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

Percentage Accurate: 75.5% → 88.3%

Time: 15.7s

Alternatives: 15

Speedup: 0.5×

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: 75.5% 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: 88.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot b}{t} + \left(a + 1\right)\\ t_2 := \frac{x + \frac{y \cdot z}{t}}{t\_1}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;z \cdot \left(\frac{x}{z \cdot t\_1} + \frac{y}{y \cdot b + t \cdot \left(a + 1\right)}\right)\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+280}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{t}{b} \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (/ (* y b) t) (+ a 1.0))) (t_2 (/ (+ x (/ (* y z) t)) t_1)))
   (if (<= t_2 (- INFINITY))
     (* z (+ (/ x (* z t_1)) (/ y (+ (* y b) (* t (+ a 1.0))))))
     (if (<= t_2 2e+280) t_2 (+ (/ z b) (* (/ t b) (/ x y)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y * b) / t) + (a + 1.0);
	double t_2 = (x + ((y * z) / t)) / t_1;
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = z * ((x / (z * t_1)) + (y / ((y * b) + (t * (a + 1.0)))));
	} else if (t_2 <= 2e+280) {
		tmp = t_2;
	} else {
		tmp = (z / b) + ((t / b) * (x / y));
	}
	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) + (a + 1.0);
	double t_2 = (x + ((y * z) / t)) / t_1;
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = z * ((x / (z * t_1)) + (y / ((y * b) + (t * (a + 1.0)))));
	} else if (t_2 <= 2e+280) {
		tmp = t_2;
	} else {
		tmp = (z / b) + ((t / b) * (x / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((y * b) / t) + (a + 1.0)
	t_2 = (x + ((y * z) / t)) / t_1
	tmp = 0
	if t_2 <= -math.inf:
		tmp = z * ((x / (z * t_1)) + (y / ((y * b) + (t * (a + 1.0)))))
	elif t_2 <= 2e+280:
		tmp = t_2
	else:
		tmp = (z / b) + ((t / b) * (x / y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(y * b) / t) + Float64(a + 1.0))
	t_2 = Float64(Float64(x + Float64(Float64(y * z) / t)) / t_1)
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(z * Float64(Float64(x / Float64(z * t_1)) + Float64(y / Float64(Float64(y * b) + Float64(t * Float64(a + 1.0))))));
	elseif (t_2 <= 2e+280)
		tmp = t_2;
	else
		tmp = Float64(Float64(z / b) + Float64(Float64(t / b) * Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((y * b) / t) + (a + 1.0);
	t_2 = (x + ((y * z) / t)) / t_1;
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = z * ((x / (z * t_1)) + (y / ((y * b) + (t * (a + 1.0)))));
	elseif (t_2 <= 2e+280)
		tmp = t_2;
	else
		tmp = (z / b) + ((t / b) * (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(z * N[(N[(x / N[(z * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(y / N[(N[(y * b), $MachinePrecision] + N[(t * N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+280], t$95$2, N[(N[(z / b), $MachinePrecision] + N[(N[(t / b), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]), $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

   1. Initial program 43.7%

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

      1. associate-/l* 50.1%

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

      2. associate-/l* 49.9%

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

   3. Simplified 49.9%

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

   5. Taylor expanded in z around inf 99.4%

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

      1. associate-+r+ 99.4%

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

      2. *-commutative 99.4%

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

      3. associate-+r+ 99.4%

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

      4. *-commutative 99.4%

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

   7. Simplified 99.4%

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

   8. Taylor expanded in t around 0 99.6%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 2.0000000000000001e280

   1. Initial program 93.6%

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

   if 2.0000000000000001e280 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t)))

   1. Initial program 5.1%

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

      1. associate-/l* 11.2%

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

      2. associate-/l* 24.5%

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

   3. Simplified 24.5%

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

   5. Taylor expanded in b around inf 6.0%

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

      1. associate-/l* 6.0%

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

      2. +-commutative 6.0%

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

      3. associate-*r/ 8.4%

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

      4. fma-undefine 8.4%

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

      5. *-commutative 8.4%

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

   7. Simplified 8.4%

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

   8. Taylor expanded in t around 0 86.5%

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

      1. times-frac 90.3%

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

   10. Simplified 90.3%

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

4. Final simplification 93.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -\infty:\\ \;\;\;\;z \cdot \left(\frac{x}{z \cdot \left(\frac{y \cdot b}{t} + \left(a + 1\right)\right)} + \frac{y}{y \cdot b + t \cdot \left(a + 1\right)}\right)\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 2 \cdot 10^{+280}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{t}{b} \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 87.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;z \cdot \left(\frac{y}{y \cdot b + t \cdot \left(a + 1\right)} + \frac{x}{z \cdot a}\right)\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+280}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{t}{b} \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (* y z) t)) (+ (/ (* y b) t) (+ a 1.0)))))
   (if (<= t_1 (- INFINITY))
     (* z (+ (/ y (+ (* y b) (* t (+ a 1.0)))) (/ x (* z a))))
     (if (<= t_1 2e+280) t_1 (+ (/ z b) (* (/ t b) (/ x y)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + ((y * z) / t)) / (((y * b) / t) + (a + 1.0));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = z * ((y / ((y * b) + (t * (a + 1.0)))) + (x / (z * a)));
	} else if (t_1 <= 2e+280) {
		tmp = t_1;
	} else {
		tmp = (z / b) + ((t / b) * (x / y));
	}
	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)) / (((y * b) / t) + (a + 1.0));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = z * ((y / ((y * b) + (t * (a + 1.0)))) + (x / (z * a)));
	} else if (t_1 <= 2e+280) {
		tmp = t_1;
	} else {
		tmp = (z / b) + ((t / b) * (x / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + ((y * z) / t)) / (((y * b) / t) + (a + 1.0))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = z * ((y / ((y * b) + (t * (a + 1.0)))) + (x / (z * a)))
	elif t_1 <= 2e+280:
		tmp = t_1
	else:
		tmp = (z / b) + ((t / b) * (x / y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(Float64(Float64(y * b) / t) + Float64(a + 1.0)))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(z * Float64(Float64(y / Float64(Float64(y * b) + Float64(t * Float64(a + 1.0)))) + Float64(x / Float64(z * a))));
	elseif (t_1 <= 2e+280)
		tmp = t_1;
	else
		tmp = Float64(Float64(z / b) + Float64(Float64(t / b) * Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + ((y * z) / t)) / (((y * b) / t) + (a + 1.0));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = z * ((y / ((y * b) + (t * (a + 1.0)))) + (x / (z * a)));
	elseif (t_1 <= 2e+280)
		tmp = t_1;
	else
		tmp = (z / b) + ((t / b) * (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(z * N[(N[(y / N[(N[(y * b), $MachinePrecision] + N[(t * N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x / N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+280], t$95$1, N[(N[(z / b), $MachinePrecision] + N[(N[(t / b), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]), $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

