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

Percentage Accurate: 75.2% → 89.2%

Time: 16.2s

Alternatives: 14

Speedup: 0.6×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 75.2% 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: 89.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{-307}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + \left(1 + \frac{y}{\frac{t}{b}}\right)}\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;\frac{\frac{t}{\frac{b}{x}}}{y} + \frac{z}{b}\\ \mathbf{elif}\;t_1 \leq 4 \cdot 10^{+294}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq \infty:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{1 + \left(a + y \cdot \frac{b}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{t}{\frac{y}{x}}}{b}\\ \end{array} \end{array} \]

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 -1e-307)
     (/ (+ x (* z (/ y t))) (+ a (+ 1.0 (/ y (/ t b)))))
     (if (<= t_1 0.0)
       (+ (/ (/ t (/ b x)) y) (/ z b))
       (if (<= t_1 4e+294)
         t_1
         (if (<= t_1 INFINITY)
           (* (/ y t) (/ z (+ 1.0 (+ a (* y (/ b t))))))
           (/ (+ z (/ t (/ y x))) 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 <= -1e-307) {
		tmp = (x + (z * (y / t))) / (a + (1.0 + (y / (t / b))));
	} else if (t_1 <= 0.0) {
		tmp = ((t / (b / x)) / y) + (z / b);
	} else if (t_1 <= 4e+294) {
		tmp = t_1;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = (y / t) * (z / (1.0 + (a + (y * (b / t)))));
	} else {
		tmp = (z + (t / (y / x))) / 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 <= -1e-307) {
		tmp = (x + (z * (y / t))) / (a + (1.0 + (y / (t / b))));
	} else if (t_1 <= 0.0) {
		tmp = ((t / (b / x)) / y) + (z / b);
	} else if (t_1 <= 4e+294) {
		tmp = t_1;
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = (y / t) * (z / (1.0 + (a + (y * (b / t)))));
	} else {
		tmp = (z + (t / (y / x))) / 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 <= -1e-307:
		tmp = (x + (z * (y / t))) / (a + (1.0 + (y / (t / b))))
	elif t_1 <= 0.0:
		tmp = ((t / (b / x)) / y) + (z / b)
	elif t_1 <= 4e+294:
		tmp = t_1
	elif t_1 <= math.inf:
		tmp = (y / t) * (z / (1.0 + (a + (y * (b / t)))))
	else:
		tmp = (z + (t / (y / x))) / 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 <= -1e-307)
		tmp = Float64(Float64(x + Float64(z * Float64(y / t))) / Float64(a + Float64(1.0 + Float64(y / Float64(t / b)))));
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(Float64(t / Float64(b / x)) / y) + Float64(z / b));
	elseif (t_1 <= 4e+294)
		tmp = t_1;
	elseif (t_1 <= Inf)
		tmp = Float64(Float64(y / t) * Float64(z / Float64(1.0 + Float64(a + Float64(y * Float64(b / t))))));
	else
		tmp = Float64(Float64(z + Float64(t / Float64(y / x))) / 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 <= -1e-307)
		tmp = (x + (z * (y / t))) / (a + (1.0 + (y / (t / b))));
	elseif (t_1 <= 0.0)
		tmp = ((t / (b / x)) / y) + (z / b);
	elseif (t_1 <= 4e+294)
		tmp = t_1;
	elseif (t_1 <= Inf)
		tmp = (y / t) * (z / (1.0 + (a + (y * (b / t)))));
	else
		tmp = (z + (t / (y / x))) / 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, -1e-307], N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + N[(1.0 + N[(y / N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(N[(N[(t / N[(b / x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] + N[(z / b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 4e+294], t$95$1, If[LessEqual[t$95$1, Infinity], N[(N[(y / t), $MachinePrecision] * N[(z / N[(1.0 + N[(a + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z + N[(t / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < -9.99999999999999909e-308

   1. Initial program 89.0%

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

      1. associate-/l* 90.3%

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

      2. associate-+l+ 90.3%

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

      3. associate-/l* 88.0%

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

   3. Simplified 88.0%

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

      1. associate-/r/ 92.2%

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

   6. Applied egg-rr 92.2%

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

   if -9.99999999999999909e-308 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 0.0

   1. Initial program 46.6%

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

      1. *-commutative 46.6%

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

      2. associate-*l/ 50.6%

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

      3. *-commutative 50.6%

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

      4. associate-*l/ 61.5%

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

   3. Simplified 61.5%

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

   5. Taylor expanded in y around -inf 64.1%

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

   6. Taylor expanded in x around inf 69.5%

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

      1. *-un-lft-identity 69.5%

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

   8. Applied egg-rr 73.8%

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

   if 0.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 4.00000000000000027e294

   1. Initial program 99.7%

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

   if 4.00000000000000027e294 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < +inf.0

