Diagrams.Solve.Tridiagonal:solveCyclicTriDiagonal from diagrams-solve-0.1, B

Percentage Accurate: 75.6% → 90.9%

Time: 13.0s

Alternatives: 14

Speedup: 0.6×

Specification

Math

\[\begin{array}{l} \\ \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t))))

C

double code(double x, double y, double z, double t, double a, double b) {
	return (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
}

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)) / ((a + 1.0d0) + ((y * b) / t))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
}

Python

def code(x, y, z, t, a, b):
	return (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t))

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(Float64(a + 1.0) + Float64(Float64(y * b) / t)))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 75.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t))))

C

double code(double x, double y, double z, double t, double a, double b) {
	return (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
}

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)) / ((a + 1.0d0) + ((y * b) / t))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
}

Python

def code(x, y, z, t, a, b):
	return (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t))

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(Float64(a + 1.0) + Float64(Float64(y * b) / t)))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 90.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot z}{t}\\ t_2 := 1 + \left(a + \frac{y}{\frac{t}{b}}\right)\\ t_3 := \frac{t\_1}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ t_4 := z \cdot \left(\frac{\frac{x}{z}}{t\_2} + \frac{y}{t \cdot t\_2}\right)\\ \mathbf{if}\;t\_3 \leq -5 \cdot 10^{+258}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t\_3 \leq 4 \cdot 10^{+305}:\\ \;\;\;\;\frac{t\_1}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \mathbf{elif}\;t\_3 \leq \infty:\\ \;\;\;\;t\_4\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (/ (* y z) t)))
        (t_2 (+ 1.0 (+ a (/ y (/ t b)))))
        (t_3 (/ t_1 (+ (+ a 1.0) (/ (* y b) t))))
        (t_4 (* z (+ (/ (/ x z) t_2) (/ y (* t t_2))))))
   (if (<= t_3 -5e+258)
     t_4
     (if (<= t_3 4e+305)
       (/ t_1 (+ (+ a 1.0) (* b (/ y t))))
       (if (<= t_3 INFINITY) t_4 (/ z b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + ((y * z) / t);
	double t_2 = 1.0 + (a + (y / (t / b)));
	double t_3 = t_1 / ((a + 1.0) + ((y * b) / t));
	double t_4 = z * (((x / z) / t_2) + (y / (t * t_2)));
	double tmp;
	if (t_3 <= -5e+258) {
		tmp = t_4;
	} else if (t_3 <= 4e+305) {
		tmp = t_1 / ((a + 1.0) + (b * (y / t)));
	} else if (t_3 <= ((double) INFINITY)) {
		tmp = t_4;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + ((y * z) / t);
	double t_2 = 1.0 + (a + (y / (t / b)));
	double t_3 = t_1 / ((a + 1.0) + ((y * b) / t));
	double t_4 = z * (((x / z) / t_2) + (y / (t * t_2)));
	double tmp;
	if (t_3 <= -5e+258) {
		tmp = t_4;
	} else if (t_3 <= 4e+305) {
		tmp = t_1 / ((a + 1.0) + (b * (y / t)));
	} else if (t_3 <= Double.POSITIVE_INFINITY) {
		tmp = t_4;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + ((y * z) / t)
	t_2 = 1.0 + (a + (y / (t / b)))
	t_3 = t_1 / ((a + 1.0) + ((y * b) / t))
	t_4 = z * (((x / z) / t_2) + (y / (t * t_2)))
	tmp = 0
	if t_3 <= -5e+258:
		tmp = t_4
	elif t_3 <= 4e+305:
		tmp = t_1 / ((a + 1.0) + (b * (y / t)))
	elif t_3 <= math.inf:
		tmp = t_4
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(Float64(y * z) / t))
	t_2 = Float64(1.0 + Float64(a + Float64(y / Float64(t / b))))
	t_3 = Float64(t_1 / Float64(Float64(a + 1.0) + Float64(Float64(y * b) / t)))
	t_4 = Float64(z * Float64(Float64(Float64(x / z) / t_2) + Float64(y / Float64(t * t_2))))
	tmp = 0.0
	if (t_3 <= -5e+258)
		tmp = t_4;
	elseif (t_3 <= 4e+305)
		tmp = Float64(t_1 / Float64(Float64(a + 1.0) + Float64(b * Float64(y / t))));
	elseif (t_3 <= Inf)
		tmp = t_4;
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + ((y * z) / t);
	t_2 = 1.0 + (a + (y / (t / b)));
	t_3 = t_1 / ((a + 1.0) + ((y * b) / t));
	t_4 = z * (((x / z) / t_2) + (y / (t * t_2)));
	tmp = 0.0;
	if (t_3 <= -5e+258)
		tmp = t_4;
	elseif (t_3 <= 4e+305)
		tmp = t_1 / ((a + 1.0) + (b * (y / t)));
	elseif (t_3 <= Inf)
		tmp = t_4;
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(1.0 + N[(a + N[(y / N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$1 / N[(N[(a + 1.0), $MachinePrecision] + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(z * N[(N[(N[(x / z), $MachinePrecision] / t$95$2), $MachinePrecision] + N[(y / N[(t * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, -5e+258], t$95$4, If[LessEqual[t$95$3, 4e+305], N[(t$95$1 / N[(N[(a + 1.0), $MachinePrecision] + N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, Infinity], t$95$4, N[(z / b), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -5e258 or 3.9999999999999998e305 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < +inf.0

   1. Initial program 49.1%

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

      1. associate-/l* 68.6%

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

      2. associate-/l* 68.6%

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

   3. Simplified 68.6%

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

   5. Taylor expanded in z around inf 87.4%

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

      1. associate-/r* 87.7%

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

      2. associate-*r/ 87.7%

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

      3. *-commutative 87.7%

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

      4. associate-/r/ 87.7%

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

      5. associate-*r/ 70.1%

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

      6. *-commutative 70.1%

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

      7. associate-/r/ 87.6%

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

   7. Simplified 87.6%

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

   if -5e258 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 3.9999999999999998e305

   1. Initial program 88.3%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. *-commutative 88.3%

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

      2. associate-/l* 90.3%

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

   4. Applied egg-rr 90.3%

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

   if +inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t)))

