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

Percentage Accurate: 75.8% → 88.9%

Time: 18.8s

Alternatives: 17

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: 75.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 88.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{-316}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;\frac{\frac{x \cdot t}{b} + \frac{t \cdot \left(z \cdot \left(-1 - a\right)\right)}{{b}^{2}}}{y} + \frac{z}{b}\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+286}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq \infty:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{\left(a + \frac{y}{\frac{t}{b}}\right) + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t)))))
   (if (<= t_1 -2e-316)
     t_1
     (if (<= t_1 0.0)
       (+
        (/ (+ (/ (* x t) b) (/ (* t (* z (- -1.0 a))) (pow b 2.0))) y)
        (/ z b))
       (if (<= t_1 5e+286)
         t_1
         (if (<= t_1 INFINITY)
           (* (/ y t) (/ z (+ (+ a (/ y (/ t b))) 1.0)))
           (/ z b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
	double tmp;
	if (t_1 <= -2e-316) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = ((((x * t) / b) + ((t * (z * (-1.0 - a))) / pow(b, 2.0))) / y) + (z / b);
	} else if (t_1 <= 5e+286) {
		tmp = t_1;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = (y / t) * (z / ((a + (y / (t / b))) + 1.0));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
	double tmp;
	if (t_1 <= -2e-316) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = ((((x * t) / b) + ((t * (z * (-1.0 - a))) / Math.pow(b, 2.0))) / y) + (z / b);
	} else if (t_1 <= 5e+286) {
		tmp = t_1;
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = (y / t) * (z / ((a + (y / (t / b))) + 1.0));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t))
	tmp = 0
	if t_1 <= -2e-316:
		tmp = t_1
	elif t_1 <= 0.0:
		tmp = ((((x * t) / b) + ((t * (z * (-1.0 - a))) / math.pow(b, 2.0))) / y) + (z / b)
	elif t_1 <= 5e+286:
		tmp = t_1
	elif t_1 <= math.inf:
		tmp = (y / t) * (z / ((a + (y / (t / b))) + 1.0))
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(Float64(a + 1.0) + Float64(Float64(y * b) / t)))
	tmp = 0.0
	if (t_1 <= -2e-316)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(Float64(Float64(Float64(x * t) / b) + Float64(Float64(t * Float64(z * Float64(-1.0 - a))) / (b ^ 2.0))) / y) + Float64(z / b));
	elseif (t_1 <= 5e+286)
		tmp = t_1;
	elseif (t_1 <= Inf)
		tmp = Float64(Float64(y / t) * Float64(z / Float64(Float64(a + Float64(y / Float64(t / b))) + 1.0)));
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
	tmp = 0.0;
	if (t_1 <= -2e-316)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = ((((x * t) / b) + ((t * (z * (-1.0 - a))) / (b ^ 2.0))) / y) + (z / b);
	elseif (t_1 <= 5e+286)
		tmp = t_1;
	elseif (t_1 <= Inf)
		tmp = (y / t) * (z / ((a + (y / (t / b))) + 1.0));
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e-316], t$95$1, If[LessEqual[t$95$1, 0.0], N[(N[(N[(N[(N[(x * t), $MachinePrecision] / b), $MachinePrecision] + N[(N[(t * N[(z * N[(-1.0 - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[Power[b, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] + N[(z / b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+286], t$95$1, If[LessEqual[t$95$1, Infinity], N[(N[(y / t), $MachinePrecision] * N[(z / N[(N[(a + N[(y / N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $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))) < -2.000000017e-316 or -0.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 5.0000000000000004e286

   1. Initial program 96.1%

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

   if -2.000000017e-316 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < -0.0

   1. Initial program 54.8%

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

      1. *-commutative 54.8%

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

      2. associate-*l/ 54.6%

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

      3. *-commutative 54.6%

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

      4. associate-*l/ 65.5%

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

   3. Simplified 65.5%

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

   5. Taylor expanded in y around -inf 69.7%

      \[\leadsto \color{blue}{-1 \cdot \frac{-1 \cdot \frac{t \cdot x}{b} - -1 \cdot \frac{t \cdot \left(z \cdot \left(1 + a\right)\right)}{{b}^{2}}}{y} + \frac{z}{b}} \]

   if 5.0000000000000004e286 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < +inf.0

   1. Initial program 13.2%

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

      1. associate-/l* 68.6%

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

      2. associate-+l+ 68.6%

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

      3. associate-/l* 68.6%

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

   3. Simplified 68.6%

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

      1. associate-/l* 68.6%

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

      2. *-commutative 68.6%

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

      3. associate-*l/ 68.6%

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

      4. div-inv 68.6%

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

      5. associate-*l* 60.2%

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

   6. Applied egg-rr 60.2%

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

   7. Taylor expanded in x around 0 43.9%

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

      1. times-frac 92.0%

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

      2. *-commutative 92.0%

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

      3. associate-/l* 91.9%

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

   9. Simplified 91.9%

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

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

   1. Initial program 0.0%

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

      1. *-commutative 0.0%

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

      2. associate-*l/ 0.5%

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

      3. *-commutative 0.5%

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

      4. associate-*l/ 14.3%

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

   3. Simplified 14.3%

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

   5. Taylor expanded in t around 0 91.2%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -2 \cdot 10^{-316}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 0:\\ \;\;\;\;\frac{\frac{x \cdot t}{b} + \frac{t \cdot \left(z \cdot \left(-1 - a\right)\right)}{{b}^{2}}}{y} + \frac{z}{b}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 5 \cdot 10^{+286}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq \infty:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{\left(a + \frac{y}{\frac{t}{b}}\right) + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 89.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{if}\;t_1 \leq -3 \cdot 10^{-218}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a + \left(b \cdot \left(y \cdot \frac{1}{t}\right) + 1\right)}\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+286}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq \infty:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{\left(a + \frac{y}{\frac{t}{b}}\right) + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t)))))
   (if (<= t_1 -3e-218)
     t_1
     (if (<= t_1 0.0)
       (/ (+ x (/ y (/ t z))) (+ a (+ (* b (* y (/ 1.0 t))) 1.0)))
       (if (<= t_1 5e+286)
         t_1
         (if (<= t_1 INFINITY)
           (* (/ y t) (/ z (+ (+ a (/ y (/ t b))) 1.0)))
           (/ z b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
	double tmp;
	if (t_1 <= -3e-218) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = (x + (y / (t / z))) / (a + ((b * (y * (1.0 / t))) + 1.0));
	} else if (t_1 <= 5e+286) {
		tmp = t_1;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = (y / t) * (z / ((a + (y / (t / b))) + 1.0));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
	double tmp;
	if (t_1 <= -3e-218) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = (x + (y / (t / z))) / (a + ((b * (y * (1.0 / t))) + 1.0));
	} else if (t_1 <= 5e+286) {
		tmp = t_1;
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = (y / t) * (z / ((a + (y / (t / b))) + 1.0));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t))
	tmp = 0
	if t_1 <= -3e-218:
		tmp = t_1
	elif t_1 <= 0.0:
		tmp = (x + (y / (t / z))) / (a + ((b * (y * (1.0 / t))) + 1.0))
	elif t_1 <= 5e+286:
		tmp = t_1
	elif t_1 <= math.inf:
		tmp = (y / t) * (z / ((a + (y / (t / b))) + 1.0))
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(Float64(a + 1.0) + Float64(Float64(y * b) / t)))
	tmp = 0.0
	if (t_1 <= -3e-218)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(x + Float64(y / Float64(t / z))) / Float64(a + Float64(Float64(b * Float64(y * Float64(1.0 / t))) + 1.0)));
	elseif (t_1 <= 5e+286)
		tmp = t_1;
	elseif (t_1 <= Inf)
		tmp = Float64(Float64(y / t) * Float64(z / Float64(Float64(a + Float64(y / Float64(t / b))) + 1.0)));
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
	tmp = 0.0;
	if (t_1 <= -3e-218)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = (x + (y / (t / z))) / (a + ((b * (y * (1.0 / t))) + 1.0));
	elseif (t_1 <= 5e+286)
		tmp = t_1;
	elseif (t_1 <= Inf)
		tmp = (y / t) * (z / ((a + (y / (t / b))) + 1.0));
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -3e-218], t$95$1, If[LessEqual[t$95$1, 0.0], N[(N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + N[(N[(b * N[(y * N[(1.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+286], t$95$1, If[LessEqual[t$95$1, Infinity], N[(N[(y / t), $MachinePrecision] * N[(z / N[(N[(a + N[(y / N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $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))) < -2.9999999999999998e-218 or -0.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 5.0000000000000004e286

