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

Percentage Accurate: 75.2% → 89.3%

Time: 14.5s

Alternatives: 16

Speedup: 0.6×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 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: 89.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ t_2 := \frac{y}{t} \cdot \frac{z}{\left(a + 1\right) + \frac{y}{\frac{t}{b}}}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+288}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t))))
        (t_2 (* (/ y t) (/ z (+ (+ a 1.0) (/ y (/ t b)))))))
   (if (<= t_1 (- INFINITY))
     t_2
     (if (<= t_1 2e+288) t_1 (if (<= t_1 INFINITY) t_2 (/ z b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
	double t_2 = (y / t) * (z / ((a + 1.0) + (y / (t / b))));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = t_2;
	} else if (t_1 <= 2e+288) {
		tmp = t_1;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = t_2;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
	double t_2 = (y / t) * (z / ((a + 1.0) + (y / (t / b))));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else if (t_1 <= 2e+288) {
		tmp = t_1;
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t))
	t_2 = (y / t) * (z / ((a + 1.0) + (y / (t / b))))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = t_2
	elif t_1 <= 2e+288:
		tmp = t_1
	elif t_1 <= math.inf:
		tmp = t_2
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(Float64(a + 1.0) + Float64(Float64(y * b) / t)))
	t_2 = Float64(Float64(y / t) * Float64(z / Float64(Float64(a + 1.0) + Float64(y / Float64(t / b)))))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = t_2;
	elseif (t_1 <= 2e+288)
		tmp = t_1;
	elseif (t_1 <= Inf)
		tmp = t_2;
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
	t_2 = (y / t) * (z / ((a + 1.0) + (y / (t / b))));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = t_2;
	elseif (t_1 <= 2e+288)
		tmp = t_1;
	elseif (t_1 <= Inf)
		tmp = t_2;
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y / t), $MachinePrecision] * N[(z / N[(N[(a + 1.0), $MachinePrecision] + N[(y / N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], t$95$2, If[LessEqual[t$95$1, 2e+288], t$95$1, If[LessEqual[t$95$1, Infinity], t$95$2, N[(z / b), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -inf.0 or 2e288 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < +inf.0

   1. Initial program 34.4%

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

      1. associate-/l* 64.2%

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

      2. associate-/l* 64.2%

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

   3. Simplified 64.2%

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

   5. Taylor expanded in x around 0 59.8%

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

      1. times-frac 76.8%

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

      2. associate-+r+ 76.8%

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

      3. associate-*r/ 65.8%

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

      4. *-commutative 65.8%

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

      5. associate-/r/ 76.7%

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

   7. Simplified 76.7%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 2e288

   1. Initial program 93.4%

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

   if +inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t)))

   1. Initial program 0.0%

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

      1. associate-/l* 0.6%

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

      2. associate-/l* 16.1%

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

   3. Simplified 16.1%

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

   5. Taylor expanded in y around inf 95.2%

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

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -\infty:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{\left(a + 1\right) + \frac{y}{\frac{t}{b}}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 2 \cdot 10^{+288}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq \infty:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{\left(a + 1\right) + \frac{y}{\frac{t}{b}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 68.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{+19}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+16}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{+165}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{1 + y \cdot \frac{b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(\frac{z}{x} + \frac{t}{y}\right)}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -2.2e+19)
   (/ (+ z (/ (* x t) y)) b)
   (if (<= y 1.5e+16)
     (/ (+ x (/ (* y z) t)) (+ a 1.0))
     (if (<= y 4.6e+165)
       (/ (+ x (* y (/ z t))) (+ 1.0 (* y (/ b t))))
       (/ (* x (+ (/ z x) (/ t y))) b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.2e+19) {
		tmp = (z + ((x * t) / y)) / b;
	} else if (y <= 1.5e+16) {
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	} else if (y <= 4.6e+165) {
		tmp = (x + (y * (z / t))) / (1.0 + (y * (b / t)));
	} else {
		tmp = (x * ((z / x) + (t / y))) / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-2.2d+19)) then
        tmp = (z + ((x * t) / y)) / b
    else if (y <= 1.5d+16) then
        tmp = (x + ((y * z) / t)) / (a + 1.0d0)
    else if (y <= 4.6d+165) then
        tmp = (x + (y * (z / t))) / (1.0d0 + (y * (b / t)))
    else
        tmp = (x * ((z / x) + (t / y))) / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.2e+19) {
		tmp = (z + ((x * t) / y)) / b;
	} else if (y <= 1.5e+16) {
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	} else if (y <= 4.6e+165) {
		tmp = (x + (y * (z / t))) / (1.0 + (y * (b / t)));
	} else {
		tmp = (x * ((z / x) + (t / y))) / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -2.2e+19:
		tmp = (z + ((x * t) / y)) / b
	elif y <= 1.5e+16:
		tmp = (x + ((y * z) / t)) / (a + 1.0)
	elif y <= 4.6e+165:
		tmp = (x + (y * (z / t))) / (1.0 + (y * (b / t)))
	else:
		tmp = (x * ((z / x) + (t / y))) / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -2.2e+19)
		tmp = Float64(Float64(z + Float64(Float64(x * t) / y)) / b);
	elseif (y <= 1.5e+16)
		tmp = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(a + 1.0));
	elseif (y <= 4.6e+165)
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(1.0 + Float64(y * Float64(b / t))));
	else
		tmp = Float64(Float64(x * Float64(Float64(z / x) + Float64(t / y))) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -2.2e+19)
		tmp = (z + ((x * t) / y)) / b;
	elseif (y <= 1.5e+16)
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	elseif (y <= 4.6e+165)
		tmp = (x + (y * (z / t))) / (1.0 + (y * (b / t)));
	else
		tmp = (x * ((z / x) + (t / y))) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -2.2e+19], N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[y, 1.5e+16], N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.6e+165], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(1.0 + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(N[(z / x), $MachinePrecision] + N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.2e19

