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

Percentage Accurate: 74.8% → 86.8%

Time: 14.3s

Alternatives: 12

Speedup: 0.7×

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: 74.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 86.8% accurate, 0.3× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 3 regimes

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

   1. Initial program 29.3%

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

      1. *-commutative 29.3%

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

      2. associate-*l/ 45.2%

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

      3. associate-+l+ 45.2%

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

      4. associate-*r/ 44.8%

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

      5. *-commutative 44.8%

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

   3. Simplified 44.8%

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

   4. Taylor expanded in x around 0 60.7%

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

      1. *-commutative 60.7%

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

      2. times-frac 68.1%

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

      3. associate-*r/ 42.4%

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

      4. +-commutative 42.4%

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

      5. associate-*r/ 68.1%

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

      6. associate-*l/ 68.1%

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

      7. *-commutative 68.1%

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

      8. fma-def 68.1%

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

   6. Simplified 68.1%

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

      1. fma-udef 68.1%

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

   8. Applied egg-rr 68.1%

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

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

   1. Initial program 93.5%

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

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

   1. Initial program 0.0%

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

      1. *-commutative 0.0%

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

      2. associate-*l/ 1.0%

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

      3. associate-+l+ 1.0%

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

      4. associate-*r/ 23.0%

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

      5. *-commutative 23.0%

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

   3. Simplified 23.0%

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

   4. Taylor expanded in b around inf 1.0%

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

   5. Taylor expanded in t around 0 21.3%

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

   6. Taylor expanded in t around 0 88.6%

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

      1. *-commutative 88.6%

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

      2. times-frac 100.0%

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

   8. Simplified 100.0%

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

4. Final simplification 93.2%

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

Alternative 2: 80.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + z \cdot \frac{y}{t}}{a + \left(1 + \frac{b}{\frac{t}{y}}\right)}\\ t_2 := \frac{z}{b} + \frac{t}{y} \cdot \frac{x}{b}\\ \mathbf{if}\;y \leq -1.05 \cdot 10^{+151}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+96}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+134}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+211}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (* z (/ y t))) (+ a (+ 1.0 (/ b (/ t y))))))
        (t_2 (+ (/ z b) (* (/ t y) (/ x b)))))
   (if (<= y -1.05e+151)
     t_2
     (if (<= y 2.3e+96)
       t_1
       (if (<= y 1.3e+134) t_2 (if (<= y 6.8e+211) t_1 (/ z b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + (z * (y / t))) / (a + (1.0 + (b / (t / y))));
	double t_2 = (z / b) + ((t / y) * (x / b));
	double tmp;
	if (y <= -1.05e+151) {
		tmp = t_2;
	} else if (y <= 2.3e+96) {
		tmp = t_1;
	} else if (y <= 1.3e+134) {
		tmp = t_2;
	} else if (y <= 6.8e+211) {
		tmp = t_1;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x + (z * (y / t))) / (a + (1.0d0 + (b / (t / y))))
    t_2 = (z / b) + ((t / y) * (x / b))
    if (y <= (-1.05d+151)) then
        tmp = t_2
    else if (y <= 2.3d+96) then
        tmp = t_1
    else if (y <= 1.3d+134) then
        tmp = t_2
    else if (y <= 6.8d+211) then
        tmp = t_1
    else
        tmp = z / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + (z * (y / t))) / (a + (1.0 + (b / (t / y))));
	double t_2 = (z / b) + ((t / y) * (x / b));
	double tmp;
	if (y <= -1.05e+151) {
		tmp = t_2;
	} else if (y <= 2.3e+96) {
		tmp = t_1;
	} else if (y <= 1.3e+134) {
		tmp = t_2;
	} else if (y <= 6.8e+211) {
		tmp = t_1;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + (z * (y / t))) / (a + (1.0 + (b / (t / y))))
	t_2 = (z / b) + ((t / y) * (x / b))
	tmp = 0
	if y <= -1.05e+151:
		tmp = t_2
	elif y <= 2.3e+96:
		tmp = t_1
	elif y <= 1.3e+134:
		tmp = t_2
	elif y <= 6.8e+211:
		tmp = t_1
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(z * Float64(y / t))) / Float64(a + Float64(1.0 + Float64(b / Float64(t / y)))))
	t_2 = Float64(Float64(z / b) + Float64(Float64(t / y) * Float64(x / b)))
	tmp = 0.0
	if (y <= -1.05e+151)
		tmp = t_2;
	elseif (y <= 2.3e+96)
		tmp = t_1;
	elseif (y <= 1.3e+134)
		tmp = t_2;
	elseif (y <= 6.8e+211)
		tmp = t_1;
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + (z * (y / t))) / (a + (1.0 + (b / (t / y))));
	t_2 = (z / b) + ((t / y) * (x / b));
	tmp = 0.0;
	if (y <= -1.05e+151)
		tmp = t_2;
	elseif (y <= 2.3e+96)
		tmp = t_1;
	elseif (y <= 1.3e+134)
		tmp = t_2;
	elseif (y <= 6.8e+211)
		tmp = t_1;
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + N[(1.0 + N[(b / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z / b), $MachinePrecision] + N[(N[(t / y), $MachinePrecision] * N[(x / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.05e+151], t$95$2, If[LessEqual[y, 2.3e+96], t$95$1, If[LessEqual[y, 1.3e+134], t$95$2, If[LessEqual[y, 6.8e+211], t$95$1, N[(z / b), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.05e151 or 2.30000000000000015e96 < y < 1.3000000000000001e134