   1. Initial program 43.7%

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

      1. associate-/l* 50.1%

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

      2. associate-/l* 49.9%

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

   3. Simplified 49.9%

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

   5. Taylor expanded in z around inf 99.4%

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

      1. associate-+r+ 99.4%

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

      2. *-commutative 99.4%

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

      3. associate-+r+ 99.4%

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

      4. *-commutative 99.4%

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

   7. Simplified 99.4%

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

   8. Taylor expanded in t around 0 99.6%

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

   9. Taylor expanded in a around inf 76.5%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 2.0000000000000001e280

   1. Initial program 93.6%

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

   if 2.0000000000000001e280 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t)))

   1. Initial program 5.1%

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

      1. associate-/l* 11.2%

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

      2. associate-/l* 24.5%

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

   3. Simplified 24.5%

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

   5. Taylor expanded in b around inf 6.0%

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

      1. associate-/l* 6.0%

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

      2. +-commutative 6.0%

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

      3. associate-*r/ 8.4%

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

      4. fma-undefine 8.4%

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

      5. *-commutative 8.4%

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

   7. Simplified 8.4%

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

   8. Taylor expanded in t around 0 86.5%

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

      1. times-frac 90.3%

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

   10. Simplified 90.3%

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

4. Final simplification 91.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -\infty:\\ \;\;\;\;z \cdot \left(\frac{y}{y \cdot b + t \cdot \left(a + 1\right)} + \frac{x}{z \cdot a}\right)\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 2 \cdot 10^{+280}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{t}{b} \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 86.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\frac{y \cdot z}{y \cdot b + t \cdot \left(a + 1\right)}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+280}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{t}{b} \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (* y z) t)) (+ (/ (* y b) t) (+ a 1.0)))))
   (if (<= t_1 (- INFINITY))
     (/ (* y z) (+ (* y b) (* t (+ a 1.0))))
     (if (<= t_1 2e+280) t_1 (+ (/ z b) (* (/ t b) (/ x y)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + ((y * z) / t)) / (((y * b) / t) + (a + 1.0));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = (y * z) / ((y * b) + (t * (a + 1.0)));
	} else if (t_1 <= 2e+280) {
		tmp = t_1;
	} else {
		tmp = (z / b) + ((t / b) * (x / y));
	}
	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)) / (((y * b) / t) + (a + 1.0));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = (y * z) / ((y * b) + (t * (a + 1.0)));
	} else if (t_1 <= 2e+280) {
		tmp = t_1;
	} else {
		tmp = (z / b) + ((t / b) * (x / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + ((y * z) / t)) / (((y * b) / t) + (a + 1.0))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = (y * z) / ((y * b) + (t * (a + 1.0)))
	elif t_1 <= 2e+280:
		tmp = t_1
	else:
		tmp = (z / b) + ((t / b) * (x / y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(Float64(Float64(y * b) / t) + Float64(a + 1.0)))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(y * z) / Float64(Float64(y * b) + Float64(t * Float64(a + 1.0))));
	elseif (t_1 <= 2e+280)
		tmp = t_1;
	else
		tmp = Float64(Float64(z / b) + Float64(Float64(t / b) * Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + ((y * z) / t)) / (((y * b) / t) + (a + 1.0));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = (y * z) / ((y * b) + (t * (a + 1.0)));
	elseif (t_1 <= 2e+280)
		tmp = t_1;
	else
		tmp = (z / b) + ((t / b) * (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(y * z), $MachinePrecision] / N[(N[(y * b), $MachinePrecision] + N[(t * N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+280], t$95$1, N[(N[(z / b), $MachinePrecision] + N[(N[(t / b), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]), $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

   1. Initial program 43.7%

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

      1. associate-/l* 50.1%

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

      2. associate-/l* 49.9%

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

   3. Simplified 49.9%

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

   5. Taylor expanded in x around 0 75.2%

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

   6. Taylor expanded in t around 0 75.2%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 2.0000000000000001e280

   1. Initial program 93.6%

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

   if 2.0000000000000001e280 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t)))