   1. Initial program 31.0%

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

      1. associate-/l* 65.5%

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

      2. associate-+l+ 65.5%

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

      3. associate-/l* 65.2%

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

   3. Simplified 65.2%

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

      1. associate-/r/ 65.3%

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

   6. Applied egg-rr 65.3%

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

   7. Taylor expanded in x around 0 47.5%

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

      1. times-frac 99.4%

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

      2. associate-*l/ 90.9%

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

      3. *-commutative 90.9%

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

   9. Simplified 90.9%

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

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

   1. 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/ 0.4%

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

      3. *-commutative 0.4%

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

      4. associate-*l/ 11.2%

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

   3. Simplified 11.2%

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

   5. Taylor expanded in y around -inf 70.9%

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

   6. Taylor expanded in x around inf 93.0%

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

   7. Taylor expanded in b around 0 93.0%

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

      1. associate-/l* 96.6%

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

   9. Simplified 96.6%

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

4. Final simplification 91.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -1 \cdot 10^{-307}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + \left(1 + \frac{y}{\frac{t}{b}}\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 0:\\ \;\;\;\;\frac{\frac{t}{\frac{b}{x}}}{y} + \frac{z}{b}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 4 \cdot 10^{+294}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq \infty:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{1 + \left(a + y \cdot \frac{b}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{t}{\frac{y}{x}}}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 81.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{-122} \lor \neg \left(t \leq 4.1 \cdot 10^{-84}\right):\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + \left(1 + \frac{y}{\frac{t}{b}}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{\frac{x \cdot t}{b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -2.3e-122) (not (<= t 4.1e-84)))
   (/ (+ x (* z (/ y t))) (+ a (+ 1.0 (/ y (/ t b)))))
   (+ (/ z b) (/ (/ (* x t) b) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -2.3e-122) || !(t <= 4.1e-84)) {
		tmp = (x + (z * (y / t))) / (a + (1.0 + (y / (t / b))));
	} else {
		tmp = (z / b) + (((x * t) / b) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-2.3d-122)) .or. (.not. (t <= 4.1d-84))) then
        tmp = (x + (z * (y / t))) / (a + (1.0d0 + (y / (t / b))))
    else
        tmp = (z / b) + (((x * t) / b) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -2.3e-122) || !(t <= 4.1e-84)) {
		tmp = (x + (z * (y / t))) / (a + (1.0 + (y / (t / b))));
	} else {
		tmp = (z / b) + (((x * t) / b) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -2.3e-122) or not (t <= 4.1e-84):
		tmp = (x + (z * (y / t))) / (a + (1.0 + (y / (t / b))))
	else:
		tmp = (z / b) + (((x * t) / b) / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -2.3e-122) || !(t <= 4.1e-84))
		tmp = Float64(Float64(x + Float64(z * Float64(y / t))) / Float64(a + Float64(1.0 + Float64(y / Float64(t / b)))));
	else
		tmp = Float64(Float64(z / b) + Float64(Float64(Float64(x * t) / b) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -2.3e-122) || ~((t <= 4.1e-84)))
		tmp = (x + (z * (y / t))) / (a + (1.0 + (y / (t / b))));
	else
		tmp = (z / b) + (((x * t) / b) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -2.3e-122], N[Not[LessEqual[t, 4.1e-84]], $MachinePrecision]], N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + N[(1.0 + N[(y / N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z / b), $MachinePrecision] + N[(N[(N[(x * t), $MachinePrecision] / b), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.30000000000000007e-122 or 4.10000000000000005e-84 < t

   1. Initial program 84.0%

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

      1. associate-/l* 87.9%

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

      2. associate-+l+ 87.9%

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

      3. associate-/l* 91.8%

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

   3. Simplified 91.8%

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

      1. associate-/r/ 92.5%

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

   6. Applied egg-rr 92.5%

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

   if -2.30000000000000007e-122 < t < 4.10000000000000005e-84

   1. Initial program 52.1%

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

      1. *-commutative 52.1%

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

      2. associate-*l/ 43.0%

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

      3. *-commutative 43.0%

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

      4. associate-*l/ 37.3%

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

   3. Simplified 37.3%

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

   5. Taylor expanded in y around -inf 73.9%

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

   6. Taylor expanded in x around inf 80.9%

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

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{-122} \lor \neg \left(t \leq 4.1 \cdot 10^{-84}\right):\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + \left(1 + \frac{y}{\frac{t}{b}}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{\frac{x \cdot t}{b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 81.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.9 \cdot 10^{-122}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-81}:\\ \;\;\;\;\frac{z}{b} + \frac{\frac{x \cdot t}{b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + \left(1 + \frac{y}{\frac{t}{b}}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.9e-122)
   (/ (+ x (* y (/ z t))) (+ (+ a 1.0) (* y (/ b t))))
   (if (<= t 2e-81)
     (+ (/ z b) (/ (/ (* x t) b) y))
     (/ (+ x (* z (/ y t))) (+ a (+ 1.0 (/ y (/ t b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.9e-122) {
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)));
	} else if (t <= 2e-81) {
		tmp = (z / b) + (((x * t) / b) / y);
	} else {
		tmp = (x + (z * (y / t))) / (a + (1.0 + (y / (t / b))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-1.9d-122)) then
        tmp = (x + (y * (z / t))) / ((a + 1.0d0) + (y * (b / t)))
    else if (t <= 2d-81) then
        tmp = (z / b) + (((x * t) / b) / y)
    else
        tmp = (x + (z * (y / t))) / (a + (1.0d0 + (y / (t / b))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.9e-122) {
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)));
	} else if (t <= 2e-81) {
		tmp = (z / b) + (((x * t) / b) / y);
	} else {
		tmp = (x + (z * (y / t))) / (a + (1.0 + (y / (t / b))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1.9e-122:
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)))
	elif t <= 2e-81:
		tmp = (z / b) + (((x * t) / b) / y)
	else:
		tmp = (x + (z * (y / t))) / (a + (1.0 + (y / (t / b))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.9e-122)
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(Float64(a + 1.0) + Float64(y * Float64(b / t))));
	elseif (t <= 2e-81)
		tmp = Float64(Float64(z / b) + Float64(Float64(Float64(x * t) / b) / y));
	else
		tmp = Float64(Float64(x + Float64(z * Float64(y / t))) / Float64(a + Float64(1.0 + Float64(y / Float64(t / b)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -1.9e-122)
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)));
	elseif (t <= 2e-81)
		tmp = (z / b) + (((x * t) / b) / y);
	else
		tmp = (x + (z * (y / t))) / (a + (1.0 + (y / (t / b))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.9e-122], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2e-81], N[(N[(z / b), $MachinePrecision] + N[(N[(N[(x * t), $MachinePrecision] / b), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + N[(1.0 + N[(y / N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.9e-122

