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

Percentage Accurate: 60.7% → 90.9%

Time: 12.7s

Alternatives: 14

Speedup: 0.7×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 60.7% 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: 90.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \frac{y + t}{t\_1}\\ t_3 := \frac{y}{t\_1}\\ \mathbf{if}\;z \leq -9.5 \cdot 10^{-135} \lor \neg \left(z \leq 2.05 \cdot 10^{-29}\right):\\ \;\;\;\;z \cdot \left(\frac{x}{t\_1} + \left(\mathsf{fma}\left(\frac{a}{z}, t\_2, t\_3\right) - \frac{b}{t\_1} \cdot \frac{y}{z}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\frac{\mathsf{fma}\left(z, \frac{x + y}{t\_1}, a \cdot t\_2\right)}{b} - t\_3\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t))) (t_2 (/ (+ y t) t_1)) (t_3 (/ y t_1)))
   (if (or (<= z -9.5e-135) (not (<= z 2.05e-29)))
     (* z (+ (/ x t_1) (- (fma (/ a z) t_2 t_3) (* (/ b t_1) (/ y z)))))
     (* b (- (/ (fma z (/ (+ x y) t_1) (* a t_2)) b) 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 = (y + t) / t_1;
	double t_3 = y / t_1;
	double tmp;
	if ((z <= -9.5e-135) || !(z <= 2.05e-29)) {
		tmp = z * ((x / t_1) + (fma((a / z), t_2, t_3) - ((b / t_1) * (y / z))));
	} else {
		tmp = b * ((fma(z, ((x + y) / t_1), (a * t_2)) / b) - t_3);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(Float64(y + t) / t_1)
	t_3 = Float64(y / t_1)
	tmp = 0.0
	if ((z <= -9.5e-135) || !(z <= 2.05e-29))
		tmp = Float64(z * Float64(Float64(x / t_1) + Float64(fma(Float64(a / z), t_2, t_3) - Float64(Float64(b / t_1) * Float64(y / z)))));
	else
		tmp = Float64(b * Float64(Float64(fma(z, Float64(Float64(x + y) / t_1), Float64(a * t_2)) / b) - t_3));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y + t), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(y / t$95$1), $MachinePrecision]}, If[Or[LessEqual[z, -9.5e-135], N[Not[LessEqual[z, 2.05e-29]], $MachinePrecision]], N[(z * N[(N[(x / t$95$1), $MachinePrecision] + N[(N[(N[(a / z), $MachinePrecision] * t$95$2 + t$95$3), $MachinePrecision] - N[(N[(b / t$95$1), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(N[(N[(z * N[(N[(x + y), $MachinePrecision] / t$95$1), $MachinePrecision] + N[(a * t$95$2), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision] - t$95$3), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 2 regimes

2. if z < -9.50000000000000007e-135 or 2.0499999999999999e-29 < z

   1. Initial program 50.0%

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

   3. Taylor expanded in z around inf 63.7%

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

      1. associate--l+ 63.7%

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

      2. +-commutative 63.7%

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

      3. associate-+r+ 63.7%

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

      4. +-commutative 63.7%

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

      5. associate-+l+ 63.7%

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

   5. Simplified 94.5%

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

   if -9.50000000000000007e-135 < z < 2.0499999999999999e-29

   1. Initial program 76.0%

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

   3. Taylor expanded in b around -inf 79.5%

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

      1. mul-1-neg 79.5%

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

      2. *-commutative 79.5%

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

      3. distribute-rgt-neg-in 79.5%

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

   5. Simplified 91.9%

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

4. Final simplification 93.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{-135} \lor \neg \left(z \leq 2.05 \cdot 10^{-29}\right):\\ \;\;\;\;z \cdot \left(\frac{x}{y + \left(x + t\right)} + \left(\mathsf{fma}\left(\frac{a}{z}, \frac{y + t}{y + \left(x + t\right)}, \frac{y}{y + \left(x + t\right)}\right) - \frac{b}{y + \left(x + t\right)} \cdot \frac{y}{z}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\frac{\mathsf{fma}\left(z, \frac{x + y}{y + \left(x + t\right)}, a \cdot \frac{y + t}{y + \left(x + t\right)}\right)}{b} - \frac{y}{y + \left(x + t\right)}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 88.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y + t\right)\\ t_2 := y + \left(x + t\right)\\ t_3 := z \cdot \left(x + y\right)\\ t_4 := \frac{\left(t\_3 + t\_1\right) - y \cdot b}{t\_2}\\ \mathbf{if}\;t\_4 \leq -\infty:\\ \;\;\;\;b \cdot \left(\frac{\mathsf{fma}\left(z, \frac{x + y}{t\_2}, a \cdot \frac{y + t}{t\_2}\right)}{b} - \frac{y}{t\_2}\right)\\ \mathbf{elif}\;t\_4 \leq 2 \cdot 10^{+257}:\\ \;\;\;\;\frac{t\_3 + \left(t\_1 - y \cdot b\right)}{t\_2}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (+ y t)))
        (t_2 (+ y (+ x t)))
        (t_3 (* z (+ x y)))
        (t_4 (/ (- (+ t_3 t_1) (* y b)) t_2)))
   (if (<= t_4 (- INFINITY))
     (* b (- (/ (fma z (/ (+ x y) t_2) (* a (/ (+ y t) t_2))) b) (/ y t_2)))
     (if (<= t_4 2e+257) (/ (+ t_3 (- t_1 (* y b))) t_2) (- (+ z a) b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (y + t);
	double t_2 = y + (x + t);
	double t_3 = z * (x + y);
	double t_4 = ((t_3 + t_1) - (y * b)) / t_2;
	double tmp;
	if (t_4 <= -((double) INFINITY)) {
		tmp = b * ((fma(z, ((x + y) / t_2), (a * ((y + t) / t_2))) / b) - (y / t_2));
	} else if (t_4 <= 2e+257) {
		tmp = (t_3 + (t_1 - (y * b))) / t_2;
	} else {
		tmp = (z + a) - b;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(y + t))
	t_2 = Float64(y + Float64(x + t))
	t_3 = Float64(z * Float64(x + y))
	t_4 = Float64(Float64(Float64(t_3 + t_1) - Float64(y * b)) / t_2)
	tmp = 0.0
	if (t_4 <= Float64(-Inf))
		tmp = Float64(b * Float64(Float64(fma(z, Float64(Float64(x + y) / t_2), Float64(a * Float64(Float64(y + t) / t_2))) / b) - Float64(y / t_2)));
	elseif (t_4 <= 2e+257)
		tmp = Float64(Float64(t_3 + Float64(t_1 - Float64(y * b))) / t_2);
	else
		tmp = Float64(Float64(z + a) - b);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(t$95$3 + t$95$1), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]}, If[LessEqual[t$95$4, (-Infinity)], N[(b * N[(N[(N[(z * N[(N[(x + y), $MachinePrecision] / t$95$2), $MachinePrecision] + N[(a * N[(N[(y + t), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision] - N[(y / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$4, 2e+257], N[(N[(t$95$3 + N[(t$95$1 - N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 6.3%

