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

Percentage Accurate: 76.1% → 90.8%

Time: 19.2s

Alternatives: 16

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: 76.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 90.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot b}{t}\\ t_2 := \frac{x + \frac{y \cdot z}{t}}{t\_1 + \left(a + 1\right)}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{y \cdot \frac{b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{-298}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;\frac{y \cdot z}{y \cdot b + t \cdot \left(a + 1\right)}\\ \mathbf{elif}\;t\_2 \leq 10^{+303}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{1 + \left(a + t\_1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* y b) t)) (t_2 (/ (+ x (/ (* y z) t)) (+ t_1 (+ a 1.0)))))
   (if (<= t_2 (- INFINITY))
     (/ (+ x (* y (/ z t))) (+ (* y (/ b t)) (+ a 1.0)))
     (if (<= t_2 -5e-298)
       t_2
       (if (<= t_2 0.0)
         (/ (* y z) (+ (* y b) (* t (+ a 1.0))))
         (if (<= t_2 1e+303)
           t_2
           (if (<= t_2 INFINITY)
             (* (/ y t) (/ z (+ 1.0 (+ a t_1))))
             (/ z b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y * b) / t;
	double t_2 = (x + ((y * z) / t)) / (t_1 + (a + 1.0));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = (x + (y * (z / t))) / ((y * (b / t)) + (a + 1.0));
	} else if (t_2 <= -5e-298) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = (y * z) / ((y * b) + (t * (a + 1.0)));
	} else if (t_2 <= 1e+303) {
		tmp = t_2;
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = (y / t) * (z / (1.0 + (a + t_1)));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y * b) / t;
	double t_2 = (x + ((y * z) / t)) / (t_1 + (a + 1.0));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = (x + (y * (z / t))) / ((y * (b / t)) + (a + 1.0));
	} else if (t_2 <= -5e-298) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = (y * z) / ((y * b) + (t * (a + 1.0)));
	} else if (t_2 <= 1e+303) {
		tmp = t_2;
	} else if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = (y / t) * (z / (1.0 + (a + t_1)));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (y * b) / t
	t_2 = (x + ((y * z) / t)) / (t_1 + (a + 1.0))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = (x + (y * (z / t))) / ((y * (b / t)) + (a + 1.0))
	elif t_2 <= -5e-298:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = (y * z) / ((y * b) + (t * (a + 1.0)))
	elif t_2 <= 1e+303:
		tmp = t_2
	elif t_2 <= math.inf:
		tmp = (y / t) * (z / (1.0 + (a + t_1)))
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y * b) / t)
	t_2 = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(t_1 + Float64(a + 1.0)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(Float64(y * Float64(b / t)) + Float64(a + 1.0)));
	elseif (t_2 <= -5e-298)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = Float64(Float64(y * z) / Float64(Float64(y * b) + Float64(t * Float64(a + 1.0))));
	elseif (t_2 <= 1e+303)
		tmp = t_2;
	elseif (t_2 <= Inf)
		tmp = Float64(Float64(y / t) * Float64(z / Float64(1.0 + Float64(a + t_1))));
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (y * b) / t;
	t_2 = (x + ((y * z) / t)) / (t_1 + (a + 1.0));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = (x + (y * (z / t))) / ((y * (b / t)) + (a + 1.0));
	elseif (t_2 <= -5e-298)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = (y * z) / ((y * b) + (t * (a + 1.0)));
	elseif (t_2 <= 1e+303)
		tmp = t_2;
	elseif (t_2 <= Inf)
		tmp = (y / t) * (z / (1.0 + (a + t_1)));
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(t$95$1 + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], 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], If[LessEqual[t$95$2, -5e-298], t$95$2, If[LessEqual[t$95$2, 0.0], N[(N[(y * z), $MachinePrecision] / N[(N[(y * b), $MachinePrecision] + N[(t * N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+303], t$95$2, If[LessEqual[t$95$2, Infinity], N[(N[(y / t), $MachinePrecision] * N[(z / N[(1.0 + N[(a + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 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 52.2%

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

      1. *-commutative 52.2%

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

      2. associate-*l/ 86.8%

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

      3. *-commutative 86.8%

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

      4. associate-*l/ 86.7%

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

   3. Simplified 86.7%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < -5.0000000000000002e-298 or 0.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 1e303

   1. Initial program 99.7%

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

   if -5.0000000000000002e-298 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 0.0

   1. Initial program 62.9%

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

      1. *-commutative 62.9%

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

      2. associate-*l/ 62.8%

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

      3. *-commutative 62.8%

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

      4. associate-*l/ 69.3%

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

   3. Simplified 69.3%

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

   5. Taylor expanded in x around 0 62.9%

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

   6. Taylor expanded in t around 0 80.4%

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

   if 1e303 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < +inf.0

   1. Initial program 31.1%

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

      1. *-commutative 31.1%

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

      2. associate-*l/ 37.3%

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

      3. *-commutative 37.3%

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

      4. associate-*l/ 37.3%

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

   3. Simplified 37.3%

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

   5. Taylor expanded in x around 0 62.0%

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

      1. times-frac 99.5%

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

      2. associate-+r+ 99.5%

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

      3. associate-/l* 93.0%

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

      4. +-commutative 93.0%

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

      5. associate-/l* 99.5%

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

      6. associate-*r/ 92.8%

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

      7. fma-define 92.9%

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

   7. Simplified 92.9%

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

   8. Taylor expanded in z around 0 99.5%

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

   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. *-commutative 0.0%

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

      2. associate-*l/ 0.3%

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

      3. *-commutative 0.3%

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

      4. associate-*l/ 9.7%

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

   3. Simplified 9.7%

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

   5. Taylor expanded in t around 0 93.8%

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

4. Final simplification 95.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -\infty:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{y \cdot \frac{b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -5 \cdot 10^{-298}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 0:\\ \;\;\;\;\frac{y \cdot z}{y \cdot b + t \cdot \left(a + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 10^{+303}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq \infty:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 60.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.35 \cdot 10^{-39}:\\ \;\;\;\;\frac{x}{y \cdot \frac{b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;t \leq -2.9 \cdot 10^{-138}:\\ \;\;\;\;\frac{y \cdot z}{y \cdot b + t \cdot \left(a + 1\right)}\\ \mathbf{elif}\;t \leq -5 \cdot 10^{-186}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-107}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{-41}:\\ \;\;\;\;\frac{x}{1 + b \cdot \frac{y}{t}}\\ \mathbf{elif}\;t \leq 4.55 \cdot 10^{+24}:\\ \;\;\;\;\frac{x}{a} + \frac{\frac{y}{t}}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -2.35e-39)
   (/ x (+ (* y (/ b t)) (+ a 1.0)))
   (if (<= t -2.9e-138)
     (/ (* y z) (+ (* y b) (* t (+ a 1.0))))
     (if (<= t -5e-186)
       (/ x (+ 1.0 (+ a (/ (* y b) t))))
       (if (<= t 4.8e-107)
         (/ z b)
         (if (<= t 3.7e-41)
           (/ x (+ 1.0 (* b (/ y t))))
           (if (<= t 4.55e+24)
             (+ (/ x a) (/ (/ y t) (/ a z)))
             (/ (+ 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 (t <= -2.35e-39) {
		tmp = x / ((y * (b / t)) + (a + 1.0));
	} else if (t <= -2.9e-138) {
		tmp = (y * z) / ((y * b) + (t * (a + 1.0)));
	} else if (t <= -5e-186) {
		tmp = x / (1.0 + (a + ((y * b) / t)));
	} else if (t <= 4.8e-107) {
		tmp = z / b;
	} else if (t <= 3.7e-41) {
		tmp = x / (1.0 + (b * (y / t)));
	} else if (t <= 4.55e+24) {
		tmp = (x / a) + ((y / t) / (a / z));
	} 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 (t <= (-2.35d-39)) then
        tmp = x / ((y * (b / t)) + (a + 1.0d0))
    else if (t <= (-2.9d-138)) then
        tmp = (y * z) / ((y * b) + (t * (a + 1.0d0)))
    else if (t <= (-5d-186)) then
        tmp = x / (1.0d0 + (a + ((y * b) / t)))
    else if (t <= 4.8d-107) then
        tmp = z / b
    else if (t <= 3.7d-41) then
        tmp = x / (1.0d0 + (b * (y / t)))
    else if (t <= 4.55d+24) then
        tmp = (x / a) + ((y / t) / (a / z))
    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 (t <= -2.35e-39) {
		tmp = x / ((y * (b / t)) + (a + 1.0));
	} else if (t <= -2.9e-138) {
		tmp = (y * z) / ((y * b) + (t * (a + 1.0)));
	} else if (t <= -5e-186) {
		tmp = x / (1.0 + (a + ((y * b) / t)));
	} else if (t <= 4.8e-107) {
		tmp = z / b;
	} else if (t <= 3.7e-41) {
		tmp = x / (1.0 + (b * (y / t)));
	} else if (t <= 4.55e+24) {
		tmp = (x / a) + ((y / t) / (a / z));
	} else {
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -2.35e-39:
		tmp = x / ((y * (b / t)) + (a + 1.0))
	elif t <= -2.9e-138:
		tmp = (y * z) / ((y * b) + (t * (a + 1.0)))
	elif t <= -5e-186:
		tmp = x / (1.0 + (a + ((y * b) / t)))
	elif t <= 4.8e-107:
		tmp = z / b
	elif t <= 3.7e-41:
		tmp = x / (1.0 + (b * (y / t)))
	elif t <= 4.55e+24:
		tmp = (x / a) + ((y / t) / (a / z))
	else:
		tmp = (x + ((y * z) / t)) / (a + 1.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -2.35e-39)
		tmp = Float64(x / Float64(Float64(y * Float64(b / t)) + Float64(a + 1.0)));
	elseif (t <= -2.9e-138)
		tmp = Float64(Float64(y * z) / Float64(Float64(y * b) + Float64(t * Float64(a + 1.0))));
	elseif (t <= -5e-186)
		tmp = Float64(x / Float64(1.0 + Float64(a + Float64(Float64(y * b) / t))));
	elseif (t <= 4.8e-107)
		tmp = Float64(z / b);
	elseif (t <= 3.7e-41)
		tmp = Float64(x / Float64(1.0 + Float64(b * Float64(y / t))));
	elseif (t <= 4.55e+24)
		tmp = Float64(Float64(x / a) + Float64(Float64(y / t) / Float64(a / z)));
	else
		tmp = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(a + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -2.35e-39)
		tmp = x / ((y * (b / t)) + (a + 1.0));
	elseif (t <= -2.9e-138)
		tmp = (y * z) / ((y * b) + (t * (a + 1.0)));
	elseif (t <= -5e-186)
		tmp = x / (1.0 + (a + ((y * b) / t)));
	elseif (t <= 4.8e-107)
		tmp = z / b;
	elseif (t <= 3.7e-41)
		tmp = x / (1.0 + (b * (y / t)));
	elseif (t <= 4.55e+24)
		tmp = (x / a) + ((y / t) / (a / z));
	else
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -2.35e-39], N[(x / N[(N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.9e-138], N[(N[(y * z), $MachinePrecision] / N[(N[(y * b), $MachinePrecision] + N[(t * N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -5e-186], N[(x / N[(1.0 + N[(a + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.8e-107], N[(z / b), $MachinePrecision], If[LessEqual[t, 3.7e-41], N[(x / N[(1.0 + N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.55e+24], N[(N[(x / a), $MachinePrecision] + N[(N[(y / t), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 7 regimes