   1. Initial program 0.0%

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

      1. associate-/l* 0.8%

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

      2. associate-/l* 11.0%

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

   3. Simplified 11.0%

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

   5. Taylor expanded in y around inf 96.7%

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

Alternative 2: 91.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot b}{t}\\ t_2 := x + \frac{y \cdot z}{t}\\ t_3 := 1 + \left(a + t\_1\right)\\ t_4 := \frac{t\_2}{\left(a + 1\right) + t\_1}\\ t_5 := z \cdot \left(\frac{x}{z \cdot t\_3} + \frac{y}{t \cdot t\_3}\right)\\ \mathbf{if}\;t\_4 \leq -5 \cdot 10^{+258}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;t\_4 \leq 4 \cdot 10^{+305}:\\ \;\;\;\;\frac{t\_2}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \mathbf{elif}\;t\_4 \leq \infty:\\ \;\;\;\;t\_5\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* y b) t))
        (t_2 (+ x (/ (* y z) t)))
        (t_3 (+ 1.0 (+ a t_1)))
        (t_4 (/ t_2 (+ (+ a 1.0) t_1)))
        (t_5 (* z (+ (/ x (* z t_3)) (/ y (* t t_3))))))
   (if (<= t_4 -5e+258)
     t_5
     (if (<= t_4 4e+305)
       (/ t_2 (+ (+ a 1.0) (* b (/ y t))))
       (if (<= t_4 INFINITY) t_5 (/ z b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y * b) / t;
	double t_2 = x + ((y * z) / t);
	double t_3 = 1.0 + (a + t_1);
	double t_4 = t_2 / ((a + 1.0) + t_1);
	double t_5 = z * ((x / (z * t_3)) + (y / (t * t_3)));
	double tmp;
	if (t_4 <= -5e+258) {
		tmp = t_5;
	} else if (t_4 <= 4e+305) {
		tmp = t_2 / ((a + 1.0) + (b * (y / t)));
	} else if (t_4 <= ((double) INFINITY)) {
		tmp = t_5;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y * b) / t;
	double t_2 = x + ((y * z) / t);
	double t_3 = 1.0 + (a + t_1);
	double t_4 = t_2 / ((a + 1.0) + t_1);
	double t_5 = z * ((x / (z * t_3)) + (y / (t * t_3)));
	double tmp;
	if (t_4 <= -5e+258) {
		tmp = t_5;
	} else if (t_4 <= 4e+305) {
		tmp = t_2 / ((a + 1.0) + (b * (y / t)));
	} else if (t_4 <= Double.POSITIVE_INFINITY) {
		tmp = t_5;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (y * b) / t
	t_2 = x + ((y * z) / t)
	t_3 = 1.0 + (a + t_1)
	t_4 = t_2 / ((a + 1.0) + t_1)
	t_5 = z * ((x / (z * t_3)) + (y / (t * t_3)))
	tmp = 0
	if t_4 <= -5e+258:
		tmp = t_5
	elif t_4 <= 4e+305:
		tmp = t_2 / ((a + 1.0) + (b * (y / t)))
	elif t_4 <= math.inf:
		tmp = t_5
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y * b) / t)
	t_2 = Float64(x + Float64(Float64(y * z) / t))
	t_3 = Float64(1.0 + Float64(a + t_1))
	t_4 = Float64(t_2 / Float64(Float64(a + 1.0) + t_1))
	t_5 = Float64(z * Float64(Float64(x / Float64(z * t_3)) + Float64(y / Float64(t * t_3))))
	tmp = 0.0
	if (t_4 <= -5e+258)
		tmp = t_5;
	elseif (t_4 <= 4e+305)
		tmp = Float64(t_2 / Float64(Float64(a + 1.0) + Float64(b * Float64(y / t))));
	elseif (t_4 <= Inf)
		tmp = t_5;
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (y * b) / t;
	t_2 = x + ((y * z) / t);
	t_3 = 1.0 + (a + t_1);
	t_4 = t_2 / ((a + 1.0) + t_1);
	t_5 = z * ((x / (z * t_3)) + (y / (t * t_3)));
	tmp = 0.0;
	if (t_4 <= -5e+258)
		tmp = t_5;
	elseif (t_4 <= 4e+305)
		tmp = t_2 / ((a + 1.0) + (b * (y / t)));
	elseif (t_4 <= Inf)
		tmp = t_5;
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(1.0 + N[(a + t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$2 / N[(N[(a + 1.0), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(z * N[(N[(x / N[(z * t$95$3), $MachinePrecision]), $MachinePrecision] + N[(y / N[(t * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$4, -5e+258], t$95$5, If[LessEqual[t$95$4, 4e+305], N[(t$95$2 / N[(N[(a + 1.0), $MachinePrecision] + N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$4, Infinity], t$95$5, N[(z / b), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -5e258 or 3.9999999999999998e305 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < +inf.0

   1. Initial program 49.1%

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

      1. associate-/l* 68.6%

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

      2. associate-/l* 68.6%

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

   3. Simplified 68.6%

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

   5. Taylor expanded in z around inf 87.4%

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

   if -5e258 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 3.9999999999999998e305

   1. Initial program 88.3%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. *-commutative 88.3%

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

      2. associate-/l* 90.3%

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

   4. Applied egg-rr 90.3%

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

   if +inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t)))

   1. Initial program 0.0%

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

      1. associate-/l* 0.8%

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

      2. associate-/l* 11.0%

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

   3. Simplified 11.0%

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

   5. Taylor expanded in y around inf 96.7%

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

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -5 \cdot 10^{+258}:\\ \;\;\;\;z \cdot \left(\frac{x}{z \cdot \left(1 + \left(a + \frac{y \cdot b}{t}\right)\right)} + \frac{y}{t \cdot \left(1 + \left(a + \frac{y \cdot b}{t}\right)\right)}\right)\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 4 \cdot 10^{+305}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq \infty:\\ \;\;\;\;z \cdot \left(\frac{x}{z \cdot \left(1 + \left(a + \frac{y \cdot b}{t}\right)\right)} + \frac{y}{t \cdot \left(1 + \left(a + \frac{y \cdot b}{t}\right)\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 90.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot z}{t}\\ t_2 := \frac{t\_1}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ t_3 := y \cdot \frac{z}{t \cdot \left(1 + \left(a + \frac{y}{\frac{t}{b}}\right)\right)}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq 4 \cdot 10^{+305}:\\ \;\;\;\;\frac{t\_1}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (/ (* y z) t)))
        (t_2 (/ t_1 (+ (+ a 1.0) (/ (* y b) t))))
        (t_3 (* y (/ z (* t (+ 1.0 (+ a (/ y (/ t b)))))))))
   (if (<= t_2 (- INFINITY))
     t_3
     (if (<= t_2 4e+305)
       (/ t_1 (+ (+ a 1.0) (* b (/ y t))))
       (if (<= t_2 INFINITY) t_3 (/ z b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + ((y * z) / t);
	double t_2 = t_1 / ((a + 1.0) + ((y * b) / t));
	double t_3 = y * (z / (t * (1.0 + (a + (y / (t / b))))));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_3;
	} else if (t_2 <= 4e+305) {
		tmp = t_1 / ((a + 1.0) + (b * (y / t)));
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = t_3;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + ((y * z) / t);
	double t_2 = t_1 / ((a + 1.0) + ((y * b) / t));
	double t_3 = y * (z / (t * (1.0 + (a + (y / (t / b))))));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_3;
	} else if (t_2 <= 4e+305) {
		tmp = t_1 / ((a + 1.0) + (b * (y / t)));
	} else if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = t_3;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + ((y * z) / t)
	t_2 = t_1 / ((a + 1.0) + ((y * b) / t))
	t_3 = y * (z / (t * (1.0 + (a + (y / (t / b))))))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_3
	elif t_2 <= 4e+305:
		tmp = t_1 / ((a + 1.0) + (b * (y / t)))
	elif t_2 <= math.inf:
		tmp = t_3
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(Float64(y * z) / t))
	t_2 = Float64(t_1 / Float64(Float64(a + 1.0) + Float64(Float64(y * b) / t)))
	t_3 = Float64(y * Float64(z / Float64(t * Float64(1.0 + Float64(a + Float64(y / Float64(t / b)))))))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_3;
	elseif (t_2 <= 4e+305)
		tmp = Float64(t_1 / Float64(Float64(a + 1.0) + Float64(b * Float64(y / t))));
	elseif (t_2 <= Inf)
		tmp = t_3;
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + ((y * z) / t);
	t_2 = t_1 / ((a + 1.0) + ((y * b) / t));
	t_3 = y * (z / (t * (1.0 + (a + (y / (t / b))))));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_3;
	elseif (t_2 <= 4e+305)
		tmp = t_1 / ((a + 1.0) + (b * (y / t)));
	elseif (t_2 <= Inf)
		tmp = t_3;
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 / N[(N[(a + 1.0), $MachinePrecision] + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y * N[(z / N[(t * N[(1.0 + N[(a + N[(y / N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$3, If[LessEqual[t$95$2, 4e+305], N[(t$95$1 / N[(N[(a + 1.0), $MachinePrecision] + N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, Infinity], t$95$3, N[(z / b), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -inf.0 or 3.9999999999999998e305 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < +inf.0