   1. Initial program 42.4%

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

      1. *-commutative 42.4%

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

      2. associate-*l/ 45.2%

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

      3. associate-+l+ 45.2%

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

      4. associate-*r/ 53.2%

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

      5. *-commutative 53.2%

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

   3. Simplified 53.2%

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

   4. Taylor expanded in b around inf 32.5%

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

   5. Taylor expanded in t around 0 46.4%

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

   6. Taylor expanded in t around 0 75.8%

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

      1. *-commutative 75.8%

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

      2. times-frac 86.8%

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

   8. Simplified 86.8%

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

   if -1.05e151 < y < 2.30000000000000015e96 or 1.3000000000000001e134 < y < 6.7999999999999998e211

   1. Initial program 91.2%

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

      1. associate-/l* 86.5%

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

      2. associate-*l/ 87.8%

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

      3. *-commutative 87.8%

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

      4. cancel-sign-sub 87.8%

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

      5. *-commutative 87.8%

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

      6. associate-*l/ 86.5%

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

      7. associate-+r- 86.5%

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

      8. associate-*l/ 87.8%

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

      9. *-commutative 87.8%

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

      10. cancel-sign-sub 87.8%

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

      11. *-commutative 87.8%

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

      12. associate-*l/ 86.5%

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

      13. *-commutative 86.5%

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

      14. associate-/l* 87.9%

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

   3. Simplified 87.9%

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

      1. associate-/r/ 92.7%

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

   5. Applied egg-rr 92.7%

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

   if 6.7999999999999998e211 < y

   1. Initial program 32.5%

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

      1. *-commutative 32.5%

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

      2. associate-*l/ 39.5%

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

      3. associate-+l+ 39.5%

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

      4. associate-*r/ 52.6%

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

      5. *-commutative 52.6%

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

   3. Simplified 52.6%

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

   4. Taylor expanded in t around 0 73.3%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+151}:\\ \;\;\;\;\frac{z}{b} + \frac{t}{y} \cdot \frac{x}{b}\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+96}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + \left(1 + \frac{b}{\frac{t}{y}}\right)}\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+134}:\\ \;\;\;\;\frac{z}{b} + \frac{t}{y} \cdot \frac{x}{b}\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+211}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + \left(1 + \frac{b}{\frac{t}{y}}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 3: 81.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{b} + \frac{t}{y} \cdot \frac{x}{b}\\ \mathbf{if}\;y \leq -8.5 \cdot 10^{+150}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+96}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + \left(1 + \frac{b}{\frac{t}{y}}\right)}\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{+134}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{+214}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + \left(1 + y \cdot \frac{b}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (/ z b) (* (/ t y) (/ x b)))))
   (if (<= y -8.5e+150)
     t_1
     (if (<= y 2.5e+96)
       (/ (+ x (* z (/ y t))) (+ a (+ 1.0 (/ b (/ t y)))))
       (if (<= y 4.1e+134)
         t_1
         (if (<= y 6.4e+214)
           (/ (+ x (* y (/ z t))) (+ a (+ 1.0 (* y (/ b t)))))
           (/ z b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z / b) + ((t / y) * (x / b));
	double tmp;
	if (y <= -8.5e+150) {
		tmp = t_1;
	} else if (y <= 2.5e+96) {
		tmp = (x + (z * (y / t))) / (a + (1.0 + (b / (t / y))));
	} else if (y <= 4.1e+134) {
		tmp = t_1;
	} else if (y <= 6.4e+214) {
		tmp = (x + (y * (z / t))) / (a + (1.0 + (y * (b / t))));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z / b) + ((t / y) * (x / b))
    if (y <= (-8.5d+150)) then
        tmp = t_1
    else if (y <= 2.5d+96) then
        tmp = (x + (z * (y / t))) / (a + (1.0d0 + (b / (t / y))))
    else if (y <= 4.1d+134) then
        tmp = t_1
    else if (y <= 6.4d+214) then
        tmp = (x + (y * (z / t))) / (a + (1.0d0 + (y * (b / t))))
    else
        tmp = z / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z / b) + ((t / y) * (x / b));
	double tmp;
	if (y <= -8.5e+150) {
		tmp = t_1;
	} else if (y <= 2.5e+96) {
		tmp = (x + (z * (y / t))) / (a + (1.0 + (b / (t / y))));
	} else if (y <= 4.1e+134) {
		tmp = t_1;
	} else if (y <= 6.4e+214) {
		tmp = (x + (y * (z / t))) / (a + (1.0 + (y * (b / t))));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z / b) + ((t / y) * (x / b))
	tmp = 0
	if y <= -8.5e+150:
		tmp = t_1
	elif y <= 2.5e+96:
		tmp = (x + (z * (y / t))) / (a + (1.0 + (b / (t / y))))
	elif y <= 4.1e+134:
		tmp = t_1
	elif y <= 6.4e+214:
		tmp = (x + (y * (z / t))) / (a + (1.0 + (y * (b / t))))
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z / b) + Float64(Float64(t / y) * Float64(x / b)))
	tmp = 0.0
	if (y <= -8.5e+150)
		tmp = t_1;
	elseif (y <= 2.5e+96)
		tmp = Float64(Float64(x + Float64(z * Float64(y / t))) / Float64(a + Float64(1.0 + Float64(b / Float64(t / y)))));
	elseif (y <= 4.1e+134)
		tmp = t_1;
	elseif (y <= 6.4e+214)
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(a + Float64(1.0 + Float64(y * Float64(b / t)))));
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z / b) + ((t / y) * (x / b));
	tmp = 0.0;
	if (y <= -8.5e+150)
		tmp = t_1;
	elseif (y <= 2.5e+96)
		tmp = (x + (z * (y / t))) / (a + (1.0 + (b / (t / y))));
	elseif (y <= 4.1e+134)
		tmp = t_1;
	elseif (y <= 6.4e+214)
		tmp = (x + (y * (z / t))) / (a + (1.0 + (y * (b / t))));
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z / b), $MachinePrecision] + N[(N[(t / y), $MachinePrecision] * N[(x / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -8.5e+150], t$95$1, If[LessEqual[y, 2.5e+96], N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + N[(1.0 + N[(b / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.1e+134], t$95$1, If[LessEqual[y, 6.4e+214], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + N[(1.0 + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -8.4999999999999999e150 or 2.5000000000000002e96 < y < 4.1000000000000003e134

