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

Percentage Accurate: 61.0% → 86.2%

Time: 13.9s

Alternatives: 16

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 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: 86.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y + t\right) \cdot a\\ t_2 := \frac{\left(t\_1 + \left(x + y\right) \cdot z\right) - y \cdot b}{y + \left(x + t\right)}\\ t_3 := x + \left(y + t\right)\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;\left(\mathsf{fma}\left(z, \frac{x + y}{t\_3 \cdot b}, \frac{y + t}{t\_3} \cdot \frac{a}{b}\right) - \frac{y}{t\_3}\right) \cdot b\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+285}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x + y, z, t\_1\right) - y \cdot b}{t\_3}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (+ y t) a))
        (t_2 (/ (- (+ t_1 (* (+ x y) z)) (* y b)) (+ y (+ x t))))
        (t_3 (+ x (+ y t))))
   (if (<= t_2 (- INFINITY))
     (*
      (- (fma z (/ (+ x y) (* t_3 b)) (* (/ (+ y t) t_3) (/ a b))) (/ y t_3))
      b)
     (if (<= t_2 2e+285)
       (/ (- (fma (+ x y) z t_1) (* y b)) t_3)
       (- (+ z a) b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y + t) * a;
	double t_2 = ((t_1 + ((x + y) * z)) - (y * b)) / (y + (x + t));
	double t_3 = x + (y + t);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = (fma(z, ((x + y) / (t_3 * b)), (((y + t) / t_3) * (a / b))) - (y / t_3)) * b;
	} else if (t_2 <= 2e+285) {
		tmp = (fma((x + y), z, t_1) - (y * b)) / t_3;
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y + t) * a)
	t_2 = Float64(Float64(Float64(t_1 + Float64(Float64(x + y) * z)) - Float64(y * b)) / Float64(y + Float64(x + t)))
	t_3 = Float64(x + Float64(y + t))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(Float64(fma(z, Float64(Float64(x + y) / Float64(t_3 * b)), Float64(Float64(Float64(y + t) / t_3) * Float64(a / b))) - Float64(y / t_3)) * b);
	elseif (t_2 <= 2e+285)
		tmp = Float64(Float64(fma(Float64(x + y), z, t_1) - Float64(y * b)) / t_3);
	else
		tmp = Float64(Float64(z + a) - b);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y + t), $MachinePrecision] * a), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(t$95$1 + N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(N[(N[(z * N[(N[(x + y), $MachinePrecision] / N[(t$95$3 * b), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y + t), $MachinePrecision] / t$95$3), $MachinePrecision] * N[(a / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y / t$95$3), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision], If[LessEqual[t$95$2, 2e+285], N[(N[(N[(N[(x + y), $MachinePrecision] * z + t$95$1), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$3), $MachinePrecision], N[(N[(z + a), $MachinePrecision] - b), $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 6.7%

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

   3. Taylor expanded in b around inf 21.2%

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

      1. +-commutative 21.2%

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

      2. mul-1-neg 21.2%

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

      3. unsub-neg 21.2%

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

   5. Simplified 69.2%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 2e285

   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

   if 2e285 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 6.6%

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

   3. Taylor expanded in y around inf 70.5%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(y + t\right) \cdot a + \left(x + y\right) \cdot z\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty:\\ \;\;\;\;\left(\mathsf{fma}\left(z, \frac{x + y}{\left(x + \left(y + t\right)\right) \cdot b}, \frac{y + t}{x + \left(y + t\right)} \cdot \frac{a}{b}\right) - \frac{y}{x + \left(y + t\right)}\right) \cdot b\\ \mathbf{elif}\;\frac{\left(\left(y + t\right) \cdot a + \left(x + y\right) \cdot z\right) - y \cdot b}{y + \left(x + t\right)} \leq 2 \cdot 10^{+285}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x + y, z, \left(y + t\right) \cdot a\right) - y \cdot b}{x + \left(y + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 86.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \left(y + t\right) \cdot a\\ t_3 := \frac{\left(t\_2 + \left(x + y\right) \cdot z\right) - y \cdot b}{t\_1}\\ \mathbf{if}\;t\_3 \leq -\infty:\\ \;\;\;\;a \cdot \frac{y + t}{t\_1} - \frac{y}{t\_1} \cdot b\\ \mathbf{elif}\;t\_3 \leq 2 \cdot 10^{+285}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x + y, z, t\_2\right) - y \cdot b}{x + \left(y + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t)))
        (t_2 (* (+ y t) a))
        (t_3 (/ (- (+ t_2 (* (+ x y) z)) (* y b)) t_1)))
   (if (<= t_3 (- INFINITY))
     (- (* a (/ (+ y t) t_1)) (* (/ y t_1) b))
     (if (<= t_3 2e+285)
       (/ (- (fma (+ x y) z t_2) (* y b)) (+ x (+ y t)))
       (- (+ z a) b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = (y + t) * a;
	double t_3 = ((t_2 + ((x + y) * z)) - (y * b)) / t_1;
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = (a * ((y + t) / t_1)) - ((y / t_1) * b);
	} else if (t_3 <= 2e+285) {
		tmp = (fma((x + y), z, t_2) - (y * b)) / (x + (y + t));
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(Float64(y + t) * a)
	t_3 = Float64(Float64(Float64(t_2 + Float64(Float64(x + y) * z)) - Float64(y * b)) / t_1)
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = Float64(Float64(a * Float64(Float64(y + t) / t_1)) - Float64(Float64(y / t_1) * b));
	elseif (t_3 <= 2e+285)
		tmp = Float64(Float64(fma(Float64(x + y), z, t_2) - Float64(y * b)) / Float64(x + Float64(y + t)));
	else
		tmp = Float64(Float64(z + a) - b);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y + t), $MachinePrecision] * a), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(t$95$2 + N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], N[(N[(a * N[(N[(y + t), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] - N[(N[(y / t$95$1), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 2e+285], N[(N[(N[(N[(x + y), $MachinePrecision] * z + t$95$2), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z + a), $MachinePrecision] - b), $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 6.7%

