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

Percentage Accurate: 60.8% → 87.8%

Time: 12.1s

Alternatives: 14

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: 87.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \left(z + a\right) - b\\ t_3 := \left(x + y\right) \cdot z\\ t_4 := \frac{\left(t\_3 + a \cdot \left(y + t\right)\right) - y \cdot b}{t\_1}\\ \mathbf{if}\;t\_4 \leq -\infty:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_4 \leq 10^{+286}:\\ \;\;\;\;\frac{\left(t\_3 + \left(y \cdot a + t \cdot a\right)\right) - y \cdot b}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t)))
        (t_2 (- (+ z a) b))
        (t_3 (* (+ x y) z))
        (t_4 (/ (- (+ t_3 (* a (+ y t))) (* y b)) t_1)))
   (if (<= t_4 (- INFINITY))
     t_2
     (if (<= t_4 1e+286)
       (/ (- (+ t_3 (+ (* y a) (* t a))) (* y b)) 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 + a) - b;
	double t_3 = (x + y) * z;
	double t_4 = ((t_3 + (a * (y + t))) - (y * b)) / t_1;
	double tmp;
	if (t_4 <= -((double) INFINITY)) {
		tmp = t_2;
	} else if (t_4 <= 1e+286) {
		tmp = ((t_3 + ((y * a) + (t * a))) - (y * b)) / t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = (z + a) - b;
	double t_3 = (x + y) * z;
	double t_4 = ((t_3 + (a * (y + t))) - (y * b)) / t_1;
	double tmp;
	if (t_4 <= -Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else if (t_4 <= 1e+286) {
		tmp = ((t_3 + ((y * a) + (t * a))) - (y * b)) / t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = (z + a) - b
	t_3 = (x + y) * z
	t_4 = ((t_3 + (a * (y + t))) - (y * b)) / t_1
	tmp = 0
	if t_4 <= -math.inf:
		tmp = t_2
	elif t_4 <= 1e+286:
		tmp = ((t_3 + ((y * a) + (t * a))) - (y * b)) / 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(z + a) - b)
	t_3 = Float64(Float64(x + y) * z)
	t_4 = Float64(Float64(Float64(t_3 + Float64(a * Float64(y + t))) - Float64(y * b)) / t_1)
	tmp = 0.0
	if (t_4 <= Float64(-Inf))
		tmp = t_2;
	elseif (t_4 <= 1e+286)
		tmp = Float64(Float64(Float64(t_3 + Float64(Float64(y * a) + Float64(t * a))) - Float64(y * b)) / t_1);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	t_2 = (z + a) - b;
	t_3 = (x + y) * z;
	t_4 = ((t_3 + (a * (y + t))) - (y * b)) / t_1;
	tmp = 0.0;
	if (t_4 <= -Inf)
		tmp = t_2;
	elseif (t_4 <= 1e+286)
		tmp = ((t_3 + ((y * a) + (t * a))) - (y * b)) / t_1;
	else
		tmp = t_2;
	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[(z + a), $MachinePrecision] - b), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(t$95$3 + N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[t$95$4, (-Infinity)], t$95$2, If[LessEqual[t$95$4, 1e+286], N[(N[(N[(t$95$3 + N[(N[(y * a), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -inf.0 or 1.00000000000000003e286 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 4.7%

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

   3. Taylor expanded in y around inf

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

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

         \[\leadsto \mathsf{\_.f64}\left(\left(a + z\right), \color{blue}{b}\right) \]

      2. +-lowering-+.f64 74.4%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(a, z\right), b\right) \]

   5. Simplified 74.4%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1.00000000000000003e286

   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. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(x, y\right), z\right), \left(a \cdot \left(t + y\right)\right)\right), \mathsf{*.f64}\left(y, b\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, t\right), y\right)\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(x, y\right), z\right), \left(a \cdot \left(y + t\right)\right)\right), \mathsf{*.f64}\left(y, b\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, t\right), y\right)\right) \]

      3. distribute-rgt-in N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(x, y\right), z\right), \left(y \cdot a + t \cdot a\right)\right), \mathsf{*.f64}\left(y, b\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, t\right), y\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(x, y\right), z\right), \mathsf{+.f64}\left(\left(y \cdot a\right), \left(t \cdot a\right)\right)\right), \mathsf{*.f64}\left(y, b\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, t\right), y\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(x, y\right), z\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, a\right), \left(t \cdot a\right)\right)\right), \mathsf{*.f64}\left(y, b\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, t\right), y\right)\right) \]

      6. *-lowering-*.f64 99.8%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(x, y\right), z\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, a\right), \mathsf{*.f64}\left(t, a\right)\right)\right), \mathsf{*.f64}\left(y, b\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, t\right), y\right)\right) \]

   4. Applied egg-rr 99.8%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;\frac{\left(\left(x + y\right) \cdot z + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 10^{+286}:\\ \;\;\;\;\frac{\left(\left(x + y\right) \cdot z + \left(y \cdot a + t \cdot a\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 87.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(\left(x + y\right) \cdot z + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ t_2 := \left(z + a\right) - b\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 10^{+286}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* (+ x y) z) (* a (+ y t))) (* y b)) (+ y (+ x t))))
        (t_2 (- (+ z a) b)))
   (if (<= t_1 (- INFINITY)) t_2 (if (<= t_1 1e+286) 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) + (a * (y + t))) - (y * b)) / (y + (x + t));
	double t_2 = (z + a) - b;
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = t_2;
	} else if (t_1 <= 1e+286) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((((x + y) * z) + (a * (y + t))) - (y * b)) / (y + (x + t));
	double t_2 = (z + a) - b;
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else if (t_1 <= 1e+286) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((((x + y) * z) + (a * (y + t))) - (y * b)) / (y + (x + t))
	t_2 = (z + a) - b
	tmp = 0
	if t_1 <= -math.inf:
		tmp = t_2
	elif t_1 <= 1e+286:
		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(a * Float64(y + t))) - Float64(y * b)) / Float64(y + Float64(x + t)))
	t_2 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = t_2;
	elseif (t_1 <= 1e+286)
		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) + (a * (y + t))) - (y * b)) / (y + (x + t));
	t_2 = (z + a) - b;
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = t_2;
	elseif (t_1 <= 1e+286)
		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[(a * N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], t$95$2, If[LessEqual[t$95$1, 1e+286], t$95$1, t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -inf.0 or 1.00000000000000003e286 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 4.7%

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

   3. Taylor expanded in y around inf

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

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

         \[\leadsto \mathsf{\_.f64}\left(\left(a + z\right), \color{blue}{b}\right) \]

      2. +-lowering-+.f64 74.4%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(a, z\right), b\right) \]

