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

Percentage Accurate: 75.4% → 93.3%

Time: 15.4s

Alternatives: 17

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: 75.4% 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: 93.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot b}{t}\\ t_2 := \frac{x + \frac{y \cdot z}{t}}{t\_1 + \left(a + 1\right)}\\ t_3 := 1 + \left(a + t\_1\right)\\ t_4 := z \cdot \left(\frac{x}{z \cdot t\_3} + \frac{y}{t \cdot t\_3}\right)\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{-314}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;\frac{z}{b} + \frac{t \cdot \left(\frac{x}{b} + \frac{z \cdot \left(-1 - a\right)}{{b}^{2}}\right)}{y}\\ \mathbf{elif}\;t\_2 \leq 10^{+277}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;t\_4\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* y b) t))
        (t_2 (/ (+ x (/ (* y z) t)) (+ t_1 (+ a 1.0))))
        (t_3 (+ 1.0 (+ a t_1)))
        (t_4 (* z (+ (/ x (* z t_3)) (/ y (* t t_3))))))
   (if (<= t_2 (- INFINITY))
     t_4
     (if (<= t_2 -5e-314)
       t_2
       (if (<= t_2 0.0)
         (+ (/ z b) (/ (* t (+ (/ x b) (/ (* z (- -1.0 a)) (pow b 2.0)))) y))
         (if (<= t_2 1e+277) t_2 (if (<= t_2 INFINITY) t_4 (/ 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 = (x + ((y * z) / t)) / (t_1 + (a + 1.0));
	double t_3 = 1.0 + (a + t_1);
	double t_4 = z * ((x / (z * t_3)) + (y / (t * t_3)));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_4;
	} else if (t_2 <= -5e-314) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = (z / b) + ((t * ((x / b) + ((z * (-1.0 - a)) / pow(b, 2.0)))) / y);
	} else if (t_2 <= 1e+277) {
		tmp = t_2;
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = t_4;
	} 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 = (x + ((y * z) / t)) / (t_1 + (a + 1.0));
	double t_3 = 1.0 + (a + t_1);
	double t_4 = z * ((x / (z * t_3)) + (y / (t * t_3)));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_4;
	} else if (t_2 <= -5e-314) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = (z / b) + ((t * ((x / b) + ((z * (-1.0 - a)) / Math.pow(b, 2.0)))) / y);
	} else if (t_2 <= 1e+277) {
		tmp = t_2;
	} else if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = t_4;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (y * b) / t
	t_2 = (x + ((y * z) / t)) / (t_1 + (a + 1.0))
	t_3 = 1.0 + (a + t_1)
	t_4 = z * ((x / (z * t_3)) + (y / (t * t_3)))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_4
	elif t_2 <= -5e-314:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = (z / b) + ((t * ((x / b) + ((z * (-1.0 - a)) / math.pow(b, 2.0)))) / y)
	elif t_2 <= 1e+277:
		tmp = t_2
	elif t_2 <= math.inf:
		tmp = t_4
	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(Float64(x + Float64(Float64(y * z) / t)) / Float64(t_1 + Float64(a + 1.0)))
	t_3 = Float64(1.0 + Float64(a + t_1))
	t_4 = Float64(z * Float64(Float64(x / Float64(z * t_3)) + Float64(y / Float64(t * t_3))))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_4;
	elseif (t_2 <= -5e-314)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = Float64(Float64(z / b) + Float64(Float64(t * Float64(Float64(x / b) + Float64(Float64(z * Float64(-1.0 - a)) / (b ^ 2.0)))) / y));
	elseif (t_2 <= 1e+277)
		tmp = t_2;
	elseif (t_2 <= Inf)
		tmp = t_4;
	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 = (x + ((y * z) / t)) / (t_1 + (a + 1.0));
	t_3 = 1.0 + (a + t_1);
	t_4 = z * ((x / (z * t_3)) + (y / (t * t_3)));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_4;
	elseif (t_2 <= -5e-314)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = (z / b) + ((t * ((x / b) + ((z * (-1.0 - a)) / (b ^ 2.0)))) / y);
	elseif (t_2 <= 1e+277)
		tmp = t_2;
	elseif (t_2 <= Inf)
		tmp = t_4;
	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[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(t$95$1 + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(1.0 + N[(a + t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(z * N[(N[(x / N[(z * t$95$3), $MachinePrecision]), $MachinePrecision] + N[(y / N[(t * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$4, If[LessEqual[t$95$2, -5e-314], t$95$2, If[LessEqual[t$95$2, 0.0], N[(N[(z / b), $MachinePrecision] + N[(N[(t * N[(N[(x / b), $MachinePrecision] + N[(N[(z * N[(-1.0 - a), $MachinePrecision]), $MachinePrecision] / N[Power[b, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+277], t$95$2, If[LessEqual[t$95$2, Infinity], t$95$4, 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 1e277 < (/.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 26.8%

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

      1. associate-/l* 48.0%

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

      2. associate-/l* 47.9%

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

   3. Simplified 47.9%

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

   5. Taylor expanded in z around inf 86.1%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -4.99999999982e-314 or -0.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 1e277

   1. Initial program 99.2%

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

   if -4.99999999982e-314 < (/.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 47.7%

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

      1. associate-/l* 47.4%

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

      2. associate-/l* 62.4%

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

   3. Simplified 62.4%

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

   5. Taylor expanded in y around -inf 63.2%

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

      1. +-commutative 63.2%

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

      2. associate-*r/ 63.2%

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

   7. Simplified 68.2%

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

   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* 0.5%

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

      2. associate-/l* 14.1%

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

   3. Simplified 14.1%

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

   5. Taylor expanded in y around inf 95.6%

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

4. Final simplification 92.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -\infty:\\ \;\;\;\;z \cdot \left(\frac{x}{z \cdot \left(1 + \left(a + \frac{y \cdot b}{t}\right)\right)} + \frac{y}{t \cdot \left(1 + \left(a + \frac{y \cdot b}{t}\right)\right)}\right)\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -5 \cdot 10^{-314}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 0:\\ \;\;\;\;\frac{z}{b} + \frac{t \cdot \left(\frac{x}{b} + \frac{z \cdot \left(-1 - a\right)}{{b}^{2}}\right)}{y}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 10^{+277}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq \infty:\\ \;\;\;\;z \cdot \left(\frac{x}{z \cdot \left(1 + \left(a + \frac{y \cdot b}{t}\right)\right)} + \frac{y}{t \cdot \left(1 + \left(a + \frac{y \cdot b}{t}\right)\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 92.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot b}{t}\\ t_2 := \frac{x + \frac{y \cdot z}{t}}{t\_1 + \left(a + 1\right)}\\ t_3 := 1 + \left(a + t\_1\right)\\ t_4 := z \cdot \left(\frac{x}{z \cdot t\_3} + \frac{y}{t \cdot t\_3}\right)\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{-314}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;x \cdot \left(\frac{1}{\left(a + 1\right) + b \cdot \frac{y}{t}} + \frac{\frac{z}{b}}{x}\right)\\ \mathbf{elif}\;t\_2 \leq 10^{+277}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;t\_4\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* y b) t))
        (t_2 (/ (+ x (/ (* y z) t)) (+ t_1 (+ a 1.0))))
        (t_3 (+ 1.0 (+ a t_1)))
        (t_4 (* z (+ (/ x (* z t_3)) (/ y (* t t_3))))))
   (if (<= t_2 (- INFINITY))
     t_4
     (if (<= t_2 -5e-314)
       t_2
       (if (<= t_2 0.0)
         (* x (+ (/ 1.0 (+ (+ a 1.0) (* b (/ y t)))) (/ (/ z b) x)))
         (if (<= t_2 1e+277) t_2 (if (<= t_2 INFINITY) t_4 (/ 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 = (x + ((y * z) / t)) / (t_1 + (a + 1.0));
	double t_3 = 1.0 + (a + t_1);
	double t_4 = z * ((x / (z * t_3)) + (y / (t * t_3)));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_4;
	} else if (t_2 <= -5e-314) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = x * ((1.0 / ((a + 1.0) + (b * (y / t)))) + ((z / b) / x));
	} else if (t_2 <= 1e+277) {
		tmp = t_2;
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = t_4;
	} 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 = (x + ((y * z) / t)) / (t_1 + (a + 1.0));
	double t_3 = 1.0 + (a + t_1);
	double t_4 = z * ((x / (z * t_3)) + (y / (t * t_3)));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_4;
	} else if (t_2 <= -5e-314) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = x * ((1.0 / ((a + 1.0) + (b * (y / t)))) + ((z / b) / x));
	} else if (t_2 <= 1e+277) {
		tmp = t_2;
	} else if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = t_4;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (y * b) / t
	t_2 = (x + ((y * z) / t)) / (t_1 + (a + 1.0))
	t_3 = 1.0 + (a + t_1)
	t_4 = z * ((x / (z * t_3)) + (y / (t * t_3)))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_4
	elif t_2 <= -5e-314:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = x * ((1.0 / ((a + 1.0) + (b * (y / t)))) + ((z / b) / x))
	elif t_2 <= 1e+277:
		tmp = t_2
	elif t_2 <= math.inf:
		tmp = t_4
	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(Float64(x + Float64(Float64(y * z) / t)) / Float64(t_1 + Float64(a + 1.0)))
	t_3 = Float64(1.0 + Float64(a + t_1))
	t_4 = Float64(z * Float64(Float64(x / Float64(z * t_3)) + Float64(y / Float64(t * t_3))))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_4;
	elseif (t_2 <= -5e-314)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = Float64(x * Float64(Float64(1.0 / Float64(Float64(a + 1.0) + Float64(b * Float64(y / t)))) + Float64(Float64(z / b) / x)));
	elseif (t_2 <= 1e+277)
		tmp = t_2;
	elseif (t_2 <= Inf)
		tmp = t_4;
	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 = (x + ((y * z) / t)) / (t_1 + (a + 1.0));
	t_3 = 1.0 + (a + t_1);
	t_4 = z * ((x / (z * t_3)) + (y / (t * t_3)));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_4;
	elseif (t_2 <= -5e-314)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = x * ((1.0 / ((a + 1.0) + (b * (y / t)))) + ((z / b) / x));
	elseif (t_2 <= 1e+277)
		tmp = t_2;
	elseif (t_2 <= Inf)
		tmp = t_4;
	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[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(t$95$1 + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(1.0 + N[(a + t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(z * N[(N[(x / N[(z * t$95$3), $MachinePrecision]), $MachinePrecision] + N[(y / N[(t * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$4, If[LessEqual[t$95$2, -5e-314], t$95$2, If[LessEqual[t$95$2, 0.0], N[(x * N[(N[(1.0 / N[(N[(a + 1.0), $MachinePrecision] + N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(z / b), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+277], t$95$2, If[LessEqual[t$95$2, Infinity], t$95$4, 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 1e277 < (/.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 26.8%

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

      1. associate-/l* 48.0%

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

      2. associate-/l* 47.9%

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

   3. Simplified 47.9%

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

   5. Taylor expanded in z around inf 86.1%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -4.99999999982e-314 or -0.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 1e277

   1. Initial program 99.2%

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

   if -4.99999999982e-314 < (/.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 47.7%