2. if t < -2.3500000000000001e-39

   1. Initial program 83.7%

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

      1. *-commutative 83.7%

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

      2. associate-*l/ 86.7%

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

      3. *-commutative 86.7%

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

      4. associate-*l/ 92.5%

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

   3. Simplified 92.5%

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

   5. Taylor expanded in x around inf 73.5%

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

   if -2.3500000000000001e-39 < t < -2.89999999999999973e-138

   1. Initial program 64.4%

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

      1. *-commutative 64.4%

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

      2. associate-*l/ 64.5%

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

      3. *-commutative 64.5%

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

      4. associate-*l/ 64.5%

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

   3. Simplified 64.5%

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

   5. Taylor expanded in x around 0 59.5%

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

   6. Taylor expanded in t around 0 64.4%

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

   if -2.89999999999999973e-138 < t < -5e-186

   1. Initial program 86.4%

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

      1. *-commutative 86.4%

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

      2. associate-*l/ 80.2%

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

      3. *-commutative 80.2%

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

      4. associate-*l/ 60.9%

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

   3. Simplified 60.9%

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

   5. Taylor expanded in x around inf 73.9%

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

   if -5e-186 < t < 4.79999999999999989e-107

   1. Initial program 56.0%

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

      1. *-commutative 56.0%

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

      2. associate-*l/ 46.2%

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

      3. *-commutative 46.2%

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

      4. associate-*l/ 41.9%

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

   3. Simplified 41.9%

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

   5. Taylor expanded in t around 0 70.5%

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

   if 4.79999999999999989e-107 < t < 3.7000000000000002e-41

   1. Initial program 88.8%

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

      1. *-commutative 88.8%

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

      2. associate-*l/ 82.9%

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

      3. *-commutative 82.9%

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

      4. associate-*l/ 77.3%

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

   3. Simplified 77.3%

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

   5. Taylor expanded in x around inf 60.4%

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

   6. Taylor expanded in a around 0 66.1%

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

      1. associate-*r/ 66.2%

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

   8. Simplified 66.2%

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

   if 3.7000000000000002e-41 < t < 4.5499999999999997e24

   1. Initial program 78.1%

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

      1. *-commutative 78.1%

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

      2. associate-*l/ 70.6%

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

      3. *-commutative 70.6%

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

      4. associate-*l/ 70.6%

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

   3. Simplified 70.6%

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

   5. Taylor expanded in a around inf 59.1%

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

   6. Taylor expanded in x around 0 59.0%

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

      1. *-commutative 59.0%

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

      2. associate-*l/ 59.2%

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

      3. *-commutative 59.2%

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

   8. Simplified 59.2%

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

      1. associate-*r/ 59.0%

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

      2. *-commutative 59.0%

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

      3. times-frac 77.4%

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

      4. clear-num 77.3%

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

      5. times-frac 77.3%

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

      6. *-un-lft-identity 77.3%

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

      7. *-commutative 77.3%

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

      8. associate-/r* 77.3%

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

   10. Applied egg-rr 77.3%

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

   if 4.5499999999999997e24 < t

   1. Initial program 83.0%

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

      1. *-commutative 83.0%

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

      2. associate-*l/ 86.4%

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

      3. *-commutative 86.4%

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

      4. associate-*l/ 89.9%

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

   3. Simplified 89.9%

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

   5. Taylor expanded in b around 0 76.2%

      \[\leadsto \color{blue}{\frac{x + \frac{y \cdot z}{t}}{1 + a}} \]
3. Recombined 7 regimes into one program.

4. Final simplification 72.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.35 \cdot 10^{-39}:\\ \;\;\;\;\frac{x}{y \cdot \frac{b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;t \leq -2.9 \cdot 10^{-138}:\\ \;\;\;\;\frac{y \cdot z}{y \cdot b + t \cdot \left(a + 1\right)}\\ \mathbf{elif}\;t \leq -5 \cdot 10^{-186}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-107}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{-41}:\\ \;\;\;\;\frac{x}{1 + b \cdot \frac{y}{t}}\\ \mathbf{elif}\;t \leq 4.55 \cdot 10^{+24}:\\ \;\;\;\;\frac{x}{a} + \frac{\frac{y}{t}}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 59.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 1 + \left(a + \frac{y \cdot b}{t}\right)\\ \mathbf{if}\;z \leq -1.08 \cdot 10^{-27}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{t\_1}\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{+38}:\\ \;\;\;\;\frac{x}{t\_1}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+142} \lor \neg \left(z \leq 4 \cdot 10^{+158}\right) \land z \leq 9.8 \cdot 10^{+181}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ 1.0 (+ a (/ (* y b) t)))))
   (if (<= z -1.08e-27)
     (* (/ y t) (/ z t_1))
     (if (<= z 4.1e+38)
       (/ x t_1)
       (if (or (<= z 1.2e+142) (and (not (<= z 4e+158)) (<= z 9.8e+181)))
         (/ (+ x (/ (* y z) t)) (+ a 1.0))
         (/ z b))))))