   1. Initial program 42.4%

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

      1. *-commutative 42.4%

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

      2. associate-*l/ 45.2%

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

      3. associate-+l+ 45.2%

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

      4. associate-*r/ 53.2%

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

      5. *-commutative 53.2%

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

   3. Simplified 53.2%

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

   4. Taylor expanded in b around inf 32.5%

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

   5. Taylor expanded in t around 0 46.4%

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

   6. Taylor expanded in t around 0 75.8%

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

      1. *-commutative 75.8%

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

      2. times-frac 86.8%

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

   8. Simplified 86.8%

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

   if -8.4999999999999999e150 < y < 2.5000000000000002e96

   1. Initial program 92.0%

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

      1. associate-/l* 87.1%

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

      2. associate-*l/ 87.4%

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

      3. *-commutative 87.4%

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

      4. cancel-sign-sub 87.4%

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

      5. *-commutative 87.4%

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

      6. associate-*l/ 87.1%

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

      7. associate-+r- 87.1%

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

      8. associate-*l/ 87.4%

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

      9. *-commutative 87.4%

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

      10. cancel-sign-sub 87.4%

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

      11. *-commutative 87.4%

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

      12. associate-*l/ 87.1%

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

      13. *-commutative 87.1%

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

      14. associate-/l* 87.5%

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

   3. Simplified 87.5%

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

      1. associate-/r/ 92.4%

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

   5. Applied egg-rr 92.4%

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

   if 4.1000000000000003e134 < y < 6.3999999999999999e214

   1. Initial program 71.0%

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

      1. *-commutative 71.0%

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

      2. associate-*l/ 71.9%

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

      3. associate-+l+ 71.9%

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

      4. associate-*r/ 99.6%

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

      5. *-commutative 99.6%

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

   3. Simplified 99.6%

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

   if 6.3999999999999999e214 < y

   1. Initial program 32.5%

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

      1. *-commutative 32.5%

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

      2. associate-*l/ 39.5%

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

      3. associate-+l+ 39.5%

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

      4. associate-*r/ 52.6%

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

      5. *-commutative 52.6%

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

   3. Simplified 52.6%

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

   4. Taylor expanded in t around 0 73.3%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{+150}:\\ \;\;\;\;\frac{z}{b} + \frac{t}{y} \cdot \frac{x}{b}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+96}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + \left(1 + \frac{b}{\frac{t}{y}}\right)}\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{+134}:\\ \;\;\;\;\frac{z}{b} + \frac{t}{y} \cdot \frac{x}{b}\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{+214}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + \left(1 + y \cdot \frac{b}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 4: 81.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.9 \cdot 10^{-165}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a + \left(1 + \frac{b}{\frac{t}{y}}\right)}\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{-208}:\\ \;\;\;\;\frac{z}{b} + \frac{t}{y} \cdot \frac{x}{b}\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-140}:\\ \;\;\;\;\frac{y \cdot z}{y \cdot b + t \cdot \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + \left(1 + y \cdot \frac{b}{t}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.9e-165)
   (/ (+ x (/ y (/ t z))) (+ a (+ 1.0 (/ b (/ t y)))))
   (if (<= t 3.4e-208)
     (+ (/ z b) (* (/ t y) (/ x b)))
     (if (<= t 6e-140)
       (/ (* y z) (+ (* y b) (* t (+ a 1.0))))
       (/ (+ x (* y (/ z t))) (+ a (+ 1.0 (* y (/ b t)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.9e-165) {
		tmp = (x + (y / (t / z))) / (a + (1.0 + (b / (t / y))));
	} else if (t <= 3.4e-208) {
		tmp = (z / b) + ((t / y) * (x / b));
	} else if (t <= 6e-140) {
		tmp = (y * z) / ((y * b) + (t * (a + 1.0)));
	} else {
		tmp = (x + (y * (z / t))) / (a + (1.0 + (y * (b / t))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-1.9d-165)) then
        tmp = (x + (y / (t / z))) / (a + (1.0d0 + (b / (t / y))))
    else if (t <= 3.4d-208) then
        tmp = (z / b) + ((t / y) * (x / b))
    else if (t <= 6d-140) then
        tmp = (y * z) / ((y * b) + (t * (a + 1.0d0)))
    else
        tmp = (x + (y * (z / t))) / (a + (1.0d0 + (y * (b / t))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.9e-165) {
		tmp = (x + (y / (t / z))) / (a + (1.0 + (b / (t / y))));
	} else if (t <= 3.4e-208) {
		tmp = (z / b) + ((t / y) * (x / b));
	} else if (t <= 6e-140) {
		tmp = (y * z) / ((y * b) + (t * (a + 1.0)));
	} else {
		tmp = (x + (y * (z / t))) / (a + (1.0 + (y * (b / t))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1.9e-165:
		tmp = (x + (y / (t / z))) / (a + (1.0 + (b / (t / y))))
	elif t <= 3.4e-208:
		tmp = (z / b) + ((t / y) * (x / b))
	elif t <= 6e-140:
		tmp = (y * z) / ((y * b) + (t * (a + 1.0)))
	else:
		tmp = (x + (y * (z / t))) / (a + (1.0 + (y * (b / t))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.9e-165)
		tmp = Float64(Float64(x + Float64(y / Float64(t / z))) / Float64(a + Float64(1.0 + Float64(b / Float64(t / y)))));
	elseif (t <= 3.4e-208)
		tmp = Float64(Float64(z / b) + Float64(Float64(t / y) * Float64(x / b)));
	elseif (t <= 6e-140)
		tmp = Float64(Float64(y * z) / Float64(Float64(y * b) + Float64(t * Float64(a + 1.0))));
	else
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(a + Float64(1.0 + Float64(y * Float64(b / t)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -1.9e-165)
		tmp = (x + (y / (t / z))) / (a + (1.0 + (b / (t / y))));
	elseif (t <= 3.4e-208)
		tmp = (z / b) + ((t / y) * (x / b));
	elseif (t <= 6e-140)
		tmp = (y * z) / ((y * b) + (t * (a + 1.0)));
	else
		tmp = (x + (y * (z / t))) / (a + (1.0 + (y * (b / t))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.9e-165], N[(N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + N[(1.0 + N[(b / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.4e-208], N[(N[(z / b), $MachinePrecision] + N[(N[(t / y), $MachinePrecision] * N[(x / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6e-140], 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[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + N[(1.0 + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.90000000000000009e-165