   1. Initial program 51.5%

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

      1. associate-/l* 57.3%

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

      2. associate-/l* 64.6%

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

   3. Simplified 64.6%

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

   5. Taylor expanded in x around inf 55.0%

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

      1. associate-+r+ 55.0%

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

      2. associate-*r/ 56.8%

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

      3. *-commutative 56.8%

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

      4. associate-/r/ 56.9%

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

      5. *-commutative 56.9%

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

      6. associate-+r+ 56.9%

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

      7. associate-*r/ 51.2%

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

      8. *-commutative 51.2%

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

      9. associate-/r/ 58.8%

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

   7. Simplified 58.8%

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

   8. Taylor expanded in b around inf 52.0%

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

      1. +-commutative 52.0%

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

   10. Simplified 52.0%

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

   11. Taylor expanded in x around 0 59.5%

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

   if -2.2e19 < y < 1.5e16

   1. Initial program 97.2%

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

      1. associate-/l* 90.6%

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

      2. associate-/l* 86.5%

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

   3. Simplified 86.5%

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

   5. Taylor expanded in b around 0 85.6%

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

   if 1.5e16 < y < 4.60000000000000032e165

   1. Initial program 73.6%

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

      1. associate-/l* 85.2%

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

      2. associate-/l* 88.1%

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

   3. Simplified 88.1%

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

   5. Taylor expanded in a around 0 70.6%

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

   if 4.60000000000000032e165 < y

   1. Initial program 48.8%

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

      1. associate-/l* 56.1%

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

      2. associate-/l* 63.4%

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

   3. Simplified 63.4%

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

   5. Taylor expanded in x around inf 44.9%

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

      1. associate-+r+ 44.9%

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

      2. associate-*r/ 48.5%

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

      3. *-commutative 48.5%

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

      4. associate-/r/ 48.5%

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

      5. *-commutative 48.5%

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

      6. associate-+r+ 48.5%

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

      7. associate-*r/ 38.0%

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

      8. *-commutative 38.0%

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

      9. associate-/r/ 48.5%

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

   7. Simplified 48.5%

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

   8. Taylor expanded in b around inf 71.1%

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

      1. +-commutative 71.1%

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

   10. Simplified 71.1%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{+19}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+16}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{+165}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{1 + y \cdot \frac{b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(\frac{z}{x} + \frac{t}{y}\right)}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z}{t}\\ t_2 := y \cdot \frac{b}{t}\\ \mathbf{if}\;a + 1 \leq -1 \cdot 10^{+16} \lor \neg \left(a + 1 \leq 2\right):\\ \;\;\;\;\frac{t\_1}{a + t\_2}\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_1}{1 + t\_2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ z t)))) (t_2 (* y (/ b t))))
   (if (or (<= (+ a 1.0) -1e+16) (not (<= (+ a 1.0) 2.0)))
     (/ t_1 (+ a t_2))
     (/ t_1 (+ 1.0 t_2)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y * (z / t));
	double t_2 = y * (b / t);
	double tmp;
	if (((a + 1.0) <= -1e+16) || !((a + 1.0) <= 2.0)) {
		tmp = t_1 / (a + t_2);
	} else {
		tmp = t_1 / (1.0 + t_2);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (y * (z / t))
    t_2 = y * (b / t)
    if (((a + 1.0d0) <= (-1d+16)) .or. (.not. ((a + 1.0d0) <= 2.0d0))) then
        tmp = t_1 / (a + t_2)
    else
        tmp = t_1 / (1.0d0 + t_2)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y * (z / t));
	double t_2 = y * (b / t);
	double tmp;
	if (((a + 1.0) <= -1e+16) || !((a + 1.0) <= 2.0)) {
		tmp = t_1 / (a + t_2);
	} else {
		tmp = t_1 / (1.0 + t_2);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (y * (z / t))
	t_2 = y * (b / t)
	tmp = 0
	if ((a + 1.0) <= -1e+16) or not ((a + 1.0) <= 2.0):
		tmp = t_1 / (a + t_2)
	else:
		tmp = t_1 / (1.0 + t_2)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(y * Float64(z / t)))
	t_2 = Float64(y * Float64(b / t))
	tmp = 0.0
	if ((Float64(a + 1.0) <= -1e+16) || !(Float64(a + 1.0) <= 2.0))
		tmp = Float64(t_1 / Float64(a + t_2));
	else
		tmp = Float64(t_1 / Float64(1.0 + t_2));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (y * (z / t));
	t_2 = y * (b / t);
	tmp = 0.0;
	if (((a + 1.0) <= -1e+16) || ~(((a + 1.0) <= 2.0)))
		tmp = t_1 / (a + t_2);
	else
		tmp = t_1 / (1.0 + t_2);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[N[(a + 1.0), $MachinePrecision], -1e+16], N[Not[LessEqual[N[(a + 1.0), $MachinePrecision], 2.0]], $MachinePrecision]], N[(t$95$1 / N[(a + t$95$2), $MachinePrecision]), $MachinePrecision], N[(t$95$1 / N[(1.0 + t$95$2), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 a #s(literal 1 binary64)) < -1e16 or 2 < (+.f64 a #s(literal 1 binary64))

