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

Percentage Accurate: 61.4% → 99.6%

Time: 14.3s

Alternatives: 17

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 61.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{t_1}\\ t_3 := \frac{x + y}{\frac{t_1}{z}}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;t_3 + \left(\frac{y + t}{\frac{t_1}{a}} - \frac{y}{\frac{t_1}{b}}\right)\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+299}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3 + \left(\frac{y}{\frac{t_1}{a - b}} + t \cdot \frac{a}{x + \left(y + t\right)}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t)))
        (t_2 (/ (- (+ (* z (+ x y)) (* a (+ y t))) (* y b)) t_1))
        (t_3 (/ (+ x y) (/ t_1 z))))
   (if (<= t_2 (- INFINITY))
     (+ t_3 (- (/ (+ y t) (/ t_1 a)) (/ y (/ t_1 b))))
     (if (<= t_2 5e+299)
       t_2
       (+ t_3 (+ (/ y (/ t_1 (- a b))) (* t (/ a (+ x (+ y t))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = (((z * (x + y)) + (a * (y + t))) - (y * b)) / t_1;
	double t_3 = (x + y) / (t_1 / z);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_3 + (((y + t) / (t_1 / a)) - (y / (t_1 / b)));
	} else if (t_2 <= 5e+299) {
		tmp = t_2;
	} else {
		tmp = t_3 + ((y / (t_1 / (a - b))) + (t * (a / (x + (y + t)))));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = (((z * (x + y)) + (a * (y + t))) - (y * b)) / t_1;
	double t_3 = (x + y) / (t_1 / z);
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_3 + (((y + t) / (t_1 / a)) - (y / (t_1 / b)));
	} else if (t_2 <= 5e+299) {
		tmp = t_2;
	} else {
		tmp = t_3 + ((y / (t_1 / (a - b))) + (t * (a / (x + (y + t)))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = (((z * (x + y)) + (a * (y + t))) - (y * b)) / t_1
	t_3 = (x + y) / (t_1 / z)
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_3 + (((y + t) / (t_1 / a)) - (y / (t_1 / b)))
	elif t_2 <= 5e+299:
		tmp = t_2
	else:
		tmp = t_3 + ((y / (t_1 / (a - b))) + (t * (a / (x + (y + t)))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(Float64(Float64(Float64(z * Float64(x + y)) + Float64(a * Float64(y + t))) - Float64(y * b)) / t_1)
	t_3 = Float64(Float64(x + y) / Float64(t_1 / z))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(t_3 + Float64(Float64(Float64(y + t) / Float64(t_1 / a)) - Float64(y / Float64(t_1 / b))));
	elseif (t_2 <= 5e+299)
		tmp = t_2;
	else
		tmp = Float64(t_3 + Float64(Float64(y / Float64(t_1 / Float64(a - b))) + Float64(t * Float64(a / Float64(x + Float64(y + t))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	t_2 = (((z * (x + y)) + (a * (y + t))) - (y * b)) / t_1;
	t_3 = (x + y) / (t_1 / z);
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_3 + (((y + t) / (t_1 / a)) - (y / (t_1 / b)));
	elseif (t_2 <= 5e+299)
		tmp = t_2;
	else
		tmp = t_3 + ((y / (t_1 / (a - b))) + (t * (a / (x + (y + t)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision] + N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x + y), $MachinePrecision] / N[(t$95$1 / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(t$95$3 + N[(N[(N[(y + t), $MachinePrecision] / N[(t$95$1 / a), $MachinePrecision]), $MachinePrecision] - N[(y / N[(t$95$1 / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+299], t$95$2, N[(t$95$3 + N[(N[(y / N[(t$95$1 / N[(a - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(a / N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 6.6%

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

      1. *-commutative 6.6%

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

      2. distribute-rgt-in 6.1%

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

      3. associate-+r+ 6.1%

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

      4. associate--l+ 6.1%

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

      5. +-commutative 6.1%

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

      6. +-commutative 6.1%

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

      7. distribute-lft-out-- 6.1%

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

      8. fma-def 6.5%

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

      9. +-commutative 6.5%

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

      10. fma-def 6.5%

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

      11. associate-+l+ 6.5%

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

      12. +-commutative 6.5%

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

   3. Simplified 6.5%

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

   4. Taylor expanded in a around -inf 6.6%

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

      1. associate-/l* 29.4%

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

      2. distribute-lft-out 29.4%

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

      3. associate-/l* 73.1%

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

      4. distribute-lft-out 73.1%

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

      5. +-commutative 73.1%

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

      6. associate-/l* 100.0%

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

   6. Simplified 100.0%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 5.0000000000000003e299

   1. Initial program 99.7%

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

   if 5.0000000000000003e299 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 5.2%

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

   3. Simplified 6.0%

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

   4. Taylor expanded in z around inf 4.9%

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

      1. associate-/l* 31.9%

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

      2. associate-/l* 67.7%

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

      3. associate-/l* 99.7%

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

   6. Simplified 99.7%

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

      1. associate-/r/ 99.8%

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

      2. +-commutative 99.8%

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

      3. +-commutative 99.8%

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

      4. associate-+l+ 99.8%

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

      5. +-commutative 99.8%

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

   8. Applied egg-rr 99.8%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty:\\ \;\;\;\;\frac{x + y}{\frac{y + \left(x + t\right)}{z}} + \left(\frac{y + t}{\frac{y + \left(x + t\right)}{a}} - \frac{y}{\frac{y + \left(x + t\right)}{b}}\right)\\ \mathbf{elif}\;\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 5 \cdot 10^{+299}:\\ \;\;\;\;\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y}{\frac{y + \left(x + t\right)}{z}} + \left(\frac{y}{\frac{y + \left(x + t\right)}{a - b}} + t \cdot \frac{a}{x + \left(y + t\right)}\right)\\ \end{array} \]

Alternative 2: 99.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{t_1}\\ \mathbf{if}\;t_2 \leq -\infty \lor \neg \left(t_2 \leq 5 \cdot 10^{+299}\right):\\ \;\;\;\;\frac{x + y}{\frac{t_1}{z}} + \left(\frac{y}{\frac{t_1}{a - b}} + t \cdot \frac{a}{x + \left(y + t\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t)))
        (t_2 (/ (- (+ (* z (+ x y)) (* a (+ y t))) (* y b)) t_1)))
   (if (or (<= t_2 (- INFINITY)) (not (<= t_2 5e+299)))
     (+
      (/ (+ x y) (/ t_1 z))
      (+ (/ y (/ t_1 (- a b))) (* t (/ a (+ x (+ y t))))))
     t_2)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = (((z * (x + y)) + (a * (y + t))) - (y * b)) / t_1;
	double tmp;
	if ((t_2 <= -((double) INFINITY)) || !(t_2 <= 5e+299)) {
		tmp = ((x + y) / (t_1 / z)) + ((y / (t_1 / (a - b))) + (t * (a / (x + (y + t)))));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = (((z * (x + y)) + (a * (y + t))) - (y * b)) / t_1;
	double tmp;
	if ((t_2 <= -Double.POSITIVE_INFINITY) || !(t_2 <= 5e+299)) {
		tmp = ((x + y) / (t_1 / z)) + ((y / (t_1 / (a - b))) + (t * (a / (x + (y + t)))));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = (((z * (x + y)) + (a * (y + t))) - (y * b)) / t_1
	tmp = 0
	if (t_2 <= -math.inf) or not (t_2 <= 5e+299):
		tmp = ((x + y) / (t_1 / z)) + ((y / (t_1 / (a - b))) + (t * (a / (x + (y + t)))))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(Float64(Float64(Float64(z * Float64(x + y)) + Float64(a * Float64(y + t))) - Float64(y * b)) / t_1)
	tmp = 0.0
	if ((t_2 <= Float64(-Inf)) || !(t_2 <= 5e+299))
		tmp = Float64(Float64(Float64(x + y) / Float64(t_1 / z)) + Float64(Float64(y / Float64(t_1 / Float64(a - b))) + Float64(t * Float64(a / Float64(x + Float64(y + t))))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	t_2 = (((z * (x + y)) + (a * (y + t))) - (y * b)) / t_1;
	tmp = 0.0;
	if ((t_2 <= -Inf) || ~((t_2 <= 5e+299)))
		tmp = ((x + y) / (t_1 / z)) + ((y / (t_1 / (a - b))) + (t * (a / (x + (y + t)))));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision] + N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[Or[LessEqual[t$95$2, (-Infinity)], N[Not[LessEqual[t$95$2, 5e+299]], $MachinePrecision]], N[(N[(N[(x + y), $MachinePrecision] / N[(t$95$1 / z), $MachinePrecision]), $MachinePrecision] + N[(N[(y / N[(t$95$1 / N[(a - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(a / N[(x + N[(y + t), $MachinePrecision]), $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 5.0000000000000003e299 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 5.8%

