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

Percentage Accurate: 61.0% → 91.8%

Time: 14.1s

Alternatives: 16

Speedup: 1.1×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 61.0% 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: 91.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y + t\right) + x\\ t_2 := \frac{y}{t\_1}\\ t_3 := \frac{y + t}{t\_1}\\ \mathbf{if}\;b \leq -1.55 \cdot 10^{-31} \lor \neg \left(b \leq 6.2 \cdot 10^{-73}\right):\\ \;\;\;\;b \cdot \left(-\mathsf{fma}\left(-1, \frac{a \cdot t\_3 + z \cdot \frac{y + x}{t\_1}}{b}, t\_2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\frac{x}{t\_1} + \left(\left(t\_2 + t\_3 \cdot \frac{a}{z}\right) - \frac{\frac{b \cdot y}{z}}{t\_1}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ y t) x)) (t_2 (/ y t_1)) (t_3 (/ (+ y t) t_1)))
   (if (or (<= b -1.55e-31) (not (<= b 6.2e-73)))
     (* b (- (fma -1.0 (/ (+ (* a t_3) (* z (/ (+ y x) t_1))) b) t_2)))
     (* z (+ (/ x t_1) (- (+ t_2 (* t_3 (/ a z))) (/ (/ (* b y) z) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y + t) + x;
	double t_2 = y / t_1;
	double t_3 = (y + t) / t_1;
	double tmp;
	if ((b <= -1.55e-31) || !(b <= 6.2e-73)) {
		tmp = b * -fma(-1.0, (((a * t_3) + (z * ((y + x) / t_1))) / b), t_2);
	} else {
		tmp = z * ((x / t_1) + ((t_2 + (t_3 * (a / z))) - (((b * y) / z) / t_1)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y + t) + x)
	t_2 = Float64(y / t_1)
	t_3 = Float64(Float64(y + t) / t_1)
	tmp = 0.0
	if ((b <= -1.55e-31) || !(b <= 6.2e-73))
		tmp = Float64(b * Float64(-fma(-1.0, Float64(Float64(Float64(a * t_3) + Float64(z * Float64(Float64(y + x) / t_1))) / b), t_2)));
	else
		tmp = Float64(z * Float64(Float64(x / t_1) + Float64(Float64(t_2 + Float64(t_3 * Float64(a / z))) - Float64(Float64(Float64(b * y) / z) / t_1))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y + t), $MachinePrecision] + x), $MachinePrecision]}, Block[{t$95$2 = N[(y / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y + t), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[Or[LessEqual[b, -1.55e-31], N[Not[LessEqual[b, 6.2e-73]], $MachinePrecision]], N[(b * (-N[(-1.0 * N[(N[(N[(a * t$95$3), $MachinePrecision] + N[(z * N[(N[(y + x), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision] + t$95$2), $MachinePrecision])), $MachinePrecision], N[(z * N[(N[(x / t$95$1), $MachinePrecision] + N[(N[(t$95$2 + N[(t$95$3 * N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(b * y), $MachinePrecision] / z), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 2 regimes