   1. Initial program 79.3%

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

      1. associate-/l* 80.9%

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

      2. associate-/l* 80.8%

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

   3. Simplified 80.8%

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

   5. Taylor expanded in a around inf 80.4%

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

   if -1e16 < (+.f64 a #s(literal 1 binary64)) < 2

   1. Initial program 80.3%

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

      1. associate-/l* 78.1%

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

      2. associate-/l* 78.9%

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

   3. Simplified 78.9%

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

   5. Taylor expanded in a around 0 77.5%

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

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a + 1 \leq -1 \cdot 10^{+16} \lor \neg \left(a + 1 \leq 2\right):\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + y \cdot \frac{b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{1 + y \cdot \frac{b}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 80.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{-166} \lor \neg \left(t \leq 7.6 \cdot 10^{-93}\right):\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot z}{y \cdot b + t \cdot \left(a + 1\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -2e-166) (not (<= t 7.6e-93)))
   (/ (+ x (* y (/ z t))) (+ (+ a 1.0) (* y (/ b t))))
   (/ (* y z) (+ (* y b) (* t (+ a 1.0))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -2e-166) || !(t <= 7.6e-93)) {
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)));
	} else {
		tmp = (y * z) / ((y * b) + (t * (a + 1.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-2d-166)) .or. (.not. (t <= 7.6d-93))) then
        tmp = (x + (y * (z / t))) / ((a + 1.0d0) + (y * (b / t)))
    else
        tmp = (y * z) / ((y * b) + (t * (a + 1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -2e-166) || !(t <= 7.6e-93)) {
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)));
	} else {
		tmp = (y * z) / ((y * b) + (t * (a + 1.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -2e-166) or not (t <= 7.6e-93):
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)))
	else:
		tmp = (y * z) / ((y * b) + (t * (a + 1.0)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -2e-166) || !(t <= 7.6e-93))
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(Float64(a + 1.0) + Float64(y * Float64(b / t))));
	else
		tmp = Float64(Float64(y * z) / Float64(Float64(y * b) + Float64(t * Float64(a + 1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -2e-166) || ~((t <= 7.6e-93)))
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)));
	else
		tmp = (y * z) / ((y * b) + (t * (a + 1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -2e-166], N[Not[LessEqual[t, 7.6e-93]], $MachinePrecision]], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * z), $MachinePrecision] / N[(N[(y * b), $MachinePrecision] + N[(t * N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.00000000000000008e-166 or 7.5999999999999998e-93 < t

   1. Initial program 85.3%

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

      1. associate-/l* 90.2%

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

      2. associate-/l* 92.4%

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

   3. Simplified 92.4%

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

   if -2.00000000000000008e-166 < t < 7.5999999999999998e-93

   1. Initial program 66.6%

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

      1. associate-/l* 54.0%

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

      2. associate-/l* 50.2%

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

   3. Simplified 50.2%

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

   5. Taylor expanded in x around 0 60.6%

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

   6. Taylor expanded in t around 0 69.6%

      \[\leadsto \frac{y \cdot z}{\color{blue}{b \cdot y + t \cdot \left(1 + a\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 85.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{-166} \lor \neg \left(t \leq 7.6 \cdot 10^{-93}\right):\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot z}{y \cdot b + t \cdot \left(a + 1\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 81.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a + 1\right) + y \cdot \frac{b}{t}\\ \mathbf{if}\;t \leq -4.2 \cdot 10^{-165}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{t\_1}\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{-152}:\\ \;\;\;\;\frac{y \cdot z}{y \cdot b + t \cdot \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{t\_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ a 1.0) (* y (/ b t)))))
   (if (<= t -4.2e-165)
     (/ (+ x (* y (/ z t))) t_1)
     (if (<= t 3.3e-152)
       (/ (* y z) (+ (* y b) (* t (+ a 1.0))))
       (/ (+ x (/ y (/ t z))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a + 1.0) + (y * (b / t));
	double tmp;
	if (t <= -4.2e-165) {
		tmp = (x + (y * (z / t))) / t_1;
	} else if (t <= 3.3e-152) {
		tmp = (y * z) / ((y * b) + (t * (a + 1.0)));
	} else {
		tmp = (x + (y / (t / z))) / 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 * (b / t))
    if (t <= (-4.2d-165)) then
        tmp = (x + (y * (z / t))) / t_1
    else if (t <= 3.3d-152) then
        tmp = (y * z) / ((y * b) + (t * (a + 1.0d0)))
    else
        tmp = (x + (y / (t / z))) / 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 * (b / t));
	double tmp;
	if (t <= -4.2e-165) {
		tmp = (x + (y * (z / t))) / t_1;
	} else if (t <= 3.3e-152) {
		tmp = (y * z) / ((y * b) + (t * (a + 1.0)));
	} else {
		tmp = (x + (y / (t / z))) / t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a + 1.0) + (y * (b / t))
	tmp = 0
	if t <= -4.2e-165:
		tmp = (x + (y * (z / t))) / t_1
	elif t <= 3.3e-152:
		tmp = (y * z) / ((y * b) + (t * (a + 1.0)))
	else:
		tmp = (x + (y / (t / z))) / t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a + 1.0) + Float64(y * Float64(b / t)))
	tmp = 0.0
	if (t <= -4.2e-165)
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / t_1);
	elseif (t <= 3.3e-152)
		tmp = Float64(Float64(y * z) / Float64(Float64(y * b) + Float64(t * Float64(a + 1.0))));
	else
		tmp = Float64(Float64(x + Float64(y / Float64(t / z))) / t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a + 1.0) + (y * (b / t));
	tmp = 0.0;
	if (t <= -4.2e-165)
		tmp = (x + (y * (z / t))) / t_1;
	elseif (t <= 3.3e-152)
		tmp = (y * z) / ((y * b) + (t * (a + 1.0)));
	else
		tmp = (x + (y / (t / z))) / t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a + 1.0), $MachinePrecision] + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.2e-165], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[t, 3.3e-152], N[(N[(y * z), $MachinePrecision] / N[(N[(y * b), $MachinePrecision] + N[(t * N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.1999999999999999e-165