   5. Simplified 74.4%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1.00000000000000003e286

   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 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;\frac{\left(\left(x + y\right) \cdot z + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 10^{+286}:\\ \;\;\;\;\frac{\left(\left(x + y\right) \cdot z + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 63.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -2.4 \cdot 10^{-87}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-146}:\\ \;\;\;\;z \cdot \left(\frac{x}{x + t} + \frac{t \cdot a}{z \cdot \left(x + t\right)}\right)\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+109}:\\ \;\;\;\;\frac{1}{x + \left(y + t\right)} \cdot \left(x \cdot z + y \cdot \left(z - b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= y -2.4e-87)
     t_1
     (if (<= y 1.15e-146)
       (* z (+ (/ x (+ x t)) (/ (* t a) (* z (+ x t)))))
       (if (<= y 1.15e+109)
         (* (/ 1.0 (+ x (+ y t))) (+ (* x z) (* y (- z b))))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -2.4e-87) {
		tmp = t_1;
	} else if (y <= 1.15e-146) {
		tmp = z * ((x / (x + t)) + ((t * a) / (z * (x + t))));
	} else if (y <= 1.15e+109) {
		tmp = (1.0 / (x + (y + t))) * ((x * z) + (y * (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 = (z + a) - b
    if (y <= (-2.4d-87)) then
        tmp = t_1
    else if (y <= 1.15d-146) then
        tmp = z * ((x / (x + t)) + ((t * a) / (z * (x + t))))
    else if (y <= 1.15d+109) then
        tmp = (1.0d0 / (x + (y + t))) * ((x * z) + (y * (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 = (z + a) - b;
	double tmp;
	if (y <= -2.4e-87) {
		tmp = t_1;
	} else if (y <= 1.15e-146) {
		tmp = z * ((x / (x + t)) + ((t * a) / (z * (x + t))));
	} else if (y <= 1.15e+109) {
		tmp = (1.0 / (x + (y + t))) * ((x * z) + (y * (z - b)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	tmp = 0
	if y <= -2.4e-87:
		tmp = t_1
	elif y <= 1.15e-146:
		tmp = z * ((x / (x + t)) + ((t * a) / (z * (x + t))))
	elif y <= 1.15e+109:
		tmp = (1.0 / (x + (y + t))) * ((x * z) + (y * (z - b)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -2.4e-87)
		tmp = t_1;
	elseif (y <= 1.15e-146)
		tmp = Float64(z * Float64(Float64(x / Float64(x + t)) + Float64(Float64(t * a) / Float64(z * Float64(x + t)))));
	elseif (y <= 1.15e+109)
		tmp = Float64(Float64(1.0 / Float64(x + Float64(y + t))) * Float64(Float64(x * z) + Float64(y * Float64(z - b))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	tmp = 0.0;
	if (y <= -2.4e-87)
		tmp = t_1;
	elseif (y <= 1.15e-146)
		tmp = z * ((x / (x + t)) + ((t * a) / (z * (x + t))));
	elseif (y <= 1.15e+109)
		tmp = (1.0 / (x + (y + t))) * ((x * z) + (y * (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[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -2.4e-87], t$95$1, If[LessEqual[y, 1.15e-146], N[(z * N[(N[(x / N[(x + t), $MachinePrecision]), $MachinePrecision] + N[(N[(t * a), $MachinePrecision] / N[(z * N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.15e+109], N[(N[(1.0 / N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(x * z), $MachinePrecision] + N[(y * N[(z - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.4e-87 or 1.15000000000000005e109 < y

   1. Initial program 42.9%

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

   3. Taylor expanded in y around inf

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

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

         \[\leadsto \mathsf{\_.f64}\left(\left(a + z\right), \color{blue}{b}\right) \]

      2. +-lowering-+.f64 72.2%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(a, z\right), b\right) \]

   5. Simplified 72.2%

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

   if -2.4e-87 < y < 1.15e-146

   1. Initial program 77.6%

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

   3. Taylor expanded in y around 0

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

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

         \[\leadsto \mathsf{/.f64}\left(\left(a \cdot t + x \cdot z\right), \color{blue}{\left(t + x\right)}\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(a \cdot t\right), \left(x \cdot z\right)\right), \left(\color{blue}{t} + x\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, t\right), \left(x \cdot z\right)\right), \left(t + x\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, t\right), \left(z \cdot x\right)\right), \left(t + x\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, t\right), \mathsf{*.f64}\left(z, x\right)\right), \left(t + x\right)\right) \]

      6. +-lowering-+.f64 62.4%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, t\right), \mathsf{*.f64}\left(z, x\right)\right), \mathsf{+.f64}\left(t, \color{blue}{x}\right)\right) \]

   5. Simplified 62.4%

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

   6. Taylor expanded in z around inf

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

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

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(\frac{x}{t + x} + \frac{a \cdot t}{z \cdot \left(t + x\right)}\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\left(\frac{x}{t + x}\right), \color{blue}{\left(\frac{a \cdot t}{z \cdot \left(t + x\right)}\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, \left(t + x\right)\right), \left(\frac{\color{blue}{a \cdot t}}{z \cdot \left(t + x\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, \mathsf{+.f64}\left(t, x\right)\right), \left(\frac{a \cdot \color{blue}{t}}{z \cdot \left(t + x\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, \mathsf{+.f64}\left(t, x\right)\right), \mathsf{/.f64}\left(\left(a \cdot t\right), \color{blue}{\left(z \cdot \left(t + x\right)\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, \mathsf{+.f64}\left(t, x\right)\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, t\right), \left(\color{blue}{z} \cdot \left(t + x\right)\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, \mathsf{+.f64}\left(t, x\right)\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, t\right), \mathsf{*.f64}\left(z, \color{blue}{\left(t + x\right)}\right)\right)\right)\right) \]

      8. +-lowering-+.f64 71.5%

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, \mathsf{+.f64}\left(t, x\right)\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, t\right), \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(t, \color{blue}{x}\right)\right)\right)\right)\right) \]

   8. Simplified 71.5%

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

   if 1.15e-146 < y < 1.15000000000000005e109

   1. Initial program 78.9%

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

      1. clear-num N/A

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

      2. associate-/r/ N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{1}{\left(x + t\right) + y}\right), \color{blue}{\left(\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \left(\left(x + t\right) + y\right)\right), \left(\color{blue}{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right)} - y \cdot b\right)\right) \]

      5. associate-+l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \left(x + \left(t + y\right)\right)\right), \left(\left(\left(x + y\right) \cdot z + \color{blue}{\left(t + y\right) \cdot a}\right) - y \cdot b\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, \left(t + y\right)\right)\right), \left(\left(\left(x + y\right) \cdot z + \color{blue}{\left(t + y\right) \cdot a}\right) - y \cdot b\right)\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, \left(y + t\right)\right)\right), \left(\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot \color{blue}{a}\right) - y \cdot b\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(y, t\right)\right)\right), \left(\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot \color{blue}{a}\right) - y \cdot b\right)\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(y, t\right)\right)\right), \left(\left(\left(t + y\right) \cdot a + \left(x + y\right) \cdot z\right) - \color{blue}{y} \cdot b\right)\right) \]