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

      1. associate-/l* 47.4%

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

      2. associate-/l* 62.4%

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

   3. Simplified 62.4%

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

   5. Taylor expanded in x around inf 47.7%

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

      1. associate-+r+ 47.7%

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

      2. associate-*r/ 57.7%

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

      3. associate-/l* 57.7%

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

      4. *-commutative 57.7%

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

      5. associate-+r+ 57.7%

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

      6. associate-*r/ 61.1%

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

   7. Simplified 61.1%

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

   8. Taylor expanded in y around inf 67.3%

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

      1. associate-/r* 67.3%

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

   10. Simplified 67.3%

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

   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* 0.5%

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

      2. associate-/l* 14.1%

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

   3. Simplified 14.1%

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

   5. Taylor expanded in y around inf 95.6%

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

4. Final simplification 92.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -\infty:\\ \;\;\;\;z \cdot \left(\frac{x}{z \cdot \left(1 + \left(a + \frac{y \cdot b}{t}\right)\right)} + \frac{y}{t \cdot \left(1 + \left(a + \frac{y \cdot b}{t}\right)\right)}\right)\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -5 \cdot 10^{-314}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 0:\\ \;\;\;\;x \cdot \left(\frac{1}{\left(a + 1\right) + b \cdot \frac{y}{t}} + \frac{\frac{z}{b}}{x}\right)\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 10^{+277}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq \infty:\\ \;\;\;\;z \cdot \left(\frac{x}{z \cdot \left(1 + \left(a + \frac{y \cdot b}{t}\right)\right)} + \frac{y}{t \cdot \left(1 + \left(a + \frac{y \cdot b}{t}\right)\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 88.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a + 1\right) + b \cdot \frac{y}{t}\\ t_2 := \frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;\frac{y \cdot z}{y \cdot b + t \cdot \left(a + 1\right)}\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{-314}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;x \cdot \left(\frac{1}{t\_1} + \frac{\frac{z}{b}}{x}\right)\\ \mathbf{elif}\;t\_2 \leq 10^{+277}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ a 1.0) (* b (/ y t))))
        (t_2 (/ (+ x (/ (* y z) t)) (+ (/ (* y b) t) (+ a 1.0)))))
   (if (<= t_2 (- INFINITY))
     (/ (* y z) (+ (* y b) (* t (+ a 1.0))))
     (if (<= t_2 -5e-314)
       t_2
       (if (<= t_2 0.0)
         (* x (+ (/ 1.0 t_1) (/ (/ z b) x)))
         (if (<= t_2 1e+277)
           t_2
           (if (<= t_2 INFINITY) (* (/ y t) (/ z t_1)) (/ z b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a + 1.0) + (b * (y / t));
	double t_2 = (x + ((y * z) / t)) / (((y * b) / t) + (a + 1.0));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = (y * z) / ((y * b) + (t * (a + 1.0)));
	} else if (t_2 <= -5e-314) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = x * ((1.0 / t_1) + ((z / b) / x));
	} else if (t_2 <= 1e+277) {
		tmp = t_2;
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = (y / t) * (z / t_1);
	} 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 = (a + 1.0) + (b * (y / t));
	double t_2 = (x + ((y * z) / t)) / (((y * b) / t) + (a + 1.0));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = (y * z) / ((y * b) + (t * (a + 1.0)));
	} else if (t_2 <= -5e-314) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = x * ((1.0 / t_1) + ((z / b) / x));
	} else if (t_2 <= 1e+277) {
		tmp = t_2;
	} else if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = (y / t) * (z / t_1);
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a + 1.0) + (b * (y / t))
	t_2 = (x + ((y * z) / t)) / (((y * b) / t) + (a + 1.0))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = (y * z) / ((y * b) + (t * (a + 1.0)))
	elif t_2 <= -5e-314:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = x * ((1.0 / t_1) + ((z / b) / x))
	elif t_2 <= 1e+277:
		tmp = t_2
	elif t_2 <= math.inf:
		tmp = (y / t) * (z / t_1)
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a + 1.0) + Float64(b * Float64(y / t)))
	t_2 = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(Float64(Float64(y * b) / t) + Float64(a + 1.0)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(Float64(y * z) / Float64(Float64(y * b) + Float64(t * Float64(a + 1.0))));
	elseif (t_2 <= -5e-314)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = Float64(x * Float64(Float64(1.0 / t_1) + Float64(Float64(z / b) / x)));
	elseif (t_2 <= 1e+277)
		tmp = t_2;
	elseif (t_2 <= Inf)
		tmp = Float64(Float64(y / t) * Float64(z / t_1));
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a + 1.0) + (b * (y / t));
	t_2 = (x + ((y * z) / t)) / (((y * b) / t) + (a + 1.0));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = (y * z) / ((y * b) + (t * (a + 1.0)));
	elseif (t_2 <= -5e-314)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = x * ((1.0 / t_1) + ((z / b) / x));
	elseif (t_2 <= 1e+277)
		tmp = t_2;
	elseif (t_2 <= Inf)
		tmp = (y / t) * (z / t_1);
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a + 1.0), $MachinePrecision] + N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(N[(y * z), $MachinePrecision] / N[(N[(y * b), $MachinePrecision] + N[(t * N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, -5e-314], t$95$2, If[LessEqual[t$95$2, 0.0], N[(x * N[(N[(1.0 / t$95$1), $MachinePrecision] + N[(N[(z / b), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+277], t$95$2, If[LessEqual[t$95$2, Infinity], N[(N[(y / t), $MachinePrecision] * N[(z / t$95$1), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 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

   1. Initial program 31.9%

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

      1. associate-/l* 53.4%

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

      2. associate-/l* 53.2%

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

   3. Simplified 53.2%

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

   5. Taylor expanded in x around 0 67.8%

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

   6. Taylor expanded in t around 0 67.8%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -4.99999999982e-314 or -0.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 1e277

   1. Initial program 99.2%

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

   if -4.99999999982e-314 < (/.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 47.7%

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

      1. associate-/l* 47.4%

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

      2. associate-/l* 62.4%

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

   3. Simplified 62.4%

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

   5. Taylor expanded in x around inf 47.7%

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

      1. associate-+r+ 47.7%

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

      2. associate-*r/ 57.7%

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

      3. associate-/l* 57.7%

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

      4. *-commutative 57.7%

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

      5. associate-+r+ 57.7%

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

      6. associate-*r/ 61.1%

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

   7. Simplified 61.1%

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

   8. Taylor expanded in y around inf 67.3%

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

      1. associate-/r* 67.3%

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

   10. Simplified 67.3%

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

   if 1e277 < (/.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 21.6%

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

      1. associate-/l* 42.7%

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

      2. associate-/l* 42.7%

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

   3. Simplified 42.7%

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

   5. Taylor expanded in x around 0 57.3%

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

      1. times-frac 88.9%

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

      2. associate-+r+ 88.9%

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

      3. associate-*r/ 82.8%

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

   7. Simplified 82.8%

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

   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* 0.5%

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

      2. associate-/l* 14.1%

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

   3. Simplified 14.1%

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

   5. Taylor expanded in y around inf 95.6%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -\infty:\\ \;\;\;\;\frac{y \cdot z}{y \cdot b + t \cdot \left(a + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -5 \cdot 10^{-314}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 0:\\ \;\;\;\;x \cdot \left(\frac{1}{\left(a + 1\right) + b \cdot \frac{y}{t}} + \frac{\frac{z}{b}}{x}\right)\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 10^{+277}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq \infty:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 89.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ t_2 := \frac{y \cdot z}{y \cdot b + t \cdot \left(a + 1\right)}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{-314}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 10^{+277}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (* y z) t)) (+ (/ (* y b) t) (+ a 1.0))))
        (t_2 (/ (* y z) (+ (* y b) (* t (+ a 1.0))))))
   (if (<= t_1 (- INFINITY))
     t_2
     (if (<= t_1 -5e-314)
       t_1
       (if (<= t_1 0.0)
         t_2
         (if (<= t_1 1e+277)
           t_1
           (if (<= t_1 INFINITY)
             (* (/ y t) (/ z (+ (+ a 1.0) (* b (/ y t)))))
             (/ z b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + ((y * z) / t)) / (((y * b) / t) + (a + 1.0));
	double t_2 = (y * z) / ((y * b) + (t * (a + 1.0)));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = t_2;
	} else if (t_1 <= -5e-314) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = t_2;
	} else if (t_1 <= 1e+277) {
		tmp = t_1;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = (y / t) * (z / ((a + 1.0) + (b * (y / t))));
	} 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)) / (((y * b) / t) + (a + 1.0));
	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 <= -5e-314) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = t_2;
	} else if (t_1 <= 1e+277) {
		tmp = t_1;
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = (y / t) * (z / ((a + 1.0) + (b * (y / t))));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + ((y * z) / t)) / (((y * b) / t) + (a + 1.0))
	t_2 = (y * z) / ((y * b) + (t * (a + 1.0)))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = t_2
	elif t_1 <= -5e-314:
		tmp = t_1
	elif t_1 <= 0.0:
		tmp = t_2
	elif t_1 <= 1e+277:
		tmp = t_1
	elif t_1 <= math.inf:
		tmp = (y / t) * (z / ((a + 1.0) + (b * (y / t))))
	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(Float64(y * b) / t) + Float64(a + 1.0)))
	t_2 = Float64(Float64(y * 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 <= -5e-314)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = t_2;
	elseif (t_1 <= 1e+277)
		tmp = t_1;
	elseif (t_1 <= Inf)
		tmp = Float64(Float64(y / t) * Float64(z / Float64(Float64(a + 1.0) + Float64(b * Float64(y / t)))));
	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)) / (((y * b) / t) + (a + 1.0));
	t_2 = (y * z) / ((y * b) + (t * (a + 1.0)));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = t_2;
	elseif (t_1 <= -5e-314)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = t_2;
	elseif (t_1 <= 1e+277)
		tmp = t_1;
	elseif (t_1 <= Inf)
		tmp = (y / t) * (z / ((a + 1.0) + (b * (y / t))));
	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[(N[(y * b), $MachinePrecision] / t), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * z), $MachinePrecision] / N[(N[(y * b), $MachinePrecision] + N[(t * N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], t$95$2, If[LessEqual[t$95$1, -5e-314], t$95$1, If[LessEqual[t$95$1, 0.0], t$95$2, If[LessEqual[t$95$1, 1e+277], t$95$1, If[LessEqual[t$95$1, Infinity], N[(N[(y / t), $MachinePrecision] * N[(z / N[(N[(a + 1.0), $MachinePrecision] + N[(b * N[(y / t), $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))) < -inf.0 or -4.99999999982e-314 < (/.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 42.6%

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

      1. associate-/l* 49.3%

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

      2. associate-/l* 59.4%

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

   3. Simplified 59.4%

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

   5. Taylor expanded in x around 0 54.2%

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

   6. Taylor expanded in t around 0 66.4%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -4.99999999982e-314 or -0.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 1e277

