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

Percentage Accurate: 60.1% → 89.1%

Time: 8.8s

Alternatives: 12

Speedup: 1.4×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 60.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 89.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\\ t_2 := \frac{y}{y + x} \cdot b\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\mathsf{fma}\left(a, \frac{y}{x + y}, z\right) - t\_2\\ \mathbf{elif}\;t\_1 \leq 10^{+218}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)))
        (t_2 (* (/ y (+ y x)) b)))
   (if (<= t_1 (- INFINITY))
     (- (fma a (/ y (+ x y)) z) t_2)
     (if (<= t_1 1e+218) t_1 (- (+ z a) t_2)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y);
	double t_2 = (y / (y + x)) * b;
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = fma(a, (y / (x + y)), z) - t_2;
	} else if (t_1 <= 1e+218) {
		tmp = t_1;
	} else {
		tmp = (z + a) - t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(Float64(Float64(x + y) * z) + Float64(Float64(t + y) * a)) - Float64(y * b)) / Float64(Float64(x + t) + y))
	t_2 = Float64(Float64(y / Float64(y + x)) * b)
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(fma(a, Float64(y / Float64(x + y)), z) - t_2);
	elseif (t_1 <= 1e+218)
		tmp = t_1;
	else
		tmp = Float64(Float64(z + a) - t_2);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + N[(N[(t + y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(N[(x + t), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y / N[(y + x), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(a * N[(y / N[(x + y), $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision] - t$95$2), $MachinePrecision], If[LessEqual[t$95$1, 1e+218], t$95$1, N[(N[(z + a), $MachinePrecision] - t$95$2), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 6.2%

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

   3. Taylor expanded in t around 0

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

      1. lower--.f64 N/A

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

   5. Applied rewrites 73.4%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 75.8%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1.00000000000000008e218

   1. Initial program 99.1%

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

   if 1.00000000000000008e218 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 11.0%

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

   3. Taylor expanded in t around 0

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

      1. lower--.f64 N/A

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

   5. Applied rewrites 74.1%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 82.2%

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

Alternative 2: 80.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -750000000000 \lor \neg \left(x \leq 9.6 \cdot 10^{+42}\right):\\ \;\;\;\;\mathsf{fma}\left(a, \frac{y}{x + y}, z\right) - \frac{y}{y + x} \cdot b\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z - b, \frac{y}{t + y}, a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= x -750000000000.0) (not (<= x 9.6e+42)))
   (- (fma a (/ y (+ x y)) z) (* (/ y (+ y x)) b))
   (fma (- z b) (/ y (+ t y)) a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x <= -750000000000.0) || !(x <= 9.6e+42)) {
		tmp = fma(a, (y / (x + y)), z) - ((y / (y + x)) * b);
	} else {
		tmp = fma((z - b), (y / (t + y)), a);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((x <= -750000000000.0) || !(x <= 9.6e+42))
		tmp = Float64(fma(a, Float64(y / Float64(x + y)), z) - Float64(Float64(y / Float64(y + x)) * b));
	else
		tmp = fma(Float64(z - b), Float64(y / Float64(t + y)), a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[x, -750000000000.0], N[Not[LessEqual[x, 9.6e+42]], $MachinePrecision]], N[(N[(a * N[(y / N[(x + y), $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision] - N[(N[(y / N[(y + x), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], N[(N[(z - b), $MachinePrecision] * N[(y / N[(t + y), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -7.5e11 or 9.5999999999999994e42 < x

