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

Percentage Accurate: 60.3% → 97.8%

Time: 13.1s

Alternatives: 13

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 60.3% 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: 97.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := a \cdot \left(y + t\right)\\ t_3 := \frac{\left(t_2 + z \cdot \left(x + y\right)\right) - y \cdot b}{t_1}\\ \mathbf{if}\;t_3 \leq -\infty \lor \neg \left(t_3 \leq 10^{+61}\right):\\ \;\;\;\;\frac{x + y}{\frac{t_1}{z}} + \left(t \cdot \frac{a}{x + \left(y + t\right)} + \frac{y}{\frac{t_1}{a - b}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x + y, z, t_2\right) - y \cdot b}{t_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t)))
        (t_2 (* a (+ y t)))
        (t_3 (/ (- (+ t_2 (* z (+ x y))) (* y b)) t_1)))
   (if (or (<= t_3 (- INFINITY)) (not (<= t_3 1e+61)))
     (+
      (/ (+ x y) (/ t_1 z))
      (+ (* t (/ a (+ x (+ y t)))) (/ y (/ t_1 (- a b)))))
     (/ (- (fma (+ x y) z t_2) (* y b)) 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 = a * (y + t);
	double t_3 = ((t_2 + (z * (x + y))) - (y * b)) / t_1;
	double tmp;
	if ((t_3 <= -((double) INFINITY)) || !(t_3 <= 1e+61)) {
		tmp = ((x + y) / (t_1 / z)) + ((t * (a / (x + (y + t)))) + (y / (t_1 / (a - b))));
	} else {
		tmp = (fma((x + y), z, t_2) - (y * b)) / t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(a * Float64(y + t))
	t_3 = Float64(Float64(Float64(t_2 + Float64(z * Float64(x + y))) - Float64(y * b)) / t_1)
	tmp = 0.0
	if ((t_3 <= Float64(-Inf)) || !(t_3 <= 1e+61))
		tmp = Float64(Float64(Float64(x + y) / Float64(t_1 / z)) + Float64(Float64(t * Float64(a / Float64(x + Float64(y + t)))) + Float64(y / Float64(t_1 / Float64(a - b)))));
	else
		tmp = Float64(Float64(fma(Float64(x + y), z, t_2) - Float64(y * b)) / t_1);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(t$95$2 + N[(z * N[(x + y), $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, 1e+61]], $MachinePrecision]], N[(N[(N[(x + y), $MachinePrecision] / N[(t$95$1 / z), $MachinePrecision]), $MachinePrecision] + N[(N[(t * N[(a / N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y / N[(t$95$1 / N[(a - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(x + y), $MachinePrecision] * z + t$95$2), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $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 9.99999999999999949e60 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 19.9%

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

      1. *-commutative 19.9%

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

      2. distribute-rgt-in 19.8%

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

      3. associate-+r+ 19.8%

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

      4. associate--l+ 19.8%

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

      5. +-commutative 19.8%

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

      6. +-commutative 19.8%

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

      7. distribute-lft-out-- 19.8%

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

      8. fma-def 20.2%

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

      9. +-commutative 20.2%

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

      10. fma-def 20.3%

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

      11. associate-+l+ 20.3%

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

      12. +-commutative 20.3%

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

   3. Simplified 20.3%

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

   4. Taylor expanded in z around inf 19.8%

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

      1. associate-/l* 45.8%

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

      2. +-commutative 45.8%

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

      3. associate-/l* 76.5%

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

   6. Simplified 76.5%

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

      1. *-un-lft-identity 76.5%

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

      2. associate-/l* 99.8%

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

      3. associate-+r+ 99.8%

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

   8. Applied egg-rr 99.8%

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

      1. *-lft-identity 99.8%

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

      2. associate-+r+ 99.8%

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

      3. associate-/r/ 99.8%

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

      4. associate-+r+ 99.8%

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

      5. +-commutative 99.8%

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

      6. +-commutative 99.8%

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

   10. Simplified 99.8%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 9.99999999999999949e60

   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. Step-by-step derivation

      1. fma-def 99.8%

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

      2. +-commutative 99.8%

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

      3. +-commutative 99.8%

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

   3. Simplified 99.8%

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

4. Final simplification 99.8%

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

Alternative 2: 97.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \frac{\left(a \cdot \left(y + t\right) + z \cdot \left(x + y\right)\right) - y \cdot b}{t_1}\\ \mathbf{if}\;t_2 \leq -\infty \lor \neg \left(t_2 \leq 10^{+61}\right):\\ \;\;\;\;\frac{x + y}{\frac{t_1}{z}} + \left(t \cdot \frac{a}{x + \left(y + t\right)} + \frac{y}{\frac{t_1}{a - b}}\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t)))
        (t_2 (/ (- (+ (* a (+ y t)) (* z (+ x y))) (* y b)) t_1)))
   (if (or (<= t_2 (- INFINITY)) (not (<= t_2 1e+61)))
     (+
      (/ (+ x y) (/ t_1 z))
      (+ (* t (/ a (+ x (+ y 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 = (((a * (y + t)) + (z * (x + y))) - (y * b)) / t_1;
	double tmp;
	if ((t_2 <= -((double) INFINITY)) || !(t_2 <= 1e+61)) {
		tmp = ((x + y) / (t_1 / z)) + ((t * (a / (x + (y + 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 = (((a * (y + t)) + (z * (x + y))) - (y * b)) / t_1;
	double tmp;
	if ((t_2 <= -Double.POSITIVE_INFINITY) || !(t_2 <= 1e+61)) {
		tmp = ((x + y) / (t_1 / z)) + ((t * (a / (x + (y + 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 = (((a * (y + t)) + (z * (x + y))) - (y * b)) / t_1
	tmp = 0
	if (t_2 <= -math.inf) or not (t_2 <= 1e+61):
		tmp = ((x + y) / (t_1 / z)) + ((t * (a / (x + (y + 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(a * Float64(y + t)) + Float64(z * Float64(x + y))) - Float64(y * b)) / t_1)
	tmp = 0.0
	if ((t_2 <= Float64(-Inf)) || !(t_2 <= 1e+61))
		tmp = Float64(Float64(Float64(x + y) / Float64(t_1 / z)) + Float64(Float64(t * Float64(a / Float64(x + Float64(y + 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 = (((a * (y + t)) + (z * (x + y))) - (y * b)) / t_1;
	tmp = 0.0;
	if ((t_2 <= -Inf) || ~((t_2 <= 1e+61)))
		tmp = ((x + y) / (t_1 / z)) + ((t * (a / (x + (y + 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[(a * N[(y + t), $MachinePrecision]), $MachinePrecision] + N[(z * N[(x + y), $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, 1e+61]], $MachinePrecision]], N[(N[(N[(x + y), $MachinePrecision] / N[(t$95$1 / z), $MachinePrecision]), $MachinePrecision] + N[(N[(t * N[(a / N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision]), $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 9.99999999999999949e60 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 19.9%

