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

Percentage Accurate: 75.9% → 90.7%

Time: 13.4s

Alternatives: 14

Speedup: 0.6×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 75.9% 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: 90.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot b}{t}\\ t_2 := \frac{x + \frac{y \cdot z}{t}}{t_1 + \left(a + 1\right)}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;\frac{y \cdot \frac{z}{1 + \left(a + t_1\right)}}{t}\\ \mathbf{elif}\;t_2 \leq -5 \cdot 10^{-234}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 10^{-184}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a + \left(1 + \frac{b}{\frac{t}{y}}\right)}\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{+287}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

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))
     (/ (* y (/ z (+ 1.0 (+ a t_1)))) t)
     (if (<= t_2 -5e-234)
       t_2
       (if (<= t_2 1e-184)
         (/ (+ x (/ y (/ t z))) (+ a (+ 1.0 (/ b (/ t y)))))
         (if (<= t_2 2e+287) t_2 (/ 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 = (y * (z / (1.0 + (a + t_1)))) / t;
	} else if (t_2 <= -5e-234) {
		tmp = t_2;
	} else if (t_2 <= 1e-184) {
		tmp = (x + (y / (t / z))) / (a + (1.0 + (b / (t / y))));
	} else if (t_2 <= 2e+287) {
		tmp = t_2;
	} 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 = (y * (z / (1.0 + (a + t_1)))) / t;
	} else if (t_2 <= -5e-234) {
		tmp = t_2;
	} else if (t_2 <= 1e-184) {
		tmp = (x + (y / (t / z))) / (a + (1.0 + (b / (t / y))));
	} else if (t_2 <= 2e+287) {
		tmp = t_2;
	} 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 = (y * (z / (1.0 + (a + t_1)))) / t
	elif t_2 <= -5e-234:
		tmp = t_2
	elif t_2 <= 1e-184:
		tmp = (x + (y / (t / z))) / (a + (1.0 + (b / (t / y))))
	elif t_2 <= 2e+287:
		tmp = t_2
	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(y * Float64(z / Float64(1.0 + Float64(a + t_1)))) / t);
	elseif (t_2 <= -5e-234)
		tmp = t_2;
	elseif (t_2 <= 1e-184)
		tmp = Float64(Float64(x + Float64(y / Float64(t / z))) / Float64(a + Float64(1.0 + Float64(b / Float64(t / y)))));
	elseif (t_2 <= 2e+287)
		tmp = t_2;
	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 = (y * (z / (1.0 + (a + t_1)))) / t;
	elseif (t_2 <= -5e-234)
		tmp = t_2;
	elseif (t_2 <= 1e-184)
		tmp = (x + (y / (t / z))) / (a + (1.0 + (b / (t / y))));
	elseif (t_2 <= 2e+287)
		tmp = t_2;
	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[(y * N[(z / N[(1.0 + N[(a + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[t$95$2, -5e-234], t$95$2, If[LessEqual[t$95$2, 1e-184], N[(N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + N[(1.0 + N[(b / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+287], t$95$2, N[(z / b), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 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 33.3%

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

      1. *-commutative 33.3%

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

      2. associate-*l/ 63.0%

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

      3. associate-+l+ 63.0%

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

      4. associate-*r/ 62.8%

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

      5. *-commutative 62.8%

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

   3. Simplified 62.8%

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

   4. Taylor expanded in x around 0 62.1%

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

      1. times-frac 76.9%

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

      2. associate-*r/ 68.9%

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

   6. Simplified 68.9%

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

      1. associate-*r/ 76.9%

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

      2. *-commutative 76.9%

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

   8. Applied egg-rr 76.9%

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

      1. associate-*l/ 84.5%

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

   10. Applied egg-rr 84.5%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < -4.99999999999999979e-234 or 1.0000000000000001e-184 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 2.0000000000000002e287

   1. Initial program 99.7%

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

   if -4.99999999999999979e-234 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 1.0000000000000001e-184

   1. Initial program 68.2%

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

      1. associate-/l* 69.6%

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

      2. associate-*l/ 81.7%

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

      3. *-commutative 81.7%

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

      4. cancel-sign-sub 81.7%

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

      5. *-commutative 81.7%

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

      6. associate-*l/ 69.6%

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

      7. associate-+r- 69.6%

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

      8. associate-*l/ 81.7%

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

      9. *-commutative 81.7%

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

      10. cancel-sign-sub 81.7%

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

      11. *-commutative 81.7%

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

      12. associate-*l/ 69.6%

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

      13. *-commutative 69.6%

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

      14. associate-/l* 81.7%

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

   3. Simplified 81.7%

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

   if 2.0000000000000002e287 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))

   1. Initial program 13.0%

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

      1. *-commutative 13.0%

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

      2. associate-*l/ 15.9%

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

      3. associate-+l+ 15.9%

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

      4. associate-*r/ 24.1%

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

      5. *-commutative 24.1%

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

   3. Simplified 24.1%

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

   4. Taylor expanded in t around 0 80.6%

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

4. Final simplification 91.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -\infty:\\ \;\;\;\;\frac{y \cdot \frac{z}{1 + \left(a + \frac{y \cdot b}{t}\right)}}{t}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -5 \cdot 10^{-234}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 10^{-184}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a + \left(1 + \frac{b}{\frac{t}{y}}\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 2 \cdot 10^{+287}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 2: 88.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot b}{t}\\ t_2 := \frac{x + \frac{y \cdot z}{t}}{t_1 + \left(a + 1\right)}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;\frac{y \cdot \frac{z}{1 + \left(a + t_1\right)}}{t}\\ \mathbf{elif}\;t_2 \leq -1 \cdot 10^{-222}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{+287}:\\ \;\;\;\;\frac{x + z \cdot \left(y \cdot \frac{1}{t}\right)}{a + \left(1 + \frac{b}{\frac{t}{y}}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

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))
     (/ (* y (/ z (+ 1.0 (+ a t_1)))) t)
     (if (<= t_2 -1e-222)
       t_2
       (if (<= t_2 2e+287)
         (/ (+ x (* z (* y (/ 1.0 t)))) (+ a (+ 1.0 (/ b (/ t y)))))
         (/ 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 = (y * (z / (1.0 + (a + t_1)))) / t;
	} else if (t_2 <= -1e-222) {
		tmp = t_2;
	} else if (t_2 <= 2e+287) {
		tmp = (x + (z * (y * (1.0 / t)))) / (a + (1.0 + (b / (t / y))));
	} 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 = (y * (z / (1.0 + (a + t_1)))) / t;
	} else if (t_2 <= -1e-222) {
		tmp = t_2;
	} else if (t_2 <= 2e+287) {
		tmp = (x + (z * (y * (1.0 / t)))) / (a + (1.0 + (b / (t / y))));
	} 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 = (y * (z / (1.0 + (a + t_1)))) / t
	elif t_2 <= -1e-222:
		tmp = t_2
	elif t_2 <= 2e+287:
		tmp = (x + (z * (y * (1.0 / t)))) / (a + (1.0 + (b / (t / y))))
	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(y * Float64(z / Float64(1.0 + Float64(a + t_1)))) / t);
	elseif (t_2 <= -1e-222)
		tmp = t_2;
	elseif (t_2 <= 2e+287)
		tmp = Float64(Float64(x + Float64(z * Float64(y * Float64(1.0 / t)))) / Float64(a + Float64(1.0 + Float64(b / Float64(t / y)))));
	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 = (y * (z / (1.0 + (a + t_1)))) / t;
	elseif (t_2 <= -1e-222)
		tmp = t_2;
	elseif (t_2 <= 2e+287)
		tmp = (x + (z * (y * (1.0 / t)))) / (a + (1.0 + (b / (t / y))));
	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[(y * N[(z / N[(1.0 + N[(a + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[t$95$2, -1e-222], t$95$2, If[LessEqual[t$95$2, 2e+287], N[(N[(x + N[(z * N[(y * N[(1.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + N[(1.0 + N[(b / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 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 33.3%

