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

Percentage Accurate: 74.4% → 92.0%

Time: 17.2s

Alternatives: 18

Speedup: 0.5×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 74.4% 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: 92.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ t_2 := y \cdot \frac{z}{y \cdot b + t \cdot \left(a + 1\right)}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq -1 \cdot 10^{-294}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;\frac{z}{b} + \frac{t \cdot \frac{x}{b}}{y}\\ \mathbf{elif}\;t\_1 \leq 10^{+283}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t))))
        (t_2 (* y (/ z (+ (* y b) (* t (+ a 1.0)))))))
   (if (<= t_1 (- INFINITY))
     t_2
     (if (<= t_1 -1e-294)
       t_1
       (if (<= t_1 0.0)
         (+ (/ z b) (/ (* t (/ x b)) y))
         (if (<= t_1 1e+283) t_1 (if (<= t_1 INFINITY) t_2 (/ z b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
	double t_2 = y * (z / ((y * b) + (t * (a + 1.0))));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = t_2;
	} else if (t_1 <= -1e-294) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = (z / b) + ((t * (x / b)) / y);
	} else if (t_1 <= 1e+283) {
		tmp = t_1;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = t_2;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
	double t_2 = y * (z / ((y * b) + (t * (a + 1.0))));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else if (t_1 <= -1e-294) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = (z / b) + ((t * (x / b)) / y);
	} else if (t_1 <= 1e+283) {
		tmp = t_1;
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t))
	t_2 = y * (z / ((y * b) + (t * (a + 1.0))))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = t_2
	elif t_1 <= -1e-294:
		tmp = t_1
	elif t_1 <= 0.0:
		tmp = (z / b) + ((t * (x / b)) / y)
	elif t_1 <= 1e+283:
		tmp = t_1
	elif t_1 <= math.inf:
		tmp = t_2
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(Float64(a + 1.0) + Float64(Float64(y * b) / t)))
	t_2 = Float64(y * Float64(z / Float64(Float64(y * b) + Float64(t * Float64(a + 1.0)))))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = t_2;
	elseif (t_1 <= -1e-294)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(z / b) + Float64(Float64(t * Float64(x / b)) / y));
	elseif (t_1 <= 1e+283)
		tmp = t_1;
	elseif (t_1 <= Inf)
		tmp = t_2;
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
	t_2 = y * (z / ((y * b) + (t * (a + 1.0))));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = t_2;
	elseif (t_1 <= -1e-294)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = (z / b) + ((t * (x / b)) / y);
	elseif (t_1 <= 1e+283)
		tmp = t_1;
	elseif (t_1 <= Inf)
		tmp = t_2;
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(z / N[(N[(y * b), $MachinePrecision] + N[(t * N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], t$95$2, If[LessEqual[t$95$1, -1e-294], t$95$1, If[LessEqual[t$95$1, 0.0], N[(N[(z / b), $MachinePrecision] + N[(N[(t * N[(x / b), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+283], t$95$1, If[LessEqual[t$95$1, Infinity], t$95$2, N[(z / b), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -inf.0 or 9.99999999999999955e282 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < +inf.0

   1. Initial program 34.5%

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

      1. associate-/l* 54.7%

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

      2. associate-/l* 54.7%

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

   3. Simplified 54.7%

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

   5. Taylor expanded in x around 0 58.6%

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

      1. associate-/l* 91.2%

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

      2. +-commutative 91.2%

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

      3. associate-*l/ 91.3%

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

      4. *-commutative 91.3%

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

      5. fma-undefine 91.3%

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

   7. Simplified 91.3%

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

   8. Taylor expanded in t around 0 91.3%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -1.00000000000000002e-294 or 0.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 9.99999999999999955e282

   1. Initial program 99.5%

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

   if -1.00000000000000002e-294 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 0.0

   1. Initial program 42.5%

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

      1. associate-/l* 44.6%

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

      2. associate-/l* 67.8%

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

   3. Simplified 67.8%

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

   5. Taylor expanded in b around inf 46.2%

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

   6. Taylor expanded in z around inf 63.6%

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

   7. Taylor expanded in z around 0 61.9%

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

      1. associate-/r* 71.0%

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

      2. associate-/l* 80.5%

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

      3. associate-*l/ 78.1%

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

      4. *-commutative 78.1%

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

      5. associate-*r/ 80.5%

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

   9. Simplified 80.5%

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

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

   1. Initial program 0.0%

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

      1. associate-/l* 0.2%

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

      2. associate-/l* 8.2%

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

   3. Simplified 8.2%

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

   5. Taylor expanded in y around inf 97.5%

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

4. Final simplification 95.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -\infty:\\ \;\;\;\;y \cdot \frac{z}{y \cdot b + t \cdot \left(a + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -1 \cdot 10^{-294}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 0:\\ \;\;\;\;\frac{z}{b} + \frac{t \cdot \frac{x}{b}}{y}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 10^{+283}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq \infty:\\ \;\;\;\;y \cdot \frac{z}{y \cdot b + t \cdot \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 89.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 1 + \mathsf{fma}\left(y, \frac{b}{t}, a\right)\\ t_2 := \frac{y \cdot b}{t}\\ t_3 := 1 + \left(a + t\_2\right)\\ t_4 := \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + t\_2}\\ t_5 := \frac{x}{t\_3} + \frac{y \cdot z}{t \cdot t\_3}\\ \mathbf{if}\;t\_4 \leq -1 \cdot 10^{-294}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;t\_4 \leq 0:\\ \;\;\;\;\frac{z}{b} + \frac{t \cdot \frac{x}{b}}{y}\\ \mathbf{elif}\;t\_4 \leq 10^{+274}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;t\_4 \leq \infty:\\ \;\;\;\;z \cdot \left(\frac{x}{z \cdot t\_1} + \frac{\frac{y}{t}}{t\_1}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ 1.0 (fma y (/ b t) a)))
        (t_2 (/ (* y b) t))
        (t_3 (+ 1.0 (+ a t_2)))
        (t_4 (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) t_2)))
        (t_5 (+ (/ x t_3) (/ (* y z) (* t t_3)))))
   (if (<= t_4 -1e-294)
     t_5
     (if (<= t_4 0.0)
       (+ (/ z b) (/ (* t (/ x b)) y))
       (if (<= t_4 1e+274)
         t_5
         (if (<= t_4 INFINITY)
           (* z (+ (/ x (* z t_1)) (/ (/ y t) t_1)))
           (/ z b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 1.0 + fma(y, (b / t), a);
	double t_2 = (y * b) / t;
	double t_3 = 1.0 + (a + t_2);
	double t_4 = (x + ((y * z) / t)) / ((a + 1.0) + t_2);
	double t_5 = (x / t_3) + ((y * z) / (t * t_3));
	double tmp;
	if (t_4 <= -1e-294) {
		tmp = t_5;
	} else if (t_4 <= 0.0) {
		tmp = (z / b) + ((t * (x / b)) / y);
	} else if (t_4 <= 1e+274) {
		tmp = t_5;
	} else if (t_4 <= ((double) INFINITY)) {
		tmp = z * ((x / (z * t_1)) + ((y / t) / t_1));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(1.0 + fma(y, Float64(b / t), a))
	t_2 = Float64(Float64(y * b) / t)
	t_3 = Float64(1.0 + Float64(a + t_2))
	t_4 = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(Float64(a + 1.0) + t_2))
	t_5 = Float64(Float64(x / t_3) + Float64(Float64(y * z) / Float64(t * t_3)))
	tmp = 0.0
	if (t_4 <= -1e-294)
		tmp = t_5;
	elseif (t_4 <= 0.0)
		tmp = Float64(Float64(z / b) + Float64(Float64(t * Float64(x / b)) / y));
	elseif (t_4 <= 1e+274)
		tmp = t_5;
	elseif (t_4 <= Inf)
		tmp = Float64(z * Float64(Float64(x / Float64(z * t_1)) + Float64(Float64(y / t) / t_1)));
	else
		tmp = Float64(z / b);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(1.0 + N[(y * N[(b / t), $MachinePrecision] + a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]}, Block[{t$95$3 = N[(1.0 + N[(a + t$95$2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + t$95$2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(x / t$95$3), $MachinePrecision] + N[(N[(y * z), $MachinePrecision] / N[(t * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$4, -1e-294], t$95$5, If[LessEqual[t$95$4, 0.0], N[(N[(z / b), $MachinePrecision] + N[(N[(t * N[(x / b), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$4, 1e+274], t$95$5, If[LessEqual[t$95$4, Infinity], N[(z * N[(N[(x / N[(z * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(N[(y / t), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -1.00000000000000002e-294 or 0.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 9.99999999999999921e273

   1. Initial program 96.6%

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

      1. associate-/l* 92.0%

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

      2. associate-/l* 89.0%

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

   3. Simplified 89.0%

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

   5. Taylor expanded in x around 0 97.8%

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

   if -1.00000000000000002e-294 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 0.0

   1. Initial program 42.5%

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

      1. associate-/l* 44.6%

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

      2. associate-/l* 67.8%

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

   3. Simplified 67.8%

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

   5. Taylor expanded in b around inf 46.2%

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

   6. Taylor expanded in z around inf 63.6%

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

   7. Taylor expanded in z around 0 61.9%

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

      1. associate-/r* 71.0%

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

      2. associate-/l* 80.5%

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

      3. associate-*l/ 78.1%

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

      4. *-commutative 78.1%

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

      5. associate-*r/ 80.5%

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

   9. Simplified 80.5%

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

   if 9.99999999999999921e273 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < +inf.0