   1. Initial program 96.9%

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

   if -2.9999999999999998e-218 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < -0.0

   1. Initial program 59.9%

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

      1. associate-/l* 61.7%

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

      2. associate-+l+ 61.7%

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

      3. associate-/l* 70.0%

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

   3. Simplified 70.0%

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

      1. associate-/l* 61.7%

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

      2. *-commutative 61.7%

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

      3. associate-*l/ 69.2%

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

      4. div-inv 69.2%

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

      5. associate-*l* 70.7%

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

   6. Applied egg-rr 70.7%

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

   if 5.0000000000000004e286 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < +inf.0

   1. Initial program 13.2%

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

      1. associate-/l* 68.6%

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

      2. associate-+l+ 68.6%

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

      3. associate-/l* 68.6%

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

   3. Simplified 68.6%

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

      1. associate-/l* 68.6%

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

      2. *-commutative 68.6%

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

      3. associate-*l/ 68.6%

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

      4. div-inv 68.6%

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

      5. associate-*l* 60.2%

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

   6. Applied egg-rr 60.2%

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

   7. Taylor expanded in x around 0 43.9%

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

      1. times-frac 92.0%

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

      2. *-commutative 92.0%

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

      3. associate-/l* 91.9%

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

   9. Simplified 91.9%

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

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

   1. Initial program 0.0%

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

      1. *-commutative 0.0%

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

      2. associate-*l/ 0.5%

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

      3. *-commutative 0.5%

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

      4. associate-*l/ 14.3%

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

   3. Simplified 14.3%

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

   5. Taylor expanded in t around 0 91.2%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -3 \cdot 10^{-218}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 0:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a + \left(b \cdot \left(y \cdot \frac{1}{t}\right) + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 5 \cdot 10^{+286}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq \infty:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{\left(a + \frac{y}{\frac{t}{b}}\right) + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 87.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{if}\;t_1 \leq 5 \cdot 10^{+286}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq \infty:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{\left(a + \frac{y}{\frac{t}{b}}\right) + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t)))))
   (if (<= t_1 5e+286)
     t_1
     (if (<= t_1 INFINITY)
       (* (/ y t) (/ z (+ (+ a (/ y (/ t b))) 1.0)))
       (/ z b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
	double tmp;
	if (t_1 <= 5e+286) {
		tmp = t_1;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = (y / t) * (z / ((a + (y / (t / b))) + 1.0));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
	double tmp;
	if (t_1 <= 5e+286) {
		tmp = t_1;
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = (y / t) * (z / ((a + (y / (t / b))) + 1.0));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t))
	tmp = 0
	if t_1 <= 5e+286:
		tmp = t_1
	elif t_1 <= math.inf:
		tmp = (y / t) * (z / ((a + (y / (t / b))) + 1.0))
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(Float64(a + 1.0) + Float64(Float64(y * b) / t)))
	tmp = 0.0
	if (t_1 <= 5e+286)
		tmp = t_1;
	elseif (t_1 <= Inf)
		tmp = Float64(Float64(y / t) * Float64(z / Float64(Float64(a + Float64(y / Float64(t / b))) + 1.0)));
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
	tmp = 0.0;
	if (t_1 <= 5e+286)
		tmp = t_1;
	elseif (t_1 <= Inf)
		tmp = (y / t) * (z / ((a + (y / (t / b))) + 1.0));
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 5e+286], t$95$1, If[LessEqual[t$95$1, Infinity], N[(N[(y / t), $MachinePrecision] * N[(z / N[(N[(a + N[(y / N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 5.0000000000000004e286

   1. Initial program 86.5%

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

   if 5.0000000000000004e286 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < +inf.0

   1. Initial program 13.2%

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

      1. associate-/l* 68.6%

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

      2. associate-+l+ 68.6%

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

      3. associate-/l* 68.6%

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

   3. Simplified 68.6%

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

      1. associate-/l* 68.6%

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

      2. *-commutative 68.6%

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

      3. associate-*l/ 68.6%

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

      4. div-inv 68.6%

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

      5. associate-*l* 60.2%

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

   6. Applied egg-rr 60.2%

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

   7. Taylor expanded in x around 0 43.9%

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

      1. times-frac 92.0%

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

      2. *-commutative 92.0%

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

      3. associate-/l* 91.9%

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

   9. Simplified 91.9%

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

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

   1. Initial program 0.0%

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

      1. *-commutative 0.0%

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

      2. associate-*l/ 0.5%

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

      3. *-commutative 0.5%

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

      4. associate-*l/ 14.3%

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

   3. Simplified 14.3%

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

   5. Taylor expanded in t around 0 91.2%

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

4. Final simplification 87.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 5 \cdot 10^{+286}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq \infty:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{\left(a + \frac{y}{\frac{t}{b}}\right) + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 68.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot z}{t}\\ \mathbf{if}\;a + 1 \leq -4 \cdot 10^{+136}:\\ \;\;\;\;\frac{t_1}{a}\\ \mathbf{elif}\;a + 1 \leq -1 \cdot 10^{+109}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a + 1 \leq -2000000000000:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;a + 1 \leq 1:\\ \;\;\;\;\frac{t_1}{\frac{y \cdot b}{t} + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_1}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (/ (* y z) t))))
   (if (<= (+ a 1.0) -4e+136)
     (/ t_1 a)
     (if (<= (+ a 1.0) -1e+109)
       (/ z b)
       (if (<= (+ a 1.0) -2000000000000.0)
         (/ x (+ (+ a 1.0) (* y (/ b t))))
         (if (<= (+ a 1.0) 1.0)
           (/ t_1 (+ (/ (* y b) t) 1.0))
           (/ t_1 (+ 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 + 1.0) <= -4e+136) {
		tmp = t_1 / a;
	} else if ((a + 1.0) <= -1e+109) {
		tmp = z / b;
	} else if ((a + 1.0) <= -2000000000000.0) {
		tmp = x / ((a + 1.0) + (y * (b / t)));
	} else if ((a + 1.0) <= 1.0) {
		tmp = t_1 / (((y * b) / t) + 1.0);
	} else {
		tmp = t_1 / (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 + 1.0d0) <= (-4d+136)) then
        tmp = t_1 / a
    else if ((a + 1.0d0) <= (-1d+109)) then
        tmp = z / b
    else if ((a + 1.0d0) <= (-2000000000000.0d0)) then
        tmp = x / ((a + 1.0d0) + (y * (b / t)))
    else if ((a + 1.0d0) <= 1.0d0) then
        tmp = t_1 / (((y * b) / t) + 1.0d0)
    else
        tmp = t_1 / (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 + 1.0) <= -4e+136) {
		tmp = t_1 / a;
	} else if ((a + 1.0) <= -1e+109) {
		tmp = z / b;
	} else if ((a + 1.0) <= -2000000000000.0) {
		tmp = x / ((a + 1.0) + (y * (b / t)));
	} else if ((a + 1.0) <= 1.0) {
		tmp = t_1 / (((y * b) / t) + 1.0);
	} else {
		tmp = t_1 / (a + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + ((y * z) / t)
	tmp = 0
	if (a + 1.0) <= -4e+136:
		tmp = t_1 / a
	elif (a + 1.0) <= -1e+109:
		tmp = z / b
	elif (a + 1.0) <= -2000000000000.0:
		tmp = x / ((a + 1.0) + (y * (b / t)))
	elif (a + 1.0) <= 1.0:
		tmp = t_1 / (((y * b) / t) + 1.0)
	else:
		tmp = t_1 / (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 (Float64(a + 1.0) <= -4e+136)
		tmp = Float64(t_1 / a);
	elseif (Float64(a + 1.0) <= -1e+109)
		tmp = Float64(z / b);
	elseif (Float64(a + 1.0) <= -2000000000000.0)
		tmp = Float64(x / Float64(Float64(a + 1.0) + Float64(y * Float64(b / t))));
	elseif (Float64(a + 1.0) <= 1.0)
		tmp = Float64(t_1 / Float64(Float64(Float64(y * b) / t) + 1.0));
	else
		tmp = Float64(t_1 / 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 + 1.0) <= -4e+136)
		tmp = t_1 / a;
	elseif ((a + 1.0) <= -1e+109)
		tmp = z / b;
	elseif ((a + 1.0) <= -2000000000000.0)
		tmp = x / ((a + 1.0) + (y * (b / t)));
	elseif ((a + 1.0) <= 1.0)
		tmp = t_1 / (((y * b) / t) + 1.0);
	else
		tmp = t_1 / (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[N[(a + 1.0), $MachinePrecision], -4e+136], N[(t$95$1 / a), $MachinePrecision], If[LessEqual[N[(a + 1.0), $MachinePrecision], -1e+109], N[(z / b), $MachinePrecision], If[LessEqual[N[(a + 1.0), $MachinePrecision], -2000000000000.0], N[(x / N[(N[(a + 1.0), $MachinePrecision] + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a + 1.0), $MachinePrecision], 1.0], N[(t$95$1 / N[(N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], N[(t$95$1 / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if (+.f64 a 1) < -4.00000000000000023e136