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

      1. *-commutative 33.3%

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

      2. associate-*l/ 63.0%

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

      3. associate-+l+ 63.0%

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

      4. associate-*r/ 62.8%

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

      5. *-commutative 62.8%

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

   3. Simplified 62.8%

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

   4. Taylor expanded in x around 0 62.1%

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

      1. times-frac 76.9%

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

      2. associate-*r/ 68.9%

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

   6. Simplified 68.9%

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

      1. associate-*r/ 76.9%

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

      2. *-commutative 76.9%

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

   8. Applied egg-rr 76.9%

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

      1. associate-*l/ 84.5%

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

   10. Applied egg-rr 84.5%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < -1.00000000000000005e-222

   1. Initial program 99.8%

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

   if -1.00000000000000005e-222 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 2.0000000000000002e287

   1. Initial program 84.3%

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

      1. associate-/l* 80.7%

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

      2. associate-*l/ 85.9%

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

      3. *-commutative 85.9%

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

      4. cancel-sign-sub 85.9%

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

      5. *-commutative 85.9%

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

      6. associate-*l/ 80.7%

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

      7. associate-+r- 80.7%

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

      8. associate-*l/ 85.9%

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

      9. *-commutative 85.9%

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

      10. cancel-sign-sub 85.9%

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

      11. *-commutative 85.9%

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

      12. associate-*l/ 80.7%

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

      13. *-commutative 80.7%

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

      14. associate-/l* 85.9%

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

   3. Simplified 85.9%

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

      1. associate-/l* 89.5%

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

      2. *-commutative 89.5%

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

      3. associate-*l/ 85.7%

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

      4. div-inv 85.7%

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

      5. associate-*l* 89.2%

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

   5. Applied egg-rr 89.2%

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

   if 2.0000000000000002e287 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))

   1. Initial program 13.0%

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

      1. *-commutative 13.0%

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

      2. associate-*l/ 15.9%

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

      3. associate-+l+ 15.9%

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

      4. associate-*r/ 24.1%

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

      5. *-commutative 24.1%

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

   3. Simplified 24.1%

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

   4. Taylor expanded in t around 0 80.6%

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

4. Final simplification 91.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -\infty:\\ \;\;\;\;\frac{y \cdot \frac{z}{1 + \left(a + \frac{y \cdot b}{t}\right)}}{t}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -1 \cdot 10^{-222}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 2 \cdot 10^{+287}:\\ \;\;\;\;\frac{x + z \cdot \left(y \cdot \frac{1}{t}\right)}{a + \left(1 + \frac{b}{\frac{t}{y}}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 3: 89.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot b}{t}\\ t_2 := \frac{x + \frac{y \cdot z}{t}}{t_1 + \left(a + 1\right)}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;\frac{y \cdot \frac{z}{1 + \left(a + t_1\right)}}{t}\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{+287}:\\ \;\;\;\;\frac{x + \left(y \cdot z\right) \cdot \frac{1}{t}}{a + \left(1 + \frac{b}{\frac{t}{y}}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

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))
     (/ (* y (/ z (+ 1.0 (+ a t_1)))) t)
     (if (<= t_2 2e+287)
       (/ (+ x (* (* y z) (/ 1.0 t))) (+ a (+ 1.0 (/ b (/ t y)))))
       (/ 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 = (y * (z / (1.0 + (a + t_1)))) / t;
	} else if (t_2 <= 2e+287) {
		tmp = (x + ((y * z) * (1.0 / t))) / (a + (1.0 + (b / (t / y))));
	} 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 = (y * (z / (1.0 + (a + t_1)))) / t;
	} else if (t_2 <= 2e+287) {
		tmp = (x + ((y * z) * (1.0 / t))) / (a + (1.0 + (b / (t / y))));
	} 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 = (y * (z / (1.0 + (a + t_1)))) / t
	elif t_2 <= 2e+287:
		tmp = (x + ((y * z) * (1.0 / t))) / (a + (1.0 + (b / (t / y))))
	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(y * Float64(z / Float64(1.0 + Float64(a + t_1)))) / t);
	elseif (t_2 <= 2e+287)
		tmp = Float64(Float64(x + Float64(Float64(y * z) * Float64(1.0 / t))) / Float64(a + Float64(1.0 + Float64(b / Float64(t / y)))));
	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 = (y * (z / (1.0 + (a + t_1)))) / t;
	elseif (t_2 <= 2e+287)
		tmp = (x + ((y * z) * (1.0 / t))) / (a + (1.0 + (b / (t / y))));
	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[(y * N[(z / N[(1.0 + N[(a + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[t$95$2, 2e+287], N[(N[(x + N[(N[(y * z), $MachinePrecision] * N[(1.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + N[(1.0 + N[(b / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 33.3%

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

      1. *-commutative 33.3%

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

      2. associate-*l/ 63.0%

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

      3. associate-+l+ 63.0%

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

      4. associate-*r/ 62.8%

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

      5. *-commutative 62.8%

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

   3. Simplified 62.8%

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

   4. Taylor expanded in x around 0 62.1%

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

      1. times-frac 76.9%

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

      2. associate-*r/ 68.9%

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

   6. Simplified 68.9%

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

      1. associate-*r/ 76.9%

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

      2. *-commutative 76.9%

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

   8. Applied egg-rr 76.9%

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

      1. associate-*l/ 84.5%

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

   10. Applied egg-rr 84.5%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 2.0000000000000002e287

   1. Initial program 90.0%

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

      1. associate-/l* 85.9%

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

      2. associate-*l/ 88.7%

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

      3. *-commutative 88.7%

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

      4. cancel-sign-sub 88.7%

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

      5. *-commutative 88.7%

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

      6. associate-*l/ 85.9%

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

      7. associate-+r- 85.9%

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

      8. associate-*l/ 88.7%

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

      9. *-commutative 88.7%

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

      10. cancel-sign-sub 88.7%

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

      11. *-commutative 88.7%

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

      12. associate-*l/ 85.9%

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

      13. *-commutative 85.9%

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

      14. associate-/l* 88.7%

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

   3. Simplified 88.7%

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

      1. associate-/l* 92.8%

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

      2. div-inv 92.8%

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

      3. *-commutative 92.8%

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

   5. Applied egg-rr 92.8%

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

   if 2.0000000000000002e287 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))