   1. Initial program 99.2%

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

   if 1e277 < (/.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 21.6%

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

      1. associate-/l* 42.7%

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

      2. associate-/l* 42.7%

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

   3. Simplified 42.7%

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

   5. Taylor expanded in x around 0 57.3%

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

      1. times-frac 88.9%

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

      2. associate-+r+ 88.9%

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

      3. associate-*r/ 82.8%

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

   7. Simplified 82.8%

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

   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* 0.5%

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

      2. associate-/l* 14.1%

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

   3. Simplified 14.1%

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

   5. Taylor expanded in y around inf 95.6%

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

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -\infty:\\ \;\;\;\;\frac{y \cdot z}{y \cdot b + t \cdot \left(a + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -5 \cdot 10^{-314}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 0:\\ \;\;\;\;\frac{y \cdot z}{y \cdot b + t \cdot \left(a + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 10^{+277}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq \infty:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 81.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{if}\;t \leq -5.2 \cdot 10^{-196}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -3.35 \cdot 10^{-223}:\\ \;\;\;\;\frac{x \cdot \left(\frac{t}{y} + \frac{z}{x}\right)}{b}\\ \mathbf{elif}\;t \leq -1.55 \cdot 10^{-242} \lor \neg \left(t \leq 2.6 \cdot 10^{-171}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (* y (/ z t))) (+ (+ a 1.0) (* y (/ b t))))))
   (if (<= t -5.2e-196)
     t_1
     (if (<= t -3.35e-223)
       (/ (* x (+ (/ t y) (/ z x))) b)
       (if (or (<= t -1.55e-242) (not (<= t 2.6e-171)))
         t_1
         (/ (+ z (/ (* x t) y)) b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)));
	double tmp;
	if (t <= -5.2e-196) {
		tmp = t_1;
	} else if (t <= -3.35e-223) {
		tmp = (x * ((t / y) + (z / x))) / b;
	} else if ((t <= -1.55e-242) || !(t <= 2.6e-171)) {
		tmp = t_1;
	} else {
		tmp = (z + ((x * t) / y)) / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + (y * (z / t))) / ((a + 1.0d0) + (y * (b / t)))
    if (t <= (-5.2d-196)) then
        tmp = t_1
    else if (t <= (-3.35d-223)) then
        tmp = (x * ((t / y) + (z / x))) / b
    else if ((t <= (-1.55d-242)) .or. (.not. (t <= 2.6d-171))) then
        tmp = t_1
    else
        tmp = (z + ((x * t) / y)) / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)));
	double tmp;
	if (t <= -5.2e-196) {
		tmp = t_1;
	} else if (t <= -3.35e-223) {
		tmp = (x * ((t / y) + (z / x))) / b;
	} else if ((t <= -1.55e-242) || !(t <= 2.6e-171)) {
		tmp = t_1;
	} else {
		tmp = (z + ((x * t) / y)) / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)))
	tmp = 0
	if t <= -5.2e-196:
		tmp = t_1
	elif t <= -3.35e-223:
		tmp = (x * ((t / y) + (z / x))) / b
	elif (t <= -1.55e-242) or not (t <= 2.6e-171):
		tmp = t_1
	else:
		tmp = (z + ((x * t) / y)) / b
	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))))
	tmp = 0.0
	if (t <= -5.2e-196)
		tmp = t_1;
	elseif (t <= -3.35e-223)
		tmp = Float64(Float64(x * Float64(Float64(t / y) + Float64(z / x))) / b);
	elseif ((t <= -1.55e-242) || !(t <= 2.6e-171))
		tmp = t_1;
	else
		tmp = Float64(Float64(z + Float64(Float64(x * t) / y)) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)));
	tmp = 0.0;
	if (t <= -5.2e-196)
		tmp = t_1;
	elseif (t <= -3.35e-223)
		tmp = (x * ((t / y) + (z / x))) / b;
	elseif ((t <= -1.55e-242) || ~((t <= 2.6e-171)))
		tmp = t_1;
	else
		tmp = (z + ((x * t) / y)) / b;
	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]}, If[LessEqual[t, -5.2e-196], t$95$1, If[LessEqual[t, -3.35e-223], N[(N[(x * N[(N[(t / y), $MachinePrecision] + N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], If[Or[LessEqual[t, -1.55e-242], N[Not[LessEqual[t, 2.6e-171]], $MachinePrecision]], t$95$1, N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.1999999999999996e-196 or -3.3500000000000001e-223 < t < -1.55000000000000008e-242 or 2.60000000000000005e-171 < t

   1. Initial program 81.3%

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

      1. associate-/l* 80.9%

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

      2. associate-/l* 84.0%

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

   3. Simplified 84.0%

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

   if -5.1999999999999996e-196 < t < -3.3500000000000001e-223

   1. Initial program 24.1%

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

      1. associate-/l* 23.6%

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

      2. associate-/l* 23.6%

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

   3. Simplified 23.6%

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

   5. Taylor expanded in x around inf 47.2%

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

      1. associate-+r+ 47.2%

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

      2. associate-*r/ 47.2%

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

      3. associate-/l* 47.0%

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

      4. *-commutative 47.0%

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

      5. associate-+r+ 47.0%

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

      6. associate-*r/ 36.3%

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

   7. Simplified 36.3%

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

   8. Taylor expanded in b around inf 88.6%

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

   if -1.55000000000000008e-242 < t < 2.60000000000000005e-171

   1. Initial program 38.2%

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

      1. associate-/l* 37.9%

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

      2. associate-/l* 27.3%

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

   3. Simplified 27.3%

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

   5. Taylor expanded in x around inf 29.6%

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

      1. associate-+r+ 29.6%

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

      2. associate-*r/ 29.6%

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

      3. associate-/l* 29.9%

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

      4. *-commutative 29.9%

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

      5. associate-+r+ 29.9%

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

      6. associate-*r/ 27.1%

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

   7. Simplified 27.1%

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

   8. Taylor expanded in b around inf 72.1%

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

   9. Taylor expanded in x around 0 84.9%

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

4. Final simplification 84.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{-196}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;t \leq -3.35 \cdot 10^{-223}:\\ \;\;\;\;\frac{x \cdot \left(\frac{t}{y} + \frac{z}{x}\right)}{b}\\ \mathbf{elif}\;t \leq -1.55 \cdot 10^{-242} \lor \neg \left(t \leq 2.6 \cdot 10^{-171}\right):\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 81.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a + 1\right) + y \cdot \frac{b}{t}\\ t_2 := x + \frac{y}{\frac{t}{z}}\\ \mathbf{if}\;t \leq -7.5 \cdot 10^{-195}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{t\_1}\\ \mathbf{elif}\;t \leq -4.5 \cdot 10^{-223}:\\ \;\;\;\;\frac{x \cdot \left(\frac{t}{y} + \frac{z}{x}\right)}{b}\\ \mathbf{elif}\;t \leq -1.55 \cdot 10^{-242}:\\ \;\;\;\;\frac{t\_2}{t\_1}\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{-171}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_2}{\left(a + 1\right) + \frac{y}{\frac{t}{b}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ a 1.0) (* y (/ b t)))) (t_2 (+ x (/ y (/ t z)))))
   (if (<= t -7.5e-195)
     (/ (+ x (* y (/ z t))) t_1)
     (if (<= t -4.5e-223)
       (/ (* x (+ (/ t y) (/ z x))) b)
       (if (<= t -1.55e-242)
         (/ t_2 t_1)
         (if (<= t 1.95e-171)
           (/ (+ z (/ (* x t) y)) b)
           (/ t_2 (+ (+ a 1.0) (/ y (/ t b))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a + 1.0) + (y * (b / t));
	double t_2 = x + (y / (t / z));
	double tmp;
	if (t <= -7.5e-195) {
		tmp = (x + (y * (z / t))) / t_1;
	} else if (t <= -4.5e-223) {
		tmp = (x * ((t / y) + (z / x))) / b;
	} else if (t <= -1.55e-242) {
		tmp = t_2 / t_1;
	} else if (t <= 1.95e-171) {
		tmp = (z + ((x * t) / y)) / b;
	} else {
		tmp = t_2 / ((a + 1.0) + (y / (t / b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (a + 1.0d0) + (y * (b / t))
    t_2 = x + (y / (t / z))
    if (t <= (-7.5d-195)) then
        tmp = (x + (y * (z / t))) / t_1
    else if (t <= (-4.5d-223)) then
        tmp = (x * ((t / y) + (z / x))) / b
    else if (t <= (-1.55d-242)) then
        tmp = t_2 / t_1
    else if (t <= 1.95d-171) then
        tmp = (z + ((x * t) / y)) / b
    else
        tmp = t_2 / ((a + 1.0d0) + (y / (t / b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a + 1.0) + (y * (b / t));
	double t_2 = x + (y / (t / z));
	double tmp;
	if (t <= -7.5e-195) {
		tmp = (x + (y * (z / t))) / t_1;
	} else if (t <= -4.5e-223) {
		tmp = (x * ((t / y) + (z / x))) / b;
	} else if (t <= -1.55e-242) {
		tmp = t_2 / t_1;
	} else if (t <= 1.95e-171) {
		tmp = (z + ((x * t) / y)) / b;
	} else {
		tmp = t_2 / ((a + 1.0) + (y / (t / b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a + 1.0) + (y * (b / t))
	t_2 = x + (y / (t / z))
	tmp = 0
	if t <= -7.5e-195:
		tmp = (x + (y * (z / t))) / t_1
	elif t <= -4.5e-223:
		tmp = (x * ((t / y) + (z / x))) / b
	elif t <= -1.55e-242:
		tmp = t_2 / t_1
	elif t <= 1.95e-171:
		tmp = (z + ((x * t) / y)) / b
	else:
		tmp = t_2 / ((a + 1.0) + (y / (t / b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a + 1.0) + Float64(y * Float64(b / t)))
	t_2 = Float64(x + Float64(y / Float64(t / z)))
	tmp = 0.0
	if (t <= -7.5e-195)
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / t_1);
	elseif (t <= -4.5e-223)
		tmp = Float64(Float64(x * Float64(Float64(t / y) + Float64(z / x))) / b);
	elseif (t <= -1.55e-242)
		tmp = Float64(t_2 / t_1);
	elseif (t <= 1.95e-171)
		tmp = Float64(Float64(z + Float64(Float64(x * t) / y)) / b);
	else
		tmp = Float64(t_2 / Float64(Float64(a + 1.0) + Float64(y / Float64(t / b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a + 1.0) + (y * (b / t));
	t_2 = x + (y / (t / z));
	tmp = 0.0;
	if (t <= -7.5e-195)
		tmp = (x + (y * (z / t))) / t_1;
	elseif (t <= -4.5e-223)
		tmp = (x * ((t / y) + (z / x))) / b;
	elseif (t <= -1.55e-242)
		tmp = t_2 / t_1;
	elseif (t <= 1.95e-171)
		tmp = (z + ((x * t) / y)) / b;
	else
		tmp = t_2 / ((a + 1.0) + (y / (t / b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a + 1.0), $MachinePrecision] + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7.5e-195], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[t, -4.5e-223], N[(N[(x * N[(N[(t / y), $MachinePrecision] + N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[t, -1.55e-242], N[(t$95$2 / t$95$1), $MachinePrecision], If[LessEqual[t, 1.95e-171], N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], N[(t$95$2 / N[(N[(a + 1.0), $MachinePrecision] + N[(y / N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -7.5e-195