   1. Initial program 39.2%

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

      1. associate-/l* 66.6%

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

      2. associate-/l* 66.6%

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

   3. Simplified 66.6%

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

   5. Taylor expanded in z around inf 88.6%

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

      1. +-commutative 88.6%

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

      2. associate-*l/ 88.6%

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

      3. *-commutative 88.6%

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

      4. fma-undefine 88.6%

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

      5. associate-/r* 99.8%

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

      6. +-commutative 99.8%

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

      7. associate-*l/ 99.8%

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

      8. *-commutative 99.8%

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

      9. fma-undefine 99.8%

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

   7. Simplified 99.8%

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

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

   1. Initial program 0.0%

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

      1. associate-/l* 0.2%

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

      2. associate-/l* 8.2%

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

   3. Simplified 8.2%

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

   5. Taylor expanded in y around inf 97.5%

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

4. Final simplification 95.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -1 \cdot 10^{-294}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)} + \frac{y \cdot z}{t \cdot \left(1 + \left(a + \frac{y \cdot b}{t}\right)\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 0:\\ \;\;\;\;\frac{z}{b} + \frac{t \cdot \frac{x}{b}}{y}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 10^{+274}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)} + \frac{y \cdot z}{t \cdot \left(1 + \left(a + \frac{y \cdot b}{t}\right)\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq \infty:\\ \;\;\;\;z \cdot \left(\frac{x}{z \cdot \left(1 + \mathsf{fma}\left(y, \frac{b}{t}, a\right)\right)} + \frac{\frac{y}{t}}{1 + \mathsf{fma}\left(y, \frac{b}{t}, a\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 89.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot b}{t}\\ t_2 := 1 + \left(a + t\_1\right)\\ t_3 := t \cdot t\_2\\ t_4 := \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + t\_1}\\ t_5 := \frac{x}{t\_2} + \frac{y \cdot z}{t\_3}\\ \mathbf{if}\;t\_4 \leq -1 \cdot 10^{-294}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;t\_4 \leq 0:\\ \;\;\;\;\frac{z}{b} + \frac{t \cdot \frac{x}{b}}{y}\\ \mathbf{elif}\;t\_4 \leq 10^{+274}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;t\_4 \leq \infty:\\ \;\;\;\;z \cdot \left(\frac{x}{z \cdot t\_2} + \frac{y}{t\_3}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* y b) t))
        (t_2 (+ 1.0 (+ a t_1)))
        (t_3 (* t t_2))
        (t_4 (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) t_1)))
        (t_5 (+ (/ x t_2) (/ (* y z) t_3))))
   (if (<= t_4 -1e-294)
     t_5
     (if (<= t_4 0.0)
       (+ (/ z b) (/ (* t (/ x b)) y))
       (if (<= t_4 1e+274)
         t_5
         (if (<= t_4 INFINITY)
           (* z (+ (/ x (* z t_2)) (/ y t_3)))
           (/ z b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y * b) / t;
	double t_2 = 1.0 + (a + t_1);
	double t_3 = t * t_2;
	double t_4 = (x + ((y * z) / t)) / ((a + 1.0) + t_1);
	double t_5 = (x / t_2) + ((y * z) / t_3);
	double tmp;
	if (t_4 <= -1e-294) {
		tmp = t_5;
	} else if (t_4 <= 0.0) {
		tmp = (z / b) + ((t * (x / b)) / y);
	} else if (t_4 <= 1e+274) {
		tmp = t_5;
	} else if (t_4 <= ((double) INFINITY)) {
		tmp = z * ((x / (z * t_2)) + (y / t_3));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y * b) / t;
	double t_2 = 1.0 + (a + t_1);
	double t_3 = t * t_2;
	double t_4 = (x + ((y * z) / t)) / ((a + 1.0) + t_1);
	double t_5 = (x / t_2) + ((y * z) / t_3);
	double tmp;
	if (t_4 <= -1e-294) {
		tmp = t_5;
	} else if (t_4 <= 0.0) {
		tmp = (z / b) + ((t * (x / b)) / y);
	} else if (t_4 <= 1e+274) {
		tmp = t_5;
	} else if (t_4 <= Double.POSITIVE_INFINITY) {
		tmp = z * ((x / (z * t_2)) + (y / t_3));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (y * b) / t
	t_2 = 1.0 + (a + t_1)
	t_3 = t * t_2
	t_4 = (x + ((y * z) / t)) / ((a + 1.0) + t_1)
	t_5 = (x / t_2) + ((y * z) / t_3)
	tmp = 0
	if t_4 <= -1e-294:
		tmp = t_5
	elif t_4 <= 0.0:
		tmp = (z / b) + ((t * (x / b)) / y)
	elif t_4 <= 1e+274:
		tmp = t_5
	elif t_4 <= math.inf:
		tmp = z * ((x / (z * t_2)) + (y / t_3))
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y * b) / t)
	t_2 = Float64(1.0 + Float64(a + t_1))
	t_3 = Float64(t * t_2)
	t_4 = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(Float64(a + 1.0) + t_1))
	t_5 = Float64(Float64(x / t_2) + Float64(Float64(y * z) / t_3))
	tmp = 0.0
	if (t_4 <= -1e-294)
		tmp = t_5;
	elseif (t_4 <= 0.0)
		tmp = Float64(Float64(z / b) + Float64(Float64(t * Float64(x / b)) / y));
	elseif (t_4 <= 1e+274)
		tmp = t_5;
	elseif (t_4 <= Inf)
		tmp = Float64(z * Float64(Float64(x / Float64(z * t_2)) + Float64(y / t_3)));
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (y * b) / t;
	t_2 = 1.0 + (a + t_1);
	t_3 = t * t_2;
	t_4 = (x + ((y * z) / t)) / ((a + 1.0) + t_1);
	t_5 = (x / t_2) + ((y * z) / t_3);
	tmp = 0.0;
	if (t_4 <= -1e-294)
		tmp = t_5;
	elseif (t_4 <= 0.0)
		tmp = (z / b) + ((t * (x / b)) / y);
	elseif (t_4 <= 1e+274)
		tmp = t_5;
	elseif (t_4 <= Inf)
		tmp = z * ((x / (z * t_2)) + (y / t_3));
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]}, Block[{t$95$2 = N[(1.0 + N[(a + t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t * t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(x / t$95$2), $MachinePrecision] + N[(N[(y * z), $MachinePrecision] / t$95$3), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$4, -1e-294], t$95$5, If[LessEqual[t$95$4, 0.0], N[(N[(z / b), $MachinePrecision] + N[(N[(t * N[(x / b), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$4, 1e+274], t$95$5, If[LessEqual[t$95$4, Infinity], N[(z * N[(N[(x / N[(z * t$95$2), $MachinePrecision]), $MachinePrecision] + N[(y / t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -1.00000000000000002e-294 or 0.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 9.99999999999999921e273

   1. Initial program 96.6%

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

      1. associate-/l* 92.0%

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

      2. associate-/l* 89.0%

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

   3. Simplified 89.0%

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

   5. Taylor expanded in x around 0 97.8%

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

   if -1.00000000000000002e-294 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 0.0

   1. Initial program 42.5%

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

      1. associate-/l* 44.6%

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

      2. associate-/l* 67.8%

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

   3. Simplified 67.8%

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

   5. Taylor expanded in b around inf 46.2%

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

   6. Taylor expanded in z around inf 63.6%

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

   7. Taylor expanded in z around 0 61.9%

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

      1. associate-/r* 71.0%

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

      2. associate-/l* 80.5%

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

      3. associate-*l/ 78.1%

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

      4. *-commutative 78.1%

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

      5. associate-*r/ 80.5%

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

   9. Simplified 80.5%

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

   if 9.99999999999999921e273 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < +inf.0

