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

Percentage Accurate: 60.6% → 99.2%

Time: 15.8s

Alternatives: 16

Speedup: 1.1×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 60.6% 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: 99.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := z \cdot \left(x + y\right)\\ t_3 := \frac{\left(t_2 + a \cdot \left(y + t\right)\right) - y \cdot b}{t_1}\\ \mathbf{if}\;t_3 \leq -\infty \lor \neg \left(t_3 \leq 2 \cdot 10^{+296}\right):\\ \;\;\;\;\frac{x + y}{\frac{t_1}{z}} + \left(\frac{a}{\frac{t_1}{t}} + \frac{y}{\frac{t_1}{a - b}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t_2 - y \cdot b}{t_1} + a \cdot \left(\frac{y}{t_1} + \frac{t}{t_1}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t)))
        (t_2 (* z (+ x y)))
        (t_3 (/ (- (+ t_2 (* a (+ y t))) (* y b)) t_1)))
   (if (or (<= t_3 (- INFINITY)) (not (<= t_3 2e+296)))
     (+ (/ (+ x y) (/ t_1 z)) (+ (/ a (/ t_1 t)) (/ y (/ t_1 (- a b)))))
     (+ (/ (- t_2 (* y b)) t_1) (* a (+ (/ y t_1) (/ t t_1)))))))

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 * (x + y);
	double t_3 = ((t_2 + (a * (y + t))) - (y * b)) / t_1;
	double tmp;
	if ((t_3 <= -((double) INFINITY)) || !(t_3 <= 2e+296)) {
		tmp = ((x + y) / (t_1 / z)) + ((a / (t_1 / t)) + (y / (t_1 / (a - b))));
	} else {
		tmp = ((t_2 - (y * b)) / t_1) + (a * ((y / t_1) + (t / t_1)));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = z * (x + y);
	double t_3 = ((t_2 + (a * (y + t))) - (y * b)) / t_1;
	double tmp;
	if ((t_3 <= -Double.POSITIVE_INFINITY) || !(t_3 <= 2e+296)) {
		tmp = ((x + y) / (t_1 / z)) + ((a / (t_1 / t)) + (y / (t_1 / (a - b))));
	} else {
		tmp = ((t_2 - (y * b)) / t_1) + (a * ((y / t_1) + (t / t_1)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = z * (x + y)
	t_3 = ((t_2 + (a * (y + t))) - (y * b)) / t_1
	tmp = 0
	if (t_3 <= -math.inf) or not (t_3 <= 2e+296):
		tmp = ((x + y) / (t_1 / z)) + ((a / (t_1 / t)) + (y / (t_1 / (a - b))))
	else:
		tmp = ((t_2 - (y * b)) / t_1) + (a * ((y / t_1) + (t / t_1)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(z * Float64(x + y))
	t_3 = Float64(Float64(Float64(t_2 + Float64(a * Float64(y + t))) - Float64(y * b)) / t_1)
	tmp = 0.0
	if ((t_3 <= Float64(-Inf)) || !(t_3 <= 2e+296))
		tmp = Float64(Float64(Float64(x + y) / Float64(t_1 / z)) + Float64(Float64(a / Float64(t_1 / t)) + Float64(y / Float64(t_1 / Float64(a - b)))));
	else
		tmp = Float64(Float64(Float64(t_2 - Float64(y * b)) / t_1) + Float64(a * Float64(Float64(y / t_1) + Float64(t / t_1))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	t_2 = z * (x + y);
	t_3 = ((t_2 + (a * (y + t))) - (y * b)) / t_1;
	tmp = 0.0;
	if ((t_3 <= -Inf) || ~((t_3 <= 2e+296)))
		tmp = ((x + y) / (t_1 / z)) + ((a / (t_1 / t)) + (y / (t_1 / (a - b))));
	else
		tmp = ((t_2 - (y * b)) / t_1) + (a * ((y / t_1) + (t / t_1)));
	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[(z * N[(x + y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(t$95$2 + N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[Or[LessEqual[t$95$3, (-Infinity)], N[Not[LessEqual[t$95$3, 2e+296]], $MachinePrecision]], N[(N[(N[(x + y), $MachinePrecision] / N[(t$95$1 / z), $MachinePrecision]), $MachinePrecision] + N[(N[(a / N[(t$95$1 / t), $MachinePrecision]), $MachinePrecision] + N[(y / N[(t$95$1 / N[(a - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(t$95$2 - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision] + N[(a * N[(N[(y / t$95$1), $MachinePrecision] + N[(t / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -inf.0 or 1.99999999999999996e296 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 4.9%

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

      1. *-commutative 4.9%

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

      2. distribute-rgt-in 4.8%

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

      3. associate-+r+ 4.8%

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

      4. associate--l+ 4.8%

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

      5. +-commutative 4.8%

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

      6. +-commutative 4.8%

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

      7. distribute-lft-out-- 5.1%

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

      8. fma-def 5.6%

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

      9. +-commutative 5.6%

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

      10. fma-def 5.9%

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

      11. associate-+l+ 5.9%

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

      12. +-commutative 5.9%

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

   3. Simplified 5.9%

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

   4. Taylor expanded in z around inf 5.1%

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

      1. associate-/l* 29.8%

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

      2. +-commutative 29.8%

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

      3. associate-/l* 52.0%

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

      4. associate-/l* 99.7%

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

   6. Simplified 99.7%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1.99999999999999996e296

   1. Initial program 99.8%

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

   2. Taylor expanded in a around 0 99.9%

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

      1. sub-neg 99.9%

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

      2. mul-1-neg 99.9%

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

      3. associate-+r+ 99.9%

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

      4. +-commutative 99.9%

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

      5. associate-+r+ 99.9%

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

   4. Simplified 99.9%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty \lor \neg \left(\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 2 \cdot 10^{+296}\right):\\ \;\;\;\;\frac{x + y}{\frac{y + \left(x + t\right)}{z}} + \left(\frac{a}{\frac{y + \left(x + t\right)}{t}} + \frac{y}{\frac{y + \left(x + t\right)}{a - b}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(x + y\right) - y \cdot b}{y + \left(x + t\right)} + a \cdot \left(\frac{y}{y + \left(x + t\right)} + \frac{t}{y + \left(x + t\right)}\right)\\ \end{array} \]

Alternative 2: 99.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{t_1}\\ \mathbf{if}\;t_2 \leq -\infty \lor \neg \left(t_2 \leq 2 \cdot 10^{+296}\right):\\ \;\;\;\;\frac{x + y}{\frac{t_1}{z}} + \left(\frac{a}{\frac{t_1}{t}} + \frac{y}{\frac{t_1}{a - b}}\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t)))
        (t_2 (/ (- (+ (* z (+ x y)) (* a (+ y t))) (* y b)) t_1)))
   (if (or (<= t_2 (- INFINITY)) (not (<= t_2 2e+296)))
     (+ (/ (+ x y) (/ t_1 z)) (+ (/ a (/ t_1 t)) (/ y (/ t_1 (- a b)))))
     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 * (x + y)) + (a * (y + t))) - (y * b)) / t_1;
	double tmp;
	if ((t_2 <= -((double) INFINITY)) || !(t_2 <= 2e+296)) {
		tmp = ((x + y) / (t_1 / z)) + ((a / (t_1 / t)) + (y / (t_1 / (a - b))));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = (((z * (x + y)) + (a * (y + t))) - (y * b)) / t_1;
	double tmp;
	if ((t_2 <= -Double.POSITIVE_INFINITY) || !(t_2 <= 2e+296)) {
		tmp = ((x + y) / (t_1 / z)) + ((a / (t_1 / t)) + (y / (t_1 / (a - b))));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = (((z * (x + y)) + (a * (y + t))) - (y * b)) / t_1
	tmp = 0
	if (t_2 <= -math.inf) or not (t_2 <= 2e+296):
		tmp = ((x + y) / (t_1 / z)) + ((a / (t_1 / t)) + (y / (t_1 / (a - b))))
	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(Float64(Float64(z * Float64(x + y)) + Float64(a * Float64(y + t))) - Float64(y * b)) / t_1)
	tmp = 0.0
	if ((t_2 <= Float64(-Inf)) || !(t_2 <= 2e+296))
		tmp = Float64(Float64(Float64(x + y) / Float64(t_1 / z)) + Float64(Float64(a / Float64(t_1 / t)) + Float64(y / Float64(t_1 / Float64(a - b)))));
	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 * (x + y)) + (a * (y + t))) - (y * b)) / t_1;
	tmp = 0.0;
	if ((t_2 <= -Inf) || ~((t_2 <= 2e+296)))
		tmp = ((x + y) / (t_1 / z)) + ((a / (t_1 / t)) + (y / (t_1 / (a - b))));
	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[(N[(N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision] + N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[Or[LessEqual[t$95$2, (-Infinity)], N[Not[LessEqual[t$95$2, 2e+296]], $MachinePrecision]], N[(N[(N[(x + y), $MachinePrecision] / N[(t$95$1 / z), $MachinePrecision]), $MachinePrecision] + N[(N[(a / N[(t$95$1 / t), $MachinePrecision]), $MachinePrecision] + N[(y / N[(t$95$1 / N[(a - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -inf.0 or 1.99999999999999996e296 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 4.9%