   1. Initial program 5.1%

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

      1. associate-/l* 11.2%

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

      2. associate-/l* 24.5%

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

   3. Simplified 24.5%

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

   5. Taylor expanded in b around inf 6.0%

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

      1. associate-/l* 6.0%

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

      2. +-commutative 6.0%

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

      3. associate-*r/ 8.4%

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

      4. fma-undefine 8.4%

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

      5. *-commutative 8.4%

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

   7. Simplified 8.4%

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

   8. Taylor expanded in t around 0 86.5%

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

      1. times-frac 90.3%

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

   10. Simplified 90.3%

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

4. Final simplification 91.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -\infty:\\ \;\;\;\;\frac{y \cdot z}{y \cdot b + t \cdot \left(a + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 2 \cdot 10^{+280}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{t}{b} \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 82.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{b} + \frac{t}{b} \cdot \frac{x}{y}\\ \mathbf{if}\;y \leq -6.2 \cdot 10^{+100}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{+49}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{+41}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 10^{+112}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (/ z b) (* (/ t b) (/ x y)))))
   (if (<= y -6.2e+100)
     t_1
     (if (<= y -4.6e+49)
       (/ (+ x (* y (/ z t))) (+ (+ a 1.0) (* y (/ b t))))
       (if (<= y -4.2e+41)
         (/ z b)
         (if (<= y 1e+112)
           (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (* b (/ y t))))
           t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z / b) + ((t / b) * (x / y));
	double tmp;
	if (y <= -6.2e+100) {
		tmp = t_1;
	} else if (y <= -4.6e+49) {
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)));
	} else if (y <= -4.2e+41) {
		tmp = z / b;
	} else if (y <= 1e+112) {
		tmp = (x + ((y * z) / t)) / ((a + 1.0) + (b * (y / t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z / b) + ((t / b) * (x / y))
    if (y <= (-6.2d+100)) then
        tmp = t_1
    else if (y <= (-4.6d+49)) then
        tmp = (x + (y * (z / t))) / ((a + 1.0d0) + (y * (b / t)))
    else if (y <= (-4.2d+41)) then
        tmp = z / b
    else if (y <= 1d+112) then
        tmp = (x + ((y * z) / t)) / ((a + 1.0d0) + (b * (y / t)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z / b) + ((t / b) * (x / y));
	double tmp;
	if (y <= -6.2e+100) {
		tmp = t_1;
	} else if (y <= -4.6e+49) {
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)));
	} else if (y <= -4.2e+41) {
		tmp = z / b;
	} else if (y <= 1e+112) {
		tmp = (x + ((y * z) / t)) / ((a + 1.0) + (b * (y / t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z / b) + ((t / b) * (x / y))
	tmp = 0
	if y <= -6.2e+100:
		tmp = t_1
	elif y <= -4.6e+49:
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)))
	elif y <= -4.2e+41:
		tmp = z / b
	elif y <= 1e+112:
		tmp = (x + ((y * z) / t)) / ((a + 1.0) + (b * (y / t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z / b) + Float64(Float64(t / b) * Float64(x / y)))
	tmp = 0.0
	if (y <= -6.2e+100)
		tmp = t_1;
	elseif (y <= -4.6e+49)
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(Float64(a + 1.0) + Float64(y * Float64(b / t))));
	elseif (y <= -4.2e+41)
		tmp = Float64(z / b);
	elseif (y <= 1e+112)
		tmp = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(Float64(a + 1.0) + Float64(b * Float64(y / t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z / b) + ((t / b) * (x / y));
	tmp = 0.0;
	if (y <= -6.2e+100)
		tmp = t_1;
	elseif (y <= -4.6e+49)
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)));
	elseif (y <= -4.2e+41)
		tmp = z / b;
	elseif (y <= 1e+112)
		tmp = (x + ((y * z) / t)) / ((a + 1.0) + (b * (y / t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z / b), $MachinePrecision] + N[(N[(t / b), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.2e+100], t$95$1, If[LessEqual[y, -4.6e+49], 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[y, -4.2e+41], N[(z / b), $MachinePrecision], If[LessEqual[y, 1e+112], N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -6.20000000000000014e100 or 9.9999999999999993e111 < y

   1. Initial program 37.7%

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

      1. associate-/l* 40.2%

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

      2. associate-/l* 50.7%

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

   3. Simplified 50.7%

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

   5. Taylor expanded in b around inf 19.7%

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

      1. associate-/l* 19.8%

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

      2. +-commutative 19.8%

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

      3. associate-*r/ 22.4%

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

      4. fma-undefine 22.4%

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

      5. *-commutative 22.4%

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

   7. Simplified 22.4%

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

   8. Taylor expanded in t around 0 68.9%

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

      1. times-frac 73.6%

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

   10. Simplified 73.6%

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

   if -6.20000000000000014e100 < y < -4.60000000000000004e49

   1. Initial program 61.2%

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

      1. associate-/l* 71.0%

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

      2. associate-/l* 80.7%

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

   3. Simplified 80.7%

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

   if -4.60000000000000004e49 < y < -4.1999999999999999e41

   1. Initial program 4.7%

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

      1. associate-/l* 4.7%

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

      2. associate-/l* 4.7%

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

   3. Simplified 4.7%

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

   5. Taylor expanded in y around inf 100.0%

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

   if -4.1999999999999999e41 < y < 9.9999999999999993e111

   1. Initial program 93.4%

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

      1. *-commutative 93.4%

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

      2. associate-/l* 93.4%

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

   4. Applied egg-rr 93.4%

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

Alternative 5: 79.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a + 1\right) + y \cdot \frac{b}{t}\\ \mathbf{if}\;t \leq -2.35 \cdot 10^{-122}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{t\_1}\\ \mathbf{elif}\;t \leq -5.1 \cdot 10^{-306}:\\ \;\;\;\;x \cdot \left(\frac{\frac{z}{b}}{x} + \frac{t}{y \cdot b}\right)\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-188}:\\ \;\;\;\;\frac{y \cdot z}{y \cdot b + t \cdot \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{t\_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ a 1.0) (* y (/ b t)))))
   (if (<= t -2.35e-122)
     (/ (+ x (* y (/ z t))) t_1)
     (if (<= t -5.1e-306)
       (* x (+ (/ (/ z b) x) (/ t (* y b))))
       (if (<= t 3e-188)
         (/ (* y z) (+ (* y b) (* t (+ a 1.0))))
         (/ (+ x (/ y (/ t z))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a + 1.0) + (y * (b / t));
	double tmp;
	if (t <= -2.35e-122) {
		tmp = (x + (y * (z / t))) / t_1;
	} else if (t <= -5.1e-306) {
		tmp = x * (((z / b) / x) + (t / (y * b)));
	} else if (t <= 3e-188) {
		tmp = (y * z) / ((y * b) + (t * (a + 1.0)));
	} else {
		tmp = (x + (y / (t / z))) / 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 = (a + 1.0d0) + (y * (b / t))
    if (t <= (-2.35d-122)) then
        tmp = (x + (y * (z / t))) / t_1
    else if (t <= (-5.1d-306)) then
        tmp = x * (((z / b) / x) + (t / (y * b)))
    else if (t <= 3d-188) then
        tmp = (y * z) / ((y * b) + (t * (a + 1.0d0)))
    else
        tmp = (x + (y / (t / z))) / 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 = (a + 1.0) + (y * (b / t));
	double tmp;
	if (t <= -2.35e-122) {
		tmp = (x + (y * (z / t))) / t_1;
	} else if (t <= -5.1e-306) {
		tmp = x * (((z / b) / x) + (t / (y * b)));
	} else if (t <= 3e-188) {
		tmp = (y * z) / ((y * b) + (t * (a + 1.0)));
	} else {
		tmp = (x + (y / (t / z))) / t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a + 1.0) + (y * (b / t))
	tmp = 0
	if t <= -2.35e-122:
		tmp = (x + (y * (z / t))) / t_1
	elif t <= -5.1e-306:
		tmp = x * (((z / b) / x) + (t / (y * b)))
	elif t <= 3e-188:
		tmp = (y * z) / ((y * b) + (t * (a + 1.0)))
	else:
		tmp = (x + (y / (t / z))) / t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a + 1.0) + Float64(y * Float64(b / t)))
	tmp = 0.0
	if (t <= -2.35e-122)
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / t_1);
	elseif (t <= -5.1e-306)
		tmp = Float64(x * Float64(Float64(Float64(z / b) / x) + Float64(t / Float64(y * b))));
	elseif (t <= 3e-188)
		tmp = Float64(Float64(y * z) / Float64(Float64(y * b) + Float64(t * Float64(a + 1.0))));
	else
		tmp = Float64(Float64(x + Float64(y / Float64(t / z))) / t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a + 1.0) + (y * (b / t));
	tmp = 0.0;
	if (t <= -2.35e-122)
		tmp = (x + (y * (z / t))) / t_1;
	elseif (t <= -5.1e-306)
		tmp = x * (((z / b) / x) + (t / (y * b)));
	elseif (t <= 3e-188)
		tmp = (y * z) / ((y * b) + (t * (a + 1.0)));
	else
		tmp = (x + (y / (t / z))) / t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a + 1.0), $MachinePrecision] + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.35e-122], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[t, -5.1e-306], N[(x * N[(N[(N[(z / b), $MachinePrecision] / x), $MachinePrecision] + N[(t / N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3e-188], N[(N[(y * z), $MachinePrecision] / N[(N[(y * b), $MachinePrecision] + N[(t * N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.35e-122