   1. Initial program 85.1%

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

      1. *-commutative 85.1%

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

      2. associate-*l/ 88.1%

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

      3. *-commutative 88.1%

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

      4. associate-*l/ 92.0%

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

   3. Simplified 92.0%

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

   if -1.9e-122 < t < 1.9999999999999999e-81

   1. Initial program 52.1%

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

      1. *-commutative 52.1%

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

      2. associate-*l/ 43.0%

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

      3. *-commutative 43.0%

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

      4. associate-*l/ 37.3%

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

   3. Simplified 37.3%

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

   5. Taylor expanded in y around -inf 73.9%

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

   6. Taylor expanded in x around inf 80.9%

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

   if 1.9999999999999999e-81 < t

   1. Initial program 82.5%

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

      1. associate-/l* 87.5%

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

      2. associate-+l+ 87.5%

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

      3. associate-/l* 91.5%

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

   3. Simplified 91.5%

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

      1. associate-/r/ 93.3%

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

   6. Applied egg-rr 93.3%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.9 \cdot 10^{-122}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-81}:\\ \;\;\;\;\frac{z}{b} + \frac{\frac{x \cdot t}{b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + \left(1 + \frac{y}{\frac{t}{b}}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 82.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + \left(1 + \frac{y}{\frac{t}{b}}\right)\\ \mathbf{if}\;t \leq -3.5 \cdot 10^{-122}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{t_1}\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{-84}:\\ \;\;\;\;\frac{z}{b} + \frac{\frac{x \cdot t}{b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{t_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ a (+ 1.0 (/ y (/ t b))))))
   (if (<= t -3.5e-122)
     (/ (+ x (/ y (/ t z))) t_1)
     (if (<= t 3.6e-84)
       (+ (/ z b) (/ (/ (* x t) b) y))
       (/ (+ x (* z (/ y t))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a + (1.0 + (y / (t / b)));
	double tmp;
	if (t <= -3.5e-122) {
		tmp = (x + (y / (t / z))) / t_1;
	} else if (t <= 3.6e-84) {
		tmp = (z / b) + (((x * t) / b) / y);
	} else {
		tmp = (x + (z * (y / t))) / t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a + (1.0d0 + (y / (t / b)))
    if (t <= (-3.5d-122)) then
        tmp = (x + (y / (t / z))) / t_1
    else if (t <= 3.6d-84) then
        tmp = (z / b) + (((x * t) / b) / y)
    else
        tmp = (x + (z * (y / t))) / t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a + (1.0 + (y / (t / b)));
	double tmp;
	if (t <= -3.5e-122) {
		tmp = (x + (y / (t / z))) / t_1;
	} else if (t <= 3.6e-84) {
		tmp = (z / b) + (((x * t) / b) / y);
	} else {
		tmp = (x + (z * (y / t))) / t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a + (1.0 + (y / (t / b)))
	tmp = 0
	if t <= -3.5e-122:
		tmp = (x + (y / (t / z))) / t_1
	elif t <= 3.6e-84:
		tmp = (z / b) + (((x * t) / b) / y)
	else:
		tmp = (x + (z * (y / t))) / t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a + Float64(1.0 + Float64(y / Float64(t / b))))
	tmp = 0.0
	if (t <= -3.5e-122)
		tmp = Float64(Float64(x + Float64(y / Float64(t / z))) / t_1);
	elseif (t <= 3.6e-84)
		tmp = Float64(Float64(z / b) + Float64(Float64(Float64(x * t) / b) / y));
	else
		tmp = Float64(Float64(x + Float64(z * Float64(y / t))) / t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a + (1.0 + (y / (t / b)));
	tmp = 0.0;
	if (t <= -3.5e-122)
		tmp = (x + (y / (t / z))) / t_1;
	elseif (t <= 3.6e-84)
		tmp = (z / b) + (((x * t) / b) / y);
	else
		tmp = (x + (z * (y / t))) / t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a + N[(1.0 + N[(y / N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.5e-122], N[(N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[t, 3.6e-84], N[(N[(z / b), $MachinePrecision] + N[(N[(N[(x * t), $MachinePrecision] / b), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.5000000000000001e-122