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

   3. Taylor expanded in z around -inf 34.6%

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

      1. mul-1-neg 34.6%

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

      2. distribute-rgt-neg-in 34.6%

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

      3. mul-1-neg 34.6%

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

      4. unsub-neg 34.6%

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

   5. Simplified 34.6%

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

      1. div-inv 34.6%

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

      2. +-commutative 34.6%

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

      3. associate-+l+ 34.6%

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

      4. +-commutative 34.6%

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

   7. Applied egg-rr 34.6%

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

      1. sub-neg 34.6%

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

      2. +-commutative 34.6%

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

      3. neg-mul-1 34.6%

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

      4. sub-neg 34.6%

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

      5. neg-mul-1 34.6%

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

      6. +-commutative 34.6%

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

   9. Simplified 34.6%

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

   10. Taylor expanded in z around 0 5.2%

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

       1. associate-/l* 47.3%

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

       2. associate-+r+ 47.3%

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

       3. +-commutative 47.3%

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

       4. associate-/l* 68.1%

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

       5. associate-+r+ 68.1%

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

       6. +-commutative 68.1%

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

   12. Simplified 68.1%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 2e285

   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

   if 2e285 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 6.6%

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

   3. Taylor expanded in y around inf 70.5%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(y + t\right) \cdot a + \left(x + y\right) \cdot z\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty:\\ \;\;\;\;a \cdot \frac{y + t}{y + \left(x + t\right)} - \frac{y}{y + \left(x + t\right)} \cdot b\\ \mathbf{elif}\;\frac{\left(\left(y + t\right) \cdot a + \left(x + y\right) \cdot z\right) - y \cdot b}{y + \left(x + t\right)} \leq 2 \cdot 10^{+285}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x + y, z, \left(y + t\right) \cdot a\right) - y \cdot b}{x + \left(y + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 86.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \frac{\left(\left(y + t\right) \cdot a + \left(x + y\right) \cdot z\right) - y \cdot b}{t\_1}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;a \cdot \frac{y + t}{t\_1} - \frac{y}{t\_1} \cdot b\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+285}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t)))
        (t_2 (/ (- (+ (* (+ y t) a) (* (+ x y) z)) (* y b)) t_1)))
   (if (<= t_2 (- INFINITY))
     (- (* a (/ (+ y t) t_1)) (* (/ y t_1) b))
     (if (<= t_2 2e+285) t_2 (- (+ z a) b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = ((((y + t) * a) + ((x + y) * z)) - (y * b)) / t_1;
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = (a * ((y + t) / t_1)) - ((y / t_1) * b);
	} else if (t_2 <= 2e+285) {
		tmp = t_2;
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = ((((y + t) * a) + ((x + y) * z)) - (y * b)) / t_1;
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = (a * ((y + t) / t_1)) - ((y / t_1) * b);
	} else if (t_2 <= 2e+285) {
		tmp = t_2;
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = ((((y + t) * a) + ((x + y) * z)) - (y * b)) / t_1
	tmp = 0
	if t_2 <= -math.inf:
		tmp = (a * ((y + t) / t_1)) - ((y / t_1) * b)
	elif t_2 <= 2e+285:
		tmp = t_2
	else:
		tmp = (z + a) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(Float64(Float64(Float64(Float64(y + t) * a) + Float64(Float64(x + y) * z)) - Float64(y * b)) / t_1)
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(Float64(a * Float64(Float64(y + t) / t_1)) - Float64(Float64(y / t_1) * b));
	elseif (t_2 <= 2e+285)
		tmp = t_2;
	else
		tmp = Float64(Float64(z + a) - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	t_2 = ((((y + t) * a) + ((x + y) * z)) - (y * b)) / t_1;
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = (a * ((y + t) / t_1)) - ((y / t_1) * b);
	elseif (t_2 <= 2e+285)
		tmp = t_2;
	else
		tmp = (z + a) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(N[(y + t), $MachinePrecision] * a), $MachinePrecision] + N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(N[(a * N[(N[(y + t), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] - N[(N[(y / t$95$1), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+285], t$95$2, N[(N[(z + a), $MachinePrecision] - b), $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 6.7%

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

   3. Taylor expanded in z around -inf 34.6%

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

      1. mul-1-neg 34.6%

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

      2. distribute-rgt-neg-in 34.6%

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

      3. mul-1-neg 34.6%

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

      4. unsub-neg 34.6%

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

   5. Simplified 34.6%

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

      1. div-inv 34.6%

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

      2. +-commutative 34.6%

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

      3. associate-+l+ 34.6%

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

      4. +-commutative 34.6%

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

   7. Applied egg-rr 34.6%

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

      1. sub-neg 34.6%

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

      2. +-commutative 34.6%

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

      3. neg-mul-1 34.6%

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

      4. sub-neg 34.6%

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

      5. neg-mul-1 34.6%

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

      6. +-commutative 34.6%

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

   9. Simplified 34.6%

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

   10. Taylor expanded in z around 0 5.2%

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

       1. associate-/l* 47.3%

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

       2. associate-+r+ 47.3%

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

       3. +-commutative 47.3%

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

       4. associate-/l* 68.1%

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

       5. associate-+r+ 68.1%

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

       6. +-commutative 68.1%

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

   12. Simplified 68.1%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 2e285

   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

   if 2e285 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 6.6%

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

   3. Taylor expanded in y around inf 70.5%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(y + t\right) \cdot a + \left(x + y\right) \cdot z\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty:\\ \;\;\;\;a \cdot \frac{y + t}{y + \left(x + t\right)} - \frac{y}{y + \left(x + t\right)} \cdot b\\ \mathbf{elif}\;\frac{\left(\left(y + t\right) \cdot a + \left(x + y\right) \cdot z\right) - y \cdot b}{y + \left(x + t\right)} \leq 2 \cdot 10^{+285}:\\ \;\;\;\;\frac{\left(\left(y + t\right) \cdot a + \left(x + y\right) \cdot z\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 68.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -3.2 \cdot 10^{+14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-123}:\\ \;\;\;\;\frac{\left(t \cdot a + x \cdot z\right) - y \cdot b}{x + \left(y + t\right)}\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-60}:\\ \;\;\;\;z \cdot \left(\frac{a}{z} + \left(x + y\right) \cdot \frac{1}{y + \left(x + t\right)}\right)\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{+48}:\\ \;\;\;\;z \cdot \left(1 - \frac{y \cdot \left(b - a\right)}{\left(x + y\right) \cdot z}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= y -3.2e+14)
     t_1
     (if (<= y 2.8e-123)
       (/ (- (+ (* t a) (* x z)) (* y b)) (+ x (+ y t)))
       (if (<= y 3.1e-60)
         (* z (+ (/ a z) (* (+ x y) (/ 1.0 (+ y (+ x t))))))
         (if (<= y 4.1e+48)
           (* z (- 1.0 (/ (* y (- b a)) (* (+ x y) z))))
           t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -3.2e+14) {
		tmp = t_1;
	} else if (y <= 2.8e-123) {
		tmp = (((t * a) + (x * z)) - (y * b)) / (x + (y + t));
	} else if (y <= 3.1e-60) {
		tmp = z * ((a / z) + ((x + y) * (1.0 / (y + (x + t)))));
	} else if (y <= 4.1e+48) {
		tmp = z * (1.0 - ((y * (b - a)) / ((x + y) * z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z + a) - b
    if (y <= (-3.2d+14)) then
        tmp = t_1
    else if (y <= 2.8d-123) then
        tmp = (((t * a) + (x * z)) - (y * b)) / (x + (y + t))
    else if (y <= 3.1d-60) then
        tmp = z * ((a / z) + ((x + y) * (1.0d0 / (y + (x + t)))))
    else if (y <= 4.1d+48) then
        tmp = z * (1.0d0 - ((y * (b - a)) / ((x + y) * z)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -3.2e+14) {
		tmp = t_1;
	} else if (y <= 2.8e-123) {
		tmp = (((t * a) + (x * z)) - (y * b)) / (x + (y + t));
	} else if (y <= 3.1e-60) {
		tmp = z * ((a / z) + ((x + y) * (1.0 / (y + (x + t)))));
	} else if (y <= 4.1e+48) {
		tmp = z * (1.0 - ((y * (b - a)) / ((x + y) * z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	tmp = 0
	if y <= -3.2e+14:
		tmp = t_1
	elif y <= 2.8e-123:
		tmp = (((t * a) + (x * z)) - (y * b)) / (x + (y + t))
	elif y <= 3.1e-60:
		tmp = z * ((a / z) + ((x + y) * (1.0 / (y + (x + t)))))
	elif y <= 4.1e+48:
		tmp = z * (1.0 - ((y * (b - a)) / ((x + y) * z)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -3.2e+14)
		tmp = t_1;
	elseif (y <= 2.8e-123)
		tmp = Float64(Float64(Float64(Float64(t * a) + Float64(x * z)) - Float64(y * b)) / Float64(x + Float64(y + t)));
	elseif (y <= 3.1e-60)
		tmp = Float64(z * Float64(Float64(a / z) + Float64(Float64(x + y) * Float64(1.0 / Float64(y + Float64(x + t))))));
	elseif (y <= 4.1e+48)
		tmp = Float64(z * Float64(1.0 - Float64(Float64(y * Float64(b - a)) / Float64(Float64(x + y) * z))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	tmp = 0.0;
	if (y <= -3.2e+14)
		tmp = t_1;
	elseif (y <= 2.8e-123)
		tmp = (((t * a) + (x * z)) - (y * b)) / (x + (y + t));
	elseif (y <= 3.1e-60)
		tmp = z * ((a / z) + ((x + y) * (1.0 / (y + (x + t)))));
	elseif (y <= 4.1e+48)
		tmp = z * (1.0 - ((y * (b - a)) / ((x + y) * z)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -3.2e+14], t$95$1, If[LessEqual[y, 2.8e-123], N[(N[(N[(N[(t * a), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.1e-60], N[(z * N[(N[(a / z), $MachinePrecision] + N[(N[(x + y), $MachinePrecision] * N[(1.0 / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.1e+48], N[(z * N[(1.0 - N[(N[(y * N[(b - a), $MachinePrecision]), $MachinePrecision] / N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.2e14 or 4.1000000000000003e48 < y

