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

Percentage Accurate: 59.9% → 87.5%

Time: 15.8s

Alternatives: 16

Speedup: 1.1×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 59.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 87.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \left(y + x\right)\\ t_2 := \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\\ t_3 := a + \left(z - b\right)\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq 10^{+252}:\\ \;\;\;\;a \cdot \left(\frac{y}{t\_1} + \frac{t}{t\_1}\right) + \frac{z \cdot x + y \cdot \left(z - b\right)}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ t (+ y x)))
        (t_2 (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)))
        (t_3 (+ a (- z b))))
   (if (<= t_2 (- INFINITY))
     t_3
     (if (<= t_2 1e+252)
       (+ (* a (+ (/ y t_1) (/ t t_1))) (/ (+ (* z x) (* y (- z b))) t_1))
       t_3))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t + (y + x);
	double t_2 = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y);
	double t_3 = a + (z - b);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_3;
	} else if (t_2 <= 1e+252) {
		tmp = (a * ((y / t_1) + (t / t_1))) + (((z * x) + (y * (z - b))) / t_1);
	} else {
		tmp = t_3;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t + (y + x);
	double t_2 = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y);
	double t_3 = a + (z - b);
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_3;
	} else if (t_2 <= 1e+252) {
		tmp = (a * ((y / t_1) + (t / t_1))) + (((z * x) + (y * (z - b))) / t_1);
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t + (y + x)
	t_2 = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y)
	t_3 = a + (z - b)
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_3
	elif t_2 <= 1e+252:
		tmp = (a * ((y / t_1) + (t / t_1))) + (((z * x) + (y * (z - b))) / t_1)
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t + Float64(y + x))
	t_2 = Float64(Float64(Float64(Float64(Float64(x + y) * z) + Float64(Float64(t + y) * a)) - Float64(y * b)) / Float64(Float64(x + t) + y))
	t_3 = Float64(a + Float64(z - b))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_3;
	elseif (t_2 <= 1e+252)
		tmp = Float64(Float64(a * Float64(Float64(y / t_1) + Float64(t / t_1))) + Float64(Float64(Float64(z * x) + Float64(y * Float64(z - b))) / t_1));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t + (y + x);
	t_2 = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y);
	t_3 = a + (z - b);
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_3;
	elseif (t_2 <= 1e+252)
		tmp = (a * ((y / t_1) + (t / t_1))) + (((z * x) + (y * (z - b))) / t_1);
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t + N[(y + x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = 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]}, Block[{t$95$3 = N[(a + N[(z - b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$3, If[LessEqual[t$95$2, 1e+252], N[(N[(a * N[(N[(y / t$95$1), $MachinePrecision] + N[(t / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(z * x), $MachinePrecision] + N[(y * N[(z - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -inf.0 or 1.0000000000000001e252 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 5.5%

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

   3. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1.0000000000000001e252

   1. Initial program 99.7%

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

   3. Taylor expanded in a around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 2: 87.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\\ t_2 := a + \left(z - b\right)\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+303}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 10^{+252}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)))
        (t_2 (+ a (- z b))))
   (if (<= t_1 -2e+303) t_2 (if (<= t_1 1e+252) t_1 t_2))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y);
	double t_2 = a + (z - b);
	double tmp;
	if (t_1 <= -2e+303) {
		tmp = t_2;
	} else if (t_1 <= 1e+252) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y)
    t_2 = a + (z - b)
    if (t_1 <= (-2d+303)) then
        tmp = t_2
    else if (t_1 <= 1d+252) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y);
	double t_2 = a + (z - b);
	double tmp;
	if (t_1 <= -2e+303) {
		tmp = t_2;
	} else if (t_1 <= 1e+252) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y)
	t_2 = a + (z - b)
	tmp = 0
	if t_1 <= -2e+303:
		tmp = t_2
	elif t_1 <= 1e+252:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(Float64(Float64(x + y) * z) + Float64(Float64(t + y) * a)) - Float64(y * b)) / Float64(Float64(x + t) + y))
	t_2 = Float64(a + Float64(z - b))
	tmp = 0.0
	if (t_1 <= -2e+303)
		tmp = t_2;
	elseif (t_1 <= 1e+252)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y);
	t_2 = a + (z - b);
	tmp = 0.0;
	if (t_1 <= -2e+303)
		tmp = t_2;
	elseif (t_1 <= 1e+252)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(N[(N[(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]}, Block[{t$95$2 = N[(a + N[(z - b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+303], t$95$2, If[LessEqual[t$95$1, 1e+252], t$95$1, t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -2e303 or 1.0000000000000001e252 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 6.3%

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

   3. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -2e303 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1.0000000000000001e252