   1. Initial program 83.6%

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

      1. associate-/l* 88.7%

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

      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

   if -2.35e-122 < t < -5.09999999999999972e-306

   1. Initial program 49.5%

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

      1. associate-/l* 39.2%

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

      2. associate-/l* 32.3%

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

   3. Simplified 32.3%

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

   5. Taylor expanded in b around inf 37.3%

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

      1. associate-/l* 35.7%

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

      2. +-commutative 35.7%

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

      3. associate-*r/ 30.1%

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

      4. fma-undefine 30.1%

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

      5. *-commutative 30.1%

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

   7. Simplified 30.1%

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

   8. Taylor expanded in x around inf 56.1%

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

      1. +-commutative 56.1%

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

      2. associate-/r* 70.0%

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

      3. *-commutative 70.0%

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

   10. Simplified 70.0%

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

   if -5.09999999999999972e-306 < t < 3.00000000000000017e-188

   1. Initial program 58.8%

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

      1. associate-/l* 40.0%

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

      2. associate-/l* 39.8%

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

   3. Simplified 39.8%

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

   5. Taylor expanded in x around 0 59.1%

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

   6. Taylor expanded in t around 0 77.9%

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

   if 3.00000000000000017e-188 < t

   1. Initial program 78.9%

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

      1. associate-/l* 77.3%

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

      2. associate-/l* 81.9%

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

   3. Simplified 81.9%

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

      1. clear-num 81.8%

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

      2. un-div-inv 82.1%

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

   6. Applied egg-rr 82.1%

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

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.35 \cdot 10^{-122}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;t \leq -5.1 \cdot 10^{-306}:\\ \;\;\;\;x \cdot \left(\frac{\frac{z}{b}}{x} + \frac{t}{y \cdot b}\right)\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-188}:\\ \;\;\;\;\frac{y \cdot z}{y \cdot b + t \cdot \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 79.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{if}\;t \leq -3.9 \cdot 10^{-123}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -7.8 \cdot 10^{-306}:\\ \;\;\;\;x \cdot \left(\frac{\frac{z}{b}}{x} + \frac{t}{y \cdot b}\right)\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-191}:\\ \;\;\;\;\frac{y \cdot z}{y \cdot b + t \cdot \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (* y (/ z t))) (+ (+ a 1.0) (* y (/ b t))))))
   (if (<= t -3.9e-123)
     t_1
     (if (<= t -7.8e-306)
       (* x (+ (/ (/ z b) x) (/ t (* y b))))
       (if (<= t 1.2e-191) (/ (* y z) (+ (* y b) (* 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 + (y * (z / t))) / ((a + 1.0) + (y * (b / t)));
	double tmp;
	if (t <= -3.9e-123) {
		tmp = t_1;
	} else if (t <= -7.8e-306) {
		tmp = x * (((z / b) / x) + (t / (y * b)));
	} else if (t <= 1.2e-191) {
		tmp = (y * z) / ((y * b) + (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 + (y * (z / t))) / ((a + 1.0d0) + (y * (b / t)))
    if (t <= (-3.9d-123)) then
        tmp = t_1
    else if (t <= (-7.8d-306)) then
        tmp = x * (((z / b) / x) + (t / (y * b)))
    else if (t <= 1.2d-191) then
        tmp = (y * z) / ((y * b) + (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 + (y * (z / t))) / ((a + 1.0) + (y * (b / t)));
	double tmp;
	if (t <= -3.9e-123) {
		tmp = t_1;
	} else if (t <= -7.8e-306) {
		tmp = x * (((z / b) / x) + (t / (y * b)));
	} else if (t <= 1.2e-191) {
		tmp = (y * z) / ((y * b) + (t * (a + 1.0)));
	} 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 <= -3.9e-123:
		tmp = t_1
	elif t <= -7.8e-306:
		tmp = x * (((z / b) / x) + (t / (y * b)))
	elif t <= 1.2e-191:
		tmp = (y * z) / ((y * b) + (t * (a + 1.0)))
	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 <= -3.9e-123)
		tmp = t_1;
	elseif (t <= -7.8e-306)
		tmp = Float64(x * Float64(Float64(Float64(z / b) / x) + Float64(t / Float64(y * b))));
	elseif (t <= 1.2e-191)
		tmp = Float64(Float64(y * z) / Float64(Float64(y * b) + 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 + (y * (z / t))) / ((a + 1.0) + (y * (b / t)));
	tmp = 0.0;
	if (t <= -3.9e-123)
		tmp = t_1;
	elseif (t <= -7.8e-306)
		tmp = x * (((z / b) / x) + (t / (y * b)));
	elseif (t <= 1.2e-191)
		tmp = (y * z) / ((y * b) + (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[(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, -3.9e-123], t$95$1, If[LessEqual[t, -7.8e-306], N[(x * N[(N[(N[(z / b), $MachinePrecision] / x), $MachinePrecision] + N[(t / N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.2e-191], N[(N[(y * z), $MachinePrecision] / N[(N[(y * b), $MachinePrecision] + N[(t * N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.89999999999999976e-123 or 1.2e-191 < 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* 82.1%