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

   3. Simplified 6.2%

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

   4. Taylor expanded in z around inf 5.4%

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

      1. associate-/l* 30.5%

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

      2. associate-/l* 68.5%

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

      3. associate-/l* 99.8%

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

   6. Simplified 99.8%

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

      1. associate-/r/ 99.8%

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

      2. +-commutative 99.8%

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

      3. +-commutative 99.8%

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

      4. associate-+l+ 99.8%

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

      5. +-commutative 99.8%

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

   8. Applied egg-rr 99.8%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 5.0000000000000003e299

   1. Initial program 99.7%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty \lor \neg \left(\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 5 \cdot 10^{+299}\right):\\ \;\;\;\;\frac{x + y}{\frac{y + \left(x + t\right)}{z}} + \left(\frac{y}{\frac{y + \left(x + t\right)}{a - b}} + t \cdot \frac{a}{x + \left(y + t\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \end{array} \]

Alternative 3: 99.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{t_1}\\ t_3 := \frac{x + y}{\frac{t_1}{z}}\\ t_4 := \frac{y}{\frac{t_1}{a - b}}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;t_3 + \left(t_4 + \frac{a}{\frac{t_1}{t}}\right)\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+299}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3 + \left(t_4 + t \cdot \frac{a}{x + \left(y + t\right)}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t)))
        (t_2 (/ (- (+ (* z (+ x y)) (* a (+ y t))) (* y b)) t_1))
        (t_3 (/ (+ x y) (/ t_1 z)))
        (t_4 (/ y (/ t_1 (- a b)))))
   (if (<= t_2 (- INFINITY))
     (+ t_3 (+ t_4 (/ a (/ t_1 t))))
     (if (<= t_2 5e+299) t_2 (+ t_3 (+ t_4 (* t (/ a (+ x (+ y t))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = (((z * (x + y)) + (a * (y + t))) - (y * b)) / t_1;
	double t_3 = (x + y) / (t_1 / z);
	double t_4 = y / (t_1 / (a - b));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_3 + (t_4 + (a / (t_1 / t)));
	} else if (t_2 <= 5e+299) {
		tmp = t_2;
	} else {
		tmp = t_3 + (t_4 + (t * (a / (x + (y + t)))));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = (((z * (x + y)) + (a * (y + t))) - (y * b)) / t_1;
	double t_3 = (x + y) / (t_1 / z);
	double t_4 = y / (t_1 / (a - b));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_3 + (t_4 + (a / (t_1 / t)));
	} else if (t_2 <= 5e+299) {
		tmp = t_2;
	} else {
		tmp = t_3 + (t_4 + (t * (a / (x + (y + t)))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = (((z * (x + y)) + (a * (y + t))) - (y * b)) / t_1
	t_3 = (x + y) / (t_1 / z)
	t_4 = y / (t_1 / (a - b))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_3 + (t_4 + (a / (t_1 / t)))
	elif t_2 <= 5e+299:
		tmp = t_2
	else:
		tmp = t_3 + (t_4 + (t * (a / (x + (y + t)))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(Float64(Float64(Float64(z * Float64(x + y)) + Float64(a * Float64(y + t))) - Float64(y * b)) / t_1)
	t_3 = Float64(Float64(x + y) / Float64(t_1 / z))
	t_4 = Float64(y / Float64(t_1 / Float64(a - b)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(t_3 + Float64(t_4 + Float64(a / Float64(t_1 / t))));
	elseif (t_2 <= 5e+299)
		tmp = t_2;
	else
		tmp = Float64(t_3 + Float64(t_4 + Float64(t * Float64(a / Float64(x + Float64(y + t))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	t_2 = (((z * (x + y)) + (a * (y + t))) - (y * b)) / t_1;
	t_3 = (x + y) / (t_1 / z);
	t_4 = y / (t_1 / (a - b));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_3 + (t_4 + (a / (t_1 / t)));
	elseif (t_2 <= 5e+299)
		tmp = t_2;
	else
		tmp = t_3 + (t_4 + (t * (a / (x + (y + t)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision] + N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x + y), $MachinePrecision] / N[(t$95$1 / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(y / N[(t$95$1 / N[(a - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(t$95$3 + N[(t$95$4 + N[(a / N[(t$95$1 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+299], t$95$2, N[(t$95$3 + N[(t$95$4 + N[(t * N[(a / N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 6.6%

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

   3. Simplified 6.5%

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

   4. Taylor expanded in z around inf 6.1%

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

      1. associate-/l* 29.0%

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

      2. associate-/l* 69.5%

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

      3. associate-/l* 99.9%

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

   6. Simplified 99.9%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 5.0000000000000003e299

   1. Initial program 99.7%

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

   if 5.0000000000000003e299 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 5.2%

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

   3. Simplified 6.0%

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

   4. Taylor expanded in z around inf 4.9%

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

      1. associate-/l* 31.9%

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

      2. associate-/l* 67.7%

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

      3. associate-/l* 99.7%

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

   6. Simplified 99.7%

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

      1. associate-/r/ 99.8%

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

      2. +-commutative 99.8%

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

      3. +-commutative 99.8%

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

      4. associate-+l+ 99.8%

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

      5. +-commutative 99.8%

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

   8. Applied egg-rr 99.8%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty:\\ \;\;\;\;\frac{x + y}{\frac{y + \left(x + t\right)}{z}} + \left(\frac{y}{\frac{y + \left(x + t\right)}{a - b}} + \frac{a}{\frac{y + \left(x + t\right)}{t}}\right)\\ \mathbf{elif}\;\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 5 \cdot 10^{+299}:\\ \;\;\;\;\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y}{\frac{y + \left(x + t\right)}{z}} + \left(\frac{y}{\frac{y + \left(x + t\right)}{a - b}} + t \cdot \frac{a}{x + \left(y + t\right)}\right)\\ \end{array} \]