   1. Initial program 99.7%

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

Alternative 3: 63.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + \left(z - b\right)\\ \mathbf{if}\;y \leq -1.3 \cdot 10^{+25}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-88}:\\ \;\;\;\;\frac{a \cdot y}{x + y} + z\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{-198}:\\ \;\;\;\;\frac{a \cdot t + z \cdot x}{t + x}\\ \mathbf{elif}\;y \leq -1.95 \cdot 10^{-264}:\\ \;\;\;\;a \cdot \frac{t + y}{x} + z\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-72}:\\ \;\;\;\;\frac{a \cdot t}{t + x} + \frac{x \cdot z}{t + x}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ a (- z b))))
   (if (<= y -1.3e+25)
     t_1
     (if (<= y -4.8e-88)
       (+ (/ (* a y) (+ x y)) z)
       (if (<= y -7.5e-198)
         (/ (+ (* a t) (* z x)) (+ t x))
         (if (<= y -1.95e-264)
           (+ (* a (/ (+ t y) x)) z)
           (if (<= y 2.8e-72)
             (+ (/ (* a t) (+ t x)) (/ (* x z) (+ t x)))
             t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a + (z - b);
	double tmp;
	if (y <= -1.3e+25) {
		tmp = t_1;
	} else if (y <= -4.8e-88) {
		tmp = ((a * y) / (x + y)) + z;
	} else if (y <= -7.5e-198) {
		tmp = ((a * t) + (z * x)) / (t + x);
	} else if (y <= -1.95e-264) {
		tmp = (a * ((t + y) / x)) + z;
	} else if (y <= 2.8e-72) {
		tmp = ((a * t) / (t + x)) + ((x * z) / (t + x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a + (z - b)
    if (y <= (-1.3d+25)) then
        tmp = t_1
    else if (y <= (-4.8d-88)) then
        tmp = ((a * y) / (x + y)) + z
    else if (y <= (-7.5d-198)) then
        tmp = ((a * t) + (z * x)) / (t + x)
    else if (y <= (-1.95d-264)) then
        tmp = (a * ((t + y) / x)) + z
    else if (y <= 2.8d-72) then
        tmp = ((a * t) / (t + x)) + ((x * z) / (t + x))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a + (z - b);
	double tmp;
	if (y <= -1.3e+25) {
		tmp = t_1;
	} else if (y <= -4.8e-88) {
		tmp = ((a * y) / (x + y)) + z;
	} else if (y <= -7.5e-198) {
		tmp = ((a * t) + (z * x)) / (t + x);
	} else if (y <= -1.95e-264) {
		tmp = (a * ((t + y) / x)) + z;
	} else if (y <= 2.8e-72) {
		tmp = ((a * t) / (t + x)) + ((x * z) / (t + x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a + (z - b)
	tmp = 0
	if y <= -1.3e+25:
		tmp = t_1
	elif y <= -4.8e-88:
		tmp = ((a * y) / (x + y)) + z
	elif y <= -7.5e-198:
		tmp = ((a * t) + (z * x)) / (t + x)
	elif y <= -1.95e-264:
		tmp = (a * ((t + y) / x)) + z
	elif y <= 2.8e-72:
		tmp = ((a * t) / (t + x)) + ((x * z) / (t + x))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a + Float64(z - b))
	tmp = 0.0
	if (y <= -1.3e+25)
		tmp = t_1;
	elseif (y <= -4.8e-88)
		tmp = Float64(Float64(Float64(a * y) / Float64(x + y)) + z);
	elseif (y <= -7.5e-198)
		tmp = Float64(Float64(Float64(a * t) + Float64(z * x)) / Float64(t + x));
	elseif (y <= -1.95e-264)
		tmp = Float64(Float64(a * Float64(Float64(t + y) / x)) + z);
	elseif (y <= 2.8e-72)
		tmp = Float64(Float64(Float64(a * t) / Float64(t + x)) + Float64(Float64(x * z) / Float64(t + x)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a + (z - b);
	tmp = 0.0;
	if (y <= -1.3e+25)
		tmp = t_1;
	elseif (y <= -4.8e-88)
		tmp = ((a * y) / (x + y)) + z;
	elseif (y <= -7.5e-198)
		tmp = ((a * t) + (z * x)) / (t + x);
	elseif (y <= -1.95e-264)
		tmp = (a * ((t + y) / x)) + z;
	elseif (y <= 2.8e-72)
		tmp = ((a * t) / (t + x)) + ((x * z) / (t + x));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a + N[(z - b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.3e+25], t$95$1, If[LessEqual[y, -4.8e-88], N[(N[(N[(a * y), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision], If[LessEqual[y, -7.5e-198], N[(N[(N[(a * t), $MachinePrecision] + N[(z * x), $MachinePrecision]), $MachinePrecision] / N[(t + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.95e-264], N[(N[(a * N[(N[(t + y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision], If[LessEqual[y, 2.8e-72], N[(N[(N[(a * t), $MachinePrecision] / N[(t + x), $MachinePrecision]), $MachinePrecision] + N[(N[(x * z), $MachinePrecision] / N[(t + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.2999999999999999e25 or 2.7999999999999998e-72 < y

   1. Initial program 43.5%

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

   3. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -1.2999999999999999e25 < y < -4.7999999999999999e-88

   1. Initial program 77.4%

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

   3. Taylor expanded in a around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   9. Taylor expanded in t around 0 0

      \[\leadsto expr\]

   11. Simplified 0

       \[\leadsto expr\]

   if -4.7999999999999999e-88 < y < -7.50000000000000064e-198

   1. Initial program 81.6%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -7.50000000000000064e-198 < y < -1.9499999999999999e-264

   1. Initial program 52.7%

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

   3. Taylor expanded in a around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   9. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   11. Simplified 0

       \[\leadsto expr\]