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

   3. Taylor expanded in b around -inf 19.6%

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

      1. mul-1-neg 19.6%

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

      2. *-commutative 19.6%

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

      3. distribute-rgt-neg-in 19.6%

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

   5. Simplified 75.0%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 2.00000000000000006e257

   1. Initial program 99.7%

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

      1. associate--l+ 99.7%

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

      2. +-commutative 99.7%

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

      3. +-commutative 99.7%

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

      4. *-commutative 99.7%

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

   4. Applied egg-rr 99.7%

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

   if 2.00000000000000006e257 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 8.3%

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

   3. Taylor expanded in y around inf 76.2%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty:\\ \;\;\;\;b \cdot \left(\frac{\mathsf{fma}\left(z, \frac{x + y}{y + \left(x + t\right)}, a \cdot \frac{y + t}{y + \left(x + t\right)}\right)}{b} - \frac{y}{y + \left(x + t\right)}\right)\\ \mathbf{elif}\;\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 2 \cdot 10^{+257}:\\ \;\;\;\;\frac{z \cdot \left(x + y\right) + \left(a \cdot \left(y + t\right) - y \cdot b\right)}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 88.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y + t\right)\\ t_2 := y + \left(x + t\right)\\ t_3 := z \cdot \left(x + y\right)\\ t_4 := \frac{\left(t\_3 + t\_1\right) - y \cdot b}{t\_2}\\ \mathbf{if}\;t\_4 \leq -\infty \lor \neg \left(t\_4 \leq 2 \cdot 10^{+257}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_3 + \left(t\_1 - y \cdot b\right)}{t\_2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (+ y t)))
        (t_2 (+ y (+ x t)))
        (t_3 (* z (+ x y)))
        (t_4 (/ (- (+ t_3 t_1) (* y b)) t_2)))
   (if (or (<= t_4 (- INFINITY)) (not (<= t_4 2e+257)))
     (- (+ z a) b)
     (/ (+ t_3 (- t_1 (* y b))) t_2))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (y + t);
	double t_2 = y + (x + t);
	double t_3 = z * (x + y);
	double t_4 = ((t_3 + t_1) - (y * b)) / t_2;
	double tmp;
	if ((t_4 <= -((double) INFINITY)) || !(t_4 <= 2e+257)) {
		tmp = (z + a) - b;
	} else {
		tmp = (t_3 + (t_1 - (y * b))) / t_2;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (y + t);
	double t_2 = y + (x + t);
	double t_3 = z * (x + y);
	double t_4 = ((t_3 + t_1) - (y * b)) / t_2;
	double tmp;
	if ((t_4 <= -Double.POSITIVE_INFINITY) || !(t_4 <= 2e+257)) {
		tmp = (z + a) - b;
	} else {
		tmp = (t_3 + (t_1 - (y * b))) / t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (y + t)
	t_2 = y + (x + t)
	t_3 = z * (x + y)
	t_4 = ((t_3 + t_1) - (y * b)) / t_2
	tmp = 0
	if (t_4 <= -math.inf) or not (t_4 <= 2e+257):
		tmp = (z + a) - b
	else:
		tmp = (t_3 + (t_1 - (y * b))) / t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(y + t))
	t_2 = Float64(y + Float64(x + t))
	t_3 = Float64(z * Float64(x + y))
	t_4 = Float64(Float64(Float64(t_3 + t_1) - Float64(y * b)) / t_2)
	tmp = 0.0
	if ((t_4 <= Float64(-Inf)) || !(t_4 <= 2e+257))
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(Float64(t_3 + Float64(t_1 - Float64(y * b))) / t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (y + t);
	t_2 = y + (x + t);
	t_3 = z * (x + y);
	t_4 = ((t_3 + t_1) - (y * b)) / t_2;
	tmp = 0.0;
	if ((t_4 <= -Inf) || ~((t_4 <= 2e+257)))
		tmp = (z + a) - b;
	else
		tmp = (t_3 + (t_1 - (y * b))) / t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(t$95$3 + t$95$1), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]}, If[Or[LessEqual[t$95$4, (-Infinity)], N[Not[LessEqual[t$95$4, 2e+257]], $MachinePrecision]], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(N[(t$95$3 + N[(t$95$1 - N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]]]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -inf.0 or 2.00000000000000006e257 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 7.4%