2. if b < -1.55e-31 or 6.19999999999999938e-73 < b

   1. Initial program 60.5%

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

   3. Taylor expanded in b around -inf 62.9%

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

      1. associate-*r* 62.9%

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

      2. neg-mul-1 62.9%

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

      3. fma-define 62.9%

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

   5. Simplified 95.7%

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

   if -1.55e-31 < b < 6.19999999999999938e-73

   1. Initial program 62.0%

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

   3. Taylor expanded in z around inf 71.8%

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

      1. associate--l+ 71.8%

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

      2. +-commutative 71.8%

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

      3. associate-+r+ 71.8%

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

      4. +-commutative 71.8%

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

      5. associate-+r+ 71.8%

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

      6. times-frac 85.5%

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

      7. +-commutative 85.5%

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

      8. +-commutative 85.5%

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

      9. associate-+r+ 85.5%

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

      10. associate-/r* 84.5%

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

   5. Simplified 84.5%

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

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.55 \cdot 10^{-31} \lor \neg \left(b \leq 6.2 \cdot 10^{-73}\right):\\ \;\;\;\;b \cdot \left(-\mathsf{fma}\left(-1, \frac{a \cdot \frac{y + t}{\left(y + t\right) + x} + z \cdot \frac{y + x}{\left(y + t\right) + x}}{b}, \frac{y}{\left(y + t\right) + x}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\frac{x}{\left(y + t\right) + x} + \left(\left(\frac{y}{\left(y + t\right) + x} + \frac{y + t}{\left(y + t\right) + x} \cdot \frac{a}{z}\right) - \frac{\frac{b \cdot y}{z}}{\left(y + t\right) + x}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 87.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y + t\right)\\ t_2 := \frac{\left(t\_1 + z \cdot \left(y + x\right)\right) - b \cdot y}{y + \left(t + x\right)}\\ \mathbf{if}\;t\_2 \leq -\infty \lor \neg \left(t\_2 \leq 4 \cdot 10^{+248}\right):\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y + x, z, t\_1\right) - b \cdot y}{\left(y + t\right) + x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (+ y t)))
        (t_2 (/ (- (+ t_1 (* z (+ y x))) (* b y)) (+ y (+ t x)))))
   (if (or (<= t_2 (- INFINITY)) (not (<= t_2 4e+248)))
     (- (+ a z) b)
     (/ (- (fma (+ y x) z t_1) (* b y)) (+ (+ y t) x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (y + t);
	double t_2 = ((t_1 + (z * (y + x))) - (b * y)) / (y + (t + x));
	double tmp;
	if ((t_2 <= -((double) INFINITY)) || !(t_2 <= 4e+248)) {
		tmp = (a + z) - b;
	} else {
		tmp = (fma((y + x), z, t_1) - (b * y)) / ((y + t) + x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(y + t))
	t_2 = Float64(Float64(Float64(t_1 + Float64(z * Float64(y + x))) - Float64(b * y)) / Float64(y + Float64(t + x)))
	tmp = 0.0
	if ((t_2 <= Float64(-Inf)) || !(t_2 <= 4e+248))
		tmp = Float64(Float64(a + z) - b);
	else
		tmp = Float64(Float64(fma(Float64(y + x), z, t_1) - Float64(b * y)) / Float64(Float64(y + t) + x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(t$95$1 + N[(z * N[(y + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * y), $MachinePrecision]), $MachinePrecision] / N[(y + N[(t + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$2, (-Infinity)], N[Not[LessEqual[t$95$2, 4e+248]], $MachinePrecision]], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision], N[(N[(N[(N[(y + x), $MachinePrecision] * z + t$95$1), $MachinePrecision] - N[(b * y), $MachinePrecision]), $MachinePrecision] / N[(N[(y + t), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -inf.0 or 4.00000000000000018e248 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 8.3%

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

   3. Taylor expanded in y around inf 68.9%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 4.00000000000000018e248

   1. Initial program 99.6%

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

      1. fma-define 99.6%

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

      2. +-commutative 99.6%

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

      3. associate-+l+ 99.6%

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

      4. +-commutative 99.6%

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

   3. Simplified 99.6%

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

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(a \cdot \left(y + t\right) + z \cdot \left(y + x\right)\right) - b \cdot y}{y + \left(t + x\right)} \leq -\infty \lor \neg \left(\frac{\left(a \cdot \left(y + t\right) + z \cdot \left(y + x\right)\right) - b \cdot y}{y + \left(t + x\right)} \leq 4 \cdot 10^{+248}\right):\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y + x, z, a \cdot \left(y + t\right)\right) - b \cdot y}{\left(y + t\right) + x}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 87.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(a \cdot \left(y + t\right) + z \cdot \left(y + x\right)\right) - b \cdot y}{y + \left(t + x\right)}\\ \mathbf{if}\;t\_1 \leq -\infty \lor \neg \left(t\_1 \leq 4 \cdot 10^{+248}\right):\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* a (+ y t)) (* z (+ y x))) (* b y)) (+ y (+ t x)))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 4e+248))) (- (+ a z) b) t_1)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (((a * (y + t)) + (z * (y + x))) - (b * y)) / (y + (t + x));
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 4e+248)) {
		tmp = (a + z) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (((a * (y + t)) + (z * (y + x))) - (b * y)) / (y + (t + x));
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 4e+248)) {
		tmp = (a + z) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (((a * (y + t)) + (z * (y + x))) - (b * y)) / (y + (t + x))
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 4e+248):
		tmp = (a + z) - b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(Float64(a * Float64(y + t)) + Float64(z * Float64(y + x))) - Float64(b * y)) / Float64(y + Float64(t + x)))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 4e+248))
		tmp = Float64(Float64(a + z) - b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (((a * (y + t)) + (z * (y + x))) - (b * y)) / (y + (t + x));
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 4e+248)))
		tmp = (a + z) - b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision] + N[(z * N[(y + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * y), $MachinePrecision]), $MachinePrecision] / N[(y + N[(t + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 4e+248]], $MachinePrecision]], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision], t$95$1]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -inf.0 or 4.00000000000000018e248 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 8.3%