   1. Initial program 43.5%

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

   3. Taylor expanded in y around inf 75.0%

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

   if -3.2e14 < y < 2.7999999999999999e-123

   1. Initial program 87.3%

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

      1. fma-define 87.3%

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

      2. +-commutative 87.3%

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

      3. associate-+l+ 87.3%

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

      4. +-commutative 87.3%

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

   3. Simplified 87.3%

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

   5. Taylor expanded in y around 0 75.5%

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

   if 2.7999999999999999e-123 < y < 3.09999999999999988e-60

   1. Initial program 70.3%

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

   3. Taylor expanded in z around -inf 94.8%

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

      1. mul-1-neg 94.8%

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

      2. distribute-rgt-neg-in 94.8%

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

      3. mul-1-neg 94.8%

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

      4. unsub-neg 94.8%

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

   5. Simplified 94.8%

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

      1. div-inv 94.7%

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

      2. +-commutative 94.7%

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

      3. associate-+l+ 94.7%

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

      4. +-commutative 94.7%

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

   7. Applied egg-rr 94.7%

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

      1. sub-neg 94.7%

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

      2. +-commutative 94.7%

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

      3. neg-mul-1 94.7%

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

      4. sub-neg 94.7%

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

      5. neg-mul-1 94.7%

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

      6. +-commutative 94.7%

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

   9. Simplified 94.7%

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

   10. Taylor expanded in t around inf 84.4%

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

   if 3.09999999999999988e-60 < y < 4.1000000000000003e48

   1. Initial program 72.1%

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

   3. Taylor expanded in z around -inf 84.0%

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

      1. mul-1-neg 84.0%

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

      2. distribute-rgt-neg-in 84.0%

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

      3. mul-1-neg 84.0%

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

      4. unsub-neg 84.0%

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

   5. Simplified 84.0%

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

   6. Taylor expanded in t around 0 74.1%

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

      1. associate--l+ 74.1%

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

      2. div-sub 74.1%

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

      3. distribute-rgt-out-- 74.1%

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

      4. +-commutative 74.1%

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

   8. Simplified 74.1%

      \[\leadsto \color{blue}{z \cdot \left(1 + \frac{y \cdot \left(a - b\right)}{z \cdot \left(y + x\right)}\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+14}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-123}:\\ \;\;\;\;\frac{\left(t \cdot a + x \cdot z\right) - y \cdot b}{x + \left(y + t\right)}\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-60}:\\ \;\;\;\;z \cdot \left(\frac{a}{z} + \left(x + y\right) \cdot \frac{1}{y + \left(x + t\right)}\right)\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{+48}:\\ \;\;\;\;z \cdot \left(1 - \frac{y \cdot \left(b - a\right)}{\left(x + y\right) \cdot z}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 64.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + y\right) \cdot z\\ t_2 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -1.06 \cdot 10^{+15}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-160}:\\ \;\;\;\;\frac{t\_1 - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{-161}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+48}:\\ \;\;\;\;z \cdot \left(1 - \frac{y \cdot \left(b - a\right)}{t\_1}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (+ x y) z)) (t_2 (- (+ z a) b)))
   (if (<= y -1.06e+15)
     t_2
     (if (<= y -2.1e-160)
       (/ (- t_1 (* y b)) (+ y (+ x t)))
       (if (<= y 6.4e-161)
         (/ (+ (* t a) (* x z)) (+ x t))
         (if (<= y 7e+48) (* z (- 1.0 (/ (* y (- b a)) t_1))) t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + y) * z;
	double t_2 = (z + a) - b;
	double tmp;
	if (y <= -1.06e+15) {
		tmp = t_2;
	} else if (y <= -2.1e-160) {
		tmp = (t_1 - (y * b)) / (y + (x + t));
	} else if (y <= 6.4e-161) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else if (y <= 7e+48) {
		tmp = z * (1.0 - ((y * (b - a)) / t_1));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x + y) * z
    t_2 = (z + a) - b
    if (y <= (-1.06d+15)) then
        tmp = t_2
    else if (y <= (-2.1d-160)) then
        tmp = (t_1 - (y * b)) / (y + (x + t))
    else if (y <= 6.4d-161) then
        tmp = ((t * a) + (x * z)) / (x + t)
    else if (y <= 7d+48) then
        tmp = z * (1.0d0 - ((y * (b - a)) / t_1))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + y) * z;
	double t_2 = (z + a) - b;
	double tmp;
	if (y <= -1.06e+15) {
		tmp = t_2;
	} else if (y <= -2.1e-160) {
		tmp = (t_1 - (y * b)) / (y + (x + t));
	} else if (y <= 6.4e-161) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else if (y <= 7e+48) {
		tmp = z * (1.0 - ((y * (b - a)) / t_1));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + y) * z
	t_2 = (z + a) - b
	tmp = 0
	if y <= -1.06e+15:
		tmp = t_2
	elif y <= -2.1e-160:
		tmp = (t_1 - (y * b)) / (y + (x + t))
	elif y <= 6.4e-161:
		tmp = ((t * a) + (x * z)) / (x + t)
	elif y <= 7e+48:
		tmp = z * (1.0 - ((y * (b - a)) / t_1))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + y) * z)
	t_2 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -1.06e+15)
		tmp = t_2;
	elseif (y <= -2.1e-160)
		tmp = Float64(Float64(t_1 - Float64(y * b)) / Float64(y + Float64(x + t)));
	elseif (y <= 6.4e-161)
		tmp = Float64(Float64(Float64(t * a) + Float64(x * z)) / Float64(x + t));
	elseif (y <= 7e+48)
		tmp = Float64(z * Float64(1.0 - Float64(Float64(y * Float64(b - a)) / t_1)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + y) * z;
	t_2 = (z + a) - b;
	tmp = 0.0;
	if (y <= -1.06e+15)
		tmp = t_2;
	elseif (y <= -2.1e-160)
		tmp = (t_1 - (y * b)) / (y + (x + t));
	elseif (y <= 6.4e-161)
		tmp = ((t * a) + (x * z)) / (x + t);
	elseif (y <= 7e+48)
		tmp = z * (1.0 - ((y * (b - a)) / t_1));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -1.06e+15], t$95$2, If[LessEqual[y, -2.1e-160], N[(N[(t$95$1 - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.4e-161], N[(N[(N[(t * a), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7e+48], N[(z * N[(1.0 - N[(N[(y * N[(b - a), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.06e15 or 6.9999999999999995e48 < y