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 (z <= -1.08e-27) {
		tmp = (y / t) * (z / t_1);
	} else if (z <= 4.1e+38) {
		tmp = x / t_1;
	} else if ((z <= 1.2e+142) || (!(z <= 4e+158) && (z <= 9.8e+181))) {
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	} else {
		tmp = z / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 1.0d0 + (a + ((y * b) / t))
    if (z <= (-1.08d-27)) then
        tmp = (y / t) * (z / t_1)
    else if (z <= 4.1d+38) then
        tmp = x / t_1
    else if ((z <= 1.2d+142) .or. (.not. (z <= 4d+158)) .and. (z <= 9.8d+181)) then
        tmp = (x + ((y * z) / t)) / (a + 1.0d0)
    else
        tmp = z / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 1.0 + (a + ((y * b) / t));
	double tmp;
	if (z <= -1.08e-27) {
		tmp = (y / t) * (z / t_1);
	} else if (z <= 4.1e+38) {
		tmp = x / t_1;
	} else if ((z <= 1.2e+142) || (!(z <= 4e+158) && (z <= 9.8e+181))) {
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = 1.0 + (a + ((y * b) / t))
	tmp = 0
	if z <= -1.08e-27:
		tmp = (y / t) * (z / t_1)
	elif z <= 4.1e+38:
		tmp = x / t_1
	elif (z <= 1.2e+142) or (not (z <= 4e+158) and (z <= 9.8e+181)):
		tmp = (x + ((y * z) / t)) / (a + 1.0)
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(1.0 + Float64(a + Float64(Float64(y * b) / t)))
	tmp = 0.0
	if (z <= -1.08e-27)
		tmp = Float64(Float64(y / t) * Float64(z / t_1));
	elseif (z <= 4.1e+38)
		tmp = Float64(x / t_1);
	elseif ((z <= 1.2e+142) || (!(z <= 4e+158) && (z <= 9.8e+181)))
		tmp = Float64(Float64(x + Float64(Float64(y * z) / 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 = 1.0 + (a + ((y * b) / t));
	tmp = 0.0;
	if (z <= -1.08e-27)
		tmp = (y / t) * (z / t_1);
	elseif (z <= 4.1e+38)
		tmp = x / t_1;
	elseif ((z <= 1.2e+142) || (~((z <= 4e+158)) && (z <= 9.8e+181)))
		tmp = (x + ((y * z) / 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[(1.0 + N[(a + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.08e-27], N[(N[(y / t), $MachinePrecision] * N[(z / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.1e+38], N[(x / t$95$1), $MachinePrecision], If[Or[LessEqual[z, 1.2e+142], And[N[Not[LessEqual[z, 4e+158]], $MachinePrecision], LessEqual[z, 9.8e+181]]], N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.08e-27

   1. Initial program 61.1%

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

      1. *-commutative 61.1%

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

      2. associate-*l/ 62.9%

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

      3. *-commutative 62.9%

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

      4. associate-*l/ 62.9%

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

   3. Simplified 62.9%

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

   5. Taylor expanded in x around 0 42.0%

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

      1. times-frac 55.3%

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

      2. associate-+r+ 55.3%

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

      3. associate-/l* 51.8%

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

      4. +-commutative 51.8%

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

      5. associate-/l* 55.3%

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

      6. associate-*r/ 51.8%

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

      7. fma-define 51.8%

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

   7. Simplified 51.8%

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

   8. Taylor expanded in z around 0 55.3%

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

   if -1.08e-27 < z < 4.1000000000000003e38

   1. Initial program 88.0%

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

      1. *-commutative 88.0%

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

      2. associate-*l/ 86.6%

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

      3. *-commutative 86.6%

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

      4. associate-*l/ 85.8%

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

   3. Simplified 85.8%

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

   5. Taylor expanded in x around inf 79.4%

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

   if 4.1000000000000003e38 < z < 1.2e142 or 3.99999999999999981e158 < z < 9.79999999999999963e181

   1. Initial program 95.6%

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

      1. *-commutative 95.6%

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

      2. associate-*l/ 82.8%

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

      3. *-commutative 82.8%

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

      4. associate-*l/ 78.6%

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

   3. Simplified 78.6%

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

   5. Taylor expanded in b around 0 87.1%

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

   if 1.2e142 < z < 3.99999999999999981e158 or 9.79999999999999963e181 < z

   1. Initial program 45.8%

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

      1. *-commutative 45.8%

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

      2. associate-*l/ 41.9%

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

      3. *-commutative 41.9%

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

      4. associate-*l/ 43.8%

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

   3. Simplified 43.8%

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

   5. Taylor expanded in t around 0 62.1%

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

4. Final simplification 71.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.08 \cdot 10^{-27}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{+38}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+142} \lor \neg \left(z \leq 4 \cdot 10^{+158}\right) \land z \leq 9.8 \cdot 10^{+181}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 52.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 + b \cdot \frac{y}{t}}\\ t_2 := \frac{x}{a + 1}\\ \mathbf{if}\;t \leq -5.2 \cdot 10^{+36}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1.95 \cdot 10^{-123}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.45 \cdot 10^{-107}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-38}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+87}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (+ 1.0 (* b (/ y t))))) (t_2 (/ x (+ a 1.0))))
   (if (<= t -5.2e+36)
     t_2
     (if (<= t -1.95e-123)
       t_1
       (if (<= t 2.45e-107)
         (/ z b)
         (if (<= t 4e-38)
           t_1
           (if (<= t 5.5e+87) (* (/ y t) (/ z (+ a 1.0))) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 + (b * (y / t)));
	double t_2 = x / (a + 1.0);
	double tmp;
	if (t <= -5.2e+36) {
		tmp = t_2;
	} else if (t <= -1.95e-123) {
		tmp = t_1;
	} else if (t <= 2.45e-107) {
		tmp = z / b;
	} else if (t <= 4e-38) {
		tmp = t_1;
	} else if (t <= 5.5e+87) {
		tmp = (y / t) * (z / (a + 1.0));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x / (1.0d0 + (b * (y / t)))
    t_2 = x / (a + 1.0d0)
    if (t <= (-5.2d+36)) then
        tmp = t_2
    else if (t <= (-1.95d-123)) then
        tmp = t_1
    else if (t <= 2.45d-107) then
        tmp = z / b
    else if (t <= 4d-38) then
        tmp = t_1
    else if (t <= 5.5d+87) then
        tmp = (y / t) * (z / (a + 1.0d0))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 + (b * (y / t)));
	double t_2 = x / (a + 1.0);
	double tmp;
	if (t <= -5.2e+36) {
		tmp = t_2;
	} else if (t <= -1.95e-123) {
		tmp = t_1;
	} else if (t <= 2.45e-107) {
		tmp = z / b;
	} else if (t <= 4e-38) {
		tmp = t_1;
	} else if (t <= 5.5e+87) {
		tmp = (y / t) * (z / (a + 1.0));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (1.0 + (b * (y / t)))
	t_2 = x / (a + 1.0)
	tmp = 0
	if t <= -5.2e+36:
		tmp = t_2
	elif t <= -1.95e-123:
		tmp = t_1
	elif t <= 2.45e-107:
		tmp = z / b
	elif t <= 4e-38:
		tmp = t_1
	elif t <= 5.5e+87:
		tmp = (y / t) * (z / (a + 1.0))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(1.0 + Float64(b * Float64(y / t))))
	t_2 = Float64(x / Float64(a + 1.0))
	tmp = 0.0
	if (t <= -5.2e+36)
		tmp = t_2;
	elseif (t <= -1.95e-123)
		tmp = t_1;
	elseif (t <= 2.45e-107)
		tmp = Float64(z / b);
	elseif (t <= 4e-38)
		tmp = t_1;
	elseif (t <= 5.5e+87)
		tmp = Float64(Float64(y / t) * Float64(z / Float64(a + 1.0)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (1.0 + (b * (y / t)));
	t_2 = x / (a + 1.0);
	tmp = 0.0;
	if (t <= -5.2e+36)
		tmp = t_2;
	elseif (t <= -1.95e-123)
		tmp = t_1;
	elseif (t <= 2.45e-107)
		tmp = z / b;
	elseif (t <= 4e-38)
		tmp = t_1;
	elseif (t <= 5.5e+87)
		tmp = (y / t) * (z / (a + 1.0));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(1.0 + N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.2e+36], t$95$2, If[LessEqual[t, -1.95e-123], t$95$1, If[LessEqual[t, 2.45e-107], N[(z / b), $MachinePrecision], If[LessEqual[t, 4e-38], t$95$1, If[LessEqual[t, 5.5e+87], N[(N[(y / t), $MachinePrecision] * N[(z / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -5.2000000000000003e36 or 5.50000000000000022e87 < t

   1. Initial program 82.6%

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

      1. *-commutative 82.6%

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

      2. associate-*l/ 87.8%

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

      3. *-commutative 87.8%

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

      4. associate-*l/ 93.8%

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

   3. Simplified 93.8%

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

   5. Taylor expanded in t around inf 69.6%

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

   if -5.2000000000000003e36 < t < -1.94999999999999988e-123 or 2.4499999999999999e-107 < t < 3.9999999999999998e-38