Alternative 4: 96.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{t_1}\\ \mathbf{if}\;t_2 \leq -\infty \lor \neg \left(t_2 \leq 5 \cdot 10^{+299}\right):\\ \;\;\;\;z + \left(\frac{y}{\frac{t_1}{a - b}} + t \cdot \frac{a}{x + \left(y + t\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t)))
        (t_2 (/ (- (+ (* z (+ x y)) (* a (+ y t))) (* y b)) t_1)))
   (if (or (<= t_2 (- INFINITY)) (not (<= t_2 5e+299)))
     (+ z (+ (/ y (/ t_1 (- a b))) (* t (/ a (+ x (+ y t))))))
     t_2)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = (((z * (x + y)) + (a * (y + t))) - (y * b)) / t_1;
	double tmp;
	if ((t_2 <= -((double) INFINITY)) || !(t_2 <= 5e+299)) {
		tmp = z + ((y / (t_1 / (a - b))) + (t * (a / (x + (y + t)))));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = (((z * (x + y)) + (a * (y + t))) - (y * b)) / t_1;
	double tmp;
	if ((t_2 <= -Double.POSITIVE_INFINITY) || !(t_2 <= 5e+299)) {
		tmp = z + ((y / (t_1 / (a - b))) + (t * (a / (x + (y + t)))));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = (((z * (x + y)) + (a * (y + t))) - (y * b)) / t_1
	tmp = 0
	if (t_2 <= -math.inf) or not (t_2 <= 5e+299):
		tmp = z + ((y / (t_1 / (a - b))) + (t * (a / (x + (y + t)))))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(Float64(Float64(Float64(z * Float64(x + y)) + Float64(a * Float64(y + t))) - Float64(y * b)) / t_1)
	tmp = 0.0
	if ((t_2 <= Float64(-Inf)) || !(t_2 <= 5e+299))
		tmp = Float64(z + Float64(Float64(y / Float64(t_1 / Float64(a - b))) + Float64(t * Float64(a / Float64(x + Float64(y + t))))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	t_2 = (((z * (x + y)) + (a * (y + t))) - (y * b)) / t_1;
	tmp = 0.0;
	if ((t_2 <= -Inf) || ~((t_2 <= 5e+299)))
		tmp = z + ((y / (t_1 / (a - b))) + (t * (a / (x + (y + t)))));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision] + N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[Or[LessEqual[t$95$2, (-Infinity)], N[Not[LessEqual[t$95$2, 5e+299]], $MachinePrecision]], N[(z + N[(N[(y / N[(t$95$1 / N[(a - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(a / N[(x + N[(y + t), $MachinePrecision]), $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 5.0000000000000003e299 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 5.8%

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

   3. Simplified 6.2%

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

   4. Taylor expanded in z around inf 5.4%

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

      1. associate-/l* 30.5%

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

      2. associate-/l* 68.5%

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

      3. associate-/l* 99.8%

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

   6. Simplified 99.8%

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

      1. associate-/r/ 99.8%

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

      2. +-commutative 99.8%

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

      3. +-commutative 99.8%

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

      4. associate-+l+ 99.8%

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

      5. +-commutative 99.8%

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

   8. Applied egg-rr 99.8%

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

   9. Taylor expanded in y around inf 95.6%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 5.0000000000000003e299

   1. Initial program 99.7%

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

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty \lor \neg \left(\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 5 \cdot 10^{+299}\right):\\ \;\;\;\;z + \left(\frac{y}{\frac{y + \left(x + t\right)}{a - b}} + t \cdot \frac{a}{x + \left(y + t\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \end{array} \]

Alternative 5: 96.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{t_1}\\ t_3 := \frac{y}{\frac{t_1}{a - b}}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;z + \left(t_3 + \frac{a}{\frac{t_1}{t}}\right)\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+299}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;z + \left(t_3 + t \cdot \frac{a}{x + \left(y + t\right)}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t)))
        (t_2 (/ (- (+ (* z (+ x y)) (* a (+ y t))) (* y b)) t_1))
        (t_3 (/ y (/ t_1 (- a b)))))
   (if (<= t_2 (- INFINITY))
     (+ z (+ t_3 (/ a (/ t_1 t))))
     (if (<= t_2 5e+299) t_2 (+ z (+ t_3 (* t (/ a (+ x (+ y t))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = (((z * (x + y)) + (a * (y + t))) - (y * b)) / t_1;
	double t_3 = y / (t_1 / (a - b));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = z + (t_3 + (a / (t_1 / t)));
	} else if (t_2 <= 5e+299) {
		tmp = t_2;
	} else {
		tmp = z + (t_3 + (t * (a / (x + (y + t)))));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = (((z * (x + y)) + (a * (y + t))) - (y * b)) / t_1;
	double t_3 = y / (t_1 / (a - b));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = z + (t_3 + (a / (t_1 / t)));
	} else if (t_2 <= 5e+299) {
		tmp = t_2;
	} else {
		tmp = z + (t_3 + (t * (a / (x + (y + t)))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = (((z * (x + y)) + (a * (y + t))) - (y * b)) / t_1
	t_3 = y / (t_1 / (a - b))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = z + (t_3 + (a / (t_1 / t)))
	elif t_2 <= 5e+299:
		tmp = t_2
	else:
		tmp = z + (t_3 + (t * (a / (x + (y + t)))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(Float64(Float64(Float64(z * Float64(x + y)) + Float64(a * Float64(y + t))) - Float64(y * b)) / t_1)
	t_3 = Float64(y / Float64(t_1 / Float64(a - b)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(z + Float64(t_3 + Float64(a / Float64(t_1 / t))));
	elseif (t_2 <= 5e+299)
		tmp = t_2;
	else
		tmp = Float64(z + Float64(t_3 + Float64(t * Float64(a / Float64(x + Float64(y + t))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	t_2 = (((z * (x + y)) + (a * (y + t))) - (y * b)) / t_1;
	t_3 = y / (t_1 / (a - b));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = z + (t_3 + (a / (t_1 / t)));
	elseif (t_2 <= 5e+299)
		tmp = t_2;
	else
		tmp = z + (t_3 + (t * (a / (x + (y + t)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision] + N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(y / N[(t$95$1 / N[(a - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(z + N[(t$95$3 + N[(a / N[(t$95$1 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+299], t$95$2, N[(z + N[(t$95$3 + N[(t * N[(a / N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 6.6%

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

   3. Simplified 6.5%

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

   4. Taylor expanded in z around inf 6.1%

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

      1. associate-/l* 29.0%

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

      2. associate-/l* 69.5%

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

      3. associate-/l* 99.9%

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

   6. Simplified 99.9%

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

   7. Taylor expanded in y around inf 97.3%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 5.0000000000000003e299

   1. Initial program 99.7%

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

   if 5.0000000000000003e299 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 5.2%

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

   3. Simplified 6.0%

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

   4. Taylor expanded in z around inf 4.9%

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

      1. associate-/l* 31.9%

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

      2. associate-/l* 67.7%

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

      3. associate-/l* 99.7%

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

   6. Simplified 99.7%

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

      1. associate-/r/ 99.8%

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

      2. +-commutative 99.8%

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

      3. +-commutative 99.8%

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

      4. associate-+l+ 99.8%

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

      5. +-commutative 99.8%

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

   8. Applied egg-rr 99.8%

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

   9. Taylor expanded in y around inf 94.1%

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

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty:\\ \;\;\;\;z + \left(\frac{y}{\frac{y + \left(x + t\right)}{a - b}} + \frac{a}{\frac{y + \left(x + t\right)}{t}}\right)\\ \mathbf{elif}\;\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 5 \cdot 10^{+299}:\\ \;\;\;\;\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;z + \left(\frac{y}{\frac{y + \left(x + t\right)}{a - b}} + t \cdot \frac{a}{x + \left(y + t\right)}\right)\\ \end{array} \]