   1. Initial program 84.7%

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

      1. associate-/l* 88.8%

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

      2. associate-/l* 91.8%

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

   3. Simplified 91.8%

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

   if -4.1999999999999999e-165 < t < 3.29999999999999998e-152

   1. Initial program 65.9%

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

      1. associate-/l* 52.2%

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

      2. associate-/l* 49.1%

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

   3. Simplified 49.1%

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

   5. Taylor expanded in x around 0 61.6%

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

   6. Taylor expanded in t around 0 72.5%

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

   if 3.29999999999999998e-152 < t

   1. Initial program 83.9%

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

      1. associate-/l* 87.9%

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

      2. associate-/l* 88.0%

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

   3. Simplified 88.0%

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

      1. clear-num 87.9%

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

      2. un-div-inv 88.0%

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

   6. Applied egg-rr 88.0%

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

4. Final simplification 85.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{-165}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{-152}:\\ \;\;\;\;\frac{y \cdot z}{y \cdot b + t \cdot \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 74.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{b}{t}\\ t_2 := a + t\_1\\ t_3 := x + y \cdot \frac{z}{t}\\ \mathbf{if}\;a \leq -2.6 \cdot 10^{+14}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{t\_2}\\ \mathbf{elif}\;a \leq 1:\\ \;\;\;\;\frac{t\_3}{1 + t\_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_3}{t\_2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (/ b t))) (t_2 (+ a t_1)) (t_3 (+ x (* y (/ z t)))))
   (if (<= a -2.6e+14)
     (/ (+ x (/ y (/ t z))) t_2)
     (if (<= a 1.0) (/ t_3 (+ 1.0 t_1)) (/ t_3 t_2)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b / t);
	double t_2 = a + t_1;
	double t_3 = x + (y * (z / t));
	double tmp;
	if (a <= -2.6e+14) {
		tmp = (x + (y / (t / z))) / t_2;
	} else if (a <= 1.0) {
		tmp = t_3 / (1.0 + t_1);
	} else {
		tmp = t_3 / t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = y * (b / t)
    t_2 = a + t_1
    t_3 = x + (y * (z / t))
    if (a <= (-2.6d+14)) then
        tmp = (x + (y / (t / z))) / t_2
    else if (a <= 1.0d0) then
        tmp = t_3 / (1.0d0 + t_1)
    else
        tmp = t_3 / t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b / t);
	double t_2 = a + t_1;
	double t_3 = x + (y * (z / t));
	double tmp;
	if (a <= -2.6e+14) {
		tmp = (x + (y / (t / z))) / t_2;
	} else if (a <= 1.0) {
		tmp = t_3 / (1.0 + t_1);
	} else {
		tmp = t_3 / t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b / t)
	t_2 = a + t_1
	t_3 = x + (y * (z / t))
	tmp = 0
	if a <= -2.6e+14:
		tmp = (x + (y / (t / z))) / t_2
	elif a <= 1.0:
		tmp = t_3 / (1.0 + t_1)
	else:
		tmp = t_3 / t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(b / t))
	t_2 = Float64(a + t_1)
	t_3 = Float64(x + Float64(y * Float64(z / t)))
	tmp = 0.0
	if (a <= -2.6e+14)
		tmp = Float64(Float64(x + Float64(y / Float64(t / z))) / t_2);
	elseif (a <= 1.0)
		tmp = Float64(t_3 / Float64(1.0 + t_1));
	else
		tmp = Float64(t_3 / t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (b / t);
	t_2 = a + t_1;
	t_3 = x + (y * (z / t));
	tmp = 0.0;
	if (a <= -2.6e+14)
		tmp = (x + (y / (t / z))) / t_2;
	elseif (a <= 1.0)
		tmp = t_3 / (1.0 + t_1);
	else
		tmp = t_3 / t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a + t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.6e+14], N[(N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision], If[LessEqual[a, 1.0], N[(t$95$3 / N[(1.0 + t$95$1), $MachinePrecision]), $MachinePrecision], N[(t$95$3 / t$95$2), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.6e14

   1. Initial program 71.7%

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

      1. associate-/l* 73.4%

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

      2. associate-/l* 74.9%

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

   3. Simplified 74.9%

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

      1. clear-num 74.9%

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

      2. un-div-inv 74.9%

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

   6. Applied egg-rr 74.9%

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

   7. Taylor expanded in a around inf 74.9%

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

   if -2.6e14 < a < 1

   1. Initial program 80.3%

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

      1. associate-/l* 78.1%

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

      2. associate-/l* 78.9%

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

   3. Simplified 78.9%

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

   5. Taylor expanded in a around 0 77.5%

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

   if 1 < a

   1. Initial program 86.5%

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

      1. associate-/l* 88.0%

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

      2. associate-/l* 86.5%

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

   3. Simplified 86.5%

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

   5. Taylor expanded in a around inf 85.6%

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

Alternative 7: 55.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y}{\frac{t}{z}}}{a}\\ \mathbf{if}\;a \leq -1.1 \cdot 10^{+45}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{-99}:\\ \;\;\;\;\frac{x}{1 + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;a \leq 1.26:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ y (/ t z))) a)))
   (if (<= a -1.1e+45)
     t_1
     (if (<= a 1.35e-99)
       (/ x (+ 1.0 (/ (* y b) t)))
       (if (<= a 1.26) (+ x (/ (* y z) t)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + (y / (t / z))) / a;
	double tmp;
	if (a <= -1.1e+45) {
		tmp = t_1;
	} else if (a <= 1.35e-99) {
		tmp = x / (1.0 + ((y * b) / t));
	} else if (a <= 1.26) {
		tmp = x + ((y * z) / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + (y / (t / z))) / a
    if (a <= (-1.1d+45)) then
        tmp = t_1
    else if (a <= 1.35d-99) then
        tmp = x / (1.0d0 + ((y * b) / t))
    else if (a <= 1.26d0) then
        tmp = x + ((y * z) / t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + (y / (t / z))) / a;
	double tmp;
	if (a <= -1.1e+45) {
		tmp = t_1;
	} else if (a <= 1.35e-99) {
		tmp = x / (1.0 + ((y * b) / t));
	} else if (a <= 1.26) {
		tmp = x + ((y * z) / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + (y / (t / z))) / a
	tmp = 0
	if a <= -1.1e+45:
		tmp = t_1
	elif a <= 1.35e-99:
		tmp = x / (1.0 + ((y * b) / t))
	elif a <= 1.26:
		tmp = x + ((y * z) / t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(y / Float64(t / z))) / a)
	tmp = 0.0
	if (a <= -1.1e+45)
		tmp = t_1;
	elseif (a <= 1.35e-99)
		tmp = Float64(x / Float64(1.0 + Float64(Float64(y * b) / t)));
	elseif (a <= 1.26)
		tmp = Float64(x + Float64(Float64(y * z) / t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + (y / (t / z))) / a;
	tmp = 0.0;
	if (a <= -1.1e+45)
		tmp = t_1;
	elseif (a <= 1.35e-99)
		tmp = x / (1.0 + ((y * b) / t));
	elseif (a <= 1.26)
		tmp = x + ((y * z) / t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[a, -1.1e+45], t$95$1, If[LessEqual[a, 1.35e-99], N[(x / N[(1.0 + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.26], N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.1e45 or 1.26000000000000001 < a