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

   3. Taylor expanded in y around inf 73.7%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 2.00000000000000006e257

   1. Initial program 99.7%

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

      1. associate--l+ 99.7%

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

      2. +-commutative 99.7%

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

      3. +-commutative 99.7%

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

      4. *-commutative 99.7%

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

   4. Applied egg-rr 99.7%

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

4. Final simplification 88.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty \lor \neg \left(\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 2 \cdot 10^{+257}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(x + y\right) + \left(a \cdot \left(y + t\right) - y \cdot b\right)}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 55.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := a \cdot \frac{y + t}{t\_1}\\ \mathbf{if}\;t \leq -1.26 \cdot 10^{+23}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -2.9 \cdot 10^{-93}:\\ \;\;\;\;b \cdot \left(\frac{z}{b} - \frac{y}{t\_1}\right)\\ \mathbf{elif}\;t \leq -1.24 \cdot 10^{-147}:\\ \;\;\;\;z + a\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{+131}:\\ \;\;\;\;\frac{z \cdot \left(x + y\right) + y \cdot \left(a - b\right)}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t))) (t_2 (* a (/ (+ y t) t_1))))
   (if (<= t -1.26e+23)
     t_2
     (if (<= t -2.9e-93)
       (* b (- (/ z b) (/ y t_1)))
       (if (<= t -1.24e-147)
         (+ z a)
         (if (<= t 1.8e+131) (/ (+ (* z (+ x y)) (* y (- a b))) t_1) t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = a * ((y + t) / t_1);
	double tmp;
	if (t <= -1.26e+23) {
		tmp = t_2;
	} else if (t <= -2.9e-93) {
		tmp = b * ((z / b) - (y / t_1));
	} else if (t <= -1.24e-147) {
		tmp = z + a;
	} else if (t <= 1.8e+131) {
		tmp = ((z * (x + y)) + (y * (a - b))) / t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y + (x + t)
    t_2 = a * ((y + t) / t_1)
    if (t <= (-1.26d+23)) then
        tmp = t_2
    else if (t <= (-2.9d-93)) then
        tmp = b * ((z / b) - (y / t_1))
    else if (t <= (-1.24d-147)) then
        tmp = z + a
    else if (t <= 1.8d+131) then
        tmp = ((z * (x + y)) + (y * (a - b))) / t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = a * ((y + t) / t_1);
	double tmp;
	if (t <= -1.26e+23) {
		tmp = t_2;
	} else if (t <= -2.9e-93) {
		tmp = b * ((z / b) - (y / t_1));
	} else if (t <= -1.24e-147) {
		tmp = z + a;
	} else if (t <= 1.8e+131) {
		tmp = ((z * (x + y)) + (y * (a - b))) / t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = a * ((y + t) / t_1)
	tmp = 0
	if t <= -1.26e+23:
		tmp = t_2
	elif t <= -2.9e-93:
		tmp = b * ((z / b) - (y / t_1))
	elif t <= -1.24e-147:
		tmp = z + a
	elif t <= 1.8e+131:
		tmp = ((z * (x + y)) + (y * (a - b))) / t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(a * Float64(Float64(y + t) / t_1))
	tmp = 0.0
	if (t <= -1.26e+23)
		tmp = t_2;
	elseif (t <= -2.9e-93)
		tmp = Float64(b * Float64(Float64(z / b) - Float64(y / t_1)));
	elseif (t <= -1.24e-147)
		tmp = Float64(z + a);
	elseif (t <= 1.8e+131)
		tmp = Float64(Float64(Float64(z * Float64(x + y)) + Float64(y * Float64(a - b))) / t_1);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	t_2 = a * ((y + t) / t_1);
	tmp = 0.0;
	if (t <= -1.26e+23)
		tmp = t_2;
	elseif (t <= -2.9e-93)
		tmp = b * ((z / b) - (y / t_1));
	elseif (t <= -1.24e-147)
		tmp = z + a;
	elseif (t <= 1.8e+131)
		tmp = ((z * (x + y)) + (y * (a - b))) / t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(y + t), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.26e+23], t$95$2, If[LessEqual[t, -2.9e-93], N[(b * N[(N[(z / b), $MachinePrecision] - N[(y / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.24e-147], N[(z + a), $MachinePrecision], If[LessEqual[t, 1.8e+131], N[(N[(N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision] + N[(y * N[(a - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.26000000000000004e23 or 1.80000000000000016e131 < t

