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

Percentage Accurate: 75.1% → 90.8%

Time: 20.1s

Alternatives: 18

Speedup: 0.6×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 75.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 90.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot b}{t}\\ t_2 := t\_1 + \left(a + 1\right)\\ t_3 := \frac{x + \frac{y \cdot z}{t}}{t\_2}\\ \mathbf{if}\;t\_3 \leq -5 \cdot 10^{-319}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{t\_2}\\ \mathbf{elif}\;t\_3 \leq 0:\\ \;\;\;\;\frac{t \cdot \frac{x}{b} + y \cdot \frac{z}{b}}{y}\\ \mathbf{elif}\;t\_3 \leq 10^{+307}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_3 \leq \infty:\\ \;\;\;\;z \cdot \left(\frac{x}{z \cdot \left(1 + \left(a + t\_1\right)\right)} + \frac{y}{y \cdot b + t \cdot \left(a + 1\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* y b) t))
        (t_2 (+ t_1 (+ a 1.0)))
        (t_3 (/ (+ x (/ (* y z) t)) t_2)))
   (if (<= t_3 -5e-319)
     (/ (+ x (* z (/ y t))) t_2)
     (if (<= t_3 0.0)
       (/ (+ (* t (/ x b)) (* y (/ z b))) y)
       (if (<= t_3 1e+307)
         t_3
         (if (<= t_3 INFINITY)
           (*
            z
            (+
             (/ x (* z (+ 1.0 (+ a t_1))))
             (/ y (+ (* y b) (* t (+ a 1.0))))))
           (/ z b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y * b) / t;
	double t_2 = t_1 + (a + 1.0);
	double t_3 = (x + ((y * z) / t)) / t_2;
	double tmp;
	if (t_3 <= -5e-319) {
		tmp = (x + (z * (y / t))) / t_2;
	} else if (t_3 <= 0.0) {
		tmp = ((t * (x / b)) + (y * (z / b))) / y;
	} else if (t_3 <= 1e+307) {
		tmp = t_3;
	} else if (t_3 <= ((double) INFINITY)) {
		tmp = z * ((x / (z * (1.0 + (a + t_1)))) + (y / ((y * b) + (t * (a + 1.0)))));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y * b) / t;
	double t_2 = t_1 + (a + 1.0);
	double t_3 = (x + ((y * z) / t)) / t_2;
	double tmp;
	if (t_3 <= -5e-319) {
		tmp = (x + (z * (y / t))) / t_2;
	} else if (t_3 <= 0.0) {
		tmp = ((t * (x / b)) + (y * (z / b))) / y;
	} else if (t_3 <= 1e+307) {
		tmp = t_3;
	} else if (t_3 <= Double.POSITIVE_INFINITY) {
		tmp = z * ((x / (z * (1.0 + (a + t_1)))) + (y / ((y * b) + (t * (a + 1.0)))));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (y * b) / t
	t_2 = t_1 + (a + 1.0)
	t_3 = (x + ((y * z) / t)) / t_2
	tmp = 0
	if t_3 <= -5e-319:
		tmp = (x + (z * (y / t))) / t_2
	elif t_3 <= 0.0:
		tmp = ((t * (x / b)) + (y * (z / b))) / y
	elif t_3 <= 1e+307:
		tmp = t_3
	elif t_3 <= math.inf:
		tmp = z * ((x / (z * (1.0 + (a + t_1)))) + (y / ((y * b) + (t * (a + 1.0)))))
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y * b) / t)
	t_2 = Float64(t_1 + Float64(a + 1.0))
	t_3 = Float64(Float64(x + Float64(Float64(y * z) / t)) / t_2)
	tmp = 0.0
	if (t_3 <= -5e-319)
		tmp = Float64(Float64(x + Float64(z * Float64(y / t))) / t_2);
	elseif (t_3 <= 0.0)
		tmp = Float64(Float64(Float64(t * Float64(x / b)) + Float64(y * Float64(z / b))) / y);
	elseif (t_3 <= 1e+307)
		tmp = t_3;
	elseif (t_3 <= Inf)
		tmp = Float64(z * Float64(Float64(x / Float64(z * Float64(1.0 + Float64(a + t_1)))) + Float64(y / Float64(Float64(y * b) + Float64(t * Float64(a + 1.0))))));
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (y * b) / t;
	t_2 = t_1 + (a + 1.0);
	t_3 = (x + ((y * z) / t)) / t_2;
	tmp = 0.0;
	if (t_3 <= -5e-319)
		tmp = (x + (z * (y / t))) / t_2;
	elseif (t_3 <= 0.0)
		tmp = ((t * (x / b)) + (y * (z / b))) / y;
	elseif (t_3 <= 1e+307)
		tmp = t_3;
	elseif (t_3 <= Inf)
		tmp = z * ((x / (z * (1.0 + (a + t_1)))) + (y / ((y * b) + (t * (a + 1.0)))));
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]}, If[LessEqual[t$95$3, -5e-319], N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision], If[LessEqual[t$95$3, 0.0], N[(N[(N[(t * N[(x / b), $MachinePrecision]), $MachinePrecision] + N[(y * N[(z / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t$95$3, 1e+307], t$95$3, If[LessEqual[t$95$3, Infinity], N[(z * N[(N[(x / N[(z * N[(1.0 + N[(a + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y / N[(N[(y * b), $MachinePrecision] + N[(t * N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $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))) < -4.9999937e-319

   1. Initial program 90.8%

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

      1. *-commutative 90.8%

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

      2. associate-/l* 92.8%

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

   4. Applied egg-rr 92.8%

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

   if -4.9999937e-319 < (/.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 45.6%

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

      1. associate-/l* 45.5%

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

      2. associate-/l* 56.9%

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

   3. Simplified 56.9%

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

   5. Taylor expanded in b around inf 49.5%

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

      1. times-frac 63.0%

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

      2. +-commutative 63.0%

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

      3. associate-*r/ 63.0%

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

      4. fma-undefine 63.0%

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

   7. Simplified 63.0%

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

   8. Taylor expanded in x around inf 45.5%

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

      1. *-commutative 45.5%

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

   10. Simplified 45.5%

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

   11. Taylor expanded in y around 0 73.1%

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

       1. associate-/l* 79.0%

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

       2. associate-/l* 79.2%

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

   13. Simplified 79.2%

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

   if -0.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 9.99999999999999986e306

   1. Initial program 98.7%

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

   if 9.99999999999999986e306 < (/.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 29.5%