   1. Initial program 60.3%

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

   3. Taylor expanded in t around 0

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

      1. lower--.f64 N/A

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

   5. Applied rewrites 80.9%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 76.5%

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

   if -7.5e11 < x < 9.5999999999999994e42

   1. Initial program 62.5%

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

   3. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-+.f64 N/A

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

      6. *-commutative N/A

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

      7. distribute-lft-out-- N/A

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

      8. lower-*.f64 N/A

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

      9. lower--.f64 N/A

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

      10. lower-+.f64 55.5

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

   5. Applied rewrites 55.5%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 87.4%

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

   10. Applied rewrites 91.9%

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

4. Final simplification 85.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -750000000000 \lor \neg \left(x \leq 9.6 \cdot 10^{+42}\right):\\ \;\;\;\;\mathsf{fma}\left(a, \frac{y}{x + y}, z\right) - \frac{y}{y + x} \cdot b\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z - b, \frac{y}{t + y}, a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -14000 \lor \neg \left(x \leq 4.1 \cdot 10^{+40}\right):\\ \;\;\;\;\left(z + a\right) - \frac{y}{y + x} \cdot b\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z - b, \frac{y}{t + y}, a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= x -14000.0) (not (<= x 4.1e+40)))
   (- (+ z a) (* (/ y (+ y x)) b))
   (fma (- z b) (/ y (+ t y)) a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x <= -14000.0) || !(x <= 4.1e+40)) {
		tmp = (z + a) - ((y / (y + x)) * b);
	} else {
		tmp = fma((z - b), (y / (t + y)), a);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((x <= -14000.0) || !(x <= 4.1e+40))
		tmp = Float64(Float64(z + a) - Float64(Float64(y / Float64(y + x)) * b));
	else
		tmp = fma(Float64(z - b), Float64(y / Float64(t + y)), a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[x, -14000.0], N[Not[LessEqual[x, 4.1e+40]], $MachinePrecision]], N[(N[(z + a), $MachinePrecision] - N[(N[(y / N[(y + x), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], N[(N[(z - b), $MachinePrecision] * N[(y / N[(t + y), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -14000 or 4.1000000000000002e40 < x

   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 0

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

      1. lower--.f64 N/A

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

   5. Applied rewrites 79.0%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 67.3%

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

   if -14000 < x < 4.1000000000000002e40

   1. Initial program 62.1%

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

   3. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-+.f64 N/A

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

      6. *-commutative N/A

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

      7. distribute-lft-out-- N/A

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

      8. lower-*.f64 N/A

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

      9. lower--.f64 N/A

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

      10. lower-+.f64 55.6

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

   5. Applied rewrites 55.6%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 87.8%

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

   10. Applied rewrites 92.4%

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

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -14000 \lor \neg \left(x \leq 4.1 \cdot 10^{+40}\right):\\ \;\;\;\;\left(z + a\right) - \frac{y}{y + x} \cdot b\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z - b, \frac{y}{t + y}, a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 58.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a + z\right) - b\\ \mathbf{if}\;y \leq -8 \cdot 10^{+103}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-187}:\\ \;\;\;\;a + z\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-125}:\\ \;\;\;\;a \cdot \frac{t}{t + x}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ a z) b)))
   (if (<= y -8e+103)
     t_1
     (if (<= y -3e-187)
       (+ a z)
       (if (<= y 1.9e-125) (* a (/ t (+ t x))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a + z) - b;
	double tmp;
	if (y <= -8e+103) {
		tmp = t_1;
	} else if (y <= -3e-187) {
		tmp = a + z;
	} else if (y <= 1.9e-125) {
		tmp = a * (t / (t + x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a + z) - b
    if (y <= (-8d+103)) then
        tmp = t_1
    else if (y <= (-3d-187)) then
        tmp = a + z
    else if (y <= 1.9d-125) then
        tmp = a * (t / (t + x))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a + z) - b;
	double tmp;
	if (y <= -8e+103) {
		tmp = t_1;
	} else if (y <= -3e-187) {
		tmp = a + z;
	} else if (y <= 1.9e-125) {
		tmp = a * (t / (t + x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a + z) - b
	tmp = 0
	if y <= -8e+103:
		tmp = t_1
	elif y <= -3e-187:
		tmp = a + z
	elif y <= 1.9e-125:
		tmp = a * (t / (t + x))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a + z) - b)
	tmp = 0.0
	if (y <= -8e+103)
		tmp = t_1;
	elseif (y <= -3e-187)
		tmp = Float64(a + z);
	elseif (y <= 1.9e-125)
		tmp = Float64(a * Float64(t / Float64(t + x)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a + z) - b;
	tmp = 0.0;
	if (y <= -8e+103)
		tmp = t_1;
	elseif (y <= -3e-187)
		tmp = a + z;
	elseif (y <= 1.9e-125)
		tmp = a * (t / (t + x));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -8e+103], t$95$1, If[LessEqual[y, -3e-187], N[(a + z), $MachinePrecision], If[LessEqual[y, 1.9e-125], N[(a * N[(t / N[(t + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -8e103 or 1.9000000000000001e-125 < 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. lower--.f64 N/A