   1. Initial program 46.4%

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

   3. Taylor expanded in a around inf 29.2%

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

      1. associate-/l* 64.2%

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

      2. +-commutative 64.2%

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

      3. associate-+r+ 64.2%

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

      4. +-commutative 64.2%

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

      5. associate-+l+ 64.2%

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

   5. Simplified 64.2%

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

   if -1.26000000000000004e23 < t < -2.8999999999999998e-93

   1. Initial program 39.1%

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

   3. Taylor expanded in b around -inf 52.0%

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

      1. mul-1-neg 52.0%

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

      2. *-commutative 52.0%

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

      3. distribute-rgt-neg-in 52.0%

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

   5. Simplified 90.0%

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

   6. Taylor expanded in x around inf 74.9%

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

   if -2.8999999999999998e-93 < t < -1.2400000000000001e-147

   1. Initial program 65.1%

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

   3. Taylor expanded in b around -inf 59.6%

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

      1. mul-1-neg 59.6%

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

      2. *-commutative 59.6%

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

      3. distribute-rgt-neg-in 59.6%

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

   5. Simplified 82.7%

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

   6. Taylor expanded in y around -inf 56.9%

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

   7. Taylor expanded in b around 0 76.2%

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

   if -1.2400000000000001e-147 < t < 1.80000000000000016e131

   1. Initial program 74.9%

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

      1. associate--l+ 74.9%

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

      2. +-commutative 74.9%

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

      3. +-commutative 74.9%

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

      4. *-commutative 74.9%

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

   4. Applied egg-rr 74.9%

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

   5. Taylor expanded in y around inf 72.1%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.26 \cdot 10^{+23}:\\ \;\;\;\;a \cdot \frac{y + t}{y + \left(x + t\right)}\\ \mathbf{elif}\;t \leq -2.9 \cdot 10^{-93}:\\ \;\;\;\;b \cdot \left(\frac{z}{b} - \frac{y}{y + \left(x + t\right)}\right)\\ \mathbf{elif}\;t \leq -1.24 \cdot 10^{-147}:\\ \;\;\;\;z + a\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{+131}:\\ \;\;\;\;\frac{z \cdot \left(x + y\right) + y \cdot \left(a - b\right)}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{y + t}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 58.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ t_2 := y + \left(x + t\right)\\ t_3 := a \cdot \frac{y + t}{t\_2}\\ t_4 := z \cdot \frac{x + y}{t\_2}\\ \mathbf{if}\;a \leq -9.2 \cdot 10^{+165}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{+52}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.25 \cdot 10^{-62}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;a \leq -7.5 \cdot 10^{-201}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 380000000000:\\ \;\;\;\;t\_4\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b))
        (t_2 (+ y (+ x t)))
        (t_3 (* a (/ (+ y t) t_2)))
        (t_4 (* z (/ (+ x y) t_2))))
   (if (<= a -9.2e+165)
     t_3
     (if (<= a -8.5e+52)
       t_1
       (if (<= a -1.25e-62)
         t_4
         (if (<= a -7.5e-201) t_1 (if (<= a 380000000000.0) t_4 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 = a * ((y + t) / t_2);
	double t_4 = z * ((x + y) / t_2);
	double tmp;
	if (a <= -9.2e+165) {
		tmp = t_3;
	} else if (a <= -8.5e+52) {
		tmp = t_1;
	} else if (a <= -1.25e-62) {
		tmp = t_4;
	} else if (a <= -7.5e-201) {
		tmp = t_1;
	} else if (a <= 380000000000.0) {
		tmp = t_4;
	} 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 = a * ((y + t) / t_2)
    t_4 = z * ((x + y) / t_2)
    if (a <= (-9.2d+165)) then
        tmp = t_3
    else if (a <= (-8.5d+52)) then
        tmp = t_1
    else if (a <= (-1.25d-62)) then
        tmp = t_4
    else if (a <= (-7.5d-201)) then
        tmp = t_1
    else if (a <= 380000000000.0d0) then
        tmp = t_4
    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 = a * ((y + t) / t_2);
	double t_4 = z * ((x + y) / t_2);
	double tmp;
	if (a <= -9.2e+165) {
		tmp = t_3;
	} else if (a <= -8.5e+52) {
		tmp = t_1;
	} else if (a <= -1.25e-62) {
		tmp = t_4;
	} else if (a <= -7.5e-201) {
		tmp = t_1;
	} else if (a <= 380000000000.0) {
		tmp = t_4;
	} 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 = a * ((y + t) / t_2)
	t_4 = z * ((x + y) / t_2)
	tmp = 0
	if a <= -9.2e+165:
		tmp = t_3
	elif a <= -8.5e+52:
		tmp = t_1
	elif a <= -1.25e-62:
		tmp = t_4
	elif a <= -7.5e-201:
		tmp = t_1
	elif a <= 380000000000.0:
		tmp = t_4
	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(a * Float64(Float64(y + t) / t_2))
	t_4 = Float64(z * Float64(Float64(x + y) / t_2))
	tmp = 0.0
	if (a <= -9.2e+165)
		tmp = t_3;
	elseif (a <= -8.5e+52)
		tmp = t_1;
	elseif (a <= -1.25e-62)
		tmp = t_4;
	elseif (a <= -7.5e-201)
		tmp = t_1;
	elseif (a <= 380000000000.0)
		tmp = t_4;
	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 = a * ((y + t) / t_2);
	t_4 = z * ((x + y) / t_2);
	tmp = 0.0;
	if (a <= -9.2e+165)
		tmp = t_3;
	elseif (a <= -8.5e+52)
		tmp = t_1;
	elseif (a <= -1.25e-62)
		tmp = t_4;
	elseif (a <= -7.5e-201)
		tmp = t_1;
	elseif (a <= 380000000000.0)
		tmp = t_4;
	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[(a * N[(N[(y + t), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(z * N[(N[(x + y), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -9.2e+165], t$95$3, If[LessEqual[a, -8.5e+52], t$95$1, If[LessEqual[a, -1.25e-62], t$95$4, If[LessEqual[a, -7.5e-201], t$95$1, If[LessEqual[a, 380000000000.0], t$95$4, t$95$3]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -9.20000000000000063e165 or 3.8e11 < a

   1. Initial program 40.1%

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

   3. Taylor expanded in a around inf 30.6%

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

      1. associate-/l* 72.1%

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

      2. +-commutative 72.1%

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

      3. associate-+r+ 72.1%

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

      4. +-commutative 72.1%

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

      5. associate-+l+ 72.1%

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

   5. Simplified 72.1%

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

   if -9.20000000000000063e165 < a < -8.49999999999999994e52 or -1.25e-62 < a < -7.49999999999999987e-201

   1. Initial program 64.0%

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

   3. Taylor expanded in y around inf 65.9%

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

   if -8.49999999999999994e52 < a < -1.25e-62 or -7.49999999999999987e-201 < a < 3.8e11

   1. Initial program 73.1%

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

   3. Taylor expanded in z around inf 41.4%

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

      1. associate-/l* 56.4%

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

      2. +-commutative 56.4%

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

      3. +-commutative 56.4%

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

      4. associate-+r+ 56.4%

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

      5. +-commutative 56.4%

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

      6. associate-+l+ 56.4%

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

   5. Simplified 56.4%

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

4. Final simplification 64.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9.2 \cdot 10^{+165}:\\ \;\;\;\;a \cdot \frac{y + t}{y + \left(x + t\right)}\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{+52}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;a \leq -1.25 \cdot 10^{-62}:\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \mathbf{elif}\;a \leq -7.5 \cdot 10^{-201}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;a \leq 380000000000:\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{y + t}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 58.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(\frac{a}{b} - \frac{y}{y + \left(x + t\right)}\right)\\ \mathbf{if}\;b \leq -2.3 \cdot 10^{+62}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -6 \cdot 10^{-285}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;b \leq 3.6 \cdot 10^{-90}:\\ \;\;\;\;\frac{t \cdot a + z \cdot x}{x + t}\\ \mathbf{elif}\;b \leq 3500000000000:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- (/ a b) (/ y (+ y (+ x t)))))))
   (if (<= b -2.3e+62)
     t_1
     (if (<= b -6e-285)
       (- (+ z a) b)
       (if (<= b 3.6e-90)
         (/ (+ (* t a) (* z x)) (+ x t))
         (if (<= b 3500000000000.0) (+ z a) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * ((a / b) - (y / (y + (x + t))));
	double tmp;
	if (b <= -2.3e+62) {
		tmp = t_1;
	} else if (b <= -6e-285) {
		tmp = (z + a) - b;
	} else if (b <= 3.6e-90) {
		tmp = ((t * a) + (z * x)) / (x + t);
	} else if (b <= 3500000000000.0) {
		tmp = z + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * ((a / b) - (y / (y + (x + t))))
    if (b <= (-2.3d+62)) then
        tmp = t_1
    else if (b <= (-6d-285)) then
        tmp = (z + a) - b
    else if (b <= 3.6d-90) then
        tmp = ((t * a) + (z * x)) / (x + t)
    else if (b <= 3500000000000.0d0) then
        tmp = z + a
    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 = b * ((a / b) - (y / (y + (x + t))));
	double tmp;
	if (b <= -2.3e+62) {
		tmp = t_1;
	} else if (b <= -6e-285) {
		tmp = (z + a) - b;
	} else if (b <= 3.6e-90) {
		tmp = ((t * a) + (z * x)) / (x + t);
	} else if (b <= 3500000000000.0) {
		tmp = z + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * ((a / b) - (y / (y + (x + t))))
	tmp = 0
	if b <= -2.3e+62:
		tmp = t_1
	elif b <= -6e-285:
		tmp = (z + a) - b
	elif b <= 3.6e-90:
		tmp = ((t * a) + (z * x)) / (x + t)
	elif b <= 3500000000000.0:
		tmp = z + a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(Float64(a / b) - Float64(y / Float64(y + Float64(x + t)))))
	tmp = 0.0
	if (b <= -2.3e+62)
		tmp = t_1;
	elseif (b <= -6e-285)
		tmp = Float64(Float64(z + a) - b);
	elseif (b <= 3.6e-90)
		tmp = Float64(Float64(Float64(t * a) + Float64(z * x)) / Float64(x + t));
	elseif (b <= 3500000000000.0)
		tmp = Float64(z + a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * ((a / b) - (y / (y + (x + t))));
	tmp = 0.0;
	if (b <= -2.3e+62)
		tmp = t_1;
	elseif (b <= -6e-285)
		tmp = (z + a) - b;
	elseif (b <= 3.6e-90)
		tmp = ((t * a) + (z * x)) / (x + t);
	elseif (b <= 3500000000000.0)
		tmp = z + a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(N[(a / b), $MachinePrecision] - N[(y / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.3e+62], t$95$1, If[LessEqual[b, -6e-285], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], If[LessEqual[b, 3.6e-90], N[(N[(N[(t * a), $MachinePrecision] + N[(z * x), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3500000000000.0], N[(z + a), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -2.29999999999999984e62 or 3.5e12 < b