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

      1. *-commutative 4.9%

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

      2. distribute-rgt-in 4.8%

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

      3. associate-+r+ 4.8%

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

      4. associate--l+ 4.8%

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

      5. +-commutative 4.8%

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

      6. +-commutative 4.8%

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

      7. distribute-lft-out-- 5.1%

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

      8. fma-def 5.6%

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

      9. +-commutative 5.6%

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

      10. fma-def 5.9%

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

      11. associate-+l+ 5.9%

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

      12. +-commutative 5.9%

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

   3. Simplified 5.9%

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

   4. Taylor expanded in z around inf 5.1%

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

      1. associate-/l* 29.8%

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

      2. +-commutative 29.8%

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

      3. associate-/l* 52.0%

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

      4. associate-/l* 99.7%

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

   6. Simplified 99.7%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1.99999999999999996e296

   1. Initial program 99.8%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty \lor \neg \left(\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 2 \cdot 10^{+296}\right):\\ \;\;\;\;\frac{x + y}{\frac{y + \left(x + t\right)}{z}} + \left(\frac{a}{\frac{y + \left(x + t\right)}{t}} + \frac{y}{\frac{y + \left(x + t\right)}{a - b}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \end{array} \]

Alternative 3: 95.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{t_1}\\ \mathbf{if}\;t_2 \leq -\infty \lor \neg \left(t_2 \leq 2 \cdot 10^{+296}\right):\\ \;\;\;\;z + \left(\frac{a}{\frac{t_1}{t}} + \frac{y}{\frac{t_1}{a - b}}\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t)))
        (t_2 (/ (- (+ (* z (+ x y)) (* a (+ y t))) (* y b)) t_1)))
   (if (or (<= t_2 (- INFINITY)) (not (<= t_2 2e+296)))
     (+ z (+ (/ a (/ t_1 t)) (/ y (/ t_1 (- a b)))))
     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 * (x + y)) + (a * (y + t))) - (y * b)) / t_1;
	double tmp;
	if ((t_2 <= -((double) INFINITY)) || !(t_2 <= 2e+296)) {
		tmp = z + ((a / (t_1 / t)) + (y / (t_1 / (a - b))));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = (((z * (x + y)) + (a * (y + t))) - (y * b)) / t_1;
	double tmp;
	if ((t_2 <= -Double.POSITIVE_INFINITY) || !(t_2 <= 2e+296)) {
		tmp = z + ((a / (t_1 / t)) + (y / (t_1 / (a - b))));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = (((z * (x + y)) + (a * (y + t))) - (y * b)) / t_1
	tmp = 0
	if (t_2 <= -math.inf) or not (t_2 <= 2e+296):
		tmp = z + ((a / (t_1 / t)) + (y / (t_1 / (a - b))))
	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(Float64(Float64(z * Float64(x + y)) + Float64(a * Float64(y + t))) - Float64(y * b)) / t_1)
	tmp = 0.0
	if ((t_2 <= Float64(-Inf)) || !(t_2 <= 2e+296))
		tmp = Float64(z + Float64(Float64(a / Float64(t_1 / t)) + Float64(y / Float64(t_1 / Float64(a - b)))));
	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 * (x + y)) + (a * (y + t))) - (y * b)) / t_1;
	tmp = 0.0;
	if ((t_2 <= -Inf) || ~((t_2 <= 2e+296)))
		tmp = z + ((a / (t_1 / t)) + (y / (t_1 / (a - b))));
	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[(N[(N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision] + N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[Or[LessEqual[t$95$2, (-Infinity)], N[Not[LessEqual[t$95$2, 2e+296]], $MachinePrecision]], N[(z + N[(N[(a / N[(t$95$1 / t), $MachinePrecision]), $MachinePrecision] + N[(y / N[(t$95$1 / N[(a - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -inf.0 or 1.99999999999999996e296 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 4.9%

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

      1. *-commutative 4.9%

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

      2. distribute-rgt-in 4.8%

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

      3. associate-+r+ 4.8%

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

      4. associate--l+ 4.8%

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

      5. +-commutative 4.8%

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

      6. +-commutative 4.8%

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

      7. distribute-lft-out-- 5.1%

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

      8. fma-def 5.6%

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

      9. +-commutative 5.6%

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

      10. fma-def 5.9%

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

      11. associate-+l+ 5.9%

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

      12. +-commutative 5.9%

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

   3. Simplified 5.9%

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

   4. Taylor expanded in z around inf 5.1%

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

      1. associate-/l* 29.8%

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

      2. +-commutative 29.8%

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

      3. associate-/l* 52.0%

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

      4. associate-/l* 99.7%

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

   6. Simplified 99.7%

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

   7. Taylor expanded in y around inf 93.9%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1.99999999999999996e296

   1. Initial program 99.8%

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

4. Final simplification 97.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty \lor \neg \left(\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 2 \cdot 10^{+296}\right):\\ \;\;\;\;z + \left(\frac{a}{\frac{y + \left(x + t\right)}{t}} + \frac{y}{\frac{y + \left(x + t\right)}{a - b}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \end{array} \]

Alternative 4: 86.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{t_1}\\ \mathbf{if}\;t_2 \leq -\infty \lor \neg \left(t_2 \leq 2 \cdot 10^{+296}\right):\\ \;\;\;\;z + \left(a + \frac{y}{\frac{t_1}{a - b}}\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t)))
        (t_2 (/ (- (+ (* z (+ x y)) (* a (+ y t))) (* y b)) t_1)))
   (if (or (<= t_2 (- INFINITY)) (not (<= t_2 2e+296)))
     (+ z (+ a (/ y (/ t_1 (- a b)))))
     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 * (x + y)) + (a * (y + t))) - (y * b)) / t_1;
	double tmp;
	if ((t_2 <= -((double) INFINITY)) || !(t_2 <= 2e+296)) {
		tmp = z + (a + (y / (t_1 / (a - b))));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = (((z * (x + y)) + (a * (y + t))) - (y * b)) / t_1;
	double tmp;
	if ((t_2 <= -Double.POSITIVE_INFINITY) || !(t_2 <= 2e+296)) {
		tmp = z + (a + (y / (t_1 / (a - b))));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = (((z * (x + y)) + (a * (y + t))) - (y * b)) / t_1
	tmp = 0
	if (t_2 <= -math.inf) or not (t_2 <= 2e+296):
		tmp = z + (a + (y / (t_1 / (a - b))))
	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(Float64(Float64(z * Float64(x + y)) + Float64(a * Float64(y + t))) - Float64(y * b)) / t_1)
	tmp = 0.0
	if ((t_2 <= Float64(-Inf)) || !(t_2 <= 2e+296))
		tmp = Float64(z + Float64(a + Float64(y / Float64(t_1 / Float64(a - b)))));
	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 * (x + y)) + (a * (y + t))) - (y * b)) / t_1;
	tmp = 0.0;
	if ((t_2 <= -Inf) || ~((t_2 <= 2e+296)))
		tmp = z + (a + (y / (t_1 / (a - b))));
	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[(N[(N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision] + N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[Or[LessEqual[t$95$2, (-Infinity)], N[Not[LessEqual[t$95$2, 2e+296]], $MachinePrecision]], N[(z + N[(a + N[(y / N[(t$95$1 / N[(a - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -inf.0 or 1.99999999999999996e296 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 4.9%