   1. Initial program 43.5%

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

   3. Taylor expanded in y around inf 75.0%

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

   if -1.06e15 < y < -2.1e-160

   1. Initial program 86.2%

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

   3. Taylor expanded in a around 0 66.0%

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

      1. +-commutative 66.0%

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

      2. *-commutative 66.0%

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

   5. Simplified 66.0%

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

   if -2.1e-160 < y < 6.39999999999999971e-161

   1. Initial program 87.7%

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

   3. Taylor expanded in y around 0 73.0%

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

   if 6.39999999999999971e-161 < y < 6.9999999999999995e48

   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 z around -inf 88.8%

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

      1. mul-1-neg 88.8%

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

      2. distribute-rgt-neg-in 88.8%

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

      3. mul-1-neg 88.8%

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

      4. unsub-neg 88.8%

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

   5. Simplified 88.8%

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

   6. Taylor expanded in t around 0 67.6%

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

      1. associate--l+ 67.6%

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

      2. div-sub 67.6%

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

      3. distribute-rgt-out-- 67.6%

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

      4. +-commutative 67.6%

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

   8. Simplified 67.6%

      \[\leadsto \color{blue}{z \cdot \left(1 + \frac{y \cdot \left(a - b\right)}{z \cdot \left(y + x\right)}\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 71.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.06 \cdot 10^{+15}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-160}:\\ \;\;\;\;\frac{\left(x + y\right) \cdot z - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{-161}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+48}:\\ \;\;\;\;z \cdot \left(1 - \frac{y \cdot \left(b - a\right)}{\left(x + y\right) \cdot z}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 65.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -1.45 \cdot 10^{-23}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-128}:\\ \;\;\;\;\frac{t \cdot a + y \cdot t\_1}{y + t}\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-161}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+48}:\\ \;\;\;\;z \cdot \left(1 - \frac{y \cdot \left(b - a\right)}{\left(x + y\right) \cdot z}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= y -1.45e-23)
     t_1
     (if (<= y -1.4e-128)
       (/ (+ (* t a) (* y t_1)) (+ y t))
       (if (<= y 5.8e-161)
         (/ (+ (* t a) (* x z)) (+ x t))
         (if (<= y 6e+48)
           (* z (- 1.0 (/ (* y (- b a)) (* (+ x y) z))))
           t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -1.45e-23) {
		tmp = t_1;
	} else if (y <= -1.4e-128) {
		tmp = ((t * a) + (y * t_1)) / (y + t);
	} else if (y <= 5.8e-161) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else if (y <= 6e+48) {
		tmp = z * (1.0 - ((y * (b - a)) / ((x + y) * z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z + a) - b
    if (y <= (-1.45d-23)) then
        tmp = t_1
    else if (y <= (-1.4d-128)) then
        tmp = ((t * a) + (y * t_1)) / (y + t)
    else if (y <= 5.8d-161) then
        tmp = ((t * a) + (x * z)) / (x + t)
    else if (y <= 6d+48) then
        tmp = z * (1.0d0 - ((y * (b - a)) / ((x + y) * z)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -1.45e-23) {
		tmp = t_1;
	} else if (y <= -1.4e-128) {
		tmp = ((t * a) + (y * t_1)) / (y + t);
	} else if (y <= 5.8e-161) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else if (y <= 6e+48) {
		tmp = z * (1.0 - ((y * (b - a)) / ((x + y) * z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	tmp = 0
	if y <= -1.45e-23:
		tmp = t_1
	elif y <= -1.4e-128:
		tmp = ((t * a) + (y * t_1)) / (y + t)
	elif y <= 5.8e-161:
		tmp = ((t * a) + (x * z)) / (x + t)
	elif y <= 6e+48:
		tmp = z * (1.0 - ((y * (b - a)) / ((x + y) * z)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -1.45e-23)
		tmp = t_1;
	elseif (y <= -1.4e-128)
		tmp = Float64(Float64(Float64(t * a) + Float64(y * t_1)) / Float64(y + t));
	elseif (y <= 5.8e-161)
		tmp = Float64(Float64(Float64(t * a) + Float64(x * z)) / Float64(x + t));
	elseif (y <= 6e+48)
		tmp = Float64(z * Float64(1.0 - Float64(Float64(y * Float64(b - a)) / Float64(Float64(x + y) * z))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	tmp = 0.0;
	if (y <= -1.45e-23)
		tmp = t_1;
	elseif (y <= -1.4e-128)
		tmp = ((t * a) + (y * t_1)) / (y + t);
	elseif (y <= 5.8e-161)
		tmp = ((t * a) + (x * z)) / (x + t);
	elseif (y <= 6e+48)
		tmp = z * (1.0 - ((y * (b - a)) / ((x + y) * z)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -1.45e-23], t$95$1, If[LessEqual[y, -1.4e-128], N[(N[(N[(t * a), $MachinePrecision] + N[(y * t$95$1), $MachinePrecision]), $MachinePrecision] / N[(y + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.8e-161], N[(N[(N[(t * a), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6e+48], N[(z * N[(1.0 - N[(N[(y * N[(b - a), $MachinePrecision]), $MachinePrecision] / N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.4500000000000001e-23 or 5.9999999999999999e48 < y