Alternative 6: 88.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{if}\;t_1 \leq -\infty \lor \neg \left(t_1 \leq 4 \cdot 10^{+261}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* z (+ x y)) (* a (+ y t))) (* y b)) (+ y (+ x t)))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 4e+261))) (- (+ z a) b) t_1)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (((z * (x + y)) + (a * (y + t))) - (y * b)) / (y + (x + t));
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 4e+261)) {
		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 = (((z * (x + y)) + (a * (y + t))) - (y * b)) / (y + (x + t));
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 4e+261)) {
		tmp = (z + a) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (((z * (x + y)) + (a * (y + t))) - (y * b)) / (y + (x + t))
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 4e+261):
		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(z * Float64(x + y)) + Float64(a * Float64(y + t))) - Float64(y * b)) / Float64(y + Float64(x + t)))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 4e+261))
		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 = (((z * (x + y)) + (a * (y + t))) - (y * b)) / (y + (x + t));
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 4e+261)))
		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[(z * N[(x + y), $MachinePrecision]), $MachinePrecision] + N[(a * N[(y + t), $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, 4e+261]], $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 3.9999999999999997e261 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 10.1%

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

   2. Taylor expanded in y around inf 76.4%

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

      1. +-commutative 76.4%

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

   4. Simplified 76.4%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 3.9999999999999997e261

   1. Initial program 99.7%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty \lor \neg \left(\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 4 \cdot 10^{+261}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \end{array} \]

Alternative 7: 66.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + y}{\frac{y + \left(x + t\right)}{z}}\\ t_2 := x + \left(y + t\right)\\ \mathbf{if}\;z \leq -1.35 \cdot 10^{+166}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{-39}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+105}:\\ \;\;\;\;\frac{a}{\frac{t_2}{y + t}} - \frac{y \cdot b}{t_2}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x y) (/ (+ y (+ x t)) z))) (t_2 (+ x (+ y t))))
   (if (<= z -1.35e+166)
     t_1
     (if (<= z -1.45e-39)
       (- (+ z a) b)
       (if (<= z 3.7e+105) (- (/ a (/ t_2 (+ y t))) (/ (* y b) t_2)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + y) / ((y + (x + t)) / z);
	double t_2 = x + (y + t);
	double tmp;
	if (z <= -1.35e+166) {
		tmp = t_1;
	} else if (z <= -1.45e-39) {
		tmp = (z + a) - b;
	} else if (z <= 3.7e+105) {
		tmp = (a / (t_2 / (y + t))) - ((y * b) / t_2);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x + y) / ((y + (x + t)) / z)
    t_2 = x + (y + t)
    if (z <= (-1.35d+166)) then
        tmp = t_1
    else if (z <= (-1.45d-39)) then
        tmp = (z + a) - b
    else if (z <= 3.7d+105) then
        tmp = (a / (t_2 / (y + t))) - ((y * b) / t_2)
    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 = (x + y) / ((y + (x + t)) / z);
	double t_2 = x + (y + t);
	double tmp;
	if (z <= -1.35e+166) {
		tmp = t_1;
	} else if (z <= -1.45e-39) {
		tmp = (z + a) - b;
	} else if (z <= 3.7e+105) {
		tmp = (a / (t_2 / (y + t))) - ((y * b) / t_2);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + y) / ((y + (x + t)) / z)
	t_2 = x + (y + t)
	tmp = 0
	if z <= -1.35e+166:
		tmp = t_1
	elif z <= -1.45e-39:
		tmp = (z + a) - b
	elif z <= 3.7e+105:
		tmp = (a / (t_2 / (y + t))) - ((y * b) / t_2)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + y) / Float64(Float64(y + Float64(x + t)) / z))
	t_2 = Float64(x + Float64(y + t))
	tmp = 0.0
	if (z <= -1.35e+166)
		tmp = t_1;
	elseif (z <= -1.45e-39)
		tmp = Float64(Float64(z + a) - b);
	elseif (z <= 3.7e+105)
		tmp = Float64(Float64(a / Float64(t_2 / Float64(y + t))) - Float64(Float64(y * b) / t_2));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + y) / ((y + (x + t)) / z);
	t_2 = x + (y + t);
	tmp = 0.0;
	if (z <= -1.35e+166)
		tmp = t_1;
	elseif (z <= -1.45e-39)
		tmp = (z + a) - b;
	elseif (z <= 3.7e+105)
		tmp = (a / (t_2 / (y + t))) - ((y * b) / t_2);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + y), $MachinePrecision] / N[(N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.35e+166], t$95$1, If[LessEqual[z, -1.45e-39], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], If[LessEqual[z, 3.7e+105], N[(N[(a / N[(t$95$2 / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y * b), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.35000000000000006e166 or 3.69999999999999985e105 < z

   1. Initial program 46.9%

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

   2. Taylor expanded in z around inf 36.8%

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

      1. associate-/l* 82.5%

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

   4. Simplified 82.5%

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

   if -1.35000000000000006e166 < z < -1.44999999999999994e-39

   1. Initial program 50.8%

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

   2. Taylor expanded in y around inf 62.1%

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

      1. +-commutative 62.1%

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

   4. Simplified 62.1%

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

   if -1.44999999999999994e-39 < z < 3.69999999999999985e105

   1. Initial program 69.5%

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

   2. Taylor expanded in z around 0 57.4%

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

      1. div-sub 57.4%

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

      2. associate-/l* 75.5%

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

      3. associate-+l+ 75.5%

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

      4. +-commutative 75.5%

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

      5. associate-+l+ 75.5%

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

      6. +-commutative 75.5%

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

   4. Applied egg-rr 75.5%

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

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+166}:\\ \;\;\;\;\frac{x + y}{\frac{y + \left(x + t\right)}{z}}\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{-39}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+105}:\\ \;\;\;\;\frac{a}{\frac{x + \left(y + t\right)}{y + t}} - \frac{y \cdot b}{x + \left(y + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y}{\frac{y + \left(x + t\right)}{z}}\\ \end{array} \]