   1. Initial program 85.7%

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

      1. *-commutative 85.7%

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

      2. associate-*l/ 80.0%

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

      3. *-commutative 80.0%

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

      4. associate-*l/ 77.2%

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

   3. Simplified 77.2%

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

   5. Taylor expanded in a around inf 73.1%

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

   if -4.00000000000000023e136 < (+.f64 a 1) < -9.99999999999999982e108

   1. Initial program 16.0%

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

      1. *-commutative 16.0%

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

      2. associate-*l/ 15.7%

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

      3. *-commutative 15.7%

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

      4. associate-*l/ 15.4%

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

   3. Simplified 15.4%

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

   5. Taylor expanded in t around 0 68.0%

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

   if -9.99999999999999982e108 < (+.f64 a 1) < -2e12

   1. Initial program 82.9%

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

      1. *-commutative 82.9%

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

      2. associate-*l/ 83.0%

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

      3. *-commutative 83.0%

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

      4. associate-*l/ 94.4%

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

   3. Simplified 94.4%

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

   5. Taylor expanded in x around inf 88.7%

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

   if -2e12 < (+.f64 a 1) < 1

   1. Initial program 78.9%

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

      1. *-commutative 78.9%

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

      2. associate-*l/ 80.3%

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

      3. *-commutative 80.3%

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

      4. associate-*l/ 79.6%

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

   3. Simplified 79.6%

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

   5. Taylor expanded in a around 0 78.9%

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

   if 1 < (+.f64 a 1)

   1. Initial program 71.5%

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

      1. *-commutative 71.5%

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

      2. associate-*l/ 72.0%

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

      3. *-commutative 72.0%

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

      4. associate-*l/ 72.0%

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

   3. Simplified 72.0%

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

   5. Taylor expanded in b around 0 59.5%

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

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a + 1 \leq -4 \cdot 10^{+136}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a}\\ \mathbf{elif}\;a + 1 \leq -1 \cdot 10^{+109}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a + 1 \leq -2000000000000:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;a + 1 \leq 1:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 77.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{-103} \lor \neg \left(t \leq -5.5 \cdot 10^{-203} \lor \neg \left(t \leq -9.5 \cdot 10^{-270}\right) \land t \leq 1.55 \cdot 10^{-201}\right):\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + \left(\frac{y}{\frac{t}{b}} + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -6.5e-103)
         (not
          (or (<= t -5.5e-203) (and (not (<= t -9.5e-270)) (<= t 1.55e-201)))))
   (/ (+ x (* z (/ y t))) (+ a (+ (/ y (/ t b)) 1.0)))
   (/ z b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -6.5e-103) || !((t <= -5.5e-203) || (!(t <= -9.5e-270) && (t <= 1.55e-201)))) {
		tmp = (x + (z * (y / t))) / (a + ((y / (t / b)) + 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 <= (-6.5d-103)) .or. (.not. (t <= (-5.5d-203)) .or. (.not. (t <= (-9.5d-270))) .and. (t <= 1.55d-201))) then
        tmp = (x + (z * (y / t))) / (a + ((y / (t / b)) + 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 <= -6.5e-103) || !((t <= -5.5e-203) || (!(t <= -9.5e-270) && (t <= 1.55e-201)))) {
		tmp = (x + (z * (y / t))) / (a + ((y / (t / b)) + 1.0));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -6.5e-103) or not ((t <= -5.5e-203) or (not (t <= -9.5e-270) and (t <= 1.55e-201))):
		tmp = (x + (z * (y / t))) / (a + ((y / (t / b)) + 1.0))
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -6.5e-103) || !((t <= -5.5e-203) || (!(t <= -9.5e-270) && (t <= 1.55e-201))))
		tmp = Float64(Float64(x + Float64(z * Float64(y / t))) / Float64(a + Float64(Float64(y / Float64(t / b)) + 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 <= -6.5e-103) || ~(((t <= -5.5e-203) || (~((t <= -9.5e-270)) && (t <= 1.55e-201)))))
		tmp = (x + (z * (y / t))) / (a + ((y / (t / b)) + 1.0));
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -6.5e-103], N[Not[Or[LessEqual[t, -5.5e-203], And[N[Not[LessEqual[t, -9.5e-270]], $MachinePrecision], LessEqual[t, 1.55e-201]]]], $MachinePrecision]], N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + N[(N[(y / N[(t / b), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -6.49999999999999966e-103 or -5.5000000000000002e-203 < t < -9.5000000000000006e-270 or 1.5499999999999999e-201 < t

   1. Initial program 81.4%

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

      1. associate-/l* 83.5%

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

      2. associate-+l+ 83.5%

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

      3. associate-/l* 85.8%

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

   3. Simplified 85.8%

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

      1. associate-/r/ 85.1%

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

   6. Applied egg-rr 85.1%

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

   if -6.49999999999999966e-103 < t < -5.5000000000000002e-203 or -9.5000000000000006e-270 < t < 1.5499999999999999e-201

   1. Initial program 51.2%

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

      1. *-commutative 51.2%

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

      2. associate-*l/ 44.7%

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

      3. *-commutative 44.7%

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

      4. associate-*l/ 36.2%

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

   3. Simplified 36.2%

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

   5. Taylor expanded in t around 0 72.7%

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

4. Final simplification 82.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{-103} \lor \neg \left(t \leq -5.5 \cdot 10^{-203} \lor \neg \left(t \leq -9.5 \cdot 10^{-270}\right) \land t \leq 1.55 \cdot 10^{-201}\right):\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + \left(\frac{y}{\frac{t}{b}} + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 62.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+174}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq -1.42 \cdot 10^{+106}:\\ \;\;\;\;z \cdot \frac{\frac{y}{t}}{a + 1}\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{+49}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-224}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+125}:\\ \;\;\;\;\frac{x}{\left(a + \frac{y \cdot b}{t}\right) + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -3.8e+174)
   (/ z b)
   (if (<= y -1.42e+106)
     (* z (/ (/ y t) (+ a 1.0)))
     (if (<= y -2.2e+49)
       (/ z b)
       (if (<= y -2.1e-224)
         (/ (+ x (/ (* y z) t)) (+ a 1.0))
         (if (<= y 2e+125) (/ x (+ (+ a (/ (* y b) t)) 1.0)) (/ z b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -3.8e+174) {
		tmp = z / b;
	} else if (y <= -1.42e+106) {
		tmp = z * ((y / t) / (a + 1.0));
	} else if (y <= -2.2e+49) {
		tmp = z / b;
	} else if (y <= -2.1e-224) {
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	} else if (y <= 2e+125) {
		tmp = x / ((a + ((y * b) / t)) + 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 (y <= (-3.8d+174)) then
        tmp = z / b
    else if (y <= (-1.42d+106)) then
        tmp = z * ((y / t) / (a + 1.0d0))
    else if (y <= (-2.2d+49)) then
        tmp = z / b
    else if (y <= (-2.1d-224)) then
        tmp = (x + ((y * z) / t)) / (a + 1.0d0)
    else if (y <= 2d+125) then
        tmp = x / ((a + ((y * b) / t)) + 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 (y <= -3.8e+174) {
		tmp = z / b;
	} else if (y <= -1.42e+106) {
		tmp = z * ((y / t) / (a + 1.0));
	} else if (y <= -2.2e+49) {
		tmp = z / b;
	} else if (y <= -2.1e-224) {
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	} else if (y <= 2e+125) {
		tmp = x / ((a + ((y * b) / t)) + 1.0);
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -3.8e+174:
		tmp = z / b
	elif y <= -1.42e+106:
		tmp = z * ((y / t) / (a + 1.0))
	elif y <= -2.2e+49:
		tmp = z / b
	elif y <= -2.1e-224:
		tmp = (x + ((y * z) / t)) / (a + 1.0)
	elif y <= 2e+125:
		tmp = x / ((a + ((y * b) / t)) + 1.0)
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -3.8e+174)
		tmp = Float64(z / b);
	elseif (y <= -1.42e+106)
		tmp = Float64(z * Float64(Float64(y / t) / Float64(a + 1.0)));
	elseif (y <= -2.2e+49)
		tmp = Float64(z / b);
	elseif (y <= -2.1e-224)
		tmp = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(a + 1.0));
	elseif (y <= 2e+125)
		tmp = Float64(x / Float64(Float64(a + Float64(Float64(y * b) / t)) + 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 (y <= -3.8e+174)
		tmp = z / b;
	elseif (y <= -1.42e+106)
		tmp = z * ((y / t) / (a + 1.0));
	elseif (y <= -2.2e+49)
		tmp = z / b;
	elseif (y <= -2.1e-224)
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	elseif (y <= 2e+125)
		tmp = x / ((a + ((y * b) / t)) + 1.0);
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -3.8e+174], N[(z / b), $MachinePrecision], If[LessEqual[y, -1.42e+106], N[(z * N[(N[(y / t), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.2e+49], N[(z / b), $MachinePrecision], If[LessEqual[y, -2.1e-224], N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2e+125], N[(x / N[(N[(a + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.8000000000000002e174 or -1.4200000000000001e106 < y < -2.2000000000000001e49 or 1.9999999999999998e125 < y