   1. Initial program 13.0%

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

      1. *-commutative 13.0%

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

      2. associate-*l/ 15.9%

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

      3. associate-+l+ 15.9%

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

      4. associate-*r/ 24.1%

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

      5. *-commutative 24.1%

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

   3. Simplified 24.1%

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

   4. Taylor expanded in t around 0 80.6%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -\infty:\\ \;\;\;\;\frac{y \cdot \frac{z}{1 + \left(a + \frac{y \cdot b}{t}\right)}}{t}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 2 \cdot 10^{+287}:\\ \;\;\;\;\frac{x + \left(y \cdot z\right) \cdot \frac{1}{t}}{a + \left(1 + \frac{b}{\frac{t}{y}}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 4: 78.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot b}{t}\\ t_2 := \frac{x + y \cdot \frac{z}{t}}{a + \left(1 + y \cdot \frac{b}{t}\right)}\\ \mathbf{if}\;t \leq -2.75 \cdot 10^{-223}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.26 \cdot 10^{-232}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{-205}:\\ \;\;\;\;\frac{y \cdot z}{t \cdot \left(1 + \left(a + t_1\right)\right)}\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{-191}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-127}:\\ \;\;\;\;\frac{x + \left(y \cdot z\right) \cdot \frac{1}{t}}{1 + t_1}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* y b) t))
        (t_2 (/ (+ x (* y (/ z t))) (+ a (+ 1.0 (* y (/ b t)))))))
   (if (<= t -2.75e-223)
     t_2
     (if (<= t 1.26e-232)
       (/ z b)
       (if (<= t 7.5e-205)
         (/ (* y z) (* t (+ 1.0 (+ a t_1))))
         (if (<= t 1.5e-191)
           (/ z b)
           (if (<= t 6e-127)
             (/ (+ x (* (* y z) (/ 1.0 t))) (+ 1.0 t_1))
             t_2)))))))

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))) / (a + (1.0 + (y * (b / t))));
	double tmp;
	if (t <= -2.75e-223) {
		tmp = t_2;
	} else if (t <= 1.26e-232) {
		tmp = z / b;
	} else if (t <= 7.5e-205) {
		tmp = (y * z) / (t * (1.0 + (a + t_1)));
	} else if (t <= 1.5e-191) {
		tmp = z / b;
	} else if (t <= 6e-127) {
		tmp = (x + ((y * z) * (1.0 / t))) / (1.0 + t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (y * b) / t
    t_2 = (x + (y * (z / t))) / (a + (1.0d0 + (y * (b / t))))
    if (t <= (-2.75d-223)) then
        tmp = t_2
    else if (t <= 1.26d-232) then
        tmp = z / b
    else if (t <= 7.5d-205) then
        tmp = (y * z) / (t * (1.0d0 + (a + t_1)))
    else if (t <= 1.5d-191) then
        tmp = z / b
    else if (t <= 6d-127) then
        tmp = (x + ((y * z) * (1.0d0 / t))) / (1.0d0 + t_1)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y * b) / t;
	double t_2 = (x + (y * (z / t))) / (a + (1.0 + (y * (b / t))));
	double tmp;
	if (t <= -2.75e-223) {
		tmp = t_2;
	} else if (t <= 1.26e-232) {
		tmp = z / b;
	} else if (t <= 7.5e-205) {
		tmp = (y * z) / (t * (1.0 + (a + t_1)));
	} else if (t <= 1.5e-191) {
		tmp = z / b;
	} else if (t <= 6e-127) {
		tmp = (x + ((y * z) * (1.0 / t))) / (1.0 + t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (y * b) / t
	t_2 = (x + (y * (z / t))) / (a + (1.0 + (y * (b / t))))
	tmp = 0
	if t <= -2.75e-223:
		tmp = t_2
	elif t <= 1.26e-232:
		tmp = z / b
	elif t <= 7.5e-205:
		tmp = (y * z) / (t * (1.0 + (a + t_1)))
	elif t <= 1.5e-191:
		tmp = z / b
	elif t <= 6e-127:
		tmp = (x + ((y * z) * (1.0 / t))) / (1.0 + t_1)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y * b) / t)
	t_2 = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(a + Float64(1.0 + Float64(y * Float64(b / t)))))
	tmp = 0.0
	if (t <= -2.75e-223)
		tmp = t_2;
	elseif (t <= 1.26e-232)
		tmp = Float64(z / b);
	elseif (t <= 7.5e-205)
		tmp = Float64(Float64(y * z) / Float64(t * Float64(1.0 + Float64(a + t_1))));
	elseif (t <= 1.5e-191)
		tmp = Float64(z / b);
	elseif (t <= 6e-127)
		tmp = Float64(Float64(x + Float64(Float64(y * z) * Float64(1.0 / t))) / Float64(1.0 + t_1));
	else
		tmp = t_2;
	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))) / (a + (1.0 + (y * (b / t))));
	tmp = 0.0;
	if (t <= -2.75e-223)
		tmp = t_2;
	elseif (t <= 1.26e-232)
		tmp = z / b;
	elseif (t <= 7.5e-205)
		tmp = (y * z) / (t * (1.0 + (a + t_1)));
	elseif (t <= 1.5e-191)
		tmp = z / b;
	elseif (t <= 6e-127)
		tmp = (x + ((y * z) * (1.0 / t))) / (1.0 + t_1);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + N[(1.0 + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.75e-223], t$95$2, If[LessEqual[t, 1.26e-232], N[(z / b), $MachinePrecision], If[LessEqual[t, 7.5e-205], N[(N[(y * z), $MachinePrecision] / N[(t * N[(1.0 + N[(a + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.5e-191], N[(z / b), $MachinePrecision], If[LessEqual[t, 6e-127], N[(N[(x + N[(N[(y * z), $MachinePrecision] * N[(1.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(1.0 + t$95$1), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.75e-223 or 6.00000000000000017e-127 < t

   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/ 84.4%

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

      3. associate-+l+ 84.4%

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

      4. associate-*r/ 89.5%

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

      5. *-commutative 89.5%

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

   3. Simplified 89.5%

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

   if -2.75e-223 < t < 1.25999999999999991e-232 or 7.4999999999999996e-205 < t < 1.5e-191

   1. Initial program 33.4%

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

      1. *-commutative 33.4%

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

      2. associate-*l/ 24.8%

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

      3. associate-+l+ 24.9%

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

      4. associate-*r/ 24.5%

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

      5. *-commutative 24.5%

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

   3. Simplified 24.5%

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

   4. Taylor expanded in t around 0 88.9%

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

   if 1.25999999999999991e-232 < t < 7.4999999999999996e-205

   1. Initial program 64.0%

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

      1. *-commutative 64.0%

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

      2. associate-*l/ 52.1%

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

      3. associate-+l+ 52.1%

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

      4. associate-*r/ 51.5%

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

      5. *-commutative 51.5%

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

   3. Simplified 51.5%

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

   4. Taylor expanded in x around 0 87.2%

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

   if 1.5e-191 < t < 6.00000000000000017e-127

   1. Initial program 99.6%

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

      1. associate-/l* 75.0%

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

      2. associate-*l/ 74.8%

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

      3. *-commutative 74.8%

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

      4. cancel-sign-sub 74.8%

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

      5. *-commutative 74.8%

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

      6. associate-*l/ 75.0%

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

      7. associate-+r- 75.0%

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

      8. associate-*l/ 74.8%

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

      9. *-commutative 74.8%

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

      10. cancel-sign-sub 74.8%

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

      11. *-commutative 74.8%

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

      12. associate-*l/ 75.0%

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

      13. *-commutative 75.0%

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

      14. associate-/l* 75.0%

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

   3. Simplified 75.0%

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

      1. associate-/l* 100.0%

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

      2. div-inv 99.8%

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

      3. *-commutative 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in a around 0 85.7%