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

      1. associate-/l* 53.1%

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

      2. associate-/l* 53.1%

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

   3. Simplified 53.1%

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

   5. Taylor expanded in z around inf 99.6%

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

   6. Taylor expanded in t around 0 99.6%

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

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

   1. Initial program 0.0%

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

      1. associate-/l* 0.0%

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

      2. associate-/l* 0.3%

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

   3. Simplified 0.3%

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

   5. Taylor expanded in y around inf 94.5%

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

4. Final simplification 92.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -5 \cdot 10^{-319}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 0:\\ \;\;\;\;\frac{t \cdot \frac{x}{b} + y \cdot \frac{z}{b}}{y}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 10^{+307}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq \infty:\\ \;\;\;\;z \cdot \left(\frac{x}{z \cdot \left(1 + \left(a + \frac{y \cdot b}{t}\right)\right)} + \frac{y}{y \cdot b + t \cdot \left(a + 1\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 90.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot b}{t} + \left(a + 1\right)\\ t_2 := \frac{x + \frac{y \cdot z}{t}}{t\_1}\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{-319}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{t\_1}\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;\frac{t \cdot \frac{x}{b} + y \cdot \frac{z}{b}}{y}\\ \mathbf{elif}\;t\_2 \leq 10^{+307}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;y \cdot \frac{z}{t \cdot \left(1 + \left(a + y \cdot \frac{b}{t}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (/ (* y b) t) (+ a 1.0))) (t_2 (/ (+ x (/ (* y z) t)) t_1)))
   (if (<= t_2 -5e-319)
     (/ (+ x (* z (/ y t))) t_1)
     (if (<= t_2 0.0)
       (/ (+ (* t (/ x b)) (* y (/ z b))) y)
       (if (<= t_2 1e+307)
         t_2
         (if (<= t_2 INFINITY)
           (* y (/ z (* t (+ 1.0 (+ a (* y (/ b t)))))))
           (/ z b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y * b) / t) + (a + 1.0);
	double t_2 = (x + ((y * z) / t)) / t_1;
	double tmp;
	if (t_2 <= -5e-319) {
		tmp = (x + (z * (y / t))) / t_1;
	} else if (t_2 <= 0.0) {
		tmp = ((t * (x / b)) + (y * (z / b))) / y;
	} else if (t_2 <= 1e+307) {
		tmp = t_2;
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = y * (z / (t * (1.0 + (a + (y * (b / 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 = ((y * b) / t) + (a + 1.0);
	double t_2 = (x + ((y * z) / t)) / t_1;
	double tmp;
	if (t_2 <= -5e-319) {
		tmp = (x + (z * (y / t))) / t_1;
	} else if (t_2 <= 0.0) {
		tmp = ((t * (x / b)) + (y * (z / b))) / y;
	} else if (t_2 <= 1e+307) {
		tmp = t_2;
	} else if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = y * (z / (t * (1.0 + (a + (y * (b / t))))));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((y * b) / t) + (a + 1.0)
	t_2 = (x + ((y * z) / t)) / t_1
	tmp = 0
	if t_2 <= -5e-319:
		tmp = (x + (z * (y / t))) / t_1
	elif t_2 <= 0.0:
		tmp = ((t * (x / b)) + (y * (z / b))) / y
	elif t_2 <= 1e+307:
		tmp = t_2
	elif t_2 <= math.inf:
		tmp = y * (z / (t * (1.0 + (a + (y * (b / t))))))
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(y * b) / t) + Float64(a + 1.0))
	t_2 = Float64(Float64(x + Float64(Float64(y * z) / t)) / t_1)
	tmp = 0.0
	if (t_2 <= -5e-319)
		tmp = Float64(Float64(x + Float64(z * Float64(y / t))) / t_1);
	elseif (t_2 <= 0.0)
		tmp = Float64(Float64(Float64(t * Float64(x / b)) + Float64(y * Float64(z / b))) / y);
	elseif (t_2 <= 1e+307)
		tmp = t_2;
	elseif (t_2 <= Inf)
		tmp = Float64(y * Float64(z / Float64(t * Float64(1.0 + Float64(a + Float64(y * Float64(b / t)))))));
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((y * b) / t) + (a + 1.0);
	t_2 = (x + ((y * z) / t)) / t_1;
	tmp = 0.0;
	if (t_2 <= -5e-319)
		tmp = (x + (z * (y / t))) / t_1;
	elseif (t_2 <= 0.0)
		tmp = ((t * (x / b)) + (y * (z / b))) / y;
	elseif (t_2 <= 1e+307)
		tmp = t_2;
	elseif (t_2 <= Inf)
		tmp = y * (z / (t * (1.0 + (a + (y * (b / t))))));
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[t$95$2, -5e-319], N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[t$95$2, 0.0], N[(N[(N[(t * N[(x / b), $MachinePrecision]), $MachinePrecision] + N[(y * N[(z / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t$95$2, 1e+307], t$95$2, If[LessEqual[t$95$2, Infinity], N[(y * N[(z / N[(t * N[(1.0 + N[(a + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $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))) < -4.9999937e-319

   1. Initial program 90.8%

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

      1. *-commutative 90.8%

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

      2. associate-/l* 92.8%

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

   4. Applied egg-rr 92.8%

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

   if -4.9999937e-319 < (/.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 45.6%

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

      1. associate-/l* 45.5%

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

      2. associate-/l* 56.9%

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

   3. Simplified 56.9%

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

   5. Taylor expanded in b around inf 49.5%

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

      1. times-frac 63.0%

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

      2. +-commutative 63.0%

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

      3. associate-*r/ 63.0%

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

      4. fma-undefine 63.0%

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

   7. Simplified 63.0%

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

   8. Taylor expanded in x around inf 45.5%

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

      1. *-commutative 45.5%

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

   10. Simplified 45.5%

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

   11. Taylor expanded in y around 0 73.1%

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

       1. associate-/l* 79.0%

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

       2. associate-/l* 79.2%

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

   13. Simplified 79.2%

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

   if -0.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 9.99999999999999986e306

   1. Initial program 98.7%

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

   if 9.99999999999999986e306 < (/.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 29.5%