   1. Initial program 80.4%

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

      1. associate-/l* 81.3%

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

      2. associate-/l* 82.9%

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

   3. Simplified 82.9%

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

      1. clear-num 82.8%

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

      2. un-div-inv 82.9%

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

   6. Applied egg-rr 82.9%

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

   7. Taylor expanded in a around inf 69.5%

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

   if -1.1e45 < a < 1.35e-99

   1. Initial program 77.4%

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

      1. associate-/l* 75.8%

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

      2. associate-/l* 75.1%

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

   3. Simplified 75.1%

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

   5. Taylor expanded in x around inf 57.5%

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

   6. Taylor expanded in a around 0 59.4%

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

   if 1.35e-99 < a < 1.26000000000000001

   1. Initial program 90.1%

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

      1. associate-/l* 89.9%

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

      2. associate-/l* 89.9%

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

   3. Simplified 89.9%

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

      1. clear-num 89.8%

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

      2. un-div-inv 90.0%

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

   6. Applied egg-rr 90.0%

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

   7. Taylor expanded in y around 0 70.8%

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

   8. Taylor expanded in a around 0 65.8%

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

4. Final simplification 64.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.1 \cdot 10^{+45}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a}\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{-99}:\\ \;\;\;\;\frac{x}{1 + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;a \leq 1.26:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 66.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{-97} \lor \neg \left(t \leq 3.2 \cdot 10^{-115}\right):\\ \;\;\;\;\frac{x}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -4.8e-97) (not (<= t 3.2e-115)))
   (/ x (+ (+ a 1.0) (* y (/ b t))))
   (/ (+ z (/ (* x t) y)) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -4.8e-97) || !(t <= 3.2e-115)) {
		tmp = x / ((a + 1.0) + (y * (b / t)));
	} else {
		tmp = (z + ((x * t) / y)) / 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 <= (-4.8d-97)) .or. (.not. (t <= 3.2d-115))) then
        tmp = x / ((a + 1.0d0) + (y * (b / t)))
    else
        tmp = (z + ((x * t) / y)) / 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 <= -4.8e-97) || !(t <= 3.2e-115)) {
		tmp = x / ((a + 1.0) + (y * (b / t)));
	} else {
		tmp = (z + ((x * t) / y)) / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -4.8e-97) or not (t <= 3.2e-115):
		tmp = x / ((a + 1.0) + (y * (b / t)))
	else:
		tmp = (z + ((x * t) / y)) / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -4.8e-97) || !(t <= 3.2e-115))
		tmp = Float64(x / Float64(Float64(a + 1.0) + Float64(y * Float64(b / t))));
	else
		tmp = Float64(Float64(z + Float64(Float64(x * t) / y)) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -4.8e-97) || ~((t <= 3.2e-115)))
		tmp = x / ((a + 1.0) + (y * (b / t)));
	else
		tmp = (z + ((x * t) / y)) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -4.8e-97], N[Not[LessEqual[t, 3.2e-115]], $MachinePrecision]], N[(x / N[(N[(a + 1.0), $MachinePrecision] + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.8e-97 or 3.2e-115 < t

   1. Initial program 86.0%

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

      1. associate-/l* 90.5%

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

      2. associate-/l* 93.3%

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

   3. Simplified 93.3%

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

   5. Taylor expanded in x around inf 72.7%

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

   if -4.8e-97 < t < 3.2e-115

   1. Initial program 66.0%

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

      1. associate-/l* 55.1%

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

      2. associate-/l* 50.4%

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

   3. Simplified 50.4%

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

   5. Taylor expanded in x around inf 63.5%

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

      1. associate-+r+ 63.5%

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

      2. associate-*r/ 63.4%

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

      3. *-commutative 63.4%

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

      4. associate-/r/ 60.1%

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

      5. *-commutative 60.1%

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

      6. associate-+r+ 60.1%

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

      7. associate-*r/ 51.7%

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

      8. *-commutative 51.7%

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

      9. associate-/r/ 57.7%

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

   7. Simplified 57.7%

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

   8. Taylor expanded in b around inf 62.4%

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

      1. +-commutative 62.4%

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

   10. Simplified 62.4%

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

   11. Taylor expanded in x around 0 66.1%

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

4. Final simplification 70.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{-97} \lor \neg \left(t \leq 3.2 \cdot 10^{-115}\right):\\ \;\;\;\;\frac{x}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 64.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.7 \cdot 10^{+19} \lor \neg \left(y \leq 3.8 \cdot 10^{+76}\right):\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -4.7e+19) (not (<= y 3.8e+76)))
   (/ (+ z (/ (* x t) y)) b)
   (/ x (+ 1.0 (+ a (/ (* y b) t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -4.7e+19) || !(y <= 3.8e+76)) {
		tmp = (z + ((x * t) / y)) / b;
	} else {
		tmp = x / (1.0 + (a + ((y * b) / t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-4.7d+19)) .or. (.not. (y <= 3.8d+76))) then
        tmp = (z + ((x * t) / y)) / b
    else
        tmp = x / (1.0d0 + (a + ((y * b) / t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -4.7e+19) || !(y <= 3.8e+76)) {
		tmp = (z + ((x * t) / y)) / b;
	} else {
		tmp = x / (1.0 + (a + ((y * b) / t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -4.7e+19) or not (y <= 3.8e+76):
		tmp = (z + ((x * t) / y)) / b
	else:
		tmp = x / (1.0 + (a + ((y * b) / t)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -4.7e+19) || !(y <= 3.8e+76))
		tmp = Float64(Float64(z + Float64(Float64(x * t) / y)) / b);
	else
		tmp = Float64(x / Float64(1.0 + Float64(a + Float64(Float64(y * b) / t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -4.7e+19) || ~((y <= 3.8e+76)))
		tmp = (z + ((x * t) / y)) / b;
	else
		tmp = x / (1.0 + (a + ((y * b) / t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -4.7e+19], N[Not[LessEqual[y, 3.8e+76]], $MachinePrecision]], N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], N[(x / N[(1.0 + N[(a + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.7e19 or 3.80000000000000024e76 < y