Alternative 8: 60.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ t_2 := y + \left(x + t\right)\\ t_3 := \frac{x + y}{\frac{t_2}{z}}\\ t_4 := \frac{a}{\frac{t_2}{y + t}}\\ \mathbf{if}\;z \leq -3.7 \cdot 10^{+167}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-55}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-269}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq 9.4 \cdot 10^{-125}:\\ \;\;\;\;\frac{a \cdot \left(y + t\right) - y \cdot b}{t_2}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-54}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+105}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b))
        (t_2 (+ y (+ x t)))
        (t_3 (/ (+ x y) (/ t_2 z)))
        (t_4 (/ a (/ t_2 (+ y t)))))
   (if (<= z -3.7e+167)
     t_3
     (if (<= z -1.1e-55)
       t_1
       (if (<= z -2.8e-269)
         t_4
         (if (<= z 9.4e-125)
           (/ (- (* a (+ y t)) (* y b)) t_2)
           (if (<= z 1.15e-54) t_4 (if (<= z 4.8e+105) t_1 t_3))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = y + (x + t);
	double t_3 = (x + y) / (t_2 / z);
	double t_4 = a / (t_2 / (y + t));
	double tmp;
	if (z <= -3.7e+167) {
		tmp = t_3;
	} else if (z <= -1.1e-55) {
		tmp = t_1;
	} else if (z <= -2.8e-269) {
		tmp = t_4;
	} else if (z <= 9.4e-125) {
		tmp = ((a * (y + t)) - (y * b)) / t_2;
	} else if (z <= 1.15e-54) {
		tmp = t_4;
	} else if (z <= 4.8e+105) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = (z + a) - b
    t_2 = y + (x + t)
    t_3 = (x + y) / (t_2 / z)
    t_4 = a / (t_2 / (y + t))
    if (z <= (-3.7d+167)) then
        tmp = t_3
    else if (z <= (-1.1d-55)) then
        tmp = t_1
    else if (z <= (-2.8d-269)) then
        tmp = t_4
    else if (z <= 9.4d-125) then
        tmp = ((a * (y + t)) - (y * b)) / t_2
    else if (z <= 1.15d-54) then
        tmp = t_4
    else if (z <= 4.8d+105) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = y + (x + t);
	double t_3 = (x + y) / (t_2 / z);
	double t_4 = a / (t_2 / (y + t));
	double tmp;
	if (z <= -3.7e+167) {
		tmp = t_3;
	} else if (z <= -1.1e-55) {
		tmp = t_1;
	} else if (z <= -2.8e-269) {
		tmp = t_4;
	} else if (z <= 9.4e-125) {
		tmp = ((a * (y + t)) - (y * b)) / t_2;
	} else if (z <= 1.15e-54) {
		tmp = t_4;
	} else if (z <= 4.8e+105) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	t_2 = y + (x + t)
	t_3 = (x + y) / (t_2 / z)
	t_4 = a / (t_2 / (y + t))
	tmp = 0
	if z <= -3.7e+167:
		tmp = t_3
	elif z <= -1.1e-55:
		tmp = t_1
	elif z <= -2.8e-269:
		tmp = t_4
	elif z <= 9.4e-125:
		tmp = ((a * (y + t)) - (y * b)) / t_2
	elif z <= 1.15e-54:
		tmp = t_4
	elif z <= 4.8e+105:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	t_2 = Float64(y + Float64(x + t))
	t_3 = Float64(Float64(x + y) / Float64(t_2 / z))
	t_4 = Float64(a / Float64(t_2 / Float64(y + t)))
	tmp = 0.0
	if (z <= -3.7e+167)
		tmp = t_3;
	elseif (z <= -1.1e-55)
		tmp = t_1;
	elseif (z <= -2.8e-269)
		tmp = t_4;
	elseif (z <= 9.4e-125)
		tmp = Float64(Float64(Float64(a * Float64(y + t)) - Float64(y * b)) / t_2);
	elseif (z <= 1.15e-54)
		tmp = t_4;
	elseif (z <= 4.8e+105)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	t_2 = y + (x + t);
	t_3 = (x + y) / (t_2 / z);
	t_4 = a / (t_2 / (y + t));
	tmp = 0.0;
	if (z <= -3.7e+167)
		tmp = t_3;
	elseif (z <= -1.1e-55)
		tmp = t_1;
	elseif (z <= -2.8e-269)
		tmp = t_4;
	elseif (z <= 9.4e-125)
		tmp = ((a * (y + t)) - (y * b)) / t_2;
	elseif (z <= 1.15e-54)
		tmp = t_4;
	elseif (z <= 4.8e+105)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x + y), $MachinePrecision] / N[(t$95$2 / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(a / N[(t$95$2 / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.7e+167], t$95$3, If[LessEqual[z, -1.1e-55], t$95$1, If[LessEqual[z, -2.8e-269], t$95$4, If[LessEqual[z, 9.4e-125], N[(N[(N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision], If[LessEqual[z, 1.15e-54], t$95$4, If[LessEqual[z, 4.8e+105], t$95$1, t$95$3]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.7000000000000001e167 or 4.7999999999999995e105 < z

   1. Initial program 46.9%

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

   2. Taylor expanded in z around inf 36.8%

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

      1. associate-/l* 82.5%

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

   4. Simplified 82.5%

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

   if -3.7000000000000001e167 < z < -1.1e-55 or 1.1499999999999999e-54 < z < 4.7999999999999995e105

   1. Initial program 60.5%

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

   2. Taylor expanded in y around inf 62.6%

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

      1. +-commutative 62.6%

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

   4. Simplified 62.6%

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

   if -1.1e-55 < z < -2.79999999999999995e-269 or 9.4000000000000001e-125 < z < 1.1499999999999999e-54

   1. Initial program 57.9%

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

   2. Taylor expanded in a around inf 37.9%

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

      1. associate-/l* 71.3%

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

   4. Simplified 71.3%

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

   if -2.79999999999999995e-269 < z < 9.4000000000000001e-125

   1. Initial program 80.1%

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

   2. Taylor expanded in z around 0 77.8%

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

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{+167}:\\ \;\;\;\;\frac{x + y}{\frac{y + \left(x + t\right)}{z}}\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-55}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-269}:\\ \;\;\;\;\frac{a}{\frac{y + \left(x + t\right)}{y + t}}\\ \mathbf{elif}\;z \leq 9.4 \cdot 10^{-125}:\\ \;\;\;\;\frac{a \cdot \left(y + t\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-54}:\\ \;\;\;\;\frac{a}{\frac{y + \left(x + t\right)}{y + t}}\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+105}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y}{\frac{y + \left(x + t\right)}{z}}\\ \end{array} \]