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

      1. *-commutative 29.5%

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

      2. associate-/l* 14.7%

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

   4. Applied egg-rr 14.7%

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

   5. Taylor expanded in x around 0 41.5%

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

      1. associate-/l* 99.8%

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

      2. *-commutative 99.8%

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

      3. associate-/l* 99.5%

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

   7. Simplified 99.5%

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

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

   1. Initial program 0.0%

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

      1. associate-/l* 0.0%

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

      2. associate-/l* 0.3%

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

   3. Simplified 0.3%

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

   5. Taylor expanded in y around inf 94.5%

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

4. Final simplification 92.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -5 \cdot 10^{-319}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 0:\\ \;\;\;\;\frac{t \cdot \frac{x}{b} + y \cdot \frac{z}{b}}{y}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 10^{+307}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq \infty:\\ \;\;\;\;y \cdot \frac{z}{t \cdot \left(1 + \left(a + y \cdot \frac{b}{t}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 58.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ t_2 := x + \frac{y \cdot z}{t}\\ \mathbf{if}\;t \leq -1.22 \cdot 10^{+97}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.8 \cdot 10^{-58}:\\ \;\;\;\;\frac{t}{b} \cdot \left(\frac{z}{t} + \frac{x}{y}\right)\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{-140}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{-82}:\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot t}{y \cdot b}\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+29}:\\ \;\;\;\;\frac{t\_2}{a}\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{+43}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (+ 1.0 (+ a (/ (* y b) t))))) (t_2 (+ x (/ (* y z) t))))
   (if (<= t -1.22e+97)
     t_1
     (if (<= t -2.8e-58)
       (* (/ t b) (+ (/ z t) (/ x y)))
       (if (<= t -6.5e-140)
         t_1
         (if (<= t 6.2e-82)
           (+ (/ z b) (/ (* x t) (* y b)))
           (if (<= t 3.2e+29) (/ t_2 a) (if (<= t 1.8e+43) t_2 t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 + (a + ((y * b) / t)));
	double t_2 = x + ((y * z) / t);
	double tmp;
	if (t <= -1.22e+97) {
		tmp = t_1;
	} else if (t <= -2.8e-58) {
		tmp = (t / b) * ((z / t) + (x / y));
	} else if (t <= -6.5e-140) {
		tmp = t_1;
	} else if (t <= 6.2e-82) {
		tmp = (z / b) + ((x * t) / (y * b));
	} else if (t <= 3.2e+29) {
		tmp = t_2 / a;
	} else if (t <= 1.8e+43) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x / (1.0d0 + (a + ((y * b) / t)))
    t_2 = x + ((y * z) / t)
    if (t <= (-1.22d+97)) then
        tmp = t_1
    else if (t <= (-2.8d-58)) then
        tmp = (t / b) * ((z / t) + (x / y))
    else if (t <= (-6.5d-140)) then
        tmp = t_1
    else if (t <= 6.2d-82) then
        tmp = (z / b) + ((x * t) / (y * b))
    else if (t <= 3.2d+29) then
        tmp = t_2 / a
    else if (t <= 1.8d+43) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 + (a + ((y * b) / t)));
	double t_2 = x + ((y * z) / t);
	double tmp;
	if (t <= -1.22e+97) {
		tmp = t_1;
	} else if (t <= -2.8e-58) {
		tmp = (t / b) * ((z / t) + (x / y));
	} else if (t <= -6.5e-140) {
		tmp = t_1;
	} else if (t <= 6.2e-82) {
		tmp = (z / b) + ((x * t) / (y * b));
	} else if (t <= 3.2e+29) {
		tmp = t_2 / a;
	} else if (t <= 1.8e+43) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (1.0 + (a + ((y * b) / t)))
	t_2 = x + ((y * z) / t)
	tmp = 0
	if t <= -1.22e+97:
		tmp = t_1
	elif t <= -2.8e-58:
		tmp = (t / b) * ((z / t) + (x / y))
	elif t <= -6.5e-140:
		tmp = t_1
	elif t <= 6.2e-82:
		tmp = (z / b) + ((x * t) / (y * b))
	elif t <= 3.2e+29:
		tmp = t_2 / a
	elif t <= 1.8e+43:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(1.0 + Float64(a + Float64(Float64(y * b) / t))))
	t_2 = Float64(x + Float64(Float64(y * z) / t))
	tmp = 0.0
	if (t <= -1.22e+97)
		tmp = t_1;
	elseif (t <= -2.8e-58)
		tmp = Float64(Float64(t / b) * Float64(Float64(z / t) + Float64(x / y)));
	elseif (t <= -6.5e-140)
		tmp = t_1;
	elseif (t <= 6.2e-82)
		tmp = Float64(Float64(z / b) + Float64(Float64(x * t) / Float64(y * b)));
	elseif (t <= 3.2e+29)
		tmp = Float64(t_2 / a);
	elseif (t <= 1.8e+43)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (1.0 + (a + ((y * b) / t)));
	t_2 = x + ((y * z) / t);
	tmp = 0.0;
	if (t <= -1.22e+97)
		tmp = t_1;
	elseif (t <= -2.8e-58)
		tmp = (t / b) * ((z / t) + (x / y));
	elseif (t <= -6.5e-140)
		tmp = t_1;
	elseif (t <= 6.2e-82)
		tmp = (z / b) + ((x * t) / (y * b));
	elseif (t <= 3.2e+29)
		tmp = t_2 / a;
	elseif (t <= 1.8e+43)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(1.0 + N[(a + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.22e+97], t$95$1, If[LessEqual[t, -2.8e-58], N[(N[(t / b), $MachinePrecision] * N[(N[(z / t), $MachinePrecision] + N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -6.5e-140], t$95$1, If[LessEqual[t, 6.2e-82], N[(N[(z / b), $MachinePrecision] + N[(N[(x * t), $MachinePrecision] / N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.2e+29], N[(t$95$2 / a), $MachinePrecision], If[LessEqual[t, 1.8e+43], t$95$2, t$95$1]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -1.21999999999999997e97 or -2.8000000000000001e-58 < t < -6.4999999999999995e-140 or 1.80000000000000005e43 < t

   1. Initial program 85.0%

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

      1. associate-/l* 89.3%

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

      2. associate-/l* 91.0%

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

   3. Simplified 91.0%

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

   5. Taylor expanded in x around inf 65.8%

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

   if -1.21999999999999997e97 < t < -2.8000000000000001e-58

   1. Initial program 77.1%

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

      1. associate-/l* 82.1%

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

      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. Taylor expanded in b around inf 37.3%

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

      1. times-frac 47.1%

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

      2. +-commutative 47.1%

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

      3. associate-*r/ 49.6%

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

      4. fma-undefine 49.6%

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

   7. Simplified 49.6%

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

   8. Taylor expanded in y around inf 52.2%

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

   if -6.4999999999999995e-140 < t < 6.19999999999999999e-82

   1. Initial program 57.0%

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

      1. associate-/l* 47.2%

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

      2. associate-/l* 41.1%

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

   3. Simplified 41.1%

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

   5. Taylor expanded in b around inf 49.2%

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

      1. times-frac 37.9%

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

      2. +-commutative 37.9%

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

      3. associate-*r/ 37.9%

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

      4. fma-undefine 37.9%

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

   7. Simplified 37.9%

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

   8. Taylor expanded in t around 0 73.6%

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

   if 6.19999999999999999e-82 < t < 3.19999999999999987e29

   1. Initial program 91.6%

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

      1. associate-/l* 87.4%

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

      2. associate-/l* 87.3%

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

   3. Simplified 87.3%

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

   5. Taylor expanded in a around inf 64.1%

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

   if 3.19999999999999987e29 < t < 1.80000000000000005e43

   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* 99.3%

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

      2. associate-/l* 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in b around 0 83.9%