   1. Initial program 45.5%

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

      1. *-commutative 45.5%

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

      2. associate-*l/ 51.1%

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

      3. *-commutative 51.1%

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

      4. associate-*l/ 59.7%

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

   3. Simplified 59.7%

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

   5. Taylor expanded in t around 0 60.6%

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

   if -3.8000000000000002e174 < y < -1.4200000000000001e106

   1. Initial program 41.5%

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

      1. *-commutative 41.5%

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

      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. *-commutative 63.0%

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

      4. associate-*l/ 77.7%

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

   3. Simplified 77.7%

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

   5. Taylor expanded in x around 0 52.7%

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

      1. associate-/r* 41.5%

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

      2. associate-*r/ 56.1%

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

      3. associate-+r+ 56.1%

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

      4. *-commutative 56.1%

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

      5. associate-*r/ 63.5%

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

   7. Simplified 63.5%

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

   8. Taylor expanded in y around 0 45.8%

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

      1. associate-/r* 42.1%

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

      2. associate-/l* 56.8%

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

   10. Simplified 56.8%

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

       1. associate-/r/ 56.9%

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

       2. *-commutative 56.9%

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

       3. *-un-lft-identity 56.9%

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

       4. times-frac 71.2%

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

       5. +-commutative 71.2%

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

   12. Applied egg-rr 71.2%

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

   if -2.2000000000000001e49 < y < -2.10000000000000006e-224

   1. Initial program 93.1%

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

      1. *-commutative 93.1%

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

      2. associate-*l/ 89.6%

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

      3. *-commutative 89.6%

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

      4. associate-*l/ 87.9%

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

   3. Simplified 87.9%

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

   5. Taylor expanded in b around 0 76.4%

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

   if -2.10000000000000006e-224 < y < 1.9999999999999998e125

   1. Initial program 93.0%

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

      1. *-commutative 93.0%

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

      2. associate-*l/ 88.4%

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

      3. *-commutative 88.4%

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

      4. associate-*l/ 81.3%

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

   3. Simplified 81.3%

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

   5. Taylor expanded in x around inf 81.7%

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

4. Final simplification 73.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+174}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq -1.42 \cdot 10^{+106}:\\ \;\;\;\;z \cdot \frac{\frac{y}{t}}{a + 1}\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{+49}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-224}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+125}:\\ \;\;\;\;\frac{x}{\left(a + \frac{y \cdot b}{t}\right) + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 61.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+174}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{+106}:\\ \;\;\;\;z \cdot \frac{\frac{y}{t}}{a + 1}\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{+45} \lor \neg \left(y \leq 3.3 \cdot 10^{+123}\right):\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(a + \frac{b}{\frac{t}{y}}\right) + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -3.8e+174)
   (/ z b)
   (if (<= y -1.15e+106)
     (* z (/ (/ y t) (+ a 1.0)))
     (if (or (<= y -3.6e+45) (not (<= y 3.3e+123)))
       (/ z b)
       (/ x (+ (+ a (/ b (/ t y))) 1.0))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -3.8e+174) {
		tmp = z / b;
	} else if (y <= -1.15e+106) {
		tmp = z * ((y / t) / (a + 1.0));
	} else if ((y <= -3.6e+45) || !(y <= 3.3e+123)) {
		tmp = z / b;
	} else {
		tmp = x / ((a + (b / (t / y))) + 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 <= (-3.8d+174)) then
        tmp = z / b
    else if (y <= (-1.15d+106)) then
        tmp = z * ((y / t) / (a + 1.0d0))
    else if ((y <= (-3.6d+45)) .or. (.not. (y <= 3.3d+123))) then
        tmp = z / b
    else
        tmp = x / ((a + (b / (t / y))) + 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 <= -3.8e+174) {
		tmp = z / b;
	} else if (y <= -1.15e+106) {
		tmp = z * ((y / t) / (a + 1.0));
	} else if ((y <= -3.6e+45) || !(y <= 3.3e+123)) {
		tmp = z / b;
	} else {
		tmp = x / ((a + (b / (t / y))) + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -3.8e+174:
		tmp = z / b
	elif y <= -1.15e+106:
		tmp = z * ((y / t) / (a + 1.0))
	elif (y <= -3.6e+45) or not (y <= 3.3e+123):
		tmp = z / b
	else:
		tmp = x / ((a + (b / (t / y))) + 1.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -3.8e+174)
		tmp = Float64(z / b);
	elseif (y <= -1.15e+106)
		tmp = Float64(z * Float64(Float64(y / t) / Float64(a + 1.0)));
	elseif ((y <= -3.6e+45) || !(y <= 3.3e+123))
		tmp = Float64(z / b);
	else
		tmp = Float64(x / Float64(Float64(a + Float64(b / Float64(t / y))) + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -3.8e+174)
		tmp = z / b;
	elseif (y <= -1.15e+106)
		tmp = z * ((y / t) / (a + 1.0));
	elseif ((y <= -3.6e+45) || ~((y <= 3.3e+123)))
		tmp = z / b;
	else
		tmp = x / ((a + (b / (t / y))) + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -3.8e+174], N[(z / b), $MachinePrecision], If[LessEqual[y, -1.15e+106], N[(z * N[(N[(y / t), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -3.6e+45], N[Not[LessEqual[y, 3.3e+123]], $MachinePrecision]], N[(z / b), $MachinePrecision], N[(x / N[(N[(a + N[(b / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.8000000000000002e174 or -1.1500000000000001e106 < y < -3.6e45 or 3.30000000000000003e123 < y