   1. Initial program 85.1%

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

      1. associate-/l* 88.1%

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

      2. associate-+l+ 88.1%

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

      3. associate-/l* 92.0%

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

   3. Simplified 92.0%

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

   if -3.5000000000000001e-122 < t < 3.60000000000000003e-84

   1. Initial program 52.1%

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

      1. *-commutative 52.1%

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

      2. associate-*l/ 43.0%

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

      3. *-commutative 43.0%

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

      4. associate-*l/ 37.3%

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

   3. Simplified 37.3%

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

   5. Taylor expanded in y around -inf 73.9%

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

   6. Taylor expanded in x around inf 80.9%

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

   if 3.60000000000000003e-84 < t

   1. Initial program 82.5%

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

      1. associate-/l* 87.5%

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

      2. associate-+l+ 87.5%

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

      3. associate-/l* 91.5%

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

   3. Simplified 91.5%

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

      1. associate-/r/ 93.3%

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

   6. Applied egg-rr 93.3%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{-122}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a + \left(1 + \frac{y}{\frac{t}{b}}\right)}\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{-84}:\\ \;\;\;\;\frac{z}{b} + \frac{\frac{x \cdot t}{b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + \left(1 + \frac{y}{\frac{t}{b}}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 57.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{a + 1}\\ \mathbf{if}\;t \leq -6 \cdot 10^{-122}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{+38}:\\ \;\;\;\;\frac{z + \frac{t}{\frac{y}{x}}}{b}\\ \mathbf{elif}\;t \leq 4.3 \cdot 10^{+98}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a}\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{+109}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (+ a 1.0))))
   (if (<= t -6e-122)
     t_1
     (if (<= t 7.5e+38)
       (/ (+ z (/ t (/ y x))) b)
       (if (<= t 4.3e+98)
         (/ (+ x (/ (* y z) t)) a)
         (if (<= t 4.6e+109) (/ z b) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a + 1.0);
	double tmp;
	if (t <= -6e-122) {
		tmp = t_1;
	} else if (t <= 7.5e+38) {
		tmp = (z + (t / (y / x))) / b;
	} else if (t <= 4.3e+98) {
		tmp = (x + ((y * z) / t)) / a;
	} else if (t <= 4.6e+109) {
		tmp = z / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (a + 1.0d0)
    if (t <= (-6d-122)) then
        tmp = t_1
    else if (t <= 7.5d+38) then
        tmp = (z + (t / (y / x))) / b
    else if (t <= 4.3d+98) then
        tmp = (x + ((y * z) / t)) / a
    else if (t <= 4.6d+109) then
        tmp = z / b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a + 1.0);
	double tmp;
	if (t <= -6e-122) {
		tmp = t_1;
	} else if (t <= 7.5e+38) {
		tmp = (z + (t / (y / x))) / b;
	} else if (t <= 4.3e+98) {
		tmp = (x + ((y * z) / t)) / a;
	} else if (t <= 4.6e+109) {
		tmp = z / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (a + 1.0)
	tmp = 0
	if t <= -6e-122:
		tmp = t_1
	elif t <= 7.5e+38:
		tmp = (z + (t / (y / x))) / b
	elif t <= 4.3e+98:
		tmp = (x + ((y * z) / t)) / a
	elif t <= 4.6e+109:
		tmp = z / b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(a + 1.0))
	tmp = 0.0
	if (t <= -6e-122)
		tmp = t_1;
	elseif (t <= 7.5e+38)
		tmp = Float64(Float64(z + Float64(t / Float64(y / x))) / b);
	elseif (t <= 4.3e+98)
		tmp = Float64(Float64(x + Float64(Float64(y * z) / t)) / a);
	elseif (t <= 4.6e+109)
		tmp = Float64(z / b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (a + 1.0);
	tmp = 0.0;
	if (t <= -6e-122)
		tmp = t_1;
	elseif (t <= 7.5e+38)
		tmp = (z + (t / (y / x))) / b;
	elseif (t <= 4.3e+98)
		tmp = (x + ((y * z) / t)) / a;
	elseif (t <= 4.6e+109)
		tmp = z / b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6e-122], t$95$1, If[LessEqual[t, 7.5e+38], N[(N[(z + N[(t / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[t, 4.3e+98], N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[t, 4.6e+109], N[(z / b), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -6.00000000000000009e-122 or 4.60000000000000021e109 < t