   if -1.9499999999999999e-264 < y < 2.7999999999999998e-72

   1. Initial program 78.4%

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

   3. Taylor expanded in a around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 4: 68.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \left(x + y\right)\\ t_2 := t + \left(y + x\right)\\ t_3 := a \cdot \left(\frac{y}{t\_2} + \frac{t}{t\_2}\right) + z\\ t_4 := a + \left(z - b\right)\\ \mathbf{if}\;y \leq -2.4 \cdot 10^{+64}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{-291}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{-254}:\\ \;\;\;\;\frac{x \cdot z}{t\_1} + \frac{y \cdot \left(z - b\right)}{t\_1}\\ \mathbf{elif}\;y \leq 5.3 \cdot 10^{-42}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ t (+ x y)))
        (t_2 (+ t (+ y x)))
        (t_3 (+ (* a (+ (/ y t_2) (/ t t_2))) z))
        (t_4 (+ a (- z b))))
   (if (<= y -2.4e+64)
     t_4
     (if (<= y 3.3e-291)
       t_3
       (if (<= y 7.8e-254)
         (+ (/ (* x z) t_1) (/ (* y (- z b)) t_1))
         (if (<= y 5.3e-42) t_3 t_4))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t + (x + y);
	double t_2 = t + (y + x);
	double t_3 = (a * ((y / t_2) + (t / t_2))) + z;
	double t_4 = a + (z - b);
	double tmp;
	if (y <= -2.4e+64) {
		tmp = t_4;
	} else if (y <= 3.3e-291) {
		tmp = t_3;
	} else if (y <= 7.8e-254) {
		tmp = ((x * z) / t_1) + ((y * (z - b)) / t_1);
	} else if (y <= 5.3e-42) {
		tmp = t_3;
	} 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 = t + (x + y)
    t_2 = t + (y + x)
    t_3 = (a * ((y / t_2) + (t / t_2))) + z
    t_4 = a + (z - b)
    if (y <= (-2.4d+64)) then
        tmp = t_4
    else if (y <= 3.3d-291) then
        tmp = t_3
    else if (y <= 7.8d-254) then
        tmp = ((x * z) / t_1) + ((y * (z - b)) / t_1)
    else if (y <= 5.3d-42) then
        tmp = t_3
    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 = t + (x + y);
	double t_2 = t + (y + x);
	double t_3 = (a * ((y / t_2) + (t / t_2))) + z;
	double t_4 = a + (z - b);
	double tmp;
	if (y <= -2.4e+64) {
		tmp = t_4;
	} else if (y <= 3.3e-291) {
		tmp = t_3;
	} else if (y <= 7.8e-254) {
		tmp = ((x * z) / t_1) + ((y * (z - b)) / t_1);
	} else if (y <= 5.3e-42) {
		tmp = t_3;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t + (x + y)
	t_2 = t + (y + x)
	t_3 = (a * ((y / t_2) + (t / t_2))) + z
	t_4 = a + (z - b)
	tmp = 0
	if y <= -2.4e+64:
		tmp = t_4
	elif y <= 3.3e-291:
		tmp = t_3
	elif y <= 7.8e-254:
		tmp = ((x * z) / t_1) + ((y * (z - b)) / t_1)
	elif y <= 5.3e-42:
		tmp = t_3
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t + Float64(x + y))
	t_2 = Float64(t + Float64(y + x))
	t_3 = Float64(Float64(a * Float64(Float64(y / t_2) + Float64(t / t_2))) + z)
	t_4 = Float64(a + Float64(z - b))
	tmp = 0.0
	if (y <= -2.4e+64)
		tmp = t_4;
	elseif (y <= 3.3e-291)
		tmp = t_3;
	elseif (y <= 7.8e-254)
		tmp = Float64(Float64(Float64(x * z) / t_1) + Float64(Float64(y * Float64(z - b)) / t_1));
	elseif (y <= 5.3e-42)
		tmp = t_3;
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t + (x + y);
	t_2 = t + (y + x);
	t_3 = (a * ((y / t_2) + (t / t_2))) + z;
	t_4 = a + (z - b);
	tmp = 0.0;
	if (y <= -2.4e+64)
		tmp = t_4;
	elseif (y <= 3.3e-291)
		tmp = t_3;
	elseif (y <= 7.8e-254)
		tmp = ((x * z) / t_1) + ((y * (z - b)) / t_1);
	elseif (y <= 5.3e-42)
		tmp = t_3;
	else
		tmp = t_4;
	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[(t + N[(y + x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(a * N[(N[(y / t$95$2), $MachinePrecision] + N[(t / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision]}, Block[{t$95$4 = N[(a + N[(z - b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.4e+64], t$95$4, If[LessEqual[y, 3.3e-291], t$95$3, If[LessEqual[y, 7.8e-254], N[(N[(N[(x * z), $MachinePrecision] / t$95$1), $MachinePrecision] + N[(N[(y * N[(z - b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.3e-42], t$95$3, t$95$4]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.39999999999999999e64 or 5.3e-42 < y

   1. Initial program 41.4%

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

   3. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -2.39999999999999999e64 < y < 3.2999999999999999e-291 or 7.8e-254 < y < 5.3e-42

   1. Initial program 73.0%

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

   3. Taylor expanded in a around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   if 3.2999999999999999e-291 < y < 7.8e-254

   1. Initial program 89.9%

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

   3. Taylor expanded in a around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in a around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 5: 63.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + \left(z - b\right)\\ t_2 := \frac{a \cdot t + z \cdot x}{t + x}\\ \mathbf{if}\;y \leq -1.35 \cdot 10^{+25}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-88}:\\ \;\;\;\;\frac{a \cdot y}{x + y} + z\\ \mathbf{elif}\;y \leq -8.8 \cdot 10^{-198}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-264}:\\ \;\;\;\;a \cdot \frac{t + y}{x} + z\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-72}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ a (- z b))) (t_2 (/ (+ (* a t) (* z x)) (+ t x))))
   (if (<= y -1.35e+25)
     t_1
     (if (<= y -2e-88)
       (+ (/ (* a y) (+ x y)) z)
       (if (<= y -8.8e-198)
         t_2
         (if (<= y -1.9e-264)
           (+ (* a (/ (+ t y) x)) z)
           (if (<= y 7e-72) t_2 t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a + (z - b);
	double t_2 = ((a * t) + (z * x)) / (t + x);
	double tmp;
	if (y <= -1.35e+25) {
		tmp = t_1;
	} else if (y <= -2e-88) {
		tmp = ((a * y) / (x + y)) + z;
	} else if (y <= -8.8e-198) {
		tmp = t_2;
	} else if (y <= -1.9e-264) {
		tmp = (a * ((t + y) / x)) + z;
	} else if (y <= 7e-72) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a + (z - b)
    t_2 = ((a * t) + (z * x)) / (t + x)
    if (y <= (-1.35d+25)) then
        tmp = t_1
    else if (y <= (-2d-88)) then
        tmp = ((a * y) / (x + y)) + z
    else if (y <= (-8.8d-198)) then
        tmp = t_2
    else if (y <= (-1.9d-264)) then
        tmp = (a * ((t + y) / x)) + z
    else if (y <= 7d-72) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a + (z - b);
	double t_2 = ((a * t) + (z * x)) / (t + x);
	double tmp;
	if (y <= -1.35e+25) {
		tmp = t_1;
	} else if (y <= -2e-88) {
		tmp = ((a * y) / (x + y)) + z;
	} else if (y <= -8.8e-198) {
		tmp = t_2;
	} else if (y <= -1.9e-264) {
		tmp = (a * ((t + y) / x)) + z;
	} else if (y <= 7e-72) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a + (z - b)
	t_2 = ((a * t) + (z * x)) / (t + x)
	tmp = 0
	if y <= -1.35e+25:
		tmp = t_1
	elif y <= -2e-88:
		tmp = ((a * y) / (x + y)) + z
	elif y <= -8.8e-198:
		tmp = t_2
	elif y <= -1.9e-264:
		tmp = (a * ((t + y) / x)) + z
	elif y <= 7e-72:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a + Float64(z - b))
	t_2 = Float64(Float64(Float64(a * t) + Float64(z * x)) / Float64(t + x))
	tmp = 0.0
	if (y <= -1.35e+25)
		tmp = t_1;
	elseif (y <= -2e-88)
		tmp = Float64(Float64(Float64(a * y) / Float64(x + y)) + z);
	elseif (y <= -8.8e-198)
		tmp = t_2;
	elseif (y <= -1.9e-264)
		tmp = Float64(Float64(a * Float64(Float64(t + y) / x)) + z);
	elseif (y <= 7e-72)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a + (z - b);
	t_2 = ((a * t) + (z * x)) / (t + x);
	tmp = 0.0;
	if (y <= -1.35e+25)
		tmp = t_1;
	elseif (y <= -2e-88)
		tmp = ((a * y) / (x + y)) + z;
	elseif (y <= -8.8e-198)
		tmp = t_2;
	elseif (y <= -1.9e-264)
		tmp = (a * ((t + y) / x)) + z;
	elseif (y <= 7e-72)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a + N[(z - b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(a * t), $MachinePrecision] + N[(z * x), $MachinePrecision]), $MachinePrecision] / N[(t + x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.35e+25], t$95$1, If[LessEqual[y, -2e-88], N[(N[(N[(a * y), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision], If[LessEqual[y, -8.8e-198], t$95$2, If[LessEqual[y, -1.9e-264], N[(N[(a * N[(N[(t + y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision], If[LessEqual[y, 7e-72], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.35e25 or 7.00000000000000001e-72 < y