   1. Initial program 39.2%

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

      1. associate-/l* 66.6%

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

      2. associate-/l* 66.6%

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

   3. Simplified 66.6%

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

   5. Taylor expanded in z around inf 88.6%

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

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

   1. Initial program 0.0%

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

      1. associate-/l* 0.2%

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

      2. associate-/l* 8.2%

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

   3. Simplified 8.2%

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

   5. Taylor expanded in y around inf 97.5%

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

4. Final simplification 94.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -1 \cdot 10^{-294}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)} + \frac{y \cdot z}{t \cdot \left(1 + \left(a + \frac{y \cdot b}{t}\right)\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 0:\\ \;\;\;\;\frac{z}{b} + \frac{t \cdot \frac{x}{b}}{y}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 10^{+274}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)} + \frac{y \cdot z}{t \cdot \left(1 + \left(a + \frac{y \cdot b}{t}\right)\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq \infty:\\ \;\;\;\;z \cdot \left(\frac{x}{z \cdot \left(1 + \left(a + \frac{y \cdot b}{t}\right)\right)} + \frac{y}{t \cdot \left(1 + \left(a + \frac{y \cdot b}{t}\right)\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 89.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot b}{t}\\ t_2 := 1 + \left(a + t\_1\right)\\ t_3 := \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + t\_1}\\ t_4 := \frac{x}{t\_2} + \frac{y \cdot z}{t \cdot t\_2}\\ \mathbf{if}\;t\_3 \leq -1 \cdot 10^{-294}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t\_3 \leq 0:\\ \;\;\;\;\frac{z}{b} + \frac{t \cdot \frac{x}{b}}{y}\\ \mathbf{elif}\;t\_3 \leq 10^{+283}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t\_3 \leq \infty:\\ \;\;\;\;y \cdot \frac{z}{y \cdot b + t \cdot \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* y b) t))
        (t_2 (+ 1.0 (+ a t_1)))
        (t_3 (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) t_1)))
        (t_4 (+ (/ x t_2) (/ (* y z) (* t t_2)))))
   (if (<= t_3 -1e-294)
     t_4
     (if (<= t_3 0.0)
       (+ (/ z b) (/ (* t (/ x b)) y))
       (if (<= t_3 1e+283)
         t_4
         (if (<= t_3 INFINITY)
           (* y (/ z (+ (* y b) (* t (+ a 1.0)))))
           (/ z b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y * b) / t;
	double t_2 = 1.0 + (a + t_1);
	double t_3 = (x + ((y * z) / t)) / ((a + 1.0) + t_1);
	double t_4 = (x / t_2) + ((y * z) / (t * t_2));
	double tmp;
	if (t_3 <= -1e-294) {
		tmp = t_4;
	} else if (t_3 <= 0.0) {
		tmp = (z / b) + ((t * (x / b)) / y);
	} else if (t_3 <= 1e+283) {
		tmp = t_4;
	} else if (t_3 <= ((double) INFINITY)) {
		tmp = y * (z / ((y * b) + (t * (a + 1.0))));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y * b) / t;
	double t_2 = 1.0 + (a + t_1);
	double t_3 = (x + ((y * z) / t)) / ((a + 1.0) + t_1);
	double t_4 = (x / t_2) + ((y * z) / (t * t_2));
	double tmp;
	if (t_3 <= -1e-294) {
		tmp = t_4;
	} else if (t_3 <= 0.0) {
		tmp = (z / b) + ((t * (x / b)) / y);
	} else if (t_3 <= 1e+283) {
		tmp = t_4;
	} else if (t_3 <= Double.POSITIVE_INFINITY) {
		tmp = y * (z / ((y * b) + (t * (a + 1.0))));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (y * b) / t
	t_2 = 1.0 + (a + t_1)
	t_3 = (x + ((y * z) / t)) / ((a + 1.0) + t_1)
	t_4 = (x / t_2) + ((y * z) / (t * t_2))
	tmp = 0
	if t_3 <= -1e-294:
		tmp = t_4
	elif t_3 <= 0.0:
		tmp = (z / b) + ((t * (x / b)) / y)
	elif t_3 <= 1e+283:
		tmp = t_4
	elif t_3 <= math.inf:
		tmp = y * (z / ((y * b) + (t * (a + 1.0))))
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y * b) / t)
	t_2 = Float64(1.0 + Float64(a + t_1))
	t_3 = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(Float64(a + 1.0) + t_1))
	t_4 = Float64(Float64(x / t_2) + Float64(Float64(y * z) / Float64(t * t_2)))
	tmp = 0.0
	if (t_3 <= -1e-294)
		tmp = t_4;
	elseif (t_3 <= 0.0)
		tmp = Float64(Float64(z / b) + Float64(Float64(t * Float64(x / b)) / y));
	elseif (t_3 <= 1e+283)
		tmp = t_4;
	elseif (t_3 <= Inf)
		tmp = Float64(y * Float64(z / Float64(Float64(y * b) + Float64(t * Float64(a + 1.0)))));
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (y * b) / t;
	t_2 = 1.0 + (a + t_1);
	t_3 = (x + ((y * z) / t)) / ((a + 1.0) + t_1);
	t_4 = (x / t_2) + ((y * z) / (t * t_2));
	tmp = 0.0;
	if (t_3 <= -1e-294)
		tmp = t_4;
	elseif (t_3 <= 0.0)
		tmp = (z / b) + ((t * (x / b)) / y);
	elseif (t_3 <= 1e+283)
		tmp = t_4;
	elseif (t_3 <= Inf)
		tmp = y * (z / ((y * b) + (t * (a + 1.0))));
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]}, Block[{t$95$2 = N[(1.0 + N[(a + t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(x / t$95$2), $MachinePrecision] + N[(N[(y * z), $MachinePrecision] / N[(t * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, -1e-294], t$95$4, If[LessEqual[t$95$3, 0.0], N[(N[(z / b), $MachinePrecision] + N[(N[(t * N[(x / b), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 1e+283], t$95$4, If[LessEqual[t$95$3, Infinity], N[(y * N[(z / N[(N[(y * b), $MachinePrecision] + N[(t * N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -1.00000000000000002e-294 or 0.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 9.99999999999999955e282

   1. Initial program 96.6%

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

      1. associate-/l* 92.1%

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

      2. associate-/l* 89.1%

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

   3. Simplified 89.1%

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

   5. Taylor expanded in x around 0 97.8%

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

   if -1.00000000000000002e-294 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 0.0

   1. Initial program 42.5%

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

      1. associate-/l* 44.6%

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

      2. associate-/l* 67.8%

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

   3. Simplified 67.8%

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

   5. Taylor expanded in b around inf 46.2%

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

   6. Taylor expanded in z around inf 63.6%

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

   7. Taylor expanded in z around 0 61.9%

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

      1. associate-/r* 71.0%

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

      2. associate-/l* 80.5%

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

      3. associate-*l/ 78.1%

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

      4. *-commutative 78.1%

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

      5. associate-*r/ 80.5%

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

   9. Simplified 80.5%

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

   if 9.99999999999999955e282 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < +inf.0

   1. Initial program 35.4%

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

      1. associate-/l* 64.5%

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

      2. associate-/l* 64.5%

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

   3. Simplified 64.5%

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

   5. Taylor expanded in x around 0 58.4%

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

      1. associate-/l* 87.7%

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

      2. +-commutative 87.7%

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

      3. associate-*l/ 87.7%

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

      4. *-commutative 87.7%

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

      5. fma-undefine 87.7%

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

   7. Simplified 87.7%

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

   8. Taylor expanded in t around 0 87.7%

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

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

   1. Initial program 0.0%

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

      1. associate-/l* 0.2%

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

      2. associate-/l* 8.2%

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

   3. Simplified 8.2%

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

   5. Taylor expanded in y around inf 97.5%

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

4. Final simplification 94.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -1 \cdot 10^{-294}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)} + \frac{y \cdot z}{t \cdot \left(1 + \left(a + \frac{y \cdot b}{t}\right)\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 0:\\ \;\;\;\;\frac{z}{b} + \frac{t \cdot \frac{x}{b}}{y}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 10^{+283}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)} + \frac{y \cdot z}{t \cdot \left(1 + \left(a + \frac{y \cdot b}{t}\right)\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq \infty:\\ \;\;\;\;y \cdot \frac{z}{y \cdot b + t \cdot \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 76.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + \frac{y}{\frac{t}{b}}}\\ t_2 := \frac{z}{b} + \frac{t \cdot \frac{x}{b}}{y}\\ \mathbf{if}\;y \leq -5.4 \cdot 10^{+106}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -1 \cdot 10^{-98}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-266}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+180}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (* y (/ z t))) (+ (+ a 1.0) (/ y (/ t b)))))
        (t_2 (+ (/ z b) (/ (* t (/ x b)) y))))
   (if (<= y -5.4e+106)
     t_2
     (if (<= y -1e-98)
       t_1
       (if (<= y 9.5e-266)
         (/ x (+ 1.0 (+ a (/ (* y b) t))))
         (if (<= y 2.4e+180) 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) + (y / (t / b)));
	double t_2 = (z / b) + ((t * (x / b)) / y);
	double tmp;
	if (y <= -5.4e+106) {
		tmp = t_2;
	} else if (y <= -1e-98) {
		tmp = t_1;
	} else if (y <= 9.5e-266) {
		tmp = x / (1.0 + (a + ((y * b) / t)));
	} else if (y <= 2.4e+180) {
		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) + (y / (t / b)))
    t_2 = (z / b) + ((t * (x / b)) / y)
    if (y <= (-5.4d+106)) then
        tmp = t_2
    else if (y <= (-1d-98)) then
        tmp = t_1
    else if (y <= 9.5d-266) then
        tmp = x / (1.0d0 + (a + ((y * b) / t)))
    else if (y <= 2.4d+180) 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) + (y / (t / b)));
	double t_2 = (z / b) + ((t * (x / b)) / y);
	double tmp;
	if (y <= -5.4e+106) {
		tmp = t_2;
	} else if (y <= -1e-98) {
		tmp = t_1;
	} else if (y <= 9.5e-266) {
		tmp = x / (1.0 + (a + ((y * b) / t)));
	} else if (y <= 2.4e+180) {
		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) + (y / (t / b)))
	t_2 = (z / b) + ((t * (x / b)) / y)
	tmp = 0
	if y <= -5.4e+106:
		tmp = t_2
	elif y <= -1e-98:
		tmp = t_1
	elif y <= 9.5e-266:
		tmp = x / (1.0 + (a + ((y * b) / t)))
	elif y <= 2.4e+180:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(Float64(a + 1.0) + Float64(y / Float64(t / b))))
	t_2 = Float64(Float64(z / b) + Float64(Float64(t * Float64(x / b)) / y))
	tmp = 0.0
	if (y <= -5.4e+106)
		tmp = t_2;
	elseif (y <= -1e-98)
		tmp = t_1;
	elseif (y <= 9.5e-266)
		tmp = Float64(x / Float64(1.0 + Float64(a + Float64(Float64(y * b) / t))));
	elseif (y <= 2.4e+180)
		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) + (y / (t / b)));
	t_2 = (z / b) + ((t * (x / b)) / y);
	tmp = 0.0;
	if (y <= -5.4e+106)
		tmp = t_2;
	elseif (y <= -1e-98)
		tmp = t_1;
	elseif (y <= 9.5e-266)
		tmp = x / (1.0 + (a + ((y * b) / t)));
	elseif (y <= 2.4e+180)
		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[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(y / N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z / b), $MachinePrecision] + N[(N[(t * N[(x / b), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.4e+106], t$95$2, If[LessEqual[y, -1e-98], t$95$1, If[LessEqual[y, 9.5e-266], N[(x / N[(1.0 + N[(a + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.4e+180], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.40000000000000012e106 or 2.3999999999999998e180 < y

   1. Initial program 31.6%

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

      1. associate-/l* 35.2%

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

      2. associate-/l* 48.4%

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

   3. Simplified 48.4%

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

   5. Taylor expanded in b around inf 24.9%

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

   6. Taylor expanded in z around inf 75.6%

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

   7. Taylor expanded in z around 0 72.2%

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

      1. associate-/r* 75.7%

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

      2. associate-/l* 78.3%

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

      3. associate-*l/ 77.0%

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

      4. *-commutative 77.0%

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

      5. associate-*r/ 78.3%

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

   9. Simplified 78.3%

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

   if -5.40000000000000012e106 < y < -9.99999999999999939e-99 or 9.49999999999999951e-266 < y < 2.3999999999999998e180