   1. Initial program 44.9%

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

      1. associate-/l* 68.7%

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

      2. associate-/l* 68.7%

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

   3. Simplified 68.7%

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

   5. Taylor expanded in x around 0 62.5%

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

      1. associate-/l* 81.3%

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

      2. associate-*r/ 62.1%

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

      3. *-commutative 62.1%

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

      4. associate-/r/ 81.1%

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

   7. Simplified 81.1%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 3.9999999999999998e305

   1. Initial program 88.4%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. *-commutative 88.4%

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

      2. associate-/l* 90.5%

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

   4. Applied egg-rr 90.5%

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

   if +inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t)))

   1. Initial program 0.0%

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

      1. associate-/l* 0.8%

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

      2. associate-/l* 11.0%

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

   3. Simplified 11.0%

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

   5. Taylor expanded in y around inf 96.7%

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

Alternative 4: 81.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{if}\;t \leq -1.6 \cdot 10^{-73}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{-175}:\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot t}{y \cdot b}\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+133}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (* y (/ z t))) (+ (+ a 1.0) (* y (/ b t))))))
   (if (<= t -1.6e-73)
     t_1
     (if (<= t 1.45e-175)
       (+ (/ z b) (/ (* x t) (* y b)))
       (if (<= t 4e+133)
         (/ (+ x (* z (/ y t))) (+ (+ a 1.0) (/ (* y b) t)))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)));
	double tmp;
	if (t <= -1.6e-73) {
		tmp = t_1;
	} else if (t <= 1.45e-175) {
		tmp = (z / b) + ((x * t) / (y * b));
	} else if (t <= 4e+133) {
		tmp = (x + (z * (y / t))) / ((a + 1.0) + ((y * b) / 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 = (x + (y * (z / t))) / ((a + 1.0d0) + (y * (b / t)))
    if (t <= (-1.6d-73)) then
        tmp = t_1
    else if (t <= 1.45d-175) then
        tmp = (z / b) + ((x * t) / (y * b))
    else if (t <= 4d+133) then
        tmp = (x + (z * (y / t))) / ((a + 1.0d0) + ((y * b) / 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 = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)));
	double tmp;
	if (t <= -1.6e-73) {
		tmp = t_1;
	} else if (t <= 1.45e-175) {
		tmp = (z / b) + ((x * t) / (y * b));
	} else if (t <= 4e+133) {
		tmp = (x + (z * (y / t))) / ((a + 1.0) + ((y * b) / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)))
	tmp = 0
	if t <= -1.6e-73:
		tmp = t_1
	elif t <= 1.45e-175:
		tmp = (z / b) + ((x * t) / (y * b))
	elif t <= 4e+133:
		tmp = (x + (z * (y / t))) / ((a + 1.0) + ((y * b) / t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(Float64(a + 1.0) + Float64(y * Float64(b / t))))
	tmp = 0.0
	if (t <= -1.6e-73)
		tmp = t_1;
	elseif (t <= 1.45e-175)
		tmp = Float64(Float64(z / b) + Float64(Float64(x * t) / Float64(y * b)));
	elseif (t <= 4e+133)
		tmp = Float64(Float64(x + Float64(z * Float64(y / t))) / Float64(Float64(a + 1.0) + Float64(Float64(y * b) / t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)));
	tmp = 0.0;
	if (t <= -1.6e-73)
		tmp = t_1;
	elseif (t <= 1.45e-175)
		tmp = (z / b) + ((x * t) / (y * b));
	elseif (t <= 4e+133)
		tmp = (x + (z * (y / t))) / ((a + 1.0) + ((y * b) / t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.6e-73], t$95$1, If[LessEqual[t, 1.45e-175], N[(N[(z / b), $MachinePrecision] + N[(N[(x * t), $MachinePrecision] / N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4e+133], N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.59999999999999993e-73 or 4.0000000000000001e133 < t