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

      2. lower-+.f64 72.7

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

   5. Applied rewrites 72.7%

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

   if -8e103 < y < -3.00000000000000004e-187

   1. Initial program 73.9%

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

   3. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 46.5

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

   5. Applied rewrites 46.5%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 32.9%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 58.9%

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

   if -3.00000000000000004e-187 < y < 1.9000000000000001e-125

   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 a around inf

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-+.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 N/A

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

      8. +-commutative N/A

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

      9. lower-+.f64 54.5

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

   5. Applied rewrites 54.5%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 64.3%

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

Alternative 5: 74.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -14000:\\ \;\;\;\;\left(z + a\right) - \frac{y}{y + x} \cdot b\\ \mathbf{elif}\;x \leq 4.1 \cdot 10^{+40}:\\ \;\;\;\;\mathsf{fma}\left(z - b, \frac{y}{t + y}, a\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{-y}{y + x}, b, a + z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -14000.0)
   (- (+ z a) (* (/ y (+ y x)) b))
   (if (<= x 4.1e+40)
     (fma (- z b) (/ y (+ t y)) a)
     (fma (/ (- y) (+ y x)) b (+ a z)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -14000.0) {
		tmp = (z + a) - ((y / (y + x)) * b);
	} else if (x <= 4.1e+40) {
		tmp = fma((z - b), (y / (t + y)), a);
	} else {
		tmp = fma((-y / (y + x)), b, (a + z));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -14000.0)
		tmp = Float64(Float64(z + a) - Float64(Float64(y / Float64(y + x)) * b));
	elseif (x <= 4.1e+40)
		tmp = fma(Float64(z - b), Float64(y / Float64(t + y)), a);
	else
		tmp = fma(Float64(Float64(-y) / Float64(y + x)), b, Float64(a + z));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -14000.0], N[(N[(z + a), $MachinePrecision] - N[(N[(y / N[(y + x), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.1e+40], N[(N[(z - b), $MachinePrecision] * N[(y / N[(t + y), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision], N[(N[((-y) / N[(y + x), $MachinePrecision]), $MachinePrecision] * b + N[(a + z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -14000

   1. Initial program 59.6%

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

   3. Taylor expanded in t around 0

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

      1. lower--.f64 N/A

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

   5. Applied rewrites 77.6%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 65.2%

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

   if -14000 < x < 4.1000000000000002e40

   1. Initial program 62.1%

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

   3. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-+.f64 N/A

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

      6. *-commutative N/A

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

      7. distribute-lft-out-- N/A

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

      8. lower-*.f64 N/A

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

      9. lower--.f64 N/A

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

      10. lower-+.f64 55.6

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

   5. Applied rewrites 55.6%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 87.8%

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

   10. Applied rewrites 92.4%

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

   if 4.1000000000000002e40 < x

   1. Initial program 62.6%

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

   3. Taylor expanded in t around 0

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

      1. lower--.f64 N/A

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

   5. Applied rewrites 81.2%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 70.2%

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

   10. Applied rewrites 70.2%

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

Alternative 6: 74.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{+139} \lor \neg \left(x \leq 2.5 \cdot 10^{+172}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{a - z}{x}, t, z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z - b, \frac{y}{t + y}, a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= x -2.4e+139) (not (<= x 2.5e+172)))
   (fma (/ (- a z) x) t z)
   (fma (- z b) (/ y (+ t y)) a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x <= -2.4e+139) || !(x <= 2.5e+172)) {
		tmp = fma(((a - z) / x), t, z);
	} else {
		tmp = fma((z - b), (y / (t + y)), a);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((x <= -2.4e+139) || !(x <= 2.5e+172))
		tmp = fma(Float64(Float64(a - z) / x), t, z);
	else
		tmp = fma(Float64(z - b), Float64(y / Float64(t + y)), a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[x, -2.4e+139], N[Not[LessEqual[x, 2.5e+172]], $MachinePrecision]], N[(N[(N[(a - z), $MachinePrecision] / x), $MachinePrecision] * t + z), $MachinePrecision], N[(N[(z - b), $MachinePrecision] * N[(y / N[(t + y), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.40000000000000008e139 or 2.5e172 < x