   1. Initial program 81.8%

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

      1. associate-/l* 81.1%

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

      2. associate-/l* 82.6%

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

   3. Simplified 82.6%

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

   if -7.5e-195 < t < -4.49999999999999968e-223

   1. Initial program 24.1%

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

      1. associate-/l* 23.6%

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

      2. associate-/l* 23.6%

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

   3. Simplified 23.6%

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

   5. Taylor expanded in x around inf 47.2%

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

      1. associate-+r+ 47.2%

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

      2. associate-*r/ 47.2%

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

      3. associate-/l* 47.0%

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

      4. *-commutative 47.0%

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

      5. associate-+r+ 47.0%

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

      6. associate-*r/ 36.3%

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

   7. Simplified 36.3%

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

   8. Taylor expanded in b around inf 88.6%

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

   if -4.49999999999999968e-223 < t < -1.55000000000000008e-242

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

      1. clear-num 100.0%

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

      2. un-div-inv 100.0%

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

   6. Applied egg-rr 100.0%

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

   if -1.55000000000000008e-242 < t < 1.9499999999999999e-171

   1. Initial program 38.2%

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

      1. associate-/l* 37.9%

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

      2. associate-/l* 27.3%

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

   3. Simplified 27.3%

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

   5. Taylor expanded in x around inf 29.6%

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

      1. associate-+r+ 29.6%

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

      2. associate-*r/ 29.6%

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

      3. associate-/l* 29.9%

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

      4. *-commutative 29.9%

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

      5. associate-+r+ 29.9%

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

      6. associate-*r/ 27.1%

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

   7. Simplified 27.1%

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

   8. Taylor expanded in b around inf 72.1%

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

   9. Taylor expanded in x around 0 84.9%

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

   if 1.9499999999999999e-171 < t

   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* 78.9%

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

      2. associate-/l* 84.7%

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

   3. Simplified 84.7%

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

      1. clear-num 84.6%

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

      2. un-div-inv 85.9%

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

   6. Applied egg-rr 85.9%

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

      1. clear-num 84.7%

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

      2. un-div-inv 85.6%

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

   8. Applied egg-rr 86.8%

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

4. Final simplification 85.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{-195}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;t \leq -4.5 \cdot 10^{-223}:\\ \;\;\;\;\frac{x \cdot \left(\frac{t}{y} + \frac{z}{x}\right)}{b}\\ \mathbf{elif}\;t \leq -1.55 \cdot 10^{-242}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{-171}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{\left(a + 1\right) + \frac{y}{\frac{t}{b}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 81.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a + 1\right) + y \cdot \frac{b}{t}\\ t_2 := x + y \cdot \frac{z}{t}\\ \mathbf{if}\;t \leq -2.1 \cdot 10^{-196}:\\ \;\;\;\;\frac{t\_2}{t\_1}\\ \mathbf{elif}\;t \leq -3.3 \cdot 10^{-221}:\\ \;\;\;\;\frac{x \cdot \left(\frac{t}{y} + \frac{z}{x}\right)}{b}\\ \mathbf{elif}\;t \leq -1.55 \cdot 10^{-242}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{t\_1}\\ \mathbf{elif}\;t \leq 1.92 \cdot 10^{-171}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_2}{\left(a + 1\right) + \frac{y}{\frac{t}{b}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ a 1.0) (* y (/ b t)))) (t_2 (+ x (* y (/ z t)))))
   (if (<= t -2.1e-196)
     (/ t_2 t_1)
     (if (<= t -3.3e-221)
       (/ (* x (+ (/ t y) (/ z x))) b)
       (if (<= t -1.55e-242)
         (/ (+ x (/ y (/ t z))) t_1)
         (if (<= t 1.92e-171)
           (/ (+ z (/ (* x t) y)) b)
           (/ t_2 (+ (+ a 1.0) (/ y (/ t b))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a + 1.0) + (y * (b / t));
	double t_2 = x + (y * (z / t));
	double tmp;
	if (t <= -2.1e-196) {
		tmp = t_2 / t_1;
	} else if (t <= -3.3e-221) {
		tmp = (x * ((t / y) + (z / x))) / b;
	} else if (t <= -1.55e-242) {
		tmp = (x + (y / (t / z))) / t_1;
	} else if (t <= 1.92e-171) {
		tmp = (z + ((x * t) / y)) / b;
	} else {
		tmp = t_2 / ((a + 1.0) + (y / (t / b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (a + 1.0d0) + (y * (b / t))
    t_2 = x + (y * (z / t))
    if (t <= (-2.1d-196)) then
        tmp = t_2 / t_1
    else if (t <= (-3.3d-221)) then
        tmp = (x * ((t / y) + (z / x))) / b
    else if (t <= (-1.55d-242)) then
        tmp = (x + (y / (t / z))) / t_1
    else if (t <= 1.92d-171) then
        tmp = (z + ((x * t) / y)) / b
    else
        tmp = t_2 / ((a + 1.0d0) + (y / (t / b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a + 1.0) + (y * (b / t));
	double t_2 = x + (y * (z / t));
	double tmp;
	if (t <= -2.1e-196) {
		tmp = t_2 / t_1;
	} else if (t <= -3.3e-221) {
		tmp = (x * ((t / y) + (z / x))) / b;
	} else if (t <= -1.55e-242) {
		tmp = (x + (y / (t / z))) / t_1;
	} else if (t <= 1.92e-171) {
		tmp = (z + ((x * t) / y)) / b;
	} else {
		tmp = t_2 / ((a + 1.0) + (y / (t / b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a + 1.0) + (y * (b / t))
	t_2 = x + (y * (z / t))
	tmp = 0
	if t <= -2.1e-196:
		tmp = t_2 / t_1
	elif t <= -3.3e-221:
		tmp = (x * ((t / y) + (z / x))) / b
	elif t <= -1.55e-242:
		tmp = (x + (y / (t / z))) / t_1
	elif t <= 1.92e-171:
		tmp = (z + ((x * t) / y)) / b
	else:
		tmp = t_2 / ((a + 1.0) + (y / (t / b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a + 1.0) + Float64(y * Float64(b / t)))
	t_2 = Float64(x + Float64(y * Float64(z / t)))
	tmp = 0.0
	if (t <= -2.1e-196)
		tmp = Float64(t_2 / t_1);
	elseif (t <= -3.3e-221)
		tmp = Float64(Float64(x * Float64(Float64(t / y) + Float64(z / x))) / b);
	elseif (t <= -1.55e-242)
		tmp = Float64(Float64(x + Float64(y / Float64(t / z))) / t_1);
	elseif (t <= 1.92e-171)
		tmp = Float64(Float64(z + Float64(Float64(x * t) / y)) / b);
	else
		tmp = Float64(t_2 / Float64(Float64(a + 1.0) + Float64(y / Float64(t / b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a + 1.0) + (y * (b / t));
	t_2 = x + (y * (z / t));
	tmp = 0.0;
	if (t <= -2.1e-196)
		tmp = t_2 / t_1;
	elseif (t <= -3.3e-221)
		tmp = (x * ((t / y) + (z / x))) / b;
	elseif (t <= -1.55e-242)
		tmp = (x + (y / (t / z))) / t_1;
	elseif (t <= 1.92e-171)
		tmp = (z + ((x * t) / y)) / b;
	else
		tmp = t_2 / ((a + 1.0) + (y / (t / b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a + 1.0), $MachinePrecision] + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.1e-196], N[(t$95$2 / t$95$1), $MachinePrecision], If[LessEqual[t, -3.3e-221], N[(N[(x * N[(N[(t / y), $MachinePrecision] + N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[t, -1.55e-242], N[(N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[t, 1.92e-171], N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], N[(t$95$2 / N[(N[(a + 1.0), $MachinePrecision] + N[(y / N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -2.09999999999999988e-196