   1. Initial program 54.0%

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

   3. Taylor expanded in b around -inf 61.4%

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

      1. mul-1-neg 61.4%

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

      2. *-commutative 61.4%

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

      3. distribute-rgt-neg-in 61.4%

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

   5. Simplified 96.9%

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

   6. Taylor expanded in t around inf 62.0%

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

   if -2.29999999999999984e62 < b < -6.00000000000000007e-285

   1. Initial program 58.1%

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

   3. Taylor expanded in y around inf 70.4%

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

   if -6.00000000000000007e-285 < b < 3.59999999999999981e-90

   1. Initial program 75.7%

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

   3. Taylor expanded in y around 0 63.8%

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

   if 3.59999999999999981e-90 < b < 3.5e12

   1. Initial program 59.9%

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

   3. Taylor expanded in b around -inf 59.9%

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

      1. mul-1-neg 59.9%

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

      2. *-commutative 59.9%

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

      3. distribute-rgt-neg-in 59.9%

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

   5. Simplified 90.0%

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

   6. Taylor expanded in y around -inf 65.2%

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

   7. Taylor expanded in b around 0 72.6%

      \[\leadsto \color{blue}{a + z} \]
3. Recombined 4 regimes into one program.

4. Final simplification 65.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.3 \cdot 10^{+62}:\\ \;\;\;\;b \cdot \left(\frac{a}{b} - \frac{y}{y + \left(x + t\right)}\right)\\ \mathbf{elif}\;b \leq -6 \cdot 10^{-285}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;b \leq 3.6 \cdot 10^{-90}:\\ \;\;\;\;\frac{t \cdot a + z \cdot x}{x + t}\\ \mathbf{elif}\;b \leq 3500000000000:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\frac{a}{b} - \frac{y}{y + \left(x + t\right)}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 58.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(\frac{z}{b} - \frac{y}{y + \left(x + t\right)}\right)\\ \mathbf{if}\;b \leq -4.8 \cdot 10^{+48}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -2.4 \cdot 10^{-285}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;b \leq 2.05 \cdot 10^{-89}:\\ \;\;\;\;\frac{t \cdot a + z \cdot x}{x + t}\\ \mathbf{elif}\;b \leq 8000000000000:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- (/ z b) (/ y (+ y (+ x t)))))))
   (if (<= b -4.8e+48)
     t_1
     (if (<= b -2.4e-285)
       (- (+ z a) b)
       (if (<= b 2.05e-89)
         (/ (+ (* t a) (* z x)) (+ x t))
         (if (<= b 8000000000000.0) (+ z a) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * ((z / b) - (y / (y + (x + t))));
	double tmp;
	if (b <= -4.8e+48) {
		tmp = t_1;
	} else if (b <= -2.4e-285) {
		tmp = (z + a) - b;
	} else if (b <= 2.05e-89) {
		tmp = ((t * a) + (z * x)) / (x + t);
	} else if (b <= 8000000000000.0) {
		tmp = z + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * ((z / b) - (y / (y + (x + t))))
    if (b <= (-4.8d+48)) then
        tmp = t_1
    else if (b <= (-2.4d-285)) then
        tmp = (z + a) - b
    else if (b <= 2.05d-89) then
        tmp = ((t * a) + (z * x)) / (x + t)
    else if (b <= 8000000000000.0d0) then
        tmp = z + a
    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 = b * ((z / b) - (y / (y + (x + t))));
	double tmp;
	if (b <= -4.8e+48) {
		tmp = t_1;
	} else if (b <= -2.4e-285) {
		tmp = (z + a) - b;
	} else if (b <= 2.05e-89) {
		tmp = ((t * a) + (z * x)) / (x + t);
	} else if (b <= 8000000000000.0) {
		tmp = z + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * ((z / b) - (y / (y + (x + t))))
	tmp = 0
	if b <= -4.8e+48:
		tmp = t_1
	elif b <= -2.4e-285:
		tmp = (z + a) - b
	elif b <= 2.05e-89:
		tmp = ((t * a) + (z * x)) / (x + t)
	elif b <= 8000000000000.0:
		tmp = z + a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(Float64(z / b) - Float64(y / Float64(y + Float64(x + t)))))
	tmp = 0.0
	if (b <= -4.8e+48)
		tmp = t_1;
	elseif (b <= -2.4e-285)
		tmp = Float64(Float64(z + a) - b);
	elseif (b <= 2.05e-89)
		tmp = Float64(Float64(Float64(t * a) + Float64(z * x)) / Float64(x + t));
	elseif (b <= 8000000000000.0)
		tmp = Float64(z + a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * ((z / b) - (y / (y + (x + t))));
	tmp = 0.0;
	if (b <= -4.8e+48)
		tmp = t_1;
	elseif (b <= -2.4e-285)
		tmp = (z + a) - b;
	elseif (b <= 2.05e-89)
		tmp = ((t * a) + (z * x)) / (x + t);
	elseif (b <= 8000000000000.0)
		tmp = z + a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(N[(z / b), $MachinePrecision] - N[(y / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -4.8e+48], t$95$1, If[LessEqual[b, -2.4e-285], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], If[LessEqual[b, 2.05e-89], N[(N[(N[(t * a), $MachinePrecision] + N[(z * x), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 8000000000000.0], N[(z + a), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -4.8000000000000002e48 or 8e12 < b

   1. Initial program 54.0%

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

   3. Taylor expanded in b around -inf 61.2%

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

      1. mul-1-neg 61.2%

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

      2. *-commutative 61.2%

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

      3. distribute-rgt-neg-in 61.2%

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

   5. Simplified 96.9%

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

   6. Taylor expanded in x around inf 67.6%

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

   if -4.8000000000000002e48 < b < -2.4e-285

   1. Initial program 58.3%

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

   3. Taylor expanded in y around inf 71.1%

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

   if -2.4e-285 < b < 2.0499999999999999e-89

   1. Initial program 75.7%

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

   3. Taylor expanded in y around 0 63.8%

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

   if 2.0499999999999999e-89 < b < 8e12

   1. Initial program 59.9%

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

   3. Taylor expanded in b around -inf 59.9%

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

      1. mul-1-neg 59.9%

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

      2. *-commutative 59.9%

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

      3. distribute-rgt-neg-in 59.9%

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

   5. Simplified 90.0%

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

   6. Taylor expanded in y around -inf 65.2%

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

   7. Taylor expanded in b around 0 72.6%

      \[\leadsto \color{blue}{a + z} \]
3. Recombined 4 regimes into one program.