   1. Initial program 83.8%

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

      1. associate-/l* 85.3%

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

      2. associate-/l* 85.3%

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

   3. Simplified 85.3%

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

      1. clear-num 85.3%

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

      2. un-div-inv 85.3%

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

   6. Applied egg-rr 85.3%

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

   if -9.99999999999999939e-99 < y < 9.49999999999999951e-266

   1. Initial program 97.4%

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

      1. associate-/l* 84.4%

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

      2. associate-/l* 78.6%

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

   3. Simplified 78.6%

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

   5. Taylor expanded in x around inf 87.5%

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

4. Final simplification 83.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.4 \cdot 10^{+106}:\\ \;\;\;\;\frac{z}{b} + \frac{t \cdot \frac{x}{b}}{y}\\ \mathbf{elif}\;y \leq -1 \cdot 10^{-98}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + \frac{y}{\frac{t}{b}}}\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-266}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+180}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + \frac{y}{\frac{t}{b}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{t \cdot \frac{x}{b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 76.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ t_2 := \frac{z}{b} + \frac{t \cdot \frac{x}{b}}{y}\\ \mathbf{if}\;y \leq -1.45 \cdot 10^{+104}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{-98}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{-267}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+180}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (* y (/ z t))) (+ (+ a 1.0) (* y (/ b t)))))
        (t_2 (+ (/ z b) (/ (* t (/ x b)) y))))
   (if (<= y -1.45e+104)
     t_2
     (if (<= y -1.35e-98)
       t_1
       (if (<= y 4.3e-267)
         (/ x (+ 1.0 (+ a (/ (* y b) t))))
         (if (<= y 2e+180) 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) + (y * (b / t)));
	double t_2 = (z / b) + ((t * (x / b)) / y);
	double tmp;
	if (y <= -1.45e+104) {
		tmp = t_2;
	} else if (y <= -1.35e-98) {
		tmp = t_1;
	} else if (y <= 4.3e-267) {
		tmp = x / (1.0 + (a + ((y * b) / t)));
	} else if (y <= 2e+180) {
		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) + (y * (b / t)))
    t_2 = (z / b) + ((t * (x / b)) / y)
    if (y <= (-1.45d+104)) then
        tmp = t_2
    else if (y <= (-1.35d-98)) then
        tmp = t_1
    else if (y <= 4.3d-267) then
        tmp = x / (1.0d0 + (a + ((y * b) / t)))
    else if (y <= 2d+180) 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) + (y * (b / t)));
	double t_2 = (z / b) + ((t * (x / b)) / y);
	double tmp;
	if (y <= -1.45e+104) {
		tmp = t_2;
	} else if (y <= -1.35e-98) {
		tmp = t_1;
	} else if (y <= 4.3e-267) {
		tmp = x / (1.0 + (a + ((y * b) / t)));
	} else if (y <= 2e+180) {
		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) + (y * (b / t)))
	t_2 = (z / b) + ((t * (x / b)) / y)
	tmp = 0
	if y <= -1.45e+104:
		tmp = t_2
	elif y <= -1.35e-98:
		tmp = t_1
	elif y <= 4.3e-267:
		tmp = x / (1.0 + (a + ((y * b) / t)))
	elif y <= 2e+180:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(Float64(a + 1.0) + Float64(y * Float64(b / t))))
	t_2 = Float64(Float64(z / b) + Float64(Float64(t * Float64(x / b)) / y))
	tmp = 0.0
	if (y <= -1.45e+104)
		tmp = t_2;
	elseif (y <= -1.35e-98)
		tmp = t_1;
	elseif (y <= 4.3e-267)
		tmp = Float64(x / Float64(1.0 + Float64(a + Float64(Float64(y * b) / t))));
	elseif (y <= 2e+180)
		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) + (y * (b / t)));
	t_2 = (z / b) + ((t * (x / b)) / y);
	tmp = 0.0;
	if (y <= -1.45e+104)
		tmp = t_2;
	elseif (y <= -1.35e-98)
		tmp = t_1;
	elseif (y <= 4.3e-267)
		tmp = x / (1.0 + (a + ((y * b) / t)));
	elseif (y <= 2e+180)
		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[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z / b), $MachinePrecision] + N[(N[(t * N[(x / b), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.45e+104], t$95$2, If[LessEqual[y, -1.35e-98], t$95$1, If[LessEqual[y, 4.3e-267], N[(x / N[(1.0 + N[(a + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2e+180], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.4499999999999999e104 or 2e180 < y

   1. Initial program 32.4%

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

      1. associate-/l* 36.0%

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

      2. associate-/l* 49.0%

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

   3. Simplified 49.0%

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

   5. Taylor expanded in b around inf 25.8%

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

   6. Taylor expanded in z around inf 75.9%

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

   7. Taylor expanded in z around 0 72.5%

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

      1. associate-/r* 76.0%

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

      2. associate-/l* 78.6%

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

      3. associate-*l/ 77.3%

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

      4. *-commutative 77.3%

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

      5. associate-*r/ 78.6%

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

   9. Simplified 78.6%

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

   if -1.4499999999999999e104 < y < -1.3499999999999999e-98 or 4.2999999999999996e-267 < y < 2e180

   1. Initial program 83.7%

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

      1. associate-/l* 85.2%

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

      2. associate-/l* 85.2%

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

   3. Simplified 85.2%

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

   if -1.3499999999999999e-98 < y < 4.2999999999999996e-267

   1. Initial program 97.4%

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

      1. associate-/l* 84.4%

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

      2. associate-/l* 78.6%

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

   3. Simplified 78.6%

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

   5. Taylor expanded in x around inf 87.5%

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

4. Final simplification 83.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{+104}:\\ \;\;\;\;\frac{z}{b} + \frac{t \cdot \frac{x}{b}}{y}\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{-98}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{-267}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+180}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{t \cdot \frac{x}{b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 67.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{b} + \frac{t \cdot \frac{x}{b}}{y}\\ t_2 := t \cdot \left(a + 1\right)\\ \mathbf{if}\;y \leq -4.2 \cdot 10^{+110}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-94}:\\ \;\;\;\;y \cdot \frac{z}{y \cdot b + t\_2}\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{-214}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-5}:\\ \;\;\;\;\frac{x}{a + 1} + \frac{y \cdot z}{t\_2}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+26}:\\ \;\;\;\;\frac{x}{1 + \left(a + y \cdot \frac{b}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (/ z b) (/ (* t (/ x b)) y))) (t_2 (* t (+ a 1.0))))
   (if (<= y -4.2e+110)
     t_1
     (if (<= y -3.5e-94)
       (* y (/ z (+ (* y b) t_2)))
       (if (<= y -1.15e-214)
         (/ x (+ 1.0 (+ a (/ (* y b) t))))
         (if (<= y 2.5e-5)
           (+ (/ x (+ a 1.0)) (/ (* y z) t_2))
           (if (<= y 2.5e+26) (/ x (+ 1.0 (+ a (* y (/ b t))))) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z / b) + ((t * (x / b)) / y);
	double t_2 = t * (a + 1.0);
	double tmp;
	if (y <= -4.2e+110) {
		tmp = t_1;
	} else if (y <= -3.5e-94) {
		tmp = y * (z / ((y * b) + t_2));
	} else if (y <= -1.15e-214) {
		tmp = x / (1.0 + (a + ((y * b) / t)));
	} else if (y <= 2.5e-5) {
		tmp = (x / (a + 1.0)) + ((y * z) / t_2);
	} else if (y <= 2.5e+26) {
		tmp = x / (1.0 + (a + (y * (b / t))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (z / b) + ((t * (x / b)) / y)
    t_2 = t * (a + 1.0d0)
    if (y <= (-4.2d+110)) then
        tmp = t_1
    else if (y <= (-3.5d-94)) then
        tmp = y * (z / ((y * b) + t_2))
    else if (y <= (-1.15d-214)) then
        tmp = x / (1.0d0 + (a + ((y * b) / t)))
    else if (y <= 2.5d-5) then
        tmp = (x / (a + 1.0d0)) + ((y * z) / t_2)
    else if (y <= 2.5d+26) then
        tmp = x / (1.0d0 + (a + (y * (b / t))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z / b) + ((t * (x / b)) / y);
	double t_2 = t * (a + 1.0);
	double tmp;
	if (y <= -4.2e+110) {
		tmp = t_1;
	} else if (y <= -3.5e-94) {
		tmp = y * (z / ((y * b) + t_2));
	} else if (y <= -1.15e-214) {
		tmp = x / (1.0 + (a + ((y * b) / t)));
	} else if (y <= 2.5e-5) {
		tmp = (x / (a + 1.0)) + ((y * z) / t_2);
	} else if (y <= 2.5e+26) {
		tmp = x / (1.0 + (a + (y * (b / t))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z / b) + ((t * (x / b)) / y)
	t_2 = t * (a + 1.0)
	tmp = 0
	if y <= -4.2e+110:
		tmp = t_1
	elif y <= -3.5e-94:
		tmp = y * (z / ((y * b) + t_2))
	elif y <= -1.15e-214:
		tmp = x / (1.0 + (a + ((y * b) / t)))
	elif y <= 2.5e-5:
		tmp = (x / (a + 1.0)) + ((y * z) / t_2)
	elif y <= 2.5e+26:
		tmp = x / (1.0 + (a + (y * (b / t))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z / b) + Float64(Float64(t * Float64(x / b)) / y))
	t_2 = Float64(t * Float64(a + 1.0))
	tmp = 0.0
	if (y <= -4.2e+110)
		tmp = t_1;
	elseif (y <= -3.5e-94)
		tmp = Float64(y * Float64(z / Float64(Float64(y * b) + t_2)));
	elseif (y <= -1.15e-214)
		tmp = Float64(x / Float64(1.0 + Float64(a + Float64(Float64(y * b) / t))));
	elseif (y <= 2.5e-5)
		tmp = Float64(Float64(x / Float64(a + 1.0)) + Float64(Float64(y * z) / t_2));
	elseif (y <= 2.5e+26)
		tmp = Float64(x / Float64(1.0 + Float64(a + Float64(y * Float64(b / t)))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z / b) + ((t * (x / b)) / y);
	t_2 = t * (a + 1.0);
	tmp = 0.0;
	if (y <= -4.2e+110)
		tmp = t_1;
	elseif (y <= -3.5e-94)
		tmp = y * (z / ((y * b) + t_2));
	elseif (y <= -1.15e-214)
		tmp = x / (1.0 + (a + ((y * b) / t)));
	elseif (y <= 2.5e-5)
		tmp = (x / (a + 1.0)) + ((y * z) / t_2);
	elseif (y <= 2.5e+26)
		tmp = x / (1.0 + (a + (y * (b / t))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z / b), $MachinePrecision] + N[(N[(t * N[(x / b), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(a + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.2e+110], t$95$1, If[LessEqual[y, -3.5e-94], N[(y * N[(z / N[(N[(y * b), $MachinePrecision] + t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.15e-214], N[(x / N[(1.0 + N[(a + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.5e-5], N[(N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision] + N[(N[(y * z), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.5e+26], N[(x / N[(1.0 + N[(a + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -4.2000000000000003e110 or 2.5e26 < y