   1. Initial program 81.8%

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

      1. associate-/l* 81.1%

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

      2. associate-/l* 82.6%

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

   3. Simplified 82.6%

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

   if -2.09999999999999988e-196 < t < -3.2999999999999999e-221

   1. Initial program 24.1%

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

      1. associate-/l* 23.6%

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

      2. associate-/l* 23.6%

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

   3. Simplified 23.6%

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

   5. Taylor expanded in x around inf 47.2%

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

      1. associate-+r+ 47.2%

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

      2. associate-*r/ 47.2%

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

      3. associate-/l* 47.0%

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

      4. *-commutative 47.0%

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

      5. associate-+r+ 47.0%

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

      6. associate-*r/ 36.3%

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

   7. Simplified 36.3%

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

   8. Taylor expanded in b around inf 88.6%

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

   if -3.2999999999999999e-221 < t < -1.55000000000000008e-242

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

      1. clear-num 100.0%

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

      2. un-div-inv 100.0%

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

   6. Applied egg-rr 100.0%

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

   if -1.55000000000000008e-242 < t < 1.9200000000000001e-171

   1. Initial program 38.2%

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

      1. associate-/l* 37.9%

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

      2. associate-/l* 27.3%

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

   3. Simplified 27.3%

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

   5. Taylor expanded in x around inf 29.6%

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

      1. associate-+r+ 29.6%

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

      2. associate-*r/ 29.6%

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

      3. associate-/l* 29.9%

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

      4. *-commutative 29.9%

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

      5. associate-+r+ 29.9%

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

      6. associate-*r/ 27.1%

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

   7. Simplified 27.1%

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

   8. Taylor expanded in b around inf 72.1%

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

   9. Taylor expanded in x around 0 84.9%

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

   if 1.9200000000000001e-171 < t

   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* 78.9%

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

      2. associate-/l* 84.7%

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

   3. Simplified 84.7%

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

      1. clear-num 84.6%

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

      2. un-div-inv 85.9%

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

   6. Applied egg-rr 85.9%

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

4. Final simplification 84.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{-196}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;t \leq -3.3 \cdot 10^{-221}:\\ \;\;\;\;\frac{x \cdot \left(\frac{t}{y} + \frac{z}{x}\right)}{b}\\ \mathbf{elif}\;t \leq -1.55 \cdot 10^{-242}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;t \leq 1.92 \cdot 10^{-171}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + \frac{y}{\frac{t}{b}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 81.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z}{t}\\ t_2 := \frac{t\_1}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{if}\;t \leq -2.05 \cdot 10^{-197}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1.35 \cdot 10^{-223}:\\ \;\;\;\;\frac{x \cdot \left(\frac{t}{y} + \frac{z}{x}\right)}{b}\\ \mathbf{elif}\;t \leq -1.55 \cdot 10^{-242}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-172}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_1}{\left(a + 1\right) + \frac{y}{\frac{t}{b}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ z t)))) (t_2 (/ t_1 (+ (+ a 1.0) (* y (/ b t))))))
   (if (<= t -2.05e-197)
     t_2
     (if (<= t -1.35e-223)
       (/ (* x (+ (/ t y) (/ z x))) b)
       (if (<= t -1.55e-242)
         t_2
         (if (<= t 9e-172)
           (/ (+ z (/ (* x t) y)) b)
           (/ t_1 (+ (+ a 1.0) (/ y (/ t b))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y * (z / t));
	double t_2 = t_1 / ((a + 1.0) + (y * (b / t)));
	double tmp;
	if (t <= -2.05e-197) {
		tmp = t_2;
	} else if (t <= -1.35e-223) {
		tmp = (x * ((t / y) + (z / x))) / b;
	} else if (t <= -1.55e-242) {
		tmp = t_2;
	} else if (t <= 9e-172) {
		tmp = (z + ((x * t) / y)) / b;
	} else {
		tmp = t_1 / ((a + 1.0) + (y / (t / b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (y * (z / t))
    t_2 = t_1 / ((a + 1.0d0) + (y * (b / t)))
    if (t <= (-2.05d-197)) then
        tmp = t_2
    else if (t <= (-1.35d-223)) then
        tmp = (x * ((t / y) + (z / x))) / b
    else if (t <= (-1.55d-242)) then
        tmp = t_2
    else if (t <= 9d-172) then
        tmp = (z + ((x * t) / y)) / b
    else
        tmp = t_1 / ((a + 1.0d0) + (y / (t / b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y * (z / t));
	double t_2 = t_1 / ((a + 1.0) + (y * (b / t)));
	double tmp;
	if (t <= -2.05e-197) {
		tmp = t_2;
	} else if (t <= -1.35e-223) {
		tmp = (x * ((t / y) + (z / x))) / b;
	} else if (t <= -1.55e-242) {
		tmp = t_2;
	} else if (t <= 9e-172) {
		tmp = (z + ((x * t) / y)) / b;
	} else {
		tmp = t_1 / ((a + 1.0) + (y / (t / b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (y * (z / t))
	t_2 = t_1 / ((a + 1.0) + (y * (b / t)))
	tmp = 0
	if t <= -2.05e-197:
		tmp = t_2
	elif t <= -1.35e-223:
		tmp = (x * ((t / y) + (z / x))) / b
	elif t <= -1.55e-242:
		tmp = t_2
	elif t <= 9e-172:
		tmp = (z + ((x * t) / y)) / b
	else:
		tmp = t_1 / ((a + 1.0) + (y / (t / b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(y * Float64(z / t)))
	t_2 = Float64(t_1 / Float64(Float64(a + 1.0) + Float64(y * Float64(b / t))))
	tmp = 0.0
	if (t <= -2.05e-197)
		tmp = t_2;
	elseif (t <= -1.35e-223)
		tmp = Float64(Float64(x * Float64(Float64(t / y) + Float64(z / x))) / b);
	elseif (t <= -1.55e-242)
		tmp = t_2;
	elseif (t <= 9e-172)
		tmp = Float64(Float64(z + Float64(Float64(x * t) / y)) / b);
	else
		tmp = Float64(t_1 / Float64(Float64(a + 1.0) + Float64(y / Float64(t / b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (y * (z / t));
	t_2 = t_1 / ((a + 1.0) + (y * (b / t)));
	tmp = 0.0;
	if (t <= -2.05e-197)
		tmp = t_2;
	elseif (t <= -1.35e-223)
		tmp = (x * ((t / y) + (z / x))) / b;
	elseif (t <= -1.55e-242)
		tmp = t_2;
	elseif (t <= 9e-172)
		tmp = (z + ((x * t) / y)) / b;
	else
		tmp = t_1 / ((a + 1.0) + (y / (t / b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 / N[(N[(a + 1.0), $MachinePrecision] + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.05e-197], t$95$2, If[LessEqual[t, -1.35e-223], N[(N[(x * N[(N[(t / y), $MachinePrecision] + N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[t, -1.55e-242], t$95$2, If[LessEqual[t, 9e-172], N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], N[(t$95$1 / N[(N[(a + 1.0), $MachinePrecision] + N[(y / N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.05e-197 or -1.34999999999999994e-223 < t < -1.55000000000000008e-242

   1. Initial program 82.8%

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

      1. 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* 83.6%

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

   3. Simplified 83.6%

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

   if -2.05e-197 < t < -1.34999999999999994e-223

   1. Initial program 24.1%

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

      1. associate-/l* 23.6%

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

      2. associate-/l* 23.6%

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

   3. Simplified 23.6%

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

   5. Taylor expanded in x around inf 47.2%

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

      1. associate-+r+ 47.2%

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

      2. associate-*r/ 47.2%

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

      3. associate-/l* 47.0%

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

      4. *-commutative 47.0%

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

      5. associate-+r+ 47.0%

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

      6. associate-*r/ 36.3%

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

   7. Simplified 36.3%

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

   8. Taylor expanded in b around inf 88.6%

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

   if -1.55000000000000008e-242 < t < 9.00000000000000008e-172

   1. Initial program 38.2%

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

      1. associate-/l* 37.9%

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

      2. associate-/l* 27.3%

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

   3. Simplified 27.3%

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

   5. Taylor expanded in x around inf 29.6%

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

      1. associate-+r+ 29.6%

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

      2. associate-*r/ 29.6%

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

      3. associate-/l* 29.9%

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

      4. *-commutative 29.9%

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

      5. associate-+r+ 29.9%

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

      6. associate-*r/ 27.1%

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

   7. Simplified 27.1%

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

   8. Taylor expanded in b around inf 72.1%

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

   9. Taylor expanded in x around 0 84.9%

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

   if 9.00000000000000008e-172 < t

   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* 78.9%

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

      2. associate-/l* 84.7%

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

   3. Simplified 84.7%

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

      1. clear-num 84.6%

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

      2. un-div-inv 85.9%

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

   6. Applied egg-rr 85.9%

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

4. Final simplification 84.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.05 \cdot 10^{-197}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;t \leq -1.35 \cdot 10^{-223}:\\ \;\;\;\;\frac{x \cdot \left(\frac{t}{y} + \frac{z}{x}\right)}{b}\\ \mathbf{elif}\;t \leq -1.55 \cdot 10^{-242}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-172}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + \frac{y}{\frac{t}{b}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 64.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{if}\;t \leq -3 \cdot 10^{-66}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \mathbf{elif}\;t \leq -1.85 \cdot 10^{-161}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -9.2 \cdot 10^{-195}:\\ \;\;\;\;\frac{1}{\frac{a}{x + \frac{y \cdot z}{t}}}\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-62}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-27}:\\ \;\;\;\;\frac{y \cdot z}{t \cdot \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + \frac{y}{\frac{t}{b}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ z (/ (* x t) y)) b)))
   (if (<= t -3e-66)
     (/ x (+ (+ a 1.0) (* b (/ y t))))
     (if (<= t -1.85e-161)
       t_1
       (if (<= t -9.2e-195)
         (/ 1.0 (/ a (+ x (/ (* y z) t))))
         (if (<= t 1.3e-62)
           t_1
           (if (<= t 4.5e-27)
             (/ (* y z) (* t (+ a 1.0)))
             (/ x (+ (+ a 1.0) (/ y (/ t b)))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + ((x * t) / y)) / b;
	double tmp;
	if (t <= -3e-66) {
		tmp = x / ((a + 1.0) + (b * (y / t)));
	} else if (t <= -1.85e-161) {
		tmp = t_1;
	} else if (t <= -9.2e-195) {
		tmp = 1.0 / (a / (x + ((y * z) / t)));
	} else if (t <= 1.3e-62) {
		tmp = t_1;
	} else if (t <= 4.5e-27) {
		tmp = (y * z) / (t * (a + 1.0));
	} else {
		tmp = x / ((a + 1.0) + (y / (t / b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z + ((x * t) / y)) / b
    if (t <= (-3d-66)) then
        tmp = x / ((a + 1.0d0) + (b * (y / t)))
    else if (t <= (-1.85d-161)) then
        tmp = t_1
    else if (t <= (-9.2d-195)) then
        tmp = 1.0d0 / (a / (x + ((y * z) / t)))
    else if (t <= 1.3d-62) then
        tmp = t_1
    else if (t <= 4.5d-27) then
        tmp = (y * z) / (t * (a + 1.0d0))
    else
        tmp = x / ((a + 1.0d0) + (y / (t / b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + ((x * t) / y)) / b;
	double tmp;
	if (t <= -3e-66) {
		tmp = x / ((a + 1.0) + (b * (y / t)));
	} else if (t <= -1.85e-161) {
		tmp = t_1;
	} else if (t <= -9.2e-195) {
		tmp = 1.0 / (a / (x + ((y * z) / t)));
	} else if (t <= 1.3e-62) {
		tmp = t_1;
	} else if (t <= 4.5e-27) {
		tmp = (y * z) / (t * (a + 1.0));
	} else {
		tmp = x / ((a + 1.0) + (y / (t / b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + ((x * t) / y)) / b
	tmp = 0
	if t <= -3e-66:
		tmp = x / ((a + 1.0) + (b * (y / t)))
	elif t <= -1.85e-161:
		tmp = t_1
	elif t <= -9.2e-195:
		tmp = 1.0 / (a / (x + ((y * z) / t)))
	elif t <= 1.3e-62:
		tmp = t_1
	elif t <= 4.5e-27:
		tmp = (y * z) / (t * (a + 1.0))
	else:
		tmp = x / ((a + 1.0) + (y / (t / b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + Float64(Float64(x * t) / y)) / b)
	tmp = 0.0
	if (t <= -3e-66)
		tmp = Float64(x / Float64(Float64(a + 1.0) + Float64(b * Float64(y / t))));
	elseif (t <= -1.85e-161)
		tmp = t_1;
	elseif (t <= -9.2e-195)
		tmp = Float64(1.0 / Float64(a / Float64(x + Float64(Float64(y * z) / t))));
	elseif (t <= 1.3e-62)
		tmp = t_1;
	elseif (t <= 4.5e-27)
		tmp = Float64(Float64(y * z) / Float64(t * Float64(a + 1.0)));
	else
		tmp = Float64(x / Float64(Float64(a + 1.0) + Float64(y / Float64(t / b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + ((x * t) / y)) / b;
	tmp = 0.0;
	if (t <= -3e-66)
		tmp = x / ((a + 1.0) + (b * (y / t)));
	elseif (t <= -1.85e-161)
		tmp = t_1;
	elseif (t <= -9.2e-195)
		tmp = 1.0 / (a / (x + ((y * z) / t)));
	elseif (t <= 1.3e-62)
		tmp = t_1;
	elseif (t <= 4.5e-27)
		tmp = (y * z) / (t * (a + 1.0));
	else
		tmp = x / ((a + 1.0) + (y / (t / b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]}, If[LessEqual[t, -3e-66], N[(x / N[(N[(a + 1.0), $MachinePrecision] + N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.85e-161], t$95$1, If[LessEqual[t, -9.2e-195], N[(1.0 / N[(a / N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.3e-62], t$95$1, If[LessEqual[t, 4.5e-27], N[(N[(y * z), $MachinePrecision] / N[(t * N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(a + 1.0), $MachinePrecision] + N[(y / N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -3.0000000000000002e-66

   1. Initial program 87.4%

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

      1. associate-/l* 89.9%

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

      2. associate-/l* 93.2%

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

   3. Simplified 93.2%

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

   5. Taylor expanded in x around inf 70.5%

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

      1. associate-+r+ 70.5%

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

      2. associate-*r/ 71.6%

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

   7. Simplified 71.6%

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

   if -3.0000000000000002e-66 < t < -1.8499999999999999e-161 or -9.2000000000000007e-195 < t < 1.3e-62

