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

Percentage Accurate: 75.9% → 90.2%

Time: 12.0s

Alternatives: 15

Speedup: 0.8×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 75.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 90.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{1 + \left(a + \frac{y}{\frac{t}{b}}\right)}\\ \mathbf{elif}\;t_1 \leq -2 \cdot 10^{-299}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;\frac{z}{b} + \frac{\frac{t}{\frac{b}{x}} - \frac{t}{b} \cdot \frac{z + z \cdot a}{b}}{y}\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+289}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot \frac{t}{b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t)))))
   (if (<= t_1 (- INFINITY))
     (* (/ y t) (/ z (+ 1.0 (+ a (/ y (/ t b))))))
     (if (<= t_1 -2e-299)
       t_1
       (if (<= t_1 0.0)
         (+ (/ z b) (/ (- (/ t (/ b x)) (* (/ t b) (/ (+ z (* z a)) b))) y))
         (if (<= t_1 2e+289) t_1 (+ (/ z b) (/ (* x (/ t b)) y))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = (y / t) * (z / (1.0 + (a + (y / (t / b)))));
	} else if (t_1 <= -2e-299) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = (z / b) + (((t / (b / x)) - ((t / b) * ((z + (z * a)) / b))) / y);
	} else if (t_1 <= 2e+289) {
		tmp = t_1;
	} else {
		tmp = (z / b) + ((x * (t / b)) / y);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = (y / t) * (z / (1.0 + (a + (y / (t / b)))));
	} else if (t_1 <= -2e-299) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = (z / b) + (((t / (b / x)) - ((t / b) * ((z + (z * a)) / b))) / y);
	} else if (t_1 <= 2e+289) {
		tmp = t_1;
	} else {
		tmp = (z / b) + ((x * (t / b)) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = (y / t) * (z / (1.0 + (a + (y / (t / b)))))
	elif t_1 <= -2e-299:
		tmp = t_1
	elif t_1 <= 0.0:
		tmp = (z / b) + (((t / (b / x)) - ((t / b) * ((z + (z * a)) / b))) / y)
	elif t_1 <= 2e+289:
		tmp = t_1
	else:
		tmp = (z / b) + ((x * (t / b)) / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(Float64(a + 1.0) + Float64(Float64(y * b) / t)))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(y / t) * Float64(z / Float64(1.0 + Float64(a + Float64(y / Float64(t / b))))));
	elseif (t_1 <= -2e-299)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(z / b) + Float64(Float64(Float64(t / Float64(b / x)) - Float64(Float64(t / b) * Float64(Float64(z + Float64(z * a)) / b))) / y));
	elseif (t_1 <= 2e+289)
		tmp = t_1;
	else
		tmp = Float64(Float64(z / b) + Float64(Float64(x * Float64(t / b)) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = (y / t) * (z / (1.0 + (a + (y / (t / b)))));
	elseif (t_1 <= -2e-299)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = (z / b) + (((t / (b / x)) - ((t / b) * ((z + (z * a)) / b))) / y);
	elseif (t_1 <= 2e+289)
		tmp = t_1;
	else
		tmp = (z / b) + ((x * (t / b)) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(y / t), $MachinePrecision] * N[(z / N[(1.0 + N[(a + N[(y / N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -2e-299], t$95$1, If[LessEqual[t$95$1, 0.0], N[(N[(z / b), $MachinePrecision] + N[(N[(N[(t / N[(b / x), $MachinePrecision]), $MachinePrecision] - N[(N[(t / b), $MachinePrecision] * N[(N[(z + N[(z * a), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+289], t$95$1, N[(N[(z / b), $MachinePrecision] + N[(N[(x * N[(t / b), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

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

   1. Initial program 22.9%

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

      1. *-un-lft-identity 22.9%

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

      2. associate-/l* 52.6%

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

   3. Applied egg-rr 52.6%

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

   4. Taylor expanded in x around 0 52.2%

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

      1. times-frac 87.3%

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

      2. associate-/l* 87.4%

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

   6. Simplified 87.4%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < -1.99999999999999998e-299 or -0.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 2.0000000000000001e289

   1. Initial program 99.8%

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

   if -1.99999999999999998e-299 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < -0.0

   1. Initial program 43.5%

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

      1. *-commutative 43.5%

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

      2. associate-/l* 27.5%

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

      3. associate-*l/ 49.9%

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

   3. Simplified 49.9%

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

   4. Taylor expanded in y around -inf 63.5%

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

      1. +-commutative 63.5%

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

      2. associate-*r/ 63.5%

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

      3. distribute-lft-out-- 63.5%

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

      4. associate-*r* 63.5%

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

      5. metadata-eval 63.5%

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

      6. *-lft-identity 63.5%

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

   6. Simplified 78.9%

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

   if 2.0000000000000001e289 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))

   1. Initial program 6.8%

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

      1. *-commutative 6.8%

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

      2. associate-/l* 15.9%

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

      3. associate-*l/ 24.4%

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

   3. Simplified 24.4%

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

   4. Taylor expanded in y around -inf 63.8%

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

      1. +-commutative 63.8%

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

      2. associate-*r/ 63.8%

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

      3. distribute-lft-out-- 63.8%

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

      4. associate-*r* 63.8%

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

      5. metadata-eval 63.8%

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

      6. *-lft-identity 63.8%

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

   6. Simplified 67.0%

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

   7. Taylor expanded in b around inf 82.2%

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

      1. associate-*l/ 88.0%

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

      2. *-commutative 88.0%

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

   9. Simplified 88.0%

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

4. Final simplification 93.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -\infty:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{1 + \left(a + \frac{y}{\frac{t}{b}}\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -2 \cdot 10^{-299}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 0:\\ \;\;\;\;\frac{z}{b} + \frac{\frac{t}{\frac{b}{x}} - \frac{t}{b} \cdot \frac{z + z \cdot a}{b}}{y}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 2 \cdot 10^{+289}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot \frac{t}{b}}{y}\\ \end{array} \]

