmp = z
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -4.9e-68) {
		tmp = a;
	} else if (t <= 1.6e+99) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -4.9e-68:
		tmp = a
	elif t <= 1.6e+99:
		tmp = z
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -4.9e-68)
		tmp = a;
	elseif (t <= 1.6e+99)
		tmp = z;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -4.9e-68)
		tmp = a;
	elseif (t <= 1.6e+99)
		tmp = z;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -4.9e-68], a, If[LessEqual[t, 1.6e+99], z, a]]

Derivation

1. Split input into 2 regimes

2. if t < -4.89999999999999977e-68 or 1.6e99 < t

   1. Initial program 45.0%

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

   3. Taylor expanded in t around inf 47.0%

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

   if -4.89999999999999977e-68 < t < 1.6e99

   1. Initial program 68.2%

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

   3. Taylor expanded in x around inf 43.4%

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

4. Final simplification 44.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.9 \cdot 10^{-68}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{+99}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 55.7% accurate, 4.2× speedup

Math

\[\begin{array}{l} \\ \left(z + a\right) - b \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 58.6%

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

3. Taylor expanded in y around inf 60.1%

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

4. Final simplification 60.1%

   \[\leadsto \left(z + a\right) - b \]
5. Add Preprocessing

Alternative 17: 32.5% accurate, 21.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 58.6%

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

3. Taylor expanded in t around inf 30.6%

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

4. Final simplification 30.6%

   \[\leadsto a \]
5. Add Preprocessing

Developer target: 82.3% accurate, 0.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024071 
(FPCore (x y z t a b)
  :name "AI.Clustering.Hierarchical.Internal:ward from clustering-0.2.1"
  :precision binary64

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

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