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

Percentage Accurate: 75.7% → 91.7%

Time: 19.1s

Alternatives: 18

Speedup: 0.6×

Specification

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = (x + ((y * z) / t)) / ((a + 1.0d0) + ((y * b) / t))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 75.7% 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: 91.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot b}{t}\\ t_2 := 1 + \left(a + t\_1\right)\\ t_3 := x + \frac{y \cdot z}{t}\\ t_4 := \frac{t\_3}{t\_1 + \left(a + 1\right)}\\ t_5 := z \cdot \left(\frac{x}{z \cdot t\_2} + \frac{y}{t \cdot t\_2}\right)\\ \mathbf{if}\;t\_4 \leq -\infty:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;t\_4 \leq 2 \cdot 10^{+272}:\\ \;\;\;\;\frac{t\_3}{b \cdot \frac{y}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;t\_4 \leq \infty:\\ \;\;\;\;t\_5\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + t \cdot \frac{\frac{x}{b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* y b) t))
        (t_2 (+ 1.0 (+ a t_1)))
        (t_3 (+ x (/ (* y z) t)))
        (t_4 (/ t_3 (+ t_1 (+ a 1.0))))
        (t_5 (* z (+ (/ x (* z t_2)) (/ y (* t t_2))))))
   (if (<= t_4 (- INFINITY))
     t_5
     (if (<= t_4 2e+272)
       (/ t_3 (+ (* b (/ y t)) (+ a 1.0)))
       (if (<= t_4 INFINITY) t_5 (+ (/ z b) (* t (/ (/ x b) y))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y * b) / t;
	double t_2 = 1.0 + (a + t_1);
	double t_3 = x + ((y * z) / t);
	double t_4 = t_3 / (t_1 + (a + 1.0));
	double t_5 = z * ((x / (z * t_2)) + (y / (t * t_2)));
	double tmp;
	if (t_4 <= -((double) INFINITY)) {
		tmp = t_5;
	} else if (t_4 <= 2e+272) {
		tmp = t_3 / ((b * (y / t)) + (a + 1.0));
	} else if (t_4 <= ((double) INFINITY)) {
		tmp = t_5;
	} else {
		tmp = (z / b) + (t * ((x / b) / 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;
	double t_2 = 1.0 + (a + t_1);
	double t_3 = x + ((y * z) / t);
	double t_4 = t_3 / (t_1 + (a + 1.0));
	double t_5 = z * ((x / (z * t_2)) + (y / (t * t_2)));
	double tmp;
	if (t_4 <= -Double.POSITIVE_INFINITY) {
		tmp = t_5;
	} else if (t_4 <= 2e+272) {
		tmp = t_3 / ((b * (y / t)) + (a + 1.0));
	} else if (t_4 <= Double.POSITIVE_INFINITY) {
		tmp = t_5;
	} else {
		tmp = (z / b) + (t * ((x / b) / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (y * b) / t
	t_2 = 1.0 + (a + t_1)
	t_3 = x + ((y * z) / t)
	t_4 = t_3 / (t_1 + (a + 1.0))
	t_5 = z * ((x / (z * t_2)) + (y / (t * t_2)))
	tmp = 0
	if t_4 <= -math.inf:
		tmp = t_5
	elif t_4 <= 2e+272:
		tmp = t_3 / ((b * (y / t)) + (a + 1.0))
	elif t_4 <= math.inf:
		tmp = t_5
	else:
		tmp = (z / b) + (t * ((x / b) / y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y * b) / t)
	t_2 = Float64(1.0 + Float64(a + t_1))
	t_3 = Float64(x + Float64(Float64(y * z) / t))
	t_4 = Float64(t_3 / Float64(t_1 + Float64(a + 1.0)))
	t_5 = Float64(z * Float64(Float64(x / Float64(z * t_2)) + Float64(y / Float64(t * t_2))))
	tmp = 0.0
	if (t_4 <= Float64(-Inf))
		tmp = t_5;
	elseif (t_4 <= 2e+272)
		tmp = Float64(t_3 / Float64(Float64(b * Float64(y / t)) + Float64(a + 1.0)));
	elseif (t_4 <= Inf)
		tmp = t_5;
	else
		tmp = Float64(Float64(z / b) + Float64(t * Float64(Float64(x / b) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (y * b) / t;
	t_2 = 1.0 + (a + t_1);
	t_3 = x + ((y * z) / t);
	t_4 = t_3 / (t_1 + (a + 1.0));
	t_5 = z * ((x / (z * t_2)) + (y / (t * t_2)));
	tmp = 0.0;
	if (t_4 <= -Inf)
		tmp = t_5;
	elseif (t_4 <= 2e+272)
		tmp = t_3 / ((b * (y / t)) + (a + 1.0));
	elseif (t_4 <= Inf)
		tmp = t_5;
	else
		tmp = (z / b) + (t * ((x / b) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]}, Block[{t$95$2 = N[(1.0 + N[(a + t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$3 / N[(t$95$1 + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(z * N[(N[(x / N[(z * t$95$2), $MachinePrecision]), $MachinePrecision] + N[(y / N[(t * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$4, (-Infinity)], t$95$5, If[LessEqual[t$95$4, 2e+272], N[(t$95$3 / N[(N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$4, Infinity], t$95$5, N[(N[(z / b), $MachinePrecision] + N[(t * N[(N[(x / b), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < -inf.0 or 2.0000000000000001e272 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < +inf.0

   1. Initial program 48.6%

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

      1. associate-/l* 57.4%

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

      2. associate-/l* 57.4%

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

   3. Simplified 57.4%

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

   5. Taylor expanded in z around inf 93.9%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 2.0000000000000001e272

   1. Initial program 90.5%

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

      1. *-commutative 90.5%

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

      2. associate-/l* 92.7%

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

   4. Applied egg-rr 92.7%

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

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

   1. Initial program 0.0%

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

      1. associate-/l* 1.0%

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

      2. associate-/l* 27.1%

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

   3. Simplified 27.1%

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

   5. Taylor expanded in x around inf 7.3%

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

      1. associate-*l/ 7.3%

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

      2. *-commutative 7.3%

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

      3. associate-/l* 9.4%

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

      4. *-commutative 9.4%

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

      5. associate-*l/ 16.8%

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

      6. *-commutative 16.8%

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

   7. Simplified 16.8%

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

   8. Taylor expanded in y around inf 72.5%

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

      1. associate-/r* 87.6%

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

   10. Simplified 87.6%

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

   11. Taylor expanded in y around inf 92.6%

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

       1. associate-/l* 94.9%

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

       2. associate-/r* 96.5%

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

   13. Simplified 96.5%

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

4. Final simplification 93.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -\infty:\\ \;\;\;\;z \cdot \left(\frac{x}{z \cdot \left(1 + \left(a + \frac{y \cdot b}{t}\right)\right)} + \frac{y}{t \cdot \left(1 + \left(a + \frac{y \cdot b}{t}\right)\right)}\right)\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 2 \cdot 10^{+272}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{b \cdot \frac{y}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq \infty:\\ \;\;\;\;z \cdot \left(\frac{x}{z \cdot \left(1 + \left(a + \frac{y \cdot b}{t}\right)\right)} + \frac{y}{t \cdot \left(1 + \left(a + \frac{y \cdot b}{t}\right)\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + t \cdot \frac{\frac{x}{b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 89.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot z}{t}\\ t_2 := \frac{t\_1}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{1 + \left(a + y \cdot \frac{b}{t}\right)}\\ \mathbf{elif}\;t\_2 \leq 10^{+299}:\\ \;\;\;\;\frac{t\_1}{b \cdot \frac{y}{t} + \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (/ (* y z) t))) (t_2 (/ t_1 (+ (/ (* y b) t) (+ a 1.0)))))
   (if (<= t_2 (- INFINITY))
     (* (/ y t) (/ z (+ 1.0 (+ a (* y (/ b t))))))
     (if (<= t_2 1e+299) (/ t_1 (+ (* b (/ y t)) (+ a 1.0))) (/ z b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + ((y * z) / t);
	double t_2 = t_1 / (((y * b) / t) + (a + 1.0));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = (y / t) * (z / (1.0 + (a + (y * (b / t)))));
	} else if (t_2 <= 1e+299) {
		tmp = t_1 / ((b * (y / t)) + (a + 1.0));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + ((y * z) / t);
	double t_2 = t_1 / (((y * b) / t) + (a + 1.0));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = (y / t) * (z / (1.0 + (a + (y * (b / t)))));
	} else if (t_2 <= 1e+299) {
		tmp = t_1 / ((b * (y / t)) + (a + 1.0));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + ((y * z) / t)
	t_2 = t_1 / (((y * b) / t) + (a + 1.0))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = (y / t) * (z / (1.0 + (a + (y * (b / t)))))
	elif t_2 <= 1e+299:
		tmp = t_1 / ((b * (y / t)) + (a + 1.0))
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(Float64(y * z) / t))
	t_2 = Float64(t_1 / Float64(Float64(Float64(y * b) / t) + Float64(a + 1.0)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(Float64(y / t) * Float64(z / Float64(1.0 + Float64(a + Float64(y * Float64(b / t))))));
	elseif (t_2 <= 1e+299)
		tmp = Float64(t_1 / Float64(Float64(b * Float64(y / t)) + Float64(a + 1.0)));
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + ((y * z) / t);
	t_2 = t_1 / (((y * b) / t) + (a + 1.0));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = (y / t) * (z / (1.0 + (a + (y * (b / t)))));
	elseif (t_2 <= 1e+299)
		tmp = t_1 / ((b * (y / t)) + (a + 1.0));
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 / N[(N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(N[(y / t), $MachinePrecision] * N[(z / N[(1.0 + N[(a + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+299], N[(t$95$1 / N[(N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < -inf.0

   1. Initial program 53.0%

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

      1. associate-/l* 53.0%

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

      2. associate-/l* 53.0%

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

   3. Simplified 53.0%

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

   5. Taylor expanded in x around 0 79.1%

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

      1. times-frac 86.3%

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

      2. associate-*l/ 86.2%

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

      3. *-commutative 86.2%

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

   7. Simplified 86.2%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 1.0000000000000001e299

   1. Initial program 90.6%

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

      1. *-commutative 90.6%

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

      2. associate-/l* 92.9%

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

   4. Applied egg-rr 92.9%

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

   if 1.0000000000000001e299 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))