   1. Initial program 51.8%

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

      1. associate-/l* 60.0%

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

      2. associate-/l* 67.2%

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

   3. Simplified 67.2%

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

   5. Taylor expanded in x around inf 53.5%

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

      1. associate-+r+ 53.5%

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

      2. associate-*r/ 56.6%

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

      3. *-commutative 56.6%

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

      4. associate-/r/ 56.6%

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

      5. *-commutative 56.6%

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

      6. associate-+r+ 56.6%

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

      7. associate-*r/ 50.5%

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

      8. *-commutative 50.5%

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

      9. associate-/r/ 57.6%

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

   7. Simplified 57.6%

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

   8. Taylor expanded in b around inf 57.3%

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

      1. +-commutative 57.3%

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

   10. Simplified 57.3%

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

   11. Taylor expanded in x around 0 60.4%

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

   if -4.7e19 < y < 3.80000000000000024e76

   1. Initial program 96.3%

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

      1. associate-/l* 90.9%

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

      2. associate-/l* 87.3%

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

   3. Simplified 87.3%

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

   5. Taylor expanded in x around inf 75.5%

      \[\leadsto \color{blue}{\frac{x}{1 + \left(a + \frac{b \cdot y}{t}\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.7 \cdot 10^{+19} \lor \neg \left(y \leq 3.8 \cdot 10^{+76}\right):\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 68.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+19}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+16}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(\frac{z}{x} + \frac{t}{y}\right)}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -7e+19)
   (/ (+ z (/ (* x t) y)) b)
   (if (<= y 8.5e+16)
     (/ (+ x (/ (* y z) t)) (+ a 1.0))
     (/ (* x (+ (/ z x) (/ t y))) b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -7e+19) {
		tmp = (z + ((x * t) / y)) / b;
	} else if (y <= 8.5e+16) {
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	} else {
		tmp = (x * ((z / x) + (t / y))) / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-7d+19)) then
        tmp = (z + ((x * t) / y)) / b
    else if (y <= 8.5d+16) then
        tmp = (x + ((y * z) / t)) / (a + 1.0d0)
    else
        tmp = (x * ((z / x) + (t / y))) / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -7e+19) {
		tmp = (z + ((x * t) / y)) / b;
	} else if (y <= 8.5e+16) {
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	} else {
		tmp = (x * ((z / x) + (t / y))) / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -7e+19:
		tmp = (z + ((x * t) / y)) / b
	elif y <= 8.5e+16:
		tmp = (x + ((y * z) / t)) / (a + 1.0)
	else:
		tmp = (x * ((z / x) + (t / y))) / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -7e+19)
		tmp = Float64(Float64(z + Float64(Float64(x * t) / y)) / b);
	elseif (y <= 8.5e+16)
		tmp = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(a + 1.0));
	else
		tmp = Float64(Float64(x * Float64(Float64(z / x) + Float64(t / y))) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -7e+19)
		tmp = (z + ((x * t) / y)) / b;
	elseif (y <= 8.5e+16)
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	else
		tmp = (x * ((z / x) + (t / y))) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -7e+19], N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[y, 8.5e+16], N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(N[(z / x), $MachinePrecision] + N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -7e19

   1. Initial program 51.5%

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

      1. associate-/l* 57.3%

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

      2. associate-/l* 64.6%

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

   3. Simplified 64.6%

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

   5. Taylor expanded in x around inf 55.0%

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

      1. associate-+r+ 55.0%

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

      2. associate-*r/ 56.8%

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

      3. *-commutative 56.8%

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

      4. associate-/r/ 56.9%

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

      5. *-commutative 56.9%

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

      6. associate-+r+ 56.9%

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

      7. associate-*r/ 51.2%

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

      8. *-commutative 51.2%

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

      9. associate-/r/ 58.8%

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

   7. Simplified 58.8%

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

   8. Taylor expanded in b around inf 52.0%

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

      1. +-commutative 52.0%

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

   10. Simplified 52.0%

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

   11. Taylor expanded in x around 0 59.5%

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

   if -7e19 < y < 8.5e16

   1. Initial program 97.2%

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

      1. associate-/l* 90.6%

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

      2. associate-/l* 86.5%

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

   3. Simplified 86.5%

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

   5. Taylor expanded in b around 0 85.6%

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

   if 8.5e16 < y

   1. Initial program 62.5%

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

      1. associate-/l* 72.1%

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

      2. associate-/l* 77.0%

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

   3. Simplified 77.0%

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

   5. Taylor expanded in x around inf 62.1%

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

      1. associate-+r+ 62.1%

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

      2. associate-*r/ 65.3%

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

      3. *-commutative 65.3%

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

      4. associate-/r/ 65.3%

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

      5. *-commutative 65.3%

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

      6. associate-+r+ 65.3%

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

      7. associate-*r/ 60.6%

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

      8. *-commutative 60.6%

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

      9. associate-/r/ 65.3%

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

   7. Simplified 65.3%

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

   8. Taylor expanded in b around inf 62.7%

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

      1. +-commutative 62.7%

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

   10. Simplified 62.7%

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

4. Final simplification 74.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+19}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+16}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(\frac{z}{x} + \frac{t}{y}\right)}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 67.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+19}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+16}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(\frac{z}{x} + \frac{t}{y}\right)}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -7e+19)
   (/ (+ z (/ (* x t) y)) b)
   (if (<= y 4e+16)
     (/ (+ x (* z (/ y t))) (+ a 1.0))
     (/ (* x (+ (/ z x) (/ t y))) b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -7e+19) {
		tmp = (z + ((x * t) / y)) / b;
	} else if (y <= 4e+16) {
		tmp = (x + (z * (y / t))) / (a + 1.0);
	} else {
		tmp = (x * ((z / x) + (t / y))) / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-7d+19)) then
        tmp = (z + ((x * t) / y)) / b
    else if (y <= 4d+16) then
        tmp = (x + (z * (y / t))) / (a + 1.0d0)
    else
        tmp = (x * ((z / x) + (t / y))) / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -7e+19) {
		tmp = (z + ((x * t) / y)) / b;
	} else if (y <= 4e+16) {
		tmp = (x + (z * (y / t))) / (a + 1.0);
	} else {
		tmp = (x * ((z / x) + (t / y))) / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -7e+19:
		tmp = (z + ((x * t) / y)) / b
	elif y <= 4e+16:
		tmp = (x + (z * (y / t))) / (a + 1.0)
	else:
		tmp = (x * ((z / x) + (t / y))) / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -7e+19)
		tmp = Float64(Float64(z + Float64(Float64(x * t) / y)) / b);
	elseif (y <= 4e+16)
		tmp = Float64(Float64(x + Float64(z * Float64(y / t))) / Float64(a + 1.0));
	else
		tmp = Float64(Float64(x * Float64(Float64(z / x) + Float64(t / y))) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -7e+19)
		tmp = (z + ((x * t) / y)) / b;
	elseif (y <= 4e+16)
		tmp = (x + (z * (y / t))) / (a + 1.0);
	else
		tmp = (x * ((z / x) + (t / y))) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -7e+19], N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[y, 4e+16], N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(N[(z / x), $MachinePrecision] + N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -7e19