   1. Initial program 43.5%

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

   3. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -1.35e25 < y < -1.99999999999999987e-88

   1. Initial program 77.4%

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

   3. Taylor expanded in a around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   9. Taylor expanded in t around 0 0

      \[\leadsto expr\]

   11. Simplified 0

       \[\leadsto expr\]

   if -1.99999999999999987e-88 < y < -8.8000000000000001e-198 or -1.90000000000000007e-264 < y < 7.00000000000000001e-72

   1. Initial program 79.4%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -8.8000000000000001e-198 < y < -1.90000000000000007e-264

   1. Initial program 52.7%

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

   3. Taylor expanded in a around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   9. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   11. Simplified 0

       \[\leadsto expr\]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 6: 63.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + \left(z - b\right)\\ t_2 := t + \left(x + y\right)\\ \mathbf{if}\;y \leq -3.7 \cdot 10^{+24}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -7.2 \cdot 10^{-137}:\\ \;\;\;\;\frac{a \cdot y}{x + y} + z\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-260}:\\ \;\;\;\;z \cdot \left(\frac{x}{t\_2} + \frac{y}{t\_2}\right)\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-78}:\\ \;\;\;\;\frac{a \cdot t}{t + x} + \frac{x \cdot z}{t + x}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ a (- z b))) (t_2 (+ t (+ x y))))
   (if (<= y -3.7e+24)
     t_1
     (if (<= y -7.2e-137)
       (+ (/ (* a y) (+ x y)) z)
       (if (<= y -2.8e-260)
         (* z (+ (/ x t_2) (/ y t_2)))
         (if (<= y 5e-78) (+ (/ (* a t) (+ t x)) (/ (* x z) (+ t x))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a + (z - b);
	double t_2 = t + (x + y);
	double tmp;
	if (y <= -3.7e+24) {
		tmp = t_1;
	} else if (y <= -7.2e-137) {
		tmp = ((a * y) / (x + y)) + z;
	} else if (y <= -2.8e-260) {
		tmp = z * ((x / t_2) + (y / t_2));
	} else if (y <= 5e-78) {
		tmp = ((a * t) / (t + x)) + ((x * z) / (t + x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a + (z - b)
    t_2 = t + (x + y)
    if (y <= (-3.7d+24)) then
        tmp = t_1
    else if (y <= (-7.2d-137)) then
        tmp = ((a * y) / (x + y)) + z
    else if (y <= (-2.8d-260)) then
        tmp = z * ((x / t_2) + (y / t_2))
    else if (y <= 5d-78) then
        tmp = ((a * t) / (t + x)) + ((x * z) / (t + x))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a + (z - b);
	double t_2 = t + (x + y);
	double tmp;
	if (y <= -3.7e+24) {
		tmp = t_1;
	} else if (y <= -7.2e-137) {
		tmp = ((a * y) / (x + y)) + z;
	} else if (y <= -2.8e-260) {
		tmp = z * ((x / t_2) + (y / t_2));
	} else if (y <= 5e-78) {
		tmp = ((a * t) / (t + x)) + ((x * z) / (t + x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a + (z - b)
	t_2 = t + (x + y)
	tmp = 0
	if y <= -3.7e+24:
		tmp = t_1
	elif y <= -7.2e-137:
		tmp = ((a * y) / (x + y)) + z
	elif y <= -2.8e-260:
		tmp = z * ((x / t_2) + (y / t_2))
	elif y <= 5e-78:
		tmp = ((a * t) / (t + x)) + ((x * z) / (t + x))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a + Float64(z - b))
	t_2 = Float64(t + Float64(x + y))
	tmp = 0.0
	if (y <= -3.7e+24)
		tmp = t_1;
	elseif (y <= -7.2e-137)
		tmp = Float64(Float64(Float64(a * y) / Float64(x + y)) + z);
	elseif (y <= -2.8e-260)
		tmp = Float64(z * Float64(Float64(x / t_2) + Float64(y / t_2)));
	elseif (y <= 5e-78)
		tmp = Float64(Float64(Float64(a * t) / Float64(t + x)) + Float64(Float64(x * z) / Float64(t + x)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a + (z - b);
	t_2 = t + (x + y);
	tmp = 0.0;
	if (y <= -3.7e+24)
		tmp = t_1;
	elseif (y <= -7.2e-137)
		tmp = ((a * y) / (x + y)) + z;
	elseif (y <= -2.8e-260)
		tmp = z * ((x / t_2) + (y / t_2));
	elseif (y <= 5e-78)
		tmp = ((a * t) / (t + x)) + ((x * z) / (t + x));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a + N[(z - b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.7e+24], t$95$1, If[LessEqual[y, -7.2e-137], N[(N[(N[(a * y), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision], If[LessEqual[y, -2.8e-260], N[(z * N[(N[(x / t$95$2), $MachinePrecision] + N[(y / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5e-78], N[(N[(N[(a * t), $MachinePrecision] / N[(t + x), $MachinePrecision]), $MachinePrecision] + N[(N[(x * z), $MachinePrecision] / N[(t + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.69999999999999999e24 or 4.9999999999999996e-78 < y