   1. Initial program 13.4%

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

      1. associate-/l* 23.0%

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

      2. associate-/l* 39.2%

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

   3. Simplified 39.2%

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

   5. Taylor expanded in y around inf 85.6%

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

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -\infty:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{1 + \left(a + y \cdot \frac{b}{t}\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 10^{+299}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{b \cdot \frac{y}{t} + \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 54.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{\frac{t}{y} + \frac{z}{x}}{b}\\ \mathbf{if}\;y \leq -5 \cdot 10^{+58}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -6.6 \cdot 10^{+38}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a}\\ \mathbf{elif}\;y \leq -20000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 420:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+72}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+94}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;y \leq 7.7 \cdot 10^{+118}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (/ (+ (/ t y) (/ z x)) b))))
   (if (<= y -5e+58)
     t_1
     (if (<= y -6.6e+38)
       (/ (+ x (* y (/ z t))) a)
       (if (<= y -20000000.0)
         t_1
         (if (<= y 420.0)
           (/ x (+ a 1.0))
           (if (<= y 4.2e+72)
             t_1
             (if (<= y 1.3e+94)
               (/ x a)
               (if (<= y 7.7e+118) (/ z b) t_1)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * (((t / y) + (z / x)) / b);
	double tmp;
	if (y <= -5e+58) {
		tmp = t_1;
	} else if (y <= -6.6e+38) {
		tmp = (x + (y * (z / t))) / a;
	} else if (y <= -20000000.0) {
		tmp = t_1;
	} else if (y <= 420.0) {
		tmp = x / (a + 1.0);
	} else if (y <= 4.2e+72) {
		tmp = t_1;
	} else if (y <= 1.3e+94) {
		tmp = x / a;
	} else if (y <= 7.7e+118) {
		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 = x * (((t / y) + (z / x)) / b)
    if (y <= (-5d+58)) then
        tmp = t_1
    else if (y <= (-6.6d+38)) then
        tmp = (x + (y * (z / t))) / a
    else if (y <= (-20000000.0d0)) then
        tmp = t_1
    else if (y <= 420.0d0) then
        tmp = x / (a + 1.0d0)
    else if (y <= 4.2d+72) then
        tmp = t_1
    else if (y <= 1.3d+94) then
        tmp = x / a
    else if (y <= 7.7d+118) 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 = x * (((t / y) + (z / x)) / b);
	double tmp;
	if (y <= -5e+58) {
		tmp = t_1;
	} else if (y <= -6.6e+38) {
		tmp = (x + (y * (z / t))) / a;
	} else if (y <= -20000000.0) {
		tmp = t_1;
	} else if (y <= 420.0) {
		tmp = x / (a + 1.0);
	} else if (y <= 4.2e+72) {
		tmp = t_1;
	} else if (y <= 1.3e+94) {
		tmp = x / a;
	} else if (y <= 7.7e+118) {
		tmp = z / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * (((t / y) + (z / x)) / b)
	tmp = 0
	if y <= -5e+58:
		tmp = t_1
	elif y <= -6.6e+38:
		tmp = (x + (y * (z / t))) / a
	elif y <= -20000000.0:
		tmp = t_1
	elif y <= 420.0:
		tmp = x / (a + 1.0)
	elif y <= 4.2e+72:
		tmp = t_1
	elif y <= 1.3e+94:
		tmp = x / a
	elif y <= 7.7e+118:
		tmp = z / b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * Float64(Float64(Float64(t / y) + Float64(z / x)) / b))
	tmp = 0.0
	if (y <= -5e+58)
		tmp = t_1;
	elseif (y <= -6.6e+38)
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / a);
	elseif (y <= -20000000.0)
		tmp = t_1;
	elseif (y <= 420.0)
		tmp = Float64(x / Float64(a + 1.0));
	elseif (y <= 4.2e+72)
		tmp = t_1;
	elseif (y <= 1.3e+94)
		tmp = Float64(x / a);
	elseif (y <= 7.7e+118)
		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 = x * (((t / y) + (z / x)) / b);
	tmp = 0.0;
	if (y <= -5e+58)
		tmp = t_1;
	elseif (y <= -6.6e+38)
		tmp = (x + (y * (z / t))) / a;
	elseif (y <= -20000000.0)
		tmp = t_1;
	elseif (y <= 420.0)
		tmp = x / (a + 1.0);
	elseif (y <= 4.2e+72)
		tmp = t_1;
	elseif (y <= 1.3e+94)
		tmp = x / a;
	elseif (y <= 7.7e+118)
		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[(x * N[(N[(N[(t / y), $MachinePrecision] + N[(z / x), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5e+58], t$95$1, If[LessEqual[y, -6.6e+38], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[y, -20000000.0], t$95$1, If[LessEqual[y, 420.0], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.2e+72], t$95$1, If[LessEqual[y, 1.3e+94], N[(x / a), $MachinePrecision], If[LessEqual[y, 7.7e+118], N[(z / b), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -4.99999999999999986e58 or -6.5999999999999998e38 < y < -2e7 or 420 < y < 4.2000000000000003e72 or 7.6999999999999997e118 < y

   1. Initial program 57.0%

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

      1. associate-/l* 60.2%

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

      2. associate-/l* 70.0%

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

   3. Simplified 70.0%

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

   5. Taylor expanded in x around inf 56.6%

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

      1. associate-*l/ 60.7%

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

      2. *-commutative 60.7%

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

      3. associate-/l* 60.5%

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

      4. *-commutative 60.5%

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

      5. associate-*l/ 61.3%

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

      6. *-commutative 61.3%

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

   7. Simplified 61.3%

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

   8. Taylor expanded in y around inf 66.5%

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

      1. associate-/r* 71.1%

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

   10. Simplified 71.1%

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

   11. Taylor expanded in b around inf 67.7%

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

       1. associate-/l* 62.5%

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

   13. Simplified 62.5%

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

   if -4.99999999999999986e58 < y < -6.5999999999999998e38

   1. Initial program 67.1%

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

      1. associate-/l* 67.1%

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

      2. associate-/l* 83.3%

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

   3. Simplified 83.3%

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

   5. Taylor expanded in a around inf 84.0%

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

   if -2e7 < y < 420

   1. Initial program 97.6%

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

      1. associate-/l* 91.4%

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

      2. associate-/l* 88.8%

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

   3. Simplified 88.8%

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

   5. Taylor expanded in y around 0 68.5%

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

   if 4.2000000000000003e72 < y < 1.3e94

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 100.0%

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

   6. Taylor expanded in a around inf 100.0%

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

   if 1.3e94 < y < 7.6999999999999997e118

   1. Initial program 64.2%

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

      1. associate-/l* 64.6%

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

      2. associate-/l* 76.7%

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

   3. Simplified 76.7%

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

   5. Taylor expanded in y around inf 64.0%

      \[\leadsto \color{blue}{\frac{z}{b}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+58}:\\ \;\;\;\;x \cdot \frac{\frac{t}{y} + \frac{z}{x}}{b}\\ \mathbf{elif}\;y \leq -6.6 \cdot 10^{+38}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a}\\ \mathbf{elif}\;y \leq -20000000:\\ \;\;\;\;x \cdot \frac{\frac{t}{y} + \frac{z}{x}}{b}\\ \mathbf{elif}\;y \leq 420:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+72}:\\ \;\;\;\;x \cdot \frac{\frac{t}{y} + \frac{z}{x}}{b}\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+94}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;y \leq 7.7 \cdot 10^{+118}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{t}{y} + \frac{z}{x}}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 58.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{b} + t \cdot \frac{\frac{x}{b}}{y}\\ \mathbf{if}\;y \leq -3.8 \cdot 10^{+50}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.85 \cdot 10^{+41}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;y \leq -20000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3500:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+72} \lor \neg \left(y \leq 6.8 \cdot 10^{+107}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (/ z b) (* t (/ (/ x b) y)))))
   (if (<= y -3.8e+50)
     t_1
     (if (<= y -1.85e+41)
       (/ x a)
       (if (<= y -20000.0)
         t_1
         (if (<= y 3500.0)
           (/ x (+ a 1.0))
           (if (or (<= y 4.2e+72) (not (<= y 6.8e+107)))
             t_1
             (/ (+ x (/ y (/ t z))) a))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z / b) + (t * ((x / b) / y));
	double tmp;
	if (y <= -3.8e+50) {
		tmp = t_1;
	} else if (y <= -1.85e+41) {
		tmp = x / a;
	} else if (y <= -20000.0) {
		tmp = t_1;
	} else if (y <= 3500.0) {
		tmp = x / (a + 1.0);
	} else if ((y <= 4.2e+72) || !(y <= 6.8e+107)) {
		tmp = t_1;
	} else {
		tmp = (x + (y / (t / z))) / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z / b) + (t * ((x / b) / y))
    if (y <= (-3.8d+50)) then
        tmp = t_1
    else if (y <= (-1.85d+41)) then
        tmp = x / a
    else if (y <= (-20000.0d0)) then
        tmp = t_1
    else if (y <= 3500.0d0) then
        tmp = x / (a + 1.0d0)
    else if ((y <= 4.2d+72) .or. (.not. (y <= 6.8d+107))) then
        tmp = t_1
    else
        tmp = (x + (y / (t / z))) / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z / b) + (t * ((x / b) / y));
	double tmp;
	if (y <= -3.8e+50) {
		tmp = t_1;
	} else if (y <= -1.85e+41) {
		tmp = x / a;
	} else if (y <= -20000.0) {
		tmp = t_1;
	} else if (y <= 3500.0) {
		tmp = x / (a + 1.0);
	} else if ((y <= 4.2e+72) || !(y <= 6.8e+107)) {
		tmp = t_1;
	} else {
		tmp = (x + (y / (t / z))) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z / b) + (t * ((x / b) / y))
	tmp = 0
	if y <= -3.8e+50:
		tmp = t_1
	elif y <= -1.85e+41:
		tmp = x / a
	elif y <= -20000.0:
		tmp = t_1
	elif y <= 3500.0:
		tmp = x / (a + 1.0)
	elif (y <= 4.2e+72) or not (y <= 6.8e+107):
		tmp = t_1
	else:
		tmp = (x + (y / (t / z))) / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z / b) + Float64(t * Float64(Float64(x / b) / y)))
	tmp = 0.0
	if (y <= -3.8e+50)
		tmp = t_1;
	elseif (y <= -1.85e+41)
		tmp = Float64(x / a);
	elseif (y <= -20000.0)
		tmp = t_1;
	elseif (y <= 3500.0)
		tmp = Float64(x / Float64(a + 1.0));
	elseif ((y <= 4.2e+72) || !(y <= 6.8e+107))
		tmp = t_1;
	else
		tmp = Float64(Float64(x + Float64(y / Float64(t / z))) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z / b) + (t * ((x / b) / y));
	tmp = 0.0;
	if (y <= -3.8e+50)
		tmp = t_1;
	elseif (y <= -1.85e+41)
		tmp = x / a;
	elseif (y <= -20000.0)
		tmp = t_1;
	elseif (y <= 3500.0)
		tmp = x / (a + 1.0);
	elseif ((y <= 4.2e+72) || ~((y <= 6.8e+107)))
		tmp = t_1;
	else
		tmp = (x + (y / (t / z))) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z / b), $MachinePrecision] + N[(t * N[(N[(x / b), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.8e+50], t$95$1, If[LessEqual[y, -1.85e+41], N[(x / a), $MachinePrecision], If[LessEqual[y, -20000.0], t$95$1, If[LessEqual[y, 3500.0], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 4.2e+72], N[Not[LessEqual[y, 6.8e+107]], $MachinePrecision]], t$95$1, N[(N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.79999999999999987e50 or -1.84999999999999991e41 < y < -2e4 or 3500 < y < 4.2000000000000003e72 or 6.7999999999999994e107 < y