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

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.75 \cdot 10^{-223}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + \left(1 + y \cdot \frac{b}{t}\right)}\\ \mathbf{elif}\;t \leq 1.26 \cdot 10^{-232}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{-205}:\\ \;\;\;\;\frac{y \cdot z}{t \cdot \left(1 + \left(a + \frac{y \cdot b}{t}\right)\right)}\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{-191}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-127}:\\ \;\;\;\;\frac{x + \left(y \cdot z\right) \cdot \frac{1}{t}}{1 + \frac{y \cdot b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + \left(1 + y \cdot \frac{b}{t}\right)}\\ \end{array} \]

Alternative 5: 66.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot z}{t}\\ \mathbf{if}\;a \leq -1.25 \cdot 10^{+190}:\\ \;\;\;\;\frac{t_1}{a}\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{+112}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq -3.5 \cdot 10^{-9}:\\ \;\;\;\;\frac{t_1}{a + 1}\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{-8}:\\ \;\;\;\;\frac{x + \left(y \cdot z\right) \cdot \frac{1}{t}}{1 + \frac{y \cdot b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (/ (* y z) t))))
   (if (<= a -1.25e+190)
     (/ t_1 a)
     (if (<= a -3.8e+112)
       (/ z b)
       (if (<= a -3.5e-9)
         (/ t_1 (+ a 1.0))
         (if (<= a 3.1e-8)
           (/ (+ x (* (* y z) (/ 1.0 t))) (+ 1.0 (/ (* y b) t)))
           (/ (+ x (* y (/ z t))) (+ a 1.0))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + ((y * z) / t);
	double tmp;
	if (a <= -1.25e+190) {
		tmp = t_1 / a;
	} else if (a <= -3.8e+112) {
		tmp = z / b;
	} else if (a <= -3.5e-9) {
		tmp = t_1 / (a + 1.0);
	} else if (a <= 3.1e-8) {
		tmp = (x + ((y * z) * (1.0 / t))) / (1.0 + ((y * b) / t));
	} else {
		tmp = (x + (y * (z / t))) / (a + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y * z) / t)
    if (a <= (-1.25d+190)) then
        tmp = t_1 / a
    else if (a <= (-3.8d+112)) then
        tmp = z / b
    else if (a <= (-3.5d-9)) then
        tmp = t_1 / (a + 1.0d0)
    else if (a <= 3.1d-8) then
        tmp = (x + ((y * z) * (1.0d0 / t))) / (1.0d0 + ((y * b) / t))
    else
        tmp = (x + (y * (z / t))) / (a + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + ((y * z) / t);
	double tmp;
	if (a <= -1.25e+190) {
		tmp = t_1 / a;
	} else if (a <= -3.8e+112) {
		tmp = z / b;
	} else if (a <= -3.5e-9) {
		tmp = t_1 / (a + 1.0);
	} else if (a <= 3.1e-8) {
		tmp = (x + ((y * z) * (1.0 / t))) / (1.0 + ((y * b) / t));
	} else {
		tmp = (x + (y * (z / t))) / (a + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + ((y * z) / t)
	tmp = 0
	if a <= -1.25e+190:
		tmp = t_1 / a
	elif a <= -3.8e+112:
		tmp = z / b
	elif a <= -3.5e-9:
		tmp = t_1 / (a + 1.0)
	elif a <= 3.1e-8:
		tmp = (x + ((y * z) * (1.0 / t))) / (1.0 + ((y * b) / t))
	else:
		tmp = (x + (y * (z / t))) / (a + 1.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(Float64(y * z) / t))
	tmp = 0.0
	if (a <= -1.25e+190)
		tmp = Float64(t_1 / a);
	elseif (a <= -3.8e+112)
		tmp = Float64(z / b);
	elseif (a <= -3.5e-9)
		tmp = Float64(t_1 / Float64(a + 1.0));
	elseif (a <= 3.1e-8)
		tmp = Float64(Float64(x + Float64(Float64(y * z) * Float64(1.0 / t))) / Float64(1.0 + Float64(Float64(y * b) / t)));
	else
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(a + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + ((y * z) / t);
	tmp = 0.0;
	if (a <= -1.25e+190)
		tmp = t_1 / a;
	elseif (a <= -3.8e+112)
		tmp = z / b;
	elseif (a <= -3.5e-9)
		tmp = t_1 / (a + 1.0);
	elseif (a <= 3.1e-8)
		tmp = (x + ((y * z) * (1.0 / t))) / (1.0 + ((y * b) / t));
	else
		tmp = (x + (y * (z / t))) / (a + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.25e+190], N[(t$95$1 / a), $MachinePrecision], If[LessEqual[a, -3.8e+112], N[(z / b), $MachinePrecision], If[LessEqual[a, -3.5e-9], N[(t$95$1 / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.1e-8], N[(N[(x + N[(N[(y * z), $MachinePrecision] * N[(1.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(1.0 + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.25000000000000009e190

   1. Initial program 78.3%

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

      1. *-commutative 78.3%

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

      2. associate-*l/ 74.2%

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

      3. associate-+l+ 74.2%

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

      4. associate-*r/ 78.3%

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

      5. *-commutative 78.3%

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

   3. Simplified 78.3%

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

   4. Taylor expanded in a around inf 75.7%

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

   if -1.25000000000000009e190 < a < -3.80000000000000008e112

   1. Initial program 56.3%

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

      1. *-commutative 56.3%

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

      2. associate-*l/ 51.3%

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

      3. associate-+l+ 51.3%

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

      4. associate-*r/ 55.6%

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

      5. *-commutative 55.6%

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

   3. Simplified 55.6%

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

   4. Taylor expanded in t around 0 66.3%

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

   if -3.80000000000000008e112 < a < -3.4999999999999999e-9

   1. Initial program 86.7%

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

      1. *-commutative 86.7%

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

      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. associate-+l+ 86.7%

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

      4. associate-*r/ 86.7%

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

      5. *-commutative 86.7%

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

   3. Simplified 86.7%

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

   4. Taylor expanded in b around 0 75.4%

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

   if -3.4999999999999999e-9 < a < 3.1e-8

   1. Initial program 80.8%

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

      1. associate-/l* 79.3%

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

      2. associate-*l/ 84.4%

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

      3. *-commutative 84.4%

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

      4. cancel-sign-sub 84.4%

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

      5. *-commutative 84.4%

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

      6. associate-*l/ 79.3%

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

      7. associate-+r- 79.3%

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

      8. associate-*l/ 84.4%

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

      9. *-commutative 84.4%

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

      10. cancel-sign-sub 84.4%

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

      11. *-commutative 84.4%

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

      12. associate-*l/ 79.3%

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

      13. *-commutative 79.3%

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

      14. associate-/l* 84.4%

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

   3. Simplified 84.4%

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

      1. associate-/l* 85.1%

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

      2. div-inv 85.1%

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

      3. *-commutative 85.1%

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

   5. Applied egg-rr 85.1%

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

   6. Taylor expanded in a around 0 80.7%

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

   if 3.1e-8 < a

   1. Initial program 69.9%

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

      1. *-commutative 69.9%

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

      2. associate-*l/ 70.0%

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

      3. associate-+l+ 70.0%

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

      4. associate-*r/ 73.3%

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

      5. *-commutative 73.3%

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

   3. Simplified 73.3%

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

   4. Taylor expanded in b around 0 63.9%

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

4. Final simplification 74.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.25 \cdot 10^{+190}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a}\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{+112}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq -3.5 \cdot 10^{-9}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{-8}:\\ \;\;\;\;\frac{x + \left(y \cdot z\right) \cdot \frac{1}{t}}{1 + \frac{y \cdot b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \end{array} \]