   1. Initial program 43.5%

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

   3. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -3.69999999999999999e24 < y < -7.20000000000000013e-137

   1. Initial program 82.3%

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

   3. Taylor expanded in a around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   9. Taylor expanded in t around 0 0

      \[\leadsto expr\]

   11. Simplified 0

       \[\leadsto expr\]

   if -7.20000000000000013e-137 < y < -2.7999999999999998e-260

   1. Initial program 61.9%

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

   3. Taylor expanded in a around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in z around inf 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   if -2.7999999999999998e-260 < y < 4.9999999999999996e-78

   1. Initial program 79.2%

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

   3. Taylor expanded in a around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 7: 57.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + \left(z - b\right)\\ \mathbf{if}\;y \leq -1.35 \cdot 10^{+32}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -3.55 \cdot 10^{-177}:\\ \;\;\;\;a + z\\ \mathbf{elif}\;y \leq -5.9 \cdot 10^{-272}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-215}:\\ \;\;\;\;a \cdot \frac{t}{t + x}\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-155}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ a (- z b))))
   (if (<= y -1.35e+32)
     t_1
     (if (<= y -3.55e-177)
       (+ a z)
       (if (<= y -5.9e-272)
         z
         (if (<= y 1.7e-215)
           (* a (/ t (+ t x)))
           (if (<= y 2.1e-155) z t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a + (z - b);
	double tmp;
	if (y <= -1.35e+32) {
		tmp = t_1;
	} else if (y <= -3.55e-177) {
		tmp = a + z;
	} else if (y <= -5.9e-272) {
		tmp = z;
	} else if (y <= 1.7e-215) {
		tmp = a * (t / (t + x));
	} else if (y <= 2.1e-155) {
		tmp = z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a + (z - b)
    if (y <= (-1.35d+32)) then
        tmp = t_1
    else if (y <= (-3.55d-177)) then
        tmp = a + z
    else if (y <= (-5.9d-272)) then
        tmp = z
    else if (y <= 1.7d-215) then
        tmp = a * (t / (t + x))
    else if (y <= 2.1d-155) then
        tmp = z
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a + (z - b);
	double tmp;
	if (y <= -1.35e+32) {
		tmp = t_1;
	} else if (y <= -3.55e-177) {
		tmp = a + z;
	} else if (y <= -5.9e-272) {
		tmp = z;
	} else if (y <= 1.7e-215) {
		tmp = a * (t / (t + x));
	} else if (y <= 2.1e-155) {
		tmp = z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a + (z - b)
	tmp = 0
	if y <= -1.35e+32:
		tmp = t_1
	elif y <= -3.55e-177:
		tmp = a + z
	elif y <= -5.9e-272:
		tmp = z
	elif y <= 1.7e-215:
		tmp = a * (t / (t + x))
	elif y <= 2.1e-155:
		tmp = z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a + Float64(z - b))
	tmp = 0.0
	if (y <= -1.35e+32)
		tmp = t_1;
	elseif (y <= -3.55e-177)
		tmp = Float64(a + z);
	elseif (y <= -5.9e-272)
		tmp = z;
	elseif (y <= 1.7e-215)
		tmp = Float64(a * Float64(t / Float64(t + x)));
	elseif (y <= 2.1e-155)
		tmp = z;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a + (z - b);
	tmp = 0.0;
	if (y <= -1.35e+32)
		tmp = t_1;
	elseif (y <= -3.55e-177)
		tmp = a + z;
	elseif (y <= -5.9e-272)
		tmp = z;
	elseif (y <= 1.7e-215)
		tmp = a * (t / (t + x));
	elseif (y <= 2.1e-155)
		tmp = z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a + N[(z - b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.35e+32], t$95$1, If[LessEqual[y, -3.55e-177], N[(a + z), $MachinePrecision], If[LessEqual[y, -5.9e-272], z, If[LessEqual[y, 1.7e-215], N[(a * N[(t / N[(t + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.1e-155], z, t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.35000000000000006e32 or 2.1000000000000002e-155 < y

   1. Initial program 47.2%

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

   3. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -1.35000000000000006e32 < y < -3.55000000000000021e-177

   1. Initial program 75.1%

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

   3. Taylor expanded in a around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   9. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   11. Simplified 0

       \[\leadsto expr\]

   if -3.55000000000000021e-177 < y < -5.8999999999999999e-272 or 1.70000000000000001e-215 < y < 2.1000000000000002e-155

   1. Initial program 69.4%

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

   3. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -5.8999999999999999e-272 < y < 1.70000000000000001e-215