   1. Initial program 80.2%

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

      1. associate-/l* 79.5%

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

      2. associate-*l/ 86.7%

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

      3. *-commutative 86.7%

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

      4. cancel-sign-sub 86.7%

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

      5. *-commutative 86.7%

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

      6. associate-*l/ 79.5%

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

      7. associate-+r- 79.5%

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

      8. associate-*l/ 86.7%

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

      9. *-commutative 86.7%

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

      10. cancel-sign-sub 86.7%

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

      11. *-commutative 86.7%

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

      12. associate-*l/ 79.5%

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

      13. *-commutative 79.5%

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

      14. associate-/l* 87.7%

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

   3. Simplified 87.7%

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

   if -1.90000000000000009e-165 < t < 3.4e-208

   1. Initial program 50.7%

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

      1. *-commutative 50.7%

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

      2. associate-*l/ 46.1%

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

      3. associate-+l+ 46.1%

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

      4. associate-*r/ 32.7%

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

      5. *-commutative 32.7%

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

   3. Simplified 32.7%

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

   4. Taylor expanded in b around inf 39.2%

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

   5. Taylor expanded in t around 0 58.8%

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

   6. Taylor expanded in t around 0 80.7%

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

      1. *-commutative 80.7%

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

      2. times-frac 78.5%

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

   8. Simplified 78.5%

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

   if 3.4e-208 < t < 6.00000000000000037e-140

   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. *-commutative 77.4%

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

      2. associate-*l/ 56.1%

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

      3. associate-+l+ 56.1%

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

      4. associate-*r/ 55.9%

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

      5. *-commutative 55.9%

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

   3. Simplified 55.9%

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

   4. Taylor expanded in x around 0 82.6%

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

   5. Taylor expanded in t around 0 91.2%

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

   if 6.00000000000000037e-140 < t

   1. Initial program 86.9%

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

      1. *-commutative 86.9%

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

      2. associate-*l/ 88.0%

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

      3. associate-+l+ 88.0%

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

      4. associate-*r/ 92.3%

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

      5. *-commutative 92.3%

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

   3. Simplified 92.3%

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

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.9 \cdot 10^{-165}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a + \left(1 + \frac{b}{\frac{t}{y}}\right)}\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{-208}:\\ \;\;\;\;\frac{z}{b} + \frac{t}{y} \cdot \frac{x}{b}\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-140}:\\ \;\;\;\;\frac{y \cdot z}{y \cdot b + t \cdot \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + \left(1 + y \cdot \frac{b}{t}\right)}\\ \end{array} \]

Alternative 5: 58.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{-6} \lor \neg \left(y \leq 2.5 \cdot 10^{-52} \lor \neg \left(y \leq 2.3 \cdot 10^{+16}\right) \land y \leq 4.4 \cdot 10^{+85}\right):\\ \;\;\;\;\frac{z}{b} + \frac{t}{y} \cdot \frac{x}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.3e-6)
         (not (or (<= y 2.5e-52) (and (not (<= y 2.3e+16)) (<= y 4.4e+85)))))
   (+ (/ z b) (* (/ t y) (/ x b)))
   (/ x (+ a 1.0))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.3e-6) || !((y <= 2.5e-52) || (!(y <= 2.3e+16) && (y <= 4.4e+85)))) {
		tmp = (z / b) + ((t / y) * (x / 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 <= (-1.3d-6)) .or. (.not. (y <= 2.5d-52) .or. (.not. (y <= 2.3d+16)) .and. (y <= 4.4d+85))) then
        tmp = (z / b) + ((t / y) * (x / 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 <= -1.3e-6) || !((y <= 2.5e-52) || (!(y <= 2.3e+16) && (y <= 4.4e+85)))) {
		tmp = (z / b) + ((t / y) * (x / b));
	} else {
		tmp = x / (a + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.3e-6) or not ((y <= 2.5e-52) or (not (y <= 2.3e+16) and (y <= 4.4e+85))):
		tmp = (z / b) + ((t / y) * (x / b))
	else:
		tmp = x / (a + 1.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.3e-6) || !((y <= 2.5e-52) || (!(y <= 2.3e+16) && (y <= 4.4e+85))))
		tmp = Float64(Float64(z / b) + Float64(Float64(t / y) * Float64(x / 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 <= -1.3e-6) || ~(((y <= 2.5e-52) || (~((y <= 2.3e+16)) && (y <= 4.4e+85)))))
		tmp = (z / b) + ((t / y) * (x / b));
	else
		tmp = x / (a + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.3e-6], N[Not[Or[LessEqual[y, 2.5e-52], And[N[Not[LessEqual[y, 2.3e+16]], $MachinePrecision], LessEqual[y, 4.4e+85]]]], $MachinePrecision]], N[(N[(z / b), $MachinePrecision] + N[(N[(t / y), $MachinePrecision] * N[(x / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.30000000000000005e-6 or 2.5e-52 < y < 2.3e16 or 4.4000000000000003e85 < y