   1. Initial program 45.5%

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

      1. *-commutative 45.5%

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

      2. associate-*l/ 51.1%

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

      3. *-commutative 51.1%

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

      4. associate-*l/ 59.7%

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

   3. Simplified 59.7%

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

   5. Taylor expanded in t around 0 60.6%

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

   if -3.8000000000000002e174 < y < -1.1500000000000001e106

   1. Initial program 41.5%

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

      1. *-commutative 41.5%

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

      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. *-commutative 63.0%

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

      4. associate-*l/ 77.7%

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

   3. Simplified 77.7%

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

   5. Taylor expanded in x around 0 52.7%

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

      1. associate-/r* 41.5%

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

      2. associate-*r/ 56.1%

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

      3. associate-+r+ 56.1%

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

      4. *-commutative 56.1%

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

      5. associate-*r/ 63.5%

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

   7. Simplified 63.5%

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

   8. Taylor expanded in y around 0 45.8%

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

      1. associate-/r* 42.1%

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

      2. associate-/l* 56.8%

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

   10. Simplified 56.8%

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

       1. associate-/r/ 56.9%

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

       2. *-commutative 56.9%

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

       3. *-un-lft-identity 56.9%

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

       4. times-frac 71.2%

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

       5. +-commutative 71.2%

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

   12. Applied egg-rr 71.2%

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

   if -3.6e45 < y < 3.30000000000000003e123

   1. Initial program 93.0%

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

      1. associate-/l* 89.6%

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

      2. associate-+l+ 89.6%

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

      3. associate-/l* 85.0%

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

   3. Simplified 85.0%

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

      1. associate-/r/ 87.4%

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

   6. Applied egg-rr 87.4%

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

   7. Taylor expanded in x around inf 76.5%

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

      1. associate-/l* 76.5%

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

   9. Simplified 76.5%

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

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+174}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{+106}:\\ \;\;\;\;z \cdot \frac{\frac{y}{t}}{a + 1}\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{+45} \lor \neg \left(y \leq 3.3 \cdot 10^{+123}\right):\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(a + \frac{b}{\frac{t}{y}}\right) + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 61.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+174}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq -1.68 \cdot 10^{+106}:\\ \;\;\;\;z \cdot \frac{\frac{y}{t}}{a + 1}\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{+49} \lor \neg \left(y \leq 5.2 \cdot 10^{+121}\right):\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(a + \frac{y \cdot b}{t}\right) + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -3.8e+174)
   (/ z b)
   (if (<= y -1.68e+106)
     (* z (/ (/ y t) (+ a 1.0)))
     (if (or (<= y -6.2e+49) (not (<= y 5.2e+121)))
       (/ z b)
       (/ x (+ (+ a (/ (* y b) t)) 1.0))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -3.8e+174) {
		tmp = z / b;
	} else if (y <= -1.68e+106) {
		tmp = z * ((y / t) / (a + 1.0));
	} else if ((y <= -6.2e+49) || !(y <= 5.2e+121)) {
		tmp = z / b;
	} else {
		tmp = x / ((a + ((y * b) / t)) + 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 <= (-3.8d+174)) then
        tmp = z / b
    else if (y <= (-1.68d+106)) then
        tmp = z * ((y / t) / (a + 1.0d0))
    else if ((y <= (-6.2d+49)) .or. (.not. (y <= 5.2d+121))) then
        tmp = z / b
    else
        tmp = x / ((a + ((y * b) / t)) + 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 <= -3.8e+174) {
		tmp = z / b;
	} else if (y <= -1.68e+106) {
		tmp = z * ((y / t) / (a + 1.0));
	} else if ((y <= -6.2e+49) || !(y <= 5.2e+121)) {
		tmp = z / b;
	} else {
		tmp = x / ((a + ((y * b) / t)) + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -3.8e+174:
		tmp = z / b
	elif y <= -1.68e+106:
		tmp = z * ((y / t) / (a + 1.0))
	elif (y <= -6.2e+49) or not (y <= 5.2e+121):
		tmp = z / b
	else:
		tmp = x / ((a + ((y * b) / t)) + 1.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -3.8e+174)
		tmp = Float64(z / b);
	elseif (y <= -1.68e+106)
		tmp = Float64(z * Float64(Float64(y / t) / Float64(a + 1.0)));
	elseif ((y <= -6.2e+49) || !(y <= 5.2e+121))
		tmp = Float64(z / b);
	else
		tmp = Float64(x / Float64(Float64(a + Float64(Float64(y * b) / t)) + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -3.8e+174)
		tmp = z / b;
	elseif (y <= -1.68e+106)
		tmp = z * ((y / t) / (a + 1.0));
	elseif ((y <= -6.2e+49) || ~((y <= 5.2e+121)))
		tmp = z / b;
	else
		tmp = x / ((a + ((y * b) / t)) + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -3.8e+174], N[(z / b), $MachinePrecision], If[LessEqual[y, -1.68e+106], N[(z * N[(N[(y / t), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -6.2e+49], N[Not[LessEqual[y, 5.2e+121]], $MachinePrecision]], N[(z / b), $MachinePrecision], N[(x / N[(N[(a + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.8000000000000002e174 or -1.68000000000000008e106 < y < -6.19999999999999985e49 or 5.1999999999999998e121 < y

   1. Initial program 45.5%

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

      1. *-commutative 45.5%

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

      2. associate-*l/ 51.1%

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

      3. *-commutative 51.1%

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

      4. associate-*l/ 59.7%

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

   3. Simplified 59.7%

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

   5. Taylor expanded in t around 0 60.6%

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

   if -3.8000000000000002e174 < y < -1.68000000000000008e106

   1. Initial program 41.5%

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

      1. *-commutative 41.5%

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

      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. *-commutative 63.0%

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

      4. associate-*l/ 77.7%

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

   3. Simplified 77.7%

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

   5. Taylor expanded in x around 0 52.7%

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

      1. associate-/r* 41.5%

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

      2. associate-*r/ 56.1%

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

      3. associate-+r+ 56.1%

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

      4. *-commutative 56.1%

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

      5. associate-*r/ 63.5%

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

   7. Simplified 63.5%

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

   8. Taylor expanded in y around 0 45.8%

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

      1. associate-/r* 42.1%

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

      2. associate-/l* 56.8%

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

   10. Simplified 56.8%

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

       1. associate-/r/ 56.9%

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

       2. *-commutative 56.9%

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

       3. *-un-lft-identity 56.9%

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

       4. times-frac 71.2%

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

       5. +-commutative 71.2%

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

   12. Applied egg-rr 71.2%

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

   if -6.19999999999999985e49 < y < 5.1999999999999998e121

   1. Initial program 93.0%

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

      1. *-commutative 93.0%

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

      2. associate-*l/ 88.8%

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

      3. *-commutative 88.8%

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

      4. associate-*l/ 83.6%

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

   3. Simplified 83.6%

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

   5. Taylor expanded in x around inf 76.5%

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

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+174}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq -1.68 \cdot 10^{+106}:\\ \;\;\;\;z \cdot \frac{\frac{y}{t}}{a + 1}\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{+49} \lor \neg \left(y \leq 5.2 \cdot 10^{+121}\right):\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(a + \frac{y \cdot b}{t}\right) + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 78.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.1 \cdot 10^{-271} \lor \neg \left(t \leq 1.28 \cdot 10^{-201}\right):\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a + \left(\frac{y}{\frac{t}{b}} + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -3.1e-271) (not (<= t 1.28e-201)))
   (/ (+ x (/ y (/ t z))) (+ a (+ (/ y (/ t b)) 1.0)))
   (/ z b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -3.1e-271) || !(t <= 1.28e-201)) {
		tmp = (x + (y / (t / z))) / (a + ((y / (t / b)) + 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 <= (-3.1d-271)) .or. (.not. (t <= 1.28d-201))) then
        tmp = (x + (y / (t / z))) / (a + ((y / (t / b)) + 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 <= -3.1e-271) || !(t <= 1.28e-201)) {
		tmp = (x + (y / (t / z))) / (a + ((y / (t / b)) + 1.0));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -3.1e-271) or not (t <= 1.28e-201):
		tmp = (x + (y / (t / z))) / (a + ((y / (t / b)) + 1.0))
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -3.1e-271) || !(t <= 1.28e-201))
		tmp = Float64(Float64(x + Float64(y / Float64(t / z))) / Float64(a + Float64(Float64(y / Float64(t / b)) + 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 <= -3.1e-271) || ~((t <= 1.28e-201)))
		tmp = (x + (y / (t / z))) / (a + ((y / (t / b)) + 1.0));
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -3.1e-271], N[Not[LessEqual[t, 1.28e-201]], $MachinePrecision]], N[(N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + N[(N[(y / N[(t / b), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.0999999999999999e-271 or 1.28e-201 < t