   1. Initial program 80.0%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]

   8. Taylor expanded in a around inf 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 8: 58.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + \left(z - b\right)\\ \mathbf{if}\;y \leq -1.05 \cdot 10^{+24}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{-272}:\\ \;\;\;\;\frac{a \cdot y}{x + y} + z\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-217}:\\ \;\;\;\;\frac{a}{\frac{y + \left(t + x\right)}{t}}\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-99}:\\ \;\;\;\;a \cdot \frac{t + y}{x} + z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ a (- z b))))
   (if (<= y -1.05e+24)
     t_1
     (if (<= y -4.5e-272)
       (+ (/ (* a y) (+ x y)) z)
       (if (<= y 1.45e-217)
         (/ a (/ (+ y (+ t x)) t))
         (if (<= y 2.1e-99) (+ (* a (/ (+ t y) x)) z) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a + (z - b);
	double tmp;
	if (y <= -1.05e+24) {
		tmp = t_1;
	} else if (y <= -4.5e-272) {
		tmp = ((a * y) / (x + y)) + z;
	} else if (y <= 1.45e-217) {
		tmp = a / ((y + (t + x)) / t);
	} else if (y <= 2.1e-99) {
		tmp = (a * ((t + y) / x)) + z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a + (z - b)
    if (y <= (-1.05d+24)) then
        tmp = t_1
    else if (y <= (-4.5d-272)) then
        tmp = ((a * y) / (x + y)) + z
    else if (y <= 1.45d-217) then
        tmp = a / ((y + (t + x)) / t)
    else if (y <= 2.1d-99) then
        tmp = (a * ((t + y) / x)) + z
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a + (z - b);
	double tmp;
	if (y <= -1.05e+24) {
		tmp = t_1;
	} else if (y <= -4.5e-272) {
		tmp = ((a * y) / (x + y)) + z;
	} else if (y <= 1.45e-217) {
		tmp = a / ((y + (t + x)) / t);
	} else if (y <= 2.1e-99) {
		tmp = (a * ((t + y) / x)) + z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a + (z - b)
	tmp = 0
	if y <= -1.05e+24:
		tmp = t_1
	elif y <= -4.5e-272:
		tmp = ((a * y) / (x + y)) + z
	elif y <= 1.45e-217:
		tmp = a / ((y + (t + x)) / t)
	elif y <= 2.1e-99:
		tmp = (a * ((t + y) / x)) + z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a + Float64(z - b))
	tmp = 0.0
	if (y <= -1.05e+24)
		tmp = t_1;
	elseif (y <= -4.5e-272)
		tmp = Float64(Float64(Float64(a * y) / Float64(x + y)) + z);
	elseif (y <= 1.45e-217)
		tmp = Float64(a / Float64(Float64(y + Float64(t + x)) / t));
	elseif (y <= 2.1e-99)
		tmp = Float64(Float64(a * Float64(Float64(t + y) / x)) + z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a + (z - b);
	tmp = 0.0;
	if (y <= -1.05e+24)
		tmp = t_1;
	elseif (y <= -4.5e-272)
		tmp = ((a * y) / (x + y)) + z;
	elseif (y <= 1.45e-217)
		tmp = a / ((y + (t + x)) / t);
	elseif (y <= 2.1e-99)
		tmp = (a * ((t + y) / x)) + z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a + N[(z - b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.05e+24], t$95$1, If[LessEqual[y, -4.5e-272], N[(N[(N[(a * y), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision], If[LessEqual[y, 1.45e-217], N[(a / N[(N[(y + N[(t + x), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.1e-99], N[(N[(a * N[(N[(t + y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.0500000000000001e24 or 2.09999999999999984e-99 < y

   1. Initial program 44.2%

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

   3. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -1.0500000000000001e24 < y < -4.4999999999999998e-272

   1. Initial program 75.8%

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

   3. Taylor expanded in a around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   9. Taylor expanded in t around 0 0

      \[\leadsto expr\]

   11. Simplified 0

       \[\leadsto expr\]

   if -4.4999999999999998e-272 < y < 1.44999999999999991e-217

   1. Initial program 80.0%

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

   3. Taylor expanded in t around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]

   if 1.44999999999999991e-217 < y < 2.09999999999999984e-99

   1. Initial program 71.2%

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

   3. Taylor expanded in a around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   9. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   11. Simplified 0

       \[\leadsto expr\]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 9: 58.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + \left(z - b\right)\\ \mathbf{if}\;y \leq -4.4 \cdot 10^{+24}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -3.4 \cdot 10^{-272}:\\ \;\;\;\;\frac{a \cdot y}{x + y} + z\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{-216}:\\ \;\;\;\;a \cdot \frac{t}{t + x}\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-100}:\\ \;\;\;\;a \cdot \frac{t + y}{x} + z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ a (- z b))))
   (if (<= y -4.4e+24)
     t_1
     (if (<= y -3.4e-272)
       (+ (/ (* a y) (+ x y)) z)
       (if (<= y 1.85e-216)
         (* a (/ t (+ t x)))
         (if (<= y 9.5e-100) (+ (* a (/ (+ t y) x)) z) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a + (z - b);
	double tmp;
	if (y <= -4.4e+24) {
		tmp = t_1;
	} else if (y <= -3.4e-272) {
		tmp = ((a * y) / (x + y)) + z;
	} else if (y <= 1.85e-216) {
		tmp = a * (t / (t + x));
	} else if (y <= 9.5e-100) {
		tmp = (a * ((t + y) / x)) + z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a + (z - b)
    if (y <= (-4.4d+24)) then
        tmp = t_1
    else if (y <= (-3.4d-272)) then
        tmp = ((a * y) / (x + y)) + z
    else if (y <= 1.85d-216) then
        tmp = a * (t / (t + x))
    else if (y <= 9.5d-100) then
        tmp = (a * ((t + y) / x)) + z
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a + (z - b);
	double tmp;
	if (y <= -4.4e+24) {
		tmp = t_1;
	} else if (y <= -3.4e-272) {
		tmp = ((a * y) / (x + y)) + z;
	} else if (y <= 1.85e-216) {
		tmp = a * (t / (t + x));
	} else if (y <= 9.5e-100) {
		tmp = (a * ((t + y) / x)) + z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a + (z - b)
	tmp = 0
	if y <= -4.4e+24:
		tmp = t_1
	elif y <= -3.4e-272:
		tmp = ((a * y) / (x + y)) + z
	elif y <= 1.85e-216:
		tmp = a * (t / (t + x))
	elif y <= 9.5e-100:
		tmp = (a * ((t + y) / x)) + z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a + Float64(z - b))
	tmp = 0.0
	if (y <= -4.4e+24)
		tmp = t_1;
	elseif (y <= -3.4e-272)
		tmp = Float64(Float64(Float64(a * y) / Float64(x + y)) + z);
	elseif (y <= 1.85e-216)
		tmp = Float64(a * Float64(t / Float64(t + x)));
	elseif (y <= 9.5e-100)
		tmp = Float64(Float64(a * Float64(Float64(t + y) / x)) + z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a + (z - b);
	tmp = 0.0;
	if (y <= -4.4e+24)
		tmp = t_1;
	elseif (y <= -3.4e-272)
		tmp = ((a * y) / (x + y)) + z;
	elseif (y <= 1.85e-216)
		tmp = a * (t / (t + x));
	elseif (y <= 9.5e-100)
		tmp = (a * ((t + y) / x)) + z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a + N[(z - b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.4e+24], t$95$1, If[LessEqual[y, -3.4e-272], N[(N[(N[(a * y), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision], If[LessEqual[y, 1.85e-216], N[(a * N[(t / N[(t + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.5e-100], N[(N[(a * N[(N[(t + y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.40000000000000003e24 or 9.4999999999999992e-100 < y