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

      1. *-commutative 19.9%

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

      2. distribute-rgt-in 19.8%

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

      3. associate-+r+ 19.8%

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

      4. associate--l+ 19.8%

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

      5. +-commutative 19.8%

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

      6. +-commutative 19.8%

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

      7. distribute-lft-out-- 19.8%

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

      8. fma-def 20.2%

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

      9. +-commutative 20.2%

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

      10. fma-def 20.3%

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

      11. associate-+l+ 20.3%

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

      12. +-commutative 20.3%

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

   3. Simplified 20.3%

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

   4. Taylor expanded in z around inf 19.8%

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

      1. associate-/l* 45.8%

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

      2. +-commutative 45.8%

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

      3. associate-/l* 76.5%

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

   6. Simplified 76.5%

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

      1. *-un-lft-identity 76.5%

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

      2. associate-/l* 99.8%

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

      3. associate-+r+ 99.8%

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

   8. Applied egg-rr 99.8%

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

      1. *-lft-identity 99.8%

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

      2. associate-+r+ 99.8%

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

      3. associate-/r/ 99.8%

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

      4. associate-+r+ 99.8%

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

      5. +-commutative 99.8%

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

      6. +-commutative 99.8%

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

   10. Simplified 99.8%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 9.99999999999999949e60

   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%

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

Alternative 3: 94.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \frac{\left(a \cdot \left(y + t\right) + z \cdot \left(x + y\right)\right) - y \cdot b}{t_1}\\ \mathbf{if}\;t_2 \leq -\infty \lor \neg \left(t_2 \leq 2 \cdot 10^{+130}\right):\\ \;\;\;\;z + \left(t \cdot \frac{a}{x + \left(y + t\right)} + \frac{y}{\frac{t_1}{a - b}}\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t)))
        (t_2 (/ (- (+ (* a (+ y t)) (* z (+ x y))) (* y b)) t_1)))
   (if (or (<= t_2 (- INFINITY)) (not (<= t_2 2e+130)))
     (+ z (+ (* t (/ a (+ x (+ y 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 = (((a * (y + t)) + (z * (x + y))) - (y * b)) / t_1;
	double tmp;
	if ((t_2 <= -((double) INFINITY)) || !(t_2 <= 2e+130)) {
		tmp = z + ((t * (a / (x + (y + 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 = (((a * (y + t)) + (z * (x + y))) - (y * b)) / t_1;
	double tmp;
	if ((t_2 <= -Double.POSITIVE_INFINITY) || !(t_2 <= 2e+130)) {
		tmp = z + ((t * (a / (x + (y + 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 = (((a * (y + t)) + (z * (x + y))) - (y * b)) / t_1
	tmp = 0
	if (t_2 <= -math.inf) or not (t_2 <= 2e+130):
		tmp = z + ((t * (a / (x + (y + 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(a * Float64(y + t)) + Float64(z * Float64(x + y))) - Float64(y * b)) / t_1)
	tmp = 0.0
	if ((t_2 <= Float64(-Inf)) || !(t_2 <= 2e+130))
		tmp = Float64(z + Float64(Float64(t * Float64(a / Float64(x + Float64(y + 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 = (((a * (y + t)) + (z * (x + y))) - (y * b)) / t_1;
	tmp = 0.0;
	if ((t_2 <= -Inf) || ~((t_2 <= 2e+130)))
		tmp = z + ((t * (a / (x + (y + 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[(a * N[(y + t), $MachinePrecision]), $MachinePrecision] + N[(z * N[(x + y), $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+130]], $MachinePrecision]], N[(z + N[(N[(t * N[(a / N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision]), $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 2.0000000000000001e130 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 14.5%