   1. Initial program 83.4%

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

      1. *-commutative 83.4%

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

      2. associate-*l/ 89.0%

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

      3. *-commutative 89.0%

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

      4. associate-*l/ 93.2%

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

   3. Simplified 93.2%

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

   5. Taylor expanded in t around inf 63.1%

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

   if -6.00000000000000009e-122 < t < 7.4999999999999999e38

   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. *-commutative 59.9%

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

      2. associate-*l/ 51.6%

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

      3. *-commutative 51.6%

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

      4. associate-*l/ 46.0%

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

   3. Simplified 46.0%

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

   5. Taylor expanded in y around -inf 70.6%

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

   6. Taylor expanded in x around inf 77.2%

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

   7. Taylor expanded in b around 0 77.2%

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

      1. associate-/l* 75.2%

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

   9. Simplified 75.2%

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

   if 7.4999999999999999e38 < t < 4.3000000000000001e98

   1. Initial program 85.8%

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

      1. *-commutative 85.8%

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

      2. associate-*l/ 85.5%

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

      3. *-commutative 85.5%

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

      4. associate-*l/ 92.5%

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

   3. Simplified 92.5%

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

   5. Taylor expanded in a around inf 64.2%

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

   if 4.3000000000000001e98 < t < 4.60000000000000021e109

   1. Initial program 7.4%

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

      1. *-commutative 7.4%

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

      2. associate-*l/ 7.4%

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

      3. *-commutative 7.4%

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

      4. associate-*l/ 54.3%

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

   3. Simplified 54.3%

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

   5. Taylor expanded in t around 0 100.0%

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

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{-122}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{+38}:\\ \;\;\;\;\frac{z + \frac{t}{\frac{y}{x}}}{b}\\ \mathbf{elif}\;t \leq 4.3 \cdot 10^{+98}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a}\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{+109}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 60.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.8 \cdot 10^{-122}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \mathbf{elif}\;t \leq 8 \cdot 10^{+38}:\\ \;\;\;\;\frac{z + \frac{t}{\frac{y}{x}}}{b}\\ \mathbf{elif}\;t \leq 6.4 \cdot 10^{+98}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a}\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{+109}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -7.8e-122)
   (/ x (+ 1.0 (+ a (/ (* y b) t))))
   (if (<= t 8e+38)
     (/ (+ z (/ t (/ y x))) b)
     (if (<= t 6.4e+98)
       (/ (+ x (/ (* y z) t)) a)
       (if (<= t 4.6e+109) (/ z b) (/ x (+ a 1.0)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -7.8e-122) {
		tmp = x / (1.0 + (a + ((y * b) / t)));
	} else if (t <= 8e+38) {
		tmp = (z + (t / (y / x))) / b;
	} else if (t <= 6.4e+98) {
		tmp = (x + ((y * z) / t)) / a;
	} else if (t <= 4.6e+109) {
		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 (t <= (-7.8d-122)) then
        tmp = x / (1.0d0 + (a + ((y * b) / t)))
    else if (t <= 8d+38) then
        tmp = (z + (t / (y / x))) / b
    else if (t <= 6.4d+98) then
        tmp = (x + ((y * z) / t)) / a
    else if (t <= 4.6d+109) 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 (t <= -7.8e-122) {
		tmp = x / (1.0 + (a + ((y * b) / t)));
	} else if (t <= 8e+38) {
		tmp = (z + (t / (y / x))) / b;
	} else if (t <= 6.4e+98) {
		tmp = (x + ((y * z) / t)) / a;
	} else if (t <= 4.6e+109) {
		tmp = z / b;
	} else {
		tmp = x / (a + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -7.8e-122:
		tmp = x / (1.0 + (a + ((y * b) / t)))
	elif t <= 8e+38:
		tmp = (z + (t / (y / x))) / b
	elif t <= 6.4e+98:
		tmp = (x + ((y * z) / t)) / a
	elif t <= 4.6e+109:
		tmp = z / b
	else:
		tmp = x / (a + 1.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -7.8e-122)
		tmp = Float64(x / Float64(1.0 + Float64(a + Float64(Float64(y * b) / t))));
	elseif (t <= 8e+38)
		tmp = Float64(Float64(z + Float64(t / Float64(y / x))) / b);
	elseif (t <= 6.4e+98)
		tmp = Float64(Float64(x + Float64(Float64(y * z) / t)) / a);
	elseif (t <= 4.6e+109)
		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 (t <= -7.8e-122)
		tmp = x / (1.0 + (a + ((y * b) / t)));
	elseif (t <= 8e+38)
		tmp = (z + (t / (y / x))) / b;
	elseif (t <= 6.4e+98)
		tmp = (x + ((y * z) / t)) / a;
	elseif (t <= 4.6e+109)
		tmp = z / b;
	else
		tmp = x / (a + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -7.8e-122], N[(x / N[(1.0 + N[(a + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8e+38], N[(N[(z + N[(t / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[t, 6.4e+98], N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[t, 4.6e+109], N[(z / b), $MachinePrecision], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -7.79999999999999979e-122