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

   6. Taylor expanded in a around 0 83.9%

      \[\leadsto \color{blue}{x + \frac{y \cdot z}{t}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 66.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.22 \cdot 10^{+97}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \mathbf{elif}\;t \leq -2.8 \cdot 10^{-58}:\\ \;\;\;\;\frac{t}{b} \cdot \left(\frac{z}{t} + \frac{x}{y}\right)\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{-140}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{-82}:\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot t}{y \cdot b}\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+29}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a}\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{+43}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 60.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ t_2 := x + \frac{y \cdot z}{t}\\ \mathbf{if}\;t \leq -1.22 \cdot 10^{+97}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -5 \cdot 10^{-58}:\\ \;\;\;\;\frac{t}{b} \cdot \left(\frac{z}{t} + \frac{x}{y}\right)\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{-140}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.56 \cdot 10^{-80}:\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot t}{y \cdot b}\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+29}:\\ \;\;\;\;\frac{t\_2}{a}\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{+43}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (+ (+ a 1.0) (* b (/ y t))))) (t_2 (+ x (/ (* y z) t))))
   (if (<= t -1.22e+97)
     t_1
     (if (<= t -5e-58)
       (* (/ t b) (+ (/ z t) (/ x y)))
       (if (<= t -6.5e-140)
         t_1
         (if (<= t 1.56e-80)
           (+ (/ z b) (/ (* x t) (* y b)))
           (if (<= t 2.8e+29) (/ t_2 a) (if (<= t 1.85e+43) t_2 t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / ((a + 1.0) + (b * (y / t)));
	double t_2 = x + ((y * z) / t);
	double tmp;
	if (t <= -1.22e+97) {
		tmp = t_1;
	} else if (t <= -5e-58) {
		tmp = (t / b) * ((z / t) + (x / y));
	} else if (t <= -6.5e-140) {
		tmp = t_1;
	} else if (t <= 1.56e-80) {
		tmp = (z / b) + ((x * t) / (y * b));
	} else if (t <= 2.8e+29) {
		tmp = t_2 / a;
	} else if (t <= 1.85e+43) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x / ((a + 1.0d0) + (b * (y / t)))
    t_2 = x + ((y * z) / t)
    if (t <= (-1.22d+97)) then
        tmp = t_1
    else if (t <= (-5d-58)) then
        tmp = (t / b) * ((z / t) + (x / y))
    else if (t <= (-6.5d-140)) then
        tmp = t_1
    else if (t <= 1.56d-80) then
        tmp = (z / b) + ((x * t) / (y * b))
    else if (t <= 2.8d+29) then
        tmp = t_2 / a
    else if (t <= 1.85d+43) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / ((a + 1.0) + (b * (y / t)));
	double t_2 = x + ((y * z) / t);
	double tmp;
	if (t <= -1.22e+97) {
		tmp = t_1;
	} else if (t <= -5e-58) {
		tmp = (t / b) * ((z / t) + (x / y));
	} else if (t <= -6.5e-140) {
		tmp = t_1;
	} else if (t <= 1.56e-80) {
		tmp = (z / b) + ((x * t) / (y * b));
	} else if (t <= 2.8e+29) {
		tmp = t_2 / a;
	} else if (t <= 1.85e+43) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / ((a + 1.0) + (b * (y / t)))
	t_2 = x + ((y * z) / t)
	tmp = 0
	if t <= -1.22e+97:
		tmp = t_1
	elif t <= -5e-58:
		tmp = (t / b) * ((z / t) + (x / y))
	elif t <= -6.5e-140:
		tmp = t_1
	elif t <= 1.56e-80:
		tmp = (z / b) + ((x * t) / (y * b))
	elif t <= 2.8e+29:
		tmp = t_2 / a
	elif t <= 1.85e+43:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(Float64(a + 1.0) + Float64(b * Float64(y / t))))
	t_2 = Float64(x + Float64(Float64(y * z) / t))
	tmp = 0.0
	if (t <= -1.22e+97)
		tmp = t_1;
	elseif (t <= -5e-58)
		tmp = Float64(Float64(t / b) * Float64(Float64(z / t) + Float64(x / y)));
	elseif (t <= -6.5e-140)
		tmp = t_1;
	elseif (t <= 1.56e-80)
		tmp = Float64(Float64(z / b) + Float64(Float64(x * t) / Float64(y * b)));
	elseif (t <= 2.8e+29)
		tmp = Float64(t_2 / a);
	elseif (t <= 1.85e+43)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / ((a + 1.0) + (b * (y / t)));
	t_2 = x + ((y * z) / t);
	tmp = 0.0;
	if (t <= -1.22e+97)
		tmp = t_1;
	elseif (t <= -5e-58)
		tmp = (t / b) * ((z / t) + (x / y));
	elseif (t <= -6.5e-140)
		tmp = t_1;
	elseif (t <= 1.56e-80)
		tmp = (z / b) + ((x * t) / (y * b));
	elseif (t <= 2.8e+29)
		tmp = t_2 / a;
	elseif (t <= 1.85e+43)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(N[(a + 1.0), $MachinePrecision] + N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.22e+97], t$95$1, If[LessEqual[t, -5e-58], N[(N[(t / b), $MachinePrecision] * N[(N[(z / t), $MachinePrecision] + N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -6.5e-140], t$95$1, If[LessEqual[t, 1.56e-80], N[(N[(z / b), $MachinePrecision] + N[(N[(x * t), $MachinePrecision] / N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.8e+29], N[(t$95$2 / a), $MachinePrecision], If[LessEqual[t, 1.85e+43], t$95$2, t$95$1]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -1.21999999999999997e97 or -4.99999999999999977e-58 < t < -6.4999999999999995e-140 or 1.85e43 < t

   1. Initial program 85.0%

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

      1. *-commutative 85.0%

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

      2. associate-/l* 89.4%

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

   4. Applied egg-rr 89.4%

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

   5. Taylor expanded in x around inf 70.2%

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

   if -1.21999999999999997e97 < t < -4.99999999999999977e-58

   1. Initial program 77.1%

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

      1. associate-/l* 82.1%

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

      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. Taylor expanded in b around inf 37.3%

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

      1. times-frac 47.1%

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

      2. +-commutative 47.1%

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

      3. associate-*r/ 49.6%

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

      4. fma-undefine 49.6%

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

   7. Simplified 49.6%

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

   8. Taylor expanded in y around inf 52.2%

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

   if -6.4999999999999995e-140 < t < 1.55999999999999994e-80

   1. Initial program 57.0%

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

      1. associate-/l* 47.2%

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

      2. associate-/l* 41.1%

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

   3. Simplified 41.1%

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

   5. Taylor expanded in b around inf 49.2%

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

      1. times-frac 37.9%

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

      2. +-commutative 37.9%

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

      3. associate-*r/ 37.9%

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

      4. fma-undefine 37.9%

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

   7. Simplified 37.9%

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

   8. Taylor expanded in t around 0 73.6%

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

   if 1.55999999999999994e-80 < t < 2.8e29

   1. Initial program 91.6%

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

      1. associate-/l* 87.4%

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

      2. associate-/l* 87.3%

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

   3. Simplified 87.3%

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

   5. Taylor expanded in a around inf 64.1%

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

   if 2.8e29 < t < 1.85e43

   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* 99.3%

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

      2. associate-/l* 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in b around 0 83.9%