   1. Initial program 44.8%

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

   3. Taylor expanded in y around inf 73.3%

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

   if -1.4500000000000001e-23 < y < -1.3999999999999999e-128

   1. Initial program 86.5%

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

   3. Taylor expanded in y around 0 86.4%

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

   4. Taylor expanded in x around 0 67.5%

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

   if -1.3999999999999999e-128 < y < 5.8e-161

   1. Initial program 87.9%

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

   3. Taylor expanded in y around 0 69.9%

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

   if 5.8e-161 < y < 5.9999999999999999e48

   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 z around -inf 88.8%

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

      1. mul-1-neg 88.8%

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

      2. distribute-rgt-neg-in 88.8%

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

      3. mul-1-neg 88.8%

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

      4. unsub-neg 88.8%

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

   5. Simplified 88.8%

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

   6. Taylor expanded in t around 0 67.6%

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

      1. associate--l+ 67.6%

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

      2. div-sub 67.6%

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

      3. distribute-rgt-out-- 67.6%

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

      4. +-commutative 67.6%

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

   8. Simplified 67.6%

      \[\leadsto \color{blue}{z \cdot \left(1 + \frac{y \cdot \left(a - b\right)}{z \cdot \left(y + x\right)}\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{-23}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-128}:\\ \;\;\;\;\frac{t \cdot a + y \cdot \left(\left(z + a\right) - b\right)}{y + t}\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-161}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+48}:\\ \;\;\;\;z \cdot \left(1 - \frac{y \cdot \left(b - a\right)}{\left(x + y\right) \cdot z}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 80.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ \mathbf{if}\;z \leq -5.2 \cdot 10^{+87} \lor \neg \left(z \leq 0.0047\right):\\ \;\;\;\;z \cdot \left(\frac{a}{z} + \left(x + y\right) \cdot \frac{1}{t\_1}\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{y + t}{t\_1} - \frac{y}{t\_1} \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t))))
   (if (or (<= z -5.2e+87) (not (<= z 0.0047)))
     (* z (+ (/ a z) (* (+ x y) (/ 1.0 t_1))))
     (- (* a (/ (+ y t) t_1)) (* (/ y t_1) b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double tmp;
	if ((z <= -5.2e+87) || !(z <= 0.0047)) {
		tmp = z * ((a / z) + ((x + y) * (1.0 / t_1)));
	} else {
		tmp = (a * ((y + t) / t_1)) - ((y / t_1) * b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y + (x + t)
    if ((z <= (-5.2d+87)) .or. (.not. (z <= 0.0047d0))) then
        tmp = z * ((a / z) + ((x + y) * (1.0d0 / t_1)))
    else
        tmp = (a * ((y + t) / t_1)) - ((y / t_1) * b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double tmp;
	if ((z <= -5.2e+87) || !(z <= 0.0047)) {
		tmp = z * ((a / z) + ((x + y) * (1.0 / t_1)));
	} else {
		tmp = (a * ((y + t) / t_1)) - ((y / t_1) * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	tmp = 0
	if (z <= -5.2e+87) or not (z <= 0.0047):
		tmp = z * ((a / z) + ((x + y) * (1.0 / t_1)))
	else:
		tmp = (a * ((y + t) / t_1)) - ((y / t_1) * b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	tmp = 0.0
	if ((z <= -5.2e+87) || !(z <= 0.0047))
		tmp = Float64(z * Float64(Float64(a / z) + Float64(Float64(x + y) * Float64(1.0 / t_1))));
	else
		tmp = Float64(Float64(a * Float64(Float64(y + t) / t_1)) - Float64(Float64(y / t_1) * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	tmp = 0.0;
	if ((z <= -5.2e+87) || ~((z <= 0.0047)))
		tmp = z * ((a / z) + ((x + y) * (1.0 / t_1)));
	else
		tmp = (a * ((y + t) / t_1)) - ((y / t_1) * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[z, -5.2e+87], N[Not[LessEqual[z, 0.0047]], $MachinePrecision]], N[(z * N[(N[(a / z), $MachinePrecision] + N[(N[(x + y), $MachinePrecision] * N[(1.0 / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * N[(N[(y + t), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] - N[(N[(y / t$95$1), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.19999999999999997e87 or 0.00470000000000000018 < z

   1. Initial program 59.9%

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

   3. Taylor expanded in z around -inf 82.5%

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

      1. mul-1-neg 82.5%

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

      2. distribute-rgt-neg-in 82.5%

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

      3. mul-1-neg 82.5%

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

      4. unsub-neg 82.5%

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

   5. Simplified 82.5%

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

      1. div-inv 82.4%

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

      2. +-commutative 82.4%

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

      3. associate-+l+ 82.4%

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

      4. +-commutative 82.4%

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

   7. Applied egg-rr 82.4%

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

      1. sub-neg 82.4%

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

      2. +-commutative 82.4%

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

      3. neg-mul-1 82.4%

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

      4. sub-neg 82.4%

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

      5. neg-mul-1 82.4%

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

      6. +-commutative 82.4%

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

   9. Simplified 82.4%

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

   10. Taylor expanded in t around inf 81.2%

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

   if -5.19999999999999997e87 < z < 0.00470000000000000018

   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 z around -inf 66.4%

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

      1. mul-1-neg 66.4%

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

      2. distribute-rgt-neg-in 66.4%

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

      3. mul-1-neg 66.4%

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

      4. unsub-neg 66.4%

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

   5. Simplified 66.4%

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

      1. div-inv 66.4%

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

      2. +-commutative 66.4%

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

      3. associate-+l+ 66.4%

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

      4. +-commutative 66.4%

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

   7. Applied egg-rr 66.4%

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

      1. sub-neg 66.4%

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

      2. +-commutative 66.4%

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

      3. neg-mul-1 66.4%

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

      4. sub-neg 66.4%

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

      5. neg-mul-1 66.4%

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

      6. +-commutative 66.4%

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

   9. Simplified 66.4%

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

   10. Taylor expanded in z around 0 52.4%

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

       1. associate-/l* 68.3%

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

       2. associate-+r+ 68.3%

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

       3. +-commutative 68.3%

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

       4. associate-/l* 73.6%

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

       5. associate-+r+ 73.6%

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

       6. +-commutative 73.6%

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

   12. Simplified 73.6%

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

4. Final simplification 76.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+87} \lor \neg \left(z \leq 0.0047\right):\\ \;\;\;\;z \cdot \left(\frac{a}{z} + \left(x + y\right) \cdot \frac{1}{y + \left(x + t\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{y + t}{y + \left(x + t\right)} - \frac{y}{y + \left(x + t\right)} \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 74.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -8.8 \cdot 10^{+105}:\\ \;\;\;\;a \cdot \frac{y + t}{t\_1} - \frac{y}{t\_1} \cdot b\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+48}:\\ \;\;\;\;\frac{t \cdot a + \left(x \cdot z + y \cdot t\_2\right)}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t))) (t_2 (- (+ z a) b)))
   (if (<= y -8.8e+105)
     (- (* a (/ (+ y t) t_1)) (* (/ y t_1) b))
     (if (<= y 4.5e+48) (/ (+ (* t a) (+ (* x z) (* y t_2))) t_1) t_2))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = (z + a) - b;
	double tmp;
	if (y <= -8.8e+105) {
		tmp = (a * ((y + t) / t_1)) - ((y / t_1) * b);
	} else if (y <= 4.5e+48) {
		tmp = ((t * a) + ((x * z) + (y * t_2))) / 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 = y + (x + t)
    t_2 = (z + a) - b
    if (y <= (-8.8d+105)) then
        tmp = (a * ((y + t) / t_1)) - ((y / t_1) * b)
    else if (y <= 4.5d+48) then
        tmp = ((t * a) + ((x * z) + (y * t_2))) / 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 = y + (x + t);
	double t_2 = (z + a) - b;
	double tmp;
	if (y <= -8.8e+105) {
		tmp = (a * ((y + t) / t_1)) - ((y / t_1) * b);
	} else if (y <= 4.5e+48) {
		tmp = ((t * a) + ((x * z) + (y * t_2))) / t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = (z + a) - b
	tmp = 0
	if y <= -8.8e+105:
		tmp = (a * ((y + t) / t_1)) - ((y / t_1) * b)
	elif y <= 4.5e+48:
		tmp = ((t * a) + ((x * z) + (y * t_2))) / t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -8.8e+105)
		tmp = Float64(Float64(a * Float64(Float64(y + t) / t_1)) - Float64(Float64(y / t_1) * b));
	elseif (y <= 4.5e+48)
		tmp = Float64(Float64(Float64(t * a) + Float64(Float64(x * z) + Float64(y * t_2))) / t_1);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	t_2 = (z + a) - b;
	tmp = 0.0;
	if (y <= -8.8e+105)
		tmp = (a * ((y + t) / t_1)) - ((y / t_1) * b);
	elseif (y <= 4.5e+48)
		tmp = ((t * a) + ((x * z) + (y * t_2))) / t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -8.8e+105], N[(N[(a * N[(N[(y + t), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] - N[(N[(y / t$95$1), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.5e+48], N[(N[(N[(t * a), $MachinePrecision] + N[(N[(x * z), $MachinePrecision] + N[(y * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.80000000000000027e105