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

   3. Taylor expanded in y around inf 68.9%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 4.00000000000000018e248

   1. Initial program 99.6%

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

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(a \cdot \left(y + t\right) + z \cdot \left(y + x\right)\right) - b \cdot y}{y + \left(t + x\right)} \leq -\infty \lor \neg \left(\frac{\left(a \cdot \left(y + t\right) + z \cdot \left(y + x\right)\right) - b \cdot y}{y + \left(t + x\right)} \leq 4 \cdot 10^{+248}\right):\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(a \cdot \left(y + t\right) + z \cdot \left(y + x\right)\right) - b \cdot y}{y + \left(t + x\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 69.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a + z\right) - b\\ \mathbf{if}\;y \leq -8.2 \cdot 10^{-37}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{-263}:\\ \;\;\;\;\frac{\left(a \cdot t + x \cdot z\right) - b \cdot y}{\left(y + t\right) + x}\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+97}:\\ \;\;\;\;a \cdot \frac{t}{t + x} + x \cdot \frac{z}{t + x}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ a z) b)))
   (if (<= y -8.2e-37)
     t_1
     (if (<= y 3.9e-263)
       (/ (- (+ (* a t) (* x z)) (* b y)) (+ (+ y t) x))
       (if (<= y 9e+97) (+ (* a (/ t (+ t x))) (* x (/ z (+ t x)))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a + z) - b;
	double tmp;
	if (y <= -8.2e-37) {
		tmp = t_1;
	} else if (y <= 3.9e-263) {
		tmp = (((a * t) + (x * z)) - (b * y)) / ((y + t) + x);
	} else if (y <= 9e+97) {
		tmp = (a * (t / (t + x))) + (x * (z / (t + x)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a + z) - b
    if (y <= (-8.2d-37)) then
        tmp = t_1
    else if (y <= 3.9d-263) then
        tmp = (((a * t) + (x * z)) - (b * y)) / ((y + t) + x)
    else if (y <= 9d+97) then
        tmp = (a * (t / (t + x))) + (x * (z / (t + x)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a + z) - b;
	double tmp;
	if (y <= -8.2e-37) {
		tmp = t_1;
	} else if (y <= 3.9e-263) {
		tmp = (((a * t) + (x * z)) - (b * y)) / ((y + t) + x);
	} else if (y <= 9e+97) {
		tmp = (a * (t / (t + x))) + (x * (z / (t + x)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a + z) - b
	tmp = 0
	if y <= -8.2e-37:
		tmp = t_1
	elif y <= 3.9e-263:
		tmp = (((a * t) + (x * z)) - (b * y)) / ((y + t) + x)
	elif y <= 9e+97:
		tmp = (a * (t / (t + x))) + (x * (z / (t + x)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a + z) - b)
	tmp = 0.0
	if (y <= -8.2e-37)
		tmp = t_1;
	elseif (y <= 3.9e-263)
		tmp = Float64(Float64(Float64(Float64(a * t) + Float64(x * z)) - Float64(b * y)) / Float64(Float64(y + t) + x));
	elseif (y <= 9e+97)
		tmp = Float64(Float64(a * Float64(t / Float64(t + x))) + Float64(x * Float64(z / Float64(t + x))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a + z) - b;
	tmp = 0.0;
	if (y <= -8.2e-37)
		tmp = t_1;
	elseif (y <= 3.9e-263)
		tmp = (((a * t) + (x * z)) - (b * y)) / ((y + t) + x);
	elseif (y <= 9e+97)
		tmp = (a * (t / (t + x))) + (x * (z / (t + x)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -8.2e-37], t$95$1, If[LessEqual[y, 3.9e-263], N[(N[(N[(N[(a * t), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision] - N[(b * y), $MachinePrecision]), $MachinePrecision] / N[(N[(y + t), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9e+97], N[(N[(a * N[(t / N[(t + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(z / N[(t + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.1999999999999996e-37 or 8.99999999999999952e97 < y