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.8 \cdot 10^{+48}:\\ \;\;\;\;b \cdot \left(\frac{z}{b} - \frac{y}{y + \left(x + t\right)}\right)\\ \mathbf{elif}\;b \leq -2.4 \cdot 10^{-285}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;b \leq 2.05 \cdot 10^{-89}:\\ \;\;\;\;\frac{t \cdot a + z \cdot x}{x + t}\\ \mathbf{elif}\;b \leq 8000000000000:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\frac{z}{b} - \frac{y}{y + \left(x + t\right)}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 58.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ t_2 := a \cdot \frac{y + t}{y + \left(x + t\right)}\\ \mathbf{if}\;t \leq -1.9 \cdot 10^{+84}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -7.3 \cdot 10^{-159}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -4 \cdot 10^{-251}:\\ \;\;\;\;z\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{+131}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)) (t_2 (* a (/ (+ y t) (+ y (+ x t))))))
   (if (<= t -1.9e+84)
     t_2
     (if (<= t -7.3e-159)
       t_1
       (if (<= t -4e-251) z (if (<= t 3.3e+131) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = a * ((y + t) / (y + (x + t)));
	double tmp;
	if (t <= -1.9e+84) {
		tmp = t_2;
	} else if (t <= -7.3e-159) {
		tmp = t_1;
	} else if (t <= -4e-251) {
		tmp = z;
	} else if (t <= 3.3e+131) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (z + a) - b
    t_2 = a * ((y + t) / (y + (x + t)))
    if (t <= (-1.9d+84)) then
        tmp = t_2
    else if (t <= (-7.3d-159)) then
        tmp = t_1
    else if (t <= (-4d-251)) then
        tmp = z
    else if (t <= 3.3d+131) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = a * ((y + t) / (y + (x + t)));
	double tmp;
	if (t <= -1.9e+84) {
		tmp = t_2;
	} else if (t <= -7.3e-159) {
		tmp = t_1;
	} else if (t <= -4e-251) {
		tmp = z;
	} else if (t <= 3.3e+131) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	t_2 = a * ((y + t) / (y + (x + t)))
	tmp = 0
	if t <= -1.9e+84:
		tmp = t_2
	elif t <= -7.3e-159:
		tmp = t_1
	elif t <= -4e-251:
		tmp = z
	elif t <= 3.3e+131:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	t_2 = Float64(a * Float64(Float64(y + t) / Float64(y + Float64(x + t))))
	tmp = 0.0
	if (t <= -1.9e+84)
		tmp = t_2;
	elseif (t <= -7.3e-159)
		tmp = t_1;
	elseif (t <= -4e-251)
		tmp = z;
	elseif (t <= 3.3e+131)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	t_2 = a * ((y + t) / (y + (x + t)));
	tmp = 0.0;
	if (t <= -1.9e+84)
		tmp = t_2;
	elseif (t <= -7.3e-159)
		tmp = t_1;
	elseif (t <= -4e-251)
		tmp = z;
	elseif (t <= 3.3e+131)
		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[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(y + t), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.9e+84], t$95$2, If[LessEqual[t, -7.3e-159], t$95$1, If[LessEqual[t, -4e-251], z, If[LessEqual[t, 3.3e+131], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.9e84 or 3.2999999999999998e131 < t

   1. Initial program 44.6%

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

   3. Taylor expanded in a around inf 30.2%

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

      1. associate-/l* 67.1%

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

      2. +-commutative 67.1%

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

      3. associate-+r+ 67.1%

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

      4. +-commutative 67.1%

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

      5. associate-+l+ 67.1%

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

   5. Simplified 67.1%

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

   if -1.9e84 < t < -7.2999999999999996e-159 or -4.00000000000000006e-251 < t < 3.2999999999999998e131

   1. Initial program 64.9%

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

   3. Taylor expanded in y around inf 58.9%

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

   if -7.2999999999999996e-159 < t < -4.00000000000000006e-251

   1. Initial program 80.0%

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

   3. Taylor expanded in x around inf 64.5%

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

4. Final simplification 62.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.9 \cdot 10^{+84}:\\ \;\;\;\;a \cdot \frac{y + t}{y + \left(x + t\right)}\\ \mathbf{elif}\;t \leq -7.3 \cdot 10^{-159}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;t \leq -4 \cdot 10^{-251}:\\ \;\;\;\;z\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{+131}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{y + t}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 63.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -49000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-9}:\\ \;\;\;\;a \cdot \frac{y + t}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq -7.8 \cdot 10^{-61}:\\ \;\;\;\;z + a\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{+36}:\\ \;\;\;\;\frac{t \cdot a + z \cdot x}{x + t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= y -49000000.0)
     t_1
     (if (<= y -5e-9)
       (* a (/ (+ y t) (+ y (+ x t))))
       (if (<= y -7.8e-61)
         (+ z a)
         (if (<= y 8.8e+36) (/ (+ (* t a) (* z x)) (+ x t)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -49000000.0) {
		tmp = t_1;
	} else if (y <= -5e-9) {
		tmp = a * ((y + t) / (y + (x + t)));
	} else if (y <= -7.8e-61) {
		tmp = z + a;
	} else if (y <= 8.8e+36) {
		tmp = ((t * a) + (z * x)) / (x + t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z + a) - b
    if (y <= (-49000000.0d0)) then
        tmp = t_1
    else if (y <= (-5d-9)) then
        tmp = a * ((y + t) / (y + (x + t)))
    else if (y <= (-7.8d-61)) then
        tmp = z + a
    else if (y <= 8.8d+36) then
        tmp = ((t * a) + (z * x)) / (x + t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -49000000.0) {
		tmp = t_1;
	} else if (y <= -5e-9) {
		tmp = a * ((y + t) / (y + (x + t)));
	} else if (y <= -7.8e-61) {
		tmp = z + a;
	} else if (y <= 8.8e+36) {
		tmp = ((t * a) + (z * x)) / (x + t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	tmp = 0
	if y <= -49000000.0:
		tmp = t_1
	elif y <= -5e-9:
		tmp = a * ((y + t) / (y + (x + t)))
	elif y <= -7.8e-61:
		tmp = z + a
	elif y <= 8.8e+36:
		tmp = ((t * a) + (z * x)) / (x + t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -49000000.0)
		tmp = t_1;
	elseif (y <= -5e-9)
		tmp = Float64(a * Float64(Float64(y + t) / Float64(y + Float64(x + t))));
	elseif (y <= -7.8e-61)
		tmp = Float64(z + a);
	elseif (y <= 8.8e+36)
		tmp = Float64(Float64(Float64(t * a) + Float64(z * x)) / Float64(x + t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	tmp = 0.0;
	if (y <= -49000000.0)
		tmp = t_1;
	elseif (y <= -5e-9)
		tmp = a * ((y + t) / (y + (x + t)));
	elseif (y <= -7.8e-61)
		tmp = z + a;
	elseif (y <= 8.8e+36)
		tmp = ((t * a) + (z * x)) / (x + t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -49000000.0], t$95$1, If[LessEqual[y, -5e-9], N[(a * N[(N[(y + t), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -7.8e-61], N[(z + a), $MachinePrecision], If[LessEqual[y, 8.8e+36], N[(N[(N[(t * a), $MachinePrecision] + N[(z * x), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.9e7 or 8.80000000000000002e36 < y