   1. Initial program 83.4%

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

      1. *-commutative 83.4%

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

      2. associate-*l/ 81.3%

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

      3. *-commutative 81.3%

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

      4. associate-*l/ 79.4%

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

   3. Simplified 79.4%

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

   5. Taylor expanded in x around inf 57.2%

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

   6. Taylor expanded in a around 0 51.2%

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

      1. associate-*r/ 51.2%

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

   8. Simplified 51.2%

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

   if -1.94999999999999988e-123 < t < 2.4499999999999999e-107

   1. Initial program 59.8%

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

      1. *-commutative 59.8%

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

      2. associate-*l/ 51.1%

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

      3. *-commutative 51.1%

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

      4. associate-*l/ 44.5%

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

   3. Simplified 44.5%

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

   5. Taylor expanded in t around 0 67.1%

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

   if 3.9999999999999998e-38 < t < 5.50000000000000022e87

   1. Initial program 81.8%

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

      1. *-commutative 81.8%

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

      2. associate-*l/ 74.4%

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

      3. *-commutative 74.4%

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

      4. associate-*l/ 74.4%

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

   3. Simplified 74.4%

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

   5. Taylor expanded in x around 0 55.6%

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

      1. times-frac 70.3%

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

      2. associate-+r+ 70.3%

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

      3. associate-/l* 70.3%

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

      4. +-commutative 70.3%

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

      5. associate-/l* 70.3%

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

      6. associate-*r/ 70.3%

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

      7. fma-define 70.3%

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

   7. Simplified 70.3%

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

   8. Taylor expanded in b around 0 58.7%

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

4. Final simplification 64.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{+36}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{elif}\;t \leq -1.95 \cdot 10^{-123}:\\ \;\;\;\;\frac{x}{1 + b \cdot \frac{y}{t}}\\ \mathbf{elif}\;t \leq 2.45 \cdot 10^{-107}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-38}:\\ \;\;\;\;\frac{x}{1 + b \cdot \frac{y}{t}}\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+87}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 59.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y \cdot \frac{b}{t} + \left(a + 1\right)}\\ \mathbf{if}\;t \leq -1.25 \cdot 10^{-123}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{-106}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-40}:\\ \;\;\;\;\frac{x}{1 + b \cdot \frac{y}{t}}\\ \mathbf{elif}\;t \leq 6.6 \cdot 10^{+43}:\\ \;\;\;\;\frac{x}{a} + \frac{\frac{y}{t}}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (+ (* y (/ b t)) (+ a 1.0)))))
   (if (<= t -1.25e-123)
     t_1
     (if (<= t 1.1e-106)
       (/ z b)
       (if (<= t 1.3e-40)
         (/ x (+ 1.0 (* b (/ y t))))
         (if (<= t 6.6e+43) (+ (/ x a) (/ (/ y t) (/ a z))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / ((y * (b / t)) + (a + 1.0));
	double tmp;
	if (t <= -1.25e-123) {
		tmp = t_1;
	} else if (t <= 1.1e-106) {
		tmp = z / b;
	} else if (t <= 1.3e-40) {
		tmp = x / (1.0 + (b * (y / t)));
	} else if (t <= 6.6e+43) {
		tmp = (x / a) + ((y / t) / (a / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / ((y * (b / t)) + (a + 1.0d0))
    if (t <= (-1.25d-123)) then
        tmp = t_1
    else if (t <= 1.1d-106) then
        tmp = z / b
    else if (t <= 1.3d-40) then
        tmp = x / (1.0d0 + (b * (y / t)))
    else if (t <= 6.6d+43) then
        tmp = (x / a) + ((y / t) / (a / z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / ((y * (b / t)) + (a + 1.0));
	double tmp;
	if (t <= -1.25e-123) {
		tmp = t_1;
	} else if (t <= 1.1e-106) {
		tmp = z / b;
	} else if (t <= 1.3e-40) {
		tmp = x / (1.0 + (b * (y / t)));
	} else if (t <= 6.6e+43) {
		tmp = (x / a) + ((y / t) / (a / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / ((y * (b / t)) + (a + 1.0))
	tmp = 0
	if t <= -1.25e-123:
		tmp = t_1
	elif t <= 1.1e-106:
		tmp = z / b
	elif t <= 1.3e-40:
		tmp = x / (1.0 + (b * (y / t)))
	elif t <= 6.6e+43:
		tmp = (x / a) + ((y / t) / (a / z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(Float64(y * Float64(b / t)) + Float64(a + 1.0)))
	tmp = 0.0
	if (t <= -1.25e-123)
		tmp = t_1;
	elseif (t <= 1.1e-106)
		tmp = Float64(z / b);
	elseif (t <= 1.3e-40)
		tmp = Float64(x / Float64(1.0 + Float64(b * Float64(y / t))));
	elseif (t <= 6.6e+43)
		tmp = Float64(Float64(x / a) + Float64(Float64(y / t) / Float64(a / z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / ((y * (b / t)) + (a + 1.0));
	tmp = 0.0;
	if (t <= -1.25e-123)
		tmp = t_1;
	elseif (t <= 1.1e-106)
		tmp = z / b;
	elseif (t <= 1.3e-40)
		tmp = x / (1.0 + (b * (y / t)));
	elseif (t <= 6.6e+43)
		tmp = (x / a) + ((y / t) / (a / z));
	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[(y * N[(b / t), $MachinePrecision]), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.25e-123], t$95$1, If[LessEqual[t, 1.1e-106], N[(z / b), $MachinePrecision], If[LessEqual[t, 1.3e-40], N[(x / N[(1.0 + N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.6e+43], N[(N[(x / a), $MachinePrecision] + N[(N[(y / t), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.25000000000000007e-123 or 6.6000000000000003e43 < t