   1. Initial program 77.7%

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

      1. associate-/l* 82.9%

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

      2. associate-/l* 93.1%

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

   3. Simplified 93.1%

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

   if -1.59999999999999993e-73 < t < 1.44999999999999999e-175

   1. Initial program 54.9%

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

      1. associate-/l* 47.7%

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

      2. associate-/l* 44.1%

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

   3. Simplified 44.1%

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

   5. Taylor expanded in b around inf 44.5%

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

      1. associate-/l* 39.4%

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

      2. associate-*r/ 39.3%

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

      3. +-commutative 39.3%

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

      4. fma-undefine 39.3%

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

      5. *-commutative 39.3%

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

   7. Simplified 39.3%

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

   8. Taylor expanded in t around 0 72.4%

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

   if 1.44999999999999999e-175 < t < 4.0000000000000001e133

   1. Initial program 86.3%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. *-commutative 86.3%

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

      2. associate-/l* 90.9%

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

   4. Applied egg-rr 90.9%

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

4. Final simplification 86.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{-73}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{-175}:\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot t}{y \cdot b}\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+133}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 56.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{b} + \frac{x \cdot t}{y \cdot b}\\ t_2 := \frac{x + z \cdot \frac{y}{t}}{a}\\ \mathbf{if}\;a \leq -420000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -3.6 \cdot 10^{-255}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.25 \cdot 10^{-303}:\\ \;\;\;\;\frac{x}{1 + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;a \leq 450000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (/ z b) (/ (* x t) (* y b)))) (t_2 (/ (+ x (* z (/ y t))) a)))
   (if (<= a -420000000.0)
     t_2
     (if (<= a -3.6e-255)
       t_1
       (if (<= a 2.25e-303)
         (/ x (+ 1.0 (/ (* y b) t)))
         (if (<= a 450000.0) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z / b) + ((x * t) / (y * b));
	double t_2 = (x + (z * (y / t))) / a;
	double tmp;
	if (a <= -420000000.0) {
		tmp = t_2;
	} else if (a <= -3.6e-255) {
		tmp = t_1;
	} else if (a <= 2.25e-303) {
		tmp = x / (1.0 + ((y * b) / t));
	} else if (a <= 450000.0) {
		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 / b) + ((x * t) / (y * b))
    t_2 = (x + (z * (y / t))) / a
    if (a <= (-420000000.0d0)) then
        tmp = t_2
    else if (a <= (-3.6d-255)) then
        tmp = t_1
    else if (a <= 2.25d-303) then
        tmp = x / (1.0d0 + ((y * b) / t))
    else if (a <= 450000.0d0) 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 / b) + ((x * t) / (y * b));
	double t_2 = (x + (z * (y / t))) / a;
	double tmp;
	if (a <= -420000000.0) {
		tmp = t_2;
	} else if (a <= -3.6e-255) {
		tmp = t_1;
	} else if (a <= 2.25e-303) {
		tmp = x / (1.0 + ((y * b) / t));
	} else if (a <= 450000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z / b) + ((x * t) / (y * b))
	t_2 = (x + (z * (y / t))) / a
	tmp = 0
	if a <= -420000000.0:
		tmp = t_2
	elif a <= -3.6e-255:
		tmp = t_1
	elif a <= 2.25e-303:
		tmp = x / (1.0 + ((y * b) / t))
	elif a <= 450000.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z / b) + Float64(Float64(x * t) / Float64(y * b)))
	t_2 = Float64(Float64(x + Float64(z * Float64(y / t))) / a)
	tmp = 0.0
	if (a <= -420000000.0)
		tmp = t_2;
	elseif (a <= -3.6e-255)
		tmp = t_1;
	elseif (a <= 2.25e-303)
		tmp = Float64(x / Float64(1.0 + Float64(Float64(y * b) / t)));
	elseif (a <= 450000.0)
		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 / b) + ((x * t) / (y * b));
	t_2 = (x + (z * (y / t))) / a;
	tmp = 0.0;
	if (a <= -420000000.0)
		tmp = t_2;
	elseif (a <= -3.6e-255)
		tmp = t_1;
	elseif (a <= 2.25e-303)
		tmp = x / (1.0 + ((y * b) / t));
	elseif (a <= 450000.0)
		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 / b), $MachinePrecision] + N[(N[(x * t), $MachinePrecision] / N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[a, -420000000.0], t$95$2, If[LessEqual[a, -3.6e-255], t$95$1, If[LessEqual[a, 2.25e-303], N[(x / N[(1.0 + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 450000.0], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.2e8 or 4.5e5 < a

   1. Initial program 71.4%

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

      1. associate-/l* 69.8%

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

      2. associate-/l* 71.4%

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

   3. Simplified 71.4%

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

   5. Taylor expanded in a around inf 63.8%

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

      1. *-commutative 71.4%

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

      2. associate-/l* 73.7%

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

   7. Applied egg-rr 67.8%

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

   if -4.2e8 < a < -3.6000000000000002e-255 or 2.25e-303 < a < 4.5e5

   1. Initial program 71.1%

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

      1. associate-/l* 70.4%

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

      2. associate-/l* 73.8%

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

   3. Simplified 73.8%

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

   5. Taylor expanded in b around inf 37.0%

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

      1. associate-/l* 36.4%

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

      2. associate-*r/ 38.9%

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

      3. +-commutative 38.9%

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

      4. fma-undefine 38.9%

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

      5. *-commutative 38.9%

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

   7. Simplified 38.9%

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

   8. Taylor expanded in t around 0 56.4%

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

   if -3.6000000000000002e-255 < a < 2.25e-303

   1. Initial program 87.2%

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

      1. associate-/l* 82.8%

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

      2. associate-/l* 82.8%

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

   3. Simplified 82.8%

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

   5. Taylor expanded in x around inf 74.7%

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

      1. associate-*r/ 78.7%

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

      2. *-commutative 78.7%

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

      3. associate-/r/ 78.4%

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

   7. Simplified 78.4%

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

   8. Taylor expanded in a around 0 74.7%

      \[\leadsto \color{blue}{\frac{x}{1 + \frac{b \cdot y}{t}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 63.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -420000000:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a}\\ \mathbf{elif}\;a \leq -3.6 \cdot 10^{-255}:\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot t}{y \cdot b}\\ \mathbf{elif}\;a \leq 2.25 \cdot 10^{-303}:\\ \;\;\;\;\frac{x}{1 + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;a \leq 450000:\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot t}{y \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 81.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{-74} \lor \neg \left(t \leq 3.6 \cdot 10^{-177}\right):\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot t}{y \cdot b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -3e-74) (not (<= t 3.6e-177)))
   (/ (+ x (* y (/ z t))) (+ (+ a 1.0) (* y (/ b t))))
   (+ (/ z b) (/ (* x t) (* y b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -3e-74) || !(t <= 3.6e-177)) {
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)));
	} else {
		tmp = (z / b) + ((x * t) / (y * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-3d-74)) .or. (.not. (t <= 3.6d-177))) then
        tmp = (x + (y * (z / t))) / ((a + 1.0d0) + (y * (b / t)))
    else
        tmp = (z / b) + ((x * t) / (y * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -3e-74) || !(t <= 3.6e-177)) {
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)));
	} else {
		tmp = (z / b) + ((x * t) / (y * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -3e-74) or not (t <= 3.6e-177):
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)))
	else:
		tmp = (z / b) + ((x * t) / (y * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -3e-74) || !(t <= 3.6e-177))
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(Float64(a + 1.0) + Float64(y * Float64(b / t))));
	else
		tmp = Float64(Float64(z / b) + Float64(Float64(x * t) / Float64(y * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -3e-74) || ~((t <= 3.6e-177)))
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)));
	else
		tmp = (z / b) + ((x * t) / (y * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -3e-74], N[Not[LessEqual[t, 3.6e-177]], $MachinePrecision]], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z / b), $MachinePrecision] + N[(N[(x * t), $MachinePrecision] / N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.00000000000000007e-74 or 3.59999999999999983e-177 < t