   1. Initial program 55.7%

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

      1. associate-/l* 58.8%

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

      2. associate-/l* 68.4%

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

   3. Simplified 68.4%

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

   5. Taylor expanded in x around inf 55.3%

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

      1. associate-*l/ 59.3%

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

      2. *-commutative 59.3%

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

      3. associate-/l* 59.2%

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

      4. *-commutative 59.2%

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

      5. associate-*l/ 59.9%

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

      6. *-commutative 59.9%

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

   7. Simplified 59.9%

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

   8. Taylor expanded in y around inf 67.2%

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

      1. associate-/r* 71.8%

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

   10. Simplified 71.8%

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

   11. Taylor expanded in y around inf 65.7%

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

       1. associate-/l* 67.1%

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

       2. associate-/r* 69.6%

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

   13. Simplified 69.6%

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

   if -3.79999999999999987e50 < y < -1.84999999999999991e41

   1. Initial program 80.5%

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

      1. associate-/l* 80.5%

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

      2. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 80.5%

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

   6. Taylor expanded in a around inf 100.0%

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

   if -2e4 < y < 3500

   1. Initial program 98.4%

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

      1. associate-/l* 92.2%

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

      2. associate-/l* 89.6%

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

   3. Simplified 89.6%

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

   5. Taylor expanded in y around 0 69.1%

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

   if 4.2000000000000003e72 < y < 6.7999999999999994e107

   1. Initial program 83.1%

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

      1. associate-/l* 83.4%

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

      2. associate-/l* 92.2%

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

   3. Simplified 92.2%

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

      1. clear-num 92.3%

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

      2. un-div-inv 92.2%

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

   6. Applied egg-rr 92.2%

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

   7. Taylor expanded in a around inf 66.5%

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

4. Final simplification 69.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+50}:\\ \;\;\;\;\frac{z}{b} + t \cdot \frac{\frac{x}{b}}{y}\\ \mathbf{elif}\;y \leq -1.85 \cdot 10^{+41}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;y \leq -20000:\\ \;\;\;\;\frac{z}{b} + t \cdot \frac{\frac{x}{b}}{y}\\ \mathbf{elif}\;y \leq 3500:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+72} \lor \neg \left(y \leq 6.8 \cdot 10^{+107}\right):\\ \;\;\;\;\frac{z}{b} + t \cdot \frac{\frac{x}{b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 66.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 1 + \left(a + y \cdot \frac{b}{t}\right)\\ \mathbf{if}\;y \leq -1.6 \cdot 10^{+120}:\\ \;\;\;\;\frac{x \cdot \left(\frac{t}{y} + \frac{z}{x}\right)}{b}\\ \mathbf{elif}\;y \leq -8.2 \cdot 10^{+25}:\\ \;\;\;\;\frac{x}{t\_1}\\ \mathbf{elif}\;y \leq -9.2 \cdot 10^{-41}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{t\_1}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+15}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{+71} \lor \neg \left(y \leq 9.4 \cdot 10^{+108}\right):\\ \;\;\;\;\frac{z}{b} + t \cdot \frac{\frac{x}{b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ 1.0 (+ a (* y (/ b t))))))
   (if (<= y -1.6e+120)
     (/ (* x (+ (/ t y) (/ z x))) b)
     (if (<= y -8.2e+25)
       (/ x t_1)
       (if (<= y -9.2e-41)
         (* (/ y t) (/ z t_1))
         (if (<= y 2.5e+15)
           (/ (+ x (/ (* y z) t)) (+ a 1.0))
           (if (or (<= y 2.15e+71) (not (<= y 9.4e+108)))
             (+ (/ z b) (* t (/ (/ x b) y)))
             (/ (+ 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 = 1.0 + (a + (y * (b / t)));
	double tmp;
	if (y <= -1.6e+120) {
		tmp = (x * ((t / y) + (z / x))) / b;
	} else if (y <= -8.2e+25) {
		tmp = x / t_1;
	} else if (y <= -9.2e-41) {
		tmp = (y / t) * (z / t_1);
	} else if (y <= 2.5e+15) {
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	} else if ((y <= 2.15e+71) || !(y <= 9.4e+108)) {
		tmp = (z / b) + (t * ((x / b) / 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) :: t_1
    real(8) :: tmp
    t_1 = 1.0d0 + (a + (y * (b / t)))
    if (y <= (-1.6d+120)) then
        tmp = (x * ((t / y) + (z / x))) / b
    else if (y <= (-8.2d+25)) then
        tmp = x / t_1
    else if (y <= (-9.2d-41)) then
        tmp = (y / t) * (z / t_1)
    else if (y <= 2.5d+15) then
        tmp = (x + ((y * z) / t)) / (a + 1.0d0)
    else if ((y <= 2.15d+71) .or. (.not. (y <= 9.4d+108))) then
        tmp = (z / b) + (t * ((x / b) / 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 t_1 = 1.0 + (a + (y * (b / t)));
	double tmp;
	if (y <= -1.6e+120) {
		tmp = (x * ((t / y) + (z / x))) / b;
	} else if (y <= -8.2e+25) {
		tmp = x / t_1;
	} else if (y <= -9.2e-41) {
		tmp = (y / t) * (z / t_1);
	} else if (y <= 2.5e+15) {
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	} else if ((y <= 2.15e+71) || !(y <= 9.4e+108)) {
		tmp = (z / b) + (t * ((x / b) / y));
	} else {
		tmp = (x + (y * (z / t))) / (a + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = 1.0 + (a + (y * (b / t)))
	tmp = 0
	if y <= -1.6e+120:
		tmp = (x * ((t / y) + (z / x))) / b
	elif y <= -8.2e+25:
		tmp = x / t_1
	elif y <= -9.2e-41:
		tmp = (y / t) * (z / t_1)
	elif y <= 2.5e+15:
		tmp = (x + ((y * z) / t)) / (a + 1.0)
	elif (y <= 2.15e+71) or not (y <= 9.4e+108):
		tmp = (z / b) + (t * ((x / b) / y))
	else:
		tmp = (x + (y * (z / t))) / (a + 1.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(1.0 + Float64(a + Float64(y * Float64(b / t))))
	tmp = 0.0
	if (y <= -1.6e+120)
		tmp = Float64(Float64(x * Float64(Float64(t / y) + Float64(z / x))) / b);
	elseif (y <= -8.2e+25)
		tmp = Float64(x / t_1);
	elseif (y <= -9.2e-41)
		tmp = Float64(Float64(y / t) * Float64(z / t_1));
	elseif (y <= 2.5e+15)
		tmp = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(a + 1.0));
	elseif ((y <= 2.15e+71) || !(y <= 9.4e+108))
		tmp = Float64(Float64(z / b) + Float64(t * Float64(Float64(x / b) / y)));
	else
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(a + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = 1.0 + (a + (y * (b / t)));
	tmp = 0.0;
	if (y <= -1.6e+120)
		tmp = (x * ((t / y) + (z / x))) / b;
	elseif (y <= -8.2e+25)
		tmp = x / t_1;
	elseif (y <= -9.2e-41)
		tmp = (y / t) * (z / t_1);
	elseif (y <= 2.5e+15)
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	elseif ((y <= 2.15e+71) || ~((y <= 9.4e+108)))
		tmp = (z / b) + (t * ((x / b) / y));
	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[(1.0 + N[(a + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.6e+120], N[(N[(x * N[(N[(t / y), $MachinePrecision] + N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[y, -8.2e+25], N[(x / t$95$1), $MachinePrecision], If[LessEqual[y, -9.2e-41], N[(N[(y / t), $MachinePrecision] * N[(z / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.5e+15], N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 2.15e+71], N[Not[LessEqual[y, 9.4e+108]], $MachinePrecision]], N[(N[(z / b), $MachinePrecision] + N[(t * N[(N[(x / b), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -1.59999999999999991e120