Alternative 2: 90.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{1 + \left(a + \frac{y}{\frac{t}{b}}\right)}\\ \mathbf{elif}\;t_1 \leq -2 \cdot 10^{-299} \lor \neg \left(t_1 \leq 0\right) \land t_1 \leq 2 \cdot 10^{+289}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot \frac{t}{b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t)))))
   (if (<= t_1 (- INFINITY))
     (* (/ y t) (/ z (+ 1.0 (+ a (/ y (/ t b))))))
     (if (or (<= t_1 -2e-299) (and (not (<= t_1 0.0)) (<= t_1 2e+289)))
       t_1
       (+ (/ z b) (/ (* x (/ t b)) y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = (y / t) * (z / (1.0 + (a + (y / (t / b)))));
	} else if ((t_1 <= -2e-299) || (!(t_1 <= 0.0) && (t_1 <= 2e+289))) {
		tmp = t_1;
	} else {
		tmp = (z / b) + ((x * (t / b)) / y);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = (y / t) * (z / (1.0 + (a + (y / (t / b)))));
	} else if ((t_1 <= -2e-299) || (!(t_1 <= 0.0) && (t_1 <= 2e+289))) {
		tmp = t_1;
	} else {
		tmp = (z / b) + ((x * (t / b)) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = (y / t) * (z / (1.0 + (a + (y / (t / b)))))
	elif (t_1 <= -2e-299) or (not (t_1 <= 0.0) and (t_1 <= 2e+289)):
		tmp = t_1
	else:
		tmp = (z / b) + ((x * (t / b)) / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(Float64(a + 1.0) + Float64(Float64(y * b) / t)))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(y / t) * Float64(z / Float64(1.0 + Float64(a + Float64(y / Float64(t / b))))));
	elseif ((t_1 <= -2e-299) || (!(t_1 <= 0.0) && (t_1 <= 2e+289)))
		tmp = t_1;
	else
		tmp = Float64(Float64(z / b) + Float64(Float64(x * Float64(t / b)) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = (y / t) * (z / (1.0 + (a + (y / (t / b)))));
	elseif ((t_1 <= -2e-299) || (~((t_1 <= 0.0)) && (t_1 <= 2e+289)))
		tmp = t_1;
	else
		tmp = (z / b) + ((x * (t / b)) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(y / t), $MachinePrecision] * N[(z / N[(1.0 + N[(a + N[(y / N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t$95$1, -2e-299], And[N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision], LessEqual[t$95$1, 2e+289]]], t$95$1, N[(N[(z / b), $MachinePrecision] + N[(N[(x * N[(t / b), $MachinePrecision]), $MachinePrecision] / y), $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 22.9%

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

      1. *-un-lft-identity 22.9%

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

      2. associate-/l* 52.6%

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

   3. Applied egg-rr 52.6%

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

   4. Taylor expanded in x around 0 52.2%

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

      1. times-frac 87.3%

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

      2. associate-/l* 87.4%

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

   6. Simplified 87.4%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < -1.99999999999999998e-299 or -0.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 2.0000000000000001e289

   1. Initial program 99.8%

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

   if -1.99999999999999998e-299 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < -0.0 or 2.0000000000000001e289 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))

   1. Initial program 29.1%

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

      1. *-commutative 29.1%

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

      2. associate-/l* 22.9%

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

      3. associate-*l/ 39.9%

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

   3. Simplified 39.9%

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

   4. Taylor expanded in y around -inf 63.6%

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

      1. +-commutative 63.6%

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

      2. associate-*r/ 63.6%

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

      3. distribute-lft-out-- 63.6%

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

      4. associate-*r* 63.6%

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

      5. metadata-eval 63.6%

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

      6. *-lft-identity 63.6%

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

   6. Simplified 74.2%

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

   7. Taylor expanded in b around inf 73.5%

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

      1. associate-*l/ 80.3%

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

      2. *-commutative 80.3%

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

   9. Simplified 80.3%

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

4. Final simplification 92.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -\infty:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{1 + \left(a + \frac{y}{\frac{t}{b}}\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -2 \cdot 10^{-299} \lor \neg \left(\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 0\right) \land \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 2 \cdot 10^{+289}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot \frac{t}{b}}{y}\\ \end{array} \]

Alternative 3: 81.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{b} + \frac{x \cdot \frac{t}{b}}{y}\\ \mathbf{if}\;y \leq -9.5 \cdot 10^{+129}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+69}:\\ \;\;\;\;\frac{x + \frac{z}{\frac{t}{y}}}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+140} \lor \neg \left(y \leq 1.7 \cdot 10^{+219}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y}{\frac{t}{b}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (/ z b) (/ (* x (/ t b)) y))))
   (if (<= y -9.5e+129)
     t_1
     (if (<= y 2.6e+69)
       (/ (+ x (/ z (/ t y))) (+ (+ a 1.0) (* b (/ y t))))
       (if (or (<= y 3.1e+140) (not (<= y 1.7e+219)))
         t_1
         (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ y (/ t b)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z / b) + ((x * (t / b)) / y);
	double tmp;
	if (y <= -9.5e+129) {
		tmp = t_1;
	} else if (y <= 2.6e+69) {
		tmp = (x + (z / (t / y))) / ((a + 1.0) + (b * (y / t)));
	} else if ((y <= 3.1e+140) || !(y <= 1.7e+219)) {
		tmp = t_1;
	} else {
		tmp = (x + ((y * z) / t)) / ((a + 1.0) + (y / (t / b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z / b) + ((x * (t / b)) / y)
    if (y <= (-9.5d+129)) then
        tmp = t_1
    else if (y <= 2.6d+69) then
        tmp = (x + (z / (t / y))) / ((a + 1.0d0) + (b * (y / t)))
    else if ((y <= 3.1d+140) .or. (.not. (y <= 1.7d+219))) then
        tmp = t_1
    else
        tmp = (x + ((y * z) / t)) / ((a + 1.0d0) + (y / (t / b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z / b) + ((x * (t / b)) / y);
	double tmp;
	if (y <= -9.5e+129) {
		tmp = t_1;
	} else if (y <= 2.6e+69) {
		tmp = (x + (z / (t / y))) / ((a + 1.0) + (b * (y / t)));
	} else if ((y <= 3.1e+140) || !(y <= 1.7e+219)) {
		tmp = t_1;
	} else {
		tmp = (x + ((y * z) / t)) / ((a + 1.0) + (y / (t / b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z / b) + ((x * (t / b)) / y)
	tmp = 0
	if y <= -9.5e+129:
		tmp = t_1
	elif y <= 2.6e+69:
		tmp = (x + (z / (t / y))) / ((a + 1.0) + (b * (y / t)))
	elif (y <= 3.1e+140) or not (y <= 1.7e+219):
		tmp = t_1
	else:
		tmp = (x + ((y * z) / t)) / ((a + 1.0) + (y / (t / b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z / b) + Float64(Float64(x * Float64(t / b)) / y))
	tmp = 0.0
	if (y <= -9.5e+129)
		tmp = t_1;
	elseif (y <= 2.6e+69)
		tmp = Float64(Float64(x + Float64(z / Float64(t / y))) / Float64(Float64(a + 1.0) + Float64(b * Float64(y / t))));
	elseif ((y <= 3.1e+140) || !(y <= 1.7e+219))
		tmp = t_1;
	else
		tmp = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(Float64(a + 1.0) + Float64(y / Float64(t / b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z / b) + ((x * (t / b)) / y);
	tmp = 0.0;
	if (y <= -9.5e+129)
		tmp = t_1;
	elseif (y <= 2.6e+69)
		tmp = (x + (z / (t / y))) / ((a + 1.0) + (b * (y / t)));
	elseif ((y <= 3.1e+140) || ~((y <= 1.7e+219)))
		tmp = t_1;
	else
		tmp = (x + ((y * z) / t)) / ((a + 1.0) + (y / (t / 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[(x * N[(t / b), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9.5e+129], t$95$1, If[LessEqual[y, 2.6e+69], N[(N[(x + N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 3.1e+140], N[Not[LessEqual[y, 1.7e+219]], $MachinePrecision]], t$95$1, N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(y / N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.5000000000000004e129 or 2.6000000000000002e69 < y < 3.1e140 or 1.70000000000000008e219 < y