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

   6. Taylor expanded in a around 0 83.9%

      \[\leadsto \color{blue}{x + \frac{y \cdot z}{t}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.22 \cdot 10^{+97}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \mathbf{elif}\;t \leq -5 \cdot 10^{-58}:\\ \;\;\;\;\frac{t}{b} \cdot \left(\frac{z}{t} + \frac{x}{y}\right)\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{-140}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \mathbf{elif}\;t \leq 1.56 \cdot 10^{-80}:\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot t}{y \cdot b}\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+29}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a}\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{+43}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 60.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ t_2 := x + \frac{y \cdot z}{t}\\ \mathbf{if}\;t \leq -2.2 \cdot 10^{+97}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.35 \cdot 10^{-58}:\\ \;\;\;\;\frac{t}{b} \cdot \left(\frac{z}{t} + \frac{x}{y}\right)\\ \mathbf{elif}\;t \leq -6 \cdot 10^{-140}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-81}:\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot t}{y \cdot b}\\ \mathbf{elif}\;t \leq 1.36 \cdot 10^{+29}:\\ \;\;\;\;\frac{t\_2}{a}\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{+43}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (+ (+ a 1.0) (* b (/ y t))))) (t_2 (+ x (/ (* y z) t))))
   (if (<= t -2.2e+97)
     t_1
     (if (<= t -2.35e-58)
       (* (/ t b) (+ (/ z t) (/ x y)))
       (if (<= t -6e-140)
         t_1
         (if (<= t 5.5e-81)
           (+ (/ z b) (/ (* x t) (* y b)))
           (if (<= t 1.36e+29)
             (/ t_2 a)
             (if (<= t 1.8e+43) t_2 (/ x (+ (+ a 1.0) (* y (/ b t))))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / ((a + 1.0) + (b * (y / t)));
	double t_2 = x + ((y * z) / t);
	double tmp;
	if (t <= -2.2e+97) {
		tmp = t_1;
	} else if (t <= -2.35e-58) {
		tmp = (t / b) * ((z / t) + (x / y));
	} else if (t <= -6e-140) {
		tmp = t_1;
	} else if (t <= 5.5e-81) {
		tmp = (z / b) + ((x * t) / (y * b));
	} else if (t <= 1.36e+29) {
		tmp = t_2 / a;
	} else if (t <= 1.8e+43) {
		tmp = t_2;
	} else {
		tmp = x / ((a + 1.0) + (y * (b / t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x / ((a + 1.0d0) + (b * (y / t)))
    t_2 = x + ((y * z) / t)
    if (t <= (-2.2d+97)) then
        tmp = t_1
    else if (t <= (-2.35d-58)) then
        tmp = (t / b) * ((z / t) + (x / y))
    else if (t <= (-6d-140)) then
        tmp = t_1
    else if (t <= 5.5d-81) then
        tmp = (z / b) + ((x * t) / (y * b))
    else if (t <= 1.36d+29) then
        tmp = t_2 / a
    else if (t <= 1.8d+43) then
        tmp = t_2
    else
        tmp = x / ((a + 1.0d0) + (y * (b / t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / ((a + 1.0) + (b * (y / t)));
	double t_2 = x + ((y * z) / t);
	double tmp;
	if (t <= -2.2e+97) {
		tmp = t_1;
	} else if (t <= -2.35e-58) {
		tmp = (t / b) * ((z / t) + (x / y));
	} else if (t <= -6e-140) {
		tmp = t_1;
	} else if (t <= 5.5e-81) {
		tmp = (z / b) + ((x * t) / (y * b));
	} else if (t <= 1.36e+29) {
		tmp = t_2 / a;
	} else if (t <= 1.8e+43) {
		tmp = t_2;
	} else {
		tmp = x / ((a + 1.0) + (y * (b / t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / ((a + 1.0) + (b * (y / t)))
	t_2 = x + ((y * z) / t)
	tmp = 0
	if t <= -2.2e+97:
		tmp = t_1
	elif t <= -2.35e-58:
		tmp = (t / b) * ((z / t) + (x / y))
	elif t <= -6e-140:
		tmp = t_1
	elif t <= 5.5e-81:
		tmp = (z / b) + ((x * t) / (y * b))
	elif t <= 1.36e+29:
		tmp = t_2 / a
	elif t <= 1.8e+43:
		tmp = t_2
	else:
		tmp = x / ((a + 1.0) + (y * (b / t)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(Float64(a + 1.0) + Float64(b * Float64(y / t))))
	t_2 = Float64(x + Float64(Float64(y * z) / t))
	tmp = 0.0
	if (t <= -2.2e+97)
		tmp = t_1;
	elseif (t <= -2.35e-58)
		tmp = Float64(Float64(t / b) * Float64(Float64(z / t) + Float64(x / y)));
	elseif (t <= -6e-140)
		tmp = t_1;
	elseif (t <= 5.5e-81)
		tmp = Float64(Float64(z / b) + Float64(Float64(x * t) / Float64(y * b)));
	elseif (t <= 1.36e+29)
		tmp = Float64(t_2 / a);
	elseif (t <= 1.8e+43)
		tmp = t_2;
	else
		tmp = Float64(x / Float64(Float64(a + 1.0) + Float64(y * Float64(b / t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / ((a + 1.0) + (b * (y / t)));
	t_2 = x + ((y * z) / t);
	tmp = 0.0;
	if (t <= -2.2e+97)
		tmp = t_1;
	elseif (t <= -2.35e-58)
		tmp = (t / b) * ((z / t) + (x / y));
	elseif (t <= -6e-140)
		tmp = t_1;
	elseif (t <= 5.5e-81)
		tmp = (z / b) + ((x * t) / (y * b));
	elseif (t <= 1.36e+29)
		tmp = t_2 / a;
	elseif (t <= 1.8e+43)
		tmp = t_2;
	else
		tmp = x / ((a + 1.0) + (y * (b / t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(N[(a + 1.0), $MachinePrecision] + N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.2e+97], t$95$1, If[LessEqual[t, -2.35e-58], N[(N[(t / b), $MachinePrecision] * N[(N[(z / t), $MachinePrecision] + N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -6e-140], t$95$1, If[LessEqual[t, 5.5e-81], N[(N[(z / b), $MachinePrecision] + N[(N[(x * t), $MachinePrecision] / N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.36e+29], N[(t$95$2 / a), $MachinePrecision], If[LessEqual[t, 1.8e+43], t$95$2, N[(x / N[(N[(a + 1.0), $MachinePrecision] + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -2.2000000000000001e97 or -2.34999999999999997e-58 < t < -6.00000000000000037e-140

   1. Initial program 81.3%

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

      1. *-commutative 81.3%

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

      2. associate-/l* 88.1%

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

   4. Applied egg-rr 88.1%

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

   5. Taylor expanded in x around inf 72.5%

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

   if -2.2000000000000001e97 < t < -2.34999999999999997e-58

   1. Initial program 77.1%

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

      1. associate-/l* 82.1%

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

      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. Taylor expanded in b around inf 37.3%

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

      1. times-frac 47.1%

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

      2. +-commutative 47.1%

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

      3. associate-*r/ 49.6%

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

      4. fma-undefine 49.6%

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

   7. Simplified 49.6%

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

   8. Taylor expanded in y around inf 52.2%

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

   if -6.00000000000000037e-140 < t < 5.50000000000000026e-81

   1. Initial program 57.0%

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

      1. associate-/l* 47.2%

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

      2. associate-/l* 41.1%

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

   3. Simplified 41.1%

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

   5. Taylor expanded in b around inf 49.2%

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

      1. times-frac 37.9%

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

      2. +-commutative 37.9%

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

      3. associate-*r/ 37.9%

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

      4. fma-undefine 37.9%

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

   7. Simplified 37.9%

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

   8. Taylor expanded in t around 0 73.6%

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

   if 5.50000000000000026e-81 < t < 1.36e29

   1. Initial program 91.6%

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

      1. associate-/l* 87.4%

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

      2. associate-/l* 87.3%

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

   3. Simplified 87.3%

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

   5. Taylor expanded in a around inf 64.1%

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

   if 1.36e29 < t < 1.80000000000000005e43

   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* 99.3%

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

      2. associate-/l* 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in b around 0 83.9%