   1. Initial program 85.1%

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

      1. *-commutative 85.1%

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

      2. associate-*l/ 88.1%

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

      3. *-commutative 88.1%

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

      4. associate-*l/ 92.0%

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

   3. Simplified 92.0%

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

   5. Taylor expanded in x around inf 62.0%

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

   if -7.79999999999999979e-122 < t < 7.99999999999999982e38

   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. *-commutative 59.9%

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

      2. associate-*l/ 51.6%

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

      3. *-commutative 51.6%

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

      4. associate-*l/ 46.0%

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

   3. Simplified 46.0%

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

   5. Taylor expanded in y around -inf 70.6%

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

   6. Taylor expanded in x around inf 77.2%

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

   7. Taylor expanded in b around 0 77.2%

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

      1. associate-/l* 75.2%

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

   9. Simplified 75.2%

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

   if 7.99999999999999982e38 < t < 6.4000000000000005e98

   1. Initial program 85.8%

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

      1. *-commutative 85.8%

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

      2. associate-*l/ 85.5%

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

      3. *-commutative 85.5%

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

      4. associate-*l/ 92.5%

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

   3. Simplified 92.5%

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

   5. Taylor expanded in a around inf 64.2%

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

   if 6.4000000000000005e98 < t < 4.60000000000000021e109

   1. Initial program 7.4%

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

      1. *-commutative 7.4%

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

      2. associate-*l/ 7.4%

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

      3. *-commutative 7.4%

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

      4. associate-*l/ 54.3%

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

   3. Simplified 54.3%

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

   5. Taylor expanded in t around 0 100.0%

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

   if 4.60000000000000021e109 < t

   1. Initial program 79.2%

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

      1. *-commutative 79.2%

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

      2. associate-*l/ 91.2%

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

      3. *-commutative 91.2%

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

      4. associate-*l/ 96.3%

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

   3. Simplified 96.3%

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

   5. Taylor expanded in t around inf 76.0%

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

4. Final simplification 69.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.8 \cdot 10^{-122}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \mathbf{elif}\;t \leq 8 \cdot 10^{+38}:\\ \;\;\;\;\frac{z + \frac{t}{\frac{y}{x}}}{b}\\ \mathbf{elif}\;t \leq 6.4 \cdot 10^{+98}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a}\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{+109}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 54.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{a + 1}\\ \mathbf{if}\;t \leq -7.8 \cdot 10^{-122}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{+35}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq 8.4 \cdot 10^{+101}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (+ a 1.0))))
   (if (<= t -7.8e-122)
     t_1
     (if (<= t 6.2e+35)
       (/ z b)
       (if (<= t 8.4e+101) (/ (+ x (/ (* y z) t)) a) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a + 1.0);
	double tmp;
	if (t <= -7.8e-122) {
		tmp = t_1;
	} else if (t <= 6.2e+35) {
		tmp = z / b;
	} else if (t <= 8.4e+101) {
		tmp = (x + ((y * z) / t)) / a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (a + 1.0d0)
    if (t <= (-7.8d-122)) then
        tmp = t_1
    else if (t <= 6.2d+35) then
        tmp = z / b
    else if (t <= 8.4d+101) then
        tmp = (x + ((y * z) / t)) / a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a + 1.0);
	double tmp;
	if (t <= -7.8e-122) {
		tmp = t_1;
	} else if (t <= 6.2e+35) {
		tmp = z / b;
	} else if (t <= 8.4e+101) {
		tmp = (x + ((y * z) / t)) / a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (a + 1.0)
	tmp = 0
	if t <= -7.8e-122:
		tmp = t_1
	elif t <= 6.2e+35:
		tmp = z / b
	elif t <= 8.4e+101:
		tmp = (x + ((y * z) / t)) / a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(a + 1.0))
	tmp = 0.0
	if (t <= -7.8e-122)
		tmp = t_1;
	elseif (t <= 6.2e+35)
		tmp = Float64(z / b);
	elseif (t <= 8.4e+101)
		tmp = Float64(Float64(x + Float64(Float64(y * z) / t)) / a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (a + 1.0);
	tmp = 0.0;
	if (t <= -7.8e-122)
		tmp = t_1;
	elseif (t <= 6.2e+35)
		tmp = z / b;
	elseif (t <= 8.4e+101)
		tmp = (x + ((y * z) / t)) / a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7.8e-122], t$95$1, If[LessEqual[t, 6.2e+35], N[(z / b), $MachinePrecision], If[LessEqual[t, 8.4e+101], N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.79999999999999979e-122 or 8.4000000000000001e101 < t

   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/ 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/ 93.2%

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

   3. Simplified 93.2%

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

   5. Taylor expanded in t around inf 62.8%

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

   if -7.79999999999999979e-122 < t < 6.19999999999999973e35

   1. Initial program 59.1%

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

      1. *-commutative 59.1%

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

      2. associate-*l/ 50.6%

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

      3. *-commutative 50.6%

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

      4. associate-*l/ 44.9%

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

   3. Simplified 44.9%

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

   5. Taylor expanded in t around 0 67.2%

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

   if 6.19999999999999973e35 < t < 8.4000000000000001e101

   1. Initial program 82.8%

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

      1. *-commutative 82.8%

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

      2. associate-*l/ 82.7%

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

      3. *-commutative 82.7%

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

      4. associate-*l/ 88.4%

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

   3. Simplified 88.4%

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

   5. Taylor expanded in a around inf 53.7%

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

4. Final simplification 63.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.8 \cdot 10^{-122}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{+35}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq 8.4 \cdot 10^{+101}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 65.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.1 \cdot 10^{-67} \lor \neg \left(t \leq 1.6 \cdot 10^{-19}\right):\\ \;\;\;\;\frac{x}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{t}{\frac{y}{x}}}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -3.1e-67) (not (<= t 1.6e-19)))
   (/ x (+ (+ a 1.0) (* y (/ b t))))
   (/ (+ z (/ t (/ y x))) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -3.1e-67) || !(t <= 1.6e-19)) {
		tmp = x / ((a + 1.0) + (y * (b / t)));
	} else {
		tmp = (z + (t / (y / x))) / 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-67)) .or. (.not. (t <= 1.6d-19))) then
        tmp = x / ((a + 1.0d0) + (y * (b / t)))
    else
        tmp = (z + (t / (y / x))) / 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-67) || !(t <= 1.6e-19)) {
		tmp = x / ((a + 1.0) + (y * (b / t)));
	} else {
		tmp = (z + (t / (y / x))) / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -3.1e-67) or not (t <= 1.6e-19):
		tmp = x / ((a + 1.0) + (y * (b / t)))
	else:
		tmp = (z + (t / (y / x))) / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -3.1e-67) || !(t <= 1.6e-19))
		tmp = Float64(x / Float64(Float64(a + 1.0) + Float64(y * Float64(b / t))));
	else
		tmp = Float64(Float64(z + Float64(t / Float64(y / x))) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -3.1e-67) || ~((t <= 1.6e-19)))
		tmp = x / ((a + 1.0) + (y * (b / t)));
	else
		tmp = (z + (t / (y / x))) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -3.1e-67], N[Not[LessEqual[t, 1.6e-19]], $MachinePrecision]], N[(x / N[(N[(a + 1.0), $MachinePrecision] + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z + N[(t / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.1000000000000003e-67 or 1.59999999999999991e-19 < t