      10. associate--l+ N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(y, t\right)\right)\right), \left(\left(t + y\right) \cdot a + \color{blue}{\left(\left(x + y\right) \cdot z - y \cdot b\right)}\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(y, t\right)\right)\right), \mathsf{+.f64}\left(\left(\left(t + y\right) \cdot a\right), \color{blue}{\left(\left(x + y\right) \cdot z - y \cdot b\right)}\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(y, t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(t + y\right), a\right), \left(\color{blue}{\left(x + y\right) \cdot z} - y \cdot b\right)\right)\right) \]

      13. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(y, t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(y + t\right), a\right), \left(\color{blue}{\left(x + y\right)} \cdot z - y \cdot b\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(y, t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, t\right), a\right), \left(\color{blue}{\left(x + y\right)} \cdot z - y \cdot b\right)\right)\right) \]

      15. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(y, t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, t\right), a\right), \mathsf{\_.f64}\left(\left(\left(x + y\right) \cdot z\right), \color{blue}{\left(y \cdot b\right)}\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(y, t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, t\right), a\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\left(x + y\right), z\right), \left(\color{blue}{y} \cdot b\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(y, t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, t\right), a\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(x, y\right), z\right), \left(y \cdot b\right)\right)\right)\right) \]

      18. *-lowering-*.f64 78.8%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(y, t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, t\right), a\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(x, y\right), z\right), \mathsf{*.f64}\left(y, \color{blue}{b}\right)\right)\right)\right) \]

   4. Applied egg-rr 78.8%

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

   5. Taylor expanded in a around 0

      \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(y, t\right)\right)\right), \color{blue}{\left(z \cdot \left(x + y\right) - b \cdot y\right)}\right) \]
   6. Step-by-step derivation

      1. distribute-rgt-in N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(y, t\right)\right)\right), \left(\left(x \cdot z + y \cdot z\right) - \color{blue}{b} \cdot y\right)\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(y, t\right)\right)\right), \left(x \cdot z + \color{blue}{\left(y \cdot z - b \cdot y\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(y, t\right)\right)\right), \mathsf{+.f64}\left(\left(x \cdot z\right), \color{blue}{\left(y \cdot z - b \cdot y\right)}\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(y, t\right)\right)\right), \mathsf{+.f64}\left(\left(z \cdot x\right), \left(\color{blue}{y \cdot z} - b \cdot y\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(y, t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, x\right), \left(\color{blue}{y \cdot z} - b \cdot y\right)\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(y, t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, x\right), \left(y \cdot z + \color{blue}{\left(\mathsf{neg}\left(b \cdot y\right)\right)}\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(y, t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, x\right), \left(y \cdot z + \left(\mathsf{neg}\left(y \cdot b\right)\right)\right)\right)\right) \]

      8. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(y, t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, x\right), \left(y \cdot z + y \cdot \color{blue}{\left(\mathsf{neg}\left(b\right)\right)}\right)\right)\right) \]

      9. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(y, t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, x\right), \left(y \cdot z + y \cdot \left(-1 \cdot \color{blue}{b}\right)\right)\right)\right) \]

      10. distribute-lft-in N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(y, t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, x\right), \left(y \cdot \color{blue}{\left(z + -1 \cdot b\right)}\right)\right)\right) \]

      11. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(y, t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, x\right), \left(y \cdot \left(z + \left(\mathsf{neg}\left(b\right)\right)\right)\right)\right)\right) \]

      12. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(y, t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, x\right), \left(y \cdot \left(z - \color{blue}{b}\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(y, t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, x\right), \mathsf{*.f64}\left(y, \color{blue}{\left(z - b\right)}\right)\right)\right) \]

      14. --lowering--.f64 60.1%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(y, t\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, x\right), \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(z, \color{blue}{b}\right)\right)\right)\right) \]

   7. Simplified 60.1%

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

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{-87}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-146}:\\ \;\;\;\;z \cdot \left(\frac{x}{x + t} + \frac{t \cdot a}{z \cdot \left(x + t\right)}\right)\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+109}:\\ \;\;\;\;\frac{1}{x + \left(y + t\right)} \cdot \left(x \cdot z + y \cdot \left(z - b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 65.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -1.65 \cdot 10^{-87}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-21}:\\ \;\;\;\;z \cdot \left(\frac{x}{x + t} + \frac{t \cdot a}{z \cdot \left(x + t\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= y -1.65e-87)
     t_1
     (if (<= y 1.25e-21)
       (* z (+ (/ x (+ x t)) (/ (* t a) (* z (+ x t)))))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -1.65e-87) {
		tmp = t_1;
	} else if (y <= 1.25e-21) {
		tmp = z * ((x / (x + t)) + ((t * a) / (z * (x + t))));
	} 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 = (z + a) - b
    if (y <= (-1.65d-87)) then
        tmp = t_1
    else if (y <= 1.25d-21) then
        tmp = z * ((x / (x + t)) + ((t * a) / (z * (x + t))))
    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 = (z + a) - b;
	double tmp;
	if (y <= -1.65e-87) {
		tmp = t_1;
	} else if (y <= 1.25e-21) {
		tmp = z * ((x / (x + t)) + ((t * a) / (z * (x + t))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	tmp = 0
	if y <= -1.65e-87:
		tmp = t_1
	elif y <= 1.25e-21:
		tmp = z * ((x / (x + t)) + ((t * a) / (z * (x + t))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -1.65e-87)
		tmp = t_1;
	elseif (y <= 1.25e-21)
		tmp = Float64(z * Float64(Float64(x / Float64(x + t)) + Float64(Float64(t * a) / Float64(z * Float64(x + t)))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	tmp = 0.0;
	if (y <= -1.65e-87)
		tmp = t_1;
	elseif (y <= 1.25e-21)
		tmp = z * ((x / (x + t)) + ((t * a) / (z * (x + t))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -1.65e-87], t$95$1, If[LessEqual[y, 1.25e-21], N[(z * N[(N[(x / N[(x + t), $MachinePrecision]), $MachinePrecision] + N[(N[(t * a), $MachinePrecision] / N[(z * N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.65e-87 or 1.24999999999999993e-21 < y

   1. Initial program 47.6%

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

   3. Taylor expanded in y around inf

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

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

         \[\leadsto \mathsf{\_.f64}\left(\left(a + z\right), \color{blue}{b}\right) \]

      2. +-lowering-+.f64 69.0%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(a, z\right), b\right) \]