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

   6. Taylor expanded in a around 0 83.9%

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

   if 1.80000000000000005e43 < t

   1. Initial program 88.9%

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

      1. associate-/l* 95.9%

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

      2. associate-/l* 97.8%

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

   3. Simplified 97.8%

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

   5. Taylor expanded in x around inf 67.7%

      \[\leadsto \frac{\color{blue}{x}}{\left(a + 1\right) + y \cdot \frac{b}{t}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{+97}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \mathbf{elif}\;t \leq -2.35 \cdot 10^{-58}:\\ \;\;\;\;\frac{t}{b} \cdot \left(\frac{z}{t} + \frac{x}{y}\right)\\ \mathbf{elif}\;t \leq -6 \cdot 10^{-140}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-81}:\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot t}{y \cdot b}\\ \mathbf{elif}\;t \leq 1.36 \cdot 10^{+29}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a}\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{+43}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 51.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot z}{t}\\ t_2 := \frac{x}{a + 1}\\ \mathbf{if}\;t \leq -1.22 \cdot 10^{+97}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1.6 \cdot 10^{-20}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq -3 \cdot 10^{-78}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -8.8 \cdot 10^{-118}:\\ \;\;\;\;t \cdot \frac{\frac{x}{b}}{y}\\ \mathbf{elif}\;t \leq -5.8 \cdot 10^{-140}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-88}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (/ (* y z) t))) (t_2 (/ x (+ a 1.0))))
   (if (<= t -1.22e+97)
     t_2
     (if (<= t -1.6e-20)
       (/ z b)
       (if (<= t -3e-78)
         t_1
         (if (<= t -8.8e-118)
           (* t (/ (/ x b) y))
           (if (<= t -5.8e-140) t_1 (if (<= t 4.5e-88) (/ z b) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + ((y * z) / t);
	double t_2 = x / (a + 1.0);
	double tmp;
	if (t <= -1.22e+97) {
		tmp = t_2;
	} else if (t <= -1.6e-20) {
		tmp = z / b;
	} else if (t <= -3e-78) {
		tmp = t_1;
	} else if (t <= -8.8e-118) {
		tmp = t * ((x / b) / y);
	} else if (t <= -5.8e-140) {
		tmp = t_1;
	} else if (t <= 4.5e-88) {
		tmp = z / b;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + ((y * z) / t)
    t_2 = x / (a + 1.0d0)
    if (t <= (-1.22d+97)) then
        tmp = t_2
    else if (t <= (-1.6d-20)) then
        tmp = z / b
    else if (t <= (-3d-78)) then
        tmp = t_1
    else if (t <= (-8.8d-118)) then
        tmp = t * ((x / b) / y)
    else if (t <= (-5.8d-140)) then
        tmp = t_1
    else if (t <= 4.5d-88) then
        tmp = z / b
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + ((y * z) / t);
	double t_2 = x / (a + 1.0);
	double tmp;
	if (t <= -1.22e+97) {
		tmp = t_2;
	} else if (t <= -1.6e-20) {
		tmp = z / b;
	} else if (t <= -3e-78) {
		tmp = t_1;
	} else if (t <= -8.8e-118) {
		tmp = t * ((x / b) / y);
	} else if (t <= -5.8e-140) {
		tmp = t_1;
	} else if (t <= 4.5e-88) {
		tmp = z / b;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + ((y * z) / t)
	t_2 = x / (a + 1.0)
	tmp = 0
	if t <= -1.22e+97:
		tmp = t_2
	elif t <= -1.6e-20:
		tmp = z / b
	elif t <= -3e-78:
		tmp = t_1
	elif t <= -8.8e-118:
		tmp = t * ((x / b) / y)
	elif t <= -5.8e-140:
		tmp = t_1
	elif t <= 4.5e-88:
		tmp = z / b
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(Float64(y * z) / t))
	t_2 = Float64(x / Float64(a + 1.0))
	tmp = 0.0
	if (t <= -1.22e+97)
		tmp = t_2;
	elseif (t <= -1.6e-20)
		tmp = Float64(z / b);
	elseif (t <= -3e-78)
		tmp = t_1;
	elseif (t <= -8.8e-118)
		tmp = Float64(t * Float64(Float64(x / b) / y));
	elseif (t <= -5.8e-140)
		tmp = t_1;
	elseif (t <= 4.5e-88)
		tmp = Float64(z / b);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + ((y * z) / t);
	t_2 = x / (a + 1.0);
	tmp = 0.0;
	if (t <= -1.22e+97)
		tmp = t_2;
	elseif (t <= -1.6e-20)
		tmp = z / b;
	elseif (t <= -3e-78)
		tmp = t_1;
	elseif (t <= -8.8e-118)
		tmp = t * ((x / b) / y);
	elseif (t <= -5.8e-140)
		tmp = t_1;
	elseif (t <= 4.5e-88)
		tmp = z / b;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.22e+97], t$95$2, If[LessEqual[t, -1.6e-20], N[(z / b), $MachinePrecision], If[LessEqual[t, -3e-78], t$95$1, If[LessEqual[t, -8.8e-118], N[(t * N[(N[(x / b), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -5.8e-140], t$95$1, If[LessEqual[t, 4.5e-88], N[(z / b), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.21999999999999997e97 or 4.49999999999999991e-88 < t

   1. Initial program 88.7%

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

      1. associate-/l* 92.6%

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

      2. associate-/l* 96.5%

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

   3. Simplified 96.5%

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

   5. Taylor expanded in y around 0 61.7%

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

   if -1.21999999999999997e97 < t < -1.59999999999999985e-20 or -5.79999999999999995e-140 < t < 4.49999999999999991e-88

   1. Initial program 59.6%

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

      1. associate-/l* 54.0%

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

      2. associate-/l* 50.2%

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

   3. Simplified 50.2%

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

   5. Taylor expanded in y around inf 55.8%

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

   if -1.59999999999999985e-20 < t < -2.99999999999999988e-78 or -8.79999999999999934e-118 < t < -5.79999999999999995e-140

   1. Initial program 91.8%

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

      1. associate-/l* 87.6%

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

      2. associate-/l* 83.8%

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

   3. Simplified 83.8%

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

   5. Taylor expanded in b around 0 71.3%

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

   6. Taylor expanded in a around 0 50.4%

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

   if -2.99999999999999988e-78 < t < -8.79999999999999934e-118

   1. Initial program 57.6%

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

      1. associate-/l* 57.6%

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

      2. associate-/l* 36.5%

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

   3. Simplified 36.5%

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

   5. Taylor expanded in b around inf 57.0%

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

      1. times-frac 61.6%

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

      2. +-commutative 61.6%

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

      3. associate-*r/ 61.8%

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

      4. fma-undefine 61.8%

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

   7. Simplified 61.8%

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

   8. Taylor expanded in x around inf 46.6%

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

      1. *-commutative 46.6%

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

   10. Simplified 46.6%

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

   11. Taylor expanded in x around inf 39.7%

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

       1. associate-/l* 39.7%

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

       2. associate-/r* 63.5%

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

   13. Simplified 63.5%

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

4. Final simplification 58.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.22 \cdot 10^{+97}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{elif}\;t \leq -1.6 \cdot 10^{-20}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq -3 \cdot 10^{-78}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{elif}\;t \leq -8.8 \cdot 10^{-118}:\\ \;\;\;\;t \cdot \frac{\frac{x}{b}}{y}\\ \mathbf{elif}\;t \leq -5.8 \cdot 10^{-140}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-88}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 82.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{if}\;t \leq -1.4 \cdot 10^{-46}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.75 \cdot 10^{-168}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{-89}:\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot t}{y \cdot b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (* y (/ z t))) (+ (+ a 1.0) (* y (/ b t))))))
   (if (<= t -1.4e-46)
     t_1
     (if (<= t -1.75e-168)
       (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (* b (/ y t))))
       (if (<= t 1.85e-89) (+ (/ z b) (/ (* x t) (* y b))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)));
	double tmp;
	if (t <= -1.4e-46) {
		tmp = t_1;
	} else if (t <= -1.75e-168) {
		tmp = (x + ((y * z) / t)) / ((a + 1.0) + (b * (y / t)));
	} else if (t <= 1.85e-89) {
		tmp = (z / b) + ((x * t) / (y * 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 = (x + (y * (z / t))) / ((a + 1.0d0) + (y * (b / t)))
    if (t <= (-1.4d-46)) then
        tmp = t_1
    else if (t <= (-1.75d-168)) then
        tmp = (x + ((y * z) / t)) / ((a + 1.0d0) + (b * (y / t)))
    else if (t <= 1.85d-89) then
        tmp = (z / b) + ((x * t) / (y * 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 = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)));
	double tmp;
	if (t <= -1.4e-46) {
		tmp = t_1;
	} else if (t <= -1.75e-168) {
		tmp = (x + ((y * z) / t)) / ((a + 1.0) + (b * (y / t)));
	} else if (t <= 1.85e-89) {
		tmp = (z / b) + ((x * t) / (y * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)))
	tmp = 0
	if t <= -1.4e-46:
		tmp = t_1
	elif t <= -1.75e-168:
		tmp = (x + ((y * z) / t)) / ((a + 1.0) + (b * (y / t)))
	elif t <= 1.85e-89:
		tmp = (z / b) + ((x * t) / (y * b))
	else:
		tmp = t_1
	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 <= -1.4e-46)
		tmp = t_1;
	elseif (t <= -1.75e-168)
		tmp = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(Float64(a + 1.0) + Float64(b * Float64(y / t))));
	elseif (t <= 1.85e-89)
		tmp = Float64(Float64(z / b) + Float64(Float64(x * t) / Float64(y * b)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)));
	tmp = 0.0;
	if (t <= -1.4e-46)
		tmp = t_1;
	elseif (t <= -1.75e-168)
		tmp = (x + ((y * z) / t)) / ((a + 1.0) + (b * (y / t)));
	elseif (t <= 1.85e-89)
		tmp = (z / b) + ((x * t) / (y * b));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.4e-46], t$95$1, If[LessEqual[t, -1.75e-168], N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.85e-89], N[(N[(z / b), $MachinePrecision] + N[(N[(x * t), $MachinePrecision] / N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.3999999999999999e-46 or 1.8499999999999999e-89 < t