   1. Initial program 59.4%

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

   3. Taylor expanded in t around 0

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

      1. lower--.f64 N/A

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

   5. Applied rewrites 80.2%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 59.6%

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

   if -2.40000000000000008e139 < x < 2.5e172

   1. Initial program 62.1%

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

   3. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-+.f64 N/A

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

      6. *-commutative N/A

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

      7. distribute-lft-out-- N/A

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

      8. lower-*.f64 N/A

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

      9. lower--.f64 N/A

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

      10. lower-+.f64 49.1

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

   5. Applied rewrites 49.1%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 79.7%

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

   10. Applied rewrites 83.3%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{+139} \lor \neg \left(x \leq 2.5 \cdot 10^{+172}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{a - z}{x}, t, z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z - b, \frac{y}{t + y}, a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 72.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{+133} \lor \neg \left(x \leq 2.5 \cdot 10^{+172}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{a - z}{x}, t, z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z - b}{t + y}, a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= x -1.4e+133) (not (<= x 2.5e+172)))
   (fma (/ (- a z) x) t z)
   (fma y (/ (- z b) (+ t y)) a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x <= -1.4e+133) || !(x <= 2.5e+172)) {
		tmp = fma(((a - z) / x), t, z);
	} else {
		tmp = fma(y, ((z - b) / (t + y)), a);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((x <= -1.4e+133) || !(x <= 2.5e+172))
		tmp = fma(Float64(Float64(a - z) / x), t, z);
	else
		tmp = fma(y, Float64(Float64(z - b) / Float64(t + y)), a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[x, -1.4e+133], N[Not[LessEqual[x, 2.5e+172]], $MachinePrecision]], N[(N[(N[(a - z), $MachinePrecision] / x), $MachinePrecision] * t + z), $MachinePrecision], N[(y * N[(N[(z - b), $MachinePrecision] / N[(t + y), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.40000000000000008e133 or 2.5e172 < x

   1. Initial program 59.1%

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

   3. Taylor expanded in t around 0

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

      1. lower--.f64 N/A

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

   5. Applied rewrites 80.9%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 59.3%

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

   if -1.40000000000000008e133 < x < 2.5e172

   1. Initial program 62.2%

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

   3. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-+.f64 N/A

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

      6. *-commutative N/A

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

      7. distribute-lft-out-- N/A

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

      8. lower-*.f64 N/A

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

      9. lower--.f64 N/A

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

      10. lower-+.f64 49.6

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

   5. Applied rewrites 49.6%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 80.0%

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

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{+133} \lor \neg \left(x \leq 2.5 \cdot 10^{+172}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{a - z}{x}, t, z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z - b}{t + y}, a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 61.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.6 \cdot 10^{+181} \lor \neg \left(t \leq 8.8 \cdot 10^{+207}\right):\\ \;\;\;\;\mathsf{fma}\left(z - b, \frac{y}{t}, a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -3.6e+181) (not (<= t 8.8e+207)))
   (fma (- z b) (/ y t) a)
   (- (+ a z) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -3.6e+181) || !(t <= 8.8e+207)) {
		tmp = fma((z - b), (y / t), a);
	} else {
		tmp = (a + z) - b;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -3.6e+181) || !(t <= 8.8e+207))
		tmp = fma(Float64(z - b), Float64(y / t), a);
	else
		tmp = Float64(Float64(a + z) - b);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -3.6e+181], N[Not[LessEqual[t, 8.8e+207]], $MachinePrecision]], N[(N[(z - b), $MachinePrecision] * N[(y / t), $MachinePrecision] + a), $MachinePrecision], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.59999999999999985e181 or 8.80000000000000034e207 < t

   1. Initial program 46.6%

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

   3. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-+.f64 N/A

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

      6. *-commutative N/A

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

      7. distribute-lft-out-- N/A

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

      8. lower-*.f64 N/A

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

      9. lower--.f64 N/A

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

      10. lower-+.f64 40.5

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

   5. Applied rewrites 40.5%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 80.1%

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

   10. Applied rewrites 80.1%

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

   11. Taylor expanded in y around 0

       \[\leadsto \mathsf{fma}\left(z - b, \frac{y}{t}, a\right) \]
   12. Step-by-step derivation