   5. Simplified 69.0%

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

   if -1.65e-87 < y < 1.24999999999999993e-21

   1. Initial program 79.3%

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

   3. Taylor expanded in y around 0

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

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

         \[\leadsto \mathsf{/.f64}\left(\left(a \cdot t + x \cdot z\right), \color{blue}{\left(t + x\right)}\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(a \cdot t\right), \left(x \cdot z\right)\right), \left(\color{blue}{t} + x\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, t\right), \left(x \cdot z\right)\right), \left(t + x\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, t\right), \left(z \cdot x\right)\right), \left(t + x\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, t\right), \mathsf{*.f64}\left(z, x\right)\right), \left(t + x\right)\right) \]

      6. +-lowering-+.f64 58.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, t\right), \mathsf{*.f64}\left(z, x\right)\right), \mathsf{+.f64}\left(t, \color{blue}{x}\right)\right) \]

   5. Simplified 58.0%

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

   6. Taylor expanded in z around inf

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

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

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(\frac{x}{t + x} + \frac{a \cdot t}{z \cdot \left(t + x\right)}\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\left(\frac{x}{t + x}\right), \color{blue}{\left(\frac{a \cdot t}{z \cdot \left(t + x\right)}\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, \left(t + x\right)\right), \left(\frac{\color{blue}{a \cdot t}}{z \cdot \left(t + x\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, \mathsf{+.f64}\left(t, x\right)\right), \left(\frac{a \cdot \color{blue}{t}}{z \cdot \left(t + x\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, \mathsf{+.f64}\left(t, x\right)\right), \mathsf{/.f64}\left(\left(a \cdot t\right), \color{blue}{\left(z \cdot \left(t + x\right)\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, \mathsf{+.f64}\left(t, x\right)\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, t\right), \left(\color{blue}{z} \cdot \left(t + x\right)\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, \mathsf{+.f64}\left(t, x\right)\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, t\right), \mathsf{*.f64}\left(z, \color{blue}{\left(t + x\right)}\right)\right)\right)\right) \]

      8. +-lowering-+.f64 66.1%

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, \mathsf{+.f64}\left(t, x\right)\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, t\right), \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(t, \color{blue}{x}\right)\right)\right)\right)\right) \]

   8. Simplified 66.1%

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

4. Final simplification 67.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{-87}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-21}:\\ \;\;\;\;z \cdot \left(\frac{x}{x + t} + \frac{t \cdot a}{z \cdot \left(x + t\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 63.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -5 \cdot 10^{-146}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-21}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= y -5e-146)
     t_1
     (if (<= y 3.2e-21) (/ (+ (* t a) (* x z)) (+ x t)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -5e-146) {
		tmp = t_1;
	} else if (y <= 3.2e-21) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} 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 = (z + a) - b
    if (y <= (-5d-146)) then
        tmp = t_1
    else if (y <= 3.2d-21) then
        tmp = ((t * a) + (x * z)) / (x + t)
    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 = (z + a) - b;
	double tmp;
	if (y <= -5e-146) {
		tmp = t_1;
	} else if (y <= 3.2e-21) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	tmp = 0
	if y <= -5e-146:
		tmp = t_1
	elif y <= 3.2e-21:
		tmp = ((t * a) + (x * z)) / (x + t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -5e-146)
		tmp = t_1;
	elseif (y <= 3.2e-21)
		tmp = Float64(Float64(Float64(t * a) + Float64(x * z)) / Float64(x + t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	tmp = 0.0;
	if (y <= -5e-146)
		tmp = t_1;
	elseif (y <= 3.2e-21)
		tmp = ((t * a) + (x * z)) / (x + t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -5e-146], t$95$1, If[LessEqual[y, 3.2e-21], N[(N[(N[(t * a), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -4.99999999999999957e-146 or 3.2000000000000002e-21 < y

   1. Initial program 48.8%

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

   3. Taylor expanded in y around inf

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

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

         \[\leadsto \mathsf{\_.f64}\left(\left(a + z\right), \color{blue}{b}\right) \]

      2. +-lowering-+.f64 67.4%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(a, z\right), b\right) \]

   5. Simplified 67.4%

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

   if -4.99999999999999957e-146 < y < 3.2000000000000002e-21

   1. Initial program 80.4%

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

   3. Taylor expanded in y around 0

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

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

         \[\leadsto \mathsf{/.f64}\left(\left(a \cdot t + x \cdot z\right), \color{blue}{\left(t + x\right)}\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(a \cdot t\right), \left(x \cdot z\right)\right), \left(\color{blue}{t} + x\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, t\right), \left(x \cdot z\right)\right), \left(t + x\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, t\right), \left(z \cdot x\right)\right), \left(t + x\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, t\right), \mathsf{*.f64}\left(z, x\right)\right), \left(t + x\right)\right) \]

      6. +-lowering-+.f64 59.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, t\right), \mathsf{*.f64}\left(z, x\right)\right), \mathsf{+.f64}\left(t, \color{blue}{x}\right)\right) \]

   5. Simplified 59.9%

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

4. Final simplification 64.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-146}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-21}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 57.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -2.9 \cdot 10^{-146}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -3.9 \cdot 10^{-267}:\\ \;\;\;\;\frac{x \cdot z}{x + t}\\ \mathbf{elif}\;y \leq 2.35 \cdot 10^{+72}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= y -2.9e-146)
     t_1
     (if (<= y -3.9e-267)
       (/ (* x z) (+ x t))
       (if (<= y 2.35e+72) (+ z a) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -2.9e-146) {
		tmp = t_1;
	} else if (y <= -3.9e-267) {
		tmp = (x * z) / (x + t);
	} else if (y <= 2.35e+72) {
		tmp = z + a;
	} 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 = (z + a) - b
    if (y <= (-2.9d-146)) then
        tmp = t_1
    else if (y <= (-3.9d-267)) then
        tmp = (x * z) / (x + t)
    else if (y <= 2.35d+72) then
        tmp = z + a
    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 = (z + a) - b;
	double tmp;
	if (y <= -2.9e-146) {
		tmp = t_1;
	} else if (y <= -3.9e-267) {
		tmp = (x * z) / (x + t);
	} else if (y <= 2.35e+72) {
		tmp = z + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	tmp = 0
	if y <= -2.9e-146:
		tmp = t_1
	elif y <= -3.9e-267:
		tmp = (x * z) / (x + t)
	elif y <= 2.35e+72:
		tmp = z + a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -2.9e-146)
		tmp = t_1;
	elseif (y <= -3.9e-267)
		tmp = Float64(Float64(x * z) / Float64(x + t));
	elseif (y <= 2.35e+72)
		tmp = Float64(z + a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	tmp = 0.0;
	if (y <= -2.9e-146)
		tmp = t_1;
	elseif (y <= -3.9e-267)
		tmp = (x * z) / (x + t);
	elseif (y <= 2.35e+72)
		tmp = z + a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -2.9e-146], t$95$1, If[LessEqual[y, -3.9e-267], N[(N[(x * z), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.35e+72], N[(z + a), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.90000000000000011e-146 or 2.35000000000000017e72 < y