   1. Initial program 42.9%

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

      1. associate-/l* 46.5%

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

      2. associate-/l* 58.2%

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

   3. Simplified 58.2%

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

   5. Taylor expanded in b around inf 29.5%

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

   6. Taylor expanded in z around inf 69.6%

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

   7. Taylor expanded in z around 0 68.1%

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

      1. associate-/r* 70.7%

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

      2. associate-/l* 73.6%

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

      3. associate-*l/ 71.8%

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

      4. *-commutative 71.8%

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

      5. associate-*r/ 73.6%

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

   9. Simplified 73.6%

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

   if -4.2000000000000003e110 < y < -3.49999999999999998e-94

   1. Initial program 79.0%

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

      1. associate-/l* 79.0%

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

      2. associate-/l* 76.6%

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

   3. Simplified 76.6%

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

   5. Taylor expanded in x around 0 56.5%

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

      1. associate-/l* 58.9%

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

      2. +-commutative 58.9%

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

      3. associate-*l/ 56.4%

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

      4. *-commutative 56.4%

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

      5. fma-undefine 56.4%

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

   7. Simplified 56.4%

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

   8. Taylor expanded in t around 0 70.3%

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

   if -3.49999999999999998e-94 < y < -1.15000000000000005e-214

   1. Initial program 95.5%

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

      1. associate-/l* 87.7%

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

      2. associate-/l* 83.8%

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

   3. Simplified 83.8%

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

   5. Taylor expanded in x around inf 94.6%

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

   if -1.15000000000000005e-214 < y < 2.50000000000000012e-5

   1. Initial program 94.5%

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

      1. associate-/l* 89.5%

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

      2. associate-/l* 85.5%

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

   3. Simplified 85.5%

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

   5. Taylor expanded in y around 0 76.3%

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

   6. Taylor expanded in x around 0 82.7%

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

   if 2.50000000000000012e-5 < y < 2.5e26

   1. Initial program 82.3%

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

      1. associate-/l* 82.5%

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

      2. associate-/l* 82.5%

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

   3. Simplified 82.5%

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

      1. clear-num 82.5%

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

      2. un-div-inv 82.5%

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

   6. Applied egg-rr 82.5%

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

      1. clear-num 82.5%

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

      2. un-div-inv 82.2%

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

   8. Applied egg-rr 82.2%

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

   9. Taylor expanded in x around inf 64.8%

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

       1. associate-*l/ 64.8%

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

       2. *-commutative 64.8%

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

   11. Simplified 64.8%

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

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+110}:\\ \;\;\;\;\frac{z}{b} + \frac{t \cdot \frac{x}{b}}{y}\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-94}:\\ \;\;\;\;y \cdot \frac{z}{y \cdot b + t \cdot \left(a + 1\right)}\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{-214}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-5}:\\ \;\;\;\;\frac{x}{a + 1} + \frac{y \cdot z}{t \cdot \left(a + 1\right)}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+26}:\\ \;\;\;\;\frac{x}{1 + \left(a + y \cdot \frac{b}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{t \cdot \frac{x}{b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 65.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z}{y \cdot b + t \cdot \left(a + 1\right)}\\ t_2 := \frac{z}{b} + \frac{t \cdot \frac{x}{b}}{y}\\ \mathbf{if}\;y \leq -1.1 \cdot 10^{+110}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -1.65 \cdot 10^{-96}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{-64}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-8}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+26}:\\ \;\;\;\;\frac{x}{1 + \left(a + y \cdot \frac{b}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (/ z (+ (* y b) (* t (+ a 1.0))))))
        (t_2 (+ (/ z b) (/ (* t (/ x b)) y))))
   (if (<= y -1.1e+110)
     t_2
     (if (<= y -1.65e-96)
       t_1
       (if (<= y 4.7e-64)
         (/ x (+ 1.0 (+ a (/ (* y b) t))))
         (if (<= y 6e-8)
           t_1
           (if (<= y 1.55e+26) (/ x (+ 1.0 (+ a (* y (/ b t))))) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (z / ((y * b) + (t * (a + 1.0))));
	double t_2 = (z / b) + ((t * (x / b)) / y);
	double tmp;
	if (y <= -1.1e+110) {
		tmp = t_2;
	} else if (y <= -1.65e-96) {
		tmp = t_1;
	} else if (y <= 4.7e-64) {
		tmp = x / (1.0 + (a + ((y * b) / t)));
	} else if (y <= 6e-8) {
		tmp = t_1;
	} else if (y <= 1.55e+26) {
		tmp = x / (1.0 + (a + (y * (b / t))));
	} 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 = y * (z / ((y * b) + (t * (a + 1.0d0))))
    t_2 = (z / b) + ((t * (x / b)) / y)
    if (y <= (-1.1d+110)) then
        tmp = t_2
    else if (y <= (-1.65d-96)) then
        tmp = t_1
    else if (y <= 4.7d-64) then
        tmp = x / (1.0d0 + (a + ((y * b) / t)))
    else if (y <= 6d-8) then
        tmp = t_1
    else if (y <= 1.55d+26) then
        tmp = x / (1.0d0 + (a + (y * (b / t))))
    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 = y * (z / ((y * b) + (t * (a + 1.0))));
	double t_2 = (z / b) + ((t * (x / b)) / y);
	double tmp;
	if (y <= -1.1e+110) {
		tmp = t_2;
	} else if (y <= -1.65e-96) {
		tmp = t_1;
	} else if (y <= 4.7e-64) {
		tmp = x / (1.0 + (a + ((y * b) / t)));
	} else if (y <= 6e-8) {
		tmp = t_1;
	} else if (y <= 1.55e+26) {
		tmp = x / (1.0 + (a + (y * (b / t))));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (z / ((y * b) + (t * (a + 1.0))))
	t_2 = (z / b) + ((t * (x / b)) / y)
	tmp = 0
	if y <= -1.1e+110:
		tmp = t_2
	elif y <= -1.65e-96:
		tmp = t_1
	elif y <= 4.7e-64:
		tmp = x / (1.0 + (a + ((y * b) / t)))
	elif y <= 6e-8:
		tmp = t_1
	elif y <= 1.55e+26:
		tmp = x / (1.0 + (a + (y * (b / t))))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(z / Float64(Float64(y * b) + Float64(t * Float64(a + 1.0)))))
	t_2 = Float64(Float64(z / b) + Float64(Float64(t * Float64(x / b)) / y))
	tmp = 0.0
	if (y <= -1.1e+110)
		tmp = t_2;
	elseif (y <= -1.65e-96)
		tmp = t_1;
	elseif (y <= 4.7e-64)
		tmp = Float64(x / Float64(1.0 + Float64(a + Float64(Float64(y * b) / t))));
	elseif (y <= 6e-8)
		tmp = t_1;
	elseif (y <= 1.55e+26)
		tmp = Float64(x / Float64(1.0 + Float64(a + Float64(y * Float64(b / t)))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (z / ((y * b) + (t * (a + 1.0))));
	t_2 = (z / b) + ((t * (x / b)) / y);
	tmp = 0.0;
	if (y <= -1.1e+110)
		tmp = t_2;
	elseif (y <= -1.65e-96)
		tmp = t_1;
	elseif (y <= 4.7e-64)
		tmp = x / (1.0 + (a + ((y * b) / t)));
	elseif (y <= 6e-8)
		tmp = t_1;
	elseif (y <= 1.55e+26)
		tmp = x / (1.0 + (a + (y * (b / t))));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(z / N[(N[(y * b), $MachinePrecision] + N[(t * N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z / b), $MachinePrecision] + N[(N[(t * N[(x / b), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.1e+110], t$95$2, If[LessEqual[y, -1.65e-96], t$95$1, If[LessEqual[y, 4.7e-64], N[(x / N[(1.0 + N[(a + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6e-8], t$95$1, If[LessEqual[y, 1.55e+26], N[(x / N[(1.0 + N[(a + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.09999999999999996e110 or 1.55e26 < y

   1. Initial program 42.9%

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

      1. associate-/l* 46.5%

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

      2. associate-/l* 58.2%

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

   3. Simplified 58.2%

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

   5. Taylor expanded in b around inf 29.5%

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

   6. Taylor expanded in z around inf 69.6%

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

   7. Taylor expanded in z around 0 68.1%

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

      1. associate-/r* 70.7%

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

      2. associate-/l* 73.6%

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

      3. associate-*l/ 71.8%

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

      4. *-commutative 71.8%

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

      5. associate-*r/ 73.6%

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

   9. Simplified 73.6%

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

   if -1.09999999999999996e110 < y < -1.64999999999999995e-96 or 4.6999999999999998e-64 < y < 5.99999999999999946e-8