   1. Initial program 39.7%

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

   3. Taylor expanded in y around inf 78.1%

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

   if -4.9e7 < y < -5.0000000000000001e-9

   1. Initial program 45.5%

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

   3. Taylor expanded in a around inf 31.9%

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

      1. associate-/l* 84.7%

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

      2. +-commutative 84.7%

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

      3. associate-+r+ 84.7%

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

      4. +-commutative 84.7%

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

      5. associate-+l+ 84.7%

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

   5. Simplified 84.7%

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

   if -5.0000000000000001e-9 < y < -7.80000000000000065e-61

   1. Initial program 85.2%

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

   3. Taylor expanded in b around -inf 77.1%

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

      1. mul-1-neg 77.1%

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

      2. *-commutative 77.1%

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

      3. distribute-rgt-neg-in 77.1%

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

   5. Simplified 77.1%

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

   6. Taylor expanded in y around -inf 46.2%

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

   7. Taylor expanded in b around 0 76.4%

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

   if -7.80000000000000065e-61 < y < 8.80000000000000002e36

   1. Initial program 74.6%

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

   3. Taylor expanded in y around 0 55.0%

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

4. Final simplification 66.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -49000000:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-9}:\\ \;\;\;\;a \cdot \frac{y + t}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq -7.8 \cdot 10^{-61}:\\ \;\;\;\;z + a\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{+36}:\\ \;\;\;\;\frac{t \cdot a + z \cdot x}{x + t}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 57.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ t_2 := a \cdot \frac{t}{y + \left(x + t\right)}\\ \mathbf{if}\;t \leq -3.1 \cdot 10^{+142}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -5.6 \cdot 10^{-159}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.25 \cdot 10^{-251}:\\ \;\;\;\;z\\ \mathbf{elif}\;t \leq 5.7 \cdot 10^{+131}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)) (t_2 (* a (/ t (+ y (+ x t))))))
   (if (<= t -3.1e+142)
     t_2
     (if (<= t -5.6e-159)
       t_1
       (if (<= t -2.25e-251) z (if (<= t 5.7e+131) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = a * (t / (y + (x + t)));
	double tmp;
	if (t <= -3.1e+142) {
		tmp = t_2;
	} else if (t <= -5.6e-159) {
		tmp = t_1;
	} else if (t <= -2.25e-251) {
		tmp = z;
	} else if (t <= 5.7e+131) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (z + a) - b
    t_2 = a * (t / (y + (x + t)))
    if (t <= (-3.1d+142)) then
        tmp = t_2
    else if (t <= (-5.6d-159)) then
        tmp = t_1
    else if (t <= (-2.25d-251)) then
        tmp = z
    else if (t <= 5.7d+131) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double t_2 = a * (t / (y + (x + t)));
	double tmp;
	if (t <= -3.1e+142) {
		tmp = t_2;
	} else if (t <= -5.6e-159) {
		tmp = t_1;
	} else if (t <= -2.25e-251) {
		tmp = z;
	} else if (t <= 5.7e+131) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	t_2 = a * (t / (y + (x + t)))
	tmp = 0
	if t <= -3.1e+142:
		tmp = t_2
	elif t <= -5.6e-159:
		tmp = t_1
	elif t <= -2.25e-251:
		tmp = z
	elif t <= 5.7e+131:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	t_2 = Float64(a * Float64(t / Float64(y + Float64(x + t))))
	tmp = 0.0
	if (t <= -3.1e+142)
		tmp = t_2;
	elseif (t <= -5.6e-159)
		tmp = t_1;
	elseif (t <= -2.25e-251)
		tmp = z;
	elseif (t <= 5.7e+131)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	t_2 = a * (t / (y + (x + t)));
	tmp = 0.0;
	if (t <= -3.1e+142)
		tmp = t_2;
	elseif (t <= -5.6e-159)
		tmp = t_1;
	elseif (t <= -2.25e-251)
		tmp = z;
	elseif (t <= 5.7e+131)
		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[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(t / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.1e+142], t$95$2, If[LessEqual[t, -5.6e-159], t$95$1, If[LessEqual[t, -2.25e-251], z, If[LessEqual[t, 5.7e+131], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.0999999999999999e142 or 5.7e131 < t

   1. Initial program 43.7%

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

   3. Taylor expanded in t around inf 28.2%

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

      1. associate-/l* 62.6%

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

      2. +-commutative 62.6%

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

      3. +-commutative 62.6%

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

   5. Applied egg-rr 62.6%

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

   if -3.0999999999999999e142 < t < -5.6000000000000004e-159 or -2.24999999999999989e-251 < t < 5.7e131