   1. Initial program 32.8%

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

      1. *-commutative 32.8%

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

      2. associate-/l* 29.7%

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

      3. associate-*l/ 44.3%

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

   3. Simplified 44.3%

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

   4. Taylor expanded in y around -inf 59.1%

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

      1. +-commutative 59.1%

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

      2. associate-*r/ 59.1%

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

      3. distribute-lft-out-- 59.1%

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

      4. associate-*r* 59.1%

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

      5. metadata-eval 59.1%

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

      6. *-lft-identity 59.1%

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

   6. Simplified 67.7%

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

   7. Taylor expanded in b around inf 74.8%

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

      1. associate-*l/ 81.5%

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

      2. *-commutative 81.5%

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

   9. Simplified 81.5%

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

   if -9.5000000000000004e129 < y < 2.6000000000000002e69

   1. Initial program 88.3%

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

      1. *-commutative 88.3%

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

      2. associate-/l* 88.8%

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

      3. associate-*l/ 89.4%

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

   3. Simplified 89.4%

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

   if 3.1e140 < y < 1.70000000000000008e219

   1. Initial program 69.4%

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

      1. associate-/l* 79.7%

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

   3. Simplified 79.7%

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

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+129}:\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot \frac{t}{b}}{y}\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+69}:\\ \;\;\;\;\frac{x + \frac{z}{\frac{t}{y}}}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+140} \lor \neg \left(y \leq 1.7 \cdot 10^{+219}\right):\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot \frac{t}{b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y}{\frac{t}{b}}}\\ \end{array} \]

Alternative 4: 81.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{+131} \lor \neg \left(y \leq 7.6 \cdot 10^{+70}\right):\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot \frac{t}{b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.45e+131) (not (<= y 7.6e+70)))
   (+ (/ z b) (/ (* x (/ t b)) y))
   (/ (+ x (* z (/ y t))) (+ (+ a 1.0) (* b (/ y t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.45e+131) || !(y <= 7.6e+70)) {
		tmp = (z / b) + ((x * (t / b)) / y);
	} else {
		tmp = (x + (z * (y / t))) / ((a + 1.0) + (b * (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 ((y <= (-1.45d+131)) .or. (.not. (y <= 7.6d+70))) then
        tmp = (z / b) + ((x * (t / b)) / y)
    else
        tmp = (x + (z * (y / t))) / ((a + 1.0d0) + (b * (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 ((y <= -1.45e+131) || !(y <= 7.6e+70)) {
		tmp = (z / b) + ((x * (t / b)) / y);
	} else {
		tmp = (x + (z * (y / t))) / ((a + 1.0) + (b * (y / t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.45e+131) or not (y <= 7.6e+70):
		tmp = (z / b) + ((x * (t / b)) / y)
	else:
		tmp = (x + (z * (y / t))) / ((a + 1.0) + (b * (y / t)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.45e+131) || !(y <= 7.6e+70))
		tmp = Float64(Float64(z / b) + Float64(Float64(x * Float64(t / b)) / y));
	else
		tmp = Float64(Float64(x + Float64(z * Float64(y / t))) / Float64(Float64(a + 1.0) + Float64(b * Float64(y / t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.45e+131) || ~((y <= 7.6e+70)))
		tmp = (z / b) + ((x * (t / b)) / y);
	else
		tmp = (x + (z * (y / t))) / ((a + 1.0) + (b * (y / t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.45e+131], N[Not[LessEqual[y, 7.6e+70]], $MachinePrecision]], N[(N[(z / b), $MachinePrecision] + N[(N[(x * N[(t / b), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.45000000000000005e131 or 7.5999999999999996e70 < y

   1. Initial program 40.6%

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

      1. *-commutative 40.6%

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

      2. associate-/l* 32.7%

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

      3. associate-*l/ 46.2%

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

   3. Simplified 46.2%

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

   4. Taylor expanded in y around -inf 53.6%

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

      1. +-commutative 53.6%

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

      2. associate-*r/ 53.6%

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

      3. distribute-lft-out-- 53.6%

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

      4. associate-*r* 53.6%

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

      5. metadata-eval 53.6%

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

      6. *-lft-identity 53.6%

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

   6. Simplified 62.4%

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

   7. Taylor expanded in b around inf 68.1%

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

      1. associate-*l/ 75.6%

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

      2. *-commutative 75.6%

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

   9. Simplified 75.6%

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

   if -1.45000000000000005e131 < y < 7.5999999999999996e70

   1. Initial program 88.3%

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

      1. *-commutative 88.3%

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

      2. associate-/l* 88.8%

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

      3. associate-*l/ 89.4%

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

   3. Simplified 89.4%

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

      1. div-inv 89.4%

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

      2. clear-num 89.4%

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

   5. Applied egg-rr 89.4%

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

4. Final simplification 84.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{+131} \lor \neg \left(y \leq 7.6 \cdot 10^{+70}\right):\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot \frac{t}{b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \end{array} \]