   1. Initial program 48.8%

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

      1. associate-/l* 51.5%

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

      2. associate-/l* 62.8%

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

   3. Simplified 62.8%

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

   5. Taylor expanded in x around inf 50.1%

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

      1. associate-*l/ 51.4%

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

      2. *-commutative 51.4%

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

      3. associate-/l* 52.4%

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

      4. *-commutative 52.4%

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

      5. associate-*l/ 54.7%

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

      6. *-commutative 54.7%

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

   7. Simplified 54.7%

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

   8. Taylor expanded in y around inf 63.2%

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

      1. associate-/r* 74.6%

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

   10. Simplified 74.6%

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

   11. Taylor expanded in b around inf 72.5%

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

   if -1.59999999999999991e120 < y < -8.19999999999999933e25

   1. Initial program 88.4%

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

      1. associate-/l* 88.4%

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

      2. associate-/l* 94.1%

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

   3. Simplified 94.1%

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

   5. Taylor expanded in x around inf 71.4%

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

      1. associate-*l/ 77.1%

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

      2. *-commutative 77.1%

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

   7. Simplified 77.1%

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

   if -8.19999999999999933e25 < y < -9.20000000000000041e-41

   1. Initial program 67.5%

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

      1. associate-/l* 67.9%

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

      2. associate-/l* 67.6%

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

   3. Simplified 67.6%

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

   5. Taylor expanded in x around 0 67.5%

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

      1. times-frac 67.5%

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

      2. associate-*l/ 67.5%

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

      3. *-commutative 67.5%

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

   7. Simplified 67.5%

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

   if -9.20000000000000041e-41 < y < 2.5e15

   1. Initial program 99.3%

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

      1. associate-/l* 93.0%

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

      2. associate-/l* 90.3%

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

   3. Simplified 90.3%

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

   5. Taylor expanded in b around 0 87.4%

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

   if 2.5e15 < y < 2.14999999999999992e71 or 9.3999999999999991e108 < y

   1. Initial program 51.1%

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

      1. associate-/l* 55.7%

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

      2. associate-/l* 67.3%

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

   3. Simplified 67.3%

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

   5. Taylor expanded in x around inf 52.5%

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

      1. associate-*l/ 59.5%

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

      2. *-commutative 59.5%

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

      3. associate-/l* 58.6%

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

      4. *-commutative 58.6%

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

      5. associate-*l/ 58.7%

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

      6. *-commutative 58.7%

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

   7. Simplified 58.7%

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

   8. Taylor expanded in y around inf 69.3%

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

      1. associate-/r* 71.0%

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

   10. Simplified 71.0%

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

   11. Taylor expanded in y around inf 62.7%

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

       1. associate-/l* 65.2%

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

       2. associate-/r* 71.7%

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

   13. Simplified 71.7%

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

   if 2.14999999999999992e71 < y < 9.3999999999999991e108

   1. Initial program 83.1%

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

      1. associate-/l* 83.4%

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

      2. associate-/l* 92.2%

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

   3. Simplified 92.2%

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

   5. Taylor expanded in y around 0 66.5%

      \[\leadsto \frac{x + y \cdot \frac{z}{t}}{\color{blue}{1 + a}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+120}:\\ \;\;\;\;\frac{x \cdot \left(\frac{t}{y} + \frac{z}{x}\right)}{b}\\ \mathbf{elif}\;y \leq -8.2 \cdot 10^{+25}:\\ \;\;\;\;\frac{x}{1 + \left(a + y \cdot \frac{b}{t}\right)}\\ \mathbf{elif}\;y \leq -9.2 \cdot 10^{-41}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{1 + \left(a + y \cdot \frac{b}{t}\right)}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+15}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{+71} \lor \neg \left(y \leq 9.4 \cdot 10^{+108}\right):\\ \;\;\;\;\frac{z}{b} + t \cdot \frac{\frac{x}{b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 59.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+117}:\\ \;\;\;\;x \cdot \frac{\frac{t}{y} + \frac{z}{x}}{b}\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+15}:\\ \;\;\;\;\frac{x}{1 + \left(a + y \cdot \frac{b}{t}\right)}\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+72} \lor \neg \left(y \leq 2.9 \cdot 10^{+107}\right):\\ \;\;\;\;\frac{z}{b} + t \cdot \frac{\frac{x}{b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -5.8e+117)
   (* x (/ (+ (/ t y) (/ z x)) b))
   (if (<= y 2.2e+15)
     (/ x (+ 1.0 (+ a (* y (/ b t)))))
     (if (or (<= y 1.3e+72) (not (<= y 2.9e+107)))
       (+ (/ z b) (* t (/ (/ x b) y)))
       (/ (+ x (/ y (/ t z))) a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -5.8e+117) {
		tmp = x * (((t / y) + (z / x)) / b);
	} else if (y <= 2.2e+15) {
		tmp = x / (1.0 + (a + (y * (b / t))));
	} else if ((y <= 1.3e+72) || !(y <= 2.9e+107)) {
		tmp = (z / b) + (t * ((x / b) / y));
	} else {
		tmp = (x + (y / (t / z))) / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-5.8d+117)) then
        tmp = x * (((t / y) + (z / x)) / b)
    else if (y <= 2.2d+15) then
        tmp = x / (1.0d0 + (a + (y * (b / t))))
    else if ((y <= 1.3d+72) .or. (.not. (y <= 2.9d+107))) then
        tmp = (z / b) + (t * ((x / b) / y))
    else
        tmp = (x + (y / (t / z))) / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -5.8e+117) {
		tmp = x * (((t / y) + (z / x)) / b);
	} else if (y <= 2.2e+15) {
		tmp = x / (1.0 + (a + (y * (b / t))));
	} else if ((y <= 1.3e+72) || !(y <= 2.9e+107)) {
		tmp = (z / b) + (t * ((x / b) / y));
	} else {
		tmp = (x + (y / (t / z))) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -5.8e+117:
		tmp = x * (((t / y) + (z / x)) / b)
	elif y <= 2.2e+15:
		tmp = x / (1.0 + (a + (y * (b / t))))
	elif (y <= 1.3e+72) or not (y <= 2.9e+107):
		tmp = (z / b) + (t * ((x / b) / y))
	else:
		tmp = (x + (y / (t / z))) / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -5.8e+117)
		tmp = Float64(x * Float64(Float64(Float64(t / y) + Float64(z / x)) / b));
	elseif (y <= 2.2e+15)
		tmp = Float64(x / Float64(1.0 + Float64(a + Float64(y * Float64(b / t)))));
	elseif ((y <= 1.3e+72) || !(y <= 2.9e+107))
		tmp = Float64(Float64(z / b) + Float64(t * Float64(Float64(x / b) / y)));
	else
		tmp = Float64(Float64(x + Float64(y / Float64(t / z))) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -5.8e+117)
		tmp = x * (((t / y) + (z / x)) / b);
	elseif (y <= 2.2e+15)
		tmp = x / (1.0 + (a + (y * (b / t))));
	elseif ((y <= 1.3e+72) || ~((y <= 2.9e+107)))
		tmp = (z / b) + (t * ((x / b) / y));
	else
		tmp = (x + (y / (t / z))) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -5.8e+117], N[(x * N[(N[(N[(t / y), $MachinePrecision] + N[(z / x), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.2e+15], N[(x / N[(1.0 + N[(a + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 1.3e+72], N[Not[LessEqual[y, 2.9e+107]], $MachinePrecision]], N[(N[(z / b), $MachinePrecision] + N[(t * N[(N[(x / b), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.80000000000000055e117

   1. Initial program 48.8%

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

      1. associate-/l* 51.5%

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

      2. associate-/l* 62.8%

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

   3. Simplified 62.8%

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

   5. Taylor expanded in x around inf 50.1%

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

      1. associate-*l/ 51.4%

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

      2. *-commutative 51.4%

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

      3. associate-/l* 52.4%

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

      4. *-commutative 52.4%

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

      5. associate-*l/ 54.7%

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

      6. *-commutative 54.7%

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

   7. Simplified 54.7%

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

   8. Taylor expanded in y around inf 63.2%

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

      1. associate-/r* 74.6%

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

   10. Simplified 74.6%

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

   11. Taylor expanded in b around inf 72.5%

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

       1. associate-/l* 69.1%

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

   13. Simplified 69.1%

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

   if -5.80000000000000055e117 < y < 2.2e15

   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* 90.2%

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

      2. associate-/l* 88.8%

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

   3. Simplified 88.8%

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

   5. Taylor expanded in x around inf 71.5%

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

      1. associate-*l/ 70.1%

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

      2. *-commutative 70.1%

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

   7. Simplified 70.1%

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

   if 2.2e15 < y < 1.29999999999999991e72 or 2.89999999999999988e107 < y

   1. Initial program 51.1%

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

      1. associate-/l* 55.7%

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

      2. associate-/l* 67.3%

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

   3. Simplified 67.3%

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

   5. Taylor expanded in x around inf 52.5%

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

      1. associate-*l/ 59.5%

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

      2. *-commutative 59.5%

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

      3. associate-/l* 58.6%

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

      4. *-commutative 58.6%

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

      5. associate-*l/ 58.7%

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

      6. *-commutative 58.7%

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

   7. Simplified 58.7%

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

   8. Taylor expanded in y around inf 69.3%

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

      1. associate-/r* 71.0%

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

   10. Simplified 71.0%

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

   11. Taylor expanded in y around inf 62.7%

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

       1. associate-/l* 65.2%

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

       2. associate-/r* 71.7%

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

   13. Simplified 71.7%

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

   if 1.29999999999999991e72 < y < 2.89999999999999988e107

   1. Initial program 83.1%

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

      1. associate-/l* 83.4%

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

      2. associate-/l* 92.2%

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

   3. Simplified 92.2%

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

      1. clear-num 92.3%

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

      2. un-div-inv 92.2%

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

   6. Applied egg-rr 92.2%

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

   7. Taylor expanded in a around inf 66.5%

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

4. Final simplification 70.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+117}:\\ \;\;\;\;x \cdot \frac{\frac{t}{y} + \frac{z}{x}}{b}\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+15}:\\ \;\;\;\;\frac{x}{1 + \left(a + y \cdot \frac{b}{t}\right)}\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+72} \lor \neg \left(y \leq 2.9 \cdot 10^{+107}\right):\\ \;\;\;\;\frac{z}{b} + t \cdot \frac{\frac{x}{b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 61.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.9 \cdot 10^{+115}:\\ \;\;\;\;x \cdot \frac{\frac{t}{y} + \frac{z}{x}}{b}\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+17}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+71} \lor \neg \left(y \leq 2.9 \cdot 10^{+107}\right):\\ \;\;\;\;\frac{z}{b} + t \cdot \frac{\frac{x}{b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -4.9e+115)
   (* x (/ (+ (/ t y) (/ z x)) b))
   (if (<= y 3.4e+17)
     (/ x (+ 1.0 (+ a (/ (* y b) t))))
     (if (or (<= y 3.8e+71) (not (<= y 2.9e+107)))
       (+ (/ z b) (* t (/ (/ x b) y)))
       (/ (+ x (/ y (/ t z))) a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -4.9e+115) {
		tmp = x * (((t / y) + (z / x)) / b);
	} else if (y <= 3.4e+17) {
		tmp = x / (1.0 + (a + ((y * b) / t)));
	} else if ((y <= 3.8e+71) || !(y <= 2.9e+107)) {
		tmp = (z / b) + (t * ((x / b) / y));
	} else {
		tmp = (x + (y / (t / z))) / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-4.9d+115)) then
        tmp = x * (((t / y) + (z / x)) / b)
    else if (y <= 3.4d+17) then
        tmp = x / (1.0d0 + (a + ((y * b) / t)))
    else if ((y <= 3.8d+71) .or. (.not. (y <= 2.9d+107))) then
        tmp = (z / b) + (t * ((x / b) / y))
    else
        tmp = (x + (y / (t / z))) / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -4.9e+115) {
		tmp = x * (((t / y) + (z / x)) / b);
	} else if (y <= 3.4e+17) {
		tmp = x / (1.0 + (a + ((y * b) / t)));
	} else if ((y <= 3.8e+71) || !(y <= 2.9e+107)) {
		tmp = (z / b) + (t * ((x / b) / y));
	} else {
		tmp = (x + (y / (t / z))) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -4.9e+115:
		tmp = x * (((t / y) + (z / x)) / b)
	elif y <= 3.4e+17:
		tmp = x / (1.0 + (a + ((y * b) / t)))
	elif (y <= 3.8e+71) or not (y <= 2.9e+107):
		tmp = (z / b) + (t * ((x / b) / y))
	else:
		tmp = (x + (y / (t / z))) / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -4.9e+115)
		tmp = Float64(x * Float64(Float64(Float64(t / y) + Float64(z / x)) / b));
	elseif (y <= 3.4e+17)
		tmp = Float64(x / Float64(1.0 + Float64(a + Float64(Float64(y * b) / t))));
	elseif ((y <= 3.8e+71) || !(y <= 2.9e+107))
		tmp = Float64(Float64(z / b) + Float64(t * Float64(Float64(x / b) / y)));
	else
		tmp = Float64(Float64(x + Float64(y / Float64(t / z))) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -4.9e+115)
		tmp = x * (((t / y) + (z / x)) / b);
	elseif (y <= 3.4e+17)
		tmp = x / (1.0 + (a + ((y * b) / t)));
	elseif ((y <= 3.8e+71) || ~((y <= 2.9e+107)))
		tmp = (z / b) + (t * ((x / b) / y));
	else
		tmp = (x + (y / (t / z))) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -4.9e+115], N[(x * N[(N[(N[(t / y), $MachinePrecision] + N[(z / x), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.4e+17], N[(x / N[(1.0 + N[(a + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 3.8e+71], N[Not[LessEqual[y, 2.9e+107]], $MachinePrecision]], N[(N[(z / b), $MachinePrecision] + N[(t * N[(N[(x / b), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.89999999999999964e115