   1. Initial program 54.3%

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

      1. associate-/l* 51.2%

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

      2. associate-/l* 46.2%

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

   3. Simplified 46.2%

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

   5. Taylor expanded in x around inf 50.2%

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

      1. associate-+r+ 50.2%

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

      2. associate-*r/ 50.1%

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

      3. associate-/l* 52.1%

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

      4. *-commutative 52.1%

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

      5. associate-+r+ 52.1%

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

      6. associate-*r/ 47.1%

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

   7. Simplified 47.1%

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

   8. Taylor expanded in b around inf 58.5%

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

   9. Taylor expanded in x around 0 68.2%

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

   if -1.8499999999999999e-161 < t < -9.2000000000000007e-195

   1. Initial program 87.9%

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

      1. associate-/l* 63.7%

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

      2. associate-/l* 63.7%

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

   3. Simplified 63.7%

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

      1. clear-num 63.7%

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

      2. inv-pow 63.7%

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

      3. +-commutative 63.7%

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

      4. fma-define 63.7%

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

      5. +-commutative 63.7%

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

      6. fma-define 63.7%

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

   6. Applied egg-rr 63.7%

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

      1. unpow-1 63.7%

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

      2. +-commutative 63.7%

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

   8. Simplified 63.7%

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

   9. Taylor expanded in a around inf 87.6%

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

   if 1.3e-62 < t < 4.5000000000000002e-27

   1. Initial program 89.4%

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

      1. associate-/l* 67.8%

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

      2. associate-/l* 57.3%

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

   3. Simplified 57.3%

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

   5. Taylor expanded in x around 0 88.7%

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

   6. Taylor expanded in y around 0 78.8%

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

   if 4.5000000000000002e-27 < t

   1. Initial program 79.6%

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

      1. associate-/l* 86.3%

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

      2. associate-/l* 96.4%

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

   3. Simplified 96.4%

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

   5. Taylor expanded in x around inf 63.3%

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

      1. associate-+r+ 63.3%

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

      2. associate-*r/ 68.3%

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

   7. Simplified 68.3%

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

      1. *-commutative 68.3%

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

      2. associate-/r/ 68.4%

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

   9. Applied egg-rr 68.4%

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

4. Final simplification 70.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{-66}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \mathbf{elif}\;t \leq -1.85 \cdot 10^{-161}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{elif}\;t \leq -9.2 \cdot 10^{-195}:\\ \;\;\;\;\frac{1}{\frac{a}{x + \frac{y \cdot z}{t}}}\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-62}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-27}:\\ \;\;\;\;\frac{y \cdot z}{t \cdot \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + \frac{y}{\frac{t}{b}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 64.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z + \frac{x \cdot t}{y}}{b}\\ t_2 := \frac{x}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \mathbf{if}\;t \leq -1.55 \cdot 10^{-67}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -2.5 \cdot 10^{-161}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{-194}:\\ \;\;\;\;\frac{1}{\frac{a}{x + \frac{y \cdot z}{t}}}\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-63}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-27}:\\ \;\;\;\;\frac{y \cdot z}{t \cdot \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ z (/ (* x t) y)) b))
        (t_2 (/ x (+ (+ a 1.0) (* b (/ y t))))))
   (if (<= t -1.55e-67)
     t_2
     (if (<= t -2.5e-161)
       t_1
       (if (<= t -1.05e-194)
         (/ 1.0 (/ a (+ x (/ (* y z) t))))
         (if (<= t 1.8e-63)
           t_1
           (if (<= t 4.6e-27) (/ (* y z) (* t (+ a 1.0))) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + ((x * t) / y)) / b;
	double t_2 = x / ((a + 1.0) + (b * (y / t)));
	double tmp;
	if (t <= -1.55e-67) {
		tmp = t_2;
	} else if (t <= -2.5e-161) {
		tmp = t_1;
	} else if (t <= -1.05e-194) {
		tmp = 1.0 / (a / (x + ((y * z) / t)));
	} else if (t <= 1.8e-63) {
		tmp = t_1;
	} else if (t <= 4.6e-27) {
		tmp = (y * z) / (t * (a + 1.0));
	} 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 = (z + ((x * t) / y)) / b
    t_2 = x / ((a + 1.0d0) + (b * (y / t)))
    if (t <= (-1.55d-67)) then
        tmp = t_2
    else if (t <= (-2.5d-161)) then
        tmp = t_1
    else if (t <= (-1.05d-194)) then
        tmp = 1.0d0 / (a / (x + ((y * z) / t)))
    else if (t <= 1.8d-63) then
        tmp = t_1
    else if (t <= 4.6d-27) then
        tmp = (y * z) / (t * (a + 1.0d0))
    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 = (z + ((x * t) / y)) / b;
	double t_2 = x / ((a + 1.0) + (b * (y / t)));
	double tmp;
	if (t <= -1.55e-67) {
		tmp = t_2;
	} else if (t <= -2.5e-161) {
		tmp = t_1;
	} else if (t <= -1.05e-194) {
		tmp = 1.0 / (a / (x + ((y * z) / t)));
	} else if (t <= 1.8e-63) {
		tmp = t_1;
	} else if (t <= 4.6e-27) {
		tmp = (y * z) / (t * (a + 1.0));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + ((x * t) / y)) / b
	t_2 = x / ((a + 1.0) + (b * (y / t)))
	tmp = 0
	if t <= -1.55e-67:
		tmp = t_2
	elif t <= -2.5e-161:
		tmp = t_1
	elif t <= -1.05e-194:
		tmp = 1.0 / (a / (x + ((y * z) / t)))
	elif t <= 1.8e-63:
		tmp = t_1
	elif t <= 4.6e-27:
		tmp = (y * z) / (t * (a + 1.0))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + Float64(Float64(x * t) / y)) / b)
	t_2 = Float64(x / Float64(Float64(a + 1.0) + Float64(b * Float64(y / t))))
	tmp = 0.0
	if (t <= -1.55e-67)
		tmp = t_2;
	elseif (t <= -2.5e-161)
		tmp = t_1;
	elseif (t <= -1.05e-194)
		tmp = Float64(1.0 / Float64(a / Float64(x + Float64(Float64(y * z) / t))));
	elseif (t <= 1.8e-63)
		tmp = t_1;
	elseif (t <= 4.6e-27)
		tmp = Float64(Float64(y * z) / Float64(t * Float64(a + 1.0)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + ((x * t) / y)) / b;
	t_2 = x / ((a + 1.0) + (b * (y / t)));
	tmp = 0.0;
	if (t <= -1.55e-67)
		tmp = t_2;
	elseif (t <= -2.5e-161)
		tmp = t_1;
	elseif (t <= -1.05e-194)
		tmp = 1.0 / (a / (x + ((y * z) / t)));
	elseif (t <= 1.8e-63)
		tmp = t_1;
	elseif (t <= 4.6e-27)
		tmp = (y * z) / (t * (a + 1.0));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(N[(a + 1.0), $MachinePrecision] + N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.55e-67], t$95$2, If[LessEqual[t, -2.5e-161], t$95$1, If[LessEqual[t, -1.05e-194], N[(1.0 / N[(a / N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.8e-63], t$95$1, If[LessEqual[t, 4.6e-27], N[(N[(y * z), $MachinePrecision] / N[(t * N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.5500000000000001e-67 or 4.5999999999999999e-27 < t

   1. Initial program 84.3%

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

      1. associate-/l* 88.4%

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

      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 x around inf 67.6%

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

      1. associate-+r+ 67.6%

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

      2. associate-*r/ 70.3%

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

   7. Simplified 70.3%

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

   if -1.5500000000000001e-67 < t < -2.5e-161 or -1.05e-194 < t < 1.80000000000000004e-63

