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

Percentage Accurate: 60.8% → 88.5%

Time: 12.2s

Alternatives: 16

Speedup: 1.0×

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: 60.8% 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: 88.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \frac{\left(z \cdot \left(x + y\right) + \left(y + t\right) \cdot a\right) - y \cdot b}{t\_1}\\ \mathbf{if}\;t\_2 \leq -\infty \lor \neg \left(t\_2 \leq 2 \cdot 10^{+304}\right):\\ \;\;\;\;b \cdot \left(\frac{\mathsf{fma}\left(z, \frac{x + y}{t\_1}, a \cdot \frac{y + t}{t\_1}\right)}{b} - \frac{y}{t\_1}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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 (or (<= t_2 (- INFINITY)) (not (<= t_2 2e+304)))
     (* b (- (/ (fma z (/ (+ x y) t_1) (* a (/ (+ y t) t_1))) b) (/ y t_1)))
     t_2)))

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)) || !(t_2 <= 2e+304)) {
		tmp = b * ((fma(z, ((x + y) / t_1), (a * ((y + t) / t_1))) / b) - (y / t_1));
	} else {
		tmp = t_2;
	}
	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)) || !(t_2 <= 2e+304))
		tmp = Float64(b * Float64(Float64(fma(z, Float64(Float64(x + y) / t_1), Float64(a * Float64(Float64(y + t) / t_1))) / b) - Float64(y / t_1)));
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(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[Or[LessEqual[t$95$2, (-Infinity)], N[Not[LessEqual[t$95$2, 2e+304]], $MachinePrecision]], N[(b * N[(N[(N[(z * N[(N[(x + y), $MachinePrecision] / t$95$1), $MachinePrecision] + N[(a * N[(N[(y + t), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision] - N[(y / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -inf.0 or 1.9999999999999999e304 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 5.0%

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

   3. Taylor expanded in b around -inf 20.3%

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

      1. mul-1-neg 20.3%

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

      2. *-commutative 20.3%

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

      3. distribute-rgt-neg-in 20.3%

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

   5. Simplified 83.1%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1.9999999999999999e304

   1. Initial program 99.8%

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

4. Final simplification 93.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z \cdot \left(x + y\right) + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty \lor \neg \left(\frac{\left(z \cdot \left(x + y\right) + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)} \leq 2 \cdot 10^{+304}\right):\\ \;\;\;\;b \cdot \left(\frac{\mathsf{fma}\left(z, \frac{x + y}{y + \left(x + t\right)}, a \cdot \frac{y + t}{y + \left(x + t\right)}\right)}{b} - \frac{y}{y + \left(x + t\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(z \cdot \left(x + y\right) + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 87.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \left(x + y\right)\\ t_2 := y + \left(x + t\right)\\ t_3 := \frac{\left(z \cdot \left(x + y\right) + \left(y + t\right) \cdot a\right) - y \cdot b}{t\_2}\\ \mathbf{if}\;t\_3 \leq -\infty:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;t\_3 \leq 2 \cdot 10^{+304}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\frac{z \cdot \left(\frac{x + y}{t\_1} + \frac{a}{z} \cdot \frac{y + t}{t\_1}\right)}{b} - \frac{y}{t\_2}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ t (+ x y)))
        (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 2e+304)
       t_3
       (*
        b
        (-
         (/ (* z (+ (/ (+ x y) t_1) (* (/ a z) (/ (+ y t) t_1)))) b)
         (/ y t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t + (x + y);
	double t_2 = y + (x + 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 <= 2e+304) {
		tmp = t_3;
	} else {
		tmp = b * (((z * (((x + y) / t_1) + ((a / z) * ((y + t) / t_1)))) / b) - (y / t_2));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t + (x + y);
	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 <= 2e+304) {
		tmp = t_3;
	} else {
		tmp = b * (((z * (((x + y) / t_1) + ((a / z) * ((y + t) / t_1)))) / b) - (y / t_2));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t + (x + y)
	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 <= 2e+304:
		tmp = t_3
	else:
		tmp = b * (((z * (((x + y) / t_1) + ((a / z) * ((y + t) / t_1)))) / b) - (y / t_2))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t + Float64(x + y))
	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 <= 2e+304)
		tmp = t_3;
	else
		tmp = Float64(b * Float64(Float64(Float64(z * Float64(Float64(Float64(x + y) / t_1) + Float64(Float64(a / z) * Float64(Float64(y + t) / t_1)))) / b) - Float64(y / t_2)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t + (x + y);
	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 <= 2e+304)
		tmp = t_3;
	else
		tmp = b * (((z * (((x + y) / t_1) + ((a / z) * ((y + t) / t_1)))) / b) - (y / t_2));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t + N[(x + y), $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, 2e+304], t$95$3, N[(b * N[(N[(N[(z * N[(N[(N[(x + y), $MachinePrecision] / t$95$1), $MachinePrecision] + N[(N[(a / z), $MachinePrecision] * N[(N[(y + t), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision] - N[(y / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 6.0%

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

   3. Taylor expanded in y around inf 77.7%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1.9999999999999999e304

   1. Initial program 99.8%

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

   if 1.9999999999999999e304 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 4.2%