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

      1. *-commutative 4.9%

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

      2. distribute-rgt-in 4.8%

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

      3. associate-+r+ 4.8%

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

      4. associate--l+ 4.8%

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

      5. +-commutative 4.8%

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

      6. +-commutative 4.8%

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

      7. distribute-lft-out-- 5.1%

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

      8. fma-def 5.6%

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

      9. +-commutative 5.6%

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

      10. fma-def 5.9%

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

      11. associate-+l+ 5.9%

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

      12. +-commutative 5.9%

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

   3. Simplified 5.9%

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

   4. Taylor expanded in z around inf 5.1%

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

      1. associate-/l* 29.8%

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

      2. +-commutative 29.8%

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

      3. associate-/l* 52.0%

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

      4. associate-/l* 99.7%

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

   6. Simplified 99.7%

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

   7. Taylor expanded in y around inf 93.9%

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

   8. Taylor expanded in t around inf 70.3%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1.99999999999999996e296

   1. Initial program 99.8%

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

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty \lor \neg \left(\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 2 \cdot 10^{+296}\right):\\ \;\;\;\;z + \left(a + \frac{y}{\frac{y + \left(x + t\right)}{a - b}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \end{array} \]

Alternative 5: 52.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ t_2 := x + \left(y + t\right)\\ t_3 := \frac{z - b}{\frac{t_2}{y}}\\ t_4 := y + \left(x + t\right)\\ \mathbf{if}\;b \leq -4.1 \cdot 10^{+146}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -1.35 \cdot 10^{+34}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -3 \cdot 10^{-277}:\\ \;\;\;\;\frac{a}{\frac{t_4}{y + t}}\\ \mathbf{elif}\;b \leq 5 \cdot 10^{-296}:\\ \;\;\;\;\frac{x + y}{\frac{t_4}{z}}\\ \mathbf{elif}\;b \leq 3.6 \cdot 10^{-243}:\\ \;\;\;\;\left(y + t\right) \cdot \frac{a}{t_2}\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{+57}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b))
        (t_2 (+ x (+ y t)))
        (t_3 (/ (- z b) (/ t_2 y)))
        (t_4 (+ y (+ x t))))
   (if (<= b -4.1e+146)
     t_3
     (if (<= b -1.35e+34)
       t_1
       (if (<= b -3e-277)
         (/ a (/ t_4 (+ y t)))
         (if (<= b 5e-296)
           (/ (+ x y) (/ t_4 z))
           (if (<= b 3.6e-243)
             (* (+ y t) (/ a t_2))
             (if (<= b 1.5e+57) t_1 t_3))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = x + (y + t);
	double t_3 = (z - b) / (t_2 / y);
	double t_4 = y + (x + t);
	double tmp;
	if (b <= -4.1e+146) {
		tmp = t_3;
	} else if (b <= -1.35e+34) {
		tmp = t_1;
	} else if (b <= -3e-277) {
		tmp = a / (t_4 / (y + t));
	} else if (b <= 5e-296) {
		tmp = (x + y) / (t_4 / z);
	} else if (b <= 3.6e-243) {
		tmp = (y + t) * (a / t_2);
	} else if (b <= 1.5e+57) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	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 = (z + a) - b
    t_2 = x + (y + t)
    t_3 = (z - b) / (t_2 / y)
    t_4 = y + (x + t)
    if (b <= (-4.1d+146)) then
        tmp = t_3
    else if (b <= (-1.35d+34)) then
        tmp = t_1
    else if (b <= (-3d-277)) then
        tmp = a / (t_4 / (y + t))
    else if (b <= 5d-296) then
        tmp = (x + y) / (t_4 / z)
    else if (b <= 3.6d-243) then
        tmp = (y + t) * (a / t_2)
    else if (b <= 1.5d+57) then
        tmp = t_1
    else
        tmp = t_3
    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 t_2 = x + (y + t);
	double t_3 = (z - b) / (t_2 / y);
	double t_4 = y + (x + t);
	double tmp;
	if (b <= -4.1e+146) {
		tmp = t_3;
	} else if (b <= -1.35e+34) {
		tmp = t_1;
	} else if (b <= -3e-277) {
		tmp = a / (t_4 / (y + t));
	} else if (b <= 5e-296) {
		tmp = (x + y) / (t_4 / z);
	} else if (b <= 3.6e-243) {
		tmp = (y + t) * (a / t_2);
	} else if (b <= 1.5e+57) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	t_2 = x + (y + t)
	t_3 = (z - b) / (t_2 / y)
	t_4 = y + (x + t)
	tmp = 0
	if b <= -4.1e+146:
		tmp = t_3
	elif b <= -1.35e+34:
		tmp = t_1
	elif b <= -3e-277:
		tmp = a / (t_4 / (y + t))
	elif b <= 5e-296:
		tmp = (x + y) / (t_4 / z)
	elif b <= 3.6e-243:
		tmp = (y + t) * (a / t_2)
	elif b <= 1.5e+57:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	t_2 = Float64(x + Float64(y + t))
	t_3 = Float64(Float64(z - b) / Float64(t_2 / y))
	t_4 = Float64(y + Float64(x + t))
	tmp = 0.0
	if (b <= -4.1e+146)
		tmp = t_3;
	elseif (b <= -1.35e+34)
		tmp = t_1;
	elseif (b <= -3e-277)
		tmp = Float64(a / Float64(t_4 / Float64(y + t)));
	elseif (b <= 5e-296)
		tmp = Float64(Float64(x + y) / Float64(t_4 / z));
	elseif (b <= 3.6e-243)
		tmp = Float64(Float64(y + t) * Float64(a / t_2));
	elseif (b <= 1.5e+57)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	t_2 = x + (y + t);
	t_3 = (z - b) / (t_2 / y);
	t_4 = y + (x + t);
	tmp = 0.0;
	if (b <= -4.1e+146)
		tmp = t_3;
	elseif (b <= -1.35e+34)
		tmp = t_1;
	elseif (b <= -3e-277)
		tmp = a / (t_4 / (y + t));
	elseif (b <= 5e-296)
		tmp = (x + y) / (t_4 / z);
	elseif (b <= 3.6e-243)
		tmp = (y + t) * (a / t_2);
	elseif (b <= 1.5e+57)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(z - b), $MachinePrecision] / N[(t$95$2 / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -4.1e+146], t$95$3, If[LessEqual[b, -1.35e+34], t$95$1, If[LessEqual[b, -3e-277], N[(a / N[(t$95$4 / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5e-296], N[(N[(x + y), $MachinePrecision] / N[(t$95$4 / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.6e-243], N[(N[(y + t), $MachinePrecision] * N[(a / t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.5e+57], t$95$1, t$95$3]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -4.1000000000000004e146 or 1.5e57 < b

   1. Initial program 49.1%

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

   2. Taylor expanded in y around inf 33.0%

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

      1. +-commutative 33.0%

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

   4. Simplified 33.0%

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

   5. Taylor expanded in a around 0 30.9%

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

      1. associate-/l* 58.1%

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

      2. associate-+r+ 58.1%

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

      3. +-commutative 58.1%

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

      4. +-commutative 58.1%

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

   7. Simplified 58.1%

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

   if -4.1000000000000004e146 < b < -1.35e34 or 3.6000000000000001e-243 < b < 1.5e57