   1. Initial program 82.4%

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

      1. *-commutative 82.4%

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

      2. associate-*l/ 85.4%

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

      3. *-commutative 85.4%

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

      4. associate-*l/ 89.7%

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

   3. Simplified 89.7%

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

   5. Taylor expanded in x around inf 70.4%

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

   if -1.25000000000000007e-123 < t < 1.09999999999999997e-106

   1. Initial program 59.8%

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

      1. *-commutative 59.8%

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

      2. associate-*l/ 51.1%

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

      3. *-commutative 51.1%

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

      4. associate-*l/ 44.5%

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

   3. Simplified 44.5%

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

   5. Taylor expanded in t around 0 67.1%

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

   if 1.09999999999999997e-106 < t < 1.3000000000000001e-40

   1. Initial program 88.8%

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

      1. *-commutative 88.8%

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

      2. associate-*l/ 82.9%

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

      3. *-commutative 82.9%

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

      4. associate-*l/ 77.3%

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

   3. Simplified 77.3%

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

   5. Taylor expanded in x around inf 60.4%

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

   6. Taylor expanded in a around 0 66.1%

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

      1. associate-*r/ 66.2%

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

   8. Simplified 66.2%

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

   if 1.3000000000000001e-40 < t < 6.6000000000000003e43

   1. Initial program 78.9%

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

      1. *-commutative 78.9%

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

      2. associate-*l/ 73.5%

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

      3. *-commutative 73.5%

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

      4. associate-*l/ 73.5%

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

   3. Simplified 73.5%

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

   5. Taylor expanded in a around inf 54.3%

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

   6. Taylor expanded in x around 0 54.0%

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

      1. *-commutative 54.0%

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

      2. associate-*l/ 54.2%

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

      3. *-commutative 54.2%

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

   8. Simplified 54.2%

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

      1. associate-*r/ 54.0%

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

      2. *-commutative 54.0%

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

      3. times-frac 72.8%

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

      4. clear-num 72.7%

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

      5. times-frac 72.7%

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

      6. *-un-lft-identity 72.7%

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

      7. *-commutative 72.7%

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

      8. associate-/r* 72.8%

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

   10. Applied egg-rr 72.8%

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

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.25 \cdot 10^{-123}:\\ \;\;\;\;\frac{x}{y \cdot \frac{b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{-106}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-40}:\\ \;\;\;\;\frac{x}{1 + b \cdot \frac{y}{t}}\\ \mathbf{elif}\;t \leq 6.6 \cdot 10^{+43}:\\ \;\;\;\;\frac{x}{a} + \frac{\frac{y}{t}}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \frac{b}{t} + \left(a + 1\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 60.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{-123}:\\ \;\;\;\;\frac{x}{y \cdot \frac{b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-107}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{-42}:\\ \;\;\;\;\frac{x}{1 + b \cdot \frac{y}{t}}\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{+43}:\\ \;\;\;\;\frac{x}{a} + \frac{\frac{y}{t}}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.2e-123)
   (/ x (+ (* y (/ b t)) (+ a 1.0)))
   (if (<= t 4.6e-107)
     (/ z b)
     (if (<= t 2.3e-42)
       (/ x (+ 1.0 (* b (/ y t))))
       (if (<= t 6.5e+43)
         (+ (/ x a) (/ (/ y t) (/ a z)))
         (/ (+ 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 (t <= -1.2e-123) {
		tmp = x / ((y * (b / t)) + (a + 1.0));
	} else if (t <= 4.6e-107) {
		tmp = z / b;
	} else if (t <= 2.3e-42) {
		tmp = x / (1.0 + (b * (y / t)));
	} else if (t <= 6.5e+43) {
		tmp = (x / a) + ((y / t) / (a / z));
	} 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 (t <= (-1.2d-123)) then
        tmp = x / ((y * (b / t)) + (a + 1.0d0))
    else if (t <= 4.6d-107) then
        tmp = z / b
    else if (t <= 2.3d-42) then
        tmp = x / (1.0d0 + (b * (y / t)))
    else if (t <= 6.5d+43) then
        tmp = (x / a) + ((y / t) / (a / z))
    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 (t <= -1.2e-123) {
		tmp = x / ((y * (b / t)) + (a + 1.0));
	} else if (t <= 4.6e-107) {
		tmp = z / b;
	} else if (t <= 2.3e-42) {
		tmp = x / (1.0 + (b * (y / t)));
	} else if (t <= 6.5e+43) {
		tmp = (x / a) + ((y / t) / (a / z));
	} else {
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1.2e-123:
		tmp = x / ((y * (b / t)) + (a + 1.0))
	elif t <= 4.6e-107:
		tmp = z / b
	elif t <= 2.3e-42:
		tmp = x / (1.0 + (b * (y / t)))
	elif t <= 6.5e+43:
		tmp = (x / a) + ((y / t) / (a / z))
	else:
		tmp = (x + ((y * z) / t)) / (a + 1.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.2e-123)
		tmp = Float64(x / Float64(Float64(y * Float64(b / t)) + Float64(a + 1.0)));
	elseif (t <= 4.6e-107)
		tmp = Float64(z / b);
	elseif (t <= 2.3e-42)
		tmp = Float64(x / Float64(1.0 + Float64(b * Float64(y / t))));
	elseif (t <= 6.5e+43)
		tmp = Float64(Float64(x / a) + Float64(Float64(y / t) / Float64(a / z)));
	else
		tmp = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(a + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -1.2e-123)
		tmp = x / ((y * (b / t)) + (a + 1.0));
	elseif (t <= 4.6e-107)
		tmp = z / b;
	elseif (t <= 2.3e-42)
		tmp = x / (1.0 + (b * (y / t)));
	elseif (t <= 6.5e+43)
		tmp = (x / a) + ((y / t) / (a / z));
	else
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.2e-123], N[(x / N[(N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.6e-107], N[(z / b), $MachinePrecision], If[LessEqual[t, 2.3e-42], N[(x / N[(1.0 + N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.5e+43], N[(N[(x / a), $MachinePrecision] + N[(N[(y / t), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -1.2e-123

   1. Initial program 81.9%

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

      1. *-commutative 81.9%

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

      2. associate-*l/ 84.4%

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

      3. *-commutative 84.4%

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

      4. associate-*l/ 89.1%

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

   3. Simplified 89.1%

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

   5. Taylor expanded in x around inf 67.8%

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

   if -1.2e-123 < t < 4.60000000000000007e-107

   1. Initial program 59.8%

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

      1. *-commutative 59.8%

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

      2. associate-*l/ 51.1%

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

      3. *-commutative 51.1%

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

      4. associate-*l/ 44.5%

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

   3. Simplified 44.5%

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

   5. Taylor expanded in t around 0 67.1%

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

   if 4.60000000000000007e-107 < t < 2.30000000000000004e-42

   1. Initial program 88.8%

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

      1. *-commutative 88.8%

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

      2. associate-*l/ 82.9%

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

      3. *-commutative 82.9%

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

      4. associate-*l/ 77.3%

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

   3. Simplified 77.3%

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

   5. Taylor expanded in x around inf 60.4%

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

   6. Taylor expanded in a around 0 66.1%

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

      1. associate-*r/ 66.2%

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

   8. Simplified 66.2%

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

   if 2.30000000000000004e-42 < t < 6.4999999999999998e43

   1. Initial program 78.9%

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

      1. *-commutative 78.9%

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

      2. associate-*l/ 73.5%

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

      3. *-commutative 73.5%

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

      4. associate-*l/ 73.5%

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

   3. Simplified 73.5%

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

   5. Taylor expanded in a around inf 54.3%

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

   6. Taylor expanded in x around 0 54.0%

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

      1. *-commutative 54.0%

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

      2. associate-*l/ 54.2%

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

      3. *-commutative 54.2%

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

   8. Simplified 54.2%

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

      1. associate-*r/ 54.0%

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

      2. *-commutative 54.0%

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

      3. times-frac 72.8%

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

      4. clear-num 72.7%

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

      5. times-frac 72.7%

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

      6. *-un-lft-identity 72.7%

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

      7. *-commutative 72.7%

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

      8. associate-/r* 72.8%

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

   10. Applied egg-rr 72.8%

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

   if 6.4999999999999998e43 < t

   1. Initial program 83.2%

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

      1. *-commutative 83.2%

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

      2. associate-*l/ 87.0%

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

      3. *-commutative 87.0%

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

      4. associate-*l/ 90.7%

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

   3. Simplified 90.7%

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

   5. Taylor expanded in b around 0 77.7%

      \[\leadsto \color{blue}{\frac{x + \frac{y \cdot z}{t}}{1 + a}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 69.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{-123}:\\ \;\;\;\;\frac{x}{y \cdot \frac{b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-107}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{-42}:\\ \;\;\;\;\frac{x}{1 + b \cdot \frac{y}{t}}\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{+43}:\\ \;\;\;\;\frac{x}{a} + \frac{\frac{y}{t}}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 79.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{-123} \lor \neg \left(t \leq 4.2 \cdot 10^{-167}\right):\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + \left(1 + \frac{y}{\frac{t}{b}}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -2.2e-123) (not (<= t 4.2e-167)))
   (/ (+ x (* z (/ y t))) (+ a (+ 1.0 (/ y (/ t b)))))
   (/ z b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -2.2e-123) || !(t <= 4.2e-167)) {
		tmp = (x + (z * (y / t))) / (a + (1.0 + (y / (t / b))));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-2.2d-123)) .or. (.not. (t <= 4.2d-167))) then
        tmp = (x + (z * (y / t))) / (a + (1.0d0 + (y / (t / b))))
    else
        tmp = z / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -2.2e-123) || !(t <= 4.2e-167)) {
		tmp = (x + (z * (y / t))) / (a + (1.0 + (y / (t / b))));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -2.2e-123) or not (t <= 4.2e-167):
		tmp = (x + (z * (y / t))) / (a + (1.0 + (y / (t / b))))
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -2.2e-123) || !(t <= 4.2e-167))
		tmp = Float64(Float64(x + Float64(z * Float64(y / t))) / Float64(a + Float64(1.0 + Float64(y / Float64(t / b)))));
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -2.2e-123) || ~((t <= 4.2e-167)))
		tmp = (x + (z * (y / t))) / (a + (1.0 + (y / (t / b))));
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -2.2e-123], N[Not[LessEqual[t, 4.2e-167]], $MachinePrecision]], N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + N[(1.0 + N[(y / N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.20000000000000006e-123 or 4.20000000000000035e-167 < t

   1. Initial program 81.1%

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

      1. associate-/l* 81.6%

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

      2. associate-+l+ 81.6%

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

      3. associate-/l* 83.9%

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

   3. Simplified 83.9%

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

      1. associate-/r/ 85.2%

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

   6. Applied egg-rr 85.2%

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

   if -2.20000000000000006e-123 < t < 4.20000000000000035e-167

   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. *-commutative 58.7%

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

      2. associate-*l/ 49.2%

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

      3. *-commutative 49.2%

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

      4. associate-*l/ 42.3%

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

   3. Simplified 42.3%

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

   5. Taylor expanded in t around 0 68.8%

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

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{-123} \lor \neg \left(t \leq 4.2 \cdot 10^{-167}\right):\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + \left(1 + \frac{y}{\frac{t}{b}}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 80.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.26 \cdot 10^{-185}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a + \left(1 + b \cdot \frac{y}{t}\right)}\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{-168}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + \left(1 + \frac{y}{\frac{t}{b}}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.26e-185)
   (/ (+ x (/ y (/ t z))) (+ a (+ 1.0 (* b (/ y t)))))
   (if (<= t 7.5e-168)
     (/ z b)
     (/ (+ x (* z (/ y t))) (+ a (+ 1.0 (/ y (/ t b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.26e-185) {
		tmp = (x + (y / (t / z))) / (a + (1.0 + (b * (y / t))));
	} else if (t <= 7.5e-168) {
		tmp = z / b;
	} else {
		tmp = (x + (z * (y / t))) / (a + (1.0 + (y / (t / b))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-1.26d-185)) then
        tmp = (x + (y / (t / z))) / (a + (1.0d0 + (b * (y / t))))
    else if (t <= 7.5d-168) then
        tmp = z / b
    else
        tmp = (x + (z * (y / t))) / (a + (1.0d0 + (y / (t / b))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.26e-185) {
		tmp = (x + (y / (t / z))) / (a + (1.0 + (b * (y / t))));
	} else if (t <= 7.5e-168) {
		tmp = z / b;
	} else {
		tmp = (x + (z * (y / t))) / (a + (1.0 + (y / (t / b))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1.26e-185:
		tmp = (x + (y / (t / z))) / (a + (1.0 + (b * (y / t))))
	elif t <= 7.5e-168:
		tmp = z / b
	else:
		tmp = (x + (z * (y / t))) / (a + (1.0 + (y / (t / b))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.26e-185)
		tmp = Float64(Float64(x + Float64(y / Float64(t / z))) / Float64(a + Float64(1.0 + Float64(b * Float64(y / t)))));
	elseif (t <= 7.5e-168)
		tmp = Float64(z / b);
	else
		tmp = Float64(Float64(x + Float64(z * Float64(y / t))) / Float64(a + Float64(1.0 + Float64(y / Float64(t / b)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -1.26e-185)
		tmp = (x + (y / (t / z))) / (a + (1.0 + (b * (y / t))));
	elseif (t <= 7.5e-168)
		tmp = z / b;
	else
		tmp = (x + (z * (y / t))) / (a + (1.0 + (y / (t / b))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.26e-185], N[(N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + N[(1.0 + N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.5e-168], N[(z / b), $MachinePrecision], N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + N[(1.0 + N[(y / N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.2599999999999999e-185