   1. Initial program 78.9%

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

      1. associate-/l* 80.9%

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

      2. associate-+l+ 80.9%

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

      3. associate-/l* 82.6%

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

   3. Simplified 82.6%

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

   if -3.0999999999999999e-271 < t < 1.28e-201

   1. Initial program 52.7%

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

      1. *-commutative 52.7%

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

      2. associate-*l/ 42.5%

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

      3. *-commutative 42.5%

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

      4. associate-*l/ 32.5%

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

   3. Simplified 32.5%

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

   5. Taylor expanded in t around 0 79.8%

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

4. Final simplification 82.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.1 \cdot 10^{-271} \lor \neg \left(t \leq 1.28 \cdot 10^{-201}\right):\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a + \left(\frac{y}{\frac{t}{b}} + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 78.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{-101}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + \left(\frac{y}{\frac{t}{b}} + 1\right)}\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{-202}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1e-101)
   (/ (+ x (* z (/ y t))) (+ a (+ (/ y (/ t b)) 1.0)))
   (if (<= t 8.2e-202)
     (/ z b)
     (/ (+ 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) {
	double tmp;
	if (t <= -1e-101) {
		tmp = (x + (z * (y / t))) / (a + ((y / (t / b)) + 1.0));
	} else if (t <= 8.2e-202) {
		tmp = z / b;
	} else {
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-1d-101)) then
        tmp = (x + (z * (y / t))) / (a + ((y / (t / b)) + 1.0d0))
    else if (t <= 8.2d-202) then
        tmp = z / b
    else
        tmp = (x + (y * (z / t))) / ((a + 1.0d0) + (y * (b / t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1e-101) {
		tmp = (x + (z * (y / t))) / (a + ((y / (t / b)) + 1.0));
	} else if (t <= 8.2e-202) {
		tmp = z / b;
	} else {
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1e-101:
		tmp = (x + (z * (y / t))) / (a + ((y / (t / b)) + 1.0))
	elif t <= 8.2e-202:
		tmp = z / b
	else:
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1e-101)
		tmp = Float64(Float64(x + Float64(z * Float64(y / t))) / Float64(a + Float64(Float64(y / Float64(t / b)) + 1.0)));
	elseif (t <= 8.2e-202)
		tmp = Float64(z / b);
	else
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(Float64(a + 1.0) + Float64(y * Float64(b / t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -1e-101)
		tmp = (x + (z * (y / t))) / (a + ((y / (t / b)) + 1.0));
	elseif (t <= 8.2e-202)
		tmp = z / b;
	else
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1e-101], N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + N[(N[(y / N[(t / b), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.2e-202], N[(z / b), $MachinePrecision], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.00000000000000005e-101

   1. Initial program 84.2%

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

      1. associate-/l* 85.6%

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

      2. associate-+l+ 85.6%

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

      3. associate-/l* 89.0%

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

   3. Simplified 89.0%

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

      1. associate-/r/ 89.5%

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

   6. Applied egg-rr 89.5%

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

   if -1.00000000000000005e-101 < t < 8.2000000000000008e-202

   1. Initial program 58.3%

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

      1. *-commutative 58.3%

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

      2. associate-*l/ 51.9%

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

      3. *-commutative 51.9%

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

      4. associate-*l/ 44.0%

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

   3. Simplified 44.0%

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

   5. Taylor expanded in t around 0 65.3%

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

   if 8.2000000000000008e-202 < t

   1. Initial program 78.8%

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

      1. *-commutative 78.8%

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

      2. associate-*l/ 81.5%

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

      3. *-commutative 81.5%

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

      4. associate-*l/ 83.5%

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

   3. Simplified 83.5%

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

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{-101}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + \left(\frac{y}{\frac{t}{b}} + 1\right)}\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{-202}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 55.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+174}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq -1.68 \cdot 10^{+106}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{a + 1}\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{+47} \lor \neg \left(y \leq 8.5 \cdot 10^{+83}\right):\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -3.8e+174)
   (/ z b)
   (if (<= y -1.68e+106)
     (* (/ y t) (/ z (+ a 1.0)))
     (if (or (<= y -1.5e+47) (not (<= y 8.5e+83))) (/ 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 <= -3.8e+174) {
		tmp = z / b;
	} else if (y <= -1.68e+106) {
		tmp = (y / t) * (z / (a + 1.0));
	} else if ((y <= -1.5e+47) || !(y <= 8.5e+83)) {
		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 <= (-3.8d+174)) then
        tmp = z / b
    else if (y <= (-1.68d+106)) then
        tmp = (y / t) * (z / (a + 1.0d0))
    else if ((y <= (-1.5d+47)) .or. (.not. (y <= 8.5d+83))) 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 <= -3.8e+174) {
		tmp = z / b;
	} else if (y <= -1.68e+106) {
		tmp = (y / t) * (z / (a + 1.0));
	} else if ((y <= -1.5e+47) || !(y <= 8.5e+83)) {
		tmp = z / b;
	} else {
		tmp = x / (a + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -3.8e+174:
		tmp = z / b
	elif y <= -1.68e+106:
		tmp = (y / t) * (z / (a + 1.0))
	elif (y <= -1.5e+47) or not (y <= 8.5e+83):
		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 <= -3.8e+174)
		tmp = Float64(z / b);
	elseif (y <= -1.68e+106)
		tmp = Float64(Float64(y / t) * Float64(z / Float64(a + 1.0)));
	elseif ((y <= -1.5e+47) || !(y <= 8.5e+83))
		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 <= -3.8e+174)
		tmp = z / b;
	elseif (y <= -1.68e+106)
		tmp = (y / t) * (z / (a + 1.0));
	elseif ((y <= -1.5e+47) || ~((y <= 8.5e+83)))
		tmp = z / b;
	else
		tmp = x / (a + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -3.8e+174], N[(z / b), $MachinePrecision], If[LessEqual[y, -1.68e+106], N[(N[(y / t), $MachinePrecision] * N[(z / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -1.5e+47], N[Not[LessEqual[y, 8.5e+83]], $MachinePrecision]], N[(z / b), $MachinePrecision], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.8000000000000002e174 or -1.68000000000000008e106 < y < -1.5000000000000001e47 or 8.4999999999999995e83 < y