   1. Initial program 76.5%

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

      1. associate-/l* 76.7%

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

      2. associate-/l* 74.7%

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

   3. Simplified 74.7%

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

   5. Taylor expanded in x around 0 58.6%

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

      1. associate-/l* 60.7%

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

      2. +-commutative 60.7%

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

      3. associate-*l/ 58.6%

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

      4. *-commutative 58.6%

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

      5. fma-undefine 58.6%

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

   7. Simplified 58.6%

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

   8. Taylor expanded in t around 0 72.0%

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

   if -1.64999999999999995e-96 < y < 4.6999999999999998e-64

   1. Initial program 97.5%

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

      1. associate-/l* 91.2%

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

      2. associate-/l* 86.9%

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

   3. Simplified 86.9%

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

   5. Taylor expanded in x around inf 85.6%

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

   if 5.99999999999999946e-8 < y < 1.55e26

   1. Initial program 82.3%

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

      1. associate-/l* 82.5%

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

      2. associate-/l* 82.5%

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

   3. Simplified 82.5%

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

      1. clear-num 82.5%

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

      2. un-div-inv 82.5%

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

   6. Applied egg-rr 82.5%

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

      1. clear-num 82.5%

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

      2. un-div-inv 82.2%

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

   8. Applied egg-rr 82.2%

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

   9. Taylor expanded in x around inf 64.8%

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

       1. associate-*l/ 64.8%

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

       2. *-commutative 64.8%

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

   11. Simplified 64.8%

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

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+110}:\\ \;\;\;\;\frac{z}{b} + \frac{t \cdot \frac{x}{b}}{y}\\ \mathbf{elif}\;y \leq -1.65 \cdot 10^{-96}:\\ \;\;\;\;y \cdot \frac{z}{y \cdot b + t \cdot \left(a + 1\right)}\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{-64}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-8}:\\ \;\;\;\;y \cdot \frac{z}{y \cdot b + t \cdot \left(a + 1\right)}\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+26}:\\ \;\;\;\;\frac{x}{1 + \left(a + y \cdot \frac{b}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{t \cdot \frac{x}{b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 58.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{b} + \frac{t \cdot \frac{x}{b}}{y}\\ \mathbf{if}\;y \leq -1 \cdot 10^{+82}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -5000:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a}\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{-116} \lor \neg \left(y \leq 2.3 \cdot 10^{+27}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (/ z b) (/ (* t (/ x b)) y))))
   (if (<= y -1e+82)
     t_1
     (if (<= y -5000.0)
       (/ (+ x (* y (/ z t))) a)
       (if (or (<= y -1.45e-116) (not (<= y 2.3e+27))) t_1 (/ x (+ a 1.0)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z / b) + ((t * (x / b)) / y);
	double tmp;
	if (y <= -1e+82) {
		tmp = t_1;
	} else if (y <= -5000.0) {
		tmp = (x + (y * (z / t))) / a;
	} else if ((y <= -1.45e-116) || !(y <= 2.3e+27)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = (z / b) + ((t * (x / b)) / y)
    if (y <= (-1d+82)) then
        tmp = t_1
    else if (y <= (-5000.0d0)) then
        tmp = (x + (y * (z / t))) / a
    else if ((y <= (-1.45d-116)) .or. (.not. (y <= 2.3d+27))) then
        tmp = t_1
    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 t_1 = (z / b) + ((t * (x / b)) / y);
	double tmp;
	if (y <= -1e+82) {
		tmp = t_1;
	} else if (y <= -5000.0) {
		tmp = (x + (y * (z / t))) / a;
	} else if ((y <= -1.45e-116) || !(y <= 2.3e+27)) {
		tmp = t_1;
	} else {
		tmp = x / (a + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z / b) + ((t * (x / b)) / y)
	tmp = 0
	if y <= -1e+82:
		tmp = t_1
	elif y <= -5000.0:
		tmp = (x + (y * (z / t))) / a
	elif (y <= -1.45e-116) or not (y <= 2.3e+27):
		tmp = t_1
	else:
		tmp = x / (a + 1.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z / b) + Float64(Float64(t * Float64(x / b)) / y))
	tmp = 0.0
	if (y <= -1e+82)
		tmp = t_1;
	elseif (y <= -5000.0)
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / a);
	elseif ((y <= -1.45e-116) || !(y <= 2.3e+27))
		tmp = t_1;
	else
		tmp = Float64(x / Float64(a + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z / b) + ((t * (x / b)) / y);
	tmp = 0.0;
	if (y <= -1e+82)
		tmp = t_1;
	elseif (y <= -5000.0)
		tmp = (x + (y * (z / t))) / a;
	elseif ((y <= -1.45e-116) || ~((y <= 2.3e+27)))
		tmp = t_1;
	else
		tmp = x / (a + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z / b), $MachinePrecision] + N[(N[(t * N[(x / b), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1e+82], t$95$1, If[LessEqual[y, -5000.0], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[Or[LessEqual[y, -1.45e-116], N[Not[LessEqual[y, 2.3e+27]], $MachinePrecision]], t$95$1, N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.9999999999999996e81 or -5e3 < y < -1.4499999999999999e-116 or 2.3000000000000001e27 < y

   1. Initial program 51.5%

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

      1. associate-/l* 54.4%

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

      2. associate-/l* 63.0%

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

   3. Simplified 63.0%

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

   5. Taylor expanded in b around inf 35.2%

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

   6. Taylor expanded in z around inf 66.9%

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

   7. Taylor expanded in z around 0 66.6%

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

      1. associate-/r* 68.8%

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

      2. associate-/l* 71.0%

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

      3. associate-*l/ 69.6%

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

      4. *-commutative 69.6%

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

      5. associate-*r/ 71.0%

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

   9. Simplified 71.0%

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

   if -9.9999999999999996e81 < y < -5e3

   1. Initial program 72.7%

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

      1. associate-/l* 72.9%

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

      2. associate-/l* 72.8%

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

   3. Simplified 72.8%

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

   5. Taylor expanded in a around inf 52.2%

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

   if -1.4499999999999999e-116 < y < 2.3000000000000001e27

   1. Initial program 93.3%

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

      1. associate-/l* 88.0%

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

      2. associate-/l* 84.4%

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

   3. Simplified 84.4%

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

   5. Taylor expanded in y around 0 66.7%

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

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+82}:\\ \;\;\;\;\frac{z}{b} + \frac{t \cdot \frac{x}{b}}{y}\\ \mathbf{elif}\;y \leq -5000:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a}\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{-116} \lor \neg \left(y \leq 2.3 \cdot 10^{+27}\right):\\ \;\;\;\;\frac{z}{b} + \frac{t \cdot \frac{x}{b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 62.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{b} + \frac{t \cdot \frac{x}{b}}{y}\\ \mathbf{if}\;y \leq -8.5 \cdot 10^{+77}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -13000:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a}\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-94}:\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot t}{y \cdot b}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+27}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (/ z b) (/ (* t (/ x b)) y))))
   (if (<= y -8.5e+77)
     t_1
     (if (<= y -13000.0)
       (/ (+ x (* y (/ z t))) a)
       (if (<= y -3.5e-94)
         (+ (/ z b) (/ (* x t) (* y b)))
         (if (<= y 1.15e+27) (/ x (+ 1.0 (+ a (/ (* y b) t)))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z / b) + ((t * (x / b)) / y);
	double tmp;
	if (y <= -8.5e+77) {
		tmp = t_1;
	} else if (y <= -13000.0) {
		tmp = (x + (y * (z / t))) / a;
	} else if (y <= -3.5e-94) {
		tmp = (z / b) + ((x * t) / (y * b));
	} else if (y <= 1.15e+27) {
		tmp = x / (1.0 + (a + ((y * b) / t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z / b) + ((t * (x / b)) / y)
    if (y <= (-8.5d+77)) then
        tmp = t_1
    else if (y <= (-13000.0d0)) then
        tmp = (x + (y * (z / t))) / a
    else if (y <= (-3.5d-94)) then
        tmp = (z / b) + ((x * t) / (y * b))
    else if (y <= 1.15d+27) then
        tmp = x / (1.0d0 + (a + ((y * b) / t)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z / b) + ((t * (x / b)) / y);
	double tmp;
	if (y <= -8.5e+77) {
		tmp = t_1;
	} else if (y <= -13000.0) {
		tmp = (x + (y * (z / t))) / a;
	} else if (y <= -3.5e-94) {
		tmp = (z / b) + ((x * t) / (y * b));
	} else if (y <= 1.15e+27) {
		tmp = x / (1.0 + (a + ((y * b) / t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z / b) + ((t * (x / b)) / y)
	tmp = 0
	if y <= -8.5e+77:
		tmp = t_1
	elif y <= -13000.0:
		tmp = (x + (y * (z / t))) / a
	elif y <= -3.5e-94:
		tmp = (z / b) + ((x * t) / (y * b))
	elif y <= 1.15e+27:
		tmp = x / (1.0 + (a + ((y * b) / t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z / b) + Float64(Float64(t * Float64(x / b)) / y))
	tmp = 0.0
	if (y <= -8.5e+77)
		tmp = t_1;
	elseif (y <= -13000.0)
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / a);
	elseif (y <= -3.5e-94)
		tmp = Float64(Float64(z / b) + Float64(Float64(x * t) / Float64(y * b)));
	elseif (y <= 1.15e+27)
		tmp = Float64(x / Float64(1.0 + Float64(a + Float64(Float64(y * b) / t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z / b) + ((t * (x / b)) / y);
	tmp = 0.0;
	if (y <= -8.5e+77)
		tmp = t_1;
	elseif (y <= -13000.0)
		tmp = (x + (y * (z / t))) / a;
	elseif (y <= -3.5e-94)
		tmp = (z / b) + ((x * t) / (y * b));
	elseif (y <= 1.15e+27)
		tmp = x / (1.0 + (a + ((y * b) / t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z / b), $MachinePrecision] + N[(N[(t * N[(x / b), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -8.5e+77], t$95$1, If[LessEqual[y, -13000.0], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[y, -3.5e-94], N[(N[(z / b), $MachinePrecision] + N[(N[(x * t), $MachinePrecision] / N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.15e+27], N[(x / N[(1.0 + N[(a + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -8.50000000000000018e77 or 1.15e27 < y