   1. Initial program 44.2%

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

   3. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -4.40000000000000003e24 < y < -3.4000000000000003e-272

   1. Initial program 75.8%

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

   3. Taylor expanded in a around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   9. Taylor expanded in t around 0 0

      \[\leadsto expr\]

   11. Simplified 0

       \[\leadsto expr\]

   if -3.4000000000000003e-272 < y < 1.84999999999999998e-216

   1. Initial program 80.0%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]

   8. Taylor expanded in a around inf 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   if 1.84999999999999998e-216 < y < 9.4999999999999992e-100

   1. Initial program 71.2%

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

   3. Taylor expanded in a around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   9. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   11. Simplified 0

       \[\leadsto expr\]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 10: 69.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \left(y + x\right)\\ t_2 := a + \left(z - b\right)\\ \mathbf{if}\;y \leq -9 \cdot 10^{+56}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 5.3 \cdot 10^{-42}:\\ \;\;\;\;a \cdot \left(\frac{y}{t\_1} + \frac{t}{t\_1}\right) + z\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ t (+ y x))) (t_2 (+ a (- z b))))
   (if (<= y -9e+56)
     t_2
     (if (<= y 5.3e-42) (+ (* a (+ (/ y t_1) (/ t t_1))) z) t_2))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t + (y + x);
	double t_2 = a + (z - b);
	double tmp;
	if (y <= -9e+56) {
		tmp = t_2;
	} else if (y <= 5.3e-42) {
		tmp = (a * ((y / t_1) + (t / t_1))) + z;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t + (y + x)
    t_2 = a + (z - b)
    if (y <= (-9d+56)) then
        tmp = t_2
    else if (y <= 5.3d-42) then
        tmp = (a * ((y / t_1) + (t / t_1))) + z
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t + (y + x);
	double t_2 = a + (z - b);
	double tmp;
	if (y <= -9e+56) {
		tmp = t_2;
	} else if (y <= 5.3e-42) {
		tmp = (a * ((y / t_1) + (t / t_1))) + z;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t + (y + x)
	t_2 = a + (z - b)
	tmp = 0
	if y <= -9e+56:
		tmp = t_2
	elif y <= 5.3e-42:
		tmp = (a * ((y / t_1) + (t / t_1))) + z
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t + Float64(y + x))
	t_2 = Float64(a + Float64(z - b))
	tmp = 0.0
	if (y <= -9e+56)
		tmp = t_2;
	elseif (y <= 5.3e-42)
		tmp = Float64(Float64(a * Float64(Float64(y / t_1) + Float64(t / t_1))) + z);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t + (y + x);
	t_2 = a + (z - b);
	tmp = 0.0;
	if (y <= -9e+56)
		tmp = t_2;
	elseif (y <= 5.3e-42)
		tmp = (a * ((y / t_1) + (t / t_1))) + z;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t + N[(y + x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a + N[(z - b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9e+56], t$95$2, If[LessEqual[y, 5.3e-42], N[(N[(a * N[(N[(y / t$95$1), $MachinePrecision] + N[(t / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if y < -9.0000000000000006e56 or 5.3e-42 < y

   1. Initial program 41.9%

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

   3. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -9.0000000000000006e56 < y < 5.3e-42

   1. Initial program 74.0%

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

   3. Taylor expanded in a around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 11: 62.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \frac{t + y}{x} + z\\ \mathbf{if}\;x \leq -1.7 \cdot 10^{+167}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 3.65 \cdot 10^{+118}:\\ \;\;\;\;a + \left(z - b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (* a (/ (+ t y) x)) z)))
   (if (<= x -1.7e+167) t_1 (if (<= x 3.65e+118) (+ a (- z b)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a * ((t + y) / x)) + z;
	double tmp;
	if (x <= -1.7e+167) {
		tmp = t_1;
	} else if (x <= 3.65e+118) {
		tmp = a + (z - b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a * ((t + y) / x)) + z
    if (x <= (-1.7d+167)) then
        tmp = t_1
    else if (x <= 3.65d+118) then
        tmp = a + (z - b)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a * ((t + y) / x)) + z;
	double tmp;
	if (x <= -1.7e+167) {
		tmp = t_1;
	} else if (x <= 3.65e+118) {
		tmp = a + (z - b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a * ((t + y) / x)) + z
	tmp = 0
	if x <= -1.7e+167:
		tmp = t_1
	elif x <= 3.65e+118:
		tmp = a + (z - b)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a * Float64(Float64(t + y) / x)) + z)
	tmp = 0.0
	if (x <= -1.7e+167)
		tmp = t_1;
	elseif (x <= 3.65e+118)
		tmp = Float64(a + Float64(z - b));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a * ((t + y) / x)) + z;
	tmp = 0.0;
	if (x <= -1.7e+167)
		tmp = t_1;
	elseif (x <= 3.65e+118)
		tmp = a + (z - b);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a * N[(N[(t + y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision]}, If[LessEqual[x, -1.7e+167], t$95$1, If[LessEqual[x, 3.65e+118], N[(a + N[(z - b), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.7e167 or 3.6500000000000002e118 < x