   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. Add Preprocessing

   3. Taylor expanded in y around inf 60.2%

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

   if -5.6000000000000004e-159 < t < -2.24999999999999989e-251

   1. Initial program 80.0%

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

   3. Taylor expanded in x around inf 64.5%

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

4. Final simplification 61.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.1 \cdot 10^{+142}:\\ \;\;\;\;a \cdot \frac{t}{y + \left(x + t\right)}\\ \mathbf{elif}\;t \leq -5.6 \cdot 10^{-159}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;t \leq -2.25 \cdot 10^{-251}:\\ \;\;\;\;z\\ \mathbf{elif}\;t \leq 5.7 \cdot 10^{+131}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t}{y + \left(x + t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 54.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;x \leq 4.8 \cdot 10^{-247}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-106}:\\ \;\;\;\;a\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{+36}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 3 \cdot 10^{+208}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= x 4.8e-247)
     t_1
     (if (<= x 1.2e-106)
       a
       (if (<= x 3.4e+36) t_1 (if (<= x 3e+208) (+ z a) z))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (x <= 4.8e-247) {
		tmp = t_1;
	} else if (x <= 1.2e-106) {
		tmp = a;
	} else if (x <= 3.4e+36) {
		tmp = t_1;
	} else if (x <= 3e+208) {
		tmp = z + 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) :: t_1
    real(8) :: tmp
    t_1 = (z + a) - b
    if (x <= 4.8d-247) then
        tmp = t_1
    else if (x <= 1.2d-106) then
        tmp = a
    else if (x <= 3.4d+36) then
        tmp = t_1
    else if (x <= 3d+208) then
        tmp = z + 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 t_1 = (z + a) - b;
	double tmp;
	if (x <= 4.8e-247) {
		tmp = t_1;
	} else if (x <= 1.2e-106) {
		tmp = a;
	} else if (x <= 3.4e+36) {
		tmp = t_1;
	} else if (x <= 3e+208) {
		tmp = z + a;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + a) - b
	tmp = 0
	if x <= 4.8e-247:
		tmp = t_1
	elif x <= 1.2e-106:
		tmp = a
	elif x <= 3.4e+36:
		tmp = t_1
	elif x <= 3e+208:
		tmp = z + a
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (x <= 4.8e-247)
		tmp = t_1;
	elseif (x <= 1.2e-106)
		tmp = a;
	elseif (x <= 3.4e+36)
		tmp = t_1;
	elseif (x <= 3e+208)
		tmp = Float64(z + a);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + a) - b;
	tmp = 0.0;
	if (x <= 4.8e-247)
		tmp = t_1;
	elseif (x <= 1.2e-106)
		tmp = a;
	elseif (x <= 3.4e+36)
		tmp = t_1;
	elseif (x <= 3e+208)
		tmp = z + a;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[x, 4.8e-247], t$95$1, If[LessEqual[x, 1.2e-106], a, If[LessEqual[x, 3.4e+36], t$95$1, If[LessEqual[x, 3e+208], N[(z + a), $MachinePrecision], z]]]]]

Derivation

1. Split input into 4 regimes

2. if x < 4.80000000000000022e-247 or 1.1999999999999999e-106 < x < 3.3999999999999998e36

   1. Initial program 57.1%

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

   3. Taylor expanded in y around inf 59.1%

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

   if 4.80000000000000022e-247 < x < 1.1999999999999999e-106

   1. Initial program 77.1%

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

   3. Taylor expanded in t around inf 65.2%

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

   if 3.3999999999999998e36 < x < 2.99999999999999995e208

   1. Initial program 62.4%

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

   3. Taylor expanded in b around -inf 59.5%

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

      1. mul-1-neg 59.5%

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

      2. *-commutative 59.5%

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

      3. distribute-rgt-neg-in 59.5%

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

   5. Simplified 75.5%

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

   6. Taylor expanded in y around -inf 21.7%

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

   7. Taylor expanded in b around 0 64.0%

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

   if 2.99999999999999995e208 < x

   1. Initial program 50.0%

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

   3. Taylor expanded in x around inf 71.9%

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

4. Final simplification 61.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 4.8 \cdot 10^{-247}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-106}:\\ \;\;\;\;a\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{+36}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;x \leq 3 \cdot 10^{+208}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 43.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{+16}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{+131}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.4e+16) a (if (<= t 1.45e+131) z a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.4e+16) {
		tmp = a;
	} else if (t <= 1.45e+131) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-1.4d+16)) then
        tmp = a
    else if (t <= 1.45d+131) then
        tmp = z
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.4e+16) {
		tmp = a;
	} else if (t <= 1.45e+131) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1.4e+16:
		tmp = a
	elif t <= 1.45e+131:
		tmp = z
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.4e+16)
		tmp = a;
	elseif (t <= 1.45e+131)
		tmp = z;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -1.4e+16)
		tmp = a;
	elseif (t <= 1.45e+131)
		tmp = z;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.4e+16], a, If[LessEqual[t, 1.45e+131], z, a]]

Derivation

1. Split input into 2 regimes

2. if t < -1.4e16 or 1.45000000000000005e131 < t

   1. Initial program 45.7%

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

   3. Taylor expanded in t around inf 56.0%

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

   if -1.4e16 < t < 1.45000000000000005e131

   1. Initial program 68.6%

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

   3. Taylor expanded in x around inf 42.8%

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

4. Final simplification 48.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{+16}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{+131}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 52.6% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 4.1 \cdot 10^{+208}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (if (<= x 4.1e+208) (+ z a) z))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= 4.1e+208) {
		tmp = z + a;
	} else {
		tmp = z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= 4.1d+208) then
        tmp = z + a
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= 4.1e+208) {
		tmp = z + a;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= 4.1e+208:
		tmp = z + a
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= 4.1e+208)
		tmp = Float64(z + a);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= 4.1e+208)
		tmp = z + a;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, 4.1e+208], N[(z + a), $MachinePrecision], z]

Derivation

1. Split input into 2 regimes

2. if x < 4.0999999999999998e208

   1. Initial program 60.0%

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

   3. Taylor expanded in b around -inf 59.6%

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

      1. mul-1-neg 59.6%

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

      2. *-commutative 59.6%

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

      3. distribute-rgt-neg-in 59.6%

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

   5. Simplified 83.4%

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

   6. Taylor expanded in y around -inf 43.5%

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

   7. Taylor expanded in b around 0 50.5%

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

   if 4.0999999999999998e208 < x

   1. Initial program 50.0%

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

   3. Taylor expanded in x around inf 71.9%

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

4. Final simplification 52.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 4.1 \cdot 10^{+208}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 32.4% 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 59.3%

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

3. Taylor expanded in t around inf 34.0%

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

4. Final simplification 34.0%

   \[\leadsto a \]
5. Add Preprocessing

Developer target: 82.9% 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 2024115 
(FPCore (x y z t a b)
  :name "AI.Clustering.Hierarchical.Internal:ward from clustering-0.2.1"
  :precision binary64

  :alt
  (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)))