   1. Initial program 80.9%

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

      1. associate-/l* 82.0%

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

      2. associate-/l* 86.9%

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

   3. Simplified 86.9%

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

   if -3.00000000000000007e-74 < t < 3.59999999999999983e-177

   1. Initial program 54.3%

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

      1. associate-/l* 47.1%

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

      2. associate-/l* 43.4%

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

   3. Simplified 43.4%

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

   5. Taylor expanded in b around inf 43.8%

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

      1. associate-/l* 38.7%

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

      2. associate-*r/ 38.5%

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

      3. +-commutative 38.5%

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

      4. fma-undefine 38.5%

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

      5. *-commutative 38.5%

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

   7. Simplified 38.5%

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

   8. Taylor expanded in t around 0 72.1%

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

4. Final simplification 82.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{-74} \lor \neg \left(t \leq 3.6 \cdot 10^{-177}\right):\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot t}{y \cdot b}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 63.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{-17}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-104}:\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot t}{y \cdot b}\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{+21}:\\ \;\;\;\;\frac{y \cdot z}{t \cdot \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 + \left(a + b \cdot \frac{y}{t}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -7e-17)
   (/ x (+ (+ a 1.0) (* y (/ b t))))
   (if (<= t 1.4e-104)
     (+ (/ z b) (/ (* x t) (* y b)))
     (if (<= t 2.1e+21)
       (/ (* y z) (* t (+ a 1.0)))
       (/ x (+ 1.0 (+ a (* b (/ y t)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -7e-17) {
		tmp = x / ((a + 1.0) + (y * (b / t)));
	} else if (t <= 1.4e-104) {
		tmp = (z / b) + ((x * t) / (y * b));
	} else if (t <= 2.1e+21) {
		tmp = (y * z) / (t * (a + 1.0));
	} else {
		tmp = x / (1.0 + (a + (b * (y / t))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-7d-17)) then
        tmp = x / ((a + 1.0d0) + (y * (b / t)))
    else if (t <= 1.4d-104) then
        tmp = (z / b) + ((x * t) / (y * b))
    else if (t <= 2.1d+21) then
        tmp = (y * z) / (t * (a + 1.0d0))
    else
        tmp = x / (1.0d0 + (a + (b * (y / t))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -7e-17) {
		tmp = x / ((a + 1.0) + (y * (b / t)));
	} else if (t <= 1.4e-104) {
		tmp = (z / b) + ((x * t) / (y * b));
	} else if (t <= 2.1e+21) {
		tmp = (y * z) / (t * (a + 1.0));
	} else {
		tmp = x / (1.0 + (a + (b * (y / t))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -7e-17:
		tmp = x / ((a + 1.0) + (y * (b / t)))
	elif t <= 1.4e-104:
		tmp = (z / b) + ((x * t) / (y * b))
	elif t <= 2.1e+21:
		tmp = (y * z) / (t * (a + 1.0))
	else:
		tmp = x / (1.0 + (a + (b * (y / t))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -7e-17)
		tmp = Float64(x / Float64(Float64(a + 1.0) + Float64(y * Float64(b / t))));
	elseif (t <= 1.4e-104)
		tmp = Float64(Float64(z / b) + Float64(Float64(x * t) / Float64(y * b)));
	elseif (t <= 2.1e+21)
		tmp = Float64(Float64(y * z) / Float64(t * Float64(a + 1.0)));
	else
		tmp = Float64(x / Float64(1.0 + Float64(a + Float64(b * Float64(y / t)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -7e-17)
		tmp = x / ((a + 1.0) + (y * (b / t)));
	elseif (t <= 1.4e-104)
		tmp = (z / b) + ((x * t) / (y * b));
	elseif (t <= 2.1e+21)
		tmp = (y * z) / (t * (a + 1.0));
	else
		tmp = x / (1.0 + (a + (b * (y / t))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -7e-17], N[(x / N[(N[(a + 1.0), $MachinePrecision] + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.4e-104], N[(N[(z / b), $MachinePrecision] + N[(N[(x * t), $MachinePrecision] / N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.1e+21], N[(N[(y * z), $MachinePrecision] / N[(t * N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(1.0 + N[(a + N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -7.0000000000000003e-17

   1. Initial program 81.4%

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

      1. associate-/l* 86.0%

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

      2. associate-/l* 93.7%

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

   3. Simplified 93.7%

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

   5. Taylor expanded in x around inf 74.2%

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

   if -7.0000000000000003e-17 < t < 1.4e-104

   1. Initial program 62.6%

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

      1. associate-/l* 55.7%

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

      2. associate-/l* 51.3%

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

   3. Simplified 51.3%

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

   5. Taylor expanded in b around inf 43.4%

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

      1. associate-/l* 39.7%

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

      2. associate-*r/ 40.4%

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

      3. +-commutative 40.4%

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

      4. fma-undefine 40.4%

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

      5. *-commutative 40.4%

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

   7. Simplified 40.4%

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

   8. Taylor expanded in t around 0 66.1%

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

   if 1.4e-104 < t < 2.1e21

   1. Initial program 99.8%

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

      1. associate-/l* 84.3%

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

      2. associate-/l* 80.4%

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

   3. Simplified 80.4%

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

   5. Taylor expanded in b around 0 80.5%

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

   6. Taylor expanded in x around 0 52.0%

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

   if 2.1e21 < t

   1. Initial program 70.3%

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

      1. associate-/l* 78.7%

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

      2. associate-/l* 90.0%

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

   3. Simplified 90.0%

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

   5. Taylor expanded in x around inf 55.9%

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

      1. associate-*r/ 60.8%

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

      2. *-commutative 60.8%

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

      3. associate-/r/ 60.8%

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

   7. Simplified 60.8%

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

      1. associate-/r/ 60.8%

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

   9. Applied egg-rr 60.8%

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

4. Final simplification 65.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{-17}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-104}:\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot t}{y \cdot b}\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{+21}:\\ \;\;\;\;\frac{y \cdot z}{t \cdot \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 + \left(a + b \cdot \frac{y}{t}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 63.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 + \left(a + b \cdot \frac{y}{t}\right)}\\ \mathbf{if}\;t \leq -6.8 \cdot 10^{-17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{-104}:\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot t}{y \cdot b}\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+22}:\\ \;\;\;\;\frac{y \cdot z}{t \cdot \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (+ 1.0 (+ a (* b (/ y t)))))))
   (if (<= t -6.8e-17)
     t_1
     (if (<= t 1.55e-104)
       (+ (/ z b) (/ (* x t) (* y b)))
       (if (<= t 3e+22) (/ (* y z) (* t (+ a 1.0))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 + (a + (b * (y / t))));
	double tmp;
	if (t <= -6.8e-17) {
		tmp = t_1;
	} else if (t <= 1.55e-104) {
		tmp = (z / b) + ((x * t) / (y * b));
	} else if (t <= 3e+22) {
		tmp = (y * z) / (t * (a + 1.0));
	} 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 = x / (1.0d0 + (a + (b * (y / t))))
    if (t <= (-6.8d-17)) then
        tmp = t_1
    else if (t <= 1.55d-104) then
        tmp = (z / b) + ((x * t) / (y * b))
    else if (t <= 3d+22) then
        tmp = (y * z) / (t * (a + 1.0d0))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 + (a + (b * (y / t))));
	double tmp;
	if (t <= -6.8e-17) {
		tmp = t_1;
	} else if (t <= 1.55e-104) {
		tmp = (z / b) + ((x * t) / (y * b));
	} else if (t <= 3e+22) {
		tmp = (y * z) / (t * (a + 1.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (1.0 + (a + (b * (y / t))))
	tmp = 0
	if t <= -6.8e-17:
		tmp = t_1
	elif t <= 1.55e-104:
		tmp = (z / b) + ((x * t) / (y * b))
	elif t <= 3e+22:
		tmp = (y * z) / (t * (a + 1.0))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(1.0 + Float64(a + Float64(b * Float64(y / t)))))
	tmp = 0.0
	if (t <= -6.8e-17)
		tmp = t_1;
	elseif (t <= 1.55e-104)
		tmp = Float64(Float64(z / b) + Float64(Float64(x * t) / Float64(y * b)));
	elseif (t <= 3e+22)
		tmp = Float64(Float64(y * z) / Float64(t * Float64(a + 1.0)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (1.0 + (a + (b * (y / t))));
	tmp = 0.0;
	if (t <= -6.8e-17)
		tmp = t_1;
	elseif (t <= 1.55e-104)
		tmp = (z / b) + ((x * t) / (y * b));
	elseif (t <= 3e+22)
		tmp = (y * z) / (t * (a + 1.0));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(1.0 + N[(a + N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6.8e-17], t$95$1, If[LessEqual[t, 1.55e-104], N[(N[(z / b), $MachinePrecision] + N[(N[(x * t), $MachinePrecision] / N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3e+22], N[(N[(y * z), $MachinePrecision] / N[(t * N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.7999999999999996e-17 or 3e22 < t