   1. Initial program 57.2%

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

      1. *-commutative 57.2%

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

      2. associate-*l/ 59.6%

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

      3. associate-+l+ 59.6%

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

      4. associate-*r/ 68.6%

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

      5. *-commutative 68.6%

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

   3. Simplified 68.6%

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

   4. Taylor expanded in b around inf 35.3%

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

   5. Taylor expanded in t around 0 42.4%

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

   6. Taylor expanded in t around 0 65.5%

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

      1. *-commutative 65.5%

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

      2. times-frac 66.9%

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

   8. Simplified 66.9%

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

   if -1.30000000000000005e-6 < y < 2.5e-52 or 2.3e16 < y < 4.4000000000000003e85

   1. Initial program 97.6%

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

      1. *-commutative 97.6%

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

      2. associate-*l/ 90.4%

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

      3. associate-+l+ 90.4%

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

      4. associate-*r/ 86.2%

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

      5. *-commutative 86.2%

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

   3. Simplified 86.2%

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

   4. Taylor expanded in t around inf 63.8%

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

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{-6} \lor \neg \left(y \leq 2.5 \cdot 10^{-52} \lor \neg \left(y \leq 2.3 \cdot 10^{+16}\right) \land y \leq 4.4 \cdot 10^{+85}\right):\\ \;\;\;\;\frac{z}{b} + \frac{t}{y} \cdot \frac{x}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \]

Alternative 6: 63.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.42 \cdot 10^{+32} \lor \neg \left(y \leq 9.6 \cdot 10^{-52} \lor \neg \left(y \leq 5.6 \cdot 10^{+14}\right) \land y \leq 5.5 \cdot 10^{+87}\right):\\ \;\;\;\;\frac{z}{b} + \frac{t}{y} \cdot \frac{x}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.42e+32)
         (not (or (<= y 9.6e-52) (and (not (<= y 5.6e+14)) (<= y 5.5e+87)))))
   (+ (/ z b) (* (/ t y) (/ x 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 <= -1.42e+32) || !((y <= 9.6e-52) || (!(y <= 5.6e+14) && (y <= 5.5e+87)))) {
		tmp = (z / b) + ((t / y) * (x / 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 <= (-1.42d+32)) .or. (.not. (y <= 9.6d-52) .or. (.not. (y <= 5.6d+14)) .and. (y <= 5.5d+87))) then
        tmp = (z / b) + ((t / y) * (x / 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 <= -1.42e+32) || !((y <= 9.6e-52) || (!(y <= 5.6e+14) && (y <= 5.5e+87)))) {
		tmp = (z / b) + ((t / y) * (x / 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 <= -1.42e+32) or not ((y <= 9.6e-52) or (not (y <= 5.6e+14) and (y <= 5.5e+87))):
		tmp = (z / b) + ((t / y) * (x / 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 <= -1.42e+32) || !((y <= 9.6e-52) || (!(y <= 5.6e+14) && (y <= 5.5e+87))))
		tmp = Float64(Float64(z / b) + Float64(Float64(t / y) * Float64(x / 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 <= -1.42e+32) || ~(((y <= 9.6e-52) || (~((y <= 5.6e+14)) && (y <= 5.5e+87)))))
		tmp = (z / b) + ((t / y) * (x / 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, -1.42e+32], N[Not[Or[LessEqual[y, 9.6e-52], And[N[Not[LessEqual[y, 5.6e+14]], $MachinePrecision], LessEqual[y, 5.5e+87]]]], $MachinePrecision]], N[(N[(z / b), $MachinePrecision] + N[(N[(t / y), $MachinePrecision] * N[(x / b), $MachinePrecision]), $MachinePrecision]), $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 < -1.41999999999999992e32 or 9.6000000000000007e-52 < y < 5.6e14 or 5.50000000000000022e87 < y

   1. Initial program 53.2%

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

      1. *-commutative 53.2%

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

      2. associate-*l/ 55.9%

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

      3. associate-+l+ 55.9%

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

      4. associate-*r/ 66.0%

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

      5. *-commutative 66.0%

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

   3. Simplified 66.0%

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

   4. Taylor expanded in b around inf 33.1%

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

   5. Taylor expanded in t around 0 41.0%

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

   6. Taylor expanded in t around 0 65.8%

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

      1. *-commutative 65.8%

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

      2. times-frac 68.3%

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

   8. Simplified 68.3%

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

   if -1.41999999999999992e32 < y < 9.6000000000000007e-52 or 5.6e14 < y < 5.50000000000000022e87

   1. Initial program 97.1%

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

      1. *-commutative 97.1%

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

      2. associate-*l/ 90.6%

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

      3. associate-+l+ 90.6%

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

      4. associate-*r/ 86.7%

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

      5. *-commutative 86.7%

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

   3. Simplified 86.7%

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

   4. Taylor expanded in x around inf 69.4%

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

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.42 \cdot 10^{+32} \lor \neg \left(y \leq 9.6 \cdot 10^{-52} \lor \neg \left(y \leq 5.6 \cdot 10^{+14}\right) \land y \leq 5.5 \cdot 10^{+87}\right):\\ \;\;\;\;\frac{z}{b} + \frac{t}{y} \cdot \frac{x}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \end{array} \]