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

      2. associate-/l* 85.3%

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

   3. Simplified 85.3%

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

   if -3.89999999999999976e-123 < t < -7.799999999999999e-306

   1. Initial program 49.5%

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

      1. associate-/l* 39.2%

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

      2. associate-/l* 32.3%

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

   3. Simplified 32.3%

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

   5. Taylor expanded in b around inf 37.3%

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

      1. associate-/l* 35.7%

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

      2. +-commutative 35.7%

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

      3. associate-*r/ 30.1%

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

      4. fma-undefine 30.1%

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

      5. *-commutative 30.1%

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

   7. Simplified 30.1%

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

   8. Taylor expanded in x around inf 56.1%

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

      1. +-commutative 56.1%

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

      2. associate-/r* 70.0%

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

      3. *-commutative 70.0%

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

   10. Simplified 70.0%

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

   if -7.799999999999999e-306 < t < 1.2e-191

   1. Initial program 58.8%

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

      1. associate-/l* 40.0%

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

      2. associate-/l* 39.8%

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

   3. Simplified 39.8%

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

   5. Taylor expanded in x around 0 59.1%

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

   6. Taylor expanded in t around 0 77.9%

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

4. Final simplification 81.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.9 \cdot 10^{-123}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;t \leq -7.8 \cdot 10^{-306}:\\ \;\;\;\;x \cdot \left(\frac{\frac{z}{b}}{x} + \frac{t}{y \cdot b}\right)\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-191}:\\ \;\;\;\;\frac{y \cdot z}{y \cdot b + t \cdot \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 68.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{b} + \frac{t}{b} \cdot \frac{x}{y}\\ \mathbf{if}\;y \leq -5.4 \cdot 10^{+100}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -7 \cdot 10^{+49}:\\ \;\;\;\;z \cdot \left(\frac{\frac{y}{t}}{a + 1} + \frac{\frac{x}{z}}{a + 1}\right)\\ \mathbf{elif}\;y \leq -3000000 \lor \neg \left(y \leq 1.4 \cdot 10^{+111}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (/ z b) (* (/ t b) (/ x y)))))
   (if (<= y -5.4e+100)
     t_1
     (if (<= y -7e+49)
       (* z (+ (/ (/ y t) (+ a 1.0)) (/ (/ x z) (+ a 1.0))))
       (if (or (<= y -3000000.0) (not (<= y 1.4e+111)))
         t_1
         (/ (+ x (/ (* y z) t)) (+ a 1.0)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z / b) + ((t / b) * (x / y));
	double tmp;
	if (y <= -5.4e+100) {
		tmp = t_1;
	} else if (y <= -7e+49) {
		tmp = z * (((y / t) / (a + 1.0)) + ((x / z) / (a + 1.0)));
	} else if ((y <= -3000000.0) || !(y <= 1.4e+111)) {
		tmp = t_1;
	} else {
		tmp = (x + ((y * z) / 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) :: t_1
    real(8) :: tmp
    t_1 = (z / b) + ((t / b) * (x / y))
    if (y <= (-5.4d+100)) then
        tmp = t_1
    else if (y <= (-7d+49)) then
        tmp = z * (((y / t) / (a + 1.0d0)) + ((x / z) / (a + 1.0d0)))
    else if ((y <= (-3000000.0d0)) .or. (.not. (y <= 1.4d+111))) then
        tmp = t_1
    else
        tmp = (x + ((y * z) / 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 t_1 = (z / b) + ((t / b) * (x / y));
	double tmp;
	if (y <= -5.4e+100) {
		tmp = t_1;
	} else if (y <= -7e+49) {
		tmp = z * (((y / t) / (a + 1.0)) + ((x / z) / (a + 1.0)));
	} else if ((y <= -3000000.0) || !(y <= 1.4e+111)) {
		tmp = t_1;
	} else {
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z / b) + ((t / b) * (x / y))
	tmp = 0
	if y <= -5.4e+100:
		tmp = t_1
	elif y <= -7e+49:
		tmp = z * (((y / t) / (a + 1.0)) + ((x / z) / (a + 1.0)))
	elif (y <= -3000000.0) or not (y <= 1.4e+111):
		tmp = t_1
	else:
		tmp = (x + ((y * z) / t)) / (a + 1.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z / b) + Float64(Float64(t / b) * Float64(x / y)))
	tmp = 0.0
	if (y <= -5.4e+100)
		tmp = t_1;
	elseif (y <= -7e+49)
		tmp = Float64(z * Float64(Float64(Float64(y / t) / Float64(a + 1.0)) + Float64(Float64(x / z) / Float64(a + 1.0))));
	elseif ((y <= -3000000.0) || !(y <= 1.4e+111))
		tmp = t_1;
	else
		tmp = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(a + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z / b) + ((t / b) * (x / y));
	tmp = 0.0;
	if (y <= -5.4e+100)
		tmp = t_1;
	elseif (y <= -7e+49)
		tmp = z * (((y / t) / (a + 1.0)) + ((x / z) / (a + 1.0)));
	elseif ((y <= -3000000.0) || ~((y <= 1.4e+111)))
		tmp = t_1;
	else
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z / b), $MachinePrecision] + N[(N[(t / b), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.4e+100], t$95$1, If[LessEqual[y, -7e+49], N[(z * N[(N[(N[(y / t), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x / z), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -3000000.0], N[Not[LessEqual[y, 1.4e+111]], $MachinePrecision]], t$95$1, N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.39999999999999997e100 or -6.9999999999999995e49 < y < -3e6 or 1.4e111 < y