   1. Initial program 48.8%

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

      1. associate-/l* 51.5%

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

      2. associate-/l* 62.8%

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

   3. Simplified 62.8%

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

   5. Taylor expanded in x around inf 50.1%

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

      1. associate-*l/ 51.4%

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

      2. *-commutative 51.4%

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

      3. associate-/l* 52.4%

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

      4. *-commutative 52.4%

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

      5. associate-*l/ 54.7%

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

      6. *-commutative 54.7%

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

   7. Simplified 54.7%

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

   8. Taylor expanded in y around inf 63.2%

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

      1. associate-/r* 74.6%

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

   10. Simplified 74.6%

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

   11. Taylor expanded in b around inf 72.5%

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

       1. associate-/l* 69.1%

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

   13. Simplified 69.1%

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

   if -4.89999999999999964e115 < y < 3.4e17

   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* 90.2%

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

      2. associate-/l* 88.8%

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

   3. Simplified 88.8%

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

   5. Taylor expanded in x around inf 71.5%

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

   if 3.4e17 < y < 3.8000000000000001e71 or 2.89999999999999988e107 < y

   1. Initial program 51.1%

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

      1. associate-/l* 55.7%

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

      2. associate-/l* 67.3%

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

   3. Simplified 67.3%

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

   5. Taylor expanded in x around inf 52.5%

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

      1. associate-*l/ 59.5%

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

      2. *-commutative 59.5%

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

      3. associate-/l* 58.6%

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

      4. *-commutative 58.6%

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

      5. associate-*l/ 58.7%

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

      6. *-commutative 58.7%

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

   7. Simplified 58.7%

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

   8. Taylor expanded in y around inf 69.3%

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

      1. associate-/r* 71.0%

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

   10. Simplified 71.0%

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

   11. Taylor expanded in y around inf 62.7%

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

       1. associate-/l* 65.2%

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

       2. associate-/r* 71.7%

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

   13. Simplified 71.7%

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

   if 3.8000000000000001e71 < y < 2.89999999999999988e107

   1. Initial program 83.1%

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

      1. associate-/l* 83.4%

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

      2. associate-/l* 92.2%

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

   3. Simplified 92.2%

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

      1. clear-num 92.3%

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

      2. un-div-inv 92.2%

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

   6. Applied egg-rr 92.2%

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

   7. Taylor expanded in a around inf 66.5%

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

4. Final simplification 70.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.9 \cdot 10^{+115}:\\ \;\;\;\;x \cdot \frac{\frac{t}{y} + \frac{z}{x}}{b}\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+17}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+71} \lor \neg \left(y \leq 2.9 \cdot 10^{+107}\right):\\ \;\;\;\;\frac{z}{b} + t \cdot \frac{\frac{x}{b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 62.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+113}:\\ \;\;\;\;\frac{x \cdot \left(\frac{t}{y} + \frac{z}{x}\right)}{b}\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+16}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+72} \lor \neg \left(y \leq 2.9 \cdot 10^{+107}\right):\\ \;\;\;\;\frac{z}{b} + t \cdot \frac{\frac{x}{b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -5.8e+113)
   (/ (* x (+ (/ t y) (/ z x))) b)
   (if (<= y 6.5e+16)
     (/ x (+ 1.0 (+ a (/ (* y b) t))))
     (if (or (<= y 2.2e+72) (not (<= y 2.9e+107)))
       (+ (/ z b) (* t (/ (/ x b) y)))
       (/ (+ x (/ y (/ t z))) a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -5.8e+113) {
		tmp = (x * ((t / y) + (z / x))) / b;
	} else if (y <= 6.5e+16) {
		tmp = x / (1.0 + (a + ((y * b) / t)));
	} else if ((y <= 2.2e+72) || !(y <= 2.9e+107)) {
		tmp = (z / b) + (t * ((x / b) / y));
	} else {
		tmp = (x + (y / (t / z))) / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-5.8d+113)) then
        tmp = (x * ((t / y) + (z / x))) / b
    else if (y <= 6.5d+16) then
        tmp = x / (1.0d0 + (a + ((y * b) / t)))
    else if ((y <= 2.2d+72) .or. (.not. (y <= 2.9d+107))) then
        tmp = (z / b) + (t * ((x / b) / y))
    else
        tmp = (x + (y / (t / z))) / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -5.8e+113) {
		tmp = (x * ((t / y) + (z / x))) / b;
	} else if (y <= 6.5e+16) {
		tmp = x / (1.0 + (a + ((y * b) / t)));
	} else if ((y <= 2.2e+72) || !(y <= 2.9e+107)) {
		tmp = (z / b) + (t * ((x / b) / y));
	} else {
		tmp = (x + (y / (t / z))) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -5.8e+113:
		tmp = (x * ((t / y) + (z / x))) / b
	elif y <= 6.5e+16:
		tmp = x / (1.0 + (a + ((y * b) / t)))
	elif (y <= 2.2e+72) or not (y <= 2.9e+107):
		tmp = (z / b) + (t * ((x / b) / y))
	else:
		tmp = (x + (y / (t / z))) / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -5.8e+113)
		tmp = Float64(Float64(x * Float64(Float64(t / y) + Float64(z / x))) / b);
	elseif (y <= 6.5e+16)
		tmp = Float64(x / Float64(1.0 + Float64(a + Float64(Float64(y * b) / t))));
	elseif ((y <= 2.2e+72) || !(y <= 2.9e+107))
		tmp = Float64(Float64(z / b) + Float64(t * Float64(Float64(x / b) / y)));
	else
		tmp = Float64(Float64(x + Float64(y / Float64(t / z))) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -5.8e+113)
		tmp = (x * ((t / y) + (z / x))) / b;
	elseif (y <= 6.5e+16)
		tmp = x / (1.0 + (a + ((y * b) / t)));
	elseif ((y <= 2.2e+72) || ~((y <= 2.9e+107)))
		tmp = (z / b) + (t * ((x / b) / y));
	else
		tmp = (x + (y / (t / z))) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -5.8e+113], N[(N[(x * N[(N[(t / y), $MachinePrecision] + N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[y, 6.5e+16], N[(x / N[(1.0 + N[(a + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 2.2e+72], N[Not[LessEqual[y, 2.9e+107]], $MachinePrecision]], N[(N[(z / b), $MachinePrecision] + N[(t * N[(N[(x / b), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.79999999999999968e113

   1. Initial program 48.8%

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

      1. associate-/l* 51.5%

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

      2. associate-/l* 62.8%

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

   3. Simplified 62.8%

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

   5. Taylor expanded in x around inf 50.1%

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

      1. associate-*l/ 51.4%

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

      2. *-commutative 51.4%

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

      3. associate-/l* 52.4%

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

      4. *-commutative 52.4%

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

      5. associate-*l/ 54.7%

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

      6. *-commutative 54.7%

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

   7. Simplified 54.7%

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

   8. Taylor expanded in y around inf 63.2%

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

      1. associate-/r* 74.6%

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

   10. Simplified 74.6%

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

   11. Taylor expanded in b around inf 72.5%

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

   if -5.79999999999999968e113 < y < 6.5e16

   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* 90.2%

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

      2. associate-/l* 88.8%

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

   3. Simplified 88.8%

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

   5. Taylor expanded in x around inf 71.5%

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

   if 6.5e16 < y < 2.2e72 or 2.89999999999999988e107 < y

   1. Initial program 51.1%

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

      1. associate-/l* 55.7%

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

      2. associate-/l* 67.3%

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

   3. Simplified 67.3%

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

   5. Taylor expanded in x around inf 52.5%

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

      1. associate-*l/ 59.5%

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

      2. *-commutative 59.5%

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

      3. associate-/l* 58.6%

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

      4. *-commutative 58.6%

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

      5. associate-*l/ 58.7%

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

      6. *-commutative 58.7%

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

   7. Simplified 58.7%

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

   8. Taylor expanded in y around inf 69.3%

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

      1. associate-/r* 71.0%

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

   10. Simplified 71.0%

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

   11. Taylor expanded in y around inf 62.7%

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

       1. associate-/l* 65.2%

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

       2. associate-/r* 71.7%

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

   13. Simplified 71.7%

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

   if 2.2e72 < y < 2.89999999999999988e107

   1. Initial program 83.1%

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

      1. associate-/l* 83.4%

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

      2. associate-/l* 92.2%

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

   3. Simplified 92.2%

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

      1. clear-num 92.3%

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

      2. un-div-inv 92.2%

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

   6. Applied egg-rr 92.2%

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

   7. Taylor expanded in a around inf 66.5%

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

4. Final simplification 71.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+113}:\\ \;\;\;\;\frac{x \cdot \left(\frac{t}{y} + \frac{z}{x}\right)}{b}\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+16}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+72} \lor \neg \left(y \leq 2.9 \cdot 10^{+107}\right):\\ \;\;\;\;\frac{z}{b} + t \cdot \frac{\frac{x}{b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 65.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{+59}:\\ \;\;\;\;\frac{x \cdot \left(\frac{t}{y} + \frac{z}{x}\right)}{b}\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{+17} \lor \neg \left(y \leq 2.4 \cdot 10^{+72}\right) \land y \leq 7.5 \cdot 10^{+110}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + t \cdot \frac{\frac{x}{b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.55e+59)
   (/ (* x (+ (/ t y) (/ z x))) b)
   (if (or (<= y 4.7e+17) (and (not (<= y 2.4e+72)) (<= y 7.5e+110)))
     (/ (+ x (* y (/ z t))) (+ a 1.0))
     (+ (/ z b) (* t (/ (/ x b) y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.55e+59) {
		tmp = (x * ((t / y) + (z / x))) / b;
	} else if ((y <= 4.7e+17) || (!(y <= 2.4e+72) && (y <= 7.5e+110))) {
		tmp = (x + (y * (z / t))) / (a + 1.0);
	} else {
		tmp = (z / b) + (t * ((x / b) / y));
	}
	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 <= (-1.55d+59)) then
        tmp = (x * ((t / y) + (z / x))) / b
    else if ((y <= 4.7d+17) .or. (.not. (y <= 2.4d+72)) .and. (y <= 7.5d+110)) then
        tmp = (x + (y * (z / t))) / (a + 1.0d0)
    else
        tmp = (z / b) + (t * ((x / b) / y))
    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 <= -1.55e+59) {
		tmp = (x * ((t / y) + (z / x))) / b;
	} else if ((y <= 4.7e+17) || (!(y <= 2.4e+72) && (y <= 7.5e+110))) {
		tmp = (x + (y * (z / t))) / (a + 1.0);
	} else {
		tmp = (z / b) + (t * ((x / b) / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.55e+59:
		tmp = (x * ((t / y) + (z / x))) / b
	elif (y <= 4.7e+17) or (not (y <= 2.4e+72) and (y <= 7.5e+110)):
		tmp = (x + (y * (z / t))) / (a + 1.0)
	else:
		tmp = (z / b) + (t * ((x / b) / y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.55e+59)
		tmp = Float64(Float64(x * Float64(Float64(t / y) + Float64(z / x))) / b);
	elseif ((y <= 4.7e+17) || (!(y <= 2.4e+72) && (y <= 7.5e+110)))
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(a + 1.0));
	else
		tmp = Float64(Float64(z / b) + Float64(t * Float64(Float64(x / b) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -1.55e+59)
		tmp = (x * ((t / y) + (z / x))) / b;
	elseif ((y <= 4.7e+17) || (~((y <= 2.4e+72)) && (y <= 7.5e+110)))
		tmp = (x + (y * (z / t))) / (a + 1.0);
	else
		tmp = (z / b) + (t * ((x / b) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.55e+59], N[(N[(x * N[(N[(t / y), $MachinePrecision] + N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], If[Or[LessEqual[y, 4.7e+17], And[N[Not[LessEqual[y, 2.4e+72]], $MachinePrecision], LessEqual[y, 7.5e+110]]], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(z / b), $MachinePrecision] + N[(t * N[(N[(x / b), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.55000000000000007e59