   1. Initial program 42.4%

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

   3. Taylor expanded in y around inf 73.6%

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

   if -8.1999999999999996e-37 < y < 3.8999999999999997e-263

   1. Initial program 83.0%

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

      1. fma-define 83.0%

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

      2. +-commutative 83.0%

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

      3. associate-+l+ 83.0%

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

      4. +-commutative 83.0%

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

   3. Simplified 83.0%

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

   5. Taylor expanded in y around 0 75.0%

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

   if 3.8999999999999997e-263 < y < 8.99999999999999952e97

   1. Initial program 66.4%

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

   3. Taylor expanded in b around -inf 57.6%

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

      1. associate-*r* 57.6%

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

      2. neg-mul-1 57.6%

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

      3. fma-define 57.6%

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

   5. Simplified 76.7%

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

   6. Taylor expanded in y around 0 41.7%

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

      1. associate-/l* 54.4%

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

      2. associate-/l* 67.1%

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

   8. Simplified 67.1%

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

4. Final simplification 72.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{-37}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{-263}:\\ \;\;\;\;\frac{\left(a \cdot t + x \cdot z\right) - b \cdot y}{\left(y + t\right) + x}\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+97}:\\ \;\;\;\;a \cdot \frac{t}{t + x} + x \cdot \frac{z}{t + x}\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 69.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a + z\right) - b\\ \mathbf{if}\;y \leq -1.8 \cdot 10^{-37}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-122}:\\ \;\;\;\;\frac{z \cdot \left(y + x\right) - b \cdot y}{y + \left(t + x\right)}\\ \mathbf{elif}\;y \leq 2.45 \cdot 10^{+98}:\\ \;\;\;\;a \cdot \frac{t}{t + x} + x \cdot \frac{z}{t + x}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ a z) b)))
   (if (<= y -1.8e-37)
     t_1
     (if (<= y -2.5e-122)
       (/ (- (* z (+ y x)) (* b y)) (+ y (+ t x)))
       (if (<= y 2.45e+98) (+ (* a (/ t (+ t x))) (* x (/ z (+ t x)))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a + z) - b;
	double tmp;
	if (y <= -1.8e-37) {
		tmp = t_1;
	} else if (y <= -2.5e-122) {
		tmp = ((z * (y + x)) - (b * y)) / (y + (t + x));
	} else if (y <= 2.45e+98) {
		tmp = (a * (t / (t + x))) + (x * (z / (t + x)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a + z) - b
    if (y <= (-1.8d-37)) then
        tmp = t_1
    else if (y <= (-2.5d-122)) then
        tmp = ((z * (y + x)) - (b * y)) / (y + (t + x))
    else if (y <= 2.45d+98) then
        tmp = (a * (t / (t + x))) + (x * (z / (t + x)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a + z) - b;
	double tmp;
	if (y <= -1.8e-37) {
		tmp = t_1;
	} else if (y <= -2.5e-122) {
		tmp = ((z * (y + x)) - (b * y)) / (y + (t + x));
	} else if (y <= 2.45e+98) {
		tmp = (a * (t / (t + x))) + (x * (z / (t + x)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a + z) - b
	tmp = 0
	if y <= -1.8e-37:
		tmp = t_1
	elif y <= -2.5e-122:
		tmp = ((z * (y + x)) - (b * y)) / (y + (t + x))
	elif y <= 2.45e+98:
		tmp = (a * (t / (t + x))) + (x * (z / (t + x)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a + z) - b)
	tmp = 0.0
	if (y <= -1.8e-37)
		tmp = t_1;
	elseif (y <= -2.5e-122)
		tmp = Float64(Float64(Float64(z * Float64(y + x)) - Float64(b * y)) / Float64(y + Float64(t + x)));
	elseif (y <= 2.45e+98)
		tmp = Float64(Float64(a * Float64(t / Float64(t + x))) + Float64(x * Float64(z / Float64(t + x))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a + z) - b;
	tmp = 0.0;
	if (y <= -1.8e-37)
		tmp = t_1;
	elseif (y <= -2.5e-122)
		tmp = ((z * (y + x)) - (b * y)) / (y + (t + x));
	elseif (y <= 2.45e+98)
		tmp = (a * (t / (t + x))) + (x * (z / (t + x)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -1.8e-37], t$95$1, If[LessEqual[y, -2.5e-122], N[(N[(N[(z * N[(y + x), $MachinePrecision]), $MachinePrecision] - N[(b * y), $MachinePrecision]), $MachinePrecision] / N[(y + N[(t + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.45e+98], N[(N[(a * N[(t / N[(t + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(z / N[(t + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.80000000000000004e-37 or 2.4499999999999999e98 < y