   1. Initial program 65.2%

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

   2. Taylor expanded in y around inf 72.5%

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

      1. +-commutative 72.5%

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

   4. Simplified 72.5%

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

   if -1.35e34 < b < -2.99999999999999978e-277

   1. Initial program 73.5%

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

   2. Taylor expanded in a around inf 47.2%

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

      1. associate-/l* 70.0%

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

   4. Simplified 70.0%

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

   if -2.99999999999999978e-277 < b < 5.0000000000000003e-296

   1. Initial program 73.6%

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

   2. Taylor expanded in z around inf 65.1%

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

      1. associate-/l* 73.9%

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

   4. Simplified 73.9%

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

   if 5.0000000000000003e-296 < b < 3.6000000000000001e-243

   1. Initial program 66.8%

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

   2. Taylor expanded in a around inf 52.7%

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

      1. associate-/l* 84.0%

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

   4. Simplified 84.0%

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

      1. associate-/r/ 84.3%

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

      2. +-commutative 84.3%

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

      3. +-commutative 84.3%

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

      4. associate-+l+ 84.3%

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

      5. +-commutative 84.3%

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

   6. Applied egg-rr 84.3%

      \[\leadsto \color{blue}{\frac{a}{x + \left(y + t\right)} \cdot \left(y + t\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 66.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.1 \cdot 10^{+146}:\\ \;\;\;\;\frac{z - b}{\frac{x + \left(y + t\right)}{y}}\\ \mathbf{elif}\;b \leq -1.35 \cdot 10^{+34}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;b \leq -3 \cdot 10^{-277}:\\ \;\;\;\;\frac{a}{\frac{y + \left(x + t\right)}{y + t}}\\ \mathbf{elif}\;b \leq 5 \cdot 10^{-296}:\\ \;\;\;\;\frac{x + y}{\frac{y + \left(x + t\right)}{z}}\\ \mathbf{elif}\;b \leq 3.6 \cdot 10^{-243}:\\ \;\;\;\;\left(y + t\right) \cdot \frac{a}{x + \left(y + t\right)}\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{+57}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{z - b}{\frac{x + \left(y + t\right)}{y}}\\ \end{array} \]

Alternative 6: 52.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ t_2 := x + \left(y + t\right)\\ t_3 := \frac{z - b}{\frac{t_2}{y}}\\ \mathbf{if}\;b \leq -4.1 \cdot 10^{+146}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -9.6 \cdot 10^{+33}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -6.8 \cdot 10^{-279}:\\ \;\;\;\;a \cdot \frac{1}{\frac{t_2}{y + t}}\\ \mathbf{elif}\;b \leq 3.4 \cdot 10^{-296}:\\ \;\;\;\;\frac{x + y}{\frac{y + \left(x + t\right)}{z}}\\ \mathbf{elif}\;b \leq 3.7 \cdot 10^{-243}:\\ \;\;\;\;\left(y + t\right) \cdot \frac{a}{t_2}\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{+57}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)) (t_2 (+ x (+ y t))) (t_3 (/ (- z b) (/ t_2 y))))
   (if (<= b -4.1e+146)
     t_3
     (if (<= b -9.6e+33)
       t_1
       (if (<= b -6.8e-279)
         (* a (/ 1.0 (/ t_2 (+ y t))))
         (if (<= b 3.4e-296)
           (/ (+ x y) (/ (+ y (+ x t)) z))
           (if (<= b 3.7e-243)
             (* (+ y t) (/ a t_2))
             (if (<= b 1.5e+57) t_1 t_3))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = x + (y + t);
	double t_3 = (z - b) / (t_2 / y);
	double tmp;
	if (b <= -4.1e+146) {
		tmp = t_3;
	} else if (b <= -9.6e+33) {
		tmp = t_1;
	} else if (b <= -6.8e-279) {
		tmp = a * (1.0 / (t_2 / (y + t)));
	} else if (b <= 3.4e-296) {
		tmp = (x + y) / ((y + (x + t)) / z);
	} else if (b <= 3.7e-243) {
		tmp = (y + t) * (a / t_2);
	} else if (b <= 1.5e+57) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	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) :: tmp
    t_1 = (z + a) - b
    t_2 = x + (y + t)
    t_3 = (z - b) / (t_2 / y)
    if (b <= (-4.1d+146)) then
        tmp = t_3
    else if (b <= (-9.6d+33)) then
        tmp = t_1
    else if (b <= (-6.8d-279)) then
        tmp = a * (1.0d0 / (t_2 / (y + t)))
    else if (b <= 3.4d-296) then
        tmp = (x + y) / ((y + (x + t)) / z)
    else if (b <= 3.7d-243) then
        tmp = (y + t) * (a / t_2)
    else if (b <= 1.5d+57) then
        tmp = t_1
    else
        tmp = t_3
    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 t_2 = x + (y + t);
	double t_3 = (z - b) / (t_2 / y);
	double tmp;
	if (b <= -4.1e+146) {
		tmp = t_3;
	} else if (b <= -9.6e+33) {
		tmp = t_1;
	} else if (b <= -6.8e-279) {
		tmp = a * (1.0 / (t_2 / (y + t)));
	} else if (b <= 3.4e-296) {
		tmp = (x + y) / ((y + (x + t)) / z);
	} else if (b <= 3.7e-243) {
		tmp = (y + t) * (a / t_2);
	} else if (b <= 1.5e+57) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	t_2 = x + (y + t)
	t_3 = (z - b) / (t_2 / y)
	tmp = 0
	if b <= -4.1e+146:
		tmp = t_3
	elif b <= -9.6e+33:
		tmp = t_1
	elif b <= -6.8e-279:
		tmp = a * (1.0 / (t_2 / (y + t)))
	elif b <= 3.4e-296:
		tmp = (x + y) / ((y + (x + t)) / z)
	elif b <= 3.7e-243:
		tmp = (y + t) * (a / t_2)
	elif b <= 1.5e+57:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	t_2 = Float64(x + Float64(y + t))
	t_3 = Float64(Float64(z - b) / Float64(t_2 / y))
	tmp = 0.0
	if (b <= -4.1e+146)
		tmp = t_3;
	elseif (b <= -9.6e+33)
		tmp = t_1;
	elseif (b <= -6.8e-279)
		tmp = Float64(a * Float64(1.0 / Float64(t_2 / Float64(y + t))));
	elseif (b <= 3.4e-296)
		tmp = Float64(Float64(x + y) / Float64(Float64(y + Float64(x + t)) / z));
	elseif (b <= 3.7e-243)
		tmp = Float64(Float64(y + t) * Float64(a / t_2));
	elseif (b <= 1.5e+57)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	t_2 = x + (y + t);
	t_3 = (z - b) / (t_2 / y);
	tmp = 0.0;
	if (b <= -4.1e+146)
		tmp = t_3;
	elseif (b <= -9.6e+33)
		tmp = t_1;
	elseif (b <= -6.8e-279)
		tmp = a * (1.0 / (t_2 / (y + t)));
	elseif (b <= 3.4e-296)
		tmp = (x + y) / ((y + (x + t)) / z);
	elseif (b <= 3.7e-243)
		tmp = (y + t) * (a / t_2);
	elseif (b <= 1.5e+57)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(z - b), $MachinePrecision] / N[(t$95$2 / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -4.1e+146], t$95$3, If[LessEqual[b, -9.6e+33], t$95$1, If[LessEqual[b, -6.8e-279], N[(a * N[(1.0 / N[(t$95$2 / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.4e-296], N[(N[(x + y), $MachinePrecision] / N[(N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.7e-243], N[(N[(y + t), $MachinePrecision] * N[(a / t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.5e+57], t$95$1, t$95$3]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -4.1000000000000004e146 or 1.5e57 < b