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

   3. Taylor expanded in b around -inf 19.8%

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

      1. mul-1-neg 19.8%

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

      2. *-commutative 19.8%

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

      3. distribute-rgt-neg-in 19.8%

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

   5. Simplified 81.8%

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

   6. Taylor expanded in z around -inf 44.1%

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

      1. mul-1-neg 44.1%

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

      2. distribute-lft-out 44.1%

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

      3. times-frac 75.1%

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

   8. Simplified 75.1%

      \[\leadsto \left(\frac{y}{\left(t + x\right) + y} - \frac{\color{blue}{-z \cdot \left(-1 \cdot \left(\frac{a}{z} \cdot \frac{t + y}{t + \left(x + y\right)} + \frac{x + y}{t + \left(x + y\right)}\right)\right)}}{b}\right) \cdot \left(-b\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 90.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z \cdot \left(x + y\right) + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;\frac{\left(z \cdot \left(x + y\right) + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)} \leq 2 \cdot 10^{+304}:\\ \;\;\;\;\frac{\left(z \cdot \left(x + y\right) + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\frac{z \cdot \left(\frac{x + y}{t + \left(x + y\right)} + \frac{a}{z} \cdot \frac{y + t}{t + \left(x + y\right)}\right)}{b} - \frac{y}{y + \left(x + t\right)}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 88.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(z \cdot \left(x + y\right) + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{if}\;t\_1 \leq -\infty \lor \neg \left(t\_1 \leq 5 \cdot 10^{+274}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* z (+ x y)) (* (+ y t) a)) (* y b)) (+ y (+ x t)))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 5e+274))) (- (+ z a) b) t_1)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (((z * (x + y)) + ((y + t) * a)) - (y * b)) / (y + (x + t));
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 5e+274)) {
		tmp = (z + a) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (((z * (x + y)) + ((y + t) * a)) - (y * b)) / (y + (x + t));
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 5e+274)) {
		tmp = (z + a) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (((z * (x + y)) + ((y + t) * a)) - (y * b)) / (y + (x + t))
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 5e+274):
		tmp = (z + a) - b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(Float64(z * Float64(x + y)) + Float64(Float64(y + t) * a)) - Float64(y * b)) / Float64(y + Float64(x + t)))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 5e+274))
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (((z * (x + y)) + ((y + t) * a)) - (y * b)) / (y + (x + t));
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 5e+274)))
		tmp = (z + a) - b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision] + N[(N[(y + t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 5e+274]], $MachinePrecision]], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], t$95$1]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -inf.0 or 4.9999999999999998e274 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 6.8%

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

   3. Taylor expanded in y around inf 73.5%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 4.9999999999999998e274

   1. Initial program 99.8%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z \cdot \left(x + y\right) + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty \lor \neg \left(\frac{\left(z \cdot \left(x + y\right) + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)} \leq 5 \cdot 10^{+274}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(z \cdot \left(x + y\right) + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \frac{\left(z \cdot \left(x + y\right) + \left(y + t\right) \cdot a\right) - y \cdot b}{t\_1}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+304}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\frac{a + y \cdot \frac{z}{y + t}}{b} - \frac{y}{t\_1}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t)))
        (t_2 (/ (- (+ (* z (+ x y)) (* (+ y t) a)) (* y b)) t_1)))
   (if (<= t_2 (- INFINITY))
     (- (+ z a) b)
     (if (<= t_2 2e+304)
       t_2
       (* b (- (/ (+ a (* y (/ z (+ y t)))) b) (/ y t_1)))))))

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 <= 2e+304) {
		tmp = t_2;
	} else {
		tmp = b * (((a + (y * (z / (y + t)))) / b) - (y / t_1));
	}
	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 <= 2e+304) {
		tmp = t_2;
	} else {
		tmp = b * (((a + (y * (z / (y + t)))) / b) - (y / t_1));
	}
	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 <= 2e+304:
		tmp = t_2
	else:
		tmp = b * (((a + (y * (z / (y + t)))) / b) - (y / t_1))
	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 <= 2e+304)
		tmp = t_2;
	else
		tmp = Float64(b * Float64(Float64(Float64(a + Float64(y * Float64(z / Float64(y + t)))) / b) - Float64(y / t_1)));
	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 <= 2e+304)
		tmp = t_2;
	else
		tmp = b * (((a + (y * (z / (y + t)))) / b) - (y / 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]}, 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, 2e+304], t$95$2, N[(b * N[(N[(N[(a + N[(y * N[(z / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision] - N[(y / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 6.0%

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

   3. Taylor expanded in y around inf 77.7%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1.9999999999999999e304

   1. Initial program 99.8%

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

   if 1.9999999999999999e304 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 4.2%