Alternative 5: 81.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.15 \cdot 10^{+130} \lor \neg \left(y \leq 2.2 \cdot 10^{+72}\right):\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot \frac{t}{b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{z}{\frac{t}{y}}}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -2.15e+130) (not (<= y 2.2e+72)))
   (+ (/ z b) (/ (* x (/ t b)) y))
   (/ (+ x (/ z (/ t y))) (+ (+ a 1.0) (* b (/ y t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.15e+130) || !(y <= 2.2e+72)) {
		tmp = (z / b) + ((x * (t / b)) / y);
	} else {
		tmp = (x + (z / (t / y))) / ((a + 1.0) + (b * (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 ((y <= (-2.15d+130)) .or. (.not. (y <= 2.2d+72))) then
        tmp = (z / b) + ((x * (t / b)) / y)
    else
        tmp = (x + (z / (t / y))) / ((a + 1.0d0) + (b * (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 ((y <= -2.15e+130) || !(y <= 2.2e+72)) {
		tmp = (z / b) + ((x * (t / b)) / y);
	} else {
		tmp = (x + (z / (t / y))) / ((a + 1.0) + (b * (y / t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -2.15e+130) or not (y <= 2.2e+72):
		tmp = (z / b) + ((x * (t / b)) / y)
	else:
		tmp = (x + (z / (t / y))) / ((a + 1.0) + (b * (y / t)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -2.15e+130) || !(y <= 2.2e+72))
		tmp = Float64(Float64(z / b) + Float64(Float64(x * Float64(t / b)) / y));
	else
		tmp = Float64(Float64(x + Float64(z / Float64(t / y))) / Float64(Float64(a + 1.0) + Float64(b * Float64(y / t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -2.15e+130) || ~((y <= 2.2e+72)))
		tmp = (z / b) + ((x * (t / b)) / y);
	else
		tmp = (x + (z / (t / y))) / ((a + 1.0) + (b * (y / t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -2.15e+130], N[Not[LessEqual[y, 2.2e+72]], $MachinePrecision]], N[(N[(z / b), $MachinePrecision] + N[(N[(x * N[(t / b), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.14999999999999992e130 or 2.2e72 < y

   1. Initial program 40.6%

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

      1. *-commutative 40.6%

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

      2. associate-/l* 32.7%

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

      3. associate-*l/ 46.2%

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

   3. Simplified 46.2%

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

   4. Taylor expanded in y around -inf 53.6%

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

      1. +-commutative 53.6%

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

      2. associate-*r/ 53.6%

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

      3. distribute-lft-out-- 53.6%

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

      4. associate-*r* 53.6%

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

      5. metadata-eval 53.6%

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

      6. *-lft-identity 53.6%

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

   6. Simplified 62.4%

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

   7. Taylor expanded in b around inf 68.1%

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

      1. associate-*l/ 75.6%

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

      2. *-commutative 75.6%

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

   9. Simplified 75.6%

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

   if -2.14999999999999992e130 < y < 2.2e72

   1. Initial program 88.3%

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

      1. *-commutative 88.3%

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

      2. associate-/l* 88.8%

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

      3. associate-*l/ 89.4%

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

   3. Simplified 89.4%

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

4. Final simplification 84.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.15 \cdot 10^{+130} \lor \neg \left(y \leq 2.2 \cdot 10^{+72}\right):\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot \frac{t}{b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{z}{\frac{t}{y}}}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \end{array} \]

Alternative 6: 65.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{a + 1}\\ t_2 := \frac{z}{b} + \frac{x \cdot \frac{t}{b}}{y}\\ \mathbf{if}\;y \leq -7.4 \cdot 10^{-54}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-69}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-28}:\\ \;\;\;\;\frac{y \cdot z}{y \cdot b + t \cdot \left(a + 1\right)}\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{+37}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (* y z) t)) (+ a 1.0)))
        (t_2 (+ (/ z b) (/ (* x (/ t b)) y))))
   (if (<= y -7.4e-54)
     t_2
     (if (<= y 2.3e-69)
       t_1
       (if (<= y 1.7e-28)
         (/ (* y z) (+ (* y b) (* t (+ a 1.0))))
         (if (<= y 7.6e+37) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + ((y * z) / t)) / (a + 1.0);
	double t_2 = (z / b) + ((x * (t / b)) / y);
	double tmp;
	if (y <= -7.4e-54) {
		tmp = t_2;
	} else if (y <= 2.3e-69) {
		tmp = t_1;
	} else if (y <= 1.7e-28) {
		tmp = (y * z) / ((y * b) + (t * (a + 1.0)));
	} else if (y <= 7.6e+37) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x + ((y * z) / t)) / (a + 1.0d0)
    t_2 = (z / b) + ((x * (t / b)) / y)
    if (y <= (-7.4d-54)) then
        tmp = t_2
    else if (y <= 2.3d-69) then
        tmp = t_1
    else if (y <= 1.7d-28) then
        tmp = (y * z) / ((y * b) + (t * (a + 1.0d0)))
    else if (y <= 7.6d+37) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + ((y * z) / t)) / (a + 1.0);
	double t_2 = (z / b) + ((x * (t / b)) / y);
	double tmp;
	if (y <= -7.4e-54) {
		tmp = t_2;
	} else if (y <= 2.3e-69) {
		tmp = t_1;
	} else if (y <= 1.7e-28) {
		tmp = (y * z) / ((y * b) + (t * (a + 1.0)));
	} else if (y <= 7.6e+37) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + ((y * z) / t)) / (a + 1.0)
	t_2 = (z / b) + ((x * (t / b)) / y)
	tmp = 0
	if y <= -7.4e-54:
		tmp = t_2
	elif y <= 2.3e-69:
		tmp = t_1
	elif y <= 1.7e-28:
		tmp = (y * z) / ((y * b) + (t * (a + 1.0)))
	elif y <= 7.6e+37:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(a + 1.0))
	t_2 = Float64(Float64(z / b) + Float64(Float64(x * Float64(t / b)) / y))
	tmp = 0.0
	if (y <= -7.4e-54)
		tmp = t_2;
	elseif (y <= 2.3e-69)
		tmp = t_1;
	elseif (y <= 1.7e-28)
		tmp = Float64(Float64(y * z) / Float64(Float64(y * b) + Float64(t * Float64(a + 1.0))));
	elseif (y <= 7.6e+37)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + ((y * z) / t)) / (a + 1.0);
	t_2 = (z / b) + ((x * (t / b)) / y);
	tmp = 0.0;
	if (y <= -7.4e-54)
		tmp = t_2;
	elseif (y <= 2.3e-69)
		tmp = t_1;
	elseif (y <= 1.7e-28)
		tmp = (y * z) / ((y * b) + (t * (a + 1.0)));
	elseif (y <= 7.6e+37)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z / b), $MachinePrecision] + N[(N[(x * N[(t / b), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7.4e-54], t$95$2, If[LessEqual[y, 2.3e-69], t$95$1, If[LessEqual[y, 1.7e-28], N[(N[(y * z), $MachinePrecision] / N[(N[(y * b), $MachinePrecision] + N[(t * N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.6e+37], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.4000000000000006e-54 or 7.59999999999999979e37 < y