   1. Initial program 45.7%

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

      1. associate-/l* 48.9%

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

      2. associate-/l* 59.7%

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

   3. Simplified 59.7%

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

   5. Taylor expanded in b around inf 31.3%

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

   6. Taylor expanded in z around inf 69.1%

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

   7. Taylor expanded in z around 0 67.7%

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

      1. associate-/r* 70.1%

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

      2. associate-/l* 72.8%

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

      3. associate-*l/ 71.1%

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

      4. *-commutative 71.1%

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

      5. associate-*r/ 72.8%

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

   9. Simplified 72.8%

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

   if -8.50000000000000018e77 < y < -13000

   1. Initial program 72.7%

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

      1. associate-/l* 72.9%

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

      2. associate-/l* 72.8%

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

   3. Simplified 72.8%

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

   5. Taylor expanded in a around inf 52.2%

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

   if -13000 < y < -3.49999999999999998e-94

   1. Initial program 87.0%

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

      1. associate-/l* 86.8%

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

      2. associate-/l* 80.5%

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

   3. Simplified 80.5%

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

   5. Taylor expanded in b around inf 58.1%

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

   6. Taylor expanded in t around 0 58.4%

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

   if -3.49999999999999998e-94 < y < 1.15e27

   1. Initial program 93.5%

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

      1. associate-/l* 88.4%

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

      2. associate-/l* 84.8%

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

   3. Simplified 84.8%

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

   5. Taylor expanded in x around inf 79.3%

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

4. Final simplification 73.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{+77}:\\ \;\;\;\;\frac{z}{b} + \frac{t \cdot \frac{x}{b}}{y}\\ \mathbf{elif}\;y \leq -13000:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a}\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-94}:\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot t}{y \cdot b}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+27}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{t \cdot \frac{x}{b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 66.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{b} + \frac{t \cdot \frac{x}{b}}{y}\\ \mathbf{if}\;y \leq -1.65 \cdot 10^{+98}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-96}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+27}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (/ z b) (/ (* t (/ x b)) y))))
   (if (<= y -1.65e+98)
     t_1
     (if (<= y -2.1e-96)
       (/ (+ x (* y (/ z t))) (+ a 1.0))
       (if (<= y 2.4e+27) (/ x (+ 1.0 (+ a (/ (* y b) t)))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z / b) + ((t * (x / b)) / y);
	double tmp;
	if (y <= -1.65e+98) {
		tmp = t_1;
	} else if (y <= -2.1e-96) {
		tmp = (x + (y * (z / t))) / (a + 1.0);
	} else if (y <= 2.4e+27) {
		tmp = x / (1.0 + (a + ((y * b) / t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z / b) + ((t * (x / b)) / y)
    if (y <= (-1.65d+98)) then
        tmp = t_1
    else if (y <= (-2.1d-96)) then
        tmp = (x + (y * (z / t))) / (a + 1.0d0)
    else if (y <= 2.4d+27) then
        tmp = x / (1.0d0 + (a + ((y * b) / t)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z / b) + ((t * (x / b)) / y);
	double tmp;
	if (y <= -1.65e+98) {
		tmp = t_1;
	} else if (y <= -2.1e-96) {
		tmp = (x + (y * (z / t))) / (a + 1.0);
	} else if (y <= 2.4e+27) {
		tmp = x / (1.0 + (a + ((y * b) / t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z / b) + ((t * (x / b)) / y)
	tmp = 0
	if y <= -1.65e+98:
		tmp = t_1
	elif y <= -2.1e-96:
		tmp = (x + (y * (z / t))) / (a + 1.0)
	elif y <= 2.4e+27:
		tmp = x / (1.0 + (a + ((y * b) / t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z / b) + Float64(Float64(t * Float64(x / b)) / y))
	tmp = 0.0
	if (y <= -1.65e+98)
		tmp = t_1;
	elseif (y <= -2.1e-96)
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(a + 1.0));
	elseif (y <= 2.4e+27)
		tmp = Float64(x / Float64(1.0 + Float64(a + Float64(Float64(y * b) / t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z / b) + ((t * (x / b)) / y);
	tmp = 0.0;
	if (y <= -1.65e+98)
		tmp = t_1;
	elseif (y <= -2.1e-96)
		tmp = (x + (y * (z / t))) / (a + 1.0);
	elseif (y <= 2.4e+27)
		tmp = x / (1.0 + (a + ((y * b) / t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z / b), $MachinePrecision] + N[(N[(t * N[(x / b), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.65e+98], t$95$1, If[LessEqual[y, -2.1e-96], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.4e+27], N[(x / N[(1.0 + N[(a + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.65000000000000014e98 or 2.39999999999999998e27 < y

   1. Initial program 43.1%

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

      1. associate-/l* 46.6%

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

      2. associate-/l* 58.1%

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

   3. Simplified 58.1%

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

   5. Taylor expanded in b around inf 30.8%

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

   6. Taylor expanded in z around inf 70.2%

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

   7. Taylor expanded in z around 0 68.7%

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

      1. associate-/r* 71.3%

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

      2. associate-/l* 74.1%

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

      3. associate-*l/ 72.3%

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

      4. *-commutative 72.3%

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

      5. associate-*r/ 74.1%

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

   9. Simplified 74.1%

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

   if -1.65000000000000014e98 < y < -2.10000000000000001e-96

   1. Initial program 80.3%

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

      1. associate-/l* 80.3%

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

      2. associate-/l* 77.9%

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

   3. Simplified 77.9%

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

   5. Taylor expanded in y around 0 52.8%

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

   if -2.10000000000000001e-96 < y < 2.39999999999999998e27

   1. Initial program 93.5%

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

      1. associate-/l* 88.4%

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

      2. associate-/l* 84.8%

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

   3. Simplified 84.8%

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

   5. Taylor expanded in x around inf 79.3%

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

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{+98}:\\ \;\;\;\;\frac{z}{b} + \frac{t \cdot \frac{x}{b}}{y}\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-96}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+27}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{t \cdot \frac{x}{b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 55.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+78}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq -3000:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a}\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-94} \lor \neg \left(y \leq 1.2 \cdot 10^{+27}\right):\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -9e+78)
   (/ z b)
   (if (<= y -3000.0)
     (/ (+ x (* y (/ z t))) a)
     (if (or (<= y -3.5e-94) (not (<= y 1.2e+27))) (/ z b) (/ x (+ a 1.0))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -9e+78) {
		tmp = z / b;
	} else if (y <= -3000.0) {
		tmp = (x + (y * (z / t))) / a;
	} else if ((y <= -3.5e-94) || !(y <= 1.2e+27)) {
		tmp = z / b;
	} else {
		tmp = x / (a + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-9d+78)) then
        tmp = z / b
    else if (y <= (-3000.0d0)) then
        tmp = (x + (y * (z / t))) / a
    else if ((y <= (-3.5d-94)) .or. (.not. (y <= 1.2d+27))) then
        tmp = z / b
    else
        tmp = x / (a + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -9e+78) {
		tmp = z / b;
	} else if (y <= -3000.0) {
		tmp = (x + (y * (z / t))) / a;
	} else if ((y <= -3.5e-94) || !(y <= 1.2e+27)) {
		tmp = z / b;
	} else {
		tmp = x / (a + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -9e+78:
		tmp = z / b
	elif y <= -3000.0:
		tmp = (x + (y * (z / t))) / a
	elif (y <= -3.5e-94) or not (y <= 1.2e+27):
		tmp = z / b
	else:
		tmp = x / (a + 1.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -9e+78)
		tmp = Float64(z / b);
	elseif (y <= -3000.0)
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / a);
	elseif ((y <= -3.5e-94) || !(y <= 1.2e+27))
		tmp = Float64(z / b);
	else
		tmp = Float64(x / Float64(a + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -9e+78)
		tmp = z / b;
	elseif (y <= -3000.0)
		tmp = (x + (y * (z / t))) / a;
	elseif ((y <= -3.5e-94) || ~((y <= 1.2e+27)))
		tmp = z / b;
	else
		tmp = x / (a + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -9e+78], N[(z / b), $MachinePrecision], If[LessEqual[y, -3000.0], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[Or[LessEqual[y, -3.5e-94], N[Not[LessEqual[y, 1.2e+27]], $MachinePrecision]], N[(z / b), $MachinePrecision], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.9999999999999999e78 or -3e3 < y < -3.49999999999999998e-94 or 1.19999999999999999e27 < y

   1. Initial program 50.4%

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

      1. associate-/l* 53.3%

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

      2. associate-/l* 62.1%

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

   3. Simplified 62.1%

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

   5. Taylor expanded in y around inf 62.9%

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

   if -8.9999999999999999e78 < y < -3e3

   1. Initial program 72.7%

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

      1. associate-/l* 72.9%

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

      2. associate-/l* 72.8%

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

   3. Simplified 72.8%

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

   5. Taylor expanded in a around inf 52.2%

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

   if -3.49999999999999998e-94 < y < 1.19999999999999999e27

   1. Initial program 93.5%

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

      1. associate-/l* 88.4%

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

      2. associate-/l* 84.8%

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

   3. Simplified 84.8%

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

   5. Taylor expanded in y around 0 65.8%

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

4. Final simplification 63.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+78}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq -3000:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a}\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-94} \lor \neg \left(y \leq 1.2 \cdot 10^{+27}\right):\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 67.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{-48} \lor \neg \left(t \leq 1.9 \cdot 10^{-24}\right):\\ \;\;\;\;\frac{x}{1 + \left(a + y \cdot \frac{b}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot t}{y \cdot b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -7e-48) (not (<= t 1.9e-24)))
   (/ x (+ 1.0 (+ a (* y (/ b t)))))
   (+ (/ z b) (/ (* x t) (* y b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -7e-48) || !(t <= 1.9e-24)) {
		tmp = x / (1.0 + (a + (y * (b / t))));
	} else {
		tmp = (z / b) + ((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 <= (-7d-48)) .or. (.not. (t <= 1.9d-24))) then
        tmp = x / (1.0d0 + (a + (y * (b / t))))
    else
        tmp = (z / b) + ((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 <= -7e-48) || !(t <= 1.9e-24)) {
		tmp = x / (1.0 + (a + (y * (b / t))));
	} else {
		tmp = (z / b) + ((x * t) / (y * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -7e-48) or not (t <= 1.9e-24):
		tmp = x / (1.0 + (a + (y * (b / t))))
	else:
		tmp = (z / b) + ((x * t) / (y * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -7e-48) || !(t <= 1.9e-24))
		tmp = Float64(x / Float64(1.0 + Float64(a + Float64(y * Float64(b / t)))));
	else
		tmp = Float64(Float64(z / b) + Float64(Float64(x * t) / Float64(y * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -7e-48) || ~((t <= 1.9e-24)))
		tmp = x / (1.0 + (a + (y * (b / t))));
	else
		tmp = (z / b) + ((x * t) / (y * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -7e-48], N[Not[LessEqual[t, 1.9e-24]], $MachinePrecision]], N[(x / N[(1.0 + N[(a + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z / b), $MachinePrecision] + N[(N[(x * t), $MachinePrecision] / N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -6.99999999999999982e-48 or 1.90000000000000013e-24 < t