   1. Initial program 85.5%

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

      1. associate-/l* 89.8%

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

      2. associate-/l* 93.5%

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

   3. Simplified 93.5%

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

   if -1.3999999999999999e-46 < t < -1.74999999999999991e-168

   1. Initial program 78.5%

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

      1. *-commutative 78.5%

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

      2. associate-/l* 78.6%

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

   4. Applied egg-rr 78.6%

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

   if -1.74999999999999991e-168 < t < 1.8499999999999999e-89

   1. Initial program 55.5%

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

      1. associate-/l* 46.1%

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

      2. associate-/l* 39.4%

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

   3. Simplified 39.4%

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

   5. Taylor expanded in b around inf 51.1%

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

      1. times-frac 37.8%

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

      2. +-commutative 37.8%

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

      3. associate-*r/ 37.8%

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

      4. fma-undefine 37.8%

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

   7. Simplified 37.8%

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

   8. Taylor expanded in t around 0 75.3%

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

4. Final simplification 86.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{-46}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;t \leq -1.75 \cdot 10^{-168}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{-89}:\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot t}{y \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 68.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + z \cdot \frac{y}{t}}{a + 1}\\ \mathbf{if}\;t \leq -1.2 \cdot 10^{+55}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{-17}:\\ \;\;\;\;\frac{t}{b} \cdot \left(\frac{z}{t} + \frac{x}{y}\right)\\ \mathbf{elif}\;t \leq -5.9 \cdot 10^{-140} \lor \neg \left(t \leq 4.2 \cdot 10^{-88}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot t}{y \cdot b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (* z (/ y t))) (+ a 1.0))))
   (if (<= t -1.2e+55)
     t_1
     (if (<= t -8.5e-17)
       (* (/ t b) (+ (/ z t) (/ x y)))
       (if (or (<= t -5.9e-140) (not (<= t 4.2e-88)))
         t_1
         (+ (/ z b) (/ (* x t) (* y b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + (z * (y / t))) / (a + 1.0);
	double tmp;
	if (t <= -1.2e+55) {
		tmp = t_1;
	} else if (t <= -8.5e-17) {
		tmp = (t / b) * ((z / t) + (x / y));
	} else if ((t <= -5.9e-140) || !(t <= 4.2e-88)) {
		tmp = t_1;
	} else {
		tmp = (z / b) + ((x * t) / (y * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + (z * (y / t))) / (a + 1.0d0)
    if (t <= (-1.2d+55)) then
        tmp = t_1
    else if (t <= (-8.5d-17)) then
        tmp = (t / b) * ((z / t) + (x / y))
    else if ((t <= (-5.9d-140)) .or. (.not. (t <= 4.2d-88))) then
        tmp = t_1
    else
        tmp = (z / b) + ((x * t) / (y * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + (z * (y / t))) / (a + 1.0);
	double tmp;
	if (t <= -1.2e+55) {
		tmp = t_1;
	} else if (t <= -8.5e-17) {
		tmp = (t / b) * ((z / t) + (x / y));
	} else if ((t <= -5.9e-140) || !(t <= 4.2e-88)) {
		tmp = t_1;
	} else {
		tmp = (z / b) + ((x * t) / (y * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + (z * (y / t))) / (a + 1.0)
	tmp = 0
	if t <= -1.2e+55:
		tmp = t_1
	elif t <= -8.5e-17:
		tmp = (t / b) * ((z / t) + (x / y))
	elif (t <= -5.9e-140) or not (t <= 4.2e-88):
		tmp = t_1
	else:
		tmp = (z / b) + ((x * t) / (y * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(z * Float64(y / t))) / Float64(a + 1.0))
	tmp = 0.0
	if (t <= -1.2e+55)
		tmp = t_1;
	elseif (t <= -8.5e-17)
		tmp = Float64(Float64(t / b) * Float64(Float64(z / t) + Float64(x / y)));
	elseif ((t <= -5.9e-140) || !(t <= 4.2e-88))
		tmp = t_1;
	else
		tmp = Float64(Float64(z / b) + Float64(Float64(x * t) / Float64(y * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + (z * (y / t))) / (a + 1.0);
	tmp = 0.0;
	if (t <= -1.2e+55)
		tmp = t_1;
	elseif (t <= -8.5e-17)
		tmp = (t / b) * ((z / t) + (x / y));
	elseif ((t <= -5.9e-140) || ~((t <= 4.2e-88)))
		tmp = t_1;
	else
		tmp = (z / b) + ((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[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.2e+55], t$95$1, If[LessEqual[t, -8.5e-17], N[(N[(t / b), $MachinePrecision] * N[(N[(z / t), $MachinePrecision] + N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, -5.9e-140], N[Not[LessEqual[t, 4.2e-88]], $MachinePrecision]], t$95$1, N[(N[(z / b), $MachinePrecision] + N[(N[(x * t), $MachinePrecision] / N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.2e55 or -8.5e-17 < t < -5.9000000000000002e-140 or 4.1999999999999999e-88 < t