   1. Initial program 49.3%

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

      1. *-commutative 49.3%

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

      2. associate-/l* 44.7%

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

      3. associate-*l/ 54.4%

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

   3. Simplified 54.4%

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

   4. Taylor expanded in y around -inf 51.9%

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

      1. +-commutative 51.9%

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

      2. associate-*r/ 51.9%

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

      3. distribute-lft-out-- 51.9%

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

      4. associate-*r* 51.9%

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

      5. metadata-eval 51.9%

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

      6. *-lft-identity 51.9%

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

   6. Simplified 60.1%

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

   7. Taylor expanded in b around inf 62.6%

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

      1. associate-*l/ 68.3%

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

      2. *-commutative 68.3%

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

   9. Simplified 68.3%

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

   if -7.4000000000000006e-54 < y < 2.3000000000000001e-69 or 1.7e-28 < y < 7.59999999999999979e37

   1. Initial program 96.5%

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

      1. *-commutative 96.5%

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

      2. associate-/l* 96.5%

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

      3. associate-*l/ 96.5%

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

   3. Simplified 96.5%

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

   4. Taylor expanded in b around 0 85.6%

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

   if 2.3000000000000001e-69 < y < 1.7e-28

   1. Initial program 89.5%

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

      1. *-commutative 89.5%

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

      2. associate-/l* 89.3%

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

      3. associate-*l/ 89.2%

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

   3. Simplified 89.2%

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

   4. Taylor expanded in x around 0 90.4%

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

   5. Taylor expanded in t around 0 90.6%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.4 \cdot 10^{-54}:\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot \frac{t}{b}}{y}\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-69}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-28}:\\ \;\;\;\;\frac{y \cdot z}{y \cdot b + t \cdot \left(a + 1\right)}\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{+37}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot \frac{t}{b}}{y}\\ \end{array} \]

Alternative 7: 58.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{-55} \lor \neg \left(y \leq 2.2 \cdot 10^{-71}\right):\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot \frac{t}{b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -9e-55) (not (<= y 2.2e-71)))
   (+ (/ z b) (/ (* x (/ t b)) y))
   (/ x (+ a 1.0))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -9e-55) || !(y <= 2.2e-71)) {
		tmp = (z / b) + ((x * (t / b)) / y);
	} 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 <= (-9d-55)) .or. (.not. (y <= 2.2d-71))) then
        tmp = (z / b) + ((x * (t / b)) / y)
    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 <= -9e-55) || !(y <= 2.2e-71)) {
		tmp = (z / b) + ((x * (t / b)) / y);
	} else {
		tmp = x / (a + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -9e-55) or not (y <= 2.2e-71):
		tmp = (z / b) + ((x * (t / b)) / y)
	else:
		tmp = x / (a + 1.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -9e-55) || !(y <= 2.2e-71))
		tmp = Float64(Float64(z / b) + Float64(Float64(x * Float64(t / b)) / y));
	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 <= -9e-55) || ~((y <= 2.2e-71)))
		tmp = (z / b) + ((x * (t / b)) / y);
	else
		tmp = x / (a + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -9e-55], N[Not[LessEqual[y, 2.2e-71]], $MachinePrecision]], N[(N[(z / b), $MachinePrecision] + N[(N[(x * N[(t / b), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.99999999999999941e-55 or 2.19999999999999997e-71 < y

   1. Initial program 55.0%

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

      1. *-commutative 55.0%

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

      2. associate-/l* 50.9%

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

      3. associate-*l/ 59.5%

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

   3. Simplified 59.5%

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

   4. Taylor expanded in y around -inf 50.0%

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

      1. +-commutative 50.0%

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

      2. associate-*r/ 50.0%

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

      3. distribute-lft-out-- 50.0%

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

      4. associate-*r* 50.0%

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

      5. metadata-eval 50.0%

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

      6. *-lft-identity 50.0%

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

   6. Simplified 57.2%

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

   7. Taylor expanded in b around inf 60.2%

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

      1. associate-*l/ 65.2%

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

      2. *-commutative 65.2%

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

   9. Simplified 65.2%

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

   if -8.99999999999999941e-55 < y < 2.19999999999999997e-71

   1. Initial program 96.2%

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

      1. *-commutative 96.2%

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

      2. associate-/l* 96.2%

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

      3. associate-*l/ 96.2%

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

   3. Simplified 96.2%

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

   4. Taylor expanded in t around inf 70.5%

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

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{-55} \lor \neg \left(y \leq 2.2 \cdot 10^{-71}\right):\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot \frac{t}{b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \]