   13. Applied rewrites 78.3%

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

   if -3.59999999999999985e181 < t < 8.80000000000000034e207

   1. Initial program 64.5%

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

   3. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 64.9

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

   5. Applied rewrites 64.9%

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

4. Final simplification 67.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.6 \cdot 10^{+181} \lor \neg \left(t \leq 8.8 \cdot 10^{+207}\right):\\ \;\;\;\;\mathsf{fma}\left(z - b, \frac{y}{t}, a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 59.2% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+103} \lor \neg \left(y \leq 2.1 \cdot 10^{-50}\right):\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;a + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -8e+103) (not (<= y 2.1e-50))) (- (+ a z) b) (+ a z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -8e+103) || !(y <= 2.1e-50)) {
		tmp = (a + z) - b;
	} else {
		tmp = a + z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-8d+103)) .or. (.not. (y <= 2.1d-50))) then
        tmp = (a + z) - b
    else
        tmp = a + z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -8e+103) || !(y <= 2.1e-50)) {
		tmp = (a + z) - b;
	} else {
		tmp = a + z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -8e+103) or not (y <= 2.1e-50):
		tmp = (a + z) - b
	else:
		tmp = a + z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -8e+103) || !(y <= 2.1e-50))
		tmp = Float64(Float64(a + z) - b);
	else
		tmp = Float64(a + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -8e+103) || ~((y <= 2.1e-50)))
		tmp = (a + z) - b;
	else
		tmp = a + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -8e+103], N[Not[LessEqual[y, 2.1e-50]], $MachinePrecision]], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision], N[(a + z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8e103 or 2.1000000000000001e-50 < y

   1. Initial program 46.1%

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

   3. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 75.2

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

   5. Applied rewrites 75.2%

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

   if -8e103 < y < 2.1000000000000001e-50

   1. Initial program 77.4%

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

   3. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 41.1

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

   5. Applied rewrites 41.1%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 34.8%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 55.9%

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

4. Final simplification 65.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+103} \lor \neg \left(y \leq 2.1 \cdot 10^{-50}\right):\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;a + z\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 51.8% accurate, 4.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.04 \cdot 10^{+263}:\\ \;\;\;\;a - b\\ \mathbf{else}:\\ \;\;\;\;a + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.04e+263) (- a b) (+ a z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.04e+263) {
		tmp = a - b;
	} else {
		tmp = a + z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-1.04d+263)) then
        tmp = a - b
    else
        tmp = a + z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.04e+263) {
		tmp = a - b;
	} else {
		tmp = a + z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.04e+263:
		tmp = a - b
	else:
		tmp = a + z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.04e+263)
		tmp = Float64(a - b);
	else
		tmp = Float64(a + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.04e+263)
		tmp = a - b;
	else
		tmp = a + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.04e+263], N[(a - b), $MachinePrecision], N[(a + z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.04e263

   1. Initial program 23.6%

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

   3. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 59.6

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

   5. Applied rewrites 59.6%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 59.6%

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

   if -1.04e263 < b

   1. Initial program 64.2%

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

   3. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 58.3

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

   5. Applied rewrites 58.3%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 39.8%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 57.8%

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

Alternative 11: 51.7% accurate, 4.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.08 \cdot 10^{+263}:\\ \;\;\;\;-b\\ \mathbf{else}:\\ \;\;\;\;a + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (if (<= b -1.08e+263) (- b) (+ a z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.08e+263) {
		tmp = -b;
	} else {
		tmp = a + z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-1.08d+263)) then
        tmp = -b
    else
        tmp = a + z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.08e+263) {
		tmp = -b;
	} else {
		tmp = a + z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.08e+263:
		tmp = -b
	else:
		tmp = a + z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.08e+263)
		tmp = Float64(-b);
	else
		tmp = Float64(a + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.08e+263)
		tmp = -b;
	else
		tmp = a + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.08e+263], (-b), N[(a + z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.08e263

   1. Initial program 23.6%

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

   3. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 59.6

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

   5. Applied rewrites 59.6%

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

   6. Taylor expanded in b around inf

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

   8. Applied rewrites 54.4%

      \[\leadsto -b \]

   if -1.08e263 < b

   1. Initial program 64.2%

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

   3. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 58.3

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

   5. Applied rewrites 58.3%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 39.8%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 57.8%

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

Alternative 12: 13.5% accurate, 15.0× speedup

Math

\[\begin{array}{l} \\ -b \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := (-b)

Derivation

1. Initial program 61.5%

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

3. Taylor expanded in y around inf

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

   1. lower--.f64 N/A

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

   2. lower-+.f64 58.4

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

5. Applied rewrites 58.4%

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

6. Taylor expanded in b around inf

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

8. Applied rewrites 14.7%

   \[\leadsto -b \]
9. 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 2024339 
(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)))