Alternative 7: 63.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{b} + \frac{t}{y} \cdot \frac{x}{b}\\ \mathbf{if}\;y \leq -1.5 \cdot 10^{+64}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 10^{-51}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+16} \lor \neg \left(y \leq 3.7 \cdot 10^{+87}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (/ z b) (* (/ t y) (/ x b)))))
   (if (<= y -1.5e+64)
     t_1
     (if (<= y 1e-51)
       (/ x (+ (+ a 1.0) (* b (/ y t))))
       (if (or (<= y 1.55e+16) (not (<= y 3.7e+87)))
         t_1
         (/ x (+ 1.0 (+ a (/ (* y b) t)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z / b) + ((t / y) * (x / b));
	double tmp;
	if (y <= -1.5e+64) {
		tmp = t_1;
	} else if (y <= 1e-51) {
		tmp = x / ((a + 1.0) + (b * (y / t)));
	} else if ((y <= 1.55e+16) || !(y <= 3.7e+87)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = (z / b) + ((t / y) * (x / b))
    if (y <= (-1.5d+64)) then
        tmp = t_1
    else if (y <= 1d-51) then
        tmp = x / ((a + 1.0d0) + (b * (y / t)))
    else if ((y <= 1.55d+16) .or. (.not. (y <= 3.7d+87))) then
        tmp = t_1
    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 t_1 = (z / b) + ((t / y) * (x / b));
	double tmp;
	if (y <= -1.5e+64) {
		tmp = t_1;
	} else if (y <= 1e-51) {
		tmp = x / ((a + 1.0) + (b * (y / t)));
	} else if ((y <= 1.55e+16) || !(y <= 3.7e+87)) {
		tmp = t_1;
	} else {
		tmp = x / (1.0 + (a + ((y * b) / t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z / b) + ((t / y) * (x / b))
	tmp = 0
	if y <= -1.5e+64:
		tmp = t_1
	elif y <= 1e-51:
		tmp = x / ((a + 1.0) + (b * (y / t)))
	elif (y <= 1.55e+16) or not (y <= 3.7e+87):
		tmp = t_1
	else:
		tmp = x / (1.0 + (a + ((y * b) / t)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z / b) + Float64(Float64(t / y) * Float64(x / b)))
	tmp = 0.0
	if (y <= -1.5e+64)
		tmp = t_1;
	elseif (y <= 1e-51)
		tmp = Float64(x / Float64(Float64(a + 1.0) + Float64(b * Float64(y / t))));
	elseif ((y <= 1.55e+16) || !(y <= 3.7e+87))
		tmp = t_1;
	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)
	t_1 = (z / b) + ((t / y) * (x / b));
	tmp = 0.0;
	if (y <= -1.5e+64)
		tmp = t_1;
	elseif (y <= 1e-51)
		tmp = x / ((a + 1.0) + (b * (y / t)));
	elseif ((y <= 1.55e+16) || ~((y <= 3.7e+87)))
		tmp = t_1;
	else
		tmp = x / (1.0 + (a + ((y * b) / t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z / b), $MachinePrecision] + N[(N[(t / y), $MachinePrecision] * N[(x / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.5e+64], t$95$1, If[LessEqual[y, 1e-51], N[(x / N[(N[(a + 1.0), $MachinePrecision] + N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 1.55e+16], N[Not[LessEqual[y, 3.7e+87]], $MachinePrecision]], t$95$1, N[(x / N[(1.0 + N[(a + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.5000000000000001e64 or 1e-51 < y < 1.55e16 or 3.70000000000000003e87 < y

   1. Initial program 52.8%

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

      1. *-commutative 52.8%

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

      2. associate-*l/ 55.9%

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

      3. associate-+l+ 55.9%

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

      4. associate-*r/ 65.2%

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

      5. *-commutative 65.2%

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

   3. Simplified 65.2%

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

   4. Taylor expanded in b around inf 35.2%

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

   5. Taylor expanded in t around 0 42.1%

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

   6. Taylor expanded in t around 0 67.8%

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

      1. *-commutative 67.8%

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

      2. times-frac 70.5%

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

   8. Simplified 70.5%

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

   if -1.5000000000000001e64 < y < 1e-51

   1. Initial program 93.4%

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

      1. *-commutative 93.4%

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

      2. associate-*l/ 86.4%

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

      3. associate-+l+ 86.4%

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

      4. associate-*r/ 83.7%

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

      5. *-commutative 83.7%

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

   3. Simplified 83.7%

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

   4. Taylor expanded in x around inf 68.4%

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

      1. associate-+r+ 68.4%

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

      2. associate-*r/ 69.1%

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

   6. Simplified 69.1%

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

   if 1.55e16 < y < 3.70000000000000003e87

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

      2. associate-*l/ 99.8%

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

      3. associate-+l+ 99.8%

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

      4. associate-*r/ 99.8%

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

      5. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 59.3%

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

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+64}:\\ \;\;\;\;\frac{z}{b} + \frac{t}{y} \cdot \frac{x}{b}\\ \mathbf{elif}\;y \leq 10^{-51}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+16} \lor \neg \left(y \leq 3.7 \cdot 10^{+87}\right):\\ \;\;\;\;\frac{z}{b} + \frac{t}{y} \cdot \frac{x}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \end{array} \]