Alternative 8: 65.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{-126} \lor \neg \left(t \leq 27500\right):\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y}{\frac{t}{b}}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -8.5e-126) (not (<= t 27500.0)))
   (/ x (+ 1.0 (+ a (/ y (/ t b)))))
   (/ (+ z (/ (* x t) y)) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -8.5e-126) || !(t <= 27500.0)) {
		tmp = x / (1.0 + (a + (y / (t / b))));
	} else {
		tmp = (z + ((x * t) / y)) / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-8.5d-126)) .or. (.not. (t <= 27500.0d0))) then
        tmp = x / (1.0d0 + (a + (y / (t / b))))
    else
        tmp = (z + ((x * t) / y)) / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -8.5e-126) || !(t <= 27500.0)) {
		tmp = x / (1.0 + (a + (y / (t / b))));
	} else {
		tmp = (z + ((x * t) / y)) / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -8.5e-126) or not (t <= 27500.0):
		tmp = x / (1.0 + (a + (y / (t / b))))
	else:
		tmp = (z + ((x * t) / y)) / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -8.5e-126) || !(t <= 27500.0))
		tmp = Float64(x / Float64(1.0 + Float64(a + Float64(y / Float64(t / b)))));
	else
		tmp = Float64(Float64(z + Float64(Float64(x * t) / y)) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -8.5e-126) || ~((t <= 27500.0)))
		tmp = x / (1.0 + (a + (y / (t / b))));
	else
		tmp = (z + ((x * t) / y)) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -8.5e-126], N[Not[LessEqual[t, 27500.0]], $MachinePrecision]], N[(x / N[(1.0 + N[(a + N[(y / N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -8.49999999999999938e-126 or 27500 < t

   1. Initial program 79.7%

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

      1. *-commutative 79.7%

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

      2. associate-/l* 83.5%

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

      3. associate-*l/ 93.7%

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

   3. Simplified 93.7%

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

   4. Taylor expanded in x around inf 64.8%

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

      1. associate-*l/ 70.4%

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

   6. Applied egg-rr 70.4%

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

      1. associate-*l/ 64.8%

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

      2. associate-/l* 70.5%

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

   8. Simplified 70.5%

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

   if -8.49999999999999938e-126 < t < 27500

   1. Initial program 60.5%

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

      1. *-commutative 60.5%

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

      2. associate-/l* 49.3%

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

      3. associate-*l/ 47.1%

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

   3. Simplified 47.1%

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

   4. Taylor expanded in y around -inf 60.3%

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

      1. +-commutative 60.3%

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

      2. associate-*r/ 60.3%

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

      3. distribute-lft-out-- 60.3%

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

      4. associate-*r* 60.3%

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

      5. metadata-eval 60.3%

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

      6. *-lft-identity 60.3%

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

   6. Simplified 59.4%

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

   7. Taylor expanded in b around inf 70.5%

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

   8. Taylor expanded in b around 0 72.2%

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

4. Final simplification 71.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{-126} \lor \neg \left(t \leq 27500\right):\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y}{\frac{t}{b}}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \end{array} \]

Alternative 9: 66.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{-53} \lor \neg \left(y \leq 1.65 \cdot 10^{+37}\right):\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot \frac{t}{b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.75e-53) (not (<= y 1.65e+37)))
   (+ (/ z b) (/ (* x (/ t b)) y))
   (/ (+ 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 ((y <= -1.75e-53) || !(y <= 1.65e+37)) {
		tmp = (z / b) + ((x * (t / b)) / y);
	} 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 ((y <= (-1.75d-53)) .or. (.not. (y <= 1.65d+37))) then
        tmp = (z / b) + ((x * (t / b)) / y)
    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 ((y <= -1.75e-53) || !(y <= 1.65e+37)) {
		tmp = (z / b) + ((x * (t / b)) / y);
	} else {
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.75e-53) or not (y <= 1.65e+37):
		tmp = (z / b) + ((x * (t / b)) / y)
	else:
		tmp = (x + ((y * z) / t)) / (a + 1.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.75e-53) || !(y <= 1.65e+37))
		tmp = Float64(Float64(z / b) + Float64(Float64(x * Float64(t / b)) / y));
	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 ((y <= -1.75e-53) || ~((y <= 1.65e+37)))
		tmp = (z / b) + ((x * (t / b)) / y);
	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[y, -1.75e-53], N[Not[LessEqual[y, 1.65e+37]], $MachinePrecision]], N[(N[(z / b), $MachinePrecision] + N[(N[(x * N[(t / b), $MachinePrecision]), $MachinePrecision] / y), $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 y < -1.74999999999999997e-53 or 1.65e37 < y

   1. Initial program 49.3%

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

      1. *-commutative 49.3%

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

      2. associate-/l* 44.7%

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

      3. associate-*l/ 54.4%

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

   3. Simplified 54.4%

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

   4. Taylor expanded in y around -inf 51.9%

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

      1. +-commutative 51.9%

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

      2. associate-*r/ 51.9%

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

      3. distribute-lft-out-- 51.9%

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

      4. associate-*r* 51.9%

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

      5. metadata-eval 51.9%

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

      6. *-lft-identity 51.9%

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

   6. Simplified 60.1%

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

   7. Taylor expanded in b around inf 62.6%

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

      1. associate-*l/ 68.3%

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

      2. *-commutative 68.3%

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

   9. Simplified 68.3%

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

   if -1.74999999999999997e-53 < y < 1.65e37

   1. Initial program 96.0%

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

      1. *-commutative 96.0%

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

      2. associate-/l* 96.0%

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

      3. associate-*l/ 96.0%

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

   3. Simplified 96.0%

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

   4. Taylor expanded in b around 0 82.7%

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

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{-53} \lor \neg \left(y \leq 1.65 \cdot 10^{+37}\right):\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot \frac{t}{b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \end{array} \]