   1. Initial program 58.7%

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

      1. associate-/l* 60.8%

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

      2. associate-/l* 70.0%

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

   3. Simplified 70.0%

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

   5. Taylor expanded in x around inf 57.9%

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

      1. associate-*l/ 58.9%

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

      2. *-commutative 58.9%

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

      3. associate-/l* 59.7%

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

      4. *-commutative 59.7%

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

      5. associate-*l/ 61.6%

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

      6. *-commutative 61.6%

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

   7. Simplified 61.6%

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

   8. Taylor expanded in y around inf 62.9%

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

      1. associate-/r* 72.1%

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

   10. Simplified 72.1%

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

   11. Taylor expanded in b around inf 69.1%

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

   if -1.55000000000000007e59 < y < 4.7e17 or 2.4000000000000001e72 < y < 7.5e110

   1. Initial program 93.9%

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

      1. associate-/l* 89.0%

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

      2. associate-/l* 88.3%

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

   3. Simplified 88.3%

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

   5. Taylor expanded in y around 0 78.2%

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

   if 4.7e17 < y < 2.4000000000000001e72 or 7.5e110 < y

   1. Initial program 51.1%

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

      1. associate-/l* 55.7%

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

      2. associate-/l* 67.3%

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

   3. Simplified 67.3%

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

   5. Taylor expanded in x around inf 52.5%

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

      1. associate-*l/ 59.5%

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

      2. *-commutative 59.5%

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

      3. associate-/l* 58.6%

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

      4. *-commutative 58.6%

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

      5. associate-*l/ 58.7%

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

      6. *-commutative 58.7%

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

   7. Simplified 58.7%

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

   8. Taylor expanded in y around inf 69.3%

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

      1. associate-/r* 71.0%

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

   10. Simplified 71.0%

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

   11. Taylor expanded in y around inf 62.7%

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

       1. associate-/l* 65.2%

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

       2. associate-/r* 71.7%

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

   13. Simplified 71.7%

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

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{+59}:\\ \;\;\;\;\frac{x \cdot \left(\frac{t}{y} + \frac{z}{x}\right)}{b}\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{+17} \lor \neg \left(y \leq 2.4 \cdot 10^{+72}\right) \land y \leq 7.5 \cdot 10^{+110}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + t \cdot \frac{\frac{x}{b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 67.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+59}:\\ \;\;\;\;\frac{x \cdot \left(\frac{t}{y} + \frac{z}{x}\right)}{b}\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{+17}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + 1}\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+72} \lor \neg \left(y \leq 3.2 \cdot 10^{+107}\right):\\ \;\;\;\;\frac{z}{b} + t \cdot \frac{\frac{x}{b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.6e+59)
   (/ (* x (+ (/ t y) (/ z x))) b)
   (if (<= y 4.4e+17)
     (/ (+ x (* z (/ y t))) (+ a 1.0))
     (if (or (<= y 1.8e+72) (not (<= y 3.2e+107)))
       (+ (/ z b) (* t (/ (/ x b) 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 <= -1.6e+59) {
		tmp = (x * ((t / y) + (z / x))) / b;
	} else if (y <= 4.4e+17) {
		tmp = (x + (z * (y / t))) / (a + 1.0);
	} else if ((y <= 1.8e+72) || !(y <= 3.2e+107)) {
		tmp = (z / b) + (t * ((x / b) / 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 <= (-1.6d+59)) then
        tmp = (x * ((t / y) + (z / x))) / b
    else if (y <= 4.4d+17) then
        tmp = (x + (z * (y / t))) / (a + 1.0d0)
    else if ((y <= 1.8d+72) .or. (.not. (y <= 3.2d+107))) then
        tmp = (z / b) + (t * ((x / b) / 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 <= -1.6e+59) {
		tmp = (x * ((t / y) + (z / x))) / b;
	} else if (y <= 4.4e+17) {
		tmp = (x + (z * (y / t))) / (a + 1.0);
	} else if ((y <= 1.8e+72) || !(y <= 3.2e+107)) {
		tmp = (z / b) + (t * ((x / b) / 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 <= -1.6e+59:
		tmp = (x * ((t / y) + (z / x))) / b
	elif y <= 4.4e+17:
		tmp = (x + (z * (y / t))) / (a + 1.0)
	elif (y <= 1.8e+72) or not (y <= 3.2e+107):
		tmp = (z / b) + (t * ((x / b) / 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 <= -1.6e+59)
		tmp = Float64(Float64(x * Float64(Float64(t / y) + Float64(z / x))) / b);
	elseif (y <= 4.4e+17)
		tmp = Float64(Float64(x + Float64(z * Float64(y / t))) / Float64(a + 1.0));
	elseif ((y <= 1.8e+72) || !(y <= 3.2e+107))
		tmp = Float64(Float64(z / b) + Float64(t * Float64(Float64(x / b) / y)));
	else
		tmp = Float64(Float64(x + Float64(y * Float64(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 <= -1.6e+59)
		tmp = (x * ((t / y) + (z / x))) / b;
	elseif (y <= 4.4e+17)
		tmp = (x + (z * (y / t))) / (a + 1.0);
	elseif ((y <= 1.8e+72) || ~((y <= 3.2e+107)))
		tmp = (z / b) + (t * ((x / b) / y));
	else
		tmp = (x + (y * (z / t))) / (a + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.6e+59], N[(N[(x * N[(N[(t / y), $MachinePrecision] + N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[y, 4.4e+17], N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 1.8e+72], N[Not[LessEqual[y, 3.2e+107]], $MachinePrecision]], N[(N[(z / b), $MachinePrecision] + N[(t * N[(N[(x / b), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.59999999999999991e59

   1. Initial program 58.7%

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

      1. associate-/l* 60.8%

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

      2. associate-/l* 70.0%

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

   3. Simplified 70.0%

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

   5. Taylor expanded in x around inf 57.9%

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

      1. associate-*l/ 58.9%

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

      2. *-commutative 58.9%

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

      3. associate-/l* 59.7%

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

      4. *-commutative 59.7%

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

      5. associate-*l/ 61.6%

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

      6. *-commutative 61.6%

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

   7. Simplified 61.6%

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

   8. Taylor expanded in y around inf 62.9%

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

      1. associate-/r* 72.1%

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

   10. Simplified 72.1%

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

   11. Taylor expanded in b around inf 69.1%

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

   if -1.59999999999999991e59 < y < 4.4e17

   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* 89.5%

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

      2. associate-/l* 88.0%

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

   3. Simplified 88.0%

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

      1. clear-num 87.9%

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

      2. un-div-inv 89.0%

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

   6. Applied egg-rr 89.0%

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

      1. associate-/r/ 90.0%

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

   8. Applied egg-rr 90.0%

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

   9. Taylor expanded in y around 0 79.8%

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

   if 4.4e17 < y < 1.80000000000000017e72 or 3.20000000000000029e107 < y

   1. Initial program 51.1%

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

      1. associate-/l* 55.7%

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

      2. associate-/l* 67.3%

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

   3. Simplified 67.3%

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

   5. Taylor expanded in x around inf 52.5%

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

      1. associate-*l/ 59.5%

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

      2. *-commutative 59.5%

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

      3. associate-/l* 58.6%

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

      4. *-commutative 58.6%

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

      5. associate-*l/ 58.7%

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

      6. *-commutative 58.7%

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

   7. Simplified 58.7%

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

   8. Taylor expanded in y around inf 69.3%

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

      1. associate-/r* 71.0%

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

   10. Simplified 71.0%

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

   11. Taylor expanded in y around inf 62.7%

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

       1. associate-/l* 65.2%

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

       2. associate-/r* 71.7%

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

   13. Simplified 71.7%

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

   if 1.80000000000000017e72 < y < 3.20000000000000029e107

   1. Initial program 83.1%

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

      1. associate-/l* 83.4%

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

      2. associate-/l* 92.2%

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

   3. Simplified 92.2%

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

   5. Taylor expanded in y around 0 66.5%

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

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+59}:\\ \;\;\;\;\frac{x \cdot \left(\frac{t}{y} + \frac{z}{x}\right)}{b}\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{+17}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + 1}\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+72} \lor \neg \left(y \leq 3.2 \cdot 10^{+107}\right):\\ \;\;\;\;\frac{z}{b} + t \cdot \frac{\frac{x}{b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 67.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+59}:\\ \;\;\;\;\frac{x \cdot \left(\frac{t}{y} + \frac{z}{x}\right)}{b}\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+16}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+70} \lor \neg \left(y \leq 4.6 \cdot 10^{+111}\right):\\ \;\;\;\;\frac{z}{b} + t \cdot \frac{\frac{x}{b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.4e+59)
   (/ (* x (+ (/ t y) (/ z x))) b)
   (if (<= y 2.3e+16)
     (/ (+ x (/ (* y z) t)) (+ a 1.0))
     (if (or (<= y 5e+70) (not (<= y 4.6e+111)))
       (+ (/ z b) (* t (/ (/ x b) 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 <= -1.4e+59) {
		tmp = (x * ((t / y) + (z / x))) / b;
	} else if (y <= 2.3e+16) {
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	} else if ((y <= 5e+70) || !(y <= 4.6e+111)) {
		tmp = (z / b) + (t * ((x / b) / 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 <= (-1.4d+59)) then
        tmp = (x * ((t / y) + (z / x))) / b
    else if (y <= 2.3d+16) then
        tmp = (x + ((y * z) / t)) / (a + 1.0d0)
    else if ((y <= 5d+70) .or. (.not. (y <= 4.6d+111))) then
        tmp = (z / b) + (t * ((x / b) / 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 <= -1.4e+59) {
		tmp = (x * ((t / y) + (z / x))) / b;
	} else if (y <= 2.3e+16) {
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	} else if ((y <= 5e+70) || !(y <= 4.6e+111)) {
		tmp = (z / b) + (t * ((x / b) / 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 <= -1.4e+59:
		tmp = (x * ((t / y) + (z / x))) / b
	elif y <= 2.3e+16:
		tmp = (x + ((y * z) / t)) / (a + 1.0)
	elif (y <= 5e+70) or not (y <= 4.6e+111):
		tmp = (z / b) + (t * ((x / b) / 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 <= -1.4e+59)
		tmp = Float64(Float64(x * Float64(Float64(t / y) + Float64(z / x))) / b);
	elseif (y <= 2.3e+16)
		tmp = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(a + 1.0));
	elseif ((y <= 5e+70) || !(y <= 4.6e+111))
		tmp = Float64(Float64(z / b) + Float64(t * Float64(Float64(x / b) / y)));
	else
		tmp = Float64(Float64(x + Float64(y * Float64(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 <= -1.4e+59)
		tmp = (x * ((t / y) + (z / x))) / b;
	elseif (y <= 2.3e+16)
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	elseif ((y <= 5e+70) || ~((y <= 4.6e+111)))
		tmp = (z / b) + (t * ((x / b) / y));
	else
		tmp = (x + (y * (z / t))) / (a + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.4e+59], N[(N[(x * N[(N[(t / y), $MachinePrecision] + N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[y, 2.3e+16], N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 5e+70], N[Not[LessEqual[y, 4.6e+111]], $MachinePrecision]], N[(N[(z / b), $MachinePrecision] + N[(t * N[(N[(x / b), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.3999999999999999e59