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

   3. Taylor expanded in b around -inf 19.8%

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

      1. mul-1-neg 19.8%

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

      2. *-commutative 19.8%

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

      3. distribute-rgt-neg-in 19.8%

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

   5. Simplified 81.8%

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

   6. Taylor expanded in x around 0 39.4%

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

      1. associate-/l* 69.6%

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

   8. Simplified 69.6%

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

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z \cdot \left(x + y\right) + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;\frac{\left(z \cdot \left(x + y\right) + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)} \leq 2 \cdot 10^{+304}:\\ \;\;\;\;\frac{\left(z \cdot \left(x + y\right) + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\frac{a + y \cdot \frac{z}{y + t}}{b} - \frac{y}{y + \left(x + t\right)}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 91.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \left(x + y\right)\\ t_2 := \frac{x + y}{t\_1}\\ \mathbf{if}\;a \leq -1.2 \cdot 10^{-53} \lor \neg \left(a \leq 3.9 \cdot 10^{-38}\right):\\ \;\;\;\;a \cdot \left(\frac{t}{t\_1} + \left(\left(\frac{y}{t\_1} + \frac{z}{a} \cdot t\_2\right) - b \cdot \frac{y}{a \cdot t\_1}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\frac{z \cdot \left(t\_2 + \frac{a}{z} \cdot \frac{y + t}{t\_1}\right)}{b} - \frac{y}{y + \left(x + t\right)}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ t (+ x y))) (t_2 (/ (+ x y) t_1)))
   (if (or (<= a -1.2e-53) (not (<= a 3.9e-38)))
     (*
      a
      (+ (/ t t_1) (- (+ (/ y t_1) (* (/ z a) t_2)) (* b (/ y (* a t_1))))))
     (*
      b
      (-
       (/ (* z (+ t_2 (* (/ a z) (/ (+ y t) t_1)))) b)
       (/ y (+ y (+ x t))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t + (x + y);
	double t_2 = (x + y) / t_1;
	double tmp;
	if ((a <= -1.2e-53) || !(a <= 3.9e-38)) {
		tmp = a * ((t / t_1) + (((y / t_1) + ((z / a) * t_2)) - (b * (y / (a * t_1)))));
	} else {
		tmp = b * (((z * (t_2 + ((a / z) * ((y + t) / t_1)))) / b) - (y / (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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t + (x + y)
    t_2 = (x + y) / t_1
    if ((a <= (-1.2d-53)) .or. (.not. (a <= 3.9d-38))) then
        tmp = a * ((t / t_1) + (((y / t_1) + ((z / a) * t_2)) - (b * (y / (a * t_1)))))
    else
        tmp = b * (((z * (t_2 + ((a / z) * ((y + t) / t_1)))) / b) - (y / (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 t_1 = t + (x + y);
	double t_2 = (x + y) / t_1;
	double tmp;
	if ((a <= -1.2e-53) || !(a <= 3.9e-38)) {
		tmp = a * ((t / t_1) + (((y / t_1) + ((z / a) * t_2)) - (b * (y / (a * t_1)))));
	} else {
		tmp = b * (((z * (t_2 + ((a / z) * ((y + t) / t_1)))) / b) - (y / (y + (x + t))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t + (x + y)
	t_2 = (x + y) / t_1
	tmp = 0
	if (a <= -1.2e-53) or not (a <= 3.9e-38):
		tmp = a * ((t / t_1) + (((y / t_1) + ((z / a) * t_2)) - (b * (y / (a * t_1)))))
	else:
		tmp = b * (((z * (t_2 + ((a / z) * ((y + t) / t_1)))) / b) - (y / (y + (x + t))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t + Float64(x + y))
	t_2 = Float64(Float64(x + y) / t_1)
	tmp = 0.0
	if ((a <= -1.2e-53) || !(a <= 3.9e-38))
		tmp = Float64(a * Float64(Float64(t / t_1) + Float64(Float64(Float64(y / t_1) + Float64(Float64(z / a) * t_2)) - Float64(b * Float64(y / Float64(a * t_1))))));
	else
		tmp = Float64(b * Float64(Float64(Float64(z * Float64(t_2 + Float64(Float64(a / z) * Float64(Float64(y + t) / t_1)))) / b) - Float64(y / Float64(y + Float64(x + t)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t + (x + y);
	t_2 = (x + y) / t_1;
	tmp = 0.0;
	if ((a <= -1.2e-53) || ~((a <= 3.9e-38)))
		tmp = a * ((t / t_1) + (((y / t_1) + ((z / a) * t_2)) - (b * (y / (a * t_1)))));
	else
		tmp = b * (((z * (t_2 + ((a / z) * ((y + t) / t_1)))) / b) - (y / (y + (x + t))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + y), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[Or[LessEqual[a, -1.2e-53], N[Not[LessEqual[a, 3.9e-38]], $MachinePrecision]], N[(a * N[(N[(t / t$95$1), $MachinePrecision] + N[(N[(N[(y / t$95$1), $MachinePrecision] + N[(N[(z / a), $MachinePrecision] * t$95$2), $MachinePrecision]), $MachinePrecision] - N[(b * N[(y / N[(a * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(N[(N[(z * N[(t$95$2 + N[(N[(a / z), $MachinePrecision] * N[(N[(y + t), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision] - N[(y / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.20000000000000004e-53 or 3.8999999999999999e-38 < a