   1. Initial program 40.9%

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

      1. associate-/l* 43.1%

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

      2. associate-/l* 52.4%

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

   3. Simplified 52.4%

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

   5. Taylor expanded in b around inf 20.9%

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

      1. associate-/l* 21.0%

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

      2. +-commutative 21.0%

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

      3. associate-*r/ 23.3%

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

      4. fma-undefine 23.3%

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

      5. *-commutative 23.3%

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

   7. Simplified 23.3%

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

   8. Taylor expanded in t around 0 68.4%

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

      1. times-frac 72.6%

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

   10. Simplified 72.6%

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

   if -5.39999999999999997e100 < y < -6.9999999999999995e49

   1. Initial program 61.2%

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

      1. associate-/l* 71.0%

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

      2. associate-/l* 80.7%

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

   3. Simplified 80.7%

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

   5. Taylor expanded in z around inf 80.1%

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

      1. associate-+r+ 80.1%

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

      2. *-commutative 80.1%

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

      3. associate-+r+ 80.1%

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

      4. *-commutative 80.1%

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

   7. Simplified 80.1%

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

   8. Taylor expanded in t around 0 80.1%

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

   9. Taylor expanded in b around 0 70.1%

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

       1. +-commutative 70.1%

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

       2. associate-/r* 70.1%

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

       3. associate-/r* 79.7%

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

   11. Simplified 79.7%

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

   if -3e6 < y < 1.4e111

   1. Initial program 93.7%

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

      1. associate-/l* 86.5%

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

      2. associate-/l* 82.0%

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

   3. Simplified 82.0%

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

   5. Taylor expanded in b around 0 78.7%

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

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.4 \cdot 10^{+100}:\\ \;\;\;\;\frac{z}{b} + \frac{t}{b} \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq -7 \cdot 10^{+49}:\\ \;\;\;\;z \cdot \left(\frac{\frac{y}{t}}{a + 1} + \frac{\frac{x}{z}}{a + 1}\right)\\ \mathbf{elif}\;y \leq -3000000 \lor \neg \left(y \leq 1.4 \cdot 10^{+111}\right):\\ \;\;\;\;\frac{z}{b} + \frac{t}{b} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 41.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.00285:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq -1.14 \cdot 10^{-225}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{-254}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-112}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+14}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -0.00285)
   (/ z b)
   (if (<= y -1.14e-225)
     (/ x a)
     (if (<= y 4.7e-254)
       x
       (if (<= y 6.5e-112) (/ x a) (if (<= y 2.4e+14) x (/ z b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -0.00285) {
		tmp = z / b;
	} else if (y <= -1.14e-225) {
		tmp = x / a;
	} else if (y <= 4.7e-254) {
		tmp = x;
	} else if (y <= 6.5e-112) {
		tmp = x / a;
	} else if (y <= 2.4e+14) {
		tmp = x;
	} 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 (y <= (-0.00285d0)) then
        tmp = z / b
    else if (y <= (-1.14d-225)) then
        tmp = x / a
    else if (y <= 4.7d-254) then
        tmp = x
    else if (y <= 6.5d-112) then
        tmp = x / a
    else if (y <= 2.4d+14) then
        tmp = x
    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 (y <= -0.00285) {
		tmp = z / b;
	} else if (y <= -1.14e-225) {
		tmp = x / a;
	} else if (y <= 4.7e-254) {
		tmp = x;
	} else if (y <= 6.5e-112) {
		tmp = x / a;
	} else if (y <= 2.4e+14) {
		tmp = x;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -0.00285:
		tmp = z / b
	elif y <= -1.14e-225:
		tmp = x / a
	elif y <= 4.7e-254:
		tmp = x
	elif y <= 6.5e-112:
		tmp = x / a
	elif y <= 2.4e+14:
		tmp = x
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -0.00285)
		tmp = Float64(z / b);
	elseif (y <= -1.14e-225)
		tmp = Float64(x / a);
	elseif (y <= 4.7e-254)
		tmp = x;
	elseif (y <= 6.5e-112)
		tmp = Float64(x / a);
	elseif (y <= 2.4e+14)
		tmp = x;
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -0.00285)
		tmp = z / b;
	elseif (y <= -1.14e-225)
		tmp = x / a;
	elseif (y <= 4.7e-254)
		tmp = x;
	elseif (y <= 6.5e-112)
		tmp = x / a;
	elseif (y <= 2.4e+14)
		tmp = x;
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -0.00285], N[(z / b), $MachinePrecision], If[LessEqual[y, -1.14e-225], N[(x / a), $MachinePrecision], If[LessEqual[y, 4.7e-254], x, If[LessEqual[y, 6.5e-112], N[(x / a), $MachinePrecision], If[LessEqual[y, 2.4e+14], x, N[(z / b), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -0.0028500000000000001 or 2.4e14 < y

   1. Initial program 47.5%

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

      1. associate-/l* 50.1%

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

      2. associate-/l* 58.3%

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

   3. Simplified 58.3%

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

   5. Taylor expanded in y around inf 59.1%

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

   if -0.0028500000000000001 < y < -1.14e-225 or 4.70000000000000027e-254 < y < 6.49999999999999956e-112

   1. Initial program 95.4%

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

      1. associate-/l* 90.1%

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

      2. associate-/l* 81.5%

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

   3. Simplified 81.5%

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

   5. Taylor expanded in x around inf 64.9%

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

   6. Taylor expanded in a around inf 50.0%

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

   if -1.14e-225 < y < 4.70000000000000027e-254 or 6.49999999999999956e-112 < y < 2.4e14

   1. Initial program 94.8%

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

      1. associate-/l* 83.2%

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

      2. associate-/l* 83.2%

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

   3. Simplified 83.2%

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

   5. Taylor expanded in x around inf 72.5%

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

   6. Taylor expanded in a around 0 56.2%

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

   7. Taylor expanded in b around 0 49.8%

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

Alternative 9: 69.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{+94} \lor \neg \left(y \leq 2.6 \cdot 10^{+109}\right):\\ \;\;\;\;\frac{z}{b} + \frac{t}{b} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -5.2e+94) (not (<= y 2.6e+109)))
   (+ (/ z b) (* (/ t b) (/ x y)))
   (/ (+ x (/ (* y z) t)) (+ a 1.0))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -5.2e+94) || !(y <= 2.6e+109)) {
		tmp = (z / b) + ((t / b) * (x / y));
	} else {
		tmp = (x + ((y * z) / 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 ((y <= (-5.2d+94)) .or. (.not. (y <= 2.6d+109))) then
        tmp = (z / b) + ((t / b) * (x / y))
    else
        tmp = (x + ((y * z) / 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 ((y <= -5.2e+94) || !(y <= 2.6e+109)) {
		tmp = (z / b) + ((t / b) * (x / y));
	} else {
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -5.2e+94) or not (y <= 2.6e+109):
		tmp = (z / b) + ((t / b) * (x / y))
	else:
		tmp = (x + ((y * z) / t)) / (a + 1.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -5.2e+94) || !(y <= 2.6e+109))
		tmp = Float64(Float64(z / b) + Float64(Float64(t / b) * Float64(x / y)));
	else
		tmp = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(a + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -5.2e+94) || ~((y <= 2.6e+109)))
		tmp = (z / b) + ((t / b) * (x / y));
	else
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -5.2e+94], N[Not[LessEqual[y, 2.6e+109]], $MachinePrecision]], N[(N[(z / b), $MachinePrecision] + N[(N[(t / b), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.1999999999999998e94 or 2.5999999999999998e109 < y