   1. Initial program 51.0%

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

   3. Taylor expanded in a around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   9. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   11. Simplified 0

       \[\leadsto expr\]

   if -1.7e167 < x < 3.6500000000000002e118

   1. Initial program 60.5%

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

   3. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 12: 59.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.4 \cdot 10^{+167}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{+202}:\\ \;\;\;\;a + \left(z - b\right)\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -3.4e+167) z (if (<= x 2.3e+202) (+ a (- z b)) z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -3.4e+167) {
		tmp = z;
	} else if (x <= 2.3e+202) {
		tmp = a + (z - b);
	} else {
		tmp = z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-3.4d+167)) then
        tmp = z
    else if (x <= 2.3d+202) then
        tmp = a + (z - b)
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -3.4e+167) {
		tmp = z;
	} else if (x <= 2.3e+202) {
		tmp = a + (z - b);
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -3.4e+167:
		tmp = z
	elif x <= 2.3e+202:
		tmp = a + (z - b)
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -3.4e+167)
		tmp = z;
	elseif (x <= 2.3e+202)
		tmp = Float64(a + Float64(z - b));
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -3.4e+167)
		tmp = z;
	elseif (x <= 2.3e+202)
		tmp = a + (z - b);
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -3.4e+167], z, If[LessEqual[x, 2.3e+202], N[(a + N[(z - b), $MachinePrecision]), $MachinePrecision], z]]

Derivation

1. Split input into 2 regimes

2. if x < -3.4e167 or 2.29999999999999999e202 < x

   1. Initial program 49.8%

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

   3. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -3.4e167 < x < 2.29999999999999999e202

   1. Initial program 60.1%

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

   3. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 13: 52.2% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.2 \cdot 10^{+92}:\\ \;\;\;\;z - b\\ \mathbf{elif}\;b \leq 1.02 \cdot 10^{+222}:\\ \;\;\;\;a + z\\ \mathbf{else}:\\ \;\;\;\;z - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -2.2e+92) (- z b) (if (<= b 1.02e+222) (+ a z) (- z b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.2e+92) {
		tmp = z - b;
	} else if (b <= 1.02e+222) {
		tmp = a + z;
	} else {
		tmp = z - b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-2.2d+92)) then
        tmp = z - b
    else if (b <= 1.02d+222) then
        tmp = a + z
    else
        tmp = z - b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.2e+92) {
		tmp = z - b;
	} else if (b <= 1.02e+222) {
		tmp = a + z;
	} else {
		tmp = z - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -2.2e+92:
		tmp = z - b
	elif b <= 1.02e+222:
		tmp = a + z
	else:
		tmp = z - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -2.2e+92)
		tmp = Float64(z - b);
	elseif (b <= 1.02e+222)
		tmp = Float64(a + z);
	else
		tmp = Float64(z - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -2.2e+92)
		tmp = z - b;
	elseif (b <= 1.02e+222)
		tmp = a + z;
	else
		tmp = z - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -2.2e+92], N[(z - b), $MachinePrecision], If[LessEqual[b, 1.02e+222], N[(a + z), $MachinePrecision], N[(z - b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if b < -2.19999999999999992e92 or 1.01999999999999995e222 < b

   1. Initial program 44.6%

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

   3. Taylor expanded in a around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in a around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   9. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   11. Simplified 0

       \[\leadsto expr\]

   if -2.19999999999999992e92 < b < 1.01999999999999995e222

   1. Initial program 63.7%

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

   3. Taylor expanded in a around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   9. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   11. Simplified 0

       \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 14: 50.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5.8 \cdot 10^{+94}:\\ \;\;\;\;-b\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{+222}:\\ \;\;\;\;a + z\\ \mathbf{else}:\\ \;\;\;\;-b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -5.8e+94) (- b) (if (<= b 1.7e+222) (+ a z) (- b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -5.8e+94) {
		tmp = -b;
	} else if (b <= 1.7e+222) {
		tmp = a + z;
	} else {
		tmp = -b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-5.8d+94)) then
        tmp = -b
    else if (b <= 1.7d+222) then
        tmp = a + z
    else
        tmp = -b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -5.8e+94) {
		tmp = -b;
	} else if (b <= 1.7e+222) {
		tmp = a + z;
	} else {
		tmp = -b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -5.8e+94:
		tmp = -b
	elif b <= 1.7e+222:
		tmp = a + z
	else:
		tmp = -b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -5.8e+94)
		tmp = Float64(-b);
	elseif (b <= 1.7e+222)
		tmp = Float64(a + z);
	else
		tmp = Float64(-b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -5.8e+94)
		tmp = -b;
	elseif (b <= 1.7e+222)
		tmp = a + z;
	else
		tmp = -b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -5.8e+94], (-b), If[LessEqual[b, 1.7e+222], N[(a + z), $MachinePrecision], (-b)]]

Derivation

1. Split input into 2 regimes

2. if b < -5.7999999999999997e94 or 1.70000000000000008e222 < b

   1. Initial program 44.6%

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

   3. Taylor expanded in b around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   if -5.7999999999999997e94 < b < 1.70000000000000008e222

   1. Initial program 63.7%

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

   3. Taylor expanded in a around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   9. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   11. Simplified 0

       \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 15: 44.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{+14}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 1.42 \cdot 10^{+48}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -3.8e+14) a (if (<= t 1.42e+48) z a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -3.8e+14) {
		tmp = a;
	} else if (t <= 1.42e+48) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-3.8d+14)) then
        tmp = a
    else if (t <= 1.42d+48) then
        tmp = z
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -3.8e+14) {
		tmp = a;
	} else if (t <= 1.42e+48) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -3.8e+14:
		tmp = a
	elif t <= 1.42e+48:
		tmp = z
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -3.8e+14)
		tmp = a;
	elseif (t <= 1.42e+48)
		tmp = z;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -3.8e+14)
		tmp = a;
	elseif (t <= 1.42e+48)
		tmp = z;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -3.8e+14], a, If[LessEqual[t, 1.42e+48], z, a]]

Derivation

1. Split input into 2 regimes

2. if t < -3.8e14 or 1.42e48 < t

   1. Initial program 47.4%

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

   3. Taylor expanded in t around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -3.8e14 < t < 1.42e48

   1. Initial program 66.8%

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

   3. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 16: 32.2% accurate, 21.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 58.5%

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

3. Taylor expanded in t around inf 0

   \[\leadsto expr\]

5. Simplified 0

   \[\leadsto expr\]
6. Add Preprocessing

Developer target: 81.5% accurate, 0.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024110 
(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)))