   1. Initial program 80.4%

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

      1. associate-/l* 81.5%

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

      2. associate-+l+ 81.5%

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

      3. associate-/l* 82.4%

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

   3. Simplified 82.4%

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

      1. associate-/r/ 85.3%

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

   6. Applied egg-rr 85.3%

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

   if -1.2599999999999999e-185 < t < 7.4999999999999995e-168

   1. Initial program 53.1%

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

      1. *-commutative 53.1%

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

      2. associate-*l/ 42.0%

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

      3. *-commutative 42.0%

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

      4. associate-*l/ 38.2%

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

   3. Simplified 38.2%

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

   5. Taylor expanded in t around 0 74.0%

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

   if 7.4999999999999995e-168 < t

   1. Initial program 80.4%

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

      1. associate-/l* 79.4%

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

      2. associate-+l+ 79.4%

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

      3. associate-/l* 79.7%

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

   3. Simplified 79.7%

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

      1. associate-/r/ 81.6%

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

   6. Applied egg-rr 81.6%

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

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.26 \cdot 10^{-185}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a + \left(1 + b \cdot \frac{y}{t}\right)}\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{-168}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + \left(1 + \frac{y}{\frac{t}{b}}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 56.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{a} + \frac{\frac{y}{t}}{\frac{a}{z}}\\ \mathbf{if}\;a \leq -8.5 \cdot 10^{+98}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -3 \cdot 10^{+15}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 2.05 \cdot 10^{+21}:\\ \;\;\;\;\frac{x}{1 + b \cdot \frac{y}{t}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (/ x a) (/ (/ y t) (/ a z)))))
   (if (<= a -8.5e+98)
     t_1
     (if (<= a -3e+15)
       (/ z b)
       (if (<= a 2.05e+21) (/ x (+ 1.0 (* b (/ y t)))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x / a) + ((y / t) / (a / z));
	double tmp;
	if (a <= -8.5e+98) {
		tmp = t_1;
	} else if (a <= -3e+15) {
		tmp = z / b;
	} else if (a <= 2.05e+21) {
		tmp = x / (1.0 + (b * (y / t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / a) + ((y / t) / (a / z))
    if (a <= (-8.5d+98)) then
        tmp = t_1
    else if (a <= (-3d+15)) then
        tmp = z / b
    else if (a <= 2.05d+21) then
        tmp = x / (1.0d0 + (b * (y / t)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x / a) + ((y / t) / (a / z));
	double tmp;
	if (a <= -8.5e+98) {
		tmp = t_1;
	} else if (a <= -3e+15) {
		tmp = z / b;
	} else if (a <= 2.05e+21) {
		tmp = x / (1.0 + (b * (y / t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x / a) + ((y / t) / (a / z))
	tmp = 0
	if a <= -8.5e+98:
		tmp = t_1
	elif a <= -3e+15:
		tmp = z / b
	elif a <= 2.05e+21:
		tmp = x / (1.0 + (b * (y / t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x / a) + Float64(Float64(y / t) / Float64(a / z)))
	tmp = 0.0
	if (a <= -8.5e+98)
		tmp = t_1;
	elseif (a <= -3e+15)
		tmp = Float64(z / b);
	elseif (a <= 2.05e+21)
		tmp = Float64(x / Float64(1.0 + Float64(b * Float64(y / t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x / a) + ((y / t) / (a / z));
	tmp = 0.0;
	if (a <= -8.5e+98)
		tmp = t_1;
	elseif (a <= -3e+15)
		tmp = z / b;
	elseif (a <= 2.05e+21)
		tmp = x / (1.0 + (b * (y / t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x / a), $MachinePrecision] + N[(N[(y / t), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -8.5e+98], t$95$1, If[LessEqual[a, -3e+15], N[(z / b), $MachinePrecision], If[LessEqual[a, 2.05e+21], N[(x / N[(1.0 + N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -8.4999999999999996e98 or 2.05e21 < a

   1. Initial program 77.5%

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

      1. *-commutative 77.5%

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

      2. associate-*l/ 74.8%

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

      3. *-commutative 74.8%

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

      4. associate-*l/ 74.0%

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

   3. Simplified 74.0%

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

   5. Taylor expanded in a around inf 66.4%

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

   6. Taylor expanded in x around 0 61.9%

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

      1. *-commutative 61.9%

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

      2. associate-*l/ 63.9%

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

      3. *-commutative 63.9%

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

   8. Simplified 63.9%

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

      1. associate-*r/ 61.9%

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

      2. *-commutative 61.9%

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

      3. times-frac 73.0%

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

      4. clear-num 73.0%

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

      5. times-frac 70.4%

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

      6. *-un-lft-identity 70.4%

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

      7. *-commutative 70.4%

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

      8. associate-/r* 73.0%

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

   10. Applied egg-rr 73.0%

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

   if -8.4999999999999996e98 < a < -3e15

   1. Initial program 48.1%

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

      1. *-commutative 48.1%

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

      2. associate-*l/ 42.7%

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

      3. *-commutative 42.7%

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

      4. associate-*l/ 48.4%

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

   3. Simplified 48.4%

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

   5. Taylor expanded in t around 0 71.7%

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

   if -3e15 < a < 2.05e21

   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. *-commutative 76.1%

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

      2. associate-*l/ 74.7%

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

      3. *-commutative 74.7%

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

      4. associate-*l/ 73.9%

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

   3. Simplified 73.9%

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

   5. Taylor expanded in x around inf 56.7%

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

   6. Taylor expanded in a around 0 56.7%

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

      1. associate-*r/ 58.9%

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

   8. Simplified 58.9%

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

4. Final simplification 65.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.5 \cdot 10^{+98}:\\ \;\;\;\;\frac{x}{a} + \frac{\frac{y}{t}}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq -3 \cdot 10^{+15}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 2.05 \cdot 10^{+21}:\\ \;\;\;\;\frac{x}{1 + b \cdot \frac{y}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a} + \frac{\frac{y}{t}}{\frac{a}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 57.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{a} + \frac{\frac{y}{t}}{\frac{a}{z}}\\ \mathbf{if}\;a \leq -8.5 \cdot 10^{+98}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -2 \cdot 10^{+31}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{+106}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (/ x a) (/ (/ y t) (/ a z)))))
   (if (<= a -8.5e+98)
     t_1
     (if (<= a -2e+31)
       (/ z b)
       (if (<= a 1.85e+106) (/ x (+ 1.0 (+ a (/ (* y b) t)))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x / a) + ((y / t) / (a / z));
	double tmp;
	if (a <= -8.5e+98) {
		tmp = t_1;
	} else if (a <= -2e+31) {
		tmp = z / b;
	} else if (a <= 1.85e+106) {
		tmp = x / (1.0 + (a + ((y * b) / t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / a) + ((y / t) / (a / z))
    if (a <= (-8.5d+98)) then
        tmp = t_1
    else if (a <= (-2d+31)) then
        tmp = z / b
    else if (a <= 1.85d+106) then
        tmp = x / (1.0d0 + (a + ((y * b) / t)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x / a) + ((y / t) / (a / z));
	double tmp;
	if (a <= -8.5e+98) {
		tmp = t_1;
	} else if (a <= -2e+31) {
		tmp = z / b;
	} else if (a <= 1.85e+106) {
		tmp = x / (1.0 + (a + ((y * b) / t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x / a) + ((y / t) / (a / z))
	tmp = 0
	if a <= -8.5e+98:
		tmp = t_1
	elif a <= -2e+31:
		tmp = z / b
	elif a <= 1.85e+106:
		tmp = x / (1.0 + (a + ((y * b) / t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x / a) + Float64(Float64(y / t) / Float64(a / z)))
	tmp = 0.0
	if (a <= -8.5e+98)
		tmp = t_1;
	elseif (a <= -2e+31)
		tmp = Float64(z / b);
	elseif (a <= 1.85e+106)
		tmp = Float64(x / Float64(1.0 + Float64(a + Float64(Float64(y * b) / t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x / a) + ((y / t) / (a / z));
	tmp = 0.0;
	if (a <= -8.5e+98)
		tmp = t_1;
	elseif (a <= -2e+31)
		tmp = z / b;
	elseif (a <= 1.85e+106)
		tmp = x / (1.0 + (a + ((y * b) / t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x / a), $MachinePrecision] + N[(N[(y / t), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -8.5e+98], t$95$1, If[LessEqual[a, -2e+31], N[(z / b), $MachinePrecision], If[LessEqual[a, 1.85e+106], N[(x / N[(1.0 + N[(a + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -8.4999999999999996e98 or 1.84999999999999997e106 < a