   1. Initial program 76.0%

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

      1. associate-/l* 82.5%

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

      2. associate-/l* 91.9%

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

   3. Simplified 91.9%

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

   5. Taylor expanded in x around inf 63.0%

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

      1. associate-*r/ 67.7%

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

      2. *-commutative 67.7%

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

      3. associate-/r/ 67.7%

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

   7. Simplified 67.7%

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

      1. associate-/r/ 67.7%

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

   9. Applied egg-rr 67.7%

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

   if -6.7999999999999996e-17 < t < 1.54999999999999988e-104

   1. Initial program 62.6%

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

      1. associate-/l* 55.7%

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

      2. associate-/l* 51.3%

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

   3. Simplified 51.3%

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

   5. Taylor expanded in b around inf 43.4%

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

      1. associate-/l* 39.7%

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

      2. associate-*r/ 40.4%

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

      3. +-commutative 40.4%

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

      4. fma-undefine 40.4%

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

      5. *-commutative 40.4%

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

   7. Simplified 40.4%

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

   8. Taylor expanded in t around 0 66.1%

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

   if 1.54999999999999988e-104 < t < 3e22

   1. Initial program 99.8%

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

      1. associate-/l* 84.3%

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

      2. associate-/l* 80.4%

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

   3. Simplified 80.4%

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

   5. Taylor expanded in b around 0 80.5%

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

   6. Taylor expanded in x around 0 52.0%

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

4. Final simplification 65.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.8 \cdot 10^{-17}:\\ \;\;\;\;\frac{x}{1 + \left(a + b \cdot \frac{y}{t}\right)}\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{-104}:\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot t}{y \cdot b}\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+22}:\\ \;\;\;\;\frac{y \cdot z}{t \cdot \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 + \left(a + b \cdot \frac{y}{t}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 57.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + z \cdot \frac{y}{t}}{a}\\ \mathbf{if}\;a \leq -155000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{-45}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 410000:\\ \;\;\;\;\frac{x}{1 + \frac{y \cdot b}{t}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (* z (/ y t))) a)))
   (if (<= a -155000000.0)
     t_1
     (if (<= a -4.2e-45)
       (/ z b)
       (if (<= a 410000.0) (/ x (+ 1.0 (/ (* y b) t))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + (z * (y / t))) / a;
	double tmp;
	if (a <= -155000000.0) {
		tmp = t_1;
	} else if (a <= -4.2e-45) {
		tmp = z / b;
	} else if (a <= 410000.0) {
		tmp = x / (1.0 + ((y * b) / 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 = (x + (z * (y / t))) / a
    if (a <= (-155000000.0d0)) then
        tmp = t_1
    else if (a <= (-4.2d-45)) then
        tmp = z / b
    else if (a <= 410000.0d0) then
        tmp = x / (1.0d0 + ((y * b) / 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 = (x + (z * (y / t))) / a;
	double tmp;
	if (a <= -155000000.0) {
		tmp = t_1;
	} else if (a <= -4.2e-45) {
		tmp = z / b;
	} else if (a <= 410000.0) {
		tmp = x / (1.0 + ((y * b) / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + (z * (y / t))) / a
	tmp = 0
	if a <= -155000000.0:
		tmp = t_1
	elif a <= -4.2e-45:
		tmp = z / b
	elif a <= 410000.0:
		tmp = x / (1.0 + ((y * b) / t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(z * Float64(y / t))) / a)
	tmp = 0.0
	if (a <= -155000000.0)
		tmp = t_1;
	elseif (a <= -4.2e-45)
		tmp = Float64(z / b);
	elseif (a <= 410000.0)
		tmp = Float64(x / Float64(1.0 + Float64(Float64(y * b) / t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + (z * (y / t))) / a;
	tmp = 0.0;
	if (a <= -155000000.0)
		tmp = t_1;
	elseif (a <= -4.2e-45)
		tmp = z / b;
	elseif (a <= 410000.0)
		tmp = x / (1.0 + ((y * b) / t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[a, -155000000.0], t$95$1, If[LessEqual[a, -4.2e-45], N[(z / b), $MachinePrecision], If[LessEqual[a, 410000.0], N[(x / N[(1.0 + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.55e8 or 4.1e5 < a