   1. Initial program 54.3%

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

      1. associate-/l* 51.2%

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

      2. associate-/l* 46.2%

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

   3. Simplified 46.2%

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

   5. Taylor expanded in x around inf 50.2%

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

      1. associate-+r+ 50.2%

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

      2. associate-*r/ 50.1%

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

      3. associate-/l* 52.1%

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

      4. *-commutative 52.1%

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

      5. associate-+r+ 52.1%

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

      6. associate-*r/ 47.1%

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

   7. Simplified 47.1%

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

   8. Taylor expanded in b around inf 58.5%

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

   9. Taylor expanded in x around 0 68.2%

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

   if -2.5e-161 < t < -1.05e-194

   1. Initial program 87.9%

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

      1. associate-/l* 63.7%

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

      2. associate-/l* 63.7%

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

   3. Simplified 63.7%

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

      1. clear-num 63.7%

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

      2. inv-pow 63.7%

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

      3. +-commutative 63.7%

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

      4. fma-define 63.7%

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

      5. +-commutative 63.7%

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

      6. fma-define 63.7%

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

   6. Applied egg-rr 63.7%

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

      1. unpow-1 63.7%

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

      2. +-commutative 63.7%

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

   8. Simplified 63.7%

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

   9. Taylor expanded in a around inf 87.6%

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

   if 1.80000000000000004e-63 < t < 4.5999999999999999e-27

   1. Initial program 89.4%

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

      1. associate-/l* 67.8%

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

      2. associate-/l* 57.3%

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

   3. Simplified 57.3%

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

   5. Taylor expanded in x around 0 88.7%

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

   6. Taylor expanded in y around 0 78.8%

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

4. Final simplification 70.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.55 \cdot 10^{-67}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \mathbf{elif}\;t \leq -2.5 \cdot 10^{-161}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{-194}:\\ \;\;\;\;\frac{1}{\frac{a}{x + \frac{y \cdot z}{t}}}\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-63}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-27}:\\ \;\;\;\;\frac{y \cdot z}{t \cdot \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 63.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z + \frac{x \cdot t}{y}}{b}\\ t_2 := \frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \mathbf{if}\;t \leq -5 \cdot 10^{-65}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1.75 \cdot 10^{-159}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{-194}:\\ \;\;\;\;\frac{1}{\frac{a}{x + \frac{y \cdot z}{t}}}\\ \mathbf{elif}\;t \leq 8 \cdot 10^{-63}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-27}:\\ \;\;\;\;\frac{y \cdot z}{t \cdot \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ z (/ (* x t) y)) b))
        (t_2 (/ x (+ 1.0 (+ a (/ (* y b) t))))))
   (if (<= t -5e-65)
     t_2
     (if (<= t -1.75e-159)
       t_1
       (if (<= t -1.05e-194)
         (/ 1.0 (/ a (+ x (/ (* y z) t))))
         (if (<= t 8e-63)
           t_1
           (if (<= t 4.5e-27) (/ (* y z) (* t (+ a 1.0))) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + ((x * t) / y)) / b;
	double t_2 = x / (1.0 + (a + ((y * b) / t)));
	double tmp;
	if (t <= -5e-65) {
		tmp = t_2;
	} else if (t <= -1.75e-159) {
		tmp = t_1;
	} else if (t <= -1.05e-194) {
		tmp = 1.0 / (a / (x + ((y * z) / t)));
	} else if (t <= 8e-63) {
		tmp = t_1;
	} else if (t <= 4.5e-27) {
		tmp = (y * z) / (t * (a + 1.0));
	} 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 = (z + ((x * t) / y)) / b
    t_2 = x / (1.0d0 + (a + ((y * b) / t)))
    if (t <= (-5d-65)) then
        tmp = t_2
    else if (t <= (-1.75d-159)) then
        tmp = t_1
    else if (t <= (-1.05d-194)) then
        tmp = 1.0d0 / (a / (x + ((y * z) / t)))
    else if (t <= 8d-63) then
        tmp = t_1
    else if (t <= 4.5d-27) then
        tmp = (y * z) / (t * (a + 1.0d0))
    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 = (z + ((x * t) / y)) / b;
	double t_2 = x / (1.0 + (a + ((y * b) / t)));
	double tmp;
	if (t <= -5e-65) {
		tmp = t_2;
	} else if (t <= -1.75e-159) {
		tmp = t_1;
	} else if (t <= -1.05e-194) {
		tmp = 1.0 / (a / (x + ((y * z) / t)));
	} else if (t <= 8e-63) {
		tmp = t_1;
	} else if (t <= 4.5e-27) {
		tmp = (y * z) / (t * (a + 1.0));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + ((x * t) / y)) / b
	t_2 = x / (1.0 + (a + ((y * b) / t)))
	tmp = 0
	if t <= -5e-65:
		tmp = t_2
	elif t <= -1.75e-159:
		tmp = t_1
	elif t <= -1.05e-194:
		tmp = 1.0 / (a / (x + ((y * z) / t)))
	elif t <= 8e-63:
		tmp = t_1
	elif t <= 4.5e-27:
		tmp = (y * z) / (t * (a + 1.0))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + Float64(Float64(x * t) / y)) / b)
	t_2 = Float64(x / Float64(1.0 + Float64(a + Float64(Float64(y * b) / t))))
	tmp = 0.0
	if (t <= -5e-65)
		tmp = t_2;
	elseif (t <= -1.75e-159)
		tmp = t_1;
	elseif (t <= -1.05e-194)
		tmp = Float64(1.0 / Float64(a / Float64(x + Float64(Float64(y * z) / t))));
	elseif (t <= 8e-63)
		tmp = t_1;
	elseif (t <= 4.5e-27)
		tmp = Float64(Float64(y * z) / Float64(t * Float64(a + 1.0)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + ((x * t) / y)) / b;
	t_2 = x / (1.0 + (a + ((y * b) / t)));
	tmp = 0.0;
	if (t <= -5e-65)
		tmp = t_2;
	elseif (t <= -1.75e-159)
		tmp = t_1;
	elseif (t <= -1.05e-194)
		tmp = 1.0 / (a / (x + ((y * z) / t)));
	elseif (t <= 8e-63)
		tmp = t_1;
	elseif (t <= 4.5e-27)
		tmp = (y * z) / (t * (a + 1.0));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(1.0 + N[(a + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5e-65], t$95$2, If[LessEqual[t, -1.75e-159], t$95$1, If[LessEqual[t, -1.05e-194], N[(1.0 / N[(a / N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8e-63], t$95$1, If[LessEqual[t, 4.5e-27], N[(N[(y * z), $MachinePrecision] / N[(t * N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -4.99999999999999983e-65 or 4.5000000000000002e-27 < t

   1. Initial program 84.3%

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

      1. associate-/l* 88.4%

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

      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 x around inf 67.6%

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

   if -4.99999999999999983e-65 < t < -1.75000000000000001e-159 or -1.05e-194 < t < 8.00000000000000053e-63

   1. Initial program 54.3%

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

      1. associate-/l* 51.2%

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

      2. associate-/l* 46.2%

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

   3. Simplified 46.2%

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

   5. Taylor expanded in x around inf 50.2%

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

      1. associate-+r+ 50.2%

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

      2. associate-*r/ 50.1%

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

      3. associate-/l* 52.1%

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

      4. *-commutative 52.1%

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

      5. associate-+r+ 52.1%

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

      6. associate-*r/ 47.1%

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

   7. Simplified 47.1%

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

   8. Taylor expanded in b around inf 58.5%

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

   9. Taylor expanded in x around 0 68.2%

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

   if -1.75000000000000001e-159 < t < -1.05e-194

   1. Initial program 87.9%

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

      1. associate-/l* 63.7%

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

      2. associate-/l* 63.7%

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

   3. Simplified 63.7%

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

      1. clear-num 63.7%

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

      2. inv-pow 63.7%

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

      3. +-commutative 63.7%

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

      4. fma-define 63.7%

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

      5. +-commutative 63.7%

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

      6. fma-define 63.7%

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

   6. Applied egg-rr 63.7%

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

      1. unpow-1 63.7%

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

      2. +-commutative 63.7%

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

   8. Simplified 63.7%

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

   9. Taylor expanded in a around inf 87.6%

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

   if 8.00000000000000053e-63 < t < 4.5000000000000002e-27

   1. Initial program 89.4%

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

      1. associate-/l* 67.8%

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

      2. associate-/l* 57.3%

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

   3. Simplified 57.3%

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

   5. Taylor expanded in x around 0 88.7%

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

   6. Taylor expanded in y around 0 78.8%

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

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{-65}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \mathbf{elif}\;t \leq -1.75 \cdot 10^{-159}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{-194}:\\ \;\;\;\;\frac{1}{\frac{a}{x + \frac{y \cdot z}{t}}}\\ \mathbf{elif}\;t \leq 8 \cdot 10^{-63}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-27}:\\ \;\;\;\;\frac{y \cdot z}{t \cdot \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 66.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z + \frac{x \cdot t}{y}}{b}\\ t_2 := x + \frac{y \cdot z}{t}\\ t_3 := \frac{t\_2}{a + 1}\\ \mathbf{if}\;t \leq -6.4 \cdot 10^{-70}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq -1.4 \cdot 10^{-160}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{-194}:\\ \;\;\;\;\frac{1}{\frac{a}{t\_2}}\\ \mathbf{elif}\;t \leq 1.36 \cdot 10^{-171}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ z (/ (* x t) y)) b))
        (t_2 (+ x (/ (* y z) t)))
        (t_3 (/ t_2 (+ a 1.0))))
   (if (<= t -6.4e-70)
     t_3
     (if (<= t -1.4e-160)
       t_1
       (if (<= t -1.05e-194)
         (/ 1.0 (/ a t_2))
         (if (<= t 1.36e-171) t_1 t_3))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + ((x * t) / y)) / b;
	double t_2 = x + ((y * z) / t);
	double t_3 = t_2 / (a + 1.0);
	double tmp;
	if (t <= -6.4e-70) {
		tmp = t_3;
	} else if (t <= -1.4e-160) {
		tmp = t_1;
	} else if (t <= -1.05e-194) {
		tmp = 1.0 / (a / t_2);
	} else if (t <= 1.36e-171) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (z + ((x * t) / y)) / b
    t_2 = x + ((y * z) / t)
    t_3 = t_2 / (a + 1.0d0)
    if (t <= (-6.4d-70)) then
        tmp = t_3
    else if (t <= (-1.4d-160)) then
        tmp = t_1
    else if (t <= (-1.05d-194)) then
        tmp = 1.0d0 / (a / t_2)
    else if (t <= 1.36d-171) then
        tmp = t_1
    else
        tmp = t_3
    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 + ((x * t) / y)) / b;
	double t_2 = x + ((y * z) / t);
	double t_3 = t_2 / (a + 1.0);
	double tmp;
	if (t <= -6.4e-70) {
		tmp = t_3;
	} else if (t <= -1.4e-160) {
		tmp = t_1;
	} else if (t <= -1.05e-194) {
		tmp = 1.0 / (a / t_2);
	} else if (t <= 1.36e-171) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + ((x * t) / y)) / b
	t_2 = x + ((y * z) / t)
	t_3 = t_2 / (a + 1.0)
	tmp = 0
	if t <= -6.4e-70:
		tmp = t_3
	elif t <= -1.4e-160:
		tmp = t_1
	elif t <= -1.05e-194:
		tmp = 1.0 / (a / t_2)
	elif t <= 1.36e-171:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + Float64(Float64(x * t) / y)) / b)
	t_2 = Float64(x + Float64(Float64(y * z) / t))
	t_3 = Float64(t_2 / Float64(a + 1.0))
	tmp = 0.0
	if (t <= -6.4e-70)
		tmp = t_3;
	elseif (t <= -1.4e-160)
		tmp = t_1;
	elseif (t <= -1.05e-194)
		tmp = Float64(1.0 / Float64(a / t_2));
	elseif (t <= 1.36e-171)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + ((x * t) / y)) / b;
	t_2 = x + ((y * z) / t);
	t_3 = t_2 / (a + 1.0);
	tmp = 0.0;
	if (t <= -6.4e-70)
		tmp = t_3;
	elseif (t <= -1.4e-160)
		tmp = t_1;
	elseif (t <= -1.05e-194)
		tmp = 1.0 / (a / t_2);
	elseif (t <= 1.36e-171)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6.4e-70], t$95$3, If[LessEqual[t, -1.4e-160], t$95$1, If[LessEqual[t, -1.05e-194], N[(1.0 / N[(a / t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.36e-171], t$95$1, t$95$3]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.3999999999999995e-70 or 1.3599999999999999e-171 < t

   1. Initial program 83.3%

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

      1. associate-/l* 84.5%

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

      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 b around 0 70.6%

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

   if -6.3999999999999995e-70 < t < -1.40000000000000008e-160 or -1.05e-194 < t < 1.3599999999999999e-171