   1. Initial program 58.7%

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

      1. associate-/l* 60.8%

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

      2. associate-/l* 70.0%

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

   3. Simplified 70.0%

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

   5. Taylor expanded in x around inf 57.9%

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

      1. associate-*l/ 58.9%

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

      2. *-commutative 58.9%

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

      3. associate-/l* 59.7%

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

      4. *-commutative 59.7%

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

      5. associate-*l/ 61.6%

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

      6. *-commutative 61.6%

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

   7. Simplified 61.6%

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

   8. Taylor expanded in y around inf 62.9%

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

      1. associate-/r* 72.1%

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

   10. Simplified 72.1%

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

   11. Taylor expanded in b around inf 69.1%

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

   if -1.3999999999999999e59 < y < 2.3e16

   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* 89.5%

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

      2. associate-/l* 88.0%

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

   3. Simplified 88.0%

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

   5. Taylor expanded in b around 0 82.2%

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

   if 2.3e16 < y < 5.0000000000000002e70 or 4.60000000000000004e111 < y

   1. Initial program 51.1%

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

      1. associate-/l* 55.7%

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

      2. associate-/l* 67.3%

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

   3. Simplified 67.3%

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

   5. Taylor expanded in x around inf 52.5%

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

      1. associate-*l/ 59.5%

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

      2. *-commutative 59.5%

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

      3. associate-/l* 58.6%

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

      4. *-commutative 58.6%

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

      5. associate-*l/ 58.7%

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

      6. *-commutative 58.7%

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

   7. Simplified 58.7%

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

   8. Taylor expanded in y around inf 69.3%

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

      1. associate-/r* 71.0%

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

   10. Simplified 71.0%

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

   11. Taylor expanded in y around inf 62.7%

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

       1. associate-/l* 65.2%

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

       2. associate-/r* 71.7%

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

   13. Simplified 71.7%

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

   if 5.0000000000000002e70 < y < 4.60000000000000004e111

   1. Initial program 83.1%

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

      1. associate-/l* 83.4%

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

      2. associate-/l* 92.2%

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

   3. Simplified 92.2%

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

   5. Taylor expanded in y around 0 66.5%

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

4. Final simplification 76.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+59}:\\ \;\;\;\;\frac{x \cdot \left(\frac{t}{y} + \frac{z}{x}\right)}{b}\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+16}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+70} \lor \neg \left(y \leq 4.6 \cdot 10^{+111}\right):\\ \;\;\;\;\frac{z}{b} + t \cdot \frac{\frac{x}{b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 79.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.1 \cdot 10^{-244} \lor \neg \left(t \leq 1.45 \cdot 10^{-205}\right):\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{y \cdot \frac{b}{t} + \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + t \cdot \frac{\frac{x}{b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -5.1e-244) (not (<= t 1.45e-205)))
   (/ (+ x (* y (/ z t))) (+ (* y (/ b t)) (+ a 1.0)))
   (+ (/ z b) (* t (/ (/ x b) y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -5.1e-244) || !(t <= 1.45e-205)) {
		tmp = (x + (y * (z / t))) / ((y * (b / t)) + (a + 1.0));
	} else {
		tmp = (z / b) + (t * ((x / b) / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-5.1d-244)) .or. (.not. (t <= 1.45d-205))) then
        tmp = (x + (y * (z / t))) / ((y * (b / t)) + (a + 1.0d0))
    else
        tmp = (z / b) + (t * ((x / b) / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -5.1e-244) || !(t <= 1.45e-205)) {
		tmp = (x + (y * (z / t))) / ((y * (b / t)) + (a + 1.0));
	} else {
		tmp = (z / b) + (t * ((x / b) / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -5.1e-244) or not (t <= 1.45e-205):
		tmp = (x + (y * (z / t))) / ((y * (b / t)) + (a + 1.0))
	else:
		tmp = (z / b) + (t * ((x / b) / y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -5.1e-244) || !(t <= 1.45e-205))
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(Float64(y * Float64(b / t)) + Float64(a + 1.0)));
	else
		tmp = Float64(Float64(z / b) + Float64(t * Float64(Float64(x / b) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -5.1e-244) || ~((t <= 1.45e-205)))
		tmp = (x + (y * (z / t))) / ((y * (b / t)) + (a + 1.0));
	else
		tmp = (z / b) + (t * ((x / b) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -5.1e-244], N[Not[LessEqual[t, 1.45e-205]], $MachinePrecision]], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z / b), $MachinePrecision] + N[(t * N[(N[(x / b), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -5.09999999999999981e-244 or 1.45000000000000009e-205 < t

   1. Initial program 79.5%

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

      1. associate-/l* 79.6%

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

      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 -5.09999999999999981e-244 < t < 1.45000000000000009e-205

   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* 32.6%

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

      2. associate-/l* 25.2%

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

   3. Simplified 25.2%

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

   5. Taylor expanded in x around inf 44.0%

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

      1. associate-*l/ 36.9%

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

      2. *-commutative 36.9%

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

      3. associate-/l* 35.9%

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

      4. *-commutative 35.9%

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

      5. associate-*l/ 32.3%

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

      6. *-commutative 32.3%

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

   7. Simplified 32.3%

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

   8. Taylor expanded in y around inf 72.5%

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

      1. associate-/r* 80.0%

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

   10. Simplified 80.0%

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

   11. Taylor expanded in y around inf 85.0%

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

       1. associate-/l* 85.1%

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

       2. associate-/r* 85.1%

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

   13. Simplified 85.1%

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

4. Final simplification 85.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.1 \cdot 10^{-244} \lor \neg \left(t \leq 1.45 \cdot 10^{-205}\right):\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{y \cdot \frac{b}{t} + \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + t \cdot \frac{\frac{x}{b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 79.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{b}{t} + \left(a + 1\right)\\ \mathbf{if}\;t \leq -3.7 \cdot 10^{-244}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{t\_1}\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-206}:\\ \;\;\;\;\frac{z}{b} + t \cdot \frac{\frac{x}{b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{t\_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (* y (/ b t)) (+ a 1.0))))
   (if (<= t -3.7e-244)
     (/ (+ x (* y (/ z t))) t_1)
     (if (<= t 2.1e-206)
       (+ (/ z b) (* t (/ (/ x b) y)))
       (/ (+ x (* z (/ y t))) t_1)))))

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 tmp;
	if (t <= -3.7e-244) {
		tmp = (x + (y * (z / t))) / t_1;
	} else if (t <= 2.1e-206) {
		tmp = (z / b) + (t * ((x / b) / y));
	} else {
		tmp = (x + (z * (y / t))) / 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 = (y * (b / t)) + (a + 1.0d0)
    if (t <= (-3.7d-244)) then
        tmp = (x + (y * (z / t))) / t_1
    else if (t <= 2.1d-206) then
        tmp = (z / b) + (t * ((x / b) / y))
    else
        tmp = (x + (z * (y / t))) / 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 = (y * (b / t)) + (a + 1.0);
	double tmp;
	if (t <= -3.7e-244) {
		tmp = (x + (y * (z / t))) / t_1;
	} else if (t <= 2.1e-206) {
		tmp = (z / b) + (t * ((x / b) / y));
	} else {
		tmp = (x + (z * (y / t))) / t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (y * (b / t)) + (a + 1.0)
	tmp = 0
	if t <= -3.7e-244:
		tmp = (x + (y * (z / t))) / t_1
	elif t <= 2.1e-206:
		tmp = (z / b) + (t * ((x / b) / y))
	else:
		tmp = (x + (z * (y / t))) / t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y * Float64(b / t)) + Float64(a + 1.0))
	tmp = 0.0
	if (t <= -3.7e-244)
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / t_1);
	elseif (t <= 2.1e-206)
		tmp = Float64(Float64(z / b) + Float64(t * Float64(Float64(x / b) / y)));
	else
		tmp = Float64(Float64(x + Float64(z * Float64(y / t))) / t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (y * (b / t)) + (a + 1.0);
	tmp = 0.0;
	if (t <= -3.7e-244)
		tmp = (x + (y * (z / t))) / t_1;
	elseif (t <= 2.1e-206)
		tmp = (z / b) + (t * ((x / b) / y));
	else
		tmp = (x + (z * (y / t))) / t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.7e-244], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[t, 2.1e-206], N[(N[(z / b), $MachinePrecision] + N[(t * N[(N[(x / b), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.7000000000000002e-244

   1. Initial program 82.8%

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

      1. associate-/l* 85.1%

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

      2. associate-/l* 89.2%

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

   3. Simplified 89.2%

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

   if -3.7000000000000002e-244 < t < 2.1000000000000001e-206

   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* 32.6%

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

      2. associate-/l* 25.2%

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

   3. Simplified 25.2%

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

   5. Taylor expanded in x around inf 44.0%

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

      1. associate-*l/ 36.9%

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

      2. *-commutative 36.9%

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

      3. associate-/l* 35.9%

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

      4. *-commutative 35.9%

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

      5. associate-*l/ 32.3%

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

      6. *-commutative 32.3%

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

   7. Simplified 32.3%

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

   8. Taylor expanded in y around inf 72.5%

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

      1. associate-/r* 80.0%

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

   10. Simplified 80.0%

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

   11. Taylor expanded in y around inf 85.0%

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

       1. associate-/l* 85.1%

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

       2. associate-/r* 85.1%

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

   13. Simplified 85.1%

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

   if 2.1000000000000001e-206 < t

   1. Initial program 76.1%

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

      1. associate-/l* 73.8%

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

      2. associate-/l* 81.3%

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

   3. Simplified 81.3%

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

      1. clear-num 81.3%

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

      2. un-div-inv 81.3%

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

   6. Applied egg-rr 81.3%

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

      1. associate-/r/ 82.4%

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

   8. Applied egg-rr 82.4%

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

4. Final simplification 85.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.7 \cdot 10^{-244}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{y \cdot \frac{b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-206}:\\ \;\;\;\;\frac{z}{b} + t \cdot \frac{\frac{x}{b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{y \cdot \frac{b}{t} + \left(a + 1\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 79.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{b}{t} + \left(a + 1\right)\\ \mathbf{if}\;t \leq -5.1 \cdot 10^{-244}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{t\_1}\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{-205}:\\ \;\;\;\;\frac{z}{b} + t \cdot \frac{\frac{x}{b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{t\_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (* y (/ b t)) (+ a 1.0))))
   (if (<= t -5.1e-244)
     (/ (+ x (/ y (/ t z))) t_1)
     (if (<= t 1.95e-205)
       (+ (/ z b) (* t (/ (/ x b) y)))
       (/ (+ x (* z (/ y t))) t_1)))))