Alternative 6: 64.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{-134}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-233}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-171}:\\ \;\;\;\;\frac{y \cdot z}{t \cdot \left(1 + \left(a + \frac{y \cdot b}{t}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -7.5e-134)
   (/ (+ x (/ (* y z) t)) (+ a 1.0))
   (if (<= t 5e-233)
     (/ z b)
     (if (<= t 3.5e-171)
       (/ (* y z) (* t (+ 1.0 (+ a (/ (* y b) t)))))
       (/ (+ 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 <= -7.5e-134) {
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	} else if (t <= 5e-233) {
		tmp = z / b;
	} else if (t <= 3.5e-171) {
		tmp = (y * z) / (t * (1.0 + (a + ((y * b) / t))));
	} 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 <= (-7.5d-134)) then
        tmp = (x + ((y * z) / t)) / (a + 1.0d0)
    else if (t <= 5d-233) then
        tmp = z / b
    else if (t <= 3.5d-171) then
        tmp = (y * z) / (t * (1.0d0 + (a + ((y * b) / t))))
    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 <= -7.5e-134) {
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	} else if (t <= 5e-233) {
		tmp = z / b;
	} else if (t <= 3.5e-171) {
		tmp = (y * z) / (t * (1.0 + (a + ((y * b) / t))));
	} else {
		tmp = (x + (y * (z / t))) / (a + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -7.5e-134:
		tmp = (x + ((y * z) / t)) / (a + 1.0)
	elif t <= 5e-233:
		tmp = z / b
	elif t <= 3.5e-171:
		tmp = (y * z) / (t * (1.0 + (a + ((y * b) / t))))
	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 <= -7.5e-134)
		tmp = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(a + 1.0));
	elseif (t <= 5e-233)
		tmp = Float64(z / b);
	elseif (t <= 3.5e-171)
		tmp = Float64(Float64(y * z) / Float64(t * Float64(1.0 + Float64(a + Float64(Float64(y * b) / t)))));
	else
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(a + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -7.5e-134)
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	elseif (t <= 5e-233)
		tmp = z / b;
	elseif (t <= 3.5e-171)
		tmp = (y * z) / (t * (1.0 + (a + ((y * b) / t))));
	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, -7.5e-134], N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5e-233], N[(z / b), $MachinePrecision], If[LessEqual[t, 3.5e-171], N[(N[(y * z), $MachinePrecision] / N[(t * N[(1.0 + N[(a + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -7.50000000000000048e-134

   1. Initial program 84.9%

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

      1. *-commutative 84.9%

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

      2. associate-*l/ 82.6%

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

      3. associate-+l+ 82.6%

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

      4. associate-*r/ 88.3%

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

      5. *-commutative 88.3%

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

   3. Simplified 88.3%

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

   4. Taylor expanded in b around 0 73.7%

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

   if -7.50000000000000048e-134 < t < 5.00000000000000012e-233

   1. Initial program 46.9%

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

      1. *-commutative 46.9%

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

      2. associate-*l/ 41.0%

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

      3. associate-+l+ 41.0%

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

      4. associate-*r/ 40.7%

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

      5. *-commutative 40.7%

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

   3. Simplified 40.7%

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

   4. Taylor expanded in t around 0 69.8%

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

   if 5.00000000000000012e-233 < t < 3.49999999999999994e-171

   1. Initial program 65.3%

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

      1. *-commutative 65.3%

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

      2. associate-*l/ 44.8%

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

      3. associate-+l+ 44.8%

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

      4. associate-*r/ 44.3%

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

      5. *-commutative 44.3%

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

   3. Simplified 44.3%

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

   4. Taylor expanded in x around 0 78.6%

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

   if 3.49999999999999994e-171 < t

   1. Initial program 85.4%

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

      1. *-commutative 85.4%

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

      2. associate-*l/ 89.1%

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

      3. associate-+l+ 89.1%

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

      4. associate-*r/ 94.5%

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

      5. *-commutative 94.5%

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

   3. Simplified 94.5%

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

   4. Taylor expanded in b around 0 75.3%

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

4. Final simplification 73.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{-134}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-233}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-171}:\\ \;\;\;\;\frac{y \cdot z}{t \cdot \left(1 + \left(a + \frac{y \cdot b}{t}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \end{array} \]

Alternative 7: 60.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 + \left(a + b \cdot \frac{y}{t}\right)}\\ \mathbf{if}\;t \leq -3.4 \cdot 10^{-46}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.25 \cdot 10^{-132}:\\ \;\;\;\;\frac{\frac{y}{\frac{a + 1}{z}}}{t}\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{-133}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{-172}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (+ 1.0 (+ a (* b (/ y t)))))))
   (if (<= t -3.4e-46)
     t_1
     (if (<= t -1.25e-132)
       (/ (/ y (/ (+ a 1.0) z)) t)
       (if (<= t -1.8e-133) x (if (<= t 3.9e-172) (/ z b) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 + (a + (b * (y / t))));
	double tmp;
	if (t <= -3.4e-46) {
		tmp = t_1;
	} else if (t <= -1.25e-132) {
		tmp = (y / ((a + 1.0) / z)) / t;
	} else if (t <= -1.8e-133) {
		tmp = x;
	} else if (t <= 3.9e-172) {
		tmp = z / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (1.0d0 + (a + (b * (y / t))))
    if (t <= (-3.4d-46)) then
        tmp = t_1
    else if (t <= (-1.25d-132)) then
        tmp = (y / ((a + 1.0d0) / z)) / t
    else if (t <= (-1.8d-133)) then
        tmp = x
    else if (t <= 3.9d-172) then
        tmp = z / b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 + (a + (b * (y / t))));
	double tmp;
	if (t <= -3.4e-46) {
		tmp = t_1;
	} else if (t <= -1.25e-132) {
		tmp = (y / ((a + 1.0) / z)) / t;
	} else if (t <= -1.8e-133) {
		tmp = x;
	} else if (t <= 3.9e-172) {
		tmp = z / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (1.0 + (a + (b * (y / t))))
	tmp = 0
	if t <= -3.4e-46:
		tmp = t_1
	elif t <= -1.25e-132:
		tmp = (y / ((a + 1.0) / z)) / t
	elif t <= -1.8e-133:
		tmp = x
	elif t <= 3.9e-172:
		tmp = z / b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(1.0 + Float64(a + Float64(b * Float64(y / t)))))
	tmp = 0.0
	if (t <= -3.4e-46)
		tmp = t_1;
	elseif (t <= -1.25e-132)
		tmp = Float64(Float64(y / Float64(Float64(a + 1.0) / z)) / t);
	elseif (t <= -1.8e-133)
		tmp = x;
	elseif (t <= 3.9e-172)
		tmp = Float64(z / b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (1.0 + (a + (b * (y / t))));
	tmp = 0.0;
	if (t <= -3.4e-46)
		tmp = t_1;
	elseif (t <= -1.25e-132)
		tmp = (y / ((a + 1.0) / z)) / t;
	elseif (t <= -1.8e-133)
		tmp = x;
	elseif (t <= 3.9e-172)
		tmp = z / b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(1.0 + N[(a + N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.4e-46], t$95$1, If[LessEqual[t, -1.25e-132], N[(N[(y / N[(N[(a + 1.0), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[t, -1.8e-133], x, If[LessEqual[t, 3.9e-172], N[(z / b), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -3.39999999999999996e-46 or 3.89999999999999973e-172 < t