   1. Initial program 84.6%

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

      1. *-commutative 84.6%

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

      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/ 95.2%

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

   3. Simplified 95.2%

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

   5. Taylor expanded in x around inf 66.5%

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

   if -3.1000000000000003e-67 < t < 1.59999999999999991e-19

   1. Initial program 56.7%

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

      1. *-commutative 56.7%

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

      2. associate-*l/ 48.2%

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

      3. *-commutative 48.2%

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

      4. associate-*l/ 41.7%

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

   3. Simplified 41.7%

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

   5. Taylor expanded in y around -inf 68.9%

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

   6. Taylor expanded in x around inf 76.7%

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

   7. Taylor expanded in b around 0 77.6%

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

      1. associate-/l* 75.5%

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

   9. Simplified 75.5%

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

4. Final simplification 70.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.1 \cdot 10^{-67} \lor \neg \left(t \leq 1.6 \cdot 10^{-19}\right):\\ \;\;\;\;\frac{x}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{t}{\frac{y}{x}}}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 66.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{-122} \lor \neg \left(t \leq 5.5 \cdot 10^{-17}\right):\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{t}{\frac{y}{x}}}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -6e-122) (not (<= t 5.5e-17)))
   (/ (+ x (/ (* y z) t)) (+ a 1.0))
   (/ (+ z (/ t (/ y x))) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -6e-122) || !(t <= 5.5e-17)) {
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	} else {
		tmp = (z + (t / (y / x))) / 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 <= (-6d-122)) .or. (.not. (t <= 5.5d-17))) then
        tmp = (x + ((y * z) / t)) / (a + 1.0d0)
    else
        tmp = (z + (t / (y / x))) / 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 <= -6e-122) || !(t <= 5.5e-17)) {
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	} else {
		tmp = (z + (t / (y / x))) / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -6e-122) or not (t <= 5.5e-17):
		tmp = (x + ((y * z) / t)) / (a + 1.0)
	else:
		tmp = (z + (t / (y / x))) / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -6e-122) || !(t <= 5.5e-17))
		tmp = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(a + 1.0));
	else
		tmp = Float64(Float64(z + Float64(t / Float64(y / x))) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -6e-122) || ~((t <= 5.5e-17)))
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	else
		tmp = (z + (t / (y / x))) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -6e-122], N[Not[LessEqual[t, 5.5e-17]], $MachinePrecision]], N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(z + N[(t / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -6.00000000000000009e-122 or 5.50000000000000001e-17 < t

   1. Initial program 83.5%

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

      1. *-commutative 83.5%

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

      2. associate-*l/ 88.2%

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

      3. *-commutative 88.2%

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

      4. associate-*l/ 93.0%

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

   3. Simplified 93.0%

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

   5. Taylor expanded in b around 0 72.0%

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

   if -6.00000000000000009e-122 < t < 5.50000000000000001e-17

   1. Initial program 56.6%

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

      1. *-commutative 56.6%

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

      2. associate-*l/ 47.5%

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

      3. *-commutative 47.5%

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

      4. associate-*l/ 41.5%

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

   3. Simplified 41.5%

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

   5. Taylor expanded in y around -inf 72.2%

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

   6. Taylor expanded in x around inf 79.4%

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

   7. Taylor expanded in b around 0 80.4%

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

      1. associate-/l* 78.1%

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

   9. Simplified 78.1%

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

4. Final simplification 74.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{-122} \lor \neg \left(t \leq 5.5 \cdot 10^{-17}\right):\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{t}{\frac{y}{x}}}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 66.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.8 \cdot 10^{-122} \lor \neg \left(t \leq 2.6 \cdot 10^{+38}\right):\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{\frac{x \cdot t}{b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -7.8e-122) (not (<= t 2.6e+38)))
   (/ (+ x (/ (* y z) t)) (+ a 1.0))
   (+ (/ z b) (/ (/ (* x t) b) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -7.8e-122) || !(t <= 2.6e+38)) {
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	} else {
		tmp = (z / b) + (((x * t) / b) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-7.8d-122)) .or. (.not. (t <= 2.6d+38))) then
        tmp = (x + ((y * z) / t)) / (a + 1.0d0)
    else
        tmp = (z / b) + (((x * t) / b) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -7.8e-122) || !(t <= 2.6e+38)) {
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	} else {
		tmp = (z / b) + (((x * t) / b) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -7.8e-122) or not (t <= 2.6e+38):
		tmp = (x + ((y * z) / t)) / (a + 1.0)
	else:
		tmp = (z / b) + (((x * t) / b) / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -7.8e-122) || !(t <= 2.6e+38))
		tmp = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(a + 1.0));
	else
		tmp = Float64(Float64(z / b) + Float64(Float64(Float64(x * t) / b) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -7.8e-122) || ~((t <= 2.6e+38)))
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	else
		tmp = (z / b) + (((x * t) / b) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -7.8e-122], N[Not[LessEqual[t, 2.6e+38]], $MachinePrecision]], N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(z / b), $MachinePrecision] + N[(N[(N[(x * t), $MachinePrecision] / b), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -7.79999999999999979e-122 or 2.5999999999999999e38 < t

   1. Initial program 82.6%

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

      1. *-commutative 82.6%

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

      2. associate-*l/ 87.6%

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

      3. *-commutative 87.6%

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

      4. associate-*l/ 92.6%

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

   3. Simplified 92.6%

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

   5. Taylor expanded in b around 0 73.1%

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

   if -7.79999999999999979e-122 < t < 2.5999999999999999e38

   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. *-commutative 59.9%

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

      2. associate-*l/ 51.6%

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

      3. *-commutative 51.6%

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

      4. associate-*l/ 46.0%

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

   3. Simplified 46.0%

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

   5. Taylor expanded in y around -inf 70.6%

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

   6. Taylor expanded in x around inf 77.2%

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

4. Final simplification 74.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.8 \cdot 10^{-122} \lor \neg \left(t \leq 2.6 \cdot 10^{+38}\right):\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{\frac{x \cdot t}{b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 37.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -9.5 \cdot 10^{-114}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq -1 \cdot 10^{-224}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 4.1 \cdot 10^{+99}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -9.5e-114)
   (/ z b)
   (if (<= a -1e-224) x (if (<= a 4.1e+99) (/ z b) (/ x a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -9.5e-114) {
		tmp = z / b;
	} else if (a <= -1e-224) {
		tmp = x;
	} else if (a <= 4.1e+99) {
		tmp = z / b;
	} else {
		tmp = x / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-9.5d-114)) then
        tmp = z / b
    else if (a <= (-1d-224)) then
        tmp = x
    else if (a <= 4.1d+99) then
        tmp = z / b
    else
        tmp = x / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -9.5e-114) {
		tmp = z / b;
	} else if (a <= -1e-224) {
		tmp = x;
	} else if (a <= 4.1e+99) {
		tmp = z / b;
	} else {
		tmp = x / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -9.5e-114:
		tmp = z / b
	elif a <= -1e-224:
		tmp = x
	elif a <= 4.1e+99:
		tmp = z / b
	else:
		tmp = x / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -9.5e-114)
		tmp = Float64(z / b);
	elseif (a <= -1e-224)
		tmp = x;
	elseif (a <= 4.1e+99)
		tmp = Float64(z / b);
	else
		tmp = Float64(x / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -9.5e-114)
		tmp = z / b;
	elseif (a <= -1e-224)
		tmp = x;
	elseif (a <= 4.1e+99)
		tmp = z / b;
	else
		tmp = x / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -9.5e-114], N[(z / b), $MachinePrecision], If[LessEqual[a, -1e-224], x, If[LessEqual[a, 4.1e+99], N[(z / b), $MachinePrecision], N[(x / a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -9.49999999999999958e-114 or -1e-224 < a < 4.09999999999999979e99