   1. Initial program 31.9%

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

   3. Taylor expanded in z around -inf 34.9%

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

      1. mul-1-neg 34.9%

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

      2. distribute-rgt-neg-in 34.9%

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

      3. mul-1-neg 34.9%

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

      4. unsub-neg 34.9%

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

   5. Simplified 34.9%

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

      1. div-inv 34.8%

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

      2. +-commutative 34.8%

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

      3. associate-+l+ 34.8%

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

      4. +-commutative 34.8%

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

   7. Applied egg-rr 34.8%

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

      1. sub-neg 34.8%

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

      2. +-commutative 34.8%

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

      3. neg-mul-1 34.8%

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

      4. sub-neg 34.8%

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

      5. neg-mul-1 34.8%

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

      6. +-commutative 34.8%

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

   9. Simplified 34.8%

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

   10. Taylor expanded in z around 0 26.7%

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

       1. associate-/l* 48.3%

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

       2. associate-+r+ 48.3%

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

       3. +-commutative 48.3%

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

       4. associate-/l* 83.2%

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

       5. associate-+r+ 83.2%

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

       6. +-commutative 83.2%

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

   12. Simplified 83.2%

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

   if -8.80000000000000027e105 < y < 4.49999999999999995e48

   1. Initial program 80.7%

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

   3. Taylor expanded in y around 0 80.7%

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

   if 4.49999999999999995e48 < y

   1. Initial program 47.9%

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

   3. Taylor expanded in y around inf 80.5%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.8 \cdot 10^{+105}:\\ \;\;\;\;a \cdot \frac{y + t}{y + \left(x + t\right)} - \frac{y}{y + \left(x + t\right)} \cdot b\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+48}:\\ \;\;\;\;\frac{t \cdot a + \left(x \cdot z + y \cdot \left(\left(z + a\right) - b\right)\right)}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 68.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -4.8 \cdot 10^{-6}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-63}:\\ \;\;\;\;\frac{\left(t \cdot a + x \cdot z\right) - y \cdot b}{x + \left(y + t\right)}\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{+48}:\\ \;\;\;\;z \cdot \left(1 - \frac{y \cdot \left(b - a\right)}{\left(x + y\right) \cdot z}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= y -4.8e-6)
     t_1
     (if (<= y 2.3e-63)
       (/ (- (+ (* t a) (* x z)) (* y b)) (+ x (+ y t)))
       (if (<= y 1.85e+48)
         (* z (- 1.0 (/ (* y (- b a)) (* (+ x y) z))))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -4.8e-6) {
		tmp = t_1;
	} else if (y <= 2.3e-63) {
		tmp = (((t * a) + (x * z)) - (y * b)) / (x + (y + t));
	} else if (y <= 1.85e+48) {
		tmp = z * (1.0 - ((y * (b - a)) / ((x + y) * z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z + a) - b
    if (y <= (-4.8d-6)) then
        tmp = t_1
    else if (y <= 2.3d-63) then
        tmp = (((t * a) + (x * z)) - (y * b)) / (x + (y + t))
    else if (y <= 1.85d+48) then
        tmp = z * (1.0d0 - ((y * (b - a)) / ((x + y) * z)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -4.8e-6) {
		tmp = t_1;
	} else if (y <= 2.3e-63) {
		tmp = (((t * a) + (x * z)) - (y * b)) / (x + (y + t));
	} else if (y <= 1.85e+48) {
		tmp = z * (1.0 - ((y * (b - a)) / ((x + y) * z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	tmp = 0
	if y <= -4.8e-6:
		tmp = t_1
	elif y <= 2.3e-63:
		tmp = (((t * a) + (x * z)) - (y * b)) / (x + (y + t))
	elif y <= 1.85e+48:
		tmp = z * (1.0 - ((y * (b - a)) / ((x + y) * z)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -4.8e-6)
		tmp = t_1;
	elseif (y <= 2.3e-63)
		tmp = Float64(Float64(Float64(Float64(t * a) + Float64(x * z)) - Float64(y * b)) / Float64(x + Float64(y + t)));
	elseif (y <= 1.85e+48)
		tmp = Float64(z * Float64(1.0 - Float64(Float64(y * Float64(b - a)) / Float64(Float64(x + y) * z))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	tmp = 0.0;
	if (y <= -4.8e-6)
		tmp = t_1;
	elseif (y <= 2.3e-63)
		tmp = (((t * a) + (x * z)) - (y * b)) / (x + (y + t));
	elseif (y <= 1.85e+48)
		tmp = z * (1.0 - ((y * (b - a)) / ((x + y) * z)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -4.8e-6], t$95$1, If[LessEqual[y, 2.3e-63], N[(N[(N[(N[(t * a), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.85e+48], N[(z * N[(1.0 - N[(N[(y * N[(b - a), $MachinePrecision]), $MachinePrecision] / N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.7999999999999998e-6 or 1.85e48 < y