   1. Initial program 45.7%

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

   3. Taylor expanded in y around inf

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

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

         \[\leadsto \mathsf{\_.f64}\left(\left(a + z\right), \color{blue}{b}\right) \]

      2. +-lowering-+.f64 68.5%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(a, z\right), b\right) \]

   5. Simplified 68.5%

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

   if -2.90000000000000011e-146 < y < -3.89999999999999977e-267

   1. Initial program 82.7%

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

   3. Taylor expanded in y around 0

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

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

         \[\leadsto \mathsf{/.f64}\left(\left(a \cdot t + x \cdot z\right), \color{blue}{\left(t + x\right)}\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(a \cdot t\right), \left(x \cdot z\right)\right), \left(\color{blue}{t} + x\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, t\right), \left(x \cdot z\right)\right), \left(t + x\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, t\right), \left(z \cdot x\right)\right), \left(t + x\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, t\right), \mathsf{*.f64}\left(z, x\right)\right), \left(t + x\right)\right) \]

      6. +-lowering-+.f64 69.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, t\right), \mathsf{*.f64}\left(z, x\right)\right), \mathsf{+.f64}\left(t, \color{blue}{x}\right)\right) \]

   5. Simplified 69.3%

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

   6. Taylor expanded in a around 0

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

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

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot z\right), \color{blue}{\left(t + x\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(z \cdot x\right), \left(\color{blue}{t} + x\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, x\right), \left(\color{blue}{t} + x\right)\right) \]

      4. +-lowering-+.f64 52.1%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, x\right), \mathsf{+.f64}\left(t, \color{blue}{x}\right)\right) \]

   8. Simplified 52.1%

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

   if -3.89999999999999977e-267 < y < 2.35000000000000017e72

   1. Initial program 78.6%

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

   3. Taylor expanded in y around inf

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

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

         \[\leadsto \mathsf{\_.f64}\left(\left(a + z\right), \color{blue}{b}\right) \]

      2. +-lowering-+.f64 41.1%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(a, z\right), b\right) \]

   5. Simplified 41.1%

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

   6. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 52.3%

         \[\leadsto \mathsf{+.f64}\left(z, \color{blue}{a}\right) \]

   8. Simplified 52.3%

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

4. Final simplification 61.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{-146}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -3.9 \cdot 10^{-267}:\\ \;\;\;\;\frac{x \cdot z}{x + t}\\ \mathbf{elif}\;y \leq 2.35 \cdot 10^{+72}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 57.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -1.5 \cdot 10^{-136}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-263}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{+71}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= y -1.5e-136)
     t_1
     (if (<= y -1.7e-263) z (if (<= y 5.4e+71) (+ z a) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -1.5e-136) {
		tmp = t_1;
	} else if (y <= -1.7e-263) {
		tmp = z;
	} else if (y <= 5.4e+71) {
		tmp = z + a;
	} 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 = (z + a) - b
    if (y <= (-1.5d-136)) then
        tmp = t_1
    else if (y <= (-1.7d-263)) then
        tmp = z
    else if (y <= 5.4d+71) then
        tmp = z + a
    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 = (z + a) - b;
	double tmp;
	if (y <= -1.5e-136) {
		tmp = t_1;
	} else if (y <= -1.7e-263) {
		tmp = z;
	} else if (y <= 5.4e+71) {
		tmp = z + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	tmp = 0
	if y <= -1.5e-136:
		tmp = t_1
	elif y <= -1.7e-263:
		tmp = z
	elif y <= 5.4e+71:
		tmp = z + a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -1.5e-136)
		tmp = t_1;
	elseif (y <= -1.7e-263)
		tmp = z;
	elseif (y <= 5.4e+71)
		tmp = Float64(z + a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	tmp = 0.0;
	if (y <= -1.5e-136)
		tmp = t_1;
	elseif (y <= -1.7e-263)
		tmp = z;
	elseif (y <= 5.4e+71)
		tmp = z + a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -1.5e-136], t$95$1, If[LessEqual[y, -1.7e-263], z, If[LessEqual[y, 5.4e+71], N[(z + a), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.4999999999999999e-136 or 5.39999999999999993e71 < y

   1. Initial program 46.0%

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

   3. Taylor expanded in y around inf

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

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

         \[\leadsto \mathsf{\_.f64}\left(\left(a + z\right), \color{blue}{b}\right) \]

      2. +-lowering-+.f64 68.3%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(a, z\right), b\right) \]

   5. Simplified 68.3%

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

   if -1.4999999999999999e-136 < y < -1.70000000000000002e-263

   1. Initial program 82.4%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 51.7%

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

   if -1.70000000000000002e-263 < y < 5.39999999999999993e71

   1. Initial program 77.9%

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

   3. Taylor expanded in y around inf

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

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

         \[\leadsto \mathsf{\_.f64}\left(\left(a + z\right), \color{blue}{b}\right) \]

      2. +-lowering-+.f64 41.3%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(a, z\right), b\right) \]

   5. Simplified 41.3%

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

   6. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 52.4%

         \[\leadsto \mathsf{+.f64}\left(z, \color{blue}{a}\right) \]

   8. Simplified 52.4%

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

4. Final simplification 61.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{-136}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-263}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{+71}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 60.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -15500000000000:\\ \;\;\;\;a + y \cdot \frac{z - b}{t}\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{+225}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a + x \cdot \frac{z - a}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -15500000000000.0)
   (+ a (* y (/ (- z b) t)))
   (if (<= t 2.3e+225) (- (+ z a) b) (+ a (* x (/ (- z a) t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -15500000000000.0) {
		tmp = a + (y * ((z - b) / t));
	} else if (t <= 2.3e+225) {
		tmp = (z + a) - b;
	} else {
		tmp = a + (x * ((z - a) / 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 <= (-15500000000000.0d0)) then
        tmp = a + (y * ((z - b) / t))
    else if (t <= 2.3d+225) then
        tmp = (z + a) - b
    else
        tmp = a + (x * ((z - a) / 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 <= -15500000000000.0) {
		tmp = a + (y * ((z - b) / t));
	} else if (t <= 2.3e+225) {
		tmp = (z + a) - b;
	} else {
		tmp = a + (x * ((z - a) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -15500000000000.0:
		tmp = a + (y * ((z - b) / t))
	elif t <= 2.3e+225:
		tmp = (z + a) - b
	else:
		tmp = a + (x * ((z - a) / t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -15500000000000.0)
		tmp = Float64(a + Float64(y * Float64(Float64(z - b) / t)));
	elseif (t <= 2.3e+225)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(a + Float64(x * Float64(Float64(z - a) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -15500000000000.0)
		tmp = a + (y * ((z - b) / t));
	elseif (t <= 2.3e+225)
		tmp = (z + a) - b;
	else
		tmp = a + (x * ((z - a) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -15500000000000.0], N[(a + N[(y * N[(N[(z - b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.3e+225], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(a + N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.55e13