   1. Initial program 85.3%

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

      1. *-commutative 85.3%

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

      2. associate-*l/ 88.1%

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

      3. associate-+l+ 88.1%

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

      4. associate-*r/ 94.3%

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

      5. *-commutative 94.3%

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

   3. Simplified 94.3%

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

   4. Taylor expanded in x around inf 69.1%

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

      1. associate-*r/ 72.5%

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

   6. Simplified 72.5%

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

   if -3.39999999999999996e-46 < t < -1.25e-132

   1. Initial program 83.6%

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

      1. *-commutative 83.6%

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

      2. associate-*l/ 67.7%

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

      3. associate-+l+ 67.7%

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

      4. associate-*r/ 67.6%

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

      5. *-commutative 67.6%

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

   3. Simplified 67.6%

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

   4. Taylor expanded in x around 0 68.1%

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

      1. times-frac 62.7%

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

      2. associate-*r/ 62.3%

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

   6. Simplified 62.3%

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

   7. Taylor expanded in y around 0 50.4%

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

      1. *-commutative 50.4%

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

      2. associate-/r* 50.3%

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

      3. associate-/l* 55.5%

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

   9. Simplified 55.5%

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

   if -1.25e-132 < t < -1.8000000000000002e-133

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. associate-*l/ 100.0%

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

      3. associate-+l+ 100.0%

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

      4. associate-*r/ 100.0%

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

      5. *-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in t around inf 100.0%

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

   5. Taylor expanded in a around 0 100.0%

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

   if -1.8000000000000002e-133 < t < 3.89999999999999973e-172

   1. Initial program 50.9%

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

      1. *-commutative 50.9%

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

      2. associate-*l/ 41.8%

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

      3. associate-+l+ 41.8%

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

      4. associate-*r/ 41.5%

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

      5. *-commutative 41.5%

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

   3. Simplified 41.5%

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

   4. Taylor expanded in t around 0 64.4%

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

4. Final simplification 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{-46}:\\ \;\;\;\;\frac{x}{1 + \left(a + b \cdot \frac{y}{t}\right)}\\ \mathbf{elif}\;t \leq -1.25 \cdot 10^{-132}:\\ \;\;\;\;\frac{\frac{y}{\frac{a + 1}{z}}}{t}\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{-133}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{-172}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 + \left(a + b \cdot \frac{y}{t}\right)}\\ \end{array} \]

Alternative 8: 40.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.25 \cdot 10^{+190}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;a \leq -2.5 \cdot 10^{+111}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq -1.32 \cdot 10^{+17}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;a \leq -1.05 \cdot 10^{-141}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{-18}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{+86}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -1.25e+190)
   (/ x a)
   (if (<= a -2.5e+111)
     (/ z b)
     (if (<= a -1.32e+17)
       (/ x a)
       (if (<= a -1.05e-141)
         (/ z b)
         (if (<= a 2.3e-18) x (if (<= a 1.75e+86) (/ z b) (/ x a))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -1.25e+190) {
		tmp = x / a;
	} else if (a <= -2.5e+111) {
		tmp = z / b;
	} else if (a <= -1.32e+17) {
		tmp = x / a;
	} else if (a <= -1.05e-141) {
		tmp = z / b;
	} else if (a <= 2.3e-18) {
		tmp = x;
	} else if (a <= 1.75e+86) {
		tmp = z / b;
	} else {
		tmp = x / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-1.25d+190)) then
        tmp = x / a
    else if (a <= (-2.5d+111)) then
        tmp = z / b
    else if (a <= (-1.32d+17)) then
        tmp = x / a
    else if (a <= (-1.05d-141)) then
        tmp = z / b
    else if (a <= 2.3d-18) then
        tmp = x
    else if (a <= 1.75d+86) then
        tmp = z / b
    else
        tmp = x / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -1.25e+190) {
		tmp = x / a;
	} else if (a <= -2.5e+111) {
		tmp = z / b;
	} else if (a <= -1.32e+17) {
		tmp = x / a;
	} else if (a <= -1.05e-141) {
		tmp = z / b;
	} else if (a <= 2.3e-18) {
		tmp = x;
	} else if (a <= 1.75e+86) {
		tmp = z / b;
	} else {
		tmp = x / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -1.25e+190:
		tmp = x / a
	elif a <= -2.5e+111:
		tmp = z / b
	elif a <= -1.32e+17:
		tmp = x / a
	elif a <= -1.05e-141:
		tmp = z / b
	elif a <= 2.3e-18:
		tmp = x
	elif a <= 1.75e+86:
		tmp = z / b
	else:
		tmp = x / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -1.25e+190)
		tmp = Float64(x / a);
	elseif (a <= -2.5e+111)
		tmp = Float64(z / b);
	elseif (a <= -1.32e+17)
		tmp = Float64(x / a);
	elseif (a <= -1.05e-141)
		tmp = Float64(z / b);
	elseif (a <= 2.3e-18)
		tmp = x;
	elseif (a <= 1.75e+86)
		tmp = Float64(z / b);
	else
		tmp = Float64(x / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -1.25e+190)
		tmp = x / a;
	elseif (a <= -2.5e+111)
		tmp = z / b;
	elseif (a <= -1.32e+17)
		tmp = x / a;
	elseif (a <= -1.05e-141)
		tmp = z / b;
	elseif (a <= 2.3e-18)
		tmp = x;
	elseif (a <= 1.75e+86)
		tmp = z / b;
	else
		tmp = x / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -1.25e+190], N[(x / a), $MachinePrecision], If[LessEqual[a, -2.5e+111], N[(z / b), $MachinePrecision], If[LessEqual[a, -1.32e+17], N[(x / a), $MachinePrecision], If[LessEqual[a, -1.05e-141], N[(z / b), $MachinePrecision], If[LessEqual[a, 2.3e-18], x, If[LessEqual[a, 1.75e+86], N[(z / b), $MachinePrecision], N[(x / a), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.25000000000000009e190 or -2.4999999999999998e111 < a < -1.32e17 or 1.75000000000000009e86 < a

   1. Initial program 77.0%

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

      1. *-commutative 77.0%

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

      2. associate-*l/ 75.9%

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

      3. associate-+l+ 75.9%

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

      4. associate-*r/ 79.3%

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

      5. *-commutative 79.3%

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

   3. Simplified 79.3%

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

   4. Taylor expanded in x around inf 57.5%

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

      1. associate-*r/ 58.8%

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

   6. Simplified 58.8%

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

   7. Taylor expanded in a around inf 56.5%

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

   if -1.25000000000000009e190 < a < -2.4999999999999998e111 or -1.32e17 < a < -1.05e-141 or 2.3000000000000001e-18 < a < 1.75000000000000009e86