   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 a around inf 73.5%

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

      1. associate--l+ 73.5%

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

      2. +-commutative 73.5%

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

      3. +-commutative 73.5%

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

      4. times-frac 86.8%

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

      5. +-commutative 86.8%

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

      6. +-commutative 86.8%

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

      7. associate-/l* 94.7%

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

      8. +-commutative 94.7%

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

   5. Simplified 94.7%

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

   if -1.20000000000000004e-53 < a < 3.8999999999999999e-38

   1. Initial program 66.7%

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

   3. Taylor expanded in b around -inf 71.4%

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

      1. mul-1-neg 71.4%

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

      2. *-commutative 71.4%

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

      3. distribute-rgt-neg-in 71.4%

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

   5. Simplified 86.7%

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

   6. Taylor expanded in z around -inf 83.5%

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

      1. mul-1-neg 83.5%

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

      2. distribute-lft-out 83.5%

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

      3. times-frac 86.7%

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

   8. Simplified 86.7%

      \[\leadsto \left(\frac{y}{\left(t + x\right) + y} - \frac{\color{blue}{-z \cdot \left(-1 \cdot \left(\frac{a}{z} \cdot \frac{t + y}{t + \left(x + y\right)} + \frac{x + y}{t + \left(x + y\right)}\right)\right)}}{b}\right) \cdot \left(-b\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 90.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.2 \cdot 10^{-53} \lor \neg \left(a \leq 3.9 \cdot 10^{-38}\right):\\ \;\;\;\;a \cdot \left(\frac{t}{t + \left(x + y\right)} + \left(\left(\frac{y}{t + \left(x + y\right)} + \frac{z}{a} \cdot \frac{x + y}{t + \left(x + y\right)}\right) - b \cdot \frac{y}{a \cdot \left(t + \left(x + y\right)\right)}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\frac{z \cdot \left(\frac{x + y}{t + \left(x + y\right)} + \frac{a}{z} \cdot \frac{y + t}{t + \left(x + y\right)}\right)}{b} - \frac{y}{y + \left(x + t\right)}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 70.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.4 \cdot 10^{+55} \lor \neg \left(y \leq 5.5 \cdot 10^{-43}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\frac{x}{x + t} + \frac{a}{z} \cdot \frac{t}{x + t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -7.4e+55) (not (<= y 5.5e-43)))
   (- (+ z a) b)
   (* z (+ (/ x (+ x t)) (* (/ a z) (/ t (+ x t)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -7.4e+55) || !(y <= 5.5e-43)) {
		tmp = (z + a) - b;
	} else {
		tmp = z * ((x / (x + t)) + ((a / z) * (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 ((y <= (-7.4d+55)) .or. (.not. (y <= 5.5d-43))) then
        tmp = (z + a) - b
    else
        tmp = z * ((x / (x + t)) + ((a / z) * (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 ((y <= -7.4e+55) || !(y <= 5.5e-43)) {
		tmp = (z + a) - b;
	} else {
		tmp = z * ((x / (x + t)) + ((a / z) * (t / (x + t))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -7.4e+55) or not (y <= 5.5e-43):
		tmp = (z + a) - b
	else:
		tmp = z * ((x / (x + t)) + ((a / z) * (t / (x + t))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -7.4e+55) || !(y <= 5.5e-43))
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(z * Float64(Float64(x / Float64(x + t)) + Float64(Float64(a / z) * Float64(t / Float64(x + t)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -7.4e+55) || ~((y <= 5.5e-43)))
		tmp = (z + a) - b;
	else
		tmp = z * ((x / (x + t)) + ((a / z) * (t / (x + t))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -7.4e+55], N[Not[LessEqual[y, 5.5e-43]], $MachinePrecision]], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(z * N[(N[(x / N[(x + t), $MachinePrecision]), $MachinePrecision] + N[(N[(a / z), $MachinePrecision] * N[(t / N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.4000000000000004e55 or 5.50000000000000013e-43 < y