   1. Initial program 55.5%

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

   3. Taylor expanded in t around -inf

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

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

         \[\leadsto \mathsf{+.f64}\left(a, \color{blue}{\left(-1 \cdot \frac{-1 \cdot \left(\left(a \cdot y + z \cdot \left(x + y\right)\right) - b \cdot y\right) - -1 \cdot \left(a \cdot \left(x + y\right)\right)}{t}\right)}\right) \]

      2. associate-*r/ N/A

         \[\leadsto \mathsf{+.f64}\left(a, \left(\frac{-1 \cdot \left(-1 \cdot \left(\left(a \cdot y + z \cdot \left(x + y\right)\right) - b \cdot y\right) - -1 \cdot \left(a \cdot \left(x + y\right)\right)\right)}{\color{blue}{t}}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(a, \mathsf{/.f64}\left(\left(-1 \cdot \left(-1 \cdot \left(\left(a \cdot y + z \cdot \left(x + y\right)\right) - b \cdot y\right) - -1 \cdot \left(a \cdot \left(x + y\right)\right)\right)\right), \color{blue}{t}\right)\right) \]

   5. Simplified 56.0%

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

   6. Taylor expanded in y around inf

      \[\leadsto \mathsf{+.f64}\left(a, \color{blue}{\left(\frac{y \cdot \left(z - b\right)}{t}\right)}\right) \]
   7. Step-by-step derivation

      1. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(a, \left(y \cdot \color{blue}{\frac{z - b}{t}}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{z - b}{t}\right)}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(\left(z - b\right), \color{blue}{t}\right)\right)\right) \]

      4. --lowering--.f64 65.8%

         \[\leadsto \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, b\right), t\right)\right)\right) \]

   8. Simplified 65.8%

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

   if -1.55e13 < t < 2.3e225

   1. Initial program 63.5%

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

   3. Taylor expanded in y around inf

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

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

         \[\leadsto \mathsf{\_.f64}\left(\left(a + z\right), \color{blue}{b}\right) \]

      2. +-lowering-+.f64 58.5%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(a, z\right), b\right) \]

   5. Simplified 58.5%

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

   if 2.3e225 < t

   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 t around -inf

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

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

         \[\leadsto \mathsf{+.f64}\left(a, \color{blue}{\left(-1 \cdot \frac{-1 \cdot \left(\left(a \cdot y + z \cdot \left(x + y\right)\right) - b \cdot y\right) - -1 \cdot \left(a \cdot \left(x + y\right)\right)}{t}\right)}\right) \]

      2. associate-*r/ N/A

         \[\leadsto \mathsf{+.f64}\left(a, \left(\frac{-1 \cdot \left(-1 \cdot \left(\left(a \cdot y + z \cdot \left(x + y\right)\right) - b \cdot y\right) - -1 \cdot \left(a \cdot \left(x + y\right)\right)\right)}{\color{blue}{t}}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(a, \mathsf{/.f64}\left(\left(-1 \cdot \left(-1 \cdot \left(\left(a \cdot y + z \cdot \left(x + y\right)\right) - b \cdot y\right) - -1 \cdot \left(a \cdot \left(x + y\right)\right)\right)\right), \color{blue}{t}\right)\right) \]

   5. Simplified 43.6%

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

   6. Taylor expanded in x around inf

      \[\leadsto \mathsf{+.f64}\left(a, \mathsf{/.f64}\left(\color{blue}{\left(x \cdot \left(z - a\right)\right)}, t\right)\right) \]
   7. Step-by-step derivation

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

         \[\leadsto \mathsf{+.f64}\left(a, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(z - a\right)\right), t\right)\right) \]

      2. --lowering--.f64 46.1%

         \[\leadsto \mathsf{+.f64}\left(a, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(z, a\right)\right), t\right)\right) \]

   8. Simplified 46.1%

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

      1. +-commutative N/A

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

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

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{x \cdot \left(z - a\right)}{t}\right), \color{blue}{a}\right) \]

      3. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot \frac{z - a}{t}\right), a\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \left(\frac{z - a}{t}\right)\right), a\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(z - a\right), t\right)\right), a\right) \]

      6. --lowering--.f64 71.0%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, a\right), t\right)\right), a\right) \]

   10. Applied egg-rr 71.0%

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

4. Final simplification 60.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -15500000000000:\\ \;\;\;\;a + y \cdot \frac{z - b}{t}\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{+225}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a + x \cdot \frac{z - a}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 59.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -15500000000000:\\ \;\;\;\;a + y \cdot \frac{z - b}{t}\\ \mathbf{elif}\;t \leq 9.6 \cdot 10^{+222}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a + \frac{x \cdot z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -15500000000000.0)
   (+ a (* y (/ (- z b) t)))
   (if (<= t 9.6e+222) (- (+ z a) b) (+ a (/ (* x z) t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -15500000000000.0) {
		tmp = a + (y * ((z - b) / t));
	} else if (t <= 9.6e+222) {
		tmp = (z + a) - b;
	} else {
		tmp = a + ((x * z) / 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 <= (-15500000000000.0d0)) then
        tmp = a + (y * ((z - b) / t))
    else if (t <= 9.6d+222) then
        tmp = (z + a) - b
    else
        tmp = a + ((x * z) / 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 <= -15500000000000.0) {
		tmp = a + (y * ((z - b) / t));
	} else if (t <= 9.6e+222) {
		tmp = (z + a) - b;
	} else {
		tmp = a + ((x * z) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -15500000000000.0:
		tmp = a + (y * ((z - b) / t))
	elif t <= 9.6e+222:
		tmp = (z + a) - b
	else:
		tmp = a + ((x * z) / t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -15500000000000.0)
		tmp = Float64(a + Float64(y * Float64(Float64(z - b) / t)));
	elseif (t <= 9.6e+222)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(a + Float64(Float64(x * z) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -15500000000000.0)
		tmp = a + (y * ((z - b) / t));
	elseif (t <= 9.6e+222)
		tmp = (z + a) - b;
	else
		tmp = a + ((x * z) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -15500000000000.0], N[(a + N[(y * N[(N[(z - b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.6e+222], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(a + N[(N[(x * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.55e13