   1. Initial program 38.0%

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

      1. associate-/l* 40.5%

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

      2. associate-/l* 51.9%

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

   3. Simplified 51.9%

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

   5. Taylor expanded in b around inf 19.3%

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

      1. associate-/l* 19.4%

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

      2. +-commutative 19.4%

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

      3. associate-*r/ 21.9%

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

      4. fma-undefine 21.9%

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

      5. *-commutative 21.9%

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

   7. Simplified 21.9%

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

   8. Taylor expanded in t around 0 68.4%

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

      1. times-frac 73.0%

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

   10. Simplified 73.0%

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

   if -5.1999999999999998e94 < y < 2.5999999999999998e109

   1. Initial program 90.4%

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

      1. associate-/l* 84.6%

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

      2. associate-/l* 80.7%

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

   3. Simplified 80.7%

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

   5. Taylor expanded in b around 0 75.4%

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

4. Final simplification 74.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{+94} \lor \neg \left(y \leq 2.6 \cdot 10^{+109}\right):\\ \;\;\;\;\frac{z}{b} + \frac{t}{b} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 65.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{+39} \lor \neg \left(y \leq 2 \cdot 10^{+113}\right):\\ \;\;\;\;\frac{z}{b} + \frac{t}{b} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -8.5e+39) (not (<= y 2e+113)))
   (+ (/ z b) (* (/ t b) (/ x y)))
   (/ x (+ (+ a 1.0) (* b (/ y t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -8.5e+39) || !(y <= 2e+113)) {
		tmp = (z / b) + ((t / b) * (x / y));
	} else {
		tmp = x / ((a + 1.0) + (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 ((y <= (-8.5d+39)) .or. (.not. (y <= 2d+113))) then
        tmp = (z / b) + ((t / b) * (x / y))
    else
        tmp = x / ((a + 1.0d0) + (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 ((y <= -8.5e+39) || !(y <= 2e+113)) {
		tmp = (z / b) + ((t / b) * (x / y));
	} else {
		tmp = x / ((a + 1.0) + (b * (y / t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -8.5e+39) or not (y <= 2e+113):
		tmp = (z / b) + ((t / b) * (x / y))
	else:
		tmp = x / ((a + 1.0) + (b * (y / t)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -8.5e+39) || !(y <= 2e+113))
		tmp = Float64(Float64(z / b) + Float64(Float64(t / b) * Float64(x / y)));
	else
		tmp = Float64(x / Float64(Float64(a + 1.0) + Float64(b * Float64(y / t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -8.5e+39) || ~((y <= 2e+113)))
		tmp = (z / b) + ((t / b) * (x / y));
	else
		tmp = x / ((a + 1.0) + (b * (y / t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -8.5e+39], N[Not[LessEqual[y, 2e+113]], $MachinePrecision]], N[(N[(z / b), $MachinePrecision] + N[(N[(t / b), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(a + 1.0), $MachinePrecision] + N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.49999999999999971e39 or 2e113 < y

   1. Initial program 39.1%

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

      1. associate-/l* 42.3%

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

      2. associate-/l* 52.4%

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

   3. Simplified 52.4%

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

   5. Taylor expanded in b around inf 17.5%

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

      1. associate-/l* 18.6%

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

      2. +-commutative 18.6%

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

      3. associate-*r/ 20.8%

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

      4. fma-undefine 20.8%

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

      5. *-commutative 20.8%

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

   7. Simplified 20.8%

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

   8. Taylor expanded in t around 0 65.0%

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

      1. times-frac 69.0%

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

   10. Simplified 69.0%

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

   if -8.49999999999999971e39 < y < 2e113

   1. Initial program 93.4%

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

      1. *-commutative 93.4%

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

      2. associate-/l* 93.4%

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

   4. Applied egg-rr 93.4%

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

   5. Taylor expanded in x around inf 70.9%

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

4. Final simplification 70.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{+39} \lor \neg \left(y \leq 2 \cdot 10^{+113}\right):\\ \;\;\;\;\frac{z}{b} + \frac{t}{b} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 65.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+40} \lor \neg \left(y \leq 1.3 \cdot 10^{+111}\right):\\ \;\;\;\;\frac{z}{b} + \frac{t}{b} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -4.4e+40) (not (<= y 1.3e+111)))
   (+ (/ z b) (* (/ t b) (/ x y)))
   (/ x (+ (/ (* y b) t) (+ a 1.0)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -4.4e+40) || !(y <= 1.3e+111)) {
		tmp = (z / b) + ((t / b) * (x / y));
	} else {
		tmp = x / (((y * b) / 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 ((y <= (-4.4d+40)) .or. (.not. (y <= 1.3d+111))) then
        tmp = (z / b) + ((t / b) * (x / y))
    else
        tmp = x / (((y * b) / 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 ((y <= -4.4e+40) || !(y <= 1.3e+111)) {
		tmp = (z / b) + ((t / b) * (x / y));
	} else {
		tmp = x / (((y * b) / t) + (a + 1.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -4.4e+40) or not (y <= 1.3e+111):
		tmp = (z / b) + ((t / b) * (x / y))
	else:
		tmp = x / (((y * b) / t) + (a + 1.0))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -4.4e+40) || !(y <= 1.3e+111))
		tmp = Float64(Float64(z / b) + Float64(Float64(t / b) * Float64(x / y)));
	else
		tmp = Float64(x / Float64(Float64(Float64(y * b) / t) + Float64(a + 1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -4.4e+40) || ~((y <= 1.3e+111)))
		tmp = (z / b) + ((t / b) * (x / y));
	else
		tmp = x / (((y * b) / t) + (a + 1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -4.4e+40], N[Not[LessEqual[y, 1.3e+111]], $MachinePrecision]], N[(N[(z / b), $MachinePrecision] + N[(N[(t / b), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.3999999999999998e40 or 1.2999999999999999e111 < y