   1. Initial program 42.4%

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

   3. Taylor expanded in y around inf 73.6%

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

   if -1.80000000000000004e-37 < y < -2.4999999999999999e-122

   1. Initial program 81.3%

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

   3. Taylor expanded in a around 0 70.5%

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

      1. +-commutative 70.5%

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

      2. *-commutative 70.5%

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

   5. Simplified 70.5%

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

   if -2.4999999999999999e-122 < y < 2.4499999999999999e98

   1. Initial program 73.3%

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

   3. Taylor expanded in b around -inf 64.4%

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

      1. associate-*r* 64.4%

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

      2. neg-mul-1 64.4%

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

      3. fma-define 64.4%

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

   5. Simplified 78.4%

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

   6. Taylor expanded in y around 0 51.1%

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

      1. associate-/l* 61.1%

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

      2. associate-/l* 69.8%

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

   8. Simplified 69.8%

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

4. Final simplification 71.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{-37}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-122}:\\ \;\;\;\;\frac{z \cdot \left(y + x\right) - b \cdot y}{y + \left(t + x\right)}\\ \mathbf{elif}\;y \leq 2.45 \cdot 10^{+98}:\\ \;\;\;\;a \cdot \frac{t}{t + x} + x \cdot \frac{z}{t + x}\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 65.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z + a \cdot \frac{t}{t + x}\\ t_2 := \left(a + z\right) - b\\ \mathbf{if}\;y \leq -1.9 \cdot 10^{-30}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-174}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-249}:\\ \;\;\;\;\frac{a \cdot t + x \cdot z}{t + x}\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+97}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ z (* a (/ t (+ t x))))) (t_2 (- (+ a z) b)))
   (if (<= y -1.9e-30)
     t_2
     (if (<= y -1.8e-174)
       t_1
       (if (<= y 3.8e-249)
         (/ (+ (* a t) (* x z)) (+ t x))
         (if (<= y 9e+97) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z + (a * (t / (t + x)));
	double t_2 = (a + z) - b;
	double tmp;
	if (y <= -1.9e-30) {
		tmp = t_2;
	} else if (y <= -1.8e-174) {
		tmp = t_1;
	} else if (y <= 3.8e-249) {
		tmp = ((a * t) + (x * z)) / (t + x);
	} else if (y <= 9e+97) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z + (a * (t / (t + x)))
    t_2 = (a + z) - b
    if (y <= (-1.9d-30)) then
        tmp = t_2
    else if (y <= (-1.8d-174)) then
        tmp = t_1
    else if (y <= 3.8d-249) then
        tmp = ((a * t) + (x * z)) / (t + x)
    else if (y <= 9d+97) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z + (a * (t / (t + x)));
	double t_2 = (a + z) - b;
	double tmp;
	if (y <= -1.9e-30) {
		tmp = t_2;
	} else if (y <= -1.8e-174) {
		tmp = t_1;
	} else if (y <= 3.8e-249) {
		tmp = ((a * t) + (x * z)) / (t + x);
	} else if (y <= 9e+97) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z + (a * (t / (t + x)))
	t_2 = (a + z) - b
	tmp = 0
	if y <= -1.9e-30:
		tmp = t_2
	elif y <= -1.8e-174:
		tmp = t_1
	elif y <= 3.8e-249:
		tmp = ((a * t) + (x * z)) / (t + x)
	elif y <= 9e+97:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z + Float64(a * Float64(t / Float64(t + x))))
	t_2 = Float64(Float64(a + z) - b)
	tmp = 0.0
	if (y <= -1.9e-30)
		tmp = t_2;
	elseif (y <= -1.8e-174)
		tmp = t_1;
	elseif (y <= 3.8e-249)
		tmp = Float64(Float64(Float64(a * t) + Float64(x * z)) / Float64(t + x));
	elseif (y <= 9e+97)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z + (a * (t / (t + x)));
	t_2 = (a + z) - b;
	tmp = 0.0;
	if (y <= -1.9e-30)
		tmp = t_2;
	elseif (y <= -1.8e-174)
		tmp = t_1;
	elseif (y <= 3.8e-249)
		tmp = ((a * t) + (x * z)) / (t + x);
	elseif (y <= 9e+97)
		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[(z + N[(a * N[(t / N[(t + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -1.9e-30], t$95$2, If[LessEqual[y, -1.8e-174], t$95$1, If[LessEqual[y, 3.8e-249], N[(N[(N[(a * t), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision] / N[(t + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9e+97], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.9000000000000002e-30 or 8.99999999999999952e97 < y

   1. Initial program 42.8%

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

   3. Taylor expanded in y around inf 73.4%

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

   if -1.9000000000000002e-30 < y < -1.79999999999999999e-174 or 3.8000000000000001e-249 < y < 8.99999999999999952e97

   1. Initial program 66.7%

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

   3. Taylor expanded in b around -inf 59.1%

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

      1. associate-*r* 59.1%

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

      2. neg-mul-1 59.1%

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

      3. fma-define 59.1%

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

   5. Simplified 78.6%

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

   6. Taylor expanded in y around 0 37.1%

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

      1. associate-/l* 48.9%

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

      2. associate-/l* 62.8%

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

   8. Simplified 62.8%

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

   9. Taylor expanded in x around inf 59.3%

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

   if -1.79999999999999999e-174 < y < 3.8000000000000001e-249

   1. Initial program 97.1%

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

   3. Taylor expanded in y around 0 74.0%

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

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{-30}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-174}:\\ \;\;\;\;z + a \cdot \frac{t}{t + x}\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-249}:\\ \;\;\;\;\frac{a \cdot t + x \cdot z}{t + x}\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+97}:\\ \;\;\;\;z + a \cdot \frac{t}{t + x}\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 69.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{-61} \lor \neg \left(y \leq 1.15 \cdot 10^{+98}\right):\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t}{t + x} + x \cdot \frac{z}{t + x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.65e-61) (not (<= y 1.15e+98)))
   (- (+ a z) b)
   (+ (* a (/ t (+ t x))) (* x (/ z (+ t x))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.65e-61) || !(y <= 1.15e+98)) {
		tmp = (a + z) - b;
	} else {
		tmp = (a * (t / (t + x))) + (x * (z / (t + x)));
	}
	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 <= (-1.65d-61)) .or. (.not. (y <= 1.15d+98))) then
        tmp = (a + z) - b
    else
        tmp = (a * (t / (t + x))) + (x * (z / (t + x)))
    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 <= -1.65e-61) || !(y <= 1.15e+98)) {
		tmp = (a + z) - b;
	} else {
		tmp = (a * (t / (t + x))) + (x * (z / (t + x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.65e-61) or not (y <= 1.15e+98):
		tmp = (a + z) - b
	else:
		tmp = (a * (t / (t + x))) + (x * (z / (t + x)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.65e-61) || !(y <= 1.15e+98))
		tmp = Float64(Float64(a + z) - b);
	else
		tmp = Float64(Float64(a * Float64(t / Float64(t + x))) + Float64(x * Float64(z / Float64(t + x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.65e-61) || ~((y <= 1.15e+98)))
		tmp = (a + z) - b;
	else
		tmp = (a * (t / (t + x))) + (x * (z / (t + x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.65e-61], N[Not[LessEqual[y, 1.15e+98]], $MachinePrecision]], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision], N[(N[(a * N[(t / N[(t + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(z / N[(t + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.64999999999999998e-61 or 1.15000000000000007e98 < 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 71.0%