   1. Initial program 49.3%

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

   3. Taylor expanded in y around inf 73.4%

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

   if -7.4000000000000004e55 < y < 5.50000000000000013e-43

   1. Initial program 74.8%

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

   3. Taylor expanded in b around -inf 68.2%

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

      1. mul-1-neg 68.2%

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

      2. *-commutative 68.2%

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

      3. distribute-rgt-neg-in 68.2%

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

   5. Simplified 83.1%

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

   6. Taylor expanded in z around -inf 61.4%

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

      1. mul-1-neg 61.4%

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

      2. distribute-lft-out 61.4%

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

      3. times-frac 72.9%

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

   8. Simplified 72.9%

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

   9. Taylor expanded in y around 0 55.5%

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

       1. +-commutative 55.5%

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

       2. times-frac 69.8%

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

       3. +-commutative 69.8%

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

   11. Simplified 69.8%

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

4. Final simplification 71.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.4 \cdot 10^{+55} \lor \neg \left(y \leq 5.5 \cdot 10^{-43}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\frac{x}{x + t} + \frac{a}{z} \cdot \frac{t}{x + t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 47.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{+42}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-215}:\\ \;\;\;\;a - b\\ \mathbf{elif}\;z \leq 7.7 \cdot 10^{-109}:\\ \;\;\;\;a\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+116}:\\ \;\;\;\;a - b\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -4.4e+42)
   z
   (if (<= z 4.4e-215)
     (- a b)
     (if (<= z 7.7e-109) a (if (<= z 1.15e+116) (- a b) z)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -4.4e+42) {
		tmp = z;
	} else if (z <= 4.4e-215) {
		tmp = a - b;
	} else if (z <= 7.7e-109) {
		tmp = a;
	} else if (z <= 1.15e+116) {
		tmp = a - b;
	} else {
		tmp = z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-4.4d+42)) then
        tmp = z
    else if (z <= 4.4d-215) then
        tmp = a - b
    else if (z <= 7.7d-109) then
        tmp = a
    else if (z <= 1.15d+116) then
        tmp = a - b
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -4.4e+42) {
		tmp = z;
	} else if (z <= 4.4e-215) {
		tmp = a - b;
	} else if (z <= 7.7e-109) {
		tmp = a;
	} else if (z <= 1.15e+116) {
		tmp = a - b;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -4.4e+42:
		tmp = z
	elif z <= 4.4e-215:
		tmp = a - b
	elif z <= 7.7e-109:
		tmp = a
	elif z <= 1.15e+116:
		tmp = a - b
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -4.4e+42)
		tmp = z;
	elseif (z <= 4.4e-215)
		tmp = Float64(a - b);
	elseif (z <= 7.7e-109)
		tmp = a;
	elseif (z <= 1.15e+116)
		tmp = Float64(a - b);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -4.4e+42)
		tmp = z;
	elseif (z <= 4.4e-215)
		tmp = a - b;
	elseif (z <= 7.7e-109)
		tmp = a;
	elseif (z <= 1.15e+116)
		tmp = a - b;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -4.4e+42], z, If[LessEqual[z, 4.4e-215], N[(a - b), $MachinePrecision], If[LessEqual[z, 7.7e-109], a, If[LessEqual[z, 1.15e+116], N[(a - b), $MachinePrecision], z]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.4000000000000003e42 or 1.14999999999999997e116 < z

   1. Initial program 45.9%

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

   3. Taylor expanded in x around inf 50.7%

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

   if -4.4000000000000003e42 < z < 4.39999999999999993e-215 or 7.70000000000000025e-109 < z < 1.14999999999999997e116

   1. Initial program 73.5%

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

   3. Taylor expanded in z around 0 59.2%

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

      1. *-commutative 59.2%

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

   5. Simplified 59.2%

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

   6. Taylor expanded in y around inf 49.5%

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

   if 4.39999999999999993e-215 < z < 7.70000000000000025e-109

   1. Initial program 80.7%

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

   3. Taylor expanded in t around inf 61.4%

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

Alternative 8: 62.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1 \cdot 10^{+67} \lor \neg \left(b \leq 2 \cdot 10^{+48}\right):\\ \;\;\;\;b \cdot \left(\frac{a}{b} - \frac{y}{y + \left(x + t\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -1e+67) (not (<= b 2e+48)))
   (* b (- (/ a b) (/ y (+ y (+ x t)))))
   (- (+ z a) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1e+67) || !(b <= 2e+48)) {
		tmp = b * ((a / b) - (y / (y + (x + t))));
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-1d+67)) .or. (.not. (b <= 2d+48))) then
        tmp = b * ((a / b) - (y / (y + (x + t))))
    else
        tmp = (z + a) - b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1e+67) || !(b <= 2e+48)) {
		tmp = b * ((a / b) - (y / (y + (x + t))));
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -1e+67) or not (b <= 2e+48):
		tmp = b * ((a / b) - (y / (y + (x + t))))
	else:
		tmp = (z + a) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -1e+67) || !(b <= 2e+48))
		tmp = Float64(b * Float64(Float64(a / b) - Float64(y / Float64(y + Float64(x + t)))));
	else
		tmp = Float64(Float64(z + a) - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -1e+67) || ~((b <= 2e+48)))
		tmp = b * ((a / b) - (y / (y + (x + t))));
	else
		tmp = (z + a) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -1e+67], N[Not[LessEqual[b, 2e+48]], $MachinePrecision]], N[(b * N[(N[(a / b), $MachinePrecision] - N[(y / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -9.99999999999999983e66 or 2.00000000000000009e48 < b

   1. Initial program 58.8%

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

   3. Taylor expanded in b around -inf 68.2%

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

      1. mul-1-neg 68.2%

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

      2. *-commutative 68.2%

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

      3. distribute-rgt-neg-in 68.2%

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

   5. Simplified 95.5%

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

   6. Taylor expanded in t around inf 72.1%

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

   if -9.99999999999999983e66 < b < 2.00000000000000009e48

   1. Initial program 65.2%

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

   3. Taylor expanded in y around inf 65.1%

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

4. Final simplification 68.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1 \cdot 10^{+67} \lor \neg \left(b \leq 2 \cdot 10^{+48}\right):\\ \;\;\;\;b \cdot \left(\frac{a}{b} - \frac{y}{y + \left(x + t\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 65.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{-64} \lor \neg \left(y \leq 1.6 \cdot 10^{-42}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -4.4e-64) (not (<= y 1.6e-42)))
   (- (+ z a) b)
   (/ (+ (* t a) (* x z)) (+ x t))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -4.4e-64) || !(y <= 1.6e-42)) {
		tmp = (z + a) - b;
	} else {
		tmp = ((t * a) + (x * z)) / (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 ((y <= (-4.4d-64)) .or. (.not. (y <= 1.6d-42))) then
        tmp = (z + a) - b
    else
        tmp = ((t * a) + (x * z)) / (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 ((y <= -4.4e-64) || !(y <= 1.6e-42)) {
		tmp = (z + a) - b;
	} else {
		tmp = ((t * a) + (x * z)) / (x + t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -4.4e-64) or not (y <= 1.6e-42):
		tmp = (z + a) - b
	else:
		tmp = ((t * a) + (x * z)) / (x + t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -4.4e-64) || !(y <= 1.6e-42))
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(Float64(Float64(t * a) + Float64(x * z)) / Float64(x + t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -4.4e-64) || ~((y <= 1.6e-42)))
		tmp = (z + a) - b;
	else
		tmp = ((t * a) + (x * z)) / (x + t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -4.4e-64], N[Not[LessEqual[y, 1.6e-42]], $MachinePrecision]], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(N[(N[(t * a), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.3999999999999999e-64 or 1.60000000000000012e-42 < y