Alternative 8: 69.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1600000 \lor \neg \left(b \leq 3.1 \cdot 10^{+56}\right):\\ \;\;\;\;\frac{z}{b} + \frac{t}{y} \cdot \frac{x}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{a + 1} \cdot \left(x + z \cdot \frac{y}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -1600000.0) (not (<= b 3.1e+56)))
   (+ (/ z b) (* (/ t y) (/ x b)))
   (* (/ 1.0 (+ a 1.0)) (+ x (* z (/ y t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1600000.0) || !(b <= 3.1e+56)) {
		tmp = (z / b) + ((t / y) * (x / b));
	} else {
		tmp = (1.0 / (a + 1.0)) * (x + (z * (y / 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 ((b <= (-1600000.0d0)) .or. (.not. (b <= 3.1d+56))) then
        tmp = (z / b) + ((t / y) * (x / b))
    else
        tmp = (1.0d0 / (a + 1.0d0)) * (x + (z * (y / 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 ((b <= -1600000.0) || !(b <= 3.1e+56)) {
		tmp = (z / b) + ((t / y) * (x / b));
	} else {
		tmp = (1.0 / (a + 1.0)) * (x + (z * (y / t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -1600000.0) or not (b <= 3.1e+56):
		tmp = (z / b) + ((t / y) * (x / b))
	else:
		tmp = (1.0 / (a + 1.0)) * (x + (z * (y / t)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -1600000.0) || !(b <= 3.1e+56))
		tmp = Float64(Float64(z / b) + Float64(Float64(t / y) * Float64(x / b)));
	else
		tmp = Float64(Float64(1.0 / Float64(a + 1.0)) * Float64(x + Float64(z * Float64(y / t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -1600000.0) || ~((b <= 3.1e+56)))
		tmp = (z / b) + ((t / y) * (x / b));
	else
		tmp = (1.0 / (a + 1.0)) * (x + (z * (y / t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -1600000.0], N[Not[LessEqual[b, 3.1e+56]], $MachinePrecision]], N[(N[(z / b), $MachinePrecision] + N[(N[(t / y), $MachinePrecision] * N[(x / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 / N[(a + 1.0), $MachinePrecision]), $MachinePrecision] * N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.6e6 or 3.10000000000000005e56 < b

   1. Initial program 59.4%

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

      1. *-commutative 59.4%

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

      2. associate-*l/ 57.9%

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

      3. associate-+l+ 57.9%

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

      4. associate-*r/ 63.6%

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

      5. *-commutative 63.6%

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

   3. Simplified 63.6%

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

   4. Taylor expanded in b around inf 39.3%

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

   5. Taylor expanded in t around 0 43.5%

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

   6. Taylor expanded in t around 0 69.4%

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

      1. *-commutative 69.4%

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

      2. times-frac 75.1%

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

   8. Simplified 75.1%

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

   if -1.6e6 < b < 3.10000000000000005e56

   1. Initial program 89.8%

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

      1. *-commutative 89.8%

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

      2. associate-*l/ 86.8%

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

      3. associate-+l+ 86.8%

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

      4. associate-*r/ 86.8%

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

      5. *-commutative 86.8%

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

   3. Simplified 86.8%

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

   4. Taylor expanded in b around 0 78.9%

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

      1. clear-num 78.5%

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

      2. associate-/r/ 78.8%

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

      3. div-inv 78.8%

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

      4. *-commutative 78.8%

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

      5. associate-*l* 79.4%

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

      6. div-inv 79.4%

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

   6. Applied egg-rr 79.4%

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

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1600000 \lor \neg \left(b \leq 3.1 \cdot 10^{+56}\right):\\ \;\;\;\;\frac{z}{b} + \frac{t}{y} \cdot \frac{x}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{a + 1} \cdot \left(x + z \cdot \frac{y}{t}\right)\\ \end{array} \]

Alternative 9: 68.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2850000 \lor \neg \left(b \leq 3 \cdot 10^{+52}\right):\\ \;\;\;\;\frac{z}{b} + \frac{t}{y} \cdot \frac{x}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -2850000.0) (not (<= b 3e+52)))
   (+ (/ z b) (* (/ t y) (/ x b)))
   (/ (+ x (/ (* y z) t)) (+ a 1.0))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -2850000.0) || !(b <= 3e+52)) {
		tmp = (z / b) + ((t / y) * (x / b));
	} else {
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-2850000.0d0)) .or. (.not. (b <= 3d+52))) then
        tmp = (z / b) + ((t / y) * (x / b))
    else
        tmp = (x + ((y * z) / t)) / (a + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -2850000.0) || !(b <= 3e+52)) {
		tmp = (z / b) + ((t / y) * (x / b));
	} else {
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -2850000.0) or not (b <= 3e+52):
		tmp = (z / b) + ((t / y) * (x / b))
	else:
		tmp = (x + ((y * z) / t)) / (a + 1.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -2850000.0) || !(b <= 3e+52))
		tmp = Float64(Float64(z / b) + Float64(Float64(t / y) * Float64(x / b)));
	else
		tmp = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(a + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -2850000.0) || ~((b <= 3e+52)))
		tmp = (z / b) + ((t / y) * (x / b));
	else
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -2850000.0], N[Not[LessEqual[b, 3e+52]], $MachinePrecision]], N[(N[(z / b), $MachinePrecision] + N[(N[(t / y), $MachinePrecision] * N[(x / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -2.85e6 or 3e52 < b

   1. Initial program 59.4%

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

      1. *-commutative 59.4%

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

      2. associate-*l/ 57.9%

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

      3. associate-+l+ 57.9%

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

      4. associate-*r/ 63.6%

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

      5. *-commutative 63.6%

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

   3. Simplified 63.6%

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

   4. Taylor expanded in b around inf 39.3%

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

   5. Taylor expanded in t around 0 43.5%

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

   6. Taylor expanded in t around 0 69.4%

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

      1. *-commutative 69.4%

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

      2. times-frac 75.1%

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

   8. Simplified 75.1%

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

   if -2.85e6 < b < 3e52

   1. Initial program 89.8%

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

      1. *-commutative 89.8%

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

      2. associate-*l/ 86.8%

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

      3. associate-+l+ 86.8%

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

      4. associate-*r/ 86.8%

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

      5. *-commutative 86.8%

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

   3. Simplified 86.8%

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

   4. Taylor expanded in b around 0 78.9%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2850000 \lor \neg \left(b \leq 3 \cdot 10^{+52}\right):\\ \;\;\;\;\frac{z}{b} + \frac{t}{y} \cdot \frac{x}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \end{array} \]