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

   if -1.64999999999999998e-61 < y < 1.15000000000000007e98

   1. Initial program 74.3%

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

   3. Taylor expanded in b around -inf 65.7%

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

      1. associate-*r* 65.7%

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

      2. neg-mul-1 65.7%

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

      3. fma-define 65.7%

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

   5. Simplified 79.5%

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

   6. Taylor expanded in y around 0 47.8%

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

      1. associate-/l* 56.6%

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

      2. associate-/l* 66.4%

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

   8. Simplified 66.4%

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

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{-61} \lor \neg \left(y \leq 1.15 \cdot 10^{+98}\right):\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t}{t + x} + x \cdot \frac{z}{t + x}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 65.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.2 \cdot 10^{-35} \lor \neg \left(y \leq 9.6 \cdot 10^{+97}\right):\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;z + a \cdot \frac{t}{t + x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -9.2e-35) (not (<= y 9.6e+97)))
   (- (+ a z) b)
   (+ z (* a (/ t (+ t x))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -9.2e-35) || !(y <= 9.6e+97)) {
		tmp = (a + z) - b;
	} else {
		tmp = z + (a * (t / (t + x)));
	}
	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 <= (-9.2d-35)) .or. (.not. (y <= 9.6d+97))) then
        tmp = (a + z) - b
    else
        tmp = z + (a * (t / (t + x)))
    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 <= -9.2e-35) || !(y <= 9.6e+97)) {
		tmp = (a + z) - b;
	} else {
		tmp = z + (a * (t / (t + x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -9.2e-35) or not (y <= 9.6e+97):
		tmp = (a + z) - b
	else:
		tmp = z + (a * (t / (t + x)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -9.2e-35) || !(y <= 9.6e+97))
		tmp = Float64(Float64(a + z) - b);
	else
		tmp = Float64(z + Float64(a * Float64(t / Float64(t + x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -9.2e-35) || ~((y <= 9.6e+97)))
		tmp = (a + z) - b;
	else
		tmp = z + (a * (t / (t + x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -9.2e-35], N[Not[LessEqual[y, 9.6e+97]], $MachinePrecision]], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision], N[(z + N[(a * N[(t / N[(t + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -9.1999999999999996e-35 or 9.6000000000000001e97 < y

   1. Initial program 42.8%

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

   3. Taylor expanded in y around inf 73.4%

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

   if -9.1999999999999996e-35 < y < 9.6000000000000001e97

   1. Initial program 74.3%

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

   3. Taylor expanded in b around -inf 65.7%

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

      1. associate-*r* 65.7%

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

      2. neg-mul-1 65.7%

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

      3. fma-define 65.7%

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

   5. Simplified 79.1%

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

   6. Taylor expanded in y around 0 46.3%

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

      1. associate-/l* 55.1%

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

      2. associate-/l* 64.4%

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

   8. Simplified 64.4%

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

   9. Taylor expanded in x around inf 57.0%

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

4. Final simplification 63.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.2 \cdot 10^{-35} \lor \neg \left(y \leq 9.6 \cdot 10^{+97}\right):\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;z + a \cdot \frac{t}{t + x}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 62.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{-121} \lor \neg \left(y \leq 1.45 \cdot 10^{+98}\right):\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;a + x \cdot \frac{z}{t + x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.55e-121) (not (<= y 1.45e+98)))
   (- (+ a z) b)
   (+ a (* x (/ z (+ t x))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.55e-121) || !(y <= 1.45e+98)) {
		tmp = (a + z) - b;
	} else {
		tmp = a + (x * (z / (t + x)));
	}
	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 <= (-1.55d-121)) .or. (.not. (y <= 1.45d+98))) then
        tmp = (a + z) - b
    else
        tmp = a + (x * (z / (t + x)))
    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 <= -1.55e-121) || !(y <= 1.45e+98)) {
		tmp = (a + z) - b;
	} else {
		tmp = a + (x * (z / (t + x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.55e-121) or not (y <= 1.45e+98):
		tmp = (a + z) - b
	else:
		tmp = a + (x * (z / (t + x)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.55e-121) || !(y <= 1.45e+98))
		tmp = Float64(Float64(a + z) - b);
	else
		tmp = Float64(a + Float64(x * Float64(z / Float64(t + x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.55e-121) || ~((y <= 1.45e+98)))
		tmp = (a + z) - b;
	else
		tmp = a + (x * (z / (t + x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.55e-121], N[Not[LessEqual[y, 1.45e+98]], $MachinePrecision]], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision], N[(a + N[(x * N[(z / N[(t + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.5499999999999999e-121 or 1.45000000000000005e98 < y