   1. Initial program 76.3%

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

      1. *-commutative 76.3%

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

      2. associate-*l/ 73.1%

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

      3. *-commutative 73.1%

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

      4. associate-*l/ 71.0%

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

   3. Simplified 71.0%

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

   5. Taylor expanded in a around inf 68.3%

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

   6. Taylor expanded in x around 0 63.0%

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

      1. *-commutative 63.0%

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

      2. associate-*l/ 65.3%

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

      3. *-commutative 65.3%

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

   8. Simplified 65.3%

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

      1. associate-*r/ 63.0%

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

      2. *-commutative 63.0%

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

      3. times-frac 76.3%

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

      4. clear-num 76.3%

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

      5. times-frac 74.2%

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

      6. *-un-lft-identity 74.2%

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

      7. *-commutative 74.2%

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

      8. associate-/r* 76.3%

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

   10. Applied egg-rr 76.3%

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

   if -8.4999999999999996e98 < a < -1.9999999999999999e31

   1. Initial program 41.3%

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

      1. *-commutative 41.3%

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

      2. associate-*l/ 35.2%

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

      3. *-commutative 35.2%

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

      4. associate-*l/ 41.6%

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

   3. Simplified 41.6%

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

   5. Taylor expanded in t around 0 80.8%

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

   if -1.9999999999999999e31 < a < 1.84999999999999997e106

   1. Initial program 77.3%

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

      1. *-commutative 77.3%

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

      2. associate-*l/ 76.1%

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

      3. *-commutative 76.1%

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

      4. associate-*l/ 76.0%

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

   3. Simplified 76.0%

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

   5. Taylor expanded in x around inf 59.2%

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

4. Final simplification 66.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.5 \cdot 10^{+98}:\\ \;\;\;\;\frac{x}{a} + \frac{\frac{y}{t}}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq -2 \cdot 10^{+31}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{+106}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a} + \frac{\frac{y}{t}}{\frac{a}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 54.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + y \cdot \frac{z}{t}}{a}\\ \mathbf{if}\;a \leq -2.4 \cdot 10^{+99}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.5 \cdot 10^{+15}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{+44}:\\ \;\;\;\;\frac{x}{1 + b \cdot \frac{y}{t}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (* y (/ z t))) a)))
   (if (<= a -2.4e+99)
     t_1
     (if (<= a -1.5e+15)
       (/ z b)
       (if (<= a 1.35e+44) (/ x (+ 1.0 (* b (/ y t)))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + (y * (z / t))) / a;
	double tmp;
	if (a <= -2.4e+99) {
		tmp = t_1;
	} else if (a <= -1.5e+15) {
		tmp = z / b;
	} else if (a <= 1.35e+44) {
		tmp = x / (1.0 + (b * (y / t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + (y * (z / t))) / a
    if (a <= (-2.4d+99)) then
        tmp = t_1
    else if (a <= (-1.5d+15)) then
        tmp = z / b
    else if (a <= 1.35d+44) then
        tmp = x / (1.0d0 + (b * (y / t)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + (y * (z / t))) / a;
	double tmp;
	if (a <= -2.4e+99) {
		tmp = t_1;
	} else if (a <= -1.5e+15) {
		tmp = z / b;
	} else if (a <= 1.35e+44) {
		tmp = x / (1.0 + (b * (y / t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + (y * (z / t))) / a
	tmp = 0
	if a <= -2.4e+99:
		tmp = t_1
	elif a <= -1.5e+15:
		tmp = z / b
	elif a <= 1.35e+44:
		tmp = x / (1.0 + (b * (y / t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(y * Float64(z / t))) / a)
	tmp = 0.0
	if (a <= -2.4e+99)
		tmp = t_1;
	elseif (a <= -1.5e+15)
		tmp = Float64(z / b);
	elseif (a <= 1.35e+44)
		tmp = Float64(x / Float64(1.0 + Float64(b * Float64(y / t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + (y * (z / t))) / a;
	tmp = 0.0;
	if (a <= -2.4e+99)
		tmp = t_1;
	elseif (a <= -1.5e+15)
		tmp = z / b;
	elseif (a <= 1.35e+44)
		tmp = x / (1.0 + (b * (y / t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[a, -2.4e+99], t$95$1, If[LessEqual[a, -1.5e+15], N[(z / b), $MachinePrecision], If[LessEqual[a, 1.35e+44], N[(x / N[(1.0 + N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.4000000000000001e99 or 1.35e44 < a

   1. Initial program 78.9%

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

      1. *-commutative 78.9%

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

      2. associate-*l/ 76.0%

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

      3. *-commutative 76.0%

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

      4. associate-*l/ 74.1%

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

   3. Simplified 74.1%

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

      1. associate-*l/ 76.1%

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

      2. *-commutative 76.1%

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

      3. clear-num 76.1%

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

      4. *-commutative 76.1%

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

   6. Applied egg-rr 76.1%

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

   7. Taylor expanded in a around inf 68.0%

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

      1. associate-*r/ 66.9%

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

   9. Simplified 66.9%

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

   if -2.4000000000000001e99 < a < -1.5e15

   1. Initial program 48.1%

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

      1. *-commutative 48.1%

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

      2. associate-*l/ 42.7%

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

      3. *-commutative 42.7%

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

      4. associate-*l/ 48.4%

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

   3. Simplified 48.4%

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

   5. Taylor expanded in t around 0 71.7%

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

   if -1.5e15 < a < 1.35e44

   1. Initial program 75.2%

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

      1. *-commutative 75.2%

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

      2. associate-*l/ 73.8%

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

      3. *-commutative 73.8%

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

      4. associate-*l/ 73.8%

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

   3. Simplified 73.8%

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

   5. Taylor expanded in x around inf 56.8%

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

   6. Taylor expanded in a around 0 54.8%

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

      1. associate-*r/ 57.6%

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

   8. Simplified 57.6%

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

4. Final simplification 62.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.4 \cdot 10^{+99}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a}\\ \mathbf{elif}\;a \leq -1.5 \cdot 10^{+15}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{+44}:\\ \;\;\;\;\frac{x}{1 + b \cdot \frac{y}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 54.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{a}\\ \mathbf{if}\;a \leq -8.5 \cdot 10^{+98}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.8 \cdot 10^{+15}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{+22}:\\ \;\;\;\;\frac{x}{1 + b \cdot \frac{y}{t}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (* y z) t)) a)))
   (if (<= a -8.5e+98)
     t_1
     (if (<= a -1.8e+15)
       (/ z b)
       (if (<= a 1.15e+22) (/ x (+ 1.0 (* b (/ y t)))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + ((y * z) / t)) / a;
	double tmp;
	if (a <= -8.5e+98) {
		tmp = t_1;
	} else if (a <= -1.8e+15) {
		tmp = z / b;
	} else if (a <= 1.15e+22) {
		tmp = x / (1.0 + (b * (y / t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + ((y * z) / t)) / a
    if (a <= (-8.5d+98)) then
        tmp = t_1
    else if (a <= (-1.8d+15)) then
        tmp = z / b
    else if (a <= 1.15d+22) then
        tmp = x / (1.0d0 + (b * (y / t)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + ((y * z) / t)) / a;
	double tmp;
	if (a <= -8.5e+98) {
		tmp = t_1;
	} else if (a <= -1.8e+15) {
		tmp = z / b;
	} else if (a <= 1.15e+22) {
		tmp = x / (1.0 + (b * (y / t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + ((y * z) / t)) / a
	tmp = 0
	if a <= -8.5e+98:
		tmp = t_1
	elif a <= -1.8e+15:
		tmp = z / b
	elif a <= 1.15e+22:
		tmp = x / (1.0 + (b * (y / t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(Float64(y * z) / t)) / a)
	tmp = 0.0
	if (a <= -8.5e+98)
		tmp = t_1;
	elseif (a <= -1.8e+15)
		tmp = Float64(z / b);
	elseif (a <= 1.15e+22)
		tmp = Float64(x / Float64(1.0 + Float64(b * Float64(y / t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + ((y * z) / t)) / a;
	tmp = 0.0;
	if (a <= -8.5e+98)
		tmp = t_1;
	elseif (a <= -1.8e+15)
		tmp = z / b;
	elseif (a <= 1.15e+22)
		tmp = x / (1.0 + (b * (y / t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[a, -8.5e+98], t$95$1, If[LessEqual[a, -1.8e+15], N[(z / b), $MachinePrecision], If[LessEqual[a, 1.15e+22], N[(x / N[(1.0 + N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -8.4999999999999996e98 or 1.1500000000000001e22 < a