Alternative 10: 57.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{-54} \lor \neg \left(y \leq 3.5 \cdot 10^{-73}\right):\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.9e-54) (not (<= y 3.5e-73)))
   (/ (+ z (/ (* x t) y)) b)
   (/ x (+ a 1.0))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.9e-54) || !(y <= 3.5e-73)) {
		tmp = (z + ((x * t) / y)) / b;
	} else {
		tmp = x / (a + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-1.9d-54)) .or. (.not. (y <= 3.5d-73))) then
        tmp = (z + ((x * t) / y)) / b
    else
        tmp = x / (a + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.9e-54) || !(y <= 3.5e-73)) {
		tmp = (z + ((x * t) / y)) / b;
	} else {
		tmp = x / (a + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.9e-54) or not (y <= 3.5e-73):
		tmp = (z + ((x * t) / y)) / b
	else:
		tmp = x / (a + 1.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.9e-54) || !(y <= 3.5e-73))
		tmp = Float64(Float64(z + Float64(Float64(x * t) / y)) / b);
	else
		tmp = Float64(x / Float64(a + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.9e-54) || ~((y <= 3.5e-73)))
		tmp = (z + ((x * t) / y)) / b;
	else
		tmp = x / (a + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.9e-54], N[Not[LessEqual[y, 3.5e-73]], $MachinePrecision]], N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.9000000000000001e-54 or 3.4999999999999998e-73 < y

   1. Initial program 55.0%

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

      1. *-commutative 55.0%

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

      2. associate-/l* 50.9%

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

      3. associate-*l/ 59.5%

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

   3. Simplified 59.5%

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

   4. Taylor expanded in y around -inf 50.0%

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

      1. +-commutative 50.0%

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

      2. associate-*r/ 50.0%

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

      3. distribute-lft-out-- 50.0%

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

      4. associate-*r* 50.0%

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

      5. metadata-eval 50.0%

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

      6. *-lft-identity 50.0%

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

   6. Simplified 57.2%

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

   7. Taylor expanded in b around inf 60.2%

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

   8. Taylor expanded in b around 0 60.2%

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

   if -1.9000000000000001e-54 < y < 3.4999999999999998e-73

   1. Initial program 96.2%

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

      1. *-commutative 96.2%

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

      2. associate-/l* 96.2%

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

      3. associate-*l/ 96.2%

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

   3. Simplified 96.2%

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

   4. Taylor expanded in t around inf 70.5%

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

4. Final simplification 64.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{-54} \lor \neg \left(y \leq 3.5 \cdot 10^{-73}\right):\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \]

Alternative 11: 42.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4 \cdot 10^{+60}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-66}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{-9}:\\ \;\;\;\;x - x \cdot a\\ \mathbf{elif}\;a \leq 8.6 \cdot 10^{+14}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -4e+60)
   (/ x a)
   (if (<= a 9.5e-66)
     (/ z b)
     (if (<= a 1.9e-9) (- x (* x a)) (if (<= a 8.6e+14) (/ z b) (/ x a))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -4e+60) {
		tmp = x / a;
	} else if (a <= 9.5e-66) {
		tmp = z / b;
	} else if (a <= 1.9e-9) {
		tmp = x - (x * a);
	} else if (a <= 8.6e+14) {
		tmp = z / b;
	} else {
		tmp = x / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-4d+60)) then
        tmp = x / a
    else if (a <= 9.5d-66) then
        tmp = z / b
    else if (a <= 1.9d-9) then
        tmp = x - (x * a)
    else if (a <= 8.6d+14) then
        tmp = z / b
    else
        tmp = x / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -4e+60) {
		tmp = x / a;
	} else if (a <= 9.5e-66) {
		tmp = z / b;
	} else if (a <= 1.9e-9) {
		tmp = x - (x * a);
	} else if (a <= 8.6e+14) {
		tmp = z / b;
	} else {
		tmp = x / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -4e+60:
		tmp = x / a
	elif a <= 9.5e-66:
		tmp = z / b
	elif a <= 1.9e-9:
		tmp = x - (x * a)
	elif a <= 8.6e+14:
		tmp = z / b
	else:
		tmp = x / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -4e+60)
		tmp = Float64(x / a);
	elseif (a <= 9.5e-66)
		tmp = Float64(z / b);
	elseif (a <= 1.9e-9)
		tmp = Float64(x - Float64(x * a));
	elseif (a <= 8.6e+14)
		tmp = Float64(z / b);
	else
		tmp = Float64(x / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -4e+60)
		tmp = x / a;
	elseif (a <= 9.5e-66)
		tmp = z / b;
	elseif (a <= 1.9e-9)
		tmp = x - (x * a);
	elseif (a <= 8.6e+14)
		tmp = z / b;
	else
		tmp = x / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -4e+60], N[(x / a), $MachinePrecision], If[LessEqual[a, 9.5e-66], N[(z / b), $MachinePrecision], If[LessEqual[a, 1.9e-9], N[(x - N[(x * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8.6e+14], N[(z / b), $MachinePrecision], N[(x / a), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.9999999999999998e60 or 8.6e14 < a

   1. Initial program 81.3%

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

      1. *-commutative 81.3%

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

      2. associate-/l* 78.7%

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

      3. associate-*l/ 81.9%

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

   3. Simplified 81.9%

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

   4. Taylor expanded in x around inf 60.9%

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

   5. Taylor expanded in a around inf 56.2%

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

   if -3.9999999999999998e60 < a < 9.5000000000000004e-66 or 1.90000000000000006e-9 < a < 8.6e14

   1. Initial program 63.9%

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

      1. *-commutative 63.9%

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

      2. associate-/l* 60.8%

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

      3. associate-*l/ 67.6%

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

   3. Simplified 67.6%

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

   4. Taylor expanded in t around 0 50.9%

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

   if 9.5000000000000004e-66 < a < 1.90000000000000006e-9

   1. Initial program 76.2%

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

      1. *-commutative 76.2%

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

      2. associate-/l* 88.1%

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

      3. associate-*l/ 88.1%

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

   3. Simplified 88.1%

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

   4. Taylor expanded in t around inf 64.9%

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

   5. Taylor expanded in a around 0 64.9%

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

      1. +-commutative 64.9%

         \[\leadsto \color{blue}{x + -1 \cdot \left(a \cdot x\right)} \]

      2. mul-1-neg 64.9%

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

      3. unsub-neg 64.9%

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

      4. *-commutative 64.9%

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

   7. Simplified 64.9%

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

4. Final simplification 53.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4 \cdot 10^{+60}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-66}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{-9}:\\ \;\;\;\;x - x \cdot a\\ \mathbf{elif}\;a \leq 8.6 \cdot 10^{+14}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \]