   1. Initial program 43.5%

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

   3. Taylor expanded in y around inf 75.0%

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

   if -4.7999999999999998e-6 < y < 2.3e-63

   1. Initial program 85.4%

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

      1. fma-define 85.4%

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

      2. +-commutative 85.4%

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

      3. associate-+l+ 85.4%

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

      4. +-commutative 85.4%

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

   3. Simplified 85.4%

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

   5. Taylor expanded in y around 0 73.8%

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

   if 2.3e-63 < y < 1.85e48

   1. Initial program 70.5%

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

   3. Taylor expanded in z around -inf 85.2%

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

      1. mul-1-neg 85.2%

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

      2. distribute-rgt-neg-in 85.2%

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

      3. mul-1-neg 85.2%

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

      4. unsub-neg 85.2%

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

   5. Simplified 85.2%

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

   6. Taylor expanded in t around 0 72.4%

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

      1. associate--l+ 72.4%

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

      2. div-sub 72.4%

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

      3. distribute-rgt-out-- 72.4%

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

      4. +-commutative 72.4%

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

   8. Simplified 72.4%

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

4. Final simplification 74.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{-6}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-63}:\\ \;\;\;\;\frac{\left(t \cdot a + x \cdot z\right) - y \cdot b}{x + \left(y + t\right)}\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{+48}:\\ \;\;\;\;z \cdot \left(1 - \frac{y \cdot \left(b - a\right)}{\left(x + y\right) \cdot z}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 68.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + y\right) \cdot z\\ t_2 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -2.7 \cdot 10^{+19}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-41}:\\ \;\;\;\;\frac{\left(y + t\right) \cdot a + t\_1}{\left(x + y\right) + t}\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{+48}:\\ \;\;\;\;z \cdot \left(1 - \frac{y \cdot \left(b - a\right)}{t\_1}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (+ x y) z)) (t_2 (- (+ z a) b)))
   (if (<= y -2.7e+19)
     t_2
     (if (<= y 2.4e-41)
       (/ (+ (* (+ y t) a) t_1) (+ (+ x y) t))
       (if (<= y 3.7e+48) (* z (- 1.0 (/ (* y (- b a)) t_1))) t_2)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + y) * z;
	double t_2 = (z + a) - b;
	double tmp;
	if (y <= -2.7e+19) {
		tmp = t_2;
	} else if (y <= 2.4e-41) {
		tmp = (((y + t) * a) + t_1) / ((x + y) + t);
	} else if (y <= 3.7e+48) {
		tmp = z * (1.0 - ((y * (b - a)) / t_1));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x + y) * z
    t_2 = (z + a) - b
    if (y <= (-2.7d+19)) then
        tmp = t_2
    else if (y <= 2.4d-41) then
        tmp = (((y + t) * a) + t_1) / ((x + y) + t)
    else if (y <= 3.7d+48) then
        tmp = z * (1.0d0 - ((y * (b - a)) / t_1))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + y) * z;
	double t_2 = (z + a) - b;
	double tmp;
	if (y <= -2.7e+19) {
		tmp = t_2;
	} else if (y <= 2.4e-41) {
		tmp = (((y + t) * a) + t_1) / ((x + y) + t);
	} else if (y <= 3.7e+48) {
		tmp = z * (1.0 - ((y * (b - a)) / t_1));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + y) * z
	t_2 = (z + a) - b
	tmp = 0
	if y <= -2.7e+19:
		tmp = t_2
	elif y <= 2.4e-41:
		tmp = (((y + t) * a) + t_1) / ((x + y) + t)
	elif y <= 3.7e+48:
		tmp = z * (1.0 - ((y * (b - a)) / t_1))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + y) * z)
	t_2 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -2.7e+19)
		tmp = t_2;
	elseif (y <= 2.4e-41)
		tmp = Float64(Float64(Float64(Float64(y + t) * a) + t_1) / Float64(Float64(x + y) + t));
	elseif (y <= 3.7e+48)
		tmp = Float64(z * Float64(1.0 - Float64(Float64(y * Float64(b - a)) / t_1)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + y) * z;
	t_2 = (z + a) - b;
	tmp = 0.0;
	if (y <= -2.7e+19)
		tmp = t_2;
	elseif (y <= 2.4e-41)
		tmp = (((y + t) * a) + t_1) / ((x + y) + t);
	elseif (y <= 3.7e+48)
		tmp = z * (1.0 - ((y * (b - a)) / t_1));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -2.7e+19], t$95$2, If[LessEqual[y, 2.4e-41], N[(N[(N[(N[(y + t), $MachinePrecision] * a), $MachinePrecision] + t$95$1), $MachinePrecision] / N[(N[(x + y), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.7e+48], N[(z * N[(1.0 - N[(N[(y * N[(b - a), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.7e19 or 3.6999999999999999e48 < y

   1. Initial program 42.9%

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

   3. Taylor expanded in y around inf 74.8%

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

   if -2.7e19 < y < 2.40000000000000022e-41

   1. Initial program 84.0%

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

   3. Taylor expanded in b around 0 70.3%

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

   if 2.40000000000000022e-41 < y < 3.6999999999999999e48

   1. Initial program 77.2%

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

   3. Taylor expanded in z around -inf 90.8%

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

      1. mul-1-neg 90.8%

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

      2. distribute-rgt-neg-in 90.8%

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

      3. mul-1-neg 90.8%

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

      4. unsub-neg 90.8%

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

   5. Simplified 90.8%

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

   6. Taylor expanded in t around 0 79.8%

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

      1. associate--l+ 79.8%

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

      2. div-sub 79.8%

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

      3. distribute-rgt-out-- 79.8%

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

      4. +-commutative 79.8%

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

   8. Simplified 79.8%

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

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+19}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-41}:\\ \;\;\;\;\frac{\left(y + t\right) \cdot a + \left(x + y\right) \cdot z}{\left(x + y\right) + t}\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{+48}:\\ \;\;\;\;z \cdot \left(1 - \frac{y \cdot \left(b - a\right)}{\left(x + y\right) \cdot z}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 64.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -9.7 \cdot 10^{+17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-161}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+48}:\\ \;\;\;\;z \cdot \left(1 - \frac{y \cdot \left(b - a\right)}{\left(x + y\right) \cdot z}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= y -9.7e+17)
     t_1
     (if (<= y 7e-161)
       (/ (+ (* t a) (* x z)) (+ x t))
       (if (<= y 3.8e+48)
         (* z (- 1.0 (/ (* y (- b a)) (* (+ x y) z))))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -9.7e+17) {
		tmp = t_1;
	} else if (y <= 7e-161) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else if (y <= 3.8e+48) {
		tmp = z * (1.0 - ((y * (b - a)) / ((x + y) * z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z + a) - b
    if (y <= (-9.7d+17)) then
        tmp = t_1
    else if (y <= 7d-161) then
        tmp = ((t * a) + (x * z)) / (x + t)
    else if (y <= 3.8d+48) then
        tmp = z * (1.0d0 - ((y * (b - a)) / ((x + y) * z)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -9.7e+17) {
		tmp = t_1;
	} else if (y <= 7e-161) {
		tmp = ((t * a) + (x * z)) / (x + t);
	} else if (y <= 3.8e+48) {
		tmp = z * (1.0 - ((y * (b - a)) / ((x + y) * z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	tmp = 0
	if y <= -9.7e+17:
		tmp = t_1
	elif y <= 7e-161:
		tmp = ((t * a) + (x * z)) / (x + t)
	elif y <= 3.8e+48:
		tmp = z * (1.0 - ((y * (b - a)) / ((x + y) * z)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -9.7e+17)
		tmp = t_1;
	elseif (y <= 7e-161)
		tmp = Float64(Float64(Float64(t * a) + Float64(x * z)) / Float64(x + t));
	elseif (y <= 3.8e+48)
		tmp = Float64(z * Float64(1.0 - Float64(Float64(y * Float64(b - a)) / Float64(Float64(x + y) * z))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	tmp = 0.0;
	if (y <= -9.7e+17)
		tmp = t_1;
	elseif (y <= 7e-161)
		tmp = ((t * a) + (x * z)) / (x + t);
	elseif (y <= 3.8e+48)
		tmp = z * (1.0 - ((y * (b - a)) / ((x + y) * z)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -9.7e+17], t$95$1, If[LessEqual[y, 7e-161], N[(N[(N[(t * a), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.8e+48], N[(z * N[(1.0 - N[(N[(y * N[(b - a), $MachinePrecision]), $MachinePrecision] / N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.7e17 or 3.8e48 < y