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

      1. *-commutative 14.5%

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

      2. distribute-rgt-in 14.3%

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

      3. associate-+r+ 14.3%

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

      4. associate--l+ 14.3%

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

      5. +-commutative 14.3%

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

      6. +-commutative 14.3%

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

      7. distribute-lft-out-- 14.4%

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

      8. fma-def 14.8%

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

      9. +-commutative 14.8%

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

      10. fma-def 14.9%

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

      11. associate-+l+ 14.9%

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

      12. +-commutative 14.9%

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

   3. Simplified 14.9%

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

   4. Taylor expanded in z around inf 14.4%

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

      1. associate-/l* 42.1%

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

      2. +-commutative 42.1%

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

      3. associate-/l* 74.9%

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

   6. Simplified 74.9%

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

      1. *-un-lft-identity 74.9%

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

      2. associate-/l* 99.8%

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

      3. associate-+r+ 99.8%

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

   8. Applied egg-rr 99.8%

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

      1. *-lft-identity 99.8%

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

      2. associate-+r+ 99.8%

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

      3. associate-/r/ 99.8%

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

      4. associate-+r+ 99.8%

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

      5. +-commutative 99.8%

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

      6. +-commutative 99.8%

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

   10. Simplified 99.8%

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

   11. Taylor expanded in y around inf 89.9%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 2.0000000000000001e130

   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 94.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(a \cdot \left(y + t\right) + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty \lor \neg \left(\frac{\left(a \cdot \left(y + t\right) + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 2 \cdot 10^{+130}\right):\\ \;\;\;\;z + \left(t \cdot \frac{a}{x + \left(y + t\right)} + \frac{y}{\frac{y + \left(x + t\right)}{a - b}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(a \cdot \left(y + t\right) + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \end{array} \]

Alternative 4: 87.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(a \cdot \left(y + t\right) + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{if}\;t_1 \leq -\infty \lor \neg \left(t_1 \leq 2 \cdot 10^{+231}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* a (+ y t)) (* z (+ x y))) (* y b)) (+ y (+ x t)))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 2e+231))) (- (+ z a) b) t_1)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (((a * (y + t)) + (z * (x + y))) - (y * b)) / (y + (x + t));
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 2e+231)) {
		tmp = (z + a) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (((a * (y + t)) + (z * (x + y))) - (y * b)) / (y + (x + t));
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 2e+231)) {
		tmp = (z + a) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (((a * (y + t)) + (z * (x + y))) - (y * b)) / (y + (x + t))
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 2e+231):
		tmp = (z + a) - b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(Float64(a * Float64(y + t)) + Float64(z * Float64(x + y))) - Float64(y * b)) / Float64(y + Float64(x + t)))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 2e+231))
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (((a * (y + t)) + (z * (x + y))) - (y * b)) / (y + (x + t));
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 2e+231)))
		tmp = (z + a) - b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision] + N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 2e+231]], $MachinePrecision]], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], t$95$1]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -inf.0 or 2.0000000000000001e231 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 5.3%

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

   2. Taylor expanded in y around inf 73.7%

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

      1. +-commutative 73.7%

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

   4. Simplified 73.7%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 2.0000000000000001e231

   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 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(a \cdot \left(y + t\right) + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty \lor \neg \left(\frac{\left(a \cdot \left(y + t\right) + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 2 \cdot 10^{+231}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(a \cdot \left(y + t\right) + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \end{array} \]

Alternative 5: 63.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot \left(a - b\right) + z \cdot \left(x + y\right)}{x + y}\\ t_2 := y + \left(x + t\right)\\ t_3 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -44000000:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -1.28 \cdot 10^{-135}:\\ \;\;\;\;\frac{y \cdot t_3}{t_2}\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-99}:\\ \;\;\;\;\frac{x \cdot z + t \cdot a}{x + t}\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-55}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{-6}:\\ \;\;\;\;\frac{x + y}{\frac{t_2}{z}}\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{+35}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ (* y (- a b)) (* z (+ x y))) (+ x y)))
        (t_2 (+ y (+ x t)))
        (t_3 (- (+ z a) b)))
   (if (<= y -44000000.0)
     t_3
     (if (<= y -1.28e-135)
       (/ (* y t_3) t_2)
       (if (<= y 1.05e-99)
         (/ (+ (* x z) (* t a)) (+ x t))
         (if (<= y 6.2e-55)
           t_1
           (if (<= y 4.3e-6)
             (/ (+ x y) (/ t_2 z))
             (if (<= y 2.65e+35) t_1 t_3))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y * (a - b)) + (z * (x + y))) / (x + y);
	double t_2 = y + (x + t);
	double t_3 = (z + a) - b;
	double tmp;
	if (y <= -44000000.0) {
		tmp = t_3;
	} else if (y <= -1.28e-135) {
		tmp = (y * t_3) / t_2;
	} else if (y <= 1.05e-99) {
		tmp = ((x * z) + (t * a)) / (x + t);
	} else if (y <= 6.2e-55) {
		tmp = t_1;
	} else if (y <= 4.3e-6) {
		tmp = (x + y) / (t_2 / z);
	} else if (y <= 2.65e+35) {
		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 = ((y * (a - b)) + (z * (x + y))) / (x + y)
    t_2 = y + (x + t)
    t_3 = (z + a) - b
    if (y <= (-44000000.0d0)) then
        tmp = t_3
    else if (y <= (-1.28d-135)) then
        tmp = (y * t_3) / t_2
    else if (y <= 1.05d-99) then
        tmp = ((x * z) + (t * a)) / (x + t)
    else if (y <= 6.2d-55) then
        tmp = t_1
    else if (y <= 4.3d-6) then
        tmp = (x + y) / (t_2 / z)
    else if (y <= 2.65d+35) 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 = ((y * (a - b)) + (z * (x + y))) / (x + y);
	double t_2 = y + (x + t);
	double t_3 = (z + a) - b;
	double tmp;
	if (y <= -44000000.0) {
		tmp = t_3;
	} else if (y <= -1.28e-135) {
		tmp = (y * t_3) / t_2;
	} else if (y <= 1.05e-99) {
		tmp = ((x * z) + (t * a)) / (x + t);
	} else if (y <= 6.2e-55) {
		tmp = t_1;
	} else if (y <= 4.3e-6) {
		tmp = (x + y) / (t_2 / z);
	} else if (y <= 2.65e+35) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((y * (a - b)) + (z * (x + y))) / (x + y)
	t_2 = y + (x + t)
	t_3 = (z + a) - b
	tmp = 0
	if y <= -44000000.0:
		tmp = t_3
	elif y <= -1.28e-135:
		tmp = (y * t_3) / t_2
	elif y <= 1.05e-99:
		tmp = ((x * z) + (t * a)) / (x + t)
	elif y <= 6.2e-55:
		tmp = t_1
	elif y <= 4.3e-6:
		tmp = (x + y) / (t_2 / z)
	elif y <= 2.65e+35:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(y * Float64(a - b)) + Float64(z * Float64(x + y))) / Float64(x + y))
	t_2 = Float64(y + Float64(x + t))
	t_3 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -44000000.0)
		tmp = t_3;
	elseif (y <= -1.28e-135)
		tmp = Float64(Float64(y * t_3) / t_2);
	elseif (y <= 1.05e-99)
		tmp = Float64(Float64(Float64(x * z) + Float64(t * a)) / Float64(x + t));
	elseif (y <= 6.2e-55)
		tmp = t_1;
	elseif (y <= 4.3e-6)
		tmp = Float64(Float64(x + y) / Float64(t_2 / z));
	elseif (y <= 2.65e+35)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((y * (a - b)) + (z * (x + y))) / (x + y);
	t_2 = y + (x + t);
	t_3 = (z + a) - b;
	tmp = 0.0;
	if (y <= -44000000.0)
		tmp = t_3;
	elseif (y <= -1.28e-135)
		tmp = (y * t_3) / t_2;
	elseif (y <= 1.05e-99)
		tmp = ((x * z) + (t * a)) / (x + t);
	elseif (y <= 6.2e-55)
		tmp = t_1;
	elseif (y <= 4.3e-6)
		tmp = (x + y) / (t_2 / z);
	elseif (y <= 2.65e+35)
		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[(N[(y * N[(a - b), $MachinePrecision]), $MachinePrecision] + N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -44000000.0], t$95$3, If[LessEqual[y, -1.28e-135], N[(N[(y * t$95$3), $MachinePrecision] / t$95$2), $MachinePrecision], If[LessEqual[y, 1.05e-99], N[(N[(N[(x * z), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.2e-55], t$95$1, If[LessEqual[y, 4.3e-6], N[(N[(x + y), $MachinePrecision] / N[(t$95$2 / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.65e+35], t$95$1, t$95$3]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -4.4e7 or 2.65000000000000005e35 < y