   1. Initial program 48.1%

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

   3. Taylor expanded in y around inf 72.9%

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

   if -4.3999999999999999e-64 < y < 1.60000000000000012e-42

   1. Initial program 80.1%

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

   3. Taylor expanded in y around 0 60.8%

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

4. Final simplification 67.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{-64} \lor \neg \left(y \leq 1.6 \cdot 10^{-42}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 56.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{-19}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+110}:\\ \;\;\;\;b \cdot \left(\frac{a}{b} - \frac{y}{y + t}\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -6e-19)
   (- (+ z a) b)
   (if (<= z 2.3e+110)
     (* b (- (/ a b) (/ y (+ y t))))
     (* z (/ (+ x y) (+ y (+ x t)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -6e-19) {
		tmp = (z + a) - b;
	} else if (z <= 2.3e+110) {
		tmp = b * ((a / b) - (y / (y + t)));
	} else {
		tmp = z * ((x + y) / (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 (z <= (-6d-19)) then
        tmp = (z + a) - b
    else if (z <= 2.3d+110) then
        tmp = b * ((a / b) - (y / (y + t)))
    else
        tmp = z * ((x + y) / (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 (z <= -6e-19) {
		tmp = (z + a) - b;
	} else if (z <= 2.3e+110) {
		tmp = b * ((a / b) - (y / (y + t)));
	} else {
		tmp = z * ((x + y) / (y + (x + t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -6e-19:
		tmp = (z + a) - b
	elif z <= 2.3e+110:
		tmp = b * ((a / b) - (y / (y + t)))
	else:
		tmp = z * ((x + y) / (y + (x + t)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -6e-19)
		tmp = Float64(Float64(z + a) - b);
	elseif (z <= 2.3e+110)
		tmp = Float64(b * Float64(Float64(a / b) - Float64(y / Float64(y + t))));
	else
		tmp = Float64(z * Float64(Float64(x + y) / Float64(y + Float64(x + t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -6e-19)
		tmp = (z + a) - b;
	elseif (z <= 2.3e+110)
		tmp = b * ((a / b) - (y / (y + t)));
	else
		tmp = z * ((x + y) / (y + (x + t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -6e-19], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], If[LessEqual[z, 2.3e+110], N[(b * N[(N[(a / b), $MachinePrecision] - N[(y / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(x + y), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.99999999999999985e-19

   1. Initial program 49.4%

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

   3. Taylor expanded in y around inf 66.4%

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

   if -5.99999999999999985e-19 < z < 2.3e110

   1. Initial program 73.4%

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

   3. Taylor expanded in z around 0 61.4%

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

      1. *-commutative 61.4%

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

   5. Simplified 61.4%

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

   6. Taylor expanded in x around 0 46.6%

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

   7. Taylor expanded in a around -inf 52.7%

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

      1. associate-*r* 52.7%

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

      2. mul-1-neg 52.7%

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

      3. sub-neg 52.7%

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

      4. associate-/l* 61.7%

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

      5. metadata-eval 61.7%

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

   9. Simplified 61.7%

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

   10. Taylor expanded in b around inf 66.3%

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

       1. +-commutative 66.3%

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

       2. mul-1-neg 66.3%

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

       3. unsub-neg 66.3%

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

       4. +-commutative 66.3%

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

   12. Simplified 66.3%

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

   if 2.3e110 < z

   1. Initial program 50.2%

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

   3. Taylor expanded in z around inf 36.4%

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

      1. associate-/l* 69.9%

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

      2. +-commutative 69.9%

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

      3. associate-+r+ 69.9%

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

   5. Simplified 69.9%

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

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{-19}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+110}:\\ \;\;\;\;b \cdot \left(\frac{a}{b} - \frac{y}{y + t}\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 58.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{+86}:\\ \;\;\;\;a - b \cdot \frac{y}{t}\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{+115}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\frac{a}{b} - \frac{y}{y + t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -2e+86)
   (- a (* b (/ y t)))
   (if (<= t 2.4e+115) (- (+ z a) b) (* b (- (/ a b) (/ y (+ y t)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -2e+86) {
		tmp = a - (b * (y / t));
	} else if (t <= 2.4e+115) {
		tmp = (z + a) - b;
	} else {
		tmp = b * ((a / b) - (y / (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) :: tmp
    if (t <= (-2d+86)) then
        tmp = a - (b * (y / t))
    else if (t <= 2.4d+115) then
        tmp = (z + a) - b
    else
        tmp = b * ((a / b) - (y / (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 tmp;
	if (t <= -2e+86) {
		tmp = a - (b * (y / t));
	} else if (t <= 2.4e+115) {
		tmp = (z + a) - b;
	} else {
		tmp = b * ((a / b) - (y / (y + t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -2e+86:
		tmp = a - (b * (y / t))
	elif t <= 2.4e+115:
		tmp = (z + a) - b
	else:
		tmp = b * ((a / b) - (y / (y + t)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -2e+86)
		tmp = Float64(a - Float64(b * Float64(y / t)));
	elseif (t <= 2.4e+115)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(b * Float64(Float64(a / b) - Float64(y / Float64(y + t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -2e+86)
		tmp = a - (b * (y / t));
	elseif (t <= 2.4e+115)
		tmp = (z + a) - b;
	else
		tmp = b * ((a / b) - (y / (y + t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -2e+86], N[(a - N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.4e+115], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(b * N[(N[(a / b), $MachinePrecision] - N[(y / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2e86