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 tmp;
	if (t <= -5.1e-244) {
		tmp = (x + (y / (t / z))) / t_1;
	} else if (t <= 1.95e-205) {
		tmp = (z / b) + (t * ((x / b) / y));
	} else {
		tmp = (x + (z * (y / t))) / 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 = (y * (b / t)) + (a + 1.0d0)
    if (t <= (-5.1d-244)) then
        tmp = (x + (y / (t / z))) / t_1
    else if (t <= 1.95d-205) then
        tmp = (z / b) + (t * ((x / b) / y))
    else
        tmp = (x + (z * (y / t))) / 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 = (y * (b / t)) + (a + 1.0);
	double tmp;
	if (t <= -5.1e-244) {
		tmp = (x + (y / (t / z))) / t_1;
	} else if (t <= 1.95e-205) {
		tmp = (z / b) + (t * ((x / b) / y));
	} else {
		tmp = (x + (z * (y / t))) / t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (y * (b / t)) + (a + 1.0)
	tmp = 0
	if t <= -5.1e-244:
		tmp = (x + (y / (t / z))) / t_1
	elif t <= 1.95e-205:
		tmp = (z / b) + (t * ((x / b) / y))
	else:
		tmp = (x + (z * (y / t))) / t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y * Float64(b / t)) + Float64(a + 1.0))
	tmp = 0.0
	if (t <= -5.1e-244)
		tmp = Float64(Float64(x + Float64(y / Float64(t / z))) / t_1);
	elseif (t <= 1.95e-205)
		tmp = Float64(Float64(z / b) + Float64(t * Float64(Float64(x / b) / y)));
	else
		tmp = Float64(Float64(x + Float64(z * Float64(y / t))) / t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (y * (b / t)) + (a + 1.0);
	tmp = 0.0;
	if (t <= -5.1e-244)
		tmp = (x + (y / (t / z))) / t_1;
	elseif (t <= 1.95e-205)
		tmp = (z / b) + (t * ((x / b) / y));
	else
		tmp = (x + (z * (y / t))) / t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.1e-244], N[(N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[t, 1.95e-205], N[(N[(z / b), $MachinePrecision] + N[(t * N[(N[(x / b), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.09999999999999981e-244

   1. Initial program 82.8%

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

      1. associate-/l* 85.1%

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

      2. associate-/l* 89.2%

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

   3. Simplified 89.2%

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

      1. clear-num 89.2%

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

      2. un-div-inv 89.6%

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

   6. Applied egg-rr 89.6%

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

   if -5.09999999999999981e-244 < t < 1.95000000000000009e-205

   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* 32.6%

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

      2. associate-/l* 25.2%

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

   3. Simplified 25.2%

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

   5. Taylor expanded in x around inf 44.0%

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

      1. associate-*l/ 36.9%

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

      2. *-commutative 36.9%

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

      3. associate-/l* 35.9%

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

      4. *-commutative 35.9%

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

      5. associate-*l/ 32.3%

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

      6. *-commutative 32.3%

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

   7. Simplified 32.3%

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

   8. Taylor expanded in y around inf 72.5%

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

      1. associate-/r* 80.0%

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

   10. Simplified 80.0%

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

   11. Taylor expanded in y around inf 85.0%

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

       1. associate-/l* 85.1%

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

       2. associate-/r* 85.1%

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

   13. Simplified 85.1%

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

   if 1.95000000000000009e-205 < t

   1. Initial program 76.1%

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

      1. associate-/l* 73.8%

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

      2. associate-/l* 81.3%

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

   3. Simplified 81.3%

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

      1. clear-num 81.3%

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

      2. un-div-inv 81.3%

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

   6. Applied egg-rr 81.3%

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

      1. associate-/r/ 82.4%

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

   8. Applied egg-rr 82.4%

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

4. Final simplification 86.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.1 \cdot 10^{-244}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{y \cdot \frac{b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{-205}:\\ \;\;\;\;\frac{z}{b} + t \cdot \frac{\frac{x}{b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{y \cdot \frac{b}{t} + \left(a + 1\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 40.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.1 \cdot 10^{+83}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;a \leq -1.6 \cdot 10^{-235}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 3 \cdot 10^{-153}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{+217}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -2.1e+83)
   (/ x a)
   (if (<= a -1.6e-235)
     (/ z b)
     (if (<= a 3e-153) x (if (<= a 1.2e+217) (/ z b) (/ x a))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -2.1e+83) {
		tmp = x / a;
	} else if (a <= -1.6e-235) {
		tmp = z / b;
	} else if (a <= 3e-153) {
		tmp = x;
	} else if (a <= 1.2e+217) {
		tmp = z / b;
	} else {
		tmp = x / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-2.1d+83)) then
        tmp = x / a
    else if (a <= (-1.6d-235)) then
        tmp = z / b
    else if (a <= 3d-153) then
        tmp = x
    else if (a <= 1.2d+217) then
        tmp = z / b
    else
        tmp = x / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -2.1e+83) {
		tmp = x / a;
	} else if (a <= -1.6e-235) {
		tmp = z / b;
	} else if (a <= 3e-153) {
		tmp = x;
	} else if (a <= 1.2e+217) {
		tmp = z / b;
	} else {
		tmp = x / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -2.1e+83:
		tmp = x / a
	elif a <= -1.6e-235:
		tmp = z / b
	elif a <= 3e-153:
		tmp = x
	elif a <= 1.2e+217:
		tmp = z / b
	else:
		tmp = x / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -2.1e+83)
		tmp = Float64(x / a);
	elseif (a <= -1.6e-235)
		tmp = Float64(z / b);
	elseif (a <= 3e-153)
		tmp = x;
	elseif (a <= 1.2e+217)
		tmp = Float64(z / b);
	else
		tmp = Float64(x / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -2.1e+83)
		tmp = x / a;
	elseif (a <= -1.6e-235)
		tmp = z / b;
	elseif (a <= 3e-153)
		tmp = x;
	elseif (a <= 1.2e+217)
		tmp = z / b;
	else
		tmp = x / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -2.1e+83], N[(x / a), $MachinePrecision], If[LessEqual[a, -1.6e-235], N[(z / b), $MachinePrecision], If[LessEqual[a, 3e-153], x, If[LessEqual[a, 1.2e+217], N[(z / b), $MachinePrecision], N[(x / a), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.10000000000000002e83 or 1.1999999999999999e217 < a

   1. Initial program 79.6%

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

      1. associate-/l* 79.8%

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

      2. associate-/l* 85.6%

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

   3. Simplified 85.6%

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

   5. Taylor expanded in x around inf 61.7%

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

   6. Taylor expanded in a around inf 59.8%

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

   if -2.10000000000000002e83 < a < -1.6000000000000001e-235 or 3e-153 < a < 1.1999999999999999e217

   1. Initial program 71.5%

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

      1. associate-/l* 69.5%

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

      2. associate-/l* 74.0%

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

   3. Simplified 74.0%

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

   5. Taylor expanded in y around inf 42.9%

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

   if -1.6000000000000001e-235 < a < 3e-153

   1. Initial program 84.5%

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

      1. associate-/l* 84.7%

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

      2. associate-/l* 86.9%

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

   3. Simplified 86.9%

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

   5. Taylor expanded in a around 0 84.7%

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

      1. associate-*l/ 86.9%

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

      2. *-commutative 86.9%

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

   7. Simplified 86.9%

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

   8. Taylor expanded in y around 0 52.5%

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

4. Final simplification 49.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.1 \cdot 10^{+83}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;a \leq -1.6 \cdot 10^{-235}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 3 \cdot 10^{-153}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{+217}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 55.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.62 \cdot 10^{+111} \lor \neg \left(y \leq 4.7 \cdot 10^{+17}\right):\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.62e+111) (not (<= y 4.7e+17))) (/ 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 <= -1.62e+111) || !(y <= 4.7e+17)) {
		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 <= (-1.62d+111)) .or. (.not. (y <= 4.7d+17))) 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 <= -1.62e+111) || !(y <= 4.7e+17)) {
		tmp = z / b;
	} else {
		tmp = x / (a + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.62e+111) or not (y <= 4.7e+17):
		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 <= -1.62e+111) || !(y <= 4.7e+17))
		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 <= -1.62e+111) || ~((y <= 4.7e+17)))
		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, -1.62e+111], N[Not[LessEqual[y, 4.7e+17]], $MachinePrecision]], N[(z / b), $MachinePrecision], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.61999999999999999e111 or 4.7e17 < y

   1. Initial program 53.3%

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

      1. associate-/l* 56.8%

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

      2. associate-/l* 68.0%

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

   3. Simplified 68.0%

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

   5. Taylor expanded in y around inf 57.0%

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

   if -1.61999999999999999e111 < y < 4.7e17

   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* 90.2%

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

      2. associate-/l* 88.8%

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

   3. Simplified 88.8%

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

   5. Taylor expanded in y around 0 63.9%

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

4. Final simplification 60.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.62 \cdot 10^{+111} \lor \neg \left(y \leq 4.7 \cdot 10^{+17}\right):\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 41.3% accurate, 1.3× speedup

Math

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

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -1.0) (not (<= a 1.0))) (/ 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 <= 1.0)) {
		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 <= 1.0d0))) 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 <= 1.0)) {
		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 <= 1.0):
		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 <= 1.0))
		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 <= 1.0)))
		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, 1.0]], $MachinePrecision]], N[(x / a), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if a < -1 or 1 < a

   1. Initial program 77.4%

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

      1. associate-/l* 75.3%

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

      2. associate-/l* 80.5%

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

   3. Simplified 80.5%

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

   5. Taylor expanded in x around inf 56.2%

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

   6. Taylor expanded in a around inf 48.6%

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

   if -1 < a < 1

   1. Initial program 74.3%

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

      1. associate-/l* 74.3%

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

      2. associate-/l* 77.9%

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

   3. Simplified 77.9%

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

   5. Taylor expanded in a around 0 73.4%

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

      1. associate-*l/ 77.1%

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

      2. *-commutative 77.1%

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

   7. Simplified 77.1%

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

   8. Taylor expanded in y around 0 35.6%

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

4. Final simplification 42.1%

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

Alternative 18: 19.8% 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 75.9%

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

   1. associate-/l* 74.8%

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

   2. associate-/l* 79.2%

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

3. Simplified 79.2%

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

5. Taylor expanded in a around 0 46.4%

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

   1. associate-*l/ 49.9%

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

   2. *-commutative 49.9%

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

7. Simplified 49.9%

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

8. Taylor expanded in y around 0 19.6%

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

9. Final simplification 19.6%

   \[\leadsto x \]
10. Add Preprocessing

Developer target: 79.7% 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 2024080 
(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))))