   1. Initial program 39.1%

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

      1. associate-/l* 42.3%

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

      2. associate-/l* 52.4%

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

   3. Simplified 52.4%

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

   5. Taylor expanded in b around inf 17.5%

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

      1. associate-/l* 18.6%

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

      2. +-commutative 18.6%

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

      3. associate-*r/ 20.8%

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

      4. fma-undefine 20.8%

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

      5. *-commutative 20.8%

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

   7. Simplified 20.8%

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

   8. Taylor expanded in t around 0 65.0%

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

      1. times-frac 69.0%

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

   10. Simplified 69.0%

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

   if -4.3999999999999998e40 < y < 1.2999999999999999e111

   1. Initial program 93.4%

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

      1. associate-/l* 86.6%

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

      2. associate-/l* 82.3%

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

   3. Simplified 82.3%

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

   5. Taylor expanded in x around inf 70.9%

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

      1. associate-+r+ 70.9%

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

      2. *-commutative 70.9%

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

   7. Simplified 70.9%

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

4. Final simplification 70.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+40} \lor \neg \left(y \leq 1.3 \cdot 10^{+111}\right):\\ \;\;\;\;\frac{z}{b} + \frac{t}{b} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 60.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -15.6 \lor \neg \left(y \leq 6.5 \cdot 10^{+15}\right):\\ \;\;\;\;\frac{z}{b} + \frac{t}{b} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -15.6) (not (<= y 6.5e+15)))
   (+ (/ z b) (* (/ t b) (/ x y)))
   (/ x (+ a 1.0))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -15.6) || !(y <= 6.5e+15)) {
		tmp = (z / b) + ((t / b) * (x / y));
	} else {
		tmp = x / (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 ((y <= (-15.6d0)) .or. (.not. (y <= 6.5d+15))) then
        tmp = (z / b) + ((t / b) * (x / y))
    else
        tmp = x / (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 ((y <= -15.6) || !(y <= 6.5e+15)) {
		tmp = (z / b) + ((t / b) * (x / y));
	} else {
		tmp = x / (a + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -15.6) or not (y <= 6.5e+15):
		tmp = (z / b) + ((t / b) * (x / y))
	else:
		tmp = x / (a + 1.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -15.6) || !(y <= 6.5e+15))
		tmp = Float64(Float64(z / b) + Float64(Float64(t / b) * Float64(x / y)));
	else
		tmp = Float64(x / Float64(a + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -15.6) || ~((y <= 6.5e+15)))
		tmp = (z / b) + ((t / b) * (x / y));
	else
		tmp = x / (a + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -15.6], N[Not[LessEqual[y, 6.5e+15]], $MachinePrecision]], N[(N[(z / b), $MachinePrecision] + N[(N[(t / b), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -15.5999999999999996 or 6.5e15 < y

   1. Initial program 47.5%

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

      1. associate-/l* 50.1%

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

      2. associate-/l* 58.3%

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

   3. Simplified 58.3%

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

   5. Taylor expanded in b around inf 21.1%

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

      1. associate-/l* 22.8%

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

      2. +-commutative 22.8%

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

      3. associate-*r/ 24.6%

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

      4. fma-undefine 24.6%

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

      5. *-commutative 24.6%

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

   7. Simplified 24.6%

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

   8. Taylor expanded in t around 0 62.0%

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

      1. times-frac 65.2%

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

   10. Simplified 65.2%

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

   if -15.5999999999999996 < y < 6.5e15

   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* 87.2%

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

      2. associate-/l* 82.2%

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

   3. Simplified 82.2%

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

   5. Taylor expanded in y around 0 66.0%

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

4. Final simplification 65.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -15.6 \lor \neg \left(y \leq 6.5 \cdot 10^{+15}\right):\\ \;\;\;\;\frac{z}{b} + \frac{t}{b} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 56.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.06 \cdot 10^{+40} \lor \neg \left(y \leq 1.5 \cdot 10^{+30}\right):\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.06e+40) (not (<= y 1.5e+30))) (/ z b) (/ x (+ a 1.0))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.06e+40) || !(y <= 1.5e+30)) {
		tmp = z / b;
	} else {
		tmp = x / (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 ((y <= (-1.06d+40)) .or. (.not. (y <= 1.5d+30))) then
        tmp = z / b
    else
        tmp = x / (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 ((y <= -1.06e+40) || !(y <= 1.5e+30)) {
		tmp = z / b;
	} else {
		tmp = x / (a + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.06e+40) or not (y <= 1.5e+30):
		tmp = z / b
	else:
		tmp = x / (a + 1.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.06e+40) || !(y <= 1.5e+30))
		tmp = Float64(z / b);
	else
		tmp = Float64(x / Float64(a + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.06e+40) || ~((y <= 1.5e+30)))
		tmp = z / b;
	else
		tmp = x / (a + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.06e+40], N[Not[LessEqual[y, 1.5e+30]], $MachinePrecision]], N[(z / b), $MachinePrecision], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.05999999999999996e40 or 1.49999999999999989e30 < y

   1. Initial program 43.6%

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

      1. associate-/l* 46.5%

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

      2. associate-/l* 55.4%

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

   3. Simplified 55.4%

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

   5. Taylor expanded in y around inf 61.5%

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

   if -1.05999999999999996e40 < y < 1.49999999999999989e30

   1. Initial program 94.8%

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

      1. associate-/l* 87.4%

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

      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 y around 0 64.3%

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

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.06 \cdot 10^{+40} \lor \neg \left(y \leq 1.5 \cdot 10^{+30}\right):\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 41.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1 \lor \neg \left(a \leq 8400000000000\right):\\ \;\;\;\;\frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -1.0) (not (<= a 8400000000000.0))) (/ x a) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -1.0) || !(a <= 8400000000000.0)) {
		tmp = x / a;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((a <= (-1.0d0)) .or. (.not. (a <= 8400000000000.0d0))) then
        tmp = x / a
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -1.0) || !(a <= 8400000000000.0)) {
		tmp = x / a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -1.0) or not (a <= 8400000000000.0):
		tmp = x / a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -1.0) || !(a <= 8400000000000.0))
		tmp = Float64(x / a);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -1.0) || ~((a <= 8400000000000.0)))
		tmp = x / a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -1.0], N[Not[LessEqual[a, 8400000000000.0]], $MachinePrecision]], N[(x / a), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if a < -1 or 8.4e12 < a

   1. Initial program 71.8%

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

      1. associate-/l* 69.0%

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

      2. associate-/l* 70.4%

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

   3. Simplified 70.4%

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

   5. Taylor expanded in x around inf 54.4%

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

   6. Taylor expanded in a around inf 51.3%

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

   if -1 < a < 8.4e12

   1. Initial program 74.4%

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

      1. associate-/l* 71.0%

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

      2. associate-/l* 71.8%

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

   3. Simplified 71.8%

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

   5. Taylor expanded in x around inf 47.6%

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

   6. Taylor expanded in a around 0 49.7%

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

   7. Taylor expanded in b around 0 38.9%

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

4. Final simplification 45.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1 \lor \neg \left(a \leq 8400000000000\right):\\ \;\;\;\;\frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 20.4% accurate, 17.0× speedup

Math

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

FPCore

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

C

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

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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := x

Derivation

1. Initial program 73.0%

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

   1. associate-/l* 70.0%

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

   2. associate-/l* 71.1%

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

3. Simplified 71.1%

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

5. Taylor expanded in x around inf 51.1%

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

6. Taylor expanded in a around 0 29.0%

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

7. Taylor expanded in b around 0 20.8%

   \[\leadsto \color{blue}{x} \]
8. Add Preprocessing

Developer target: 79.8% 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 2024089 
(FPCore (x y z t a b)
  :name "Diagrams.Solve.Tridiagonal:solveCyclicTriDiagonal from diagrams-solve-0.1, B"
  :precision binary64

  :alt
  (if (< t -1.3659085366310088e-271) (* 1.0 (* (+ x (* (/ y t) z)) (/ 1.0 (+ (+ a 1.0) (* (/ y t) b))))) (if (< t 3.036967103737246e-130) (/ z b) (* 1.0 (* (+ x (* (/ y t) z)) (/ 1.0 (+ (+ a 1.0) (* (/ y t) b)))))))

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