   1. Initial program 49.1%

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

   2. Taylor expanded in y around inf 33.0%

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

      1. +-commutative 33.0%

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

   4. Simplified 33.0%

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

   5. Taylor expanded in a around 0 30.9%

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

      1. associate-/l* 58.1%

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

      2. associate-+r+ 58.1%

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

      3. +-commutative 58.1%

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

      4. +-commutative 58.1%

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

   7. Simplified 58.1%

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

   if -4.1000000000000004e146 < b < -9.5999999999999999e33 or 3.7e-243 < b < 1.5e57

   1. Initial program 65.2%

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

   2. Taylor expanded in y around inf 72.5%

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

      1. +-commutative 72.5%

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

   4. Simplified 72.5%

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

   if -9.5999999999999999e33 < b < -6.8000000000000003e-279

   1. Initial program 73.5%

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

   2. Taylor expanded in a around inf 47.2%

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

      1. associate-/l* 70.0%

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

   4. Simplified 70.0%

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

      1. div-inv 70.0%

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

      2. +-commutative 70.0%

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

      3. +-commutative 70.0%

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

      4. associate-+l+ 70.0%

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

      5. +-commutative 70.0%

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

   6. Applied egg-rr 70.0%

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

   if -6.8000000000000003e-279 < b < 3.39999999999999997e-296

   1. Initial program 73.6%

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

   2. Taylor expanded in z around inf 65.1%

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

      1. associate-/l* 73.9%

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

   4. Simplified 73.9%

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

   if 3.39999999999999997e-296 < b < 3.7e-243

   1. Initial program 66.8%

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

   2. Taylor expanded in a around inf 52.7%

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

      1. associate-/l* 84.0%

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

   4. Simplified 84.0%

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

      1. associate-/r/ 84.3%

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

      2. +-commutative 84.3%

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

      3. +-commutative 84.3%

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

      4. associate-+l+ 84.3%

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

      5. +-commutative 84.3%

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

   6. Applied egg-rr 84.3%

      \[\leadsto \color{blue}{\frac{a}{x + \left(y + t\right)} \cdot \left(y + t\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 66.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.1 \cdot 10^{+146}:\\ \;\;\;\;\frac{z - b}{\frac{x + \left(y + t\right)}{y}}\\ \mathbf{elif}\;b \leq -9.6 \cdot 10^{+33}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;b \leq -6.8 \cdot 10^{-279}:\\ \;\;\;\;a \cdot \frac{1}{\frac{x + \left(y + t\right)}{y + t}}\\ \mathbf{elif}\;b \leq 3.4 \cdot 10^{-296}:\\ \;\;\;\;\frac{x + y}{\frac{y + \left(x + t\right)}{z}}\\ \mathbf{elif}\;b \leq 3.7 \cdot 10^{-243}:\\ \;\;\;\;\left(y + t\right) \cdot \frac{a}{x + \left(y + t\right)}\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{+57}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{z - b}{\frac{x + \left(y + t\right)}{y}}\\ \end{array} \]

Alternative 7: 73.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+62} \lor \neg \left(y \leq 0.08\right):\\ \;\;\;\;\frac{y}{x + \left(y + t\right)} \cdot \left(z + \left(a - b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z + \frac{a \cdot \left(y + t\right) - y \cdot b}{y + \left(x + t\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -2.4e+62) (not (<= y 0.08)))
   (* (/ y (+ x (+ y t))) (+ z (- a b)))
   (+ z (/ (- (* a (+ y t)) (* y b)) (+ y (+ x t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.4e+62) || !(y <= 0.08)) {
		tmp = (y / (x + (y + t))) * (z + (a - b));
	} else {
		tmp = z + (((a * (y + t)) - (y * b)) / (y + (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 <= (-2.4d+62)) .or. (.not. (y <= 0.08d0))) then
        tmp = (y / (x + (y + t))) * (z + (a - b))
    else
        tmp = z + (((a * (y + t)) - (y * b)) / (y + (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 <= -2.4e+62) || !(y <= 0.08)) {
		tmp = (y / (x + (y + t))) * (z + (a - b));
	} else {
		tmp = z + (((a * (y + t)) - (y * b)) / (y + (x + t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -2.4e+62) or not (y <= 0.08):
		tmp = (y / (x + (y + t))) * (z + (a - b))
	else:
		tmp = z + (((a * (y + t)) - (y * b)) / (y + (x + t)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -2.4e+62) || !(y <= 0.08))
		tmp = Float64(Float64(y / Float64(x + Float64(y + t))) * Float64(z + Float64(a - b)));
	else
		tmp = Float64(z + Float64(Float64(Float64(a * Float64(y + t)) - Float64(y * b)) / Float64(y + Float64(x + t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -2.4e+62) || ~((y <= 0.08)))
		tmp = (y / (x + (y + t))) * (z + (a - b));
	else
		tmp = z + (((a * (y + t)) - (y * b)) / (y + (x + t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -2.4e+62], N[Not[LessEqual[y, 0.08]], $MachinePrecision]], N[(N[(y / N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(z + N[(a - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z + N[(N[(N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.4e62 or 0.0800000000000000017 < y

   1. Initial program 39.0%

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

   2. Taylor expanded in y around inf 36.0%

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

      1. +-commutative 36.0%

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

   4. Simplified 36.0%

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

      1. expm1-log1p-u 26.4%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y \cdot \left(\left(z + a\right) - b\right)}{\left(x + t\right) + y}\right)\right)} \]

      2. expm1-udef 16.8%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{y \cdot \left(\left(z + a\right) - b\right)}{\left(x + t\right) + y}\right)} - 1} \]

      3. associate-/l* 36.4%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{y}{\frac{\left(x + t\right) + y}{\left(z + a\right) - b}}}\right)} - 1 \]

      4. associate-+l+ 36.4%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{y}{\frac{\color{blue}{x + \left(t + y\right)}}{\left(z + a\right) - b}}\right)} - 1 \]

      5. +-commutative 36.4%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{y}{\frac{x + \color{blue}{\left(y + t\right)}}{\left(z + a\right) - b}}\right)} - 1 \]

   6. Applied egg-rr 36.4%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{y}{\frac{x + \left(y + t\right)}{\left(z + a\right) - b}}\right)} - 1} \]
   7. Step-by-step derivation

      1. expm1-def 42.4%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y}{\frac{x + \left(y + t\right)}{\left(z + a\right) - b}}\right)\right)} \]

      2. expm1-log1p 81.0%

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

      3. associate-/r/ 84.7%

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

      4. +-commutative 84.7%

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

      5. associate--l+ 84.7%

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

   8. Simplified 84.7%

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

   if -2.4e62 < y < 0.0800000000000000017

   1. Initial program 77.8%

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

   2. Taylor expanded in z around inf 77.8%

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

      1. associate--l+ 77.8%

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

      2. associate-/l* 78.5%

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

      3. div-sub 78.5%

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

   4. Simplified 78.5%

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

   5. Taylor expanded in y around inf 72.4%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+62} \lor \neg \left(y \leq 0.08\right):\\ \;\;\;\;\frac{y}{x + \left(y + t\right)} \cdot \left(z + \left(a - b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z + \frac{a \cdot \left(y + t\right) - y \cdot b}{y + \left(x + t\right)}\\ \end{array} \]