   1. Initial program 48.0%

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

   3. Taylor expanded in z around 0 39.4%

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

      1. *-commutative 39.4%

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

   5. Simplified 39.4%

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

   6. Taylor expanded in x around 0 37.2%

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

   7. Taylor expanded in a around -inf 58.4%

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

      1. associate-*r* 58.4%

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

      2. mul-1-neg 58.4%

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

      3. sub-neg 58.4%

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

      4. associate-/l* 67.1%

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

      5. metadata-eval 67.1%

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

   9. Simplified 67.1%

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

   10. Taylor expanded in y around 0 60.9%

       \[\leadsto \color{blue}{a + -1 \cdot \frac{b \cdot y}{t}} \]
   11. Step-by-step derivation

       1. mul-1-neg 60.9%

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

       2. unsub-neg 60.9%

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

       3. associate-/l* 73.9%

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

   12. Simplified 73.9%

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

   if -2e86 < t < 2.4e115

   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 y around inf 66.2%

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

   if 2.4e115 < t

   1. Initial program 54.0%

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

   3. Taylor expanded in z around 0 40.9%

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

      1. *-commutative 40.9%

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

   5. Simplified 40.9%

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

   6. Taylor expanded in x around 0 38.2%

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

   7. Taylor expanded in a around -inf 53.3%

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

      1. associate-*r* 53.3%

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

      2. mul-1-neg 53.3%

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

      3. sub-neg 53.3%

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

      4. associate-/l* 57.9%

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

      5. metadata-eval 57.9%

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

   9. Simplified 57.9%

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

   10. Taylor expanded in b around inf 57.7%

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

       1. +-commutative 57.7%

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

       2. mul-1-neg 57.7%

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

       3. unsub-neg 57.7%

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

       4. +-commutative 57.7%

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

   12. Simplified 57.7%

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

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{+86}:\\ \;\;\;\;a - b \cdot \frac{y}{t}\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{+115}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\frac{a}{b} - \frac{y}{y + t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 59.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{+86}:\\ \;\;\;\;a - b \cdot \frac{y}{t}\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+141}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{y + t}{y + \left(x + t\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -8.5e+86)
   (- a (* b (/ y t)))
   (if (<= t 4e+141) (- (+ 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 (t <= -8.5e+86) {
		tmp = a - (b * (y / t));
	} else if (t <= 4e+141) {
		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 (t <= (-8.5d+86)) then
        tmp = a - (b * (y / t))
    else if (t <= 4d+141) 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 (t <= -8.5e+86) {
		tmp = a - (b * (y / t));
	} else if (t <= 4e+141) {
		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 t <= -8.5e+86:
		tmp = a - (b * (y / t))
	elif t <= 4e+141:
		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 (t <= -8.5e+86)
		tmp = Float64(a - Float64(b * Float64(y / t)));
	elseif (t <= 4e+141)
		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 (t <= -8.5e+86)
		tmp = a - (b * (y / t));
	elseif (t <= 4e+141)
		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[t, -8.5e+86], N[(a - N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4e+141], 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 3 regimes

2. if t < -8.5000000000000005e86

   1. Initial program 48.0%

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

   3. Taylor expanded in z around 0 39.4%

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

      1. *-commutative 39.4%

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

   5. Simplified 39.4%

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

   6. Taylor expanded in x around 0 37.2%

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

   7. Taylor expanded in a around -inf 58.4%

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

      1. associate-*r* 58.4%

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

      2. mul-1-neg 58.4%

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

      3. sub-neg 58.4%

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

      4. associate-/l* 67.1%

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

      5. metadata-eval 67.1%

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

   9. Simplified 67.1%

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

   10. Taylor expanded in y around 0 60.9%

       \[\leadsto \color{blue}{a + -1 \cdot \frac{b \cdot y}{t}} \]
   11. Step-by-step derivation