   1. Initial program 55.5%

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

   3. Taylor expanded in t around -inf

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

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

         \[\leadsto \mathsf{+.f64}\left(a, \color{blue}{\left(-1 \cdot \frac{-1 \cdot \left(\left(a \cdot y + z \cdot \left(x + y\right)\right) - b \cdot y\right) - -1 \cdot \left(a \cdot \left(x + y\right)\right)}{t}\right)}\right) \]

      2. associate-*r/ N/A

         \[\leadsto \mathsf{+.f64}\left(a, \left(\frac{-1 \cdot \left(-1 \cdot \left(\left(a \cdot y + z \cdot \left(x + y\right)\right) - b \cdot y\right) - -1 \cdot \left(a \cdot \left(x + y\right)\right)\right)}{\color{blue}{t}}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(a, \mathsf{/.f64}\left(\left(-1 \cdot \left(-1 \cdot \left(\left(a \cdot y + z \cdot \left(x + y\right)\right) - b \cdot y\right) - -1 \cdot \left(a \cdot \left(x + y\right)\right)\right)\right), \color{blue}{t}\right)\right) \]

   5. Simplified 56.0%

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

   6. Taylor expanded in y around inf

      \[\leadsto \mathsf{+.f64}\left(a, \color{blue}{\left(\frac{y \cdot \left(z - b\right)}{t}\right)}\right) \]
   7. Step-by-step derivation

      1. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(a, \left(y \cdot \color{blue}{\frac{z - b}{t}}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{z - b}{t}\right)}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(\left(z - b\right), \color{blue}{t}\right)\right)\right) \]

      4. --lowering--.f64 65.8%

         \[\leadsto \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, b\right), t\right)\right)\right) \]

   8. Simplified 65.8%

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

   if -1.55e13 < t < 9.6000000000000004e222

   1. Initial program 63.5%

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

   3. Taylor expanded in y around inf

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

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

         \[\leadsto \mathsf{\_.f64}\left(\left(a + z\right), \color{blue}{b}\right) \]

      2. +-lowering-+.f64 58.5%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(a, z\right), b\right) \]

   5. Simplified 58.5%

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

   if 9.6000000000000004e222 < t

   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 t around -inf

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

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

         \[\leadsto \mathsf{+.f64}\left(a, \color{blue}{\left(-1 \cdot \frac{-1 \cdot \left(\left(a \cdot y + z \cdot \left(x + y\right)\right) - b \cdot y\right) - -1 \cdot \left(a \cdot \left(x + y\right)\right)}{t}\right)}\right) \]

      2. associate-*r/ N/A

         \[\leadsto \mathsf{+.f64}\left(a, \left(\frac{-1 \cdot \left(-1 \cdot \left(\left(a \cdot y + z \cdot \left(x + y\right)\right) - b \cdot y\right) - -1 \cdot \left(a \cdot \left(x + y\right)\right)\right)}{\color{blue}{t}}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(a, \mathsf{/.f64}\left(\left(-1 \cdot \left(-1 \cdot \left(\left(a \cdot y + z \cdot \left(x + y\right)\right) - b \cdot y\right) - -1 \cdot \left(a \cdot \left(x + y\right)\right)\right)\right), \color{blue}{t}\right)\right) \]

   5. Simplified 43.6%

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

   6. Taylor expanded in x around inf

      \[\leadsto \mathsf{+.f64}\left(a, \mathsf{/.f64}\left(\color{blue}{\left(x \cdot \left(z - a\right)\right)}, t\right)\right) \]
   7. Step-by-step derivation

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

         \[\leadsto \mathsf{+.f64}\left(a, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(z - a\right)\right), t\right)\right) \]

      2. --lowering--.f64 46.1%

         \[\leadsto \mathsf{+.f64}\left(a, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(z, a\right)\right), t\right)\right) \]

   8. Simplified 46.1%

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

   9. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(a, \color{blue}{\left(\frac{x \cdot z}{t}\right)}\right) \]
   10. Step-by-step derivation

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

          \[\leadsto \mathsf{+.f64}\left(a, \mathsf{/.f64}\left(\left(x \cdot z\right), \color{blue}{t}\right)\right) \]

       2. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(a, \mathsf{/.f64}\left(\left(z \cdot x\right), t\right)\right) \]

       3. *-lowering-*.f64 62.3%

          \[\leadsto \mathsf{+.f64}\left(a, \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, x\right), t\right)\right) \]

   11. Simplified 62.3%

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

4. Final simplification 60.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -15500000000000:\\ \;\;\;\;a + y \cdot \frac{z - b}{t}\\ \mathbf{elif}\;t \leq 9.6 \cdot 10^{+222}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a + \frac{x \cdot z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 52.2% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -9.5 \cdot 10^{+134}:\\ \;\;\;\;a - b\\ \mathbf{elif}\;b \leq 1.95 \cdot 10^{+202}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;z - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -9.5e+134) (- a b) (if (<= b 1.95e+202) (+ z a) (- z b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -9.5e+134) {
		tmp = a - b;
	} else if (b <= 1.95e+202) {
		tmp = z + a;
	} 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 <= (-9.5d+134)) then
        tmp = a - b
    else if (b <= 1.95d+202) then
        tmp = z + a
    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 <= -9.5e+134) {
		tmp = a - b;
	} else if (b <= 1.95e+202) {
		tmp = z + a;
	} else {
		tmp = z - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -9.5e+134:
		tmp = a - b
	elif b <= 1.95e+202:
		tmp = z + a
	else:
		tmp = z - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -9.5e+134)
		tmp = Float64(a - b);
	elseif (b <= 1.95e+202)
		tmp = Float64(z + a);
	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 <= -9.5e+134)
		tmp = a - b;
	elseif (b <= 1.95e+202)
		tmp = z + a;
	else
		tmp = z - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -9.5e+134], N[(a - b), $MachinePrecision], If[LessEqual[b, 1.95e+202], N[(z + a), $MachinePrecision], N[(z - b), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -9.5000000000000004e134

   1. Initial program 48.9%

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

   3. Taylor expanded in y around inf

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

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

         \[\leadsto \mathsf{\_.f64}\left(\left(a + z\right), \color{blue}{b}\right) \]

      2. +-lowering-+.f64 47.8%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(a, z\right), b\right) \]

   5. Simplified 47.8%

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

   6. Taylor expanded in z around 0

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

      1. --lowering--.f64 44.8%

         \[\leadsto \mathsf{\_.f64}\left(a, \color{blue}{b}\right) \]

   8. Simplified 44.8%

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

   if -9.5000000000000004e134 < b < 1.94999999999999992e202

   1. Initial program 64.8%

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

   3. Taylor expanded in y around inf

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

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

         \[\leadsto \mathsf{\_.f64}\left(\left(a + z\right), \color{blue}{b}\right) \]

      2. +-lowering-+.f64 56.8%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(a, z\right), b\right) \]