   1. Initial program 49.6%

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

   3. Taylor expanded in y around inf 66.7%

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

   if -1.5499999999999999e-121 < y < 1.45000000000000005e98

   1. Initial program 73.5%

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

   3. Taylor expanded in b around -inf 63.9%

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

      1. associate-*r* 63.9%

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

      2. neg-mul-1 63.9%

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

      3. fma-define 63.9%

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

   5. Simplified 77.8%

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

   6. Taylor expanded in y around 0 50.8%

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

      1. associate-/l* 60.7%

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

      2. associate-/l* 69.3%

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

   8. Simplified 69.3%

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

   9. Taylor expanded in t around inf 53.6%

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

4. Final simplification 60.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{-121} \lor \neg \left(y \leq 1.45 \cdot 10^{+98}\right):\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;a + x \cdot \frac{z}{t + x}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 56.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 2.8 \cdot 10^{+78}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{1}{\frac{t + x}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x 2.8e+78) (- (+ a z) b) (* z (/ 1.0 (/ (+ t x) x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= 2.8e+78) {
		tmp = (a + z) - b;
	} else {
		tmp = z * (1.0 / ((t + x) / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= 2.8d+78) then
        tmp = (a + z) - b
    else
        tmp = z * (1.0d0 / ((t + x) / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= 2.8e+78) {
		tmp = (a + z) - b;
	} else {
		tmp = z * (1.0 / ((t + x) / x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= 2.8e+78:
		tmp = (a + z) - b
	else:
		tmp = z * (1.0 / ((t + x) / x))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= 2.8e+78)
		tmp = Float64(Float64(a + z) - b);
	else
		tmp = Float64(z * Float64(1.0 / Float64(Float64(t + x) / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= 2.8e+78)
		tmp = (a + z) - b;
	else
		tmp = z * (1.0 / ((t + x) / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, 2.8e+78], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision], N[(z * N[(1.0 / N[(N[(t + x), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 2.8000000000000001e78

   1. Initial program 63.6%

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

   3. Taylor expanded in y around inf 54.8%

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

   if 2.8000000000000001e78 < x

   1. Initial program 50.3%

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

   3. Taylor expanded in z around inf 29.6%

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

      1. associate-/l* 63.2%

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

      2. +-commutative 63.2%

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

      3. +-commutative 63.2%

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

      4. associate-+r+ 63.2%

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

   5. Simplified 63.2%

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

      1. clear-num 63.3%

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

      2. inv-pow 63.3%

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

      3. associate-+r+ 63.3%

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

      4. +-commutative 63.3%

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

      5. +-commutative 63.3%

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

   7. Applied egg-rr 63.3%

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

      1. unpow-1 63.3%

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

   9. Simplified 63.3%

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

   10. Taylor expanded in y around 0 62.5%

       \[\leadsto z \cdot \frac{1}{\color{blue}{\frac{t + x}{x}}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 11: 55.9% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1.75 \cdot 10^{+78}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x}{t + x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x 1.75e+78) (- (+ a z) b) (* z (/ x (+ t x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= 1.75e+78) {
		tmp = (a + z) - b;
	} else {
		tmp = z * (x / (t + x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= 1.75d+78) then
        tmp = (a + z) - b
    else
        tmp = z * (x / (t + x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= 1.75e+78) {
		tmp = (a + z) - b;
	} else {
		tmp = z * (x / (t + x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= 1.75e+78:
		tmp = (a + z) - b
	else:
		tmp = z * (x / (t + x))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= 1.75e+78)
		tmp = Float64(Float64(a + z) - b);
	else
		tmp = Float64(z * Float64(x / Float64(t + x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= 1.75e+78)
		tmp = (a + z) - b;
	else
		tmp = z * (x / (t + x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, 1.75e+78], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision], N[(z * N[(x / N[(t + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 1.7500000000000001e78