   1. Initial program 46.5%

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

      1. *-commutative 46.5%

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

      2. associate-*l/ 51.7%

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

      3. *-commutative 51.7%

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

      4. associate-*l/ 59.8%

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

   3. Simplified 59.8%

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

   5. Taylor expanded in t around 0 59.6%

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

   if -3.8000000000000002e174 < y < -1.68000000000000008e106

   1. Initial program 41.5%

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

      1. *-commutative 41.5%

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

      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. *-commutative 63.0%

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

      4. associate-*l/ 77.7%

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

   3. Simplified 77.7%

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

   5. Taylor expanded in x around 0 52.7%

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

      1. associate-/r* 41.5%

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

      2. associate-*r/ 56.1%

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

      3. associate-+r+ 56.1%

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

      4. *-commutative 56.1%

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

      5. associate-*r/ 63.5%

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

   7. Simplified 63.5%

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

   8. Taylor expanded in y around 0 45.8%

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

      1. associate-/r* 42.1%

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

      2. associate-/l* 56.8%

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

   10. Simplified 56.8%

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

   11. Taylor expanded in y around 0 45.8%

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

       1. times-frac 63.8%

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

       2. +-commutative 63.8%

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

       3. *-commutative 63.8%

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

       4. +-commutative 63.8%

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

   13. Simplified 63.8%

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

   if -1.5000000000000001e47 < y < 8.4999999999999995e83

   1. Initial program 94.0%

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

      1. *-commutative 94.0%

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

      2. associate-*l/ 89.7%

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

      3. *-commutative 89.7%

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

      4. associate-*l/ 84.3%

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

   3. Simplified 84.3%

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

   5. Taylor expanded in t around inf 67.0%

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

4. Final simplification 64.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+174}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq -1.68 \cdot 10^{+106}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{a + 1}\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{+47} \lor \neg \left(y \leq 8.5 \cdot 10^{+83}\right):\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 55.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+175}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq -1.68 \cdot 10^{+106}:\\ \;\;\;\;\frac{z}{\left(a + 1\right) \cdot \frac{t}{y}}\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{+49} \lor \neg \left(y \leq 2.4 \cdot 10^{+83}\right):\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -4e+175)
   (/ z b)
   (if (<= y -1.68e+106)
     (/ z (* (+ a 1.0) (/ t y)))
     (if (or (<= y -1.25e+49) (not (<= y 2.4e+83))) (/ 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 <= -4e+175) {
		tmp = z / b;
	} else if (y <= -1.68e+106) {
		tmp = z / ((a + 1.0) * (t / y));
	} else if ((y <= -1.25e+49) || !(y <= 2.4e+83)) {
		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 <= (-4d+175)) then
        tmp = z / b
    else if (y <= (-1.68d+106)) then
        tmp = z / ((a + 1.0d0) * (t / y))
    else if ((y <= (-1.25d+49)) .or. (.not. (y <= 2.4d+83))) 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 <= -4e+175) {
		tmp = z / b;
	} else if (y <= -1.68e+106) {
		tmp = z / ((a + 1.0) * (t / y));
	} else if ((y <= -1.25e+49) || !(y <= 2.4e+83)) {
		tmp = z / b;
	} else {
		tmp = x / (a + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -4e+175:
		tmp = z / b
	elif y <= -1.68e+106:
		tmp = z / ((a + 1.0) * (t / y))
	elif (y <= -1.25e+49) or not (y <= 2.4e+83):
		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 <= -4e+175)
		tmp = Float64(z / b);
	elseif (y <= -1.68e+106)
		tmp = Float64(z / Float64(Float64(a + 1.0) * Float64(t / y)));
	elseif ((y <= -1.25e+49) || !(y <= 2.4e+83))
		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 <= -4e+175)
		tmp = z / b;
	elseif (y <= -1.68e+106)
		tmp = z / ((a + 1.0) * (t / y));
	elseif ((y <= -1.25e+49) || ~((y <= 2.4e+83)))
		tmp = z / b;
	else
		tmp = x / (a + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -4e+175], N[(z / b), $MachinePrecision], If[LessEqual[y, -1.68e+106], N[(z / N[(N[(a + 1.0), $MachinePrecision] * N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -1.25e+49], N[Not[LessEqual[y, 2.4e+83]], $MachinePrecision]], N[(z / b), $MachinePrecision], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.9999999999999997e175 or -1.68000000000000008e106 < y < -1.2500000000000001e49 or 2.39999999999999991e83 < y

   1. Initial program 46.5%

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

      1. *-commutative 46.5%

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

      2. associate-*l/ 51.7%

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

      3. *-commutative 51.7%

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

      4. associate-*l/ 59.8%

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

   3. Simplified 59.8%

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

   5. Taylor expanded in t around 0 59.6%

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

   if -3.9999999999999997e175 < y < -1.68000000000000008e106

   1. Initial program 41.5%

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

      1. *-commutative 41.5%

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

      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. *-commutative 63.0%

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

      4. associate-*l/ 77.7%

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

   3. Simplified 77.7%

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

   5. Taylor expanded in x around 0 52.7%

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

      1. associate-/r* 41.5%

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

      2. associate-*r/ 56.1%

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

      3. associate-+r+ 56.1%

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

      4. *-commutative 56.1%

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

      5. associate-*r/ 63.5%

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

   7. Simplified 63.5%

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

   8. Taylor expanded in y around 0 45.8%

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

      1. associate-/r* 42.1%

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

      2. associate-/l* 56.8%

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

   10. Simplified 56.8%

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

       1. associate-/r/ 56.9%

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

       2. *-commutative 56.9%

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

       3. *-un-lft-identity 56.9%

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

       4. times-frac 71.2%

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

       5. +-commutative 71.2%

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

   12. Applied egg-rr 71.2%

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

       1. /-rgt-identity 71.2%

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

       2. clear-num 71.2%

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

       3. un-div-inv 70.9%

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

       4. div-inv 70.7%

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

       5. +-commutative 70.7%

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

       6. clear-num 71.0%

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

   14. Applied egg-rr 71.0%

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

   if -1.2500000000000001e49 < y < 2.39999999999999991e83

   1. Initial program 94.0%

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

      1. *-commutative 94.0%

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

      2. associate-*l/ 89.7%

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

      3. *-commutative 89.7%

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

      4. associate-*l/ 84.3%

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

   3. Simplified 84.3%

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

   5. Taylor expanded in t around inf 67.0%

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

4. Final simplification 64.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+175}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq -1.68 \cdot 10^{+106}:\\ \;\;\;\;\frac{z}{\left(a + 1\right) \cdot \frac{t}{y}}\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{+49} \lor \neg \left(y \leq 2.4 \cdot 10^{+83}\right):\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 55.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+174}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq -1.68 \cdot 10^{+106}:\\ \;\;\;\;z \cdot \frac{\frac{y}{t}}{a + 1}\\ \mathbf{elif}\;y \leq -4 \cdot 10^{+46} \lor \neg \left(y \leq 4.9 \cdot 10^{+82}\right):\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -3.8e+174)
   (/ z b)
   (if (<= y -1.68e+106)
     (* z (/ (/ y t) (+ a 1.0)))
     (if (or (<= y -4e+46) (not (<= y 4.9e+82))) (/ 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 <= -3.8e+174) {
		tmp = z / b;
	} else if (y <= -1.68e+106) {
		tmp = z * ((y / t) / (a + 1.0));
	} else if ((y <= -4e+46) || !(y <= 4.9e+82)) {
		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 <= (-3.8d+174)) then
        tmp = z / b
    else if (y <= (-1.68d+106)) then
        tmp = z * ((y / t) / (a + 1.0d0))
    else if ((y <= (-4d+46)) .or. (.not. (y <= 4.9d+82))) 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 <= -3.8e+174) {
		tmp = z / b;
	} else if (y <= -1.68e+106) {
		tmp = z * ((y / t) / (a + 1.0));
	} else if ((y <= -4e+46) || !(y <= 4.9e+82)) {
		tmp = z / b;
	} else {
		tmp = x / (a + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -3.8e+174:
		tmp = z / b
	elif y <= -1.68e+106:
		tmp = z * ((y / t) / (a + 1.0))
	elif (y <= -4e+46) or not (y <= 4.9e+82):
		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 <= -3.8e+174)
		tmp = Float64(z / b);
	elseif (y <= -1.68e+106)
		tmp = Float64(z * Float64(Float64(y / t) / Float64(a + 1.0)));
	elseif ((y <= -4e+46) || !(y <= 4.9e+82))
		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 <= -3.8e+174)
		tmp = z / b;
	elseif (y <= -1.68e+106)
		tmp = z * ((y / t) / (a + 1.0));
	elseif ((y <= -4e+46) || ~((y <= 4.9e+82)))
		tmp = z / b;
	else
		tmp = x / (a + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -3.8e+174], N[(z / b), $MachinePrecision], If[LessEqual[y, -1.68e+106], N[(z * N[(N[(y / t), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -4e+46], N[Not[LessEqual[y, 4.9e+82]], $MachinePrecision]], N[(z / b), $MachinePrecision], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.8000000000000002e174 or -1.68000000000000008e106 < y < -4e46 or 4.9000000000000001e82 < y