   1. Initial program 37.0%

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

   2. Taylor expanded in y around inf 74.2%

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

      1. +-commutative 74.2%

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

   4. Simplified 74.2%

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

   if -4.4e7 < y < -1.27999999999999997e-135

   1. Initial program 79.5%

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

   2. Taylor expanded in y around inf 58.6%

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

      1. +-commutative 58.6%

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

   4. Simplified 58.6%

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

   if -1.27999999999999997e-135 < y < 1.04999999999999992e-99

   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 y around 0 65.2%

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

   if 1.04999999999999992e-99 < y < 6.19999999999999993e-55 or 4.30000000000000033e-6 < y < 2.65000000000000005e35

   1. Initial program 81.9%

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

      1. *-commutative 81.9%

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

      2. distribute-rgt-in 81.9%

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

      3. associate-+r+ 81.9%

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

      4. associate--l+ 81.9%

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

      5. +-commutative 81.9%

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

      6. +-commutative 81.9%

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

      7. distribute-lft-out-- 81.9%

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

      8. fma-def 81.9%

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

      9. +-commutative 81.9%

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

      10. fma-def 81.9%

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

      11. associate-+l+ 81.9%

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

      12. +-commutative 81.9%

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

   3. Simplified 81.9%

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

   4. Taylor expanded in t around 0 78.4%

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

   if 6.19999999999999993e-55 < y < 4.30000000000000033e-6

   1. Initial program 53.8%

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

   2. Taylor expanded in z around inf 18.6%

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

      1. associate-/l* 64.8%

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

   4. Simplified 64.8%

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

4. Final simplification 69.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -44000000:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -1.28 \cdot 10^{-135}:\\ \;\;\;\;\frac{y \cdot \left(\left(z + a\right) - b\right)}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-99}:\\ \;\;\;\;\frac{x \cdot z + t \cdot a}{x + t}\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-55}:\\ \;\;\;\;\frac{y \cdot \left(a - b\right) + z \cdot \left(x + y\right)}{x + y}\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{-6}:\\ \;\;\;\;\frac{x + y}{\frac{y + \left(x + t\right)}{z}}\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{+35}:\\ \;\;\;\;\frac{y \cdot \left(a - b\right) + z \cdot \left(x + y\right)}{x + y}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]