Alternative 10: 54.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{-6} \lor \neg \left(y \leq 10^{-51}\right) \land \left(y \leq 2.7 \cdot 10^{+15} \lor \neg \left(y \leq 3.4 \cdot 10^{+84}\right)\right):\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -2.2e-6)
         (and (not (<= y 1e-51)) (or (<= y 2.7e+15) (not (<= y 3.4e+84)))))
   (/ 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 <= -2.2e-6) || (!(y <= 1e-51) && ((y <= 2.7e+15) || !(y <= 3.4e+84)))) {
		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 <= (-2.2d-6)) .or. (.not. (y <= 1d-51)) .and. (y <= 2.7d+15) .or. (.not. (y <= 3.4d+84))) 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 <= -2.2e-6) || (!(y <= 1e-51) && ((y <= 2.7e+15) || !(y <= 3.4e+84)))) {
		tmp = z / b;
	} else {
		tmp = x / (a + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -2.2e-6) or (not (y <= 1e-51) and ((y <= 2.7e+15) or not (y <= 3.4e+84))):
		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 <= -2.2e-6) || (!(y <= 1e-51) && ((y <= 2.7e+15) || !(y <= 3.4e+84))))
		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 <= -2.2e-6) || (~((y <= 1e-51)) && ((y <= 2.7e+15) || ~((y <= 3.4e+84)))))
		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, -2.2e-6], And[N[Not[LessEqual[y, 1e-51]], $MachinePrecision], Or[LessEqual[y, 2.7e+15], N[Not[LessEqual[y, 3.4e+84]], $MachinePrecision]]]], N[(z / b), $MachinePrecision], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.2000000000000001e-6 or 1e-51 < y < 2.7e15 or 3.3999999999999998e84 < y

   1. Initial program 57.2%

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

      1. *-commutative 57.2%

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

      2. associate-*l/ 59.6%

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

      3. associate-+l+ 59.6%

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

      4. associate-*r/ 68.6%

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

      5. *-commutative 68.6%

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

   3. Simplified 68.6%

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

   4. Taylor expanded in t around 0 61.3%

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

   if -2.2000000000000001e-6 < y < 1e-51 or 2.7e15 < y < 3.3999999999999998e84

   1. Initial program 97.6%

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

      1. *-commutative 97.6%

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

      2. associate-*l/ 90.4%

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

      3. associate-+l+ 90.4%

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

      4. associate-*r/ 86.2%

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

      5. *-commutative 86.2%

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

   3. Simplified 86.2%

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

   4. Taylor expanded in t around inf 63.8%

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

4. Final simplification 62.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{-6} \lor \neg \left(y \leq 10^{-51}\right) \land \left(y \leq 2.7 \cdot 10^{+15} \lor \neg \left(y \leq 3.4 \cdot 10^{+84}\right)\right):\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \]

Alternative 11: 40.8% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2 \cdot 10^{+185} \lor \neg \left(a \leq 6.3 \cdot 10^{+28}\right):\\ \;\;\;\;\frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -2e+185) (not (<= a 6.3e+28))) (/ x a) (/ z b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -2e+185) || !(a <= 6.3e+28)) {
		tmp = x / a;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((a <= (-2d+185)) .or. (.not. (a <= 6.3d+28))) then
        tmp = x / a
    else
        tmp = z / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -2e+185) || !(a <= 6.3e+28)) {
		tmp = x / a;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -2e+185) or not (a <= 6.3e+28):
		tmp = x / a
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -2e+185) || !(a <= 6.3e+28))
		tmp = Float64(x / a);
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -2e+185) || ~((a <= 6.3e+28)))
		tmp = x / a;
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -2e+185], N[Not[LessEqual[a, 6.3e+28]], $MachinePrecision]], N[(x / a), $MachinePrecision], N[(z / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2e185 or 6.3000000000000001e28 < a

   1. Initial program 87.7%

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

      1. *-commutative 87.7%

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

      2. associate-*l/ 85.3%

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

      3. associate-+l+ 85.3%

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

      4. associate-*r/ 84.0%

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

      5. *-commutative 84.0%

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

   3. Simplified 84.0%

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

   4. Taylor expanded in x around inf 65.1%

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

   5. Taylor expanded in a around inf 61.7%

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

   if -2e185 < a < 6.3000000000000001e28

   1. Initial program 73.2%

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

      1. *-commutative 73.2%

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

      2. associate-*l/ 70.8%

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

      3. associate-+l+ 70.8%

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

      4. associate-*r/ 74.7%

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

      5. *-commutative 74.7%

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

   3. Simplified 74.7%

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

   4. Taylor expanded in t around 0 43.5%

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

4. Final simplification 49.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2 \cdot 10^{+185} \lor \neg \left(a \leq 6.3 \cdot 10^{+28}\right):\\ \;\;\;\;\frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 12: 24.8% accurate, 5.7× speedup

Math

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

FPCore

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

C

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

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 / a
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(x / a), $MachinePrecision]

Derivation

1. Initial program 77.7%

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

   1. *-commutative 77.7%

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

   2. associate-*l/ 75.3%

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

   3. associate-+l+ 75.3%

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

   4. associate-*r/ 77.6%

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

   5. *-commutative 77.6%

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

3. Simplified 77.6%

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

4. Taylor expanded in x around inf 51.2%

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

5. Taylor expanded in a around inf 25.7%

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

6. Final simplification 25.7%

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

Developer target: 79.5% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023305 
(FPCore (x y z t a b)
  :name "Diagrams.Solve.Tridiagonal:solveCyclicTriDiagonal from diagrams-solve-0.1, B"
  :precision binary64

  :herbie-target
  (if (< t -1.3659085366310088e-271) (* 1.0 (* (+ x (* (/ y t) z)) (/ 1.0 (+ (+ a 1.0) (* (/ y t) b))))) (if (< t 3.036967103737246e-130) (/ z b) (* 1.0 (* (+ x (* (/ y t) z)) (/ 1.0 (+ (+ a 1.0) (* (/ y t) b)))))))

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