   1. Initial program 63.6%

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

   3. Taylor expanded in y around inf 54.8%

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

   if 1.7500000000000001e78 < x

   1. Initial program 50.3%

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

   3. Taylor expanded in z around inf 29.6%

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

      1. associate-/l* 63.2%

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

      2. +-commutative 63.2%

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

      3. +-commutative 63.2%

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

      4. associate-+r+ 63.2%

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

   5. Simplified 63.2%

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

   6. Taylor expanded in y around 0 62.4%

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

Alternative 12: 54.6% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1.06 \cdot 10^{+78}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{t + x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x 1.06e+78) (- (+ a z) b) (* x (/ z (+ t x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= 1.06e+78) {
		tmp = (a + z) - b;
	} else {
		tmp = x * (z / (t + x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= 1.06d+78) then
        tmp = (a + z) - b
    else
        tmp = x * (z / (t + x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= 1.06e+78) {
		tmp = (a + z) - b;
	} else {
		tmp = x * (z / (t + x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= 1.06e+78:
		tmp = (a + z) - b
	else:
		tmp = x * (z / (t + x))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= 1.06e+78)
		tmp = Float64(Float64(a + z) - b);
	else
		tmp = Float64(x * Float64(z / Float64(t + x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= 1.06e+78)
		tmp = (a + z) - b;
	else
		tmp = x * (z / (t + x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, 1.06e+78], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision], N[(x * N[(z / N[(t + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 1.06e78

   1. Initial program 63.6%

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

   3. Taylor expanded in y around inf 54.8%

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

   if 1.06e78 < x

   1. Initial program 50.3%

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

   3. Taylor expanded in z around inf 29.6%

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

      1. associate-/l* 63.2%

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

      2. +-commutative 63.2%

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

      3. +-commutative 63.2%

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

      4. associate-+r+ 63.2%

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

   5. Simplified 63.2%

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

   6. Taylor expanded in y around 0 29.6%

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

      1. associate-/l* 57.7%

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

   8. Simplified 57.7%

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

Alternative 13: 43.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.06 \cdot 10^{+96}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 7000000000000:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -2.06e+96) z (if (<= z 7000000000000.0) a z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2.06e+96) {
		tmp = z;
	} else if (z <= 7000000000000.0) {
		tmp = a;
	} else {
		tmp = z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-2.06d+96)) then
        tmp = z
    else if (z <= 7000000000000.0d0) then
        tmp = a
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2.06e+96) {
		tmp = z;
	} else if (z <= 7000000000000.0) {
		tmp = a;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -2.06e+96:
		tmp = z
	elif z <= 7000000000000.0:
		tmp = a
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -2.06e+96)
		tmp = z;
	elseif (z <= 7000000000000.0)
		tmp = a;
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -2.06e+96)
		tmp = z;
	elseif (z <= 7000000000000.0)
		tmp = a;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -2.06e+96], z, If[LessEqual[z, 7000000000000.0], a, z]]

Derivation

1. Split input into 2 regimes

2. if z < -2.05999999999999997e96 or 7e12 < z

   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 x around inf 53.8%

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

   if -2.05999999999999997e96 < z < 7e12

   1. Initial program 74.4%

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

   3. Taylor expanded in t around inf 36.4%

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

Alternative 14: 55.2% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 2.9 \cdot 10^{+78}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (if (<= x 2.9e+78) (- (+ a z) b) z))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= 2.9e+78) {
		tmp = (a + z) - b;
	} else {
		tmp = z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= 2.9d+78) then
        tmp = (a + z) - b
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= 2.9e+78) {
		tmp = (a + z) - b;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= 2.9e+78:
		tmp = (a + z) - b
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= 2.9e+78)
		tmp = Float64(Float64(a + z) - b);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= 2.9e+78)
		tmp = (a + z) - b;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, 2.9e+78], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision], z]

Derivation

1. Split input into 2 regimes

2. if x < 2.90000000000000017e78

   1. Initial program 63.6%

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

   3. Taylor expanded in y around inf 54.8%

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

   if 2.90000000000000017e78 < x

   1. Initial program 50.3%

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

   3. Taylor expanded in x around inf 54.2%

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

Alternative 15: 51.2% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 3.6 \cdot 10^{+183}:\\ \;\;\;\;a + z\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (if (<= x 3.6e+183) (+ a z) z))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= 3.6e+183) {
		tmp = a + z;
	} else {
		tmp = z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= 3.6d+183) then
        tmp = a + z
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= 3.6e+183) {
		tmp = a + z;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= 3.6e+183:
		tmp = a + z
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= 3.6e+183)
		tmp = Float64(a + z);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= 3.6e+183)
		tmp = a + z;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, 3.6e+183], N[(a + z), $MachinePrecision], z]

Derivation

1. Split input into 2 regimes

2. if x < 3.60000000000000023e183

   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 b around 0 44.9%

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

   4. Taylor expanded in y around inf 49.1%

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

   if 3.60000000000000023e183 < x

   1. Initial program 52.7%

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

   3. Taylor expanded in x around inf 60.2%

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

Alternative 16: 32.0% 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 61.1%

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

3. Taylor expanded in t around inf 27.3%

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

Developer Target 1: 81.5% accurate, 0.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024144 
(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)))