Alternative 6: 65.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.32 \cdot 10^{+37} \lor \neg \left(y \leq 1.5 \cdot 10^{+74}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y}{\frac{y + \left(x + t\right)}{z}} + \left(a + \frac{y \cdot \left(a - b\right)}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.32e+37) (not (<= y 1.5e+74)))
   (- (+ z a) b)
   (+ (/ (+ x y) (/ (+ y (+ x t)) z)) (+ a (/ (* y (- a b)) t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.32e+37) || !(y <= 1.5e+74)) {
		tmp = (z + a) - b;
	} else {
		tmp = ((x + y) / ((y + (x + t)) / z)) + (a + ((y * (a - b)) / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-1.32d+37)) .or. (.not. (y <= 1.5d+74))) then
        tmp = (z + a) - b
    else
        tmp = ((x + y) / ((y + (x + t)) / z)) + (a + ((y * (a - b)) / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.32e+37) || !(y <= 1.5e+74)) {
		tmp = (z + a) - b;
	} else {
		tmp = ((x + y) / ((y + (x + t)) / z)) + (a + ((y * (a - b)) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.32e+37) or not (y <= 1.5e+74):
		tmp = (z + a) - b
	else:
		tmp = ((x + y) / ((y + (x + t)) / z)) + (a + ((y * (a - b)) / t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.32e+37) || !(y <= 1.5e+74))
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(Float64(Float64(x + y) / Float64(Float64(y + Float64(x + t)) / z)) + Float64(a + Float64(Float64(y * Float64(a - b)) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.32e+37) || ~((y <= 1.5e+74)))
		tmp = (z + a) - b;
	else
		tmp = ((x + y) / ((y + (x + t)) / z)) + (a + ((y * (a - b)) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.32e+37], N[Not[LessEqual[y, 1.5e+74]], $MachinePrecision]], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(N[(N[(x + y), $MachinePrecision] / N[(N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(a + N[(N[(y * N[(a - b), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.3199999999999999e37 or 1.5e74 < y

   1. Initial program 32.9%

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

   2. Taylor expanded in y around inf 78.0%

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

      1. +-commutative 78.0%

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

   4. Simplified 78.0%

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

   if -1.3199999999999999e37 < y < 1.5e74

   1. Initial program 74.3%

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

      1. *-commutative 74.3%

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

      2. distribute-rgt-in 74.3%

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

      3. associate-+r+ 74.3%

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

      4. associate--l+ 74.3%

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

      5. +-commutative 74.3%

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

      6. +-commutative 74.3%

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

      7. distribute-lft-out-- 74.3%

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

      8. fma-def 74.3%

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

      9. +-commutative 74.3%

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

      10. fma-def 74.3%

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

      11. associate-+l+ 74.3%

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

      12. +-commutative 74.3%

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

   3. Simplified 74.3%

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

   4. Taylor expanded in z around inf 74.3%

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

      1. associate-/l* 82.3%

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

      2. +-commutative 82.3%

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

      3. associate-/l* 81.0%

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

   6. Simplified 81.0%

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

   7. Taylor expanded in t around inf 81.6%

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

   8. Taylor expanded in t around inf 70.7%

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

4. Final simplification 74.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.32 \cdot 10^{+37} \lor \neg \left(y \leq 1.5 \cdot 10^{+74}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y}{\frac{y + \left(x + t\right)}{z}} + \left(a + \frac{y \cdot \left(a - b\right)}{t}\right)\\ \end{array} \]

Alternative 7: 63.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -24000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -3.3 \cdot 10^{-130}:\\ \;\;\;\;\frac{y \cdot t_2}{t_1}\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{-119}:\\ \;\;\;\;\frac{x \cdot z + t \cdot a}{x + t}\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-54}:\\ \;\;\;\;\frac{a}{\frac{t_1}{y + t}}\\ \mathbf{elif}\;y \leq 2.45 \cdot 10^{-46}:\\ \;\;\;\;a + \frac{x \cdot \left(z - a\right)}{t}\\ \mathbf{elif}\;y \leq 1700000:\\ \;\;\;\;\frac{x + y}{\frac{t_1}{z}}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t))) (t_2 (- (+ z a) b)))
   (if (<= y -24000000.0)
     t_2
     (if (<= y -3.3e-130)
       (/ (* y t_2) t_1)
       (if (<= y 4.9e-119)
         (/ (+ (* x z) (* t a)) (+ x t))
         (if (<= y 3.4e-54)
           (/ a (/ t_1 (+ y t)))
           (if (<= y 2.45e-46)
             (+ a (/ (* x (- z a)) t))
             (if (<= y 1700000.0) (/ (+ x y) (/ t_1 z)) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = (z + a) - b;
	double tmp;
	if (y <= -24000000.0) {
		tmp = t_2;
	} else if (y <= -3.3e-130) {
		tmp = (y * t_2) / t_1;
	} else if (y <= 4.9e-119) {
		tmp = ((x * z) + (t * a)) / (x + t);
	} else if (y <= 3.4e-54) {
		tmp = a / (t_1 / (y + t));
	} else if (y <= 2.45e-46) {
		tmp = a + ((x * (z - a)) / t);
	} else if (y <= 1700000.0) {
		tmp = (x + y) / (t_1 / z);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y + (x + t)
    t_2 = (z + a) - b
    if (y <= (-24000000.0d0)) then
        tmp = t_2
    else if (y <= (-3.3d-130)) then
        tmp = (y * t_2) / t_1
    else if (y <= 4.9d-119) then
        tmp = ((x * z) + (t * a)) / (x + t)
    else if (y <= 3.4d-54) then
        tmp = a / (t_1 / (y + t))
    else if (y <= 2.45d-46) then
        tmp = a + ((x * (z - a)) / t)
    else if (y <= 1700000.0d0) then
        tmp = (x + y) / (t_1 / z)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = (z + a) - b;
	double tmp;
	if (y <= -24000000.0) {
		tmp = t_2;
	} else if (y <= -3.3e-130) {
		tmp = (y * t_2) / t_1;
	} else if (y <= 4.9e-119) {
		tmp = ((x * z) + (t * a)) / (x + t);
	} else if (y <= 3.4e-54) {
		tmp = a / (t_1 / (y + t));
	} else if (y <= 2.45e-46) {
		tmp = a + ((x * (z - a)) / t);
	} else if (y <= 1700000.0) {
		tmp = (x + y) / (t_1 / z);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = (z + a) - b
	tmp = 0
	if y <= -24000000.0:
		tmp = t_2
	elif y <= -3.3e-130:
		tmp = (y * t_2) / t_1
	elif y <= 4.9e-119:
		tmp = ((x * z) + (t * a)) / (x + t)
	elif y <= 3.4e-54:
		tmp = a / (t_1 / (y + t))
	elif y <= 2.45e-46:
		tmp = a + ((x * (z - a)) / t)
	elif y <= 1700000.0:
		tmp = (x + y) / (t_1 / z)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -24000000.0)
		tmp = t_2;
	elseif (y <= -3.3e-130)
		tmp = Float64(Float64(y * t_2) / t_1);
	elseif (y <= 4.9e-119)
		tmp = Float64(Float64(Float64(x * z) + Float64(t * a)) / Float64(x + t));
	elseif (y <= 3.4e-54)
		tmp = Float64(a / Float64(t_1 / Float64(y + t)));
	elseif (y <= 2.45e-46)
		tmp = Float64(a + Float64(Float64(x * Float64(z - a)) / t));
	elseif (y <= 1700000.0)
		tmp = Float64(Float64(x + y) / Float64(t_1 / z));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	t_2 = (z + a) - b;
	tmp = 0.0;
	if (y <= -24000000.0)
		tmp = t_2;
	elseif (y <= -3.3e-130)
		tmp = (y * t_2) / t_1;
	elseif (y <= 4.9e-119)
		tmp = ((x * z) + (t * a)) / (x + t);
	elseif (y <= 3.4e-54)
		tmp = a / (t_1 / (y + t));
	elseif (y <= 2.45e-46)
		tmp = a + ((x * (z - a)) / t);
	elseif (y <= 1700000.0)
		tmp = (x + y) / (t_1 / z);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -24000000.0], t$95$2, If[LessEqual[y, -3.3e-130], N[(N[(y * t$95$2), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[y, 4.9e-119], N[(N[(N[(x * z), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.4e-54], N[(a / N[(t$95$1 / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.45e-46], N[(a + N[(N[(x * N[(z - a), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1700000.0], N[(N[(x + y), $MachinePrecision] / N[(t$95$1 / z), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -2.4e7 or 1.7e6 < y