Alternative 9: 61.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -3 \cdot 10^{-35}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.85 \cdot 10^{-105}:\\ \;\;\;\;\left(y + t\right) \cdot \frac{a}{x + \left(y + t\right)}\\ \mathbf{elif}\;y \leq 7.1 \cdot 10^{-130}:\\ \;\;\;\;\frac{x \cdot z + t \cdot a}{x + t}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-15}:\\ \;\;\;\;\frac{x + y}{\frac{t_1}{z}}\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+67}:\\ \;\;\;\;\frac{a}{\frac{t_1}{y + t}}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t))) (t_2 (- (+ z a) b)))
   (if (<= y -3e-35)
     t_2
     (if (<= y -1.85e-105)
       (* (+ y t) (/ a (+ x (+ y t))))
       (if (<= y 7.1e-130)
         (/ (+ (* x z) (* t a)) (+ x t))
         (if (<= y 1.2e-15)
           (/ (+ x y) (/ t_1 z))
           (if (<= y 1.5e+67) (/ a (/ t_1 (+ y t))) 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 <= -3e-35) {
		tmp = t_2;
	} else if (y <= -1.85e-105) {
		tmp = (y + t) * (a / (x + (y + t)));
	} else if (y <= 7.1e-130) {
		tmp = ((x * z) + (t * a)) / (x + t);
	} else if (y <= 1.2e-15) {
		tmp = (x + y) / (t_1 / z);
	} else if (y <= 1.5e+67) {
		tmp = a / (t_1 / (y + t));
	} 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 <= (-3d-35)) then
        tmp = t_2
    else if (y <= (-1.85d-105)) then
        tmp = (y + t) * (a / (x + (y + t)))
    else if (y <= 7.1d-130) then
        tmp = ((x * z) + (t * a)) / (x + t)
    else if (y <= 1.2d-15) then
        tmp = (x + y) / (t_1 / z)
    else if (y <= 1.5d+67) then
        tmp = a / (t_1 / (y + t))
    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 <= -3e-35) {
		tmp = t_2;
	} else if (y <= -1.85e-105) {
		tmp = (y + t) * (a / (x + (y + t)));
	} else if (y <= 7.1e-130) {
		tmp = ((x * z) + (t * a)) / (x + t);
	} else if (y <= 1.2e-15) {
		tmp = (x + y) / (t_1 / z);
	} else if (y <= 1.5e+67) {
		tmp = a / (t_1 / (y + t));
	} 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 <= -3e-35:
		tmp = t_2
	elif y <= -1.85e-105:
		tmp = (y + t) * (a / (x + (y + t)))
	elif y <= 7.1e-130:
		tmp = ((x * z) + (t * a)) / (x + t)
	elif y <= 1.2e-15:
		tmp = (x + y) / (t_1 / z)
	elif y <= 1.5e+67:
		tmp = a / (t_1 / (y + t))
	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 <= -3e-35)
		tmp = t_2;
	elseif (y <= -1.85e-105)
		tmp = Float64(Float64(y + t) * Float64(a / Float64(x + Float64(y + t))));
	elseif (y <= 7.1e-130)
		tmp = Float64(Float64(Float64(x * z) + Float64(t * a)) / Float64(x + t));
	elseif (y <= 1.2e-15)
		tmp = Float64(Float64(x + y) / Float64(t_1 / z));
	elseif (y <= 1.5e+67)
		tmp = Float64(a / Float64(t_1 / Float64(y + t)));
	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 <= -3e-35)
		tmp = t_2;
	elseif (y <= -1.85e-105)
		tmp = (y + t) * (a / (x + (y + t)));
	elseif (y <= 7.1e-130)
		tmp = ((x * z) + (t * a)) / (x + t);
	elseif (y <= 1.2e-15)
		tmp = (x + y) / (t_1 / z);
	elseif (y <= 1.5e+67)
		tmp = a / (t_1 / (y + t));
	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, -3e-35], t$95$2, If[LessEqual[y, -1.85e-105], N[(N[(y + t), $MachinePrecision] * N[(a / N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.1e-130], N[(N[(N[(x * z), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.2e-15], N[(N[(x + y), $MachinePrecision] / N[(t$95$1 / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.5e+67], N[(a / N[(t$95$1 / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -2.99999999999999989e-35 or 1.50000000000000005e67 < y

   1. Initial program 40.2%

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

   2. Taylor expanded in y around inf 77.7%

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

      1. +-commutative 77.7%

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

   4. Simplified 77.7%

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

   if -2.99999999999999989e-35 < y < -1.85000000000000004e-105

   1. Initial program 69.2%

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

   2. Taylor expanded in a around inf 43.4%

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

   3. Taylor expanded in a around 0 43.4%

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

      1. associate-/l* 67.8%

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

      2. associate-+r+ 67.8%

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

      3. +-commutative 67.8%

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

      4. associate-/r/ 67.9%

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

      5. +-commutative 67.9%

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

      6. +-commutative 67.9%

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

   5. Simplified 67.9%

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

   if -1.85000000000000004e-105 < y < 7.1000000000000001e-130

   1. Initial program 81.8%

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

   2. Taylor expanded in y around 0 67.6%

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

   if 7.1000000000000001e-130 < y < 1.19999999999999997e-15

   1. Initial program 72.0%

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

   2. Taylor expanded in z around inf 42.5%

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

      1. associate-/l* 61.0%

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

   4. Simplified 61.0%

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

   if 1.19999999999999997e-15 < y < 1.50000000000000005e67

   1. Initial program 80.7%

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

   2. Taylor expanded in a around inf 49.8%

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

      1. associate-/l* 63.8%

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

   4. Simplified 63.8%

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

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{-35}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -1.85 \cdot 10^{-105}:\\ \;\;\;\;\left(y + t\right) \cdot \frac{a}{x + \left(y + t\right)}\\ \mathbf{elif}\;y \leq 7.1 \cdot 10^{-130}:\\ \;\;\;\;\frac{x \cdot z + t \cdot a}{x + t}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-15}:\\ \;\;\;\;\frac{x + y}{\frac{y + \left(x + t\right)}{z}}\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+67}:\\ \;\;\;\;\frac{a}{\frac{y + \left(x + t\right)}{y + t}}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]

Alternative 10: 55.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a}{\frac{y + \left(x + t\right)}{y + t}}\\ t_2 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -6.5 \cdot 10^{-35}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-194}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{-58}:\\ \;\;\;\;\frac{z}{\frac{x + t}{x}}\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{+67}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ a (/ (+ y (+ x t)) (+ y t)))) (t_2 (- (+ z a) b)))
   (if (<= y -6.5e-35)
     t_2
     (if (<= y 1.6e-194)
       t_1
       (if (<= y 1.95e-58) (/ z (/ (+ x t) x)) (if (<= y 4.7e+67) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a / ((y + (x + t)) / (y + t));
	double t_2 = (z + a) - b;
	double tmp;
	if (y <= -6.5e-35) {
		tmp = t_2;
	} else if (y <= 1.6e-194) {
		tmp = t_1;
	} else if (y <= 1.95e-58) {
		tmp = z / ((x + t) / x);
	} else if (y <= 4.7e+67) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a / ((y + (x + t)) / (y + t))
    t_2 = (z + a) - b
    if (y <= (-6.5d-35)) then
        tmp = t_2
    else if (y <= 1.6d-194) then
        tmp = t_1
    else if (y <= 1.95d-58) then
        tmp = z / ((x + t) / x)
    else if (y <= 4.7d+67) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a / ((y + (x + t)) / (y + t));
	double t_2 = (z + a) - b;
	double tmp;
	if (y <= -6.5e-35) {
		tmp = t_2;
	} else if (y <= 1.6e-194) {
		tmp = t_1;
	} else if (y <= 1.95e-58) {
		tmp = z / ((x + t) / x);
	} else if (y <= 4.7e+67) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a / ((y + (x + t)) / (y + t))
	t_2 = (z + a) - b
	tmp = 0
	if y <= -6.5e-35:
		tmp = t_2
	elif y <= 1.6e-194:
		tmp = t_1
	elif y <= 1.95e-58:
		tmp = z / ((x + t) / x)
	elif y <= 4.7e+67:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a / Float64(Float64(y + Float64(x + t)) / Float64(y + t)))
	t_2 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -6.5e-35)
		tmp = t_2;
	elseif (y <= 1.6e-194)
		tmp = t_1;
	elseif (y <= 1.95e-58)
		tmp = Float64(z / Float64(Float64(x + t) / x));
	elseif (y <= 4.7e+67)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a / ((y + (x + t)) / (y + t));
	t_2 = (z + a) - b;
	tmp = 0.0;
	if (y <= -6.5e-35)
		tmp = t_2;
	elseif (y <= 1.6e-194)
		tmp = t_1;
	elseif (y <= 1.95e-58)
		tmp = z / ((x + t) / x);
	elseif (y <= 4.7e+67)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a / N[(N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision] / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -6.5e-35], t$95$2, If[LessEqual[y, 1.6e-194], t$95$1, If[LessEqual[y, 1.95e-58], N[(z / N[(N[(x + t), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.7e+67], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.4999999999999999e-35 or 4.70000000000000017e67 < y

   1. Initial program 40.2%

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

   2. Taylor expanded in y around inf 77.7%

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

      1. +-commutative 77.7%

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

   4. Simplified 77.7%

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

   if -6.4999999999999999e-35 < y < 1.6000000000000001e-194 or 1.94999999999999996e-58 < y < 4.70000000000000017e67

   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. Taylor expanded in a around inf 46.2%