Alternative 12: 55.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{-125} \lor \neg \left(t \leq 24500\right):\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -1.15e-125) (not (<= t 24500.0))) (/ x (+ a 1.0)) (/ z b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.15e-125) || !(t <= 24500.0)) {
		tmp = x / (a + 1.0);
	} else {
		tmp = z / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-1.15d-125)) .or. (.not. (t <= 24500.0d0))) then
        tmp = x / (a + 1.0d0)
    else
        tmp = z / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.15e-125) || !(t <= 24500.0)) {
		tmp = x / (a + 1.0);
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -1.15e-125) or not (t <= 24500.0):
		tmp = x / (a + 1.0)
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -1.15e-125) || !(t <= 24500.0))
		tmp = Float64(x / Float64(a + 1.0));
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -1.15e-125) || ~((t <= 24500.0)))
		tmp = x / (a + 1.0);
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -1.15e-125], N[Not[LessEqual[t, 24500.0]], $MachinePrecision]], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.15e-125 or 24500 < t

   1. Initial program 79.7%

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

      1. *-commutative 79.7%

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

      2. associate-/l* 83.5%

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

      3. associate-*l/ 93.7%

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

   3. Simplified 93.7%

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

   4. Taylor expanded in t around inf 57.9%

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

   if -1.15e-125 < t < 24500

   1. Initial program 60.5%

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

      1. *-commutative 60.5%

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

      2. associate-/l* 49.3%

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

      3. associate-*l/ 47.1%

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

   3. Simplified 47.1%

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

   4. Taylor expanded in t around 0 63.4%

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

4. Final simplification 60.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{-125} \lor \neg \left(t \leq 24500\right):\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 13: 42.4% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7.6 \cdot 10^{-19}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;a \leq 25500000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -7.6e-19) (/ x a) (if (<= a 25500000.0) x (/ x a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -7.6e-19) {
		tmp = x / a;
	} else if (a <= 25500000.0) {
		tmp = x;
	} else {
		tmp = x / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-7.6d-19)) then
        tmp = x / a
    else if (a <= 25500000.0d0) then
        tmp = x
    else
        tmp = x / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -7.6e-19) {
		tmp = x / a;
	} else if (a <= 25500000.0) {
		tmp = x;
	} else {
		tmp = x / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -7.6e-19:
		tmp = x / a
	elif a <= 25500000.0:
		tmp = x
	else:
		tmp = x / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -7.6e-19)
		tmp = Float64(x / a);
	elseif (a <= 25500000.0)
		tmp = x;
	else
		tmp = Float64(x / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -7.6e-19)
		tmp = x / a;
	elseif (a <= 25500000.0)
		tmp = x;
	else
		tmp = x / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -7.6e-19], N[(x / a), $MachinePrecision], If[LessEqual[a, 25500000.0], x, N[(x / a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -7.6e-19 or 2.55e7 < a

   1. Initial program 79.6%

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

      1. *-commutative 79.6%

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

      2. associate-/l* 74.4%

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

      3. associate-*l/ 79.1%

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

   3. Simplified 79.1%

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

   4. Taylor expanded in x around inf 57.8%

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

   5. Taylor expanded in a around inf 49.0%

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

   if -7.6e-19 < a < 2.55e7

   1. Initial program 63.2%

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

      1. *-commutative 63.2%

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

      2. associate-/l* 63.7%

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

      3. associate-*l/ 69.2%

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

   3. Simplified 69.2%

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

   4. Taylor expanded in t around inf 31.3%

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

   5. Taylor expanded in a around 0 31.3%

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

4. Final simplification 40.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.6 \cdot 10^{-19}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;a \leq 25500000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \]

Alternative 14: 42.6% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7.2 \cdot 10^{+67}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{+14}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -7.2e+67) (/ x a) (if (<= a 6.8e+14) (/ z b) (/ x a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -7.2e+67) {
		tmp = x / a;
	} else if (a <= 6.8e+14) {
		tmp = z / b;
	} else {
		tmp = x / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-7.2d+67)) then
        tmp = x / a
    else if (a <= 6.8d+14) then
        tmp = z / b
    else
        tmp = x / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -7.2e+67) {
		tmp = x / a;
	} else if (a <= 6.8e+14) {
		tmp = z / b;
	} else {
		tmp = x / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -7.2e+67:
		tmp = x / a
	elif a <= 6.8e+14:
		tmp = z / b
	else:
		tmp = x / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -7.2e+67)
		tmp = Float64(x / a);
	elseif (a <= 6.8e+14)
		tmp = Float64(z / b);
	else
		tmp = Float64(x / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -7.2e+67)
		tmp = x / a;
	elseif (a <= 6.8e+14)
		tmp = z / b;
	else
		tmp = x / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -7.2e+67], N[(x / a), $MachinePrecision], If[LessEqual[a, 6.8e+14], N[(z / b), $MachinePrecision], N[(x / a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -7.1999999999999998e67 or 6.8e14 < a

   1. Initial program 81.3%

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

      1. *-commutative 81.3%

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

      2. associate-/l* 78.7%

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

      3. associate-*l/ 81.9%

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

   3. Simplified 81.9%

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

   4. Taylor expanded in x around inf 60.9%

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

   5. Taylor expanded in a around inf 56.2%

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

   if -7.1999999999999998e67 < a < 6.8e14

   1. Initial program 64.6%

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

      1. *-commutative 64.6%

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

      2. associate-/l* 62.3%

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

      3. associate-*l/ 68.7%

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

   3. Simplified 68.7%

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

   4. Taylor expanded in t around 0 48.9%

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

4. Final simplification 52.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.2 \cdot 10^{+67}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{+14}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \]

Alternative 15: 20.7% accurate, 17.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 71.8%

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

   1. *-commutative 71.8%

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

   2. associate-/l* 69.3%

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

   3. associate-*l/ 74.4%

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

3. Simplified 74.4%

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

4. Taylor expanded in t around inf 40.9%

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

5. Taylor expanded in a around 0 16.9%

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

6. Final simplification 16.9%

   \[\leadsto x \]

Developer target: 80.1% 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 2023223 
(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))))