   1. Initial program 38.8%

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

   2. Taylor expanded in y around inf 72.7%

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

      1. +-commutative 72.7%

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

   4. Simplified 72.7%

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

   if -2.4e7 < y < -3.2999999999999998e-130

   1. Initial program 79.5%

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

   2. Taylor expanded in y around inf 58.6%

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

      1. +-commutative 58.6%

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

   4. Simplified 58.6%

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

   if -3.2999999999999998e-130 < y < 4.9e-119

   1. Initial program 75.4%

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

   2. Taylor expanded in y around 0 66.6%

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

   if 4.9e-119 < y < 3.39999999999999987e-54

   1. Initial program 71.1%

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

   2. Taylor expanded in a around inf 51.9%

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

      1. associate-/l* 80.3%

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

   4. Simplified 80.3%

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

   if 3.39999999999999987e-54 < y < 2.45e-46

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 100.0%

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

   3. Taylor expanded in t around -inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. unsub-neg 100.0%

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

      3. distribute-lft-out-- 100.0%

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

      4. distribute-rgt-out-- 100.0%

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

      5. associate-*r* 100.0%

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

      6. neg-mul-1 100.0%

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

   5. Simplified 100.0%

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

   if 2.45e-46 < y < 1.7e6

   1. Initial program 53.8%

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

   2. Taylor expanded in z around inf 19.4%

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

      1. associate-/l* 65.4%

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

   4. Simplified 65.4%

      \[\leadsto \color{blue}{\frac{y + x}{\frac{y + \left(t + x\right)}{z}}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -24000000:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -3.3 \cdot 10^{-130}:\\ \;\;\;\;\frac{y \cdot \left(\left(z + a\right) - b\right)}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{-119}:\\ \;\;\;\;\frac{x \cdot z + t \cdot a}{x + t}\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-54}:\\ \;\;\;\;\frac{a}{\frac{y + \left(x + t\right)}{y + t}}\\ \mathbf{elif}\;y \leq 2.45 \cdot 10^{-46}:\\ \;\;\;\;a + \frac{x \cdot \left(z - a\right)}{t}\\ \mathbf{elif}\;y \leq 1700000:\\ \;\;\;\;\frac{x + y}{\frac{y + \left(x + t\right)}{z}}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]