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

      1. associate-/l* 56.2%

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

   4. Simplified 56.2%

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

   if 1.6000000000000001e-194 < y < 1.94999999999999996e-58

   1. Initial program 63.7%

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

   2. Taylor expanded in z around inf 42.2%

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

      1. associate-/l* 62.0%

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

   4. Simplified 62.0%

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

   5. Taylor expanded in y around 0 33.9%

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

      1. associate-/l* 57.8%

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

      2. +-commutative 57.8%

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

   7. Simplified 57.8%

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

4. Final simplification 66.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{-35}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-194}:\\ \;\;\;\;\frac{a}{\frac{y + \left(x + t\right)}{y + t}}\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{-58}:\\ \;\;\;\;\frac{z}{\frac{x + t}{x}}\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{+67}:\\ \;\;\;\;\frac{a}{\frac{y + \left(x + t\right)}{y + t}}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]

Alternative 11: 55.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \frac{a}{\frac{t_1}{y + t}}\\ t_3 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -4.8 \cdot 10^{-35}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-188}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-21}:\\ \;\;\;\;\frac{x + y}{\frac{t_1}{z}}\\ \mathbf{elif}\;y \leq 1.68 \cdot 10^{+75}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t))) (t_2 (/ a (/ t_1 (+ y t)))) (t_3 (- (+ z a) b)))
   (if (<= y -4.8e-35)
     t_3
     (if (<= y 3.5e-188)
       t_2
       (if (<= y 4.8e-21)
         (/ (+ x y) (/ t_1 z))
         (if (<= y 1.68e+75) t_2 t_3))))))

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 / (t_1 / (y + t));
	double t_3 = (z + a) - b;
	double tmp;
	if (y <= -4.8e-35) {
		tmp = t_3;
	} else if (y <= 3.5e-188) {
		tmp = t_2;
	} else if (y <= 4.8e-21) {
		tmp = (x + y) / (t_1 / z);
	} else if (y <= 1.68e+75) {
		tmp = t_2;
	} 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 + (x + t)
    t_2 = a / (t_1 / (y + t))
    t_3 = (z + a) - b
    if (y <= (-4.8d-35)) then
        tmp = t_3
    else if (y <= 3.5d-188) then
        tmp = t_2
    else if (y <= 4.8d-21) then
        tmp = (x + y) / (t_1 / z)
    else if (y <= 1.68d+75) then
        tmp = t_2
    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 + (x + t);
	double t_2 = a / (t_1 / (y + t));
	double t_3 = (z + a) - b;
	double tmp;
	if (y <= -4.8e-35) {
		tmp = t_3;
	} else if (y <= 3.5e-188) {
		tmp = t_2;
	} else if (y <= 4.8e-21) {
		tmp = (x + y) / (t_1 / z);
	} else if (y <= 1.68e+75) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = a / (t_1 / (y + t))
	t_3 = (z + a) - b
	tmp = 0
	if y <= -4.8e-35:
		tmp = t_3
	elif y <= 3.5e-188:
		tmp = t_2
	elif y <= 4.8e-21:
		tmp = (x + y) / (t_1 / z)
	elif y <= 1.68e+75:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(a / Float64(t_1 / Float64(y + t)))
	t_3 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -4.8e-35)
		tmp = t_3;
	elseif (y <= 3.5e-188)
		tmp = t_2;
	elseif (y <= 4.8e-21)
		tmp = Float64(Float64(x + y) / Float64(t_1 / z));
	elseif (y <= 1.68e+75)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	t_2 = a / (t_1 / (y + t));
	t_3 = (z + a) - b;
	tmp = 0.0;
	if (y <= -4.8e-35)
		tmp = t_3;
	elseif (y <= 3.5e-188)
		tmp = t_2;
	elseif (y <= 4.8e-21)
		tmp = (x + y) / (t_1 / z);
	elseif (y <= 1.68e+75)
		tmp = t_2;
	else
		tmp = t_3;
	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[(a / N[(t$95$1 / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -4.8e-35], t$95$3, If[LessEqual[y, 3.5e-188], t$95$2, If[LessEqual[y, 4.8e-21], N[(N[(x + y), $MachinePrecision] / N[(t$95$1 / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.68e+75], t$95$2, t$95$3]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.8000000000000003e-35 or 1.6799999999999999e75 < y

   1. Initial program 40.2%

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

   2. Taylor expanded in y around inf 77.7%

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

      1. +-commutative 77.7%

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

   4. Simplified 77.7%

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

   if -4.8000000000000003e-35 < y < 3.5e-188 or 4.7999999999999999e-21 < y < 1.6799999999999999e75

   1. Initial program 81.1%

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

   2. Taylor expanded in a around inf 46.4%

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

      1. associate-/l* 56.9%

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

   4. Simplified 56.9%

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

   if 3.5e-188 < y < 4.7999999999999999e-21

   1. Initial program 70.0%

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

   2. Taylor expanded in z around inf 42.0%

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

      1. associate-/l* 61.7%

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

   4. Simplified 61.7%

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

4. Final simplification 66.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{-35}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-188}:\\ \;\;\;\;\frac{a}{\frac{y + \left(x + t\right)}{y + t}}\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-21}:\\ \;\;\;\;\frac{x + y}{\frac{y + \left(x + t\right)}{z}}\\ \mathbf{elif}\;y \leq 1.68 \cdot 10^{+75}:\\ \;\;\;\;\frac{a}{\frac{y + \left(x + t\right)}{y + t}}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]

Alternative 12: 59.2% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+221}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+154}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a - \frac{a}{\frac{y + t}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.05e+221)
   a
   (if (<= t 1.4e+154) (- (+ z a) b) (- a (/ a (/ (+ y t) x))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.05e+221) {
		tmp = a;
	} else if (t <= 1.4e+154) {
		tmp = (z + a) - b;
	} else {
		tmp = a - (a / ((y + t) / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-1.05d+221)) then
        tmp = a
    else if (t <= 1.4d+154) then
        tmp = (z + a) - b
    else
        tmp = a - (a / ((y + t) / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.05e+221) {
		tmp = a;
	} else if (t <= 1.4e+154) {
		tmp = (z + a) - b;
	} else {
		tmp = a - (a / ((y + t) / x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1.05e+221:
		tmp = a
	elif t <= 1.4e+154:
		tmp = (z + a) - b
	else:
		tmp = a - (a / ((y + t) / x))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.05e+221)
		tmp = a;
	elseif (t <= 1.4e+154)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(a - Float64(a / Float64(Float64(y + t) / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -1.05e+221)
		tmp = a;
	elseif (t <= 1.4e+154)
		tmp = (z + a) - b;
	else
		tmp = a - (a / ((y + t) / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.05e+221], a, If[LessEqual[t, 1.4e+154], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(a - N[(a / N[(N[(y + t), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.05000000000000001e221

   1. Initial program 38.9%

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

   2. Taylor expanded in t around inf 89.1%

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

   if -1.05000000000000001e221 < t < 1.4e154

   1. Initial program 63.8%

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

   2. Taylor expanded in y around inf 59.3%

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

      1. +-commutative 59.3%

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

   4. Simplified 59.3%

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

   if 1.4e154 < t

   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 a around inf 33.8%

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

   3. Taylor expanded in x around 0 56.5%

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

      1. +-commutative 56.5%

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

      2. mul-1-neg 56.5%

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

      3. unsub-neg 56.5%

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

      4. associate-/l* 62.2%

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

      5. +-commutative 62.2%

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

   5. Simplified 62.2%

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

4. Final simplification 61.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+221}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+154}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a - \frac{a}{\frac{y + t}{x}}\\ \end{array} \]