   1. Initial program 42.9%

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

   3. Taylor expanded in y around inf 74.8%

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

   if -9.7e17 < y < 7.00000000000000039e-161

   1. Initial program 87.2%

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

   3. Taylor expanded in y around 0 63.0%

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

   if 7.00000000000000039e-161 < y < 3.8e48

   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 z around -inf 88.8%

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

      1. mul-1-neg 88.8%

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

      2. distribute-rgt-neg-in 88.8%

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

      3. mul-1-neg 88.8%

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

      4. unsub-neg 88.8%

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

   5. Simplified 88.8%

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

   6. Taylor expanded in t around 0 67.6%

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

      1. associate--l+ 67.6%

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

      2. div-sub 67.6%

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

      3. distribute-rgt-out-- 67.6%

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

      4. +-commutative 67.6%

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

   8. Simplified 67.6%

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

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.7 \cdot 10^{+17}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-161}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+48}:\\ \;\;\;\;z \cdot \left(1 - \frac{y \cdot \left(b - a\right)}{\left(x + y\right) \cdot z}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 60.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y + t\right)\\ t_2 := z \cdot \frac{x + y}{t\_1}\\ \mathbf{if}\;z \leq -4.6 \cdot 10^{+114}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-148}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-5}:\\ \;\;\;\;a \cdot \frac{y + t}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (+ y t))) (t_2 (* z (/ (+ x y) t_1))))
   (if (<= z -4.6e+114)
     t_2
     (if (<= z -2.9e-148)
       (- (+ z a) b)
       (if (<= z 4.6e-5) (* a (/ (+ y t) t_1)) t_2)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y + t);
	double t_2 = z * ((x + y) / t_1);
	double tmp;
	if (z <= -4.6e+114) {
		tmp = t_2;
	} else if (z <= -2.9e-148) {
		tmp = (z + a) - b;
	} else if (z <= 4.6e-5) {
		tmp = a * ((y + t) / t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (y + t)
    t_2 = z * ((x + y) / t_1)
    if (z <= (-4.6d+114)) then
        tmp = t_2
    else if (z <= (-2.9d-148)) then
        tmp = (z + a) - b
    else if (z <= 4.6d-5) then
        tmp = a * ((y + t) / t_1)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y + t);
	double t_2 = z * ((x + y) / t_1);
	double tmp;
	if (z <= -4.6e+114) {
		tmp = t_2;
	} else if (z <= -2.9e-148) {
		tmp = (z + a) - b;
	} else if (z <= 4.6e-5) {
		tmp = a * ((y + t) / t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (y + t)
	t_2 = z * ((x + y) / t_1)
	tmp = 0
	if z <= -4.6e+114:
		tmp = t_2
	elif z <= -2.9e-148:
		tmp = (z + a) - b
	elif z <= 4.6e-5:
		tmp = a * ((y + t) / t_1)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(y + t))
	t_2 = Float64(z * Float64(Float64(x + y) / t_1))
	tmp = 0.0
	if (z <= -4.6e+114)
		tmp = t_2;
	elseif (z <= -2.9e-148)
		tmp = Float64(Float64(z + a) - b);
	elseif (z <= 4.6e-5)
		tmp = Float64(a * Float64(Float64(y + t) / t_1));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (y + t);
	t_2 = z * ((x + y) / t_1);
	tmp = 0.0;
	if (z <= -4.6e+114)
		tmp = t_2;
	elseif (z <= -2.9e-148)
		tmp = (z + a) - b;
	elseif (z <= 4.6e-5)
		tmp = a * ((y + t) / t_1);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(N[(x + y), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.6e+114], t$95$2, If[LessEqual[z, -2.9e-148], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], If[LessEqual[z, 4.6e-5], N[(a * N[(N[(y + t), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.6000000000000001e114 or 4.6e-5 < z

   1. Initial program 56.3%

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

   3. Taylor expanded in z around inf 46.6%

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

      1. associate-/l* 78.0%

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

      2. +-commutative 78.0%

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

      3. +-commutative 78.0%

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

      4. associate-+r+ 78.0%

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

   5. Simplified 78.0%

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

   if -4.6000000000000001e114 < z < -2.8999999999999998e-148

   1. Initial program 78.8%

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

   3. Taylor expanded in y around inf 56.8%

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

   if -2.8999999999999998e-148 < z < 4.6e-5

   1. Initial program 74.5%

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

   3. Taylor expanded in a around inf 34.8%

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

      1. associate-/l* 54.2%

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

      2. +-commutative 54.2%

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

      3. +-commutative 54.2%

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

      4. associate-+r+ 54.2%

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

   5. Simplified 54.2%

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

4. Final simplification 64.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{+114}:\\ \;\;\;\;z \cdot \frac{x + y}{x + \left(y + t\right)}\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-148}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-5}:\\ \;\;\;\;a \cdot \frac{y + t}{x + \left(y + t\right)}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x + y}{x + \left(y + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 63.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+15} \lor \neg \left(y \leq 5.2 \cdot 10^{-51}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.5e+15) (not (<= y 5.2e-51)))
   (- (+ z a) b)
   (/ (+ (* t a) (* x z)) (+ x t))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.5e+15) || !(y <= 5.2e-51)) {
		tmp = (z + a) - b;
	} else {
		tmp = ((t * a) + (x * z)) / (x + t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-1.5d+15)) .or. (.not. (y <= 5.2d-51))) then
        tmp = (z + a) - b
    else
        tmp = ((t * a) + (x * z)) / (x + t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.5e+15) || !(y <= 5.2e-51)) {
		tmp = (z + a) - b;
	} else {
		tmp = ((t * a) + (x * z)) / (x + t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.5e+15) or not (y <= 5.2e-51):
		tmp = (z + a) - b
	else:
		tmp = ((t * a) + (x * z)) / (x + t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.5e+15) || !(y <= 5.2e-51))
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(Float64(Float64(t * a) + Float64(x * z)) / Float64(x + t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.5e+15) || ~((y <= 5.2e-51)))
		tmp = (z + a) - b;
	else
		tmp = ((t * a) + (x * z)) / (x + t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.5e+15], N[Not[LessEqual[y, 5.2e-51]], $MachinePrecision]], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(N[(N[(t * a), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.5e15 or 5.2e-51 < y

   1. Initial program 48.3%

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

   3. Taylor expanded in y around inf 70.8%

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

   if -1.5e15 < y < 5.2e-51

   1. Initial program 85.1%

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

   3. Taylor expanded in y around 0 61.8%

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

4. Final simplification 66.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+15} \lor \neg \left(y \leq 5.2 \cdot 10^{-51}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot a + x \cdot z}{x + t}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 57.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.2 \cdot 10^{+59}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 2 \cdot 10^{+120}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -9.2e+59) z (if (<= x 2e+120) (- (+ z a) b) z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -9.2e+59) {
		tmp = z;
	} else if (x <= 2e+120) {
		tmp = (z + a) - b;
	} else {
		tmp = z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-9.2d+59)) then
        tmp = z
    else if (x <= 2d+120) then
        tmp = (z + a) - b
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -9.2e+59) {
		tmp = z;
	} else if (x <= 2e+120) {
		tmp = (z + a) - b;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -9.2e+59:
		tmp = z
	elif x <= 2e+120:
		tmp = (z + a) - b
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -9.2e+59)
		tmp = z;
	elseif (x <= 2e+120)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -9.2e+59)
		tmp = z;
	elseif (x <= 2e+120)
		tmp = (z + a) - b;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -9.2e+59], z, If[LessEqual[x, 2e+120], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], z]]

Derivation

1. Split input into 2 regimes

2. if x < -9.20000000000000032e59 or 2e120 < x

   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 x around inf 56.8%

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

   if -9.20000000000000032e59 < x < 2e120

   1. Initial program 72.1%

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

   3. Taylor expanded in y around inf 60.8%

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

4. Final simplification 59.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.2 \cdot 10^{+59}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 2 \cdot 10^{+120}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 43.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.0112:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 5.4 \cdot 10^{-80}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -0.0112) z (if (<= x 5.4e-80) a z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -0.0112) {
		tmp = z;
	} else if (x <= 5.4e-80) {
		tmp = a;
	} else {
		tmp = z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-0.0112d0)) then
        tmp = z
    else if (x <= 5.4d-80) then
        tmp = a
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -0.0112) {
		tmp = z;
	} else if (x <= 5.4e-80) {
		tmp = a;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -0.0112:
		tmp = z
	elif x <= 5.4e-80:
		tmp = a
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -0.0112)
		tmp = z;
	elseif (x <= 5.4e-80)
		tmp = a;
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -0.0112)
		tmp = z;
	elseif (x <= 5.4e-80)
		tmp = a;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -0.0112], z, If[LessEqual[x, 5.4e-80], a, z]]

Derivation

1. Split input into 2 regimes

2. if x < -0.0111999999999999999 or 5.4000000000000004e-80 < x

   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 x around inf 50.5%

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

   if -0.0111999999999999999 < x < 5.4000000000000004e-80

   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 t around inf 43.2%

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

Alternative 16: 32.6% 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 68.0%

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

3. Taylor expanded in t around inf 25.3%

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

Developer Target 1: 82.7% 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 2024160 
(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)))