   1. Initial program 72.2%

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

      1. *-commutative 72.2%

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

      2. associate-*l/ 69.6%

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

      3. *-commutative 69.6%

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

      4. associate-*l/ 71.0%

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

   3. Simplified 71.0%

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

   5. Taylor expanded in t around 0 43.3%

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

   if -9.49999999999999958e-114 < a < -1e-224

   1. Initial program 75.0%

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

      1. *-commutative 75.0%

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

      2. associate-*l/ 85.0%

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

      3. *-commutative 85.0%

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

      4. associate-*l/ 80.1%

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

   3. Simplified 80.1%

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

   5. Taylor expanded in x around inf 63.2%

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

   6. Taylor expanded in a around 0 68.1%

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

   7. Taylor expanded in b around 0 62.7%

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

   if 4.09999999999999979e99 < a

   1. Initial program 78.1%

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

      1. *-commutative 78.1%

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

      2. associate-*l/ 82.7%

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

      3. *-commutative 82.7%

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

      4. associate-*l/ 82.7%

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

   3. Simplified 82.7%

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

   5. Taylor expanded in x around inf 69.7%

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

   6. Taylor expanded in a around inf 67.4%

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

4. Final simplification 48.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9.5 \cdot 10^{-114}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq -1 \cdot 10^{-224}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 4.1 \cdot 10^{+99}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 56.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.8 \cdot 10^{-122} \lor \neg \left(t \leq 1.1 \cdot 10^{-16}\right):\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -7.8e-122) (not (<= t 1.1e-16))) (/ x (+ a 1.0)) (/ z b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -7.8e-122) || !(t <= 1.1e-16)) {
		tmp = x / (a + 1.0);
	} else {
		tmp = z / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-7.8d-122)) .or. (.not. (t <= 1.1d-16))) then
        tmp = x / (a + 1.0d0)
    else
        tmp = z / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -7.8e-122) || !(t <= 1.1e-16)) {
		tmp = x / (a + 1.0);
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -7.8e-122) or not (t <= 1.1e-16):
		tmp = x / (a + 1.0)
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -7.8e-122) || !(t <= 1.1e-16))
		tmp = Float64(x / Float64(a + 1.0));
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -7.8e-122) || ~((t <= 1.1e-16)))
		tmp = x / (a + 1.0);
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -7.8e-122], N[Not[LessEqual[t, 1.1e-16]], $MachinePrecision]], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -7.79999999999999979e-122 or 1.1e-16 < t

   1. Initial program 83.5%

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

      1. *-commutative 83.5%

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

      2. associate-*l/ 88.2%

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

      3. *-commutative 88.2%

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

      4. associate-*l/ 93.0%

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

   3. Simplified 93.0%

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

   5. Taylor expanded in t around inf 58.5%

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

   if -7.79999999999999979e-122 < t < 1.1e-16

   1. Initial program 56.6%

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

      1. *-commutative 56.6%

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

      2. associate-*l/ 47.5%

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

      3. *-commutative 47.5%

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

      4. associate-*l/ 41.5%

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

   3. Simplified 41.5%

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

   5. Taylor expanded in t around 0 68.6%

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

4. Final simplification 62.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.8 \cdot 10^{-122} \lor \neg \left(t \leq 1.1 \cdot 10^{-16}\right):\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 41.4% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if a < -1 or 1 < a

   1. Initial program 71.2%

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

      1. *-commutative 71.2%

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

      2. associate-*l/ 71.3%

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

      3. *-commutative 71.3%

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

      4. associate-*l/ 74.1%

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

   3. Simplified 74.1%

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

   5. Taylor expanded in x around inf 49.3%

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

   6. Taylor expanded in a around inf 43.0%

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

   if -1 < a < 1

   1. Initial program 75.8%

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

      1. *-commutative 75.8%

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

      2. associate-*l/ 74.7%

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

      3. *-commutative 74.7%

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

      4. associate-*l/ 73.2%

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

   3. Simplified 73.2%

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

   5. Taylor expanded in x around inf 51.2%

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

   6. Taylor expanded in a around 0 50.2%

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

   7. Taylor expanded in b around 0 37.1%

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

4. Final simplification 40.2%

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

Alternative 14: 19.6% accurate, 17.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 73.4%

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

   1. *-commutative 73.4%

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

   2. associate-*l/ 72.9%

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

   3. *-commutative 72.9%

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

   4. associate-*l/ 73.7%

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

3. Simplified 73.7%

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

5. Taylor expanded in x around inf 50.2%

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

6. Taylor expanded in a around 0 29.9%

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

7. Taylor expanded in b around 0 19.9%

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

8. Final simplification 19.9%

   \[\leadsto x \]
9. Add Preprocessing

Developer target: 79.7% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024018 
(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))))