   1. Initial program 78.8%

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

      1. associate-/l* 81.8%

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

      2. associate-/l* 91.9%

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

   3. Simplified 91.9%

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

      1. clear-num 91.9%

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

      2. un-div-inv 92.0%

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

   6. Applied egg-rr 92.0%

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

      1. clear-num 92.0%

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

      2. un-div-inv 92.0%

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

   8. Applied egg-rr 92.0%

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

   9. Taylor expanded in x around inf 65.6%

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

       1. associate-*l/ 70.3%

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

       2. *-commutative 70.3%

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

   11. Simplified 70.3%

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

   if -6.99999999999999982e-48 < t < 1.90000000000000013e-24

   1. Initial program 62.2%

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

      1. associate-/l* 58.0%

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

      2. associate-/l* 54.4%

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

   3. Simplified 54.4%

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

   5. Taylor expanded in b around inf 41.3%

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

   6. Taylor expanded in t around 0 67.6%

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

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{-48} \lor \neg \left(t \leq 1.9 \cdot 10^{-24}\right):\\ \;\;\;\;\frac{x}{1 + \left(a + y \cdot \frac{b}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot t}{y \cdot b}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 61.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{+44} \lor \neg \left(t \leq 1.4 \cdot 10^{+60}\right):\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot t}{y \cdot b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -1.4e+44) (not (<= t 1.4e+60)))
   (/ x (+ a 1.0))
   (+ (/ z b) (/ (* x t) (* y b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.4e+44) || !(t <= 1.4e+60)) {
		tmp = x / (a + 1.0);
	} else {
		tmp = (z / b) + ((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 <= (-1.4d+44)) .or. (.not. (t <= 1.4d+60))) then
        tmp = x / (a + 1.0d0)
    else
        tmp = (z / b) + ((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 <= -1.4e+44) || !(t <= 1.4e+60)) {
		tmp = x / (a + 1.0);
	} else {
		tmp = (z / b) + ((x * t) / (y * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -1.4e+44) or not (t <= 1.4e+60):
		tmp = x / (a + 1.0)
	else:
		tmp = (z / b) + ((x * t) / (y * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -1.4e+44) || !(t <= 1.4e+60))
		tmp = Float64(x / Float64(a + 1.0));
	else
		tmp = Float64(Float64(z / b) + Float64(Float64(x * t) / Float64(y * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -1.4e+44) || ~((t <= 1.4e+60)))
		tmp = x / (a + 1.0);
	else
		tmp = (z / b) + ((x * t) / (y * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -1.4e+44], N[Not[LessEqual[t, 1.4e+60]], $MachinePrecision]], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(z / b), $MachinePrecision] + N[(N[(x * t), $MachinePrecision] / N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.4e44 or 1.4e60 < t

   1. Initial program 77.5%

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

      1. associate-/l* 81.7%

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

      2. associate-/l* 94.5%

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

   3. Simplified 94.5%

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

   5. Taylor expanded in y around 0 67.6%

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

   if -1.4e44 < t < 1.4e60

   1. Initial program 66.1%

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

      1. associate-/l* 62.8%

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

      2. associate-/l* 60.5%

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

   3. Simplified 60.5%

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

   5. Taylor expanded in b around inf 39.0%

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

   6. Taylor expanded in t around 0 63.5%

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

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{+44} \lor \neg \left(t \leq 1.4 \cdot 10^{+60}\right):\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot t}{y \cdot b}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 43.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{+46}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+60}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{+209}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.6e+46)
   (/ x a)
   (if (<= t 1.9e+60) (/ z b) (if (<= t 1.05e+209) (/ x a) x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.6e+46) {
		tmp = x / a;
	} else if (t <= 1.9e+60) {
		tmp = z / b;
	} else if (t <= 1.05e+209) {
		tmp = x / a;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-1.6d+46)) then
        tmp = x / a
    else if (t <= 1.9d+60) then
        tmp = z / b
    else if (t <= 1.05d+209) then
        tmp = x / a
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.6e+46) {
		tmp = x / a;
	} else if (t <= 1.9e+60) {
		tmp = z / b;
	} else if (t <= 1.05e+209) {
		tmp = x / a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1.6e+46:
		tmp = x / a
	elif t <= 1.9e+60:
		tmp = z / b
	elif t <= 1.05e+209:
		tmp = x / a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.6e+46)
		tmp = Float64(x / a);
	elseif (t <= 1.9e+60)
		tmp = Float64(z / b);
	elseif (t <= 1.05e+209)
		tmp = Float64(x / a);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -1.6e+46)
		tmp = x / a;
	elseif (t <= 1.9e+60)
		tmp = z / b;
	elseif (t <= 1.05e+209)
		tmp = x / a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.6e+46], N[(x / a), $MachinePrecision], If[LessEqual[t, 1.9e+60], N[(z / b), $MachinePrecision], If[LessEqual[t, 1.05e+209], N[(x / a), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.5999999999999999e46 or 1.90000000000000005e60 < t < 1.05e209

   1. Initial program 76.1%

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

      1. associate-/l* 81.6%

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

      2. associate-/l* 95.6%

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

   3. Simplified 95.6%

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

   5. Taylor expanded in y around 0 68.8%

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

   6. Taylor expanded in a around inf 48.5%

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

   if -1.5999999999999999e46 < t < 1.90000000000000005e60

   1. Initial program 66.1%

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

      1. associate-/l* 62.8%

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

      2. associate-/l* 60.5%

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

   3. Simplified 60.5%

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

   5. Taylor expanded in y around inf 54.0%

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

   if 1.05e209 < t

   1. Initial program 82.0%

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

      1. associate-/l* 82.2%

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

      2. associate-/l* 91.1%

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

   3. Simplified 91.1%

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

   5. Taylor expanded in y around 0 63.9%

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

   6. Taylor expanded in a around 0 42.4%

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

Alternative 16: 55.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{-94} \lor \neg \left(y \leq 10^{+26}\right):\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -2.3e-94) (not (<= y 1e+26))) (/ z b) (/ x (+ a 1.0))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.3e-94) || !(y <= 1e+26)) {
		tmp = z / b;
	} else {
		tmp = x / (a + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-2.3d-94)) .or. (.not. (y <= 1d+26))) then
        tmp = z / b
    else
        tmp = x / (a + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.3e-94) || !(y <= 1e+26)) {
		tmp = z / b;
	} else {
		tmp = x / (a + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -2.3e-94) or not (y <= 1e+26):
		tmp = z / b
	else:
		tmp = x / (a + 1.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -2.3e-94) || !(y <= 1e+26))
		tmp = Float64(z / b);
	else
		tmp = Float64(x / Float64(a + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -2.3e-94) || ~((y <= 1e+26)))
		tmp = z / b;
	else
		tmp = x / (a + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -2.3e-94], N[Not[LessEqual[y, 1e+26]], $MachinePrecision]], N[(z / b), $MachinePrecision], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.2999999999999999e-94 or 1.00000000000000005e26 < y

   1. Initial program 53.1%

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

      1. associate-/l* 55.7%

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

      2. associate-/l* 63.4%

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

   3. Simplified 63.4%

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

   5. Taylor expanded in y around inf 57.8%

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

   if -2.2999999999999999e-94 < y < 1.00000000000000005e26

   1. Initial program 93.5%

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

      1. associate-/l* 88.4%

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

      2. associate-/l* 84.8%

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

   3. Simplified 84.8%

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

   5. Taylor expanded in y around 0 65.8%

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

4. Final simplification 61.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{-94} \lor \neg \left(y \leq 10^{+26}\right):\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 41.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1 \lor \neg \left(a \leq 2.35 \cdot 10^{-5}\right):\\ \;\;\;\;\frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -1.0) (not (<= a 2.35e-5))) (/ x a) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -1.0) || !(a <= 2.35e-5)) {
		tmp = x / a;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((a <= (-1.0d0)) .or. (.not. (a <= 2.35d-5))) then
        tmp = x / a
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -1.0) || !(a <= 2.35e-5)) {
		tmp = x / a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -1.0) or not (a <= 2.35e-5):
		tmp = x / a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -1.0) || !(a <= 2.35e-5))
		tmp = Float64(x / a);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -1.0) || ~((a <= 2.35e-5)))
		tmp = x / a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -1.0], N[Not[LessEqual[a, 2.35e-5]], $MachinePrecision]], N[(x / a), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if a < -1 or 2.34999999999999986e-5 < a

   1. Initial program 74.7%

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

      1. associate-/l* 76.3%

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

      2. associate-/l* 77.7%

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

   3. Simplified 77.7%

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

   5. Taylor expanded in y around 0 49.4%

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

   6. Taylor expanded in a around inf 47.1%

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

   if -1 < a < 2.34999999999999986e-5

   1. Initial program 65.6%

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

      1. associate-/l* 62.7%

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

      2. associate-/l* 67.1%

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

   3. Simplified 67.1%

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

   5. Taylor expanded in y around 0 28.8%

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

   6. Taylor expanded in a around 0 27.8%

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

4. Final simplification 37.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1 \lor \neg \left(a \leq 2.35 \cdot 10^{-5}\right):\\ \;\;\;\;\frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 19.7% accurate, 17.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 70.1%

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

   1. associate-/l* 69.5%

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

   2. associate-/l* 72.4%

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

3. Simplified 72.4%

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

5. Taylor expanded in y around 0 39.1%

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

6. Taylor expanded in a around 0 16.0%

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

Developer target: 79.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 1 \cdot \left(\left(x + \frac{y}{t} \cdot z\right) \cdot \frac{1}{\left(a + 1\right) + \frac{y}{t} \cdot b}\right)\\ \mathbf{if}\;t < -1.3659085366310088 \cdot 10^{-271}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t < 3.036967103737246 \cdot 10^{-130}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024107 
(FPCore (x y z t a b)
  :name "Diagrams.Solve.Tridiagonal:solveCyclicTriDiagonal from diagrams-solve-0.1, B"
  :precision binary64

  :alt
  (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))))