   1. Initial program 51.5%

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

      1. associate-/l* 57.3%

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

      2. associate-/l* 64.6%

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

   3. Simplified 64.6%

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

   5. Taylor expanded in x around inf 55.0%

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

      1. associate-+r+ 55.0%

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

      2. associate-*r/ 56.8%

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

      3. *-commutative 56.8%

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

      4. associate-/r/ 56.9%

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

      5. *-commutative 56.9%

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

      6. associate-+r+ 56.9%

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

      7. associate-*r/ 51.2%

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

      8. *-commutative 51.2%

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

      9. associate-/r/ 58.8%

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

   7. Simplified 58.8%

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

   8. Taylor expanded in b around inf 52.0%

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

      1. +-commutative 52.0%

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

   10. Simplified 52.0%

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

   11. Taylor expanded in x around 0 59.5%

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

   if -7e19 < y < 4e16

   1. Initial program 97.2%

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

      1. associate-/l* 90.6%

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

      2. associate-/l* 86.5%

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

   3. Simplified 86.5%

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

      1. clear-num 86.5%

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

      2. un-div-inv 86.6%

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

   6. Applied egg-rr 86.6%

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

   7. Taylor expanded in y around 0 81.0%

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

      1. associate-/r/ 83.6%

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

   9. Applied egg-rr 83.6%

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

   if 4e16 < y

   1. Initial program 62.5%

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

      1. associate-/l* 72.1%

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

      2. associate-/l* 77.0%

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

   3. Simplified 77.0%

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

   5. Taylor expanded in x around inf 62.1%

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

      1. associate-+r+ 62.1%

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

      2. associate-*r/ 65.3%

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

      3. *-commutative 65.3%

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

      4. associate-/r/ 65.3%

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

      5. *-commutative 65.3%

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

      6. associate-+r+ 65.3%

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

      7. associate-*r/ 60.6%

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

      8. *-commutative 60.6%

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

      9. associate-/r/ 65.3%

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

   7. Simplified 65.3%

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

   8. Taylor expanded in b around inf 62.7%

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

      1. +-commutative 62.7%

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

   10. Simplified 62.7%

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

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+19}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+16}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(\frac{z}{x} + \frac{t}{y}\right)}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 59.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+19} \lor \neg \left(y \leq 190000000\right):\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -2.5e+19) (not (<= y 190000000.0)))
   (/ (+ z (/ (* x t) y)) b)
   (/ x (+ a 1.0))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.5e+19) || !(y <= 190000000.0)) {
		tmp = (z + ((x * t) / y)) / b;
	} else {
		tmp = x / (a + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-2.5d+19)) .or. (.not. (y <= 190000000.0d0))) then
        tmp = (z + ((x * t) / y)) / b
    else
        tmp = x / (a + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.5e+19) || !(y <= 190000000.0)) {
		tmp = (z + ((x * t) / y)) / b;
	} else {
		tmp = x / (a + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -2.5e+19) or not (y <= 190000000.0):
		tmp = (z + ((x * t) / y)) / b
	else:
		tmp = x / (a + 1.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -2.5e+19) || !(y <= 190000000.0))
		tmp = Float64(Float64(z + Float64(Float64(x * t) / y)) / b);
	else
		tmp = Float64(x / Float64(a + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -2.5e+19) || ~((y <= 190000000.0)))
		tmp = (z + ((x * t) / y)) / b;
	else
		tmp = x / (a + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -2.5e+19], N[Not[LessEqual[y, 190000000.0]], $MachinePrecision]], N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.5e19 or 1.9e8 < y