   1. Initial program 46.5%

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

      1. *-commutative 46.5%

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

      2. associate-*l/ 51.7%

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

      3. *-commutative 51.7%

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

      4. associate-*l/ 59.8%

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

   3. Simplified 59.8%

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

   5. Taylor expanded in t around 0 59.6%

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

   if -3.8000000000000002e174 < y < -1.68000000000000008e106

   1. Initial program 41.5%

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

      1. *-commutative 41.5%

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

      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. *-commutative 63.0%

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

      4. associate-*l/ 77.7%

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

   3. Simplified 77.7%

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

   5. Taylor expanded in x around 0 52.7%

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

      1. associate-/r* 41.5%

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

      2. associate-*r/ 56.1%

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

      3. associate-+r+ 56.1%

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

      4. *-commutative 56.1%

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

      5. associate-*r/ 63.5%

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

   7. Simplified 63.5%

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

   8. Taylor expanded in y around 0 45.8%

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

      1. associate-/r* 42.1%

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

      2. associate-/l* 56.8%

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

   10. Simplified 56.8%

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

       1. associate-/r/ 56.9%

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

       2. *-commutative 56.9%

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

       3. *-un-lft-identity 56.9%

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

       4. times-frac 71.2%

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

       5. +-commutative 71.2%

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

   12. Applied egg-rr 71.2%

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

   if -4e46 < y < 4.9000000000000001e82

   1. Initial program 94.0%

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

      1. *-commutative 94.0%

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

      2. associate-*l/ 89.7%

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

      3. *-commutative 89.7%

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

      4. associate-*l/ 84.3%

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

   3. Simplified 84.3%

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

   5. Taylor expanded in t around inf 67.0%

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

4. Final simplification 64.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+174}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq -1.68 \cdot 10^{+106}:\\ \;\;\;\;z \cdot \frac{\frac{y}{t}}{a + 1}\\ \mathbf{elif}\;y \leq -4 \cdot 10^{+46} \lor \neg \left(y \leq 4.9 \cdot 10^{+82}\right):\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 39.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.1 \cdot 10^{+176}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -1.45 \cdot 10^{-36}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-129}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{+184}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -3.1e+176)
   x
   (if (<= t -1.45e-36)
     (/ x a)
     (if (<= t 9e-129) (/ z b) (if (<= t 3.3e+184) (/ x a) x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -3.1e+176) {
		tmp = x;
	} else if (t <= -1.45e-36) {
		tmp = x / a;
	} else if (t <= 9e-129) {
		tmp = z / b;
	} else if (t <= 3.3e+184) {
		tmp = x / a;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-3.1d+176)) then
        tmp = x
    else if (t <= (-1.45d-36)) then
        tmp = x / a
    else if (t <= 9d-129) then
        tmp = z / b
    else if (t <= 3.3d+184) then
        tmp = x / a
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -3.1e+176) {
		tmp = x;
	} else if (t <= -1.45e-36) {
		tmp = x / a;
	} else if (t <= 9e-129) {
		tmp = z / b;
	} else if (t <= 3.3e+184) {
		tmp = x / a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -3.1e+176:
		tmp = x
	elif t <= -1.45e-36:
		tmp = x / a
	elif t <= 9e-129:
		tmp = z / b
	elif t <= 3.3e+184:
		tmp = x / a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -3.1e+176)
		tmp = x;
	elseif (t <= -1.45e-36)
		tmp = Float64(x / a);
	elseif (t <= 9e-129)
		tmp = Float64(z / b);
	elseif (t <= 3.3e+184)
		tmp = Float64(x / a);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -3.1e+176)
		tmp = x;
	elseif (t <= -1.45e-36)
		tmp = x / a;
	elseif (t <= 9e-129)
		tmp = z / b;
	elseif (t <= 3.3e+184)
		tmp = x / a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -3.1e+176], x, If[LessEqual[t, -1.45e-36], N[(x / a), $MachinePrecision], If[LessEqual[t, 9e-129], N[(z / b), $MachinePrecision], If[LessEqual[t, 3.3e+184], N[(x / a), $MachinePrecision], x]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.0999999999999999e176 or 3.2999999999999998e184 < t

   1. Initial program 83.9%

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

      1. *-commutative 83.9%

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

      2. associate-*l/ 90.4%

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

      3. *-commutative 90.4%

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

      4. associate-*l/ 98.4%

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

   3. Simplified 98.4%

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

   5. Taylor expanded in t around inf 79.5%

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

   6. Taylor expanded in a around 0 52.0%

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

   if -3.0999999999999999e176 < t < -1.45000000000000006e-36 or 9.00000000000000061e-129 < t < 3.2999999999999998e184

   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/ 86.2%

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

      3. *-commutative 86.2%

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

      4. associate-*l/ 88.9%

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

   3. Simplified 88.9%

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

   5. Taylor expanded in x around inf 63.8%

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

   6. Taylor expanded in a around inf 37.2%

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

   if -1.45000000000000006e-36 < t < 9.00000000000000061e-129

   1. Initial program 61.4%

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

      1. *-commutative 61.4%

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

      2. associate-*l/ 56.1%

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

      3. *-commutative 56.1%

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

      4. associate-*l/ 48.1%

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

   3. Simplified 48.1%

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

   5. Taylor expanded in t around 0 57.4%

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

4. Final simplification 48.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.1 \cdot 10^{+176}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -1.45 \cdot 10^{-36}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-129}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{+184}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 56.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+47} \lor \neg \left(y \leq 2.85 \cdot 10^{+85}\right):\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.9e+47) (not (<= y 2.85e+85))) (/ z b) (/ x (+ a 1.0))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.9e+47) || !(y <= 2.85e+85)) {
		tmp = z / b;
	} else {
		tmp = x / (a + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-1.9d+47)) .or. (.not. (y <= 2.85d+85))) then
        tmp = z / b
    else
        tmp = x / (a + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.9e+47) || !(y <= 2.85e+85)) {
		tmp = z / b;
	} else {
		tmp = x / (a + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.9e+47) or not (y <= 2.85e+85):
		tmp = z / b
	else:
		tmp = x / (a + 1.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.9e+47) || !(y <= 2.85e+85))
		tmp = Float64(z / b);
	else
		tmp = Float64(x / Float64(a + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.9e+47) || ~((y <= 2.85e+85)))
		tmp = z / b;
	else
		tmp = x / (a + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.9e+47], N[Not[LessEqual[y, 2.85e+85]], $MachinePrecision]], N[(z / b), $MachinePrecision], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.9000000000000002e47 or 2.8500000000000001e85 < y

   1. Initial program 45.8%

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

      1. *-commutative 45.8%

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

      2. associate-*l/ 53.3%

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

      3. *-commutative 53.3%

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

      4. associate-*l/ 62.2%

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

   3. Simplified 62.2%

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

   5. Taylor expanded in t around 0 54.0%

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

   if -1.9000000000000002e47 < y < 2.8500000000000001e85

   1. Initial program 94.0%

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

      1. *-commutative 94.0%

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

      2. associate-*l/ 89.7%

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

      3. *-commutative 89.7%

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

      4. associate-*l/ 84.3%

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

   3. Simplified 84.3%

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

   5. Taylor expanded in t around inf 67.0%

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

4. Final simplification 62.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+47} \lor \neg \left(y \leq 2.85 \cdot 10^{+85}\right):\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 41.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.3 \cdot 10^{-6} \lor \neg \left(a \leq 1\right):\\ \;\;\;\;\frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -3.3e-6) (not (<= a 1.0))) (/ x a) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -3.3e-6) || !(a <= 1.0)) {
		tmp = x / a;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((a <= (-3.3d-6)) .or. (.not. (a <= 1.0d0))) then
        tmp = x / a
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -3.3e-6) || !(a <= 1.0)) {
		tmp = x / a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -3.3e-6) or not (a <= 1.0):
		tmp = x / a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -3.3e-6) || !(a <= 1.0))
		tmp = Float64(x / a);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -3.3e-6) || ~((a <= 1.0)))
		tmp = x / a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -3.3e-6], N[Not[LessEqual[a, 1.0]], $MachinePrecision]], N[(x / a), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if a < -3.30000000000000017e-6 or 1 < a

   1. Initial program 73.6%

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

      1. *-commutative 73.6%

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

      2. associate-*l/ 72.4%

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

      3. *-commutative 72.4%

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

      4. associate-*l/ 73.1%

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

   3. Simplified 73.1%

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

   5. Taylor expanded in x around inf 59.1%

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

   6. Taylor expanded in a around inf 50.8%

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

   if -3.30000000000000017e-6 < a < 1

   1. Initial program 78.4%

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

      1. *-commutative 78.4%

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

      2. associate-*l/ 79.8%

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

      3. *-commutative 79.8%

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

      4. associate-*l/ 79.1%

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

   3. Simplified 79.1%

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

   5. Taylor expanded in t around inf 43.7%

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

   6. Taylor expanded in a around 0 43.6%

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

4. Final simplification 47.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.3 \cdot 10^{-6} \lor \neg \left(a \leq 1\right):\\ \;\;\;\;\frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 19.7% accurate, 17.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = x
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 75.9%

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

   1. *-commutative 75.9%

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

   2. associate-*l/ 76.0%

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

   3. *-commutative 76.0%

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

   4. associate-*l/ 76.0%

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

3. Simplified 76.0%

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

5. Taylor expanded in t around inf 47.9%

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

6. Taylor expanded in a around 0 23.1%

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

7. Final simplification 23.1%

   \[\leadsto x \]
8. Add Preprocessing

Developer target: 79.5% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 1.0d0 * ((x + ((y / t) * z)) * (1.0d0 / ((a + 1.0d0) + ((y / t) * b))))
    if (t < (-1.3659085366310088d-271)) then
        tmp = t_1
    else if (t < 3.036967103737246d-130) then
        tmp = z / b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024024 
(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))))