   1. Initial program 71.4%

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

      1. associate-/l* 69.8%

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

      2. associate-/l* 71.4%

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

   3. Simplified 71.4%

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

   5. Taylor expanded in a around inf 63.8%

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

      1. *-commutative 71.4%

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

      2. associate-/l* 73.7%

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

   7. Applied egg-rr 67.8%

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

   if -1.55e8 < a < -4.1999999999999999e-45

   1. Initial program 54.2%

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

      1. associate-/l* 48.1%

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

      2. associate-/l* 54.4%

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

   3. Simplified 54.4%

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

   5. Taylor expanded in y around inf 58.6%

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

   if -4.1999999999999999e-45 < a < 4.1e5

   1. Initial program 76.1%

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

      1. associate-/l* 75.4%

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

      2. associate-/l* 77.8%

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

   3. Simplified 77.8%

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

   5. Taylor expanded in x around inf 48.4%

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

      1. associate-*r/ 51.6%

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

      2. *-commutative 51.6%

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

      3. associate-/r/ 50.0%

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

   7. Simplified 50.0%

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

   8. Taylor expanded in a around 0 48.4%

      \[\leadsto \color{blue}{\frac{x}{1 + \frac{b \cdot y}{t}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 58.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -155000000:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a}\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{-45}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 410000:\\ \;\;\;\;\frac{x}{1 + \frac{y \cdot b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 52.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{a + 1}\\ \mathbf{if}\;t \leq -8.2:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{-177}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq 2.05 \cdot 10^{+85}:\\ \;\;\;\;y \cdot \frac{z}{t \cdot \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (+ a 1.0))))
   (if (<= t -8.2)
     t_1
     (if (<= t 5.6e-177)
       (/ z b)
       (if (<= t 2.05e+85) (* y (/ z (* t (+ a 1.0)))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a + 1.0);
	double tmp;
	if (t <= -8.2) {
		tmp = t_1;
	} else if (t <= 5.6e-177) {
		tmp = z / b;
	} else if (t <= 2.05e+85) {
		tmp = y * (z / (t * (a + 1.0)));
	} 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 = x / (a + 1.0d0)
    if (t <= (-8.2d0)) then
        tmp = t_1
    else if (t <= 5.6d-177) then
        tmp = z / b
    else if (t <= 2.05d+85) then
        tmp = y * (z / (t * (a + 1.0d0)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a + 1.0);
	double tmp;
	if (t <= -8.2) {
		tmp = t_1;
	} else if (t <= 5.6e-177) {
		tmp = z / b;
	} else if (t <= 2.05e+85) {
		tmp = y * (z / (t * (a + 1.0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (a + 1.0)
	tmp = 0
	if t <= -8.2:
		tmp = t_1
	elif t <= 5.6e-177:
		tmp = z / b
	elif t <= 2.05e+85:
		tmp = y * (z / (t * (a + 1.0)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(a + 1.0))
	tmp = 0.0
	if (t <= -8.2)
		tmp = t_1;
	elseif (t <= 5.6e-177)
		tmp = Float64(z / b);
	elseif (t <= 2.05e+85)
		tmp = Float64(y * Float64(z / Float64(t * Float64(a + 1.0))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (a + 1.0);
	tmp = 0.0;
	if (t <= -8.2)
		tmp = t_1;
	elseif (t <= 5.6e-177)
		tmp = z / b;
	elseif (t <= 2.05e+85)
		tmp = y * (z / (t * (a + 1.0)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -8.2], t$95$1, If[LessEqual[t, 5.6e-177], N[(z / b), $MachinePrecision], If[LessEqual[t, 2.05e+85], N[(y * N[(z / N[(t * N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -8.1999999999999993 or 2.04999999999999989e85 < t

   1. Initial program 75.6%

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

      1. associate-/l* 81.1%

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

      2. associate-/l* 91.8%

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

   3. Simplified 91.8%

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

   5. Taylor expanded in y around 0 56.9%

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

   if -8.1999999999999993 < t < 5.59999999999999973e-177

   1. Initial program 59.5%

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

      1. associate-/l* 53.5%

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

      2. associate-/l* 50.4%

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

   3. Simplified 50.4%

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

   5. Taylor expanded in y around inf 59.3%

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

   if 5.59999999999999973e-177 < t < 2.04999999999999989e85

   1. Initial program 89.7%

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

      1. associate-/l* 82.4%

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

      2. associate-/l* 77.1%

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

   3. Simplified 77.1%

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

   5. Taylor expanded in b around 0 64.3%

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

   6. Taylor expanded in x around 0 46.0%

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

      1. associate-/l* 49.5%

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

   8. Simplified 49.5%

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

4. Final simplification 56.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.2:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{-177}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq 2.05 \cdot 10^{+85}:\\ \;\;\;\;y \cdot \frac{z}{t \cdot \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 64.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.6 \cdot 10^{+71} \lor \neg \left(b \leq 1.75 \cdot 10^{-72}\right):\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot t}{y \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -1.6e+71) (not (<= b 1.75e-72)))
   (+ (/ z b) (/ (* x t) (* y b)))
   (/ (+ x (* z (/ y t))) (+ a 1.0))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.6e+71) || !(b <= 1.75e-72)) {
		tmp = (z / b) + ((x * t) / (y * b));
	} else {
		tmp = (x + (z * (y / t))) / (a + 1.0);
	}
	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 ((b <= (-1.6d+71)) .or. (.not. (b <= 1.75d-72))) then
        tmp = (z / b) + ((x * t) / (y * b))
    else
        tmp = (x + (z * (y / t))) / (a + 1.0d0)
    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 ((b <= -1.6e+71) || !(b <= 1.75e-72)) {
		tmp = (z / b) + ((x * t) / (y * b));
	} else {
		tmp = (x + (z * (y / t))) / (a + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -1.6e+71) or not (b <= 1.75e-72):
		tmp = (z / b) + ((x * t) / (y * b))
	else:
		tmp = (x + (z * (y / t))) / (a + 1.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -1.6e+71) || !(b <= 1.75e-72))
		tmp = Float64(Float64(z / b) + Float64(Float64(x * t) / Float64(y * b)));
	else
		tmp = Float64(Float64(x + Float64(z * Float64(y / t))) / Float64(a + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -1.6e+71) || ~((b <= 1.75e-72)))
		tmp = (z / b) + ((x * t) / (y * b));
	else
		tmp = (x + (z * (y / t))) / (a + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -1.6e+71], N[Not[LessEqual[b, 1.75e-72]], $MachinePrecision]], N[(N[(z / b), $MachinePrecision] + N[(N[(x * t), $MachinePrecision] / N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.60000000000000012e71 or 1.75e-72 < b

   1. Initial program 58.0%

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

      1. associate-/l* 58.1%

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

      2. associate-/l* 62.0%

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

   3. Simplified 62.0%

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

   5. Taylor expanded in b around inf 38.9%

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

      1. associate-/l* 37.6%

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

      2. associate-*r/ 39.3%

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

      3. +-commutative 39.3%

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

      4. fma-undefine 39.3%

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

      5. *-commutative 39.3%

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

   7. Simplified 39.3%

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

   8. Taylor expanded in t around 0 64.2%

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

   if -1.60000000000000012e71 < b < 1.75e-72

   1. Initial program 86.3%

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

      1. associate-/l* 83.4%

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

      2. associate-/l* 84.1%

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

   3. Simplified 84.1%

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

   5. Taylor expanded in b around 0 79.3%

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

      1. *-commutative 86.3%

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

      2. associate-/l* 86.9%

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

   7. Applied egg-rr 82.1%

      \[\leadsto \frac{x + \color{blue}{z \cdot \frac{y}{t}}}{1 + a} \]
3. Recombined 2 regimes into one program.