Alternative 8: 64.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -1.65 \cdot 10^{+37}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.02 \cdot 10^{-204}:\\ \;\;\;\;\frac{\left(y \cdot z + a \cdot \left(y + t\right)\right) - y \cdot b}{y + t}\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-104}:\\ \;\;\;\;\frac{x \cdot z + t \cdot a}{x + t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= y -1.65e+37)
     t_1
     (if (<= y -1.02e-204)
       (/ (- (+ (* y z) (* a (+ y t))) (* y b)) (+ y t))
       (if (<= y 1.8e-104) (/ (+ (* x z) (* t a)) (+ x t)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -1.65e+37) {
		tmp = t_1;
	} else if (y <= -1.02e-204) {
		tmp = (((y * z) + (a * (y + t))) - (y * b)) / (y + t);
	} else if (y <= 1.8e-104) {
		tmp = ((x * z) + (t * a)) / (x + t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z + a) - b
    if (y <= (-1.65d+37)) then
        tmp = t_1
    else if (y <= (-1.02d-204)) then
        tmp = (((y * z) + (a * (y + t))) - (y * b)) / (y + t)
    else if (y <= 1.8d-104) then
        tmp = ((x * z) + (t * a)) / (x + t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -1.65e+37) {
		tmp = t_1;
	} else if (y <= -1.02e-204) {
		tmp = (((y * z) + (a * (y + t))) - (y * b)) / (y + t);
	} else if (y <= 1.8e-104) {
		tmp = ((x * z) + (t * a)) / (x + t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	tmp = 0
	if y <= -1.65e+37:
		tmp = t_1
	elif y <= -1.02e-204:
		tmp = (((y * z) + (a * (y + t))) - (y * b)) / (y + t)
	elif y <= 1.8e-104:
		tmp = ((x * z) + (t * a)) / (x + t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -1.65e+37)
		tmp = t_1;
	elseif (y <= -1.02e-204)
		tmp = Float64(Float64(Float64(Float64(y * z) + Float64(a * Float64(y + t))) - Float64(y * b)) / Float64(y + t));
	elseif (y <= 1.8e-104)
		tmp = Float64(Float64(Float64(x * z) + Float64(t * a)) / Float64(x + t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	tmp = 0.0;
	if (y <= -1.65e+37)
		tmp = t_1;
	elseif (y <= -1.02e-204)
		tmp = (((y * z) + (a * (y + t))) - (y * b)) / (y + t);
	elseif (y <= 1.8e-104)
		tmp = ((x * z) + (t * a)) / (x + t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -1.65e+37], t$95$1, If[LessEqual[y, -1.02e-204], N[(N[(N[(N[(y * z), $MachinePrecision] + N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.8e-104], N[(N[(N[(x * z), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.65e37 or 1.7999999999999999e-104 < y

   1. Initial program 40.6%

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

   2. Taylor expanded in y around inf 72.0%

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

      1. +-commutative 72.0%

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

   4. Simplified 72.0%

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

   if -1.65e37 < y < -1.0200000000000001e-204

   1. Initial program 76.1%

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

   2. Taylor expanded in x around 0 60.5%

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

   if -1.0200000000000001e-204 < y < 1.7999999999999999e-104

   1. Initial program 75.2%

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

   2. Taylor expanded in y around 0 66.9%

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

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{+37}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -1.02 \cdot 10^{-204}:\\ \;\;\;\;\frac{\left(y \cdot z + a \cdot \left(y + t\right)\right) - y \cdot b}{y + t}\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-104}:\\ \;\;\;\;\frac{x \cdot z + t \cdot a}{x + t}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]

Alternative 9: 58.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -32000000 \lor \neg \left(t \leq 2 \cdot 10^{+150}\right):\\ \;\;\;\;\frac{a}{\frac{y + \left(x + t\right)}{y + t}}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -32000000.0) (not (<= t 2e+150)))
   (/ a (/ (+ y (+ x t)) (+ y t)))
   (- (+ z a) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -32000000.0) || !(t <= 2e+150)) {
		tmp = a / ((y + (x + t)) / (y + 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 <= (-32000000.0d0)) .or. (.not. (t <= 2d+150))) then
        tmp = a / ((y + (x + t)) / (y + 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 <= -32000000.0) || !(t <= 2e+150)) {
		tmp = a / ((y + (x + t)) / (y + t));
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -32000000.0) or not (t <= 2e+150):
		tmp = a / ((y + (x + t)) / (y + t))
	else:
		tmp = (z + a) - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -32000000.0) || !(t <= 2e+150))
		tmp = Float64(a / Float64(Float64(y + Float64(x + t)) / Float64(y + 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 <= -32000000.0) || ~((t <= 2e+150)))
		tmp = a / ((y + (x + t)) / (y + t));
	else
		tmp = (z + a) - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -32000000.0], N[Not[LessEqual[t, 2e+150]], $MachinePrecision]], N[(a / N[(N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision] / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.2e7 or 1.99999999999999996e150 < t

   1. Initial program 48.1%

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

   2. Taylor expanded in a around inf 29.8%

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

      1. associate-/l* 59.4%

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

   4. Simplified 59.4%

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

   if -3.2e7 < t < 1.99999999999999996e150

   1. Initial program 60.2%

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

   2. Taylor expanded in y around inf 67.9%

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

      1. +-commutative 67.9%

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

   4. Simplified 67.9%

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

4. Final simplification 64.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -32000000 \lor \neg \left(t \leq 2 \cdot 10^{+150}\right):\\ \;\;\;\;\frac{a}{\frac{y + \left(x + t\right)}{y + t}}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]

Alternative 10: 57.5% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9.2 \cdot 10^{+45}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 6.6 \cdot 10^{+173}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a + \frac{x \cdot \left(z - a\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -9.2e+45)
   a
   (if (<= t 6.6e+173) (- (+ z a) b) (+ a (/ (* x (- z a)) t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -9.2e+45) {
		tmp = a;
	} else if (t <= 6.6e+173) {
		tmp = (z + a) - b;
	} else {
		tmp = a + ((x * (z - a)) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-9.2d+45)) then
        tmp = a
    else if (t <= 6.6d+173) then
        tmp = (z + a) - b
    else
        tmp = a + ((x * (z - a)) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -9.2e+45) {
		tmp = a;
	} else if (t <= 6.6e+173) {
		tmp = (z + a) - b;
	} else {
		tmp = a + ((x * (z - a)) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -9.2e+45:
		tmp = a
	elif t <= 6.6e+173:
		tmp = (z + a) - b
	else:
		tmp = a + ((x * (z - a)) / t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -9.2e+45)
		tmp = a;
	elseif (t <= 6.6e+173)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(a + Float64(Float64(x * Float64(z - a)) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -9.2e+45)
		tmp = a;
	elseif (t <= 6.6e+173)
		tmp = (z + a) - b;
	else
		tmp = a + ((x * (z - a)) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -9.2e+45], a, If[LessEqual[t, 6.6e+173], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(a + N[(N[(x * N[(z - a), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -9.20000000000000049e45