   1. Initial program 77.5%

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

      1. *-commutative 77.5%

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

      2. associate-*l/ 74.8%

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

      3. *-commutative 74.8%

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

      4. associate-*l/ 74.0%

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

   3. Simplified 74.0%

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

   5. Taylor expanded in a around inf 66.4%

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

   if -8.4999999999999996e98 < a < -1.8e15

   1. Initial program 48.1%

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

      1. *-commutative 48.1%

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

      2. associate-*l/ 42.7%

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

      3. *-commutative 42.7%

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

      4. associate-*l/ 48.4%

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

   3. Simplified 48.4%

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

   5. Taylor expanded in t around 0 71.7%

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

   if -1.8e15 < a < 1.1500000000000001e22

   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. *-commutative 76.1%

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

      2. associate-*l/ 74.7%

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

      3. *-commutative 74.7%

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

      4. associate-*l/ 73.9%

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

   3. Simplified 73.9%

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

   5. Taylor expanded in x around inf 56.7%

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

   6. Taylor expanded in a around 0 56.7%

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

      1. associate-*r/ 58.9%

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

   8. Simplified 58.9%

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

4. Final simplification 62.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.5 \cdot 10^{+98}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a}\\ \mathbf{elif}\;a \leq -1.8 \cdot 10^{+15}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{+22}:\\ \;\;\;\;\frac{x}{1 + b \cdot \frac{y}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 42.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{+36}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;t \leq 8.4 \cdot 10^{-45}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{+166}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -6.5e+36)
   (/ x a)
   (if (<= t 8.4e-45) (/ z b) (if (<= t 2.7e+166) (/ x a) x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -6.5e+36) {
		tmp = x / a;
	} else if (t <= 8.4e-45) {
		tmp = z / b;
	} else if (t <= 2.7e+166) {
		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 (t <= (-6.5d+36)) then
        tmp = x / a
    else if (t <= 8.4d-45) then
        tmp = z / b
    else if (t <= 2.7d+166) 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 (t <= -6.5e+36) {
		tmp = x / a;
	} else if (t <= 8.4e-45) {
		tmp = z / b;
	} else if (t <= 2.7e+166) {
		tmp = x / a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -6.5e+36:
		tmp = x / a
	elif t <= 8.4e-45:
		tmp = z / b
	elif t <= 2.7e+166:
		tmp = x / a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -6.5e+36)
		tmp = Float64(x / a);
	elseif (t <= 8.4e-45)
		tmp = Float64(z / b);
	elseif (t <= 2.7e+166)
		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 (t <= -6.5e+36)
		tmp = x / a;
	elseif (t <= 8.4e-45)
		tmp = z / b;
	elseif (t <= 2.7e+166)
		tmp = x / a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -6.5e+36], N[(x / a), $MachinePrecision], If[LessEqual[t, 8.4e-45], N[(z / b), $MachinePrecision], If[LessEqual[t, 2.7e+166], N[(x / a), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.4999999999999998e36 or 8.3999999999999998e-45 < t < 2.70000000000000012e166

   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. *-commutative 82.8%

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

      2. associate-*l/ 83.8%

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

      3. *-commutative 83.8%

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

      4. associate-*l/ 86.8%

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

   3. Simplified 86.8%

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

   5. Taylor expanded in x around inf 65.5%

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

   6. Taylor expanded in a around inf 42.8%

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

   if -6.4999999999999998e36 < t < 8.3999999999999998e-45

   1. Initial program 67.3%

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

      1. *-commutative 67.3%

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

      2. associate-*l/ 60.8%

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

      3. *-commutative 60.8%

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

      4. associate-*l/ 56.4%

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

   3. Simplified 56.4%

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

   5. Taylor expanded in t around 0 55.8%

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

   if 2.70000000000000012e166 < t

   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. *-commutative 83.1%

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

      2. associate-*l/ 89.9%

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

      3. *-commutative 89.9%

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

      4. associate-*l/ 96.5%

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

   3. Simplified 96.5%

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

   5. Taylor expanded in t around inf 80.4%

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

   6. Taylor expanded in a around 0 56.9%

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

4. Final simplification 51.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{+36}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;t \leq 8.4 \cdot 10^{-45}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{+166}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 55.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{+36} \lor \neg \left(t \leq 1.95 \cdot 10^{-45}\right):\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -1.8e+36) (not (<= t 1.95e-45))) (/ x (+ a 1.0)) (/ z b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.8e+36) || !(t <= 1.95e-45)) {
		tmp = x / (a + 1.0);
	} else {
		tmp = z / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-1.8d+36)) .or. (.not. (t <= 1.95d-45))) then
        tmp = x / (a + 1.0d0)
    else
        tmp = z / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.8e+36) || !(t <= 1.95e-45)) {
		tmp = x / (a + 1.0);
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -1.8e+36) or not (t <= 1.95e-45):
		tmp = x / (a + 1.0)
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -1.8e+36) || !(t <= 1.95e-45))
		tmp = Float64(x / Float64(a + 1.0));
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -1.8e+36) || ~((t <= 1.95e-45)))
		tmp = x / (a + 1.0);
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -1.8e+36], N[Not[LessEqual[t, 1.95e-45]], $MachinePrecision]], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.7999999999999999e36 or 1.95e-45 < t

   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. *-commutative 82.8%

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

      2. associate-*l/ 85.2%

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

      3. *-commutative 85.2%

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

      4. associate-*l/ 89.1%

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

   3. Simplified 89.1%

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

   5. Taylor expanded in t around inf 62.8%

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

   if -1.7999999999999999e36 < t < 1.95e-45

   1. Initial program 67.3%

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

      1. *-commutative 67.3%

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

      2. associate-*l/ 60.8%

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

      3. *-commutative 60.8%

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

      4. associate-*l/ 56.4%

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

   3. Simplified 56.4%

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

   5. Taylor expanded in t around 0 55.8%

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

4. Final simplification 59.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{+36} \lor \neg \left(t \leq 1.95 \cdot 10^{-45}\right):\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 41.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7.5 \cdot 10^{-14} \lor \neg \left(a \leq 2.9 \cdot 10^{-13}\right):\\ \;\;\;\;\frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -7.5e-14) (not (<= a 2.9e-13))) (/ x a) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -7.5e-14) || !(a <= 2.9e-13)) {
		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 <= (-7.5d-14)) .or. (.not. (a <= 2.9d-13))) 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 <= -7.5e-14) || !(a <= 2.9e-13)) {
		tmp = x / a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -7.5e-14) or not (a <= 2.9e-13):
		tmp = x / a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -7.5e-14) || !(a <= 2.9e-13))
		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 <= -7.5e-14) || ~((a <= 2.9e-13)))
		tmp = x / a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -7.5e-14], N[Not[LessEqual[a, 2.9e-13]], $MachinePrecision]], N[(x / a), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if a < -7.4999999999999996e-14 or 2.8999999999999998e-13 < a

   1. Initial program 73.4%

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

      1. *-commutative 73.4%

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

      2. associate-*l/ 70.5%

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

      3. *-commutative 70.5%

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

      4. associate-*l/ 70.6%

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

   3. Simplified 70.6%

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

   5. Taylor expanded in x around inf 52.4%

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

   6. Taylor expanded in a around inf 42.9%

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

   if -7.4999999999999996e-14 < a < 2.8999999999999998e-13

   1. Initial program 76.4%

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

      1. *-commutative 76.4%

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

      2. associate-*l/ 74.8%

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

      3. *-commutative 74.8%

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

      4. associate-*l/ 74.0%

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

   3. Simplified 74.0%

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

   5. Taylor expanded in t around inf 34.0%

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

   6. Taylor expanded in a around 0 34.0%

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

4. Final simplification 38.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.5 \cdot 10^{-14} \lor \neg \left(a \leq 2.9 \cdot 10^{-13}\right):\\ \;\;\;\;\frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 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 74.8%

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

   1. *-commutative 74.8%

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

   2. associate-*l/ 72.6%

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

   3. *-commutative 72.6%

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

   4. associate-*l/ 72.2%

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

3. Simplified 72.2%

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

5. Taylor expanded in t around inf 38.6%

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

6. Taylor expanded in a around 0 18.5%

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

7. Final simplification 18.5%

   \[\leadsto x \]
8. Add Preprocessing

Developer target: 80.1% 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 2024034 
(FPCore (x y z t a b)
  :name "Diagrams.Solve.Tridiagonal:solveCyclicTriDiagonal from diagrams-solve-0.1, B"
  :precision binary64

  :herbie-target
  (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))))