4. Final simplification 73.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.6 \cdot 10^{+71} \lor \neg \left(b \leq 1.75 \cdot 10^{-72}\right):\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot t}{y \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 55.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -10 \lor \neg \left(t \leq 1.55 \cdot 10^{-104}\right):\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -10.0) (not (<= t 1.55e-104))) (/ x (+ a 1.0)) (/ z b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -10.0) || !(t <= 1.55e-104)) {
		tmp = x / (a + 1.0);
	} else {
		tmp = z / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-10.0d0)) .or. (.not. (t <= 1.55d-104))) then
        tmp = x / (a + 1.0d0)
    else
        tmp = z / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -10.0) || !(t <= 1.55e-104)) {
		tmp = x / (a + 1.0);
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -10.0) or not (t <= 1.55e-104):
		tmp = x / (a + 1.0)
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -10.0) || !(t <= 1.55e-104))
		tmp = Float64(x / Float64(a + 1.0));
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -10.0) || ~((t <= 1.55e-104)))
		tmp = x / (a + 1.0);
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -10.0], N[Not[LessEqual[t, 1.55e-104]], $MachinePrecision]], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -10 or 1.54999999999999988e-104 < t

   1. Initial program 79.7%

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

      1. associate-/l* 82.4%

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

      2. associate-/l* 89.7%

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

   3. Simplified 89.7%

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

   5. Taylor expanded in y around 0 49.9%

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

   if -10 < t < 1.54999999999999988e-104

   1. Initial program 63.6%

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

      1. associate-/l* 56.8%

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

      2. associate-/l* 52.6%

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

   3. Simplified 52.6%

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

   5. Taylor expanded in y around inf 56.6%

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

4. Final simplification 52.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -10 \lor \neg \left(t \leq 1.55 \cdot 10^{-104}\right):\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 42.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{-153} \lor \neg \left(y \leq 5.2 \cdot 10^{-32}\right):\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -2.1e-153) (not (<= y 5.2e-32))) (/ z b) (/ x a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.1e-153) || !(y <= 5.2e-32)) {
		tmp = z / b;
	} else {
		tmp = x / 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 ((y <= (-2.1d-153)) .or. (.not. (y <= 5.2d-32))) then
        tmp = z / b
    else
        tmp = x / 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 ((y <= -2.1e-153) || !(y <= 5.2e-32)) {
		tmp = z / b;
	} else {
		tmp = x / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -2.1e-153) or not (y <= 5.2e-32):
		tmp = z / b
	else:
		tmp = x / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -2.1e-153) || !(y <= 5.2e-32))
		tmp = Float64(z / b);
	else
		tmp = Float64(x / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -2.1e-153) || ~((y <= 5.2e-32)))
		tmp = z / b;
	else
		tmp = x / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -2.1e-153], N[Not[LessEqual[y, 5.2e-32]], $MachinePrecision]], N[(z / b), $MachinePrecision], N[(x / a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.10000000000000004e-153 or 5.1999999999999995e-32 < y

   1. Initial program 61.6%

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

      1. associate-/l* 64.5%

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

      2. associate-/l* 70.7%

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

   3. Simplified 70.7%

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

   5. Taylor expanded in y around inf 47.3%

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

   if -2.10000000000000004e-153 < y < 5.1999999999999995e-32

   1. Initial program 95.2%

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

      1. associate-/l* 84.9%

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

      2. associate-/l* 79.2%

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

   3. Simplified 79.2%

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

   5. Taylor expanded in x around inf 68.2%

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

      1. associate-*r/ 68.2%

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

      2. *-commutative 68.2%

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

      3. associate-/r/ 65.8%

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

   7. Simplified 65.8%

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

   8. Taylor expanded in a around inf 36.3%

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

4. Final simplification 43.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{-153} \lor \neg \left(y \leq 5.2 \cdot 10^{-32}\right):\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 25.3% accurate, 5.7× speedup

Math

\[\begin{array}{l} \\ \frac{x}{a} \end{array} \]

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b) {
	return x / 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 = x / a
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(x / a), $MachinePrecision]

Derivation

1. Initial program 72.7%

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

   1. associate-/l* 71.2%

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

   2. associate-/l* 73.5%

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

3. Simplified 73.5%

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

5. Taylor expanded in x around inf 44.3%

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

   1. associate-*r/ 46.5%

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

   2. *-commutative 46.5%

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

   3. associate-/r/ 45.4%

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

7. Simplified 45.4%

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

8. Taylor expanded in a around inf 21.2%

   \[\leadsto \color{blue}{\frac{x}{a}} \]
9. Add Preprocessing

Developer Target 1: 79.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 1 \cdot \left(\left(x + \frac{y}{t} \cdot z\right) \cdot \frac{1}{\left(a + 1\right) + \frac{y}{t} \cdot b}\right)\\ \mathbf{if}\;t < -1.3659085366310088 \cdot 10^{-271}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t < 3.036967103737246 \cdot 10^{-130}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (* 1.0 (* (+ x (* (/ y t) z)) (/ 1.0 (+ (+ a 1.0) (* (/ y t) b)))))))
   (if (< t -1.3659085366310088e-271)
     t_1
     (if (< t 3.036967103737246e-130) (/ z b) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 1.0 * ((x + ((y / t) * z)) * (1.0 / ((a + 1.0) + ((y / t) * b))));
	double tmp;
	if (t < -1.3659085366310088e-271) {
		tmp = t_1;
	} else if (t < 3.036967103737246e-130) {
		tmp = z / b;
	} 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 = 1.0d0 * ((x + ((y / t) * z)) * (1.0d0 / ((a + 1.0d0) + ((y / t) * b))))
    if (t < (-1.3659085366310088d-271)) then
        tmp = t_1
    else if (t < 3.036967103737246d-130) then
        tmp = z / b
    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 = 1.0 * ((x + ((y / t) * z)) * (1.0 / ((a + 1.0) + ((y / t) * b))));
	double tmp;
	if (t < -1.3659085366310088e-271) {
		tmp = t_1;
	} else if (t < 3.036967103737246e-130) {
		tmp = z / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = 1.0 * ((x + ((y / t) * z)) * (1.0 / ((a + 1.0) + ((y / t) * b))))
	tmp = 0
	if t < -1.3659085366310088e-271:
		tmp = t_1
	elif t < 3.036967103737246e-130:
		tmp = z / b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(1.0 * Float64(Float64(x + Float64(Float64(y / t) * z)) * Float64(1.0 / Float64(Float64(a + 1.0) + Float64(Float64(y / t) * b)))))
	tmp = 0.0
	if (t < -1.3659085366310088e-271)
		tmp = t_1;
	elseif (t < 3.036967103737246e-130)
		tmp = Float64(z / b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = 1.0 * ((x + ((y / t) * z)) * (1.0 / ((a + 1.0) + ((y / t) * b))));
	tmp = 0.0;
	if (t < -1.3659085366310088e-271)
		tmp = t_1;
	elseif (t < 3.036967103737246e-130)
		tmp = z / b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(1.0 * N[(N[(x + N[(N[(y / t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] * N[(1.0 / N[(N[(a + 1.0), $MachinePrecision] + N[(N[(y / t), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -1.3659085366310088e-271], t$95$1, If[Less[t, 3.036967103737246e-130], N[(z / b), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2024157 
(FPCore (x y z t a b)
  :name "Diagrams.Solve.Tridiagonal:solveCyclicTriDiagonal from diagrams-solve-0.1, B"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< t -1707385670788761/12500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (* 1 (* (+ x (* (/ y t) z)) (/ 1 (+ (+ a 1) (* (/ y t) b))))) (if (< t 1518483551868623/5000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (/ z b) (* 1 (* (+ x (* (/ y t) z)) (/ 1 (+ (+ a 1) (* (/ y t) b))))))))

  (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t))))