   1. Initial program 63.5%

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

      1. *-commutative 63.5%

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

      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. associate-+l+ 60.9%

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

      4. associate-*r/ 67.4%

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

      5. *-commutative 67.4%

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

   3. Simplified 67.4%

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

   4. Taylor expanded in t around 0 51.8%

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

   if -1.05e-141 < a < 2.3000000000000001e-18

   1. Initial program 86.0%

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

      1. *-commutative 86.0%

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

      2. associate-*l/ 85.1%

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

      3. associate-+l+ 85.1%

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

      4. associate-*r/ 88.0%

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

      5. *-commutative 88.0%

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

   3. Simplified 88.0%

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

   4. Taylor expanded in t around inf 53.0%

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

   5. Taylor expanded in a around 0 53.0%

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

4. Final simplification 53.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.25 \cdot 10^{+190}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;a \leq -2.5 \cdot 10^{+111}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq -1.32 \cdot 10^{+17}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;a \leq -1.05 \cdot 10^{-141}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{-18}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{+86}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \]

Alternative 9: 65.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{-133} \lor \neg \left(t \leq 7.7 \cdot 10^{-171}\right):\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -1.35e-133) (not (<= t 7.7e-171)))
   (/ (+ 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 tmp;
	if ((t <= -1.35e-133) || !(t <= 7.7e-171)) {
		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) :: tmp
    if ((t <= (-1.35d-133)) .or. (.not. (t <= 7.7d-171))) 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 tmp;
	if ((t <= -1.35e-133) || !(t <= 7.7e-171)) {
		tmp = (x + (y * (z / t))) / (a + 1.0);
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -1.35e-133) or not (t <= 7.7e-171):
		tmp = (x + (y * (z / t))) / (a + 1.0)
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -1.35e-133) || !(t <= 7.7e-171))
		tmp = Float64(Float64(x + Float64(y * Float64(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)
	tmp = 0.0;
	if ((t <= -1.35e-133) || ~((t <= 7.7e-171)))
		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_] := If[Or[LessEqual[t, -1.35e-133], N[Not[LessEqual[t, 7.7e-171]], $MachinePrecision]], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.3499999999999999e-133 or 7.6999999999999996e-171 < t

   1. Initial program 85.2%

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

      1. *-commutative 85.2%

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

      2. associate-*l/ 86.3%

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

      3. associate-+l+ 86.3%

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

      4. associate-*r/ 91.8%

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

      5. *-commutative 91.8%

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

   3. Simplified 91.8%

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

   4. Taylor expanded in b around 0 73.7%

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

   if -1.3499999999999999e-133 < t < 7.6999999999999996e-171

   1. Initial program 50.9%

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

      1. *-commutative 50.9%

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

      2. associate-*l/ 41.8%

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

      3. associate-+l+ 41.8%

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

      4. associate-*r/ 41.5%

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

      5. *-commutative 41.5%

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

   3. Simplified 41.5%

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

   4. Taylor expanded in t around 0 64.4%

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

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{-133} \lor \neg \left(t \leq 7.7 \cdot 10^{-171}\right):\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 10: 64.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{-133}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \mathbf{elif}\;t \leq 7.7 \cdot 10^{-171}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.1e-133)
   (/ (+ x (/ (* y z) t)) (+ a 1.0))
   (if (<= t 7.7e-171) (/ z b) (/ (+ 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 <= -1.1e-133) {
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	} else if (t <= 7.7e-171) {
		tmp = z / b;
	} 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 <= (-1.1d-133)) then
        tmp = (x + ((y * z) / t)) / (a + 1.0d0)
    else if (t <= 7.7d-171) then
        tmp = z / b
    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 <= -1.1e-133) {
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	} else if (t <= 7.7e-171) {
		tmp = z / b;
	} else {
		tmp = (x + (y * (z / t))) / (a + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1.1e-133:
		tmp = (x + ((y * z) / t)) / (a + 1.0)
	elif t <= 7.7e-171:
		tmp = z / b
	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 <= -1.1e-133)
		tmp = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(a + 1.0));
	elseif (t <= 7.7e-171)
		tmp = Float64(z / b);
	else
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(a + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -1.1e-133)
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	elseif (t <= 7.7e-171)
		tmp = z / b;
	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, -1.1e-133], N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.7e-171], N[(z / b), $MachinePrecision], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.1e-133

   1. Initial program 84.9%

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

      1. *-commutative 84.9%

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

      2. associate-*l/ 82.6%

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

      3. associate-+l+ 82.6%

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

      4. associate-*r/ 88.3%

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

      5. *-commutative 88.3%

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

   3. Simplified 88.3%

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

   4. Taylor expanded in b around 0 73.7%

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

   if -1.1e-133 < t < 7.6999999999999996e-171

   1. Initial program 50.9%

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

      1. *-commutative 50.9%

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

      2. associate-*l/ 41.8%

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

      3. associate-+l+ 41.8%

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

      4. associate-*r/ 41.5%

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

      5. *-commutative 41.5%

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

   3. Simplified 41.5%

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

   4. Taylor expanded in t around 0 64.4%

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

   if 7.6999999999999996e-171 < t

   1. Initial program 85.4%

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

      1. *-commutative 85.4%

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

      2. associate-*l/ 89.1%

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

      3. associate-+l+ 89.1%

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

      4. associate-*r/ 94.5%

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

      5. *-commutative 94.5%

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

   3. Simplified 94.5%

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

   4. Taylor expanded in b around 0 75.3%

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

4. Final simplification 72.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{-133}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \mathbf{elif}\;t \leq 7.7 \cdot 10^{-171}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \end{array} \]

Alternative 11: 40.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.65 \cdot 10^{+192}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;a \leq -3.1 \cdot 10^{+112}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq -1:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{-18}:\\ \;\;\;\;x - x \cdot a\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{+85}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -1.65e+192)
   (/ x a)
   (if (<= a -3.1e+112)
     (/ z b)
     (if (<= a -1.0)
       (/ x a)
       (if (<= a 2.4e-18)
         (- x (* x a))
         (if (<= a 1.9e+85) (/ z b) (/ x a)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -1.65e+192) {
		tmp = x / a;
	} else if (a <= -3.1e+112) {
		tmp = z / b;
	} else if (a <= -1.0) {
		tmp = x / a;
	} else if (a <= 2.4e-18) {
		tmp = x - (x * a);
	} else if (a <= 1.9e+85) {
		tmp = z / b;
	} else {
		tmp = x / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-1.65d+192)) then
        tmp = x / a
    else if (a <= (-3.1d+112)) then
        tmp = z / b
    else if (a <= (-1.0d0)) then
        tmp = x / a
    else if (a <= 2.4d-18) then
        tmp = x - (x * a)
    else if (a <= 1.9d+85) then
        tmp = z / b
    else
        tmp = x / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -1.65e+192) {
		tmp = x / a;
	} else if (a <= -3.1e+112) {
		tmp = z / b;
	} else if (a <= -1.0) {
		tmp = x / a;
	} else if (a <= 2.4e-18) {
		tmp = x - (x * a);
	} else if (a <= 1.9e+85) {
		tmp = z / b;
	} else {
		tmp = x / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -1.65e+192:
		tmp = x / a
	elif a <= -3.1e+112:
		tmp = z / b
	elif a <= -1.0:
		tmp = x / a
	elif a <= 2.4e-18:
		tmp = x - (x * a)
	elif a <= 1.9e+85:
		tmp = z / b
	else:
		tmp = x / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -1.65e+192)
		tmp = Float64(x / a);
	elseif (a <= -3.1e+112)
		tmp = Float64(z / b);
	elseif (a <= -1.0)
		tmp = Float64(x / a);
	elseif (a <= 2.4e-18)
		tmp = Float64(x - Float64(x * a));
	elseif (a <= 1.9e+85)
		tmp = Float64(z / b);
	else
		tmp = Float64(x / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -1.65e+192)
		tmp = x / a;
	elseif (a <= -3.1e+112)
		tmp = z / b;
	elseif (a <= -1.0)
		tmp = x / a;
	elseif (a <= 2.4e-18)
		tmp = x - (x * a);
	elseif (a <= 1.9e+85)
		tmp = z / b;
	else
		tmp = x / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -1.65e+192], N[(x / a), $MachinePrecision], If[LessEqual[a, -3.1e+112], N[(z / b), $MachinePrecision], If[LessEqual[a, -1.0], N[(x / a), $MachinePrecision], If[LessEqual[a, 2.4e-18], N[(x - N[(x * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.9e+85], N[(z / b), $MachinePrecision], N[(x / a), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.65000000000000005e192 or -3.09999999999999983e112 < a < -1 or 1.89999999999999996e85 < 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/ 76.4%