       1. mul-1-neg 60.9%

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

       2. unsub-neg 60.9%

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

       3. associate-/l* 73.9%

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

   12. Simplified 73.9%

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

   if -8.5000000000000005e86 < t < 4.00000000000000007e141

   1. Initial program 68.5%

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

   3. Taylor expanded in y around inf 64.7%

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

   if 4.00000000000000007e141 < t

   1. Initial program 50.5%

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

   3. Taylor expanded in a around inf 37.0%

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

      1. associate-/l* 60.2%

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

      2. associate-+r+ 60.2%

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

   5. Simplified 60.2%

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

4. Final simplification 65.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{+86}:\\ \;\;\;\;a - b \cdot \frac{y}{t}\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+141}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{y + t}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 59.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.8 \cdot 10^{+85} \lor \neg \left(t \leq 4.1 \cdot 10^{+141}\right):\\ \;\;\;\;a - b \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -8.8e+85) (not (<= t 4.1e+141)))
   (- a (* b (/ y t)))
   (- (+ z a) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -8.8e+85) || !(t <= 4.1e+141)) {
		tmp = a - (b * (y / t));
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-8.8d+85)) .or. (.not. (t <= 4.1d+141))) then
        tmp = a - (b * (y / t))
    else
        tmp = (z + a) - b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -8.8e+85) || !(t <= 4.1e+141)) {
		tmp = a - (b * (y / t));
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -8.8e+85) or not (t <= 4.1e+141):
		tmp = a - (b * (y / t))
	else:
		tmp = (z + a) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -8.8e+85) || !(t <= 4.1e+141))
		tmp = Float64(a - Float64(b * Float64(y / t)));
	else
		tmp = Float64(Float64(z + a) - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -8.8e+85) || ~((t <= 4.1e+141)))
		tmp = a - (b * (y / t));
	else
		tmp = (z + a) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -8.8e+85], N[Not[LessEqual[t, 4.1e+141]], $MachinePrecision]], N[(a - N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -8.8000000000000007e85 or 4.10000000000000022e141 < t

   1. Initial program 49.1%

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

   3. Taylor expanded in z around 0 39.7%

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

      1. *-commutative 39.7%

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

   5. Simplified 39.7%

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

   6. Taylor expanded in x around 0 38.4%

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

   7. Taylor expanded in a around -inf 58.2%

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

      1. associate-*r* 58.2%

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

      2. mul-1-neg 58.2%

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

      3. sub-neg 58.2%

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

      4. associate-/l* 65.4%

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

      5. metadata-eval 65.4%

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

   9. Simplified 65.4%

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

   10. Taylor expanded in y around 0 59.6%

       \[\leadsto \color{blue}{a + -1 \cdot \frac{b \cdot y}{t}} \]
   11. Step-by-step derivation

       1. mul-1-neg 59.6%

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

       2. unsub-neg 59.6%

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

       3. associate-/l* 66.7%

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

   12. Simplified 66.7%

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

   if -8.8000000000000007e85 < t < 4.10000000000000022e141

   1. Initial program 68.5%

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

   3. Taylor expanded in y around inf 64.7%

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

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.8 \cdot 10^{+85} \lor \neg \left(t \leq 4.1 \cdot 10^{+141}\right):\\ \;\;\;\;a - b \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 58.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.55 \cdot 10^{+130}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{+143}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.55e+130) a (if (<= t 5.6e+143) (- (+ z a) b) a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.55e+130) {
		tmp = a;
	} else if (t <= 5.6e+143) {
		tmp = (z + a) - b;
	} 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 <= (-1.55d+130)) then
        tmp = a
    else if (t <= 5.6d+143) then
        tmp = (z + a) - b
    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 <= -1.55e+130) {
		tmp = a;
	} else if (t <= 5.6e+143) {
		tmp = (z + a) - b;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1.55e+130:
		tmp = a
	elif t <= 5.6e+143:
		tmp = (z + a) - b
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.55e+130)
		tmp = a;
	elseif (t <= 5.6e+143)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -1.55e+130)
		tmp = a;
	elseif (t <= 5.6e+143)
		tmp = (z + a) - b;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.55e+130], a, If[LessEqual[t, 5.6e+143], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], a]]

Derivation

1. Split input into 2 regimes

2. if t < -1.55e130 or 5.59999999999999996e143 < t

   1. Initial program 49.4%

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

   3. Taylor expanded in t around inf 57.8%

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

   if -1.55e130 < t < 5.59999999999999996e143

   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 y around inf 64.0%

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

4. Final simplification 62.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.55 \cdot 10^{+130}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{+143}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 43.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{+174}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{+42}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -1.15e+174) z (if (<= x 8.2e+42) a z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.15e+174) {
		tmp = z;
	} else if (x <= 8.2e+42) {
		tmp = a;
	} else {
		tmp = z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-1.15d+174)) then
        tmp = z
    else if (x <= 8.2d+42) then
        tmp = a
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.15e+174) {
		tmp = z;
	} else if (x <= 8.2e+42) {
		tmp = a;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -1.15e+174:
		tmp = z
	elif x <= 8.2e+42:
		tmp = a
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -1.15e+174)
		tmp = z;
	elseif (x <= 8.2e+42)
		tmp = a;
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -1.15e+174)
		tmp = z;
	elseif (x <= 8.2e+42)
		tmp = a;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -1.15e+174], z, If[LessEqual[x, 8.2e+42], a, z]]

Derivation

1. Split input into 2 regimes

2. if x < -1.1499999999999999e174 or 8.2000000000000001e42 < x

   1. Initial program 51.4%

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

   3. Taylor expanded in x around inf 52.3%

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

   if -1.1499999999999999e174 < x < 8.2000000000000001e42

   1. Initial program 67.9%

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

   3. Taylor expanded in t around inf 44.8%

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

Alternative 16: 33.1% 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 62.4%

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

3. Taylor expanded in t around inf 33.3%

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

Developer target: 82.6% accurate, 0.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024106 
(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)))