   1. Initial program 50.7%

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

      1. associate-/l* 49.3%

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

      2. associate-/l* 43.3%

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

   3. Simplified 43.3%

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

   5. Taylor expanded in x around inf 46.8%

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

      1. associate-+r+ 46.8%

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

      2. associate-*r/ 46.7%

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

      3. associate-/l* 49.1%

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

      4. *-commutative 49.1%

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

      5. associate-+r+ 49.1%

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

      6. associate-*r/ 45.5%

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

   7. Simplified 45.5%

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

   8. Taylor expanded in b around inf 65.4%

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

   9. Taylor expanded in x around 0 73.6%

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

   if -1.40000000000000008e-160 < t < -1.05e-194

   1. Initial program 87.9%

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

      1. associate-/l* 63.7%

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

      2. associate-/l* 63.7%

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

   3. Simplified 63.7%

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

      1. clear-num 63.7%

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

      2. inv-pow 63.7%

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

      3. +-commutative 63.7%

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

      4. fma-define 63.7%

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

      5. +-commutative 63.7%

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

      6. fma-define 63.7%

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

   6. Applied egg-rr 63.7%

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

      1. unpow-1 63.7%

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

      2. +-commutative 63.7%

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

   8. Simplified 63.7%

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

   9. Taylor expanded in a around inf 87.6%

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

4. Final simplification 72.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.4 \cdot 10^{-70}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \mathbf{elif}\;t \leq -1.4 \cdot 10^{-160}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{-194}:\\ \;\;\;\;\frac{1}{\frac{a}{x + \frac{y \cdot z}{t}}}\\ \mathbf{elif}\;t \leq 1.36 \cdot 10^{-171}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 56.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{if}\;y \leq -2.55 \cdot 10^{+95}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{+15}:\\ \;\;\;\;\frac{y \cdot \frac{z}{t}}{a + 1}\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-113} \lor \neg \left(y \leq 8100000000\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ z (/ (* x t) y)) b)))
   (if (<= y -2.55e+95)
     t_1
     (if (<= y -1.35e+15)
       (/ (* y (/ z t)) (+ a 1.0))
       (if (or (<= y -2.1e-113) (not (<= y 8100000000.0)))
         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 + ((x * t) / y)) / b;
	double tmp;
	if (y <= -2.55e+95) {
		tmp = t_1;
	} else if (y <= -1.35e+15) {
		tmp = (y * (z / t)) / (a + 1.0);
	} else if ((y <= -2.1e-113) || !(y <= 8100000000.0)) {
		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 + ((x * t) / y)) / b
    if (y <= (-2.55d+95)) then
        tmp = t_1
    else if (y <= (-1.35d+15)) then
        tmp = (y * (z / t)) / (a + 1.0d0)
    else if ((y <= (-2.1d-113)) .or. (.not. (y <= 8100000000.0d0))) 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 + ((x * t) / y)) / b;
	double tmp;
	if (y <= -2.55e+95) {
		tmp = t_1;
	} else if (y <= -1.35e+15) {
		tmp = (y * (z / t)) / (a + 1.0);
	} else if ((y <= -2.1e-113) || !(y <= 8100000000.0)) {
		tmp = t_1;
	} else {
		tmp = x / (a + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + ((x * t) / y)) / b
	tmp = 0
	if y <= -2.55e+95:
		tmp = t_1
	elif y <= -1.35e+15:
		tmp = (y * (z / t)) / (a + 1.0)
	elif (y <= -2.1e-113) or not (y <= 8100000000.0):
		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 + Float64(Float64(x * t) / y)) / b)
	tmp = 0.0
	if (y <= -2.55e+95)
		tmp = t_1;
	elseif (y <= -1.35e+15)
		tmp = Float64(Float64(y * Float64(z / t)) / Float64(a + 1.0));
	elseif ((y <= -2.1e-113) || !(y <= 8100000000.0))
		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 + ((x * t) / y)) / b;
	tmp = 0.0;
	if (y <= -2.55e+95)
		tmp = t_1;
	elseif (y <= -1.35e+15)
		tmp = (y * (z / t)) / (a + 1.0);
	elseif ((y <= -2.1e-113) || ~((y <= 8100000000.0)))
		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 + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]}, If[LessEqual[y, -2.55e+95], t$95$1, If[LessEqual[y, -1.35e+15], N[(N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -2.1e-113], N[Not[LessEqual[y, 8100000000.0]], $MachinePrecision]], t$95$1, N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.55000000000000001e95 or -1.35e15 < y < -2.1e-113 or 8.1e9 < y

   1. Initial program 56.8%

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

      1. associate-/l* 59.8%

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

      2. associate-/l* 64.0%

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

   3. Simplified 64.0%

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

   5. Taylor expanded in x around inf 53.5%

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

      1. associate-+r+ 53.5%

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

      2. associate-*r/ 55.5%

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

      3. associate-/l* 60.6%

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

      4. *-commutative 60.6%

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

      5. associate-+r+ 60.6%

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

      6. associate-*r/ 58.7%

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

   7. Simplified 58.7%

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

   8. Taylor expanded in b around inf 53.5%

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

   9. Taylor expanded in x around 0 58.2%

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

   if -2.55000000000000001e95 < y < -1.35e15

   1. Initial program 74.2%

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

      1. associate-/l* 87.5%

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

      2. associate-/l* 93.9%

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

   3. Simplified 93.9%

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

   5. Taylor expanded in x around 0 54.3%

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

   6. Taylor expanded in y around 0 48.3%

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

      1. associate-/r* 48.6%

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

      2. associate-*r/ 61.7%

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

   8. Simplified 61.7%

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

   if -2.1e-113 < y < 8.1e9

   1. Initial program 93.6%

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

      1. associate-/l* 87.1%

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

      2. associate-/l* 83.5%

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

   3. Simplified 83.5%

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

   5. Taylor expanded in y around 0 69.8%

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

4. Final simplification 63.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.55 \cdot 10^{+95}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{+15}:\\ \;\;\;\;\frac{y \cdot \frac{z}{t}}{a + 1}\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-113} \lor \neg \left(y \leq 8100000000\right):\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 56.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{a + 1}\\ \mathbf{if}\;y \leq -3.5 \cdot 10^{+95}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-151}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{-101}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a}\\ \mathbf{elif}\;y \leq 4600000000000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (+ a 1.0))))
   (if (<= y -3.5e+95)
     (/ z b)
     (if (<= y 2.4e-151)
       t_1
       (if (<= y 2.2e-101)
         (/ (+ x (/ (* y z) t)) a)
         (if (<= y 4600000000000.0) t_1 (/ z b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a + 1.0);
	double tmp;
	if (y <= -3.5e+95) {
		tmp = z / b;
	} else if (y <= 2.4e-151) {
		tmp = t_1;
	} else if (y <= 2.2e-101) {
		tmp = (x + ((y * z) / t)) / a;
	} else if (y <= 4600000000000.0) {
		tmp = t_1;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (a + 1.0d0)
    if (y <= (-3.5d+95)) then
        tmp = z / b
    else if (y <= 2.4d-151) then
        tmp = t_1
    else if (y <= 2.2d-101) then
        tmp = (x + ((y * z) / t)) / a
    else if (y <= 4600000000000.0d0) then
        tmp = t_1
    else
        tmp = z / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a + 1.0);
	double tmp;
	if (y <= -3.5e+95) {
		tmp = z / b;
	} else if (y <= 2.4e-151) {
		tmp = t_1;
	} else if (y <= 2.2e-101) {
		tmp = (x + ((y * z) / t)) / a;
	} else if (y <= 4600000000000.0) {
		tmp = t_1;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (a + 1.0)
	tmp = 0
	if y <= -3.5e+95:
		tmp = z / b
	elif y <= 2.4e-151:
		tmp = t_1
	elif y <= 2.2e-101:
		tmp = (x + ((y * z) / t)) / a
	elif y <= 4600000000000.0:
		tmp = t_1
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(a + 1.0))
	tmp = 0.0
	if (y <= -3.5e+95)
		tmp = Float64(z / b);
	elseif (y <= 2.4e-151)
		tmp = t_1;
	elseif (y <= 2.2e-101)
		tmp = Float64(Float64(x + Float64(Float64(y * z) / t)) / a);
	elseif (y <= 4600000000000.0)
		tmp = t_1;
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (a + 1.0);
	tmp = 0.0;
	if (y <= -3.5e+95)
		tmp = z / b;
	elseif (y <= 2.4e-151)
		tmp = t_1;
	elseif (y <= 2.2e-101)
		tmp = (x + ((y * z) / t)) / a;
	elseif (y <= 4600000000000.0)
		tmp = t_1;
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.5e+95], N[(z / b), $MachinePrecision], If[LessEqual[y, 2.4e-151], t$95$1, If[LessEqual[y, 2.2e-101], N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[y, 4600000000000.0], t$95$1, N[(z / b), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.5e95 or 4.6e12 < y

   1. Initial program 48.9%

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

      1. associate-/l* 52.8%

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

      2. associate-/l* 60.3%

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

   3. Simplified 60.3%

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

   5. Taylor expanded in y around inf 60.2%

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

   if -3.5e95 < y < 2.4e-151 or 2.1999999999999999e-101 < y < 4.6e12

   1. Initial program 88.3%

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

      1. associate-/l* 86.9%

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

      2. associate-/l* 83.7%

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

   3. Simplified 83.7%

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

   5. Taylor expanded in y around 0 59.0%

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

   if 2.4e-151 < y < 2.1999999999999999e-101

   1. Initial program 99.8%

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

      1. associate-/l* 58.6%

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

      2. associate-/l* 58.6%

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

   3. Simplified 58.6%

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

   5. Taylor expanded in a around inf 99.8%

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

4. Final simplification 60.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{+95}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-151}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{-101}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a}\\ \mathbf{elif}\;y \leq 4600000000000:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 57.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+95} \lor \neg \left(y \leq 1750000000000\right):\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -2.7e+95) (not (<= y 1750000000000.0)))
   (/ 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 <= -2.7e+95) || !(y <= 1750000000000.0)) {
		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 <= (-2.7d+95)) .or. (.not. (y <= 1750000000000.0d0))) 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 <= -2.7e+95) || !(y <= 1750000000000.0)) {
		tmp = z / b;
	} else {
		tmp = x / (a + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -2.7e+95) or not (y <= 1750000000000.0):
		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 <= -2.7e+95) || !(y <= 1750000000000.0))
		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 <= -2.7e+95) || ~((y <= 1750000000000.0)))
		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, -2.7e+95], N[Not[LessEqual[y, 1750000000000.0]], $MachinePrecision]], N[(z / b), $MachinePrecision], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.7e95 or 1.75e12 < y

   1. Initial program 48.9%

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

      1. associate-/l* 52.8%

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

      2. associate-/l* 60.3%

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

   3. Simplified 60.3%

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

   5. Taylor expanded in y around inf 60.2%

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

   if -2.7e95 < y < 1.75e12

   1. Initial program 88.8%

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

      1. associate-/l* 85.7%

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

      2. associate-/l* 82.6%

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

   3. Simplified 82.6%

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

   5. Taylor expanded in y around 0 57.8%

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

4. Final simplification 58.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+95} \lor \neg \left(y \leq 1750000000000\right):\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 42.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{-138} \lor \neg \left(y \leq 5800000000\right):\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -2.5e-138) (not (<= y 5800000000.0))) (/ z b) (/ x a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.5e-138) || !(y <= 5800000000.0)) {
		tmp = z / b;
	} else {
		tmp = x / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-2.5d-138)) .or. (.not. (y <= 5800000000.0d0))) then
        tmp = z / b
    else
        tmp = x / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.5e-138) || !(y <= 5800000000.0)) {
		tmp = z / b;
	} else {
		tmp = x / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -2.5e-138) or not (y <= 5800000000.0):
		tmp = z / b
	else:
		tmp = x / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -2.5e-138) || !(y <= 5800000000.0))
		tmp = Float64(z / b);
	else
		tmp = Float64(x / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -2.5e-138) || ~((y <= 5800000000.0)))
		tmp = z / b;
	else
		tmp = x / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -2.5e-138], N[Not[LessEqual[y, 5800000000.0]], $MachinePrecision]], N[(z / b), $MachinePrecision], N[(x / a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.49999999999999994e-138 or 5.8e9 < y

   1. Initial program 58.9%

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

      1. associate-/l* 62.8%

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

      2. associate-/l* 67.2%

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

   3. Simplified 67.2%

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

   5. Taylor expanded in y around inf 48.2%

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

   if -2.49999999999999994e-138 < y < 5.8e9

   1. Initial program 93.6%

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

      1. associate-/l* 87.0%

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

      2. associate-/l* 83.4%

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

   3. Simplified 83.4%

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

   5. Taylor expanded in x around inf 75.9%

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

      1. associate-+r+ 75.9%

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

      2. associate-*r/ 75.9%

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

   7. Simplified 75.9%

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

   8. Taylor expanded in a around inf 41.1%

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

4. Final simplification 45.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{-138} \lor \neg \left(y \leq 5800000000\right):\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 25.9% accurate, 5.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 73.2%

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

   1. associate-/l* 72.8%

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

   2. associate-/l* 73.9%

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

3. Simplified 73.9%

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

5. Taylor expanded in x around inf 53.1%

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

   1. associate-+r+ 53.1%

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

   2. associate-*r/ 54.2%

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

7. Simplified 54.2%

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

8. Taylor expanded in a around inf 27.2%

   \[\leadsto \color{blue}{\frac{x}{a}} \]
9. Add Preprocessing

Developer target: 79.8% 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 2024103 
(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))))