Alternative 13: 59.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.4 \cdot 10^{+218}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{+155}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a - \frac{a}{\frac{t}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -6.4e+218)
   a
   (if (<= t 1.5e+155) (- (+ z a) b) (- a (/ a (/ t x))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -6.4e+218) {
		tmp = a;
	} else if (t <= 1.5e+155) {
		tmp = (z + a) - b;
	} else {
		tmp = a - (a / (t / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-6.4d+218)) then
        tmp = a
    else if (t <= 1.5d+155) then
        tmp = (z + a) - b
    else
        tmp = a - (a / (t / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -6.4e+218) {
		tmp = a;
	} else if (t <= 1.5e+155) {
		tmp = (z + a) - b;
	} else {
		tmp = a - (a / (t / x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -6.4e+218:
		tmp = a
	elif t <= 1.5e+155:
		tmp = (z + a) - b
	else:
		tmp = a - (a / (t / x))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -6.4e+218)
		tmp = a;
	elseif (t <= 1.5e+155)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(a - Float64(a / Float64(t / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -6.4e+218)
		tmp = a;
	elseif (t <= 1.5e+155)
		tmp = (z + a) - b;
	else
		tmp = a - (a / (t / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -6.4e+218], a, If[LessEqual[t, 1.5e+155], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(a - N[(a / N[(t / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.39999999999999975e218

   1. Initial program 38.9%

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

   2. Taylor expanded in t around inf 89.1%

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

   if -6.39999999999999975e218 < t < 1.5000000000000001e155

   1. Initial program 63.8%

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

   2. Taylor expanded in y around inf 59.3%

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

      1. +-commutative 59.3%

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

   4. Simplified 59.3%

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

   if 1.5000000000000001e155 < t

   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 a around inf 33.8%

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

   3. Taylor expanded in x around 0 56.5%

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

      1. +-commutative 56.5%

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

      2. mul-1-neg 56.5%

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

      3. unsub-neg 56.5%

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

      4. associate-/l* 62.2%

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

      5. +-commutative 62.2%

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

   5. Simplified 62.2%

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

   6. Taylor expanded in t around inf 56.3%

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

      1. associate-/l* 62.0%

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

   8. Simplified 62.0%

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

4. Final simplification 61.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.4 \cdot 10^{+218}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{+155}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a - \frac{a}{\frac{t}{x}}\\ \end{array} \]

Alternative 14: 59.2% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{+219}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{+157}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.2e+219) a (if (<= t 7.2e+157) (- (+ z a) b) a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.2e+219) {
		tmp = a;
	} else if (t <= 7.2e+157) {
		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 <= (-1.2d+219)) then
        tmp = a
    else if (t <= 7.2d+157) 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 <= -1.2e+219) {
		tmp = a;
	} else if (t <= 7.2e+157) {
		tmp = (z + a) - b;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1.2e+219:
		tmp = a
	elif t <= 7.2e+157:
		tmp = (z + a) - b
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.2e+219)
		tmp = a;
	elseif (t <= 7.2e+157)
		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 <= -1.2e+219)
		tmp = a;
	elseif (t <= 7.2e+157)
		tmp = (z + a) - b;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.2e+219], a, If[LessEqual[t, 7.2e+157], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], a]]

Derivation

1. Split input into 2 regimes

2. if t < -1.2e219 or 7.20000000000000049e157 < t

   1. Initial program 50.5%

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

   2. Taylor expanded in t around inf 70.0%

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

   if -1.2e219 < t < 7.20000000000000049e157

   1. Initial program 63.8%

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

   2. Taylor expanded in y around inf 59.3%

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

      1. +-commutative 59.3%

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

   4. Simplified 59.3%

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

4. Final simplification 61.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{+219}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{+157}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]

Alternative 15: 47.7% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+143}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+101}:\\ \;\;\;\;a - b\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -2.5e+143) z (if (<= z 3.4e+101) (- a b) z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2.5e+143) {
		tmp = z;
	} else if (z <= 3.4e+101) {
		tmp = a - b;
	} else {
		tmp = z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-2.5d+143)) then
        tmp = z
    else if (z <= 3.4d+101) then
        tmp = a - b
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2.5e+143) {
		tmp = z;
	} else if (z <= 3.4e+101) {
		tmp = a - b;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -2.5e+143:
		tmp = z
	elif z <= 3.4e+101:
		tmp = a - b
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -2.5e+143)
		tmp = z;
	elseif (z <= 3.4e+101)
		tmp = Float64(a - b);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -2.5e+143)
		tmp = z;
	elseif (z <= 3.4e+101)
		tmp = a - b;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -2.5e+143], z, If[LessEqual[z, 3.4e+101], N[(a - b), $MachinePrecision], z]]

Derivation

1. Split input into 2 regimes

2. if z < -2.50000000000000006e143 or 3.40000000000000017e101 < z

   1. Initial program 46.1%

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

   2. Taylor expanded in x around inf 64.2%

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

   if -2.50000000000000006e143 < z < 3.40000000000000017e101

   1. Initial program 66.7%

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

   2. Taylor expanded in z around 0 51.6%

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

   3. Taylor expanded in y around -inf 50.1%

      \[\leadsto \color{blue}{-1 \cdot \left(-1 \cdot a - -1 \cdot b\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 50.1%

         \[\leadsto \color{blue}{-\left(-1 \cdot a - -1 \cdot b\right)} \]

      2. distribute-lft-out-- 50.1%

         \[\leadsto -\color{blue}{-1 \cdot \left(a - b\right)} \]

      3. distribute-lft-neg-in 50.1%

         \[\leadsto \color{blue}{\left(--1\right) \cdot \left(a - b\right)} \]

      4. metadata-eval 50.1%

         \[\leadsto \color{blue}{1} \cdot \left(a - b\right) \]

   5. Simplified 50.1%

      \[\leadsto \color{blue}{1 \cdot \left(a - b\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 53.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+143}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+101}:\\ \;\;\;\;a - b\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 16: 44.3% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.05 \cdot 10^{-8}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{+104}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -2.05e-8) z (if (<= z 2.15e+104) a z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2.05e-8) {
		tmp = z;
	} else if (z <= 2.15e+104) {
		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 <= (-2.05d-8)) then
        tmp = z
    else if (z <= 2.15d+104) 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 <= -2.05e-8) {
		tmp = z;
	} else if (z <= 2.15e+104) {
		tmp = a;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -2.05e-8:
		tmp = z
	elif z <= 2.15e+104:
		tmp = a
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -2.05e-8)
		tmp = z;
	elseif (z <= 2.15e+104)
		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 <= -2.05e-8)
		tmp = z;
	elseif (z <= 2.15e+104)
		tmp = a;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -2.05e-8], z, If[LessEqual[z, 2.15e+104], a, z]]

Derivation

1. Split input into 2 regimes

2. if z < -2.05000000000000016e-8 or 2.1500000000000001e104 < z

   1. Initial program 47.8%

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

   2. Taylor expanded in x around inf 54.4%

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

   if -2.05000000000000016e-8 < z < 2.1500000000000001e104

   1. Initial program 69.2%

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

   2. Taylor expanded in t around inf 46.7%

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

4. Final simplification 49.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.05 \cdot 10^{-8}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{+104}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 17: 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 61.2%

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

2. Taylor expanded in t around inf 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 2023230 
(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)))