Alternative 8: 60.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{x + \left(y + t\right)} \cdot \left(z + \left(a - b\right)\right)\\ t_2 := y + \left(x + t\right)\\ \mathbf{if}\;y \leq -5.7 \cdot 10^{-42}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -3.9 \cdot 10^{-170}:\\ \;\;\;\;\frac{x + y}{\frac{t_2}{z}}\\ \mathbf{elif}\;y \leq 0.00094:\\ \;\;\;\;\frac{a}{\frac{t_2}{y + t}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (/ y (+ x (+ y t))) (+ z (- a b)))) (t_2 (+ y (+ x t))))
   (if (<= y -5.7e-42)
     t_1
     (if (<= y -3.9e-170)
       (/ (+ x y) (/ t_2 z))
       (if (<= y 0.00094) (/ a (/ t_2 (+ y t))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y / (x + (y + t))) * (z + (a - b));
	double t_2 = y + (x + t);
	double tmp;
	if (y <= -5.7e-42) {
		tmp = t_1;
	} else if (y <= -3.9e-170) {
		tmp = (x + y) / (t_2 / z);
	} else if (y <= 0.00094) {
		tmp = a / (t_2 / (y + t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (y / (x + (y + t))) * (z + (a - b))
    t_2 = y + (x + t)
    if (y <= (-5.7d-42)) then
        tmp = t_1
    else if (y <= (-3.9d-170)) then
        tmp = (x + y) / (t_2 / z)
    else if (y <= 0.00094d0) then
        tmp = a / (t_2 / (y + t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y / (x + (y + t))) * (z + (a - b));
	double t_2 = y + (x + t);
	double tmp;
	if (y <= -5.7e-42) {
		tmp = t_1;
	} else if (y <= -3.9e-170) {
		tmp = (x + y) / (t_2 / z);
	} else if (y <= 0.00094) {
		tmp = a / (t_2 / (y + t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (y / (x + (y + t))) * (z + (a - b))
	t_2 = y + (x + t)
	tmp = 0
	if y <= -5.7e-42:
		tmp = t_1
	elif y <= -3.9e-170:
		tmp = (x + y) / (t_2 / z)
	elif y <= 0.00094:
		tmp = a / (t_2 / (y + t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y / Float64(x + Float64(y + t))) * Float64(z + Float64(a - b)))
	t_2 = Float64(y + Float64(x + t))
	tmp = 0.0
	if (y <= -5.7e-42)
		tmp = t_1;
	elseif (y <= -3.9e-170)
		tmp = Float64(Float64(x + y) / Float64(t_2 / z));
	elseif (y <= 0.00094)
		tmp = Float64(a / Float64(t_2 / Float64(y + t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (y / (x + (y + t))) * (z + (a - b));
	t_2 = y + (x + t);
	tmp = 0.0;
	if (y <= -5.7e-42)
		tmp = t_1;
	elseif (y <= -3.9e-170)
		tmp = (x + y) / (t_2 / z);
	elseif (y <= 0.00094)
		tmp = a / (t_2 / (y + t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y / N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(z + N[(a - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.7e-42], t$95$1, If[LessEqual[y, -3.9e-170], N[(N[(x + y), $MachinePrecision] / N[(t$95$2 / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 0.00094], N[(a / N[(t$95$2 / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.6999999999999999e-42 or 9.39999999999999972e-4 < y

   1. Initial program 47.1%

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

   2. Taylor expanded in y around inf 39.0%

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

      1. +-commutative 39.0%

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

   4. Simplified 39.0%

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

      1. expm1-log1p-u 27.6%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y \cdot \left(\left(z + a\right) - b\right)}{\left(x + t\right) + y}\right)\right)} \]

      2. expm1-udef 17.3%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{y \cdot \left(\left(z + a\right) - b\right)}{\left(x + t\right) + y}\right)} - 1} \]

      3. associate-/l* 32.7%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{y}{\frac{\left(x + t\right) + y}{\left(z + a\right) - b}}}\right)} - 1 \]

      4. associate-+l+ 32.7%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{y}{\frac{\color{blue}{x + \left(t + y\right)}}{\left(z + a\right) - b}}\right)} - 1 \]

      5. +-commutative 32.7%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{y}{\frac{x + \color{blue}{\left(y + t\right)}}{\left(z + a\right) - b}}\right)} - 1 \]

   6. Applied egg-rr 32.7%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{y}{\frac{x + \left(y + t\right)}{\left(z + a\right) - b}}\right)} - 1} \]
   7. Step-by-step derivation

      1. expm1-def 40.2%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y}{\frac{x + \left(y + t\right)}{\left(z + a\right) - b}}\right)\right)} \]

      2. expm1-log1p 75.2%

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

      3. associate-/r/ 78.9%

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

      4. +-commutative 78.9%

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

      5. associate--l+ 78.9%

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

   8. Simplified 78.9%

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

   if -5.6999999999999999e-42 < y < -3.90000000000000021e-170

   1. Initial program 80.3%

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

   2. Taylor expanded in z around inf 48.8%

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

      1. associate-/l* 51.8%

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

   4. Simplified 51.8%

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

   if -3.90000000000000021e-170 < y < 9.39999999999999972e-4

   1. Initial program 75.1%

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

   2. Taylor expanded in a around inf 43.5%

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

      1. associate-/l* 56.2%

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

   4. Simplified 56.2%

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

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.7 \cdot 10^{-42}:\\ \;\;\;\;\frac{y}{x + \left(y + t\right)} \cdot \left(z + \left(a - b\right)\right)\\ \mathbf{elif}\;y \leq -3.9 \cdot 10^{-170}:\\ \;\;\;\;\frac{x + y}{\frac{y + \left(x + t\right)}{z}}\\ \mathbf{elif}\;y \leq 0.00094:\\ \;\;\;\;\frac{a}{\frac{y + \left(x + t\right)}{y + t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{x + \left(y + t\right)} \cdot \left(z + \left(a - b\right)\right)\\ \end{array} \]

Alternative 9: 68.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ \mathbf{if}\;a \leq -1.15 \cdot 10^{+151} \lor \neg \left(a \leq 3.5 \cdot 10^{+116}\right):\\ \;\;\;\;\frac{a}{\frac{t_1}{y + t}}\\ \mathbf{else}:\\ \;\;\;\;z + \left(a + \frac{y}{\frac{t_1}{a - b}}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t))))
   (if (or (<= a -1.15e+151) (not (<= a 3.5e+116)))
     (/ a (/ t_1 (+ y t)))
     (+ z (+ a (/ y (/ t_1 (- a 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 ((a <= -1.15e+151) || !(a <= 3.5e+116)) {
		tmp = a / (t_1 / (y + t));
	} else {
		tmp = z + (a + (y / (t_1 / (a - b))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y + (x + t)
    if ((a <= (-1.15d+151)) .or. (.not. (a <= 3.5d+116))) then
        tmp = a / (t_1 / (y + t))
    else
        tmp = z + (a + (y / (t_1 / (a - b))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double tmp;
	if ((a <= -1.15e+151) || !(a <= 3.5e+116)) {
		tmp = a / (t_1 / (y + t));
	} else {
		tmp = z + (a + (y / (t_1 / (a - b))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	tmp = 0
	if (a <= -1.15e+151) or not (a <= 3.5e+116):
		tmp = a / (t_1 / (y + t))
	else:
		tmp = z + (a + (y / (t_1 / (a - b))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	tmp = 0.0
	if ((a <= -1.15e+151) || !(a <= 3.5e+116))
		tmp = Float64(a / Float64(t_1 / Float64(y + t)));
	else
		tmp = Float64(z + Float64(a + Float64(y / Float64(t_1 / Float64(a - 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 ((a <= -1.15e+151) || ~((a <= 3.5e+116)))
		tmp = a / (t_1 / (y + t));
	else
		tmp = z + (a + (y / (t_1 / (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]}, If[Or[LessEqual[a, -1.15e+151], N[Not[LessEqual[a, 3.5e+116]], $MachinePrecision]], N[(a / N[(t$95$1 / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z + N[(a + N[(y / N[(t$95$1 / N[(a - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.15e151 or 3.49999999999999997e116 < a

   1. Initial program 40.1%

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

   2. Taylor expanded in a around inf 35.8%

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

      1. associate-/l* 76.6%

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

   4. Simplified 76.6%

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

   if -1.15e151 < a < 3.49999999999999997e116

   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. Step-by-step derivation

      1. *-commutative 70.3%

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

      2. distribute-rgt-in 70.3%

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

      3. associate-+r+ 70.3%

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

      4. associate--l+ 70.3%

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

      5. +-commutative 70.3%

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

      6. +-commutative 70.3%

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

      7. distribute-lft-out-- 70.3%

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

      8. fma-def 70.5%

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

      9. +-commutative 70.5%

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

      10. fma-def 70.5%

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

      11. associate-+l+ 70.5%

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

      12. +-commutative 70.5%

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

   3. Simplified 70.5%

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

   4. Taylor expanded in z around inf 70.4%

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

      1. associate-/l* 74.3%

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

      2. +-commutative 74.3%

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

      3. associate-/l* 77.6%

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

      4. associate-/l* 90.7%

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

   6. Simplified 90.7%

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

   7. Taylor expanded in y around inf 84.2%

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

   8. Taylor expanded in t around inf 74.3%

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

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.15 \cdot 10^{+151} \lor \neg \left(a \leq 3.5 \cdot 10^{+116}\right):\\ \;\;\;\;\frac{a}{\frac{y + \left(x + t\right)}{y + t}}\\ \mathbf{else}:\\ \;\;\;\;z + \left(a + \frac{y}{\frac{y + \left(x + t\right)}{a - b}}\right)\\ \end{array} \]