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

      3. associate-+l+ 76.4%

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

      4. associate-*r/ 79.7%

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

      5. *-commutative 79.7%

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

   3. Simplified 79.7%

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

   4. Taylor expanded in x around inf 57.4%

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

      1. associate-*r/ 58.7%

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

   6. Simplified 58.7%

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

   7. Taylor expanded in a around inf 55.7%

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

   if -1.65000000000000005e192 < a < -3.09999999999999983e112 or 2.39999999999999994e-18 < a < 1.89999999999999996e85

   1. Initial program 54.5%

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

      1. *-commutative 54.5%

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

      2. associate-*l/ 51.6%

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

      3. associate-+l+ 51.6%

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

      4. associate-*r/ 54.1%

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

      5. *-commutative 54.1%

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

   3. Simplified 54.1%

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

   4. Taylor expanded in t around 0 63.4%

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

   if -1 < a < 2.39999999999999994e-18

   1. Initial program 81.7%

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

      1. *-commutative 81.7%

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

      2. associate-*l/ 80.3%

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

      3. associate-+l+ 80.3%

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

      4. associate-*r/ 85.3%

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

      5. *-commutative 85.3%

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

   3. Simplified 85.3%

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

   4. Taylor expanded in t around inf 48.3%

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

   5. Taylor expanded in a around 0 47.9%

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

      1. mul-1-neg 47.9%

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

      2. unsub-neg 47.9%

         \[\leadsto \color{blue}{x - a \cdot x} \]

   7. Simplified 47.9%

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

4. Final simplification 52.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.65 \cdot 10^{+192}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;a \leq -3.1 \cdot 10^{+112}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq -1:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{-18}:\\ \;\;\;\;x - x \cdot a\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{+85}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \]

Alternative 12: 55.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{+45} \lor \neg \left(y \leq 10^{+65}\right):\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -7.2e+45) (not (<= y 1e+65))) (/ z b) (/ x (+ a 1.0))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -7.2e+45) || !(y <= 1e+65)) {
		tmp = z / b;
	} else {
		tmp = x / (a + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-7.2d+45)) .or. (.not. (y <= 1d+65))) then
        tmp = z / b
    else
        tmp = x / (a + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -7.2e+45) || !(y <= 1e+65)) {
		tmp = z / b;
	} else {
		tmp = x / (a + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -7.2e+45) or not (y <= 1e+65):
		tmp = z / b
	else:
		tmp = x / (a + 1.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -7.2e+45) || !(y <= 1e+65))
		tmp = Float64(z / b);
	else
		tmp = Float64(x / Float64(a + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -7.2e+45) || ~((y <= 1e+65)))
		tmp = z / b;
	else
		tmp = x / (a + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -7.2e+45], N[Not[LessEqual[y, 1e+65]], $MachinePrecision]], N[(z / b), $MachinePrecision], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.2e45 or 9.9999999999999999e64 < y

   1. Initial program 52.6%

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

      1. *-commutative 52.6%

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

      2. associate-*l/ 57.7%

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

      3. associate-+l+ 57.7%

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

      4. associate-*r/ 68.7%

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

      5. *-commutative 68.7%

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

   3. Simplified 68.7%

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

   4. Taylor expanded in t around 0 55.0%

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

   if -7.2e45 < y < 9.9999999999999999e64

   1. Initial program 91.3%

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

      1. *-commutative 91.3%

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

      2. associate-*l/ 85.8%

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

      3. associate-+l+ 85.8%

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

      4. associate-*r/ 85.6%

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

      5. *-commutative 85.6%

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

   3. Simplified 85.6%

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

   4. Taylor expanded in t around inf 65.3%

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

4. Final simplification 61.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{+45} \lor \neg \left(y \leq 10^{+65}\right):\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \]

Alternative 13: 40.6% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1 \lor \neg \left(a \leq 2.5 \cdot 10^{-18}\right):\\ \;\;\;\;\frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -1.0) (not (<= a 2.5e-18))) (/ x a) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -1.0) || !(a <= 2.5e-18)) {
		tmp = x / a;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((a <= (-1.0d0)) .or. (.not. (a <= 2.5d-18))) then
        tmp = x / a
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -1.0) || !(a <= 2.5e-18)) {
		tmp = x / a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -1.0) or not (a <= 2.5e-18):
		tmp = x / a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -1.0) || !(a <= 2.5e-18))
		tmp = Float64(x / a);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -1.0) || ~((a <= 2.5e-18)))
		tmp = x / a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -1.0], N[Not[LessEqual[a, 2.5e-18]], $MachinePrecision]], N[(x / a), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if a < -1 or 2.50000000000000018e-18 < a

   1. Initial program 71.1%

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

      1. *-commutative 71.1%

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

      2. associate-*l/ 69.6%

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

      3. associate-+l+ 69.6%

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

      4. associate-*r/ 72.7%

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

      5. *-commutative 72.7%

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

   3. Simplified 72.7%

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

   4. Taylor expanded in x around inf 49.9%

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

      1. associate-*r/ 50.8%

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

   6. Simplified 50.8%

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

   7. Taylor expanded in a around inf 46.8%

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

   if -1 < a < 2.50000000000000018e-18

   1. Initial program 81.7%

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

      1. *-commutative 81.7%

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

      2. associate-*l/ 80.3%

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

      3. associate-+l+ 80.3%

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

      4. associate-*r/ 85.3%

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

      5. *-commutative 85.3%

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

   3. Simplified 85.3%

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

   4. Taylor expanded in t around inf 48.3%

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

   5. Taylor expanded in a around 0 47.2%

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

4. Final simplification 47.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1 \lor \neg \left(a \leq 2.5 \cdot 10^{-18}\right):\\ \;\;\;\;\frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 14: 20.0% 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 76.6%

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

   1. *-commutative 76.6%

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

   2. associate-*l/ 75.1%

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

   3. associate-+l+ 75.2%

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

   4. associate-*r/ 79.2%

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

   5. *-commutative 79.2%

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

3. Simplified 79.2%

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

4. Taylor expanded in t around inf 48.0%

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

5. Taylor expanded in a around 0 26.7%

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

6. Final simplification 26.7%

   \[\leadsto x \]

Developer target: 79.4% accurate, 0.7× 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 2023298 
(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))))