   1. Initial program 57.3%

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

      1. associate-/l* 65.2%

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

      2. associate-/l* 71.2%

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

   3. Simplified 71.2%

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

   5. Taylor expanded in x around inf 58.8%

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

      1. associate-+r+ 58.8%

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

      2. associate-*r/ 61.4%

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

      3. *-commutative 61.4%

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

      4. associate-/r/ 61.4%

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

      5. *-commutative 61.4%

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

      6. associate-+r+ 61.4%

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

      7. associate-*r/ 56.2%

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

      8. *-commutative 56.2%

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

      9. associate-/r/ 62.3%

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

   7. Simplified 62.3%

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

   8. Taylor expanded in b around inf 57.8%

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

      1. +-commutative 57.8%

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

   10. Simplified 57.8%

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

   11. Taylor expanded in x around 0 59.5%

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

   if -2.5e19 < y < 1.9e8

   1. Initial program 97.2%

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

      1. associate-/l* 90.6%

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

      2. associate-/l* 86.5%

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

   3. Simplified 86.5%

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

   5. Taylor expanded in y around 0 68.5%

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

4. Final simplification 64.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+19} \lor \neg \left(y \leq 190000000\right):\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 42.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.28 \cdot 10^{+45}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;a \leq -1.4 \cdot 10^{-174}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -1.28e+45)
   (/ x a)
   (if (<= a -1.4e-174) (/ z b) (if (<= a 1.0) x (/ x a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -1.28e+45) {
		tmp = x / a;
	} else if (a <= -1.4e-174) {
		tmp = z / b;
	} else if (a <= 1.0) {
		tmp = x;
	} else {
		tmp = x / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-1.28d+45)) then
        tmp = x / a
    else if (a <= (-1.4d-174)) then
        tmp = z / b
    else if (a <= 1.0d0) then
        tmp = x
    else
        tmp = x / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -1.28e+45) {
		tmp = x / a;
	} else if (a <= -1.4e-174) {
		tmp = z / b;
	} else if (a <= 1.0) {
		tmp = x;
	} else {
		tmp = x / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -1.28e+45:
		tmp = x / a
	elif a <= -1.4e-174:
		tmp = z / b
	elif a <= 1.0:
		tmp = x
	else:
		tmp = x / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -1.28e+45)
		tmp = Float64(x / a);
	elseif (a <= -1.4e-174)
		tmp = Float64(z / b);
	elseif (a <= 1.0)
		tmp = x;
	else
		tmp = Float64(x / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -1.28e+45)
		tmp = x / a;
	elseif (a <= -1.4e-174)
		tmp = z / b;
	elseif (a <= 1.0)
		tmp = x;
	else
		tmp = x / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -1.28e+45], N[(x / a), $MachinePrecision], If[LessEqual[a, -1.4e-174], N[(z / b), $MachinePrecision], If[LessEqual[a, 1.0], x, N[(x / a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.28000000000000002e45 or 1 < a

   1. Initial program 80.4%

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

      1. associate-/l* 81.3%

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

      2. associate-/l* 82.9%

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

   3. Simplified 82.9%

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

   5. Taylor expanded in x around inf 63.1%

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

   6. Taylor expanded in a around inf 55.4%

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

   if -1.28000000000000002e45 < a < -1.39999999999999999e-174

   1. Initial program 69.7%

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

      1. associate-/l* 67.5%

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

      2. associate-/l* 62.9%

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

   3. Simplified 62.9%

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

   5. Taylor expanded in y around inf 45.4%

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

   if -1.39999999999999999e-174 < a < 1

   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. associate-/l* 82.5%

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

      2. associate-/l* 83.6%

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

   3. Simplified 83.6%

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

   5. Taylor expanded in x around inf 62.2%

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

   6. Taylor expanded in a around 0 61.4%

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

   7. Taylor expanded in b around 0 46.0%

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

Alternative 14: 56.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+20} \lor \neg \left(y \leq 4.3 \cdot 10^{+75}\right):\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.1e+20) (not (<= y 4.3e+75))) (/ z b) (/ x (+ a 1.0))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.1e+20) || !(y <= 4.3e+75)) {
		tmp = z / b;
	} else {
		tmp = x / (a + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-1.1d+20)) .or. (.not. (y <= 4.3d+75))) then
        tmp = z / b
    else
        tmp = x / (a + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.1e+20) || !(y <= 4.3e+75)) {
		tmp = z / b;
	} else {
		tmp = x / (a + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.1e+20) or not (y <= 4.3e+75):
		tmp = z / b
	else:
		tmp = x / (a + 1.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.1e+20) || !(y <= 4.3e+75))
		tmp = Float64(z / b);
	else
		tmp = Float64(x / Float64(a + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.1e+20) || ~((y <= 4.3e+75)))
		tmp = z / b;
	else
		tmp = x / (a + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.1e+20], N[Not[LessEqual[y, 4.3e+75]], $MachinePrecision]], N[(z / b), $MachinePrecision], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.1e20 or 4.3000000000000001e75 < y

   1. Initial program 51.8%

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

      1. associate-/l* 60.0%

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

      2. associate-/l* 67.2%

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

   3. Simplified 67.2%

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

   5. Taylor expanded in y around inf 56.7%

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

   if -1.1e20 < y < 4.3000000000000001e75

   1. Initial program 96.3%

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

      1. associate-/l* 90.9%

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

      2. associate-/l* 87.3%

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

   3. Simplified 87.3%

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

   5. Taylor expanded in y around 0 66.1%

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

4. Final simplification 62.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+20} \lor \neg \left(y \leq 4.3 \cdot 10^{+75}\right):\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 40.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.1 \cdot 10^{+48} \lor \neg \left(a \leq 1\right):\\ \;\;\;\;\frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -5.1e+48) (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 <= -5.1e+48) || !(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 <= (-5.1d+48)) .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 <= -5.1e+48) || !(a <= 1.0)) {
		tmp = x / a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -5.1e+48) 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 <= -5.1e+48) || !(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 <= -5.1e+48) || ~((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, -5.1e+48], N[Not[LessEqual[a, 1.0]], $MachinePrecision]], N[(x / a), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if a < -5.0999999999999998e48 or 1 < a

   1. Initial program 81.0%

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

      1. associate-/l* 81.1%

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

      2. associate-/l* 82.7%

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

   3. Simplified 82.7%

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

   5. Taylor expanded in x around inf 63.6%

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

   6. Taylor expanded in a around inf 55.8%

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

   if -5.0999999999999998e48 < a < 1

   1. Initial program 78.7%

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

      1. associate-/l* 78.1%

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

      2. associate-/l* 77.4%

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

   3. Simplified 77.4%

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

   5. Taylor expanded in x around inf 54.9%

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

   6. Taylor expanded in a around 0 56.0%

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

   7. Taylor expanded in b around 0 40.6%

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

4. Final simplification 47.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.1 \cdot 10^{+48} \lor \neg \left(a \leq 1\right):\\ \;\;\;\;\frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 19.8% accurate, 17.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 79.8%

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

   1. associate-/l* 79.5%

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

   2. associate-/l* 79.9%

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

3. Simplified 79.9%

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

5. Taylor expanded in x around inf 58.9%

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

6. Taylor expanded in a around 0 36.5%

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

7. Taylor expanded in b around 0 24.0%

   \[\leadsto \color{blue}{x} \]
8. Add Preprocessing

Developer Target 1: 79.3% 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 2024112 
(FPCore (x y z t a b)
  :name "Diagrams.Solve.Tridiagonal:solveCyclicTriDiagonal from diagrams-solve-0.1, B"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< t -1707385670788761/12500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (* 1 (* (+ x (* (/ y t) z)) (/ 1 (+ (+ a 1) (* (/ y t) b))))) (if (< t 1518483551868623/5000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (/ z b) (* 1 (* (+ x (* (/ y t) z)) (/ 1 (+ (+ a 1) (* (/ y t) b))))))))

  (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t))))