Alternative 10: 58.5% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{+92}:\\ \;\;\;\;\frac{a}{\frac{y + \left(x + t\right)}{y + t}}\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+165}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{\frac{x + t}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -3.2e+92)
   (/ a (/ (+ y (+ x t)) (+ y t)))
   (if (<= t 1.9e+165) (- (+ z a) b) (/ a (/ (+ x t) t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -3.2e+92) {
		tmp = a / ((y + (x + t)) / (y + t));
	} else if (t <= 1.9e+165) {
		tmp = (z + a) - b;
	} else {
		tmp = a / ((x + t) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-3.2d+92)) then
        tmp = a / ((y + (x + t)) / (y + t))
    else if (t <= 1.9d+165) then
        tmp = (z + a) - b
    else
        tmp = a / ((x + t) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -3.2e+92) {
		tmp = a / ((y + (x + t)) / (y + t));
	} else if (t <= 1.9e+165) {
		tmp = (z + a) - b;
	} else {
		tmp = a / ((x + t) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -3.2e+92:
		tmp = a / ((y + (x + t)) / (y + t))
	elif t <= 1.9e+165:
		tmp = (z + a) - b
	else:
		tmp = a / ((x + t) / t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -3.2e+92)
		tmp = Float64(a / Float64(Float64(y + Float64(x + t)) / Float64(y + t)));
	elseif (t <= 1.9e+165)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(a / Float64(Float64(x + t) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -3.2e+92)
		tmp = a / ((y + (x + t)) / (y + t));
	elseif (t <= 1.9e+165)
		tmp = (z + a) - b;
	else
		tmp = a / ((x + t) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -3.2e+92], N[(a / N[(N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision] / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.9e+165], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(a / N[(N[(x + t), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.20000000000000025e92

   1. Initial program 48.2%

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

   2. Taylor expanded in a around inf 26.9%

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

      1. associate-/l* 56.8%

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

   4. Simplified 56.8%

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

   if -3.20000000000000025e92 < t < 1.89999999999999995e165

   1. Initial program 67.5%

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

   2. Taylor expanded in y around inf 59.0%

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

      1. +-commutative 59.0%

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

   4. Simplified 59.0%

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

   if 1.89999999999999995e165 < t

   1. Initial program 37.1%

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

   2. Taylor expanded in a around inf 37.9%

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

      1. associate-/l* 86.6%

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

   4. Simplified 86.6%

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

   5. Taylor expanded in y around 0 81.5%

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

      1. +-commutative 81.5%

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

   7. Simplified 81.5%

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

   8. Taylor expanded in y around 0 37.9%

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

      1. associate-/l* 86.6%

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

   10. Simplified 86.6%

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

4. Final simplification 61.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{+92}:\\ \;\;\;\;\frac{a}{\frac{y + \left(x + t\right)}{y + t}}\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+165}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{\frac{x + t}{t}}\\ \end{array} \]

Alternative 11: 59.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{+183} \lor \neg \left(t \leq 1.6 \cdot 10^{+166}\right):\\ \;\;\;\;\frac{a}{1 + \frac{x}{t}}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -3.5e+183) (not (<= t 1.6e+166)))
   (/ a (+ 1.0 (/ x t)))
   (- (+ z a) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -3.5e+183) || !(t <= 1.6e+166)) {
		tmp = a / (1.0 + (x / t));
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-3.5d+183)) .or. (.not. (t <= 1.6d+166))) then
        tmp = a / (1.0d0 + (x / t))
    else
        tmp = (z + a) - b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -3.5e+183) || !(t <= 1.6e+166)) {
		tmp = a / (1.0 + (x / t));
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -3.5e+183) or not (t <= 1.6e+166):
		tmp = a / (1.0 + (x / t))
	else:
		tmp = (z + a) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -3.5e+183) || !(t <= 1.6e+166))
		tmp = Float64(a / Float64(1.0 + Float64(x / t)));
	else
		tmp = Float64(Float64(z + a) - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -3.5e+183) || ~((t <= 1.6e+166)))
		tmp = a / (1.0 + (x / t));
	else
		tmp = (z + a) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -3.5e+183], N[Not[LessEqual[t, 1.6e+166]], $MachinePrecision]], N[(a / N[(1.0 + N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.49999999999999987e183 or 1.59999999999999984e166 < t

   1. Initial program 42.0%

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

   2. Taylor expanded in a around inf 33.9%

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

      1. associate-/l* 75.0%

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

   4. Simplified 75.0%

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

   5. Taylor expanded in t around inf 73.1%

      \[\leadsto \frac{a}{\color{blue}{1 + \frac{x}{t}}} \]

   if -3.49999999999999987e183 < t < 1.59999999999999984e166

   1. Initial program 66.3%

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

   2. Taylor expanded in y around inf 58.4%

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

      1. +-commutative 58.4%

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

   4. Simplified 58.4%

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

4. Final simplification 61.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{+183} \lor \neg \left(t \leq 1.6 \cdot 10^{+166}\right):\\ \;\;\;\;\frac{a}{1 + \frac{x}{t}}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]

Alternative 12: 59.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{+183}:\\ \;\;\;\;\frac{a}{1 + \frac{x}{t}}\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{+167}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{\frac{x + t}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -3.5e+183)
   (/ a (+ 1.0 (/ x t)))
   (if (<= t 3.5e+167) (- (+ z a) b) (/ a (/ (+ x t) t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -3.5e+183) {
		tmp = a / (1.0 + (x / t));
	} else if (t <= 3.5e+167) {
		tmp = (z + a) - b;
	} else {
		tmp = a / ((x + t) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-3.5d+183)) then
        tmp = a / (1.0d0 + (x / t))
    else if (t <= 3.5d+167) then
        tmp = (z + a) - b
    else
        tmp = a / ((x + t) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -3.5e+183) {
		tmp = a / (1.0 + (x / t));
	} else if (t <= 3.5e+167) {
		tmp = (z + a) - b;
	} else {
		tmp = a / ((x + t) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -3.5e+183:
		tmp = a / (1.0 + (x / t))
	elif t <= 3.5e+167:
		tmp = (z + a) - b
	else:
		tmp = a / ((x + t) / t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -3.5e+183)
		tmp = Float64(a / Float64(1.0 + Float64(x / t)));
	elseif (t <= 3.5e+167)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(a / Float64(Float64(x + t) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -3.5e+183)
		tmp = a / (1.0 + (x / t));
	elseif (t <= 3.5e+167)
		tmp = (z + a) - b;
	else
		tmp = a / ((x + t) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -3.5e+183], N[(a / N[(1.0 + N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.5e+167], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(a / N[(N[(x + t), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.49999999999999987e183