   1. Initial program 56.5%

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

   2. Taylor expanded in t around inf 55.9%

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

   if -9.20000000000000049e45 < t < 6.59999999999999993e173

   1. Initial program 59.1%

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

   2. Taylor expanded in y around inf 66.8%

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

      1. +-commutative 66.8%

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

   4. Simplified 66.8%

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

   if 6.59999999999999993e173 < t

   1. Initial program 38.8%

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

   2. Taylor expanded in y around 0 27.4%

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

   3. Taylor expanded in t around -inf 56.1%

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

      1. mul-1-neg 56.1%

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

      2. unsub-neg 56.1%

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

      3. distribute-lft-out-- 56.1%

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

      4. distribute-rgt-out-- 56.2%

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

      5. associate-*r* 56.2%

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

      6. neg-mul-1 56.2%

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

   5. Simplified 56.2%

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

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.2 \cdot 10^{+45}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 6.6 \cdot 10^{+173}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a + \frac{x \cdot \left(z - a\right)}{t}\\ \end{array} \]

Alternative 11: 42.8% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.85 \cdot 10^{+234}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{+156}:\\ \;\;\;\;a\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{+86}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{-16}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -2.85e+234)
   z
   (if (<= z -1.9e+156) a (if (<= z -1.6e+86) z (if (<= z 7.8e-16) a z)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2.85e+234) {
		tmp = z;
	} else if (z <= -1.9e+156) {
		tmp = a;
	} else if (z <= -1.6e+86) {
		tmp = z;
	} else if (z <= 7.8e-16) {
		tmp = a;
	} else {
		tmp = z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-2.85d+234)) then
        tmp = z
    else if (z <= (-1.9d+156)) then
        tmp = a
    else if (z <= (-1.6d+86)) then
        tmp = z
    else if (z <= 7.8d-16) then
        tmp = a
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2.85e+234) {
		tmp = z;
	} else if (z <= -1.9e+156) {
		tmp = a;
	} else if (z <= -1.6e+86) {
		tmp = z;
	} else if (z <= 7.8e-16) {
		tmp = a;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -2.85e+234:
		tmp = z
	elif z <= -1.9e+156:
		tmp = a
	elif z <= -1.6e+86:
		tmp = z
	elif z <= 7.8e-16:
		tmp = a
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -2.85e+234)
		tmp = z;
	elseif (z <= -1.9e+156)
		tmp = a;
	elseif (z <= -1.6e+86)
		tmp = z;
	elseif (z <= 7.8e-16)
		tmp = a;
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -2.85e+234)
		tmp = z;
	elseif (z <= -1.9e+156)
		tmp = a;
	elseif (z <= -1.6e+86)
		tmp = z;
	elseif (z <= 7.8e-16)
		tmp = a;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -2.85e+234], z, If[LessEqual[z, -1.9e+156], a, If[LessEqual[z, -1.6e+86], z, If[LessEqual[z, 7.8e-16], a, z]]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.85000000000000002e234 or -1.90000000000000012e156 < z < -1.6e86 or 7.79999999999999954e-16 < z

   1. Initial program 44.5%

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

   2. Taylor expanded in x around inf 57.9%

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

   if -2.85000000000000002e234 < z < -1.90000000000000012e156 or -1.6e86 < z < 7.79999999999999954e-16

   1. Initial program 62.7%

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

   2. Taylor expanded in t around inf 49.5%

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

4. Final simplification 52.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.85 \cdot 10^{+234}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{+156}:\\ \;\;\;\;a\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{+86}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{-16}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 12: 57.9% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9.2 \cdot 10^{+45}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{+172}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -9.2e+45) a (if (<= t 5.6e+172) (- (+ z a) b) a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -9.2e+45) {
		tmp = a;
	} else if (t <= 5.6e+172) {
		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 <= (-9.2d+45)) then
        tmp = a
    else if (t <= 5.6d+172) 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 <= -9.2e+45) {
		tmp = a;
	} else if (t <= 5.6e+172) {
		tmp = (z + a) - b;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -9.2e+45:
		tmp = a
	elif t <= 5.6e+172:
		tmp = (z + a) - b
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -9.2e+45)
		tmp = a;
	elseif (t <= 5.6e+172)
		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 <= -9.2e+45)
		tmp = a;
	elseif (t <= 5.6e+172)
		tmp = (z + a) - b;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -9.2e+45], a, If[LessEqual[t, 5.6e+172], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], a]]

Derivation

1. Split input into 2 regimes

2. if t < -9.20000000000000049e45 or 5.5999999999999999e172 < t

   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 t around inf 54.8%

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

   if -9.20000000000000049e45 < t < 5.5999999999999999e172

   1. Initial program 58.9%

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

   2. Taylor expanded in y around inf 67.1%

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

      1. +-commutative 67.1%

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

   4. Simplified 67.1%

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

4. Final simplification 62.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.2 \cdot 10^{+45}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{+172}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]

Alternative 13: 32.8% 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 55.5%

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

2. Taylor expanded in t around inf 36.1%

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

3. Final simplification 36.1%

   \[\leadsto a \]

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 2023213 
(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)))