   5. Simplified 56.8%

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

   6. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 58.1%

         \[\leadsto \mathsf{+.f64}\left(z, \color{blue}{a}\right) \]

   8. Simplified 58.1%

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

   if 1.94999999999999992e202 < 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 y around inf

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

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

         \[\leadsto \mathsf{\_.f64}\left(\left(a + z\right), \color{blue}{b}\right) \]

      2. +-lowering-+.f64 41.9%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(a, z\right), b\right) \]

   5. Simplified 41.9%

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

   6. Taylor expanded in a around 0

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

      1. --lowering--.f64 42.0%

         \[\leadsto \mathsf{\_.f64}\left(z, \color{blue}{b}\right) \]

   8. Simplified 42.0%

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

Alternative 11: 52.1% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.4 \cdot 10^{+135}:\\ \;\;\;\;a - b\\ \mathbf{elif}\;b \leq 9 \cdot 10^{+192}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;a - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.4e+135) (- a b) (if (<= b 9e+192) (+ z a) (- a b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.4e+135) {
		tmp = a - b;
	} else if (b <= 9e+192) {
		tmp = z + a;
	} else {
		tmp = 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 <= (-1.4d+135)) then
        tmp = a - b
    else if (b <= 9d+192) then
        tmp = z + a
    else
        tmp = 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 <= -1.4e+135) {
		tmp = a - b;
	} else if (b <= 9e+192) {
		tmp = z + a;
	} else {
		tmp = a - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.4e+135:
		tmp = a - b
	elif b <= 9e+192:
		tmp = z + a
	else:
		tmp = a - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.4e+135)
		tmp = Float64(a - b);
	elseif (b <= 9e+192)
		tmp = Float64(z + a);
	else
		tmp = Float64(a - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.4e+135)
		tmp = a - b;
	elseif (b <= 9e+192)
		tmp = z + a;
	else
		tmp = a - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.4e+135], N[(a - b), $MachinePrecision], If[LessEqual[b, 9e+192], N[(z + a), $MachinePrecision], N[(a - b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if b < -1.40000000000000001e135 or 9e192 < b

   1. Initial program 46.3%

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

   3. Taylor expanded in y around inf

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

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

         \[\leadsto \mathsf{\_.f64}\left(\left(a + z\right), \color{blue}{b}\right) \]

      2. +-lowering-+.f64 46.3%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(a, z\right), b\right) \]

   5. Simplified 46.3%

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

   6. Taylor expanded in z around 0

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

      1. --lowering--.f64 42.0%

         \[\leadsto \mathsf{\_.f64}\left(a, \color{blue}{b}\right) \]

   8. Simplified 42.0%

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

   if -1.40000000000000001e135 < b < 9e192

   1. Initial program 65.1%

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

   3. Taylor expanded in y around inf

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

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

         \[\leadsto \mathsf{\_.f64}\left(\left(a + z\right), \color{blue}{b}\right) \]

      2. +-lowering-+.f64 56.6%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(a, z\right), b\right) \]

   5. Simplified 56.6%

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

   6. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 58.1%

         \[\leadsto \mathsf{+.f64}\left(z, \color{blue}{a}\right) \]

   8. Simplified 58.1%

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

Alternative 12: 44.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4 \cdot 10^{+65}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 9 \cdot 10^{+46}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -4e+65) a (if (<= a 9e+46) z a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -4e+65) {
		tmp = a;
	} else if (a <= 9e+46) {
		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 (a <= (-4d+65)) then
        tmp = a
    else if (a <= 9d+46) 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 (a <= -4e+65) {
		tmp = a;
	} else if (a <= 9e+46) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -4e+65:
		tmp = a
	elif a <= 9e+46:
		tmp = z
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -4e+65)
		tmp = a;
	elseif (a <= 9e+46)
		tmp = z;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -4e+65)
		tmp = a;
	elseif (a <= 9e+46)
		tmp = z;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -4e+65], a, If[LessEqual[a, 9e+46], z, a]]

Derivation

1. Split input into 2 regimes

2. if a < -4e65 or 9.00000000000000019e46 < a

   1. Initial program 44.7%

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

   3. Taylor expanded in t around inf

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

   5. Simplified 51.3%

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

   if -4e65 < a < 9.00000000000000019e46

   1. Initial program 71.8%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 44.1%

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

Alternative 13: 51.4% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 3.6 \cdot 10^{+195}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;0 - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 3.6e+195) (+ z a) (- 0.0 b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 3.6e+195) {
		tmp = z + a;
	} else {
		tmp = 0.0 - 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 <= 3.6d+195) then
        tmp = z + a
    else
        tmp = 0.0d0 - 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 <= 3.6e+195) {
		tmp = z + a;
	} else {
		tmp = 0.0 - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 3.6e+195:
		tmp = z + a
	else:
		tmp = 0.0 - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 3.6e+195)
		tmp = Float64(z + a);
	else
		tmp = Float64(0.0 - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 3.6e+195)
		tmp = z + a;
	else
		tmp = 0.0 - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 3.6e+195], N[(z + a), $MachinePrecision], N[(0.0 - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 3.5999999999999999e195

   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 y around inf

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

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

         \[\leadsto \mathsf{\_.f64}\left(\left(a + z\right), \color{blue}{b}\right) \]

      2. +-lowering-+.f64 55.5%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(a, z\right), b\right) \]

   5. Simplified 55.5%

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

   6. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 53.7%

         \[\leadsto \mathsf{+.f64}\left(z, \color{blue}{a}\right) \]

   8. Simplified 53.7%

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

   if 3.5999999999999999e195 < 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 t around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\color{blue}{\left(a \cdot t\right)}, \mathsf{*.f64}\left(y, b\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, t\right), y\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 36.6%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, t\right), \mathsf{*.f64}\left(y, b\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(\color{blue}{x}, t\right), y\right)\right) \]

   5. Simplified 36.6%

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

   6. Taylor expanded in y around inf

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

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(b\right) \]

      2. neg-lowering-neg.f64 35.6%

         \[\leadsto \mathsf{neg.f64}\left(b\right) \]

   8. Simplified 35.6%

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

4. Final simplification 52.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 3.6 \cdot 10^{+195}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;0 - b\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 32.5% accurate, 21.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 60.8%

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

3. Taylor expanded in t around inf

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

5. Simplified 29.3%

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

Developer Target 1: 81.7% 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 2024163 
(FPCore (x y z t a b)
  :name "AI.Clustering.Hierarchical.Internal:ward from clustering-0.2.1"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)) -3581311708415056400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (+ z a) b) (if (< (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)) 12285964308315609000000000000000000000000000000000000000000000000000000000000000000) (/ 1 (/ (+ (+ x t) y) (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)))) (- (+ z a) b))))

  (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)))