   1. Initial program 47.8%

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

   2. Taylor expanded in a around inf 29.1%

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

      1. associate-/l* 60.9%

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

   4. Simplified 60.9%

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

   5. Taylor expanded in t around inf 56.8%

      \[\leadsto \frac{a}{\color{blue}{1 + \frac{x}{t}}} \]

   if -3.49999999999999987e183 < t < 3.49999999999999987e167

   1. Initial program 66.3%

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

   2. Taylor expanded in y around inf 58.4%

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

      1. +-commutative 58.4%

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

   4. Simplified 58.4%

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

   if 3.49999999999999987e167 < t

   1. Initial program 37.1%

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

   2. Taylor expanded in a around inf 37.9%

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

      1. associate-/l* 86.6%

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

   4. Simplified 86.6%

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

   5. Taylor expanded in y around 0 81.5%

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

      1. +-commutative 81.5%

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

   7. Simplified 81.5%

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

   8. Taylor expanded in y around 0 37.9%

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

      1. associate-/l* 86.6%

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

   10. Simplified 86.6%

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

4. Final simplification 61.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{+183}:\\ \;\;\;\;\frac{a}{1 + \frac{x}{t}}\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{+167}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{\frac{x + t}{t}}\\ \end{array} \]

Alternative 13: 58.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.45 \cdot 10^{+183}:\\ \;\;\;\;a \cdot \frac{y + t}{x + t}\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{+166}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{\frac{x + t}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -3.45e+183)
   (* a (/ (+ y t) (+ x t)))
   (if (<= t 5.2e+166) (- (+ z a) b) (/ a (/ (+ x t) t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -3.45e+183) {
		tmp = a * ((y + t) / (x + t));
	} else if (t <= 5.2e+166) {
		tmp = (z + a) - b;
	} else {
		tmp = a / ((x + t) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-3.45d+183)) then
        tmp = a * ((y + t) / (x + t))
    else if (t <= 5.2d+166) then
        tmp = (z + a) - b
    else
        tmp = a / ((x + t) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -3.45e+183) {
		tmp = a * ((y + t) / (x + t));
	} else if (t <= 5.2e+166) {
		tmp = (z + a) - b;
	} else {
		tmp = a / ((x + t) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -3.45e+183:
		tmp = a * ((y + t) / (x + t))
	elif t <= 5.2e+166:
		tmp = (z + a) - b
	else:
		tmp = a / ((x + t) / t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -3.45e+183)
		tmp = Float64(a * Float64(Float64(y + t) / Float64(x + t)));
	elseif (t <= 5.2e+166)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(a / Float64(Float64(x + t) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -3.45e+183)
		tmp = a * ((y + t) / (x + t));
	elseif (t <= 5.2e+166)
		tmp = (z + a) - b;
	else
		tmp = a / ((x + t) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -3.45e+183], N[(a * N[(N[(y + t), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.2e+166], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(a / N[(N[(x + t), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.4500000000000002e183

   1. Initial program 47.8%

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

   2. Taylor expanded in a around inf 29.1%

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

      1. associate-/l* 60.9%

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

   4. Simplified 60.9%

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

   5. Taylor expanded in y around 0 57.7%

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

      1. +-commutative 57.7%

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

   7. Simplified 57.7%

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

      1. clear-num 57.7%

         \[\leadsto \frac{a}{\color{blue}{\frac{1}{\frac{y + t}{x + t}}}} \]

      2. inv-pow 57.7%

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

   9. Applied egg-rr 57.7%

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

       1. unpow-1 57.7%

          \[\leadsto \frac{a}{\color{blue}{\frac{1}{\frac{y + t}{x + t}}}} \]

       2. +-commutative 57.7%

          \[\leadsto \frac{a}{\frac{1}{\frac{y + t}{\color{blue}{t + x}}}} \]

   11. Simplified 57.7%

       \[\leadsto \frac{a}{\color{blue}{\frac{1}{\frac{y + t}{t + x}}}} \]
   12. Step-by-step derivation

       1. associate-/r/ 57.7%

          \[\leadsto \color{blue}{\frac{a}{1} \cdot \frac{y + t}{t + x}} \]

       2. /-rgt-identity 57.7%

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

   13. Applied egg-rr 57.7%

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

   if -3.4500000000000002e183 < t < 5.1999999999999999e166

   1. Initial program 66.3%

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

   2. Taylor expanded in y around inf 58.4%

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

      1. +-commutative 58.4%

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

   4. Simplified 58.4%

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

   if 5.1999999999999999e166 < t

   1. Initial program 37.1%

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

   2. Taylor expanded in a around inf 37.9%

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

      1. associate-/l* 86.6%

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

   4. Simplified 86.6%

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

   5. Taylor expanded in y around 0 81.5%

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

      1. +-commutative 81.5%

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

   7. Simplified 81.5%

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

   8. Taylor expanded in y around 0 37.9%

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

      1. associate-/l* 86.6%

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

   10. Simplified 86.6%

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

4. Final simplification 61.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.45 \cdot 10^{+183}:\\ \;\;\;\;a \cdot \frac{y + t}{x + t}\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{+166}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{\frac{x + t}{t}}\\ \end{array} \]

Alternative 14: 57.3% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.1 \cdot 10^{+94}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{+169}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -4.1e+94) a (if (<= t 2.7e+169) (- (+ z a) b) a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -4.1e+94) {
		tmp = a;
	} else if (t <= 2.7e+169) {
		tmp = (z + a) - b;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-4.1d+94)) then
        tmp = a
    else if (t <= 2.7d+169) then
        tmp = (z + a) - b
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -4.1e+94) {
		tmp = a;
	} else if (t <= 2.7e+169) {
		tmp = (z + a) - b;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -4.1e+94:
		tmp = a
	elif t <= 2.7e+169:
		tmp = (z + a) - b
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -4.1e+94)
		tmp = a;
	elseif (t <= 2.7e+169)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -4.1e+94)
		tmp = a;
	elseif (t <= 2.7e+169)
		tmp = (z + a) - b;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -4.1e+94], a, If[LessEqual[t, 2.7e+169], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], a]]

Derivation

1. Split input into 2 regimes

2. if t < -4.10000000000000031e94 or 2.69999999999999991e169 < t

   1. Initial program 43.3%

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

   2. Taylor expanded in t around inf 61.0%

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

   if -4.10000000000000031e94 < t < 2.69999999999999991e169

   1. Initial program 67.5%

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

   2. Taylor expanded in y around inf 59.0%

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

      1. +-commutative 59.0%

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

   4. Simplified 59.0%

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

4. Final simplification 59.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.1 \cdot 10^{+94}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{+169}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]

Alternative 15: 43.5% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.15 \cdot 10^{-30}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{+41}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -2.15e-30) a (if (<= t 4.8e+41) z a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -2.15e-30) {
		tmp = a;
	} else if (t <= 4.8e+41) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-2.15d-30)) then
        tmp = a
    else if (t <= 4.8d+41) then
        tmp = z
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -2.15e-30) {
		tmp = a;
	} else if (t <= 4.8e+41) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -2.15e-30:
		tmp = a
	elif t <= 4.8e+41:
		tmp = z
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -2.15e-30)
		tmp = a;
	elseif (t <= 4.8e+41)
		tmp = z;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -2.15e-30)
		tmp = a;
	elseif (t <= 4.8e+41)
		tmp = z;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -2.15e-30], a, If[LessEqual[t, 4.8e+41], z, a]]

Derivation

1. Split input into 2 regimes

2. if t < -2.14999999999999983e-30 or 4.8000000000000003e41 < t

   1. Initial program 51.1%

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

   2. Taylor expanded in t around inf 47.8%

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

   if -2.14999999999999983e-30 < t < 4.8000000000000003e41

   1. Initial program 70.1%

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

   2. Taylor expanded in x around inf 48.6%

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

4. Final simplification 48.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.15 \cdot 10^{-30}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{+41}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]

Alternative 16: 31.6% 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 61.2%

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

2. Taylor expanded in t around inf 31.2%

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

3. Final simplification 31.2%

   \[\leadsto a \]

Developer target: 82.5% accurate, 0.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023185 
(FPCore (x y z t a b)
  :name "AI.Clustering.Hierarchical.Internal:ward from clustering-0.2.1"
  :precision binary64

  :herbie-target
  (if (< (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)) -3.5813117084150564e+153) (- (+ z a) b) (if (< (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)) 1.2285964308315609e+82) (/ 1.0 (/ (+ (+ x t) y) (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)))) (- (+ z a) b)))

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