   1. Initial program 86.3%

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

      1. associate-/l* 89.8%

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

      2. associate-/l* 91.5%

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

   3. Simplified 91.5%

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

   5. Taylor expanded in b around 0 75.9%

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

      1. *-commutative 86.3%

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

      2. associate-/l* 88.1%

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

   7. Applied egg-rr 77.1%

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

   if -1.2e55 < t < -8.5e-17

   1. Initial program 68.3%

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

      1. associate-/l* 68.4%

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

      2. associate-/l* 68.4%

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

   3. Simplified 68.4%

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

   5. Taylor expanded in b around inf 48.7%

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

      1. times-frac 67.4%

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

      2. +-commutative 67.4%

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

      3. associate-*r/ 67.4%

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

      4. fma-undefine 67.4%

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

   7. Simplified 67.4%

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

   8. Taylor expanded in y around inf 73.9%

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

   if -5.9000000000000002e-140 < t < 4.1999999999999999e-88

   1. Initial program 56.4%

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

      1. associate-/l* 46.5%

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

      2. associate-/l* 40.4%

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

   3. Simplified 40.4%

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

   5. Taylor expanded in b around inf 49.7%

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

      1. times-frac 38.2%

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

      2. +-commutative 38.2%

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

      3. associate-*r/ 38.2%

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

      4. fma-undefine 38.2%

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

   7. Simplified 38.2%

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

   8. Taylor expanded in t around 0 74.4%

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

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{+55}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + 1}\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{-17}:\\ \;\;\;\;\frac{t}{b} \cdot \left(\frac{z}{t} + \frac{x}{y}\right)\\ \mathbf{elif}\;t \leq -5.9 \cdot 10^{-140} \lor \neg \left(t \leq 4.2 \cdot 10^{-88}\right):\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot t}{y \cdot b}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 68.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + z \cdot \frac{y}{t}}{a + 1}\\ \mathbf{if}\;t \leq -5.2 \cdot 10^{+54}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -4 \cdot 10^{-17}:\\ \;\;\;\;\frac{t}{b} \cdot \left(\frac{z}{t} + \frac{x}{y}\right)\\ \mathbf{elif}\;t \leq -5 \cdot 10^{-140}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{-88}:\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot t}{y \cdot b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (* z (/ y t))) (+ a 1.0))))
   (if (<= t -5.2e+54)
     t_1
     (if (<= t -4e-17)
       (* (/ t b) (+ (/ z t) (/ x y)))
       (if (<= t -5e-140)
         (/ (+ x (/ (* y z) t)) (+ a 1.0))
         (if (<= t 1.1e-88) (+ (/ z b) (/ (* x t) (* y b))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + (z * (y / t))) / (a + 1.0);
	double tmp;
	if (t <= -5.2e+54) {
		tmp = t_1;
	} else if (t <= -4e-17) {
		tmp = (t / b) * ((z / t) + (x / y));
	} else if (t <= -5e-140) {
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	} else if (t <= 1.1e-88) {
		tmp = (z / b) + ((x * t) / (y * 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 = (x + (z * (y / t))) / (a + 1.0d0)
    if (t <= (-5.2d+54)) then
        tmp = t_1
    else if (t <= (-4d-17)) then
        tmp = (t / b) * ((z / t) + (x / y))
    else if (t <= (-5d-140)) then
        tmp = (x + ((y * z) / t)) / (a + 1.0d0)
    else if (t <= 1.1d-88) then
        tmp = (z / b) + ((x * t) / (y * 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 = (x + (z * (y / t))) / (a + 1.0);
	double tmp;
	if (t <= -5.2e+54) {
		tmp = t_1;
	} else if (t <= -4e-17) {
		tmp = (t / b) * ((z / t) + (x / y));
	} else if (t <= -5e-140) {
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	} else if (t <= 1.1e-88) {
		tmp = (z / b) + ((x * t) / (y * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + (z * (y / t))) / (a + 1.0)
	tmp = 0
	if t <= -5.2e+54:
		tmp = t_1
	elif t <= -4e-17:
		tmp = (t / b) * ((z / t) + (x / y))
	elif t <= -5e-140:
		tmp = (x + ((y * z) / t)) / (a + 1.0)
	elif t <= 1.1e-88:
		tmp = (z / b) + ((x * t) / (y * b))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(z * Float64(y / t))) / Float64(a + 1.0))
	tmp = 0.0
	if (t <= -5.2e+54)
		tmp = t_1;
	elseif (t <= -4e-17)
		tmp = Float64(Float64(t / b) * Float64(Float64(z / t) + Float64(x / y)));
	elseif (t <= -5e-140)
		tmp = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(a + 1.0));
	elseif (t <= 1.1e-88)
		tmp = Float64(Float64(z / b) + Float64(Float64(x * t) / Float64(y * b)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + (z * (y / t))) / (a + 1.0);
	tmp = 0.0;
	if (t <= -5.2e+54)
		tmp = t_1;
	elseif (t <= -4e-17)
		tmp = (t / b) * ((z / t) + (x / y));
	elseif (t <= -5e-140)
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	elseif (t <= 1.1e-88)
		tmp = (z / b) + ((x * t) / (y * b));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.2e+54], t$95$1, If[LessEqual[t, -4e-17], N[(N[(t / b), $MachinePrecision] * N[(N[(z / t), $MachinePrecision] + N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -5e-140], N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.1e-88], N[(N[(z / b), $MachinePrecision] + N[(N[(x * t), $MachinePrecision] / N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -5.20000000000000013e54 or 1.10000000000000002e-88 < t

   1. Initial program 87.2%

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

      1. associate-/l* 92.3%

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

      2. associate-/l* 96.7%

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

   3. Simplified 96.7%

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

   5. Taylor expanded in b around 0 80.1%

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

      1. *-commutative 87.2%

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

      2. associate-/l* 90.3%

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

   7. Applied egg-rr 81.7%

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

   if -5.20000000000000013e54 < t < -4.00000000000000029e-17

   1. Initial program 68.3%

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

      1. associate-/l* 68.4%

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

      2. associate-/l* 68.4%

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

   3. Simplified 68.4%

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

   5. Taylor expanded in b around inf 48.7%

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

      1. times-frac 67.4%

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

      2. +-commutative 67.4%

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

      3. associate-*r/ 67.4%

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

      4. fma-undefine 67.4%

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

   7. Simplified 67.4%

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

   8. Taylor expanded in y around inf 73.9%

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

   if -4.00000000000000029e-17 < t < -5.00000000000000015e-140

   1. Initial program 83.0%

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

      1. associate-/l* 80.0%

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

      2. associate-/l* 71.7%

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

   3. Simplified 71.7%

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

   5. Taylor expanded in b around 0 60.0%

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

   if -5.00000000000000015e-140 < t < 1.10000000000000002e-88

   1. Initial program 56.4%

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

      1. associate-/l* 46.5%

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

      2. associate-/l* 40.4%

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

   3. Simplified 40.4%

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

   5. Taylor expanded in b around inf 49.7%

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

      1. times-frac 38.2%

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

      2. +-commutative 38.2%

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

      3. associate-*r/ 38.2%

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

      4. fma-undefine 38.2%

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

   7. Simplified 38.2%

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

   8. Taylor expanded in t around 0 74.4%

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

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{+54}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + 1}\\ \mathbf{elif}\;t \leq -4 \cdot 10^{-17}:\\ \;\;\;\;\frac{t}{b} \cdot \left(\frac{z}{t} + \frac{x}{y}\right)\\ \mathbf{elif}\;t \leq -5 \cdot 10^{-140}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{-88}:\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot t}{y \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 54.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot z}{t}\\ t_2 := \frac{t\_1}{a}\\ \mathbf{if}\;a \leq -0.0135:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-276}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 4.3 \cdot 10^{-213}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 0.017:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (/ (* y z) t))) (t_2 (/ t_1 a)))
   (if (<= a -0.0135)
     t_2
     (if (<= a 1.2e-276)
       t_1
       (if (<= a 4.3e-213) (/ z b) (if (<= a 0.017) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + ((y * z) / t);
	double t_2 = t_1 / a;
	double tmp;
	if (a <= -0.0135) {
		tmp = t_2;
	} else if (a <= 1.2e-276) {
		tmp = t_1;
	} else if (a <= 4.3e-213) {
		tmp = z / b;
	} else if (a <= 0.017) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + ((y * z) / t)
    t_2 = t_1 / a
    if (a <= (-0.0135d0)) then
        tmp = t_2
    else if (a <= 1.2d-276) then
        tmp = t_1
    else if (a <= 4.3d-213) then
        tmp = z / b
    else if (a <= 0.017d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + ((y * z) / t);
	double t_2 = t_1 / a;
	double tmp;
	if (a <= -0.0135) {
		tmp = t_2;
	} else if (a <= 1.2e-276) {
		tmp = t_1;
	} else if (a <= 4.3e-213) {
		tmp = z / b;
	} else if (a <= 0.017) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + ((y * z) / t)
	t_2 = t_1 / a
	tmp = 0
	if a <= -0.0135:
		tmp = t_2
	elif a <= 1.2e-276:
		tmp = t_1
	elif a <= 4.3e-213:
		tmp = z / b
	elif a <= 0.017:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(Float64(y * z) / t))
	t_2 = Float64(t_1 / a)
	tmp = 0.0
	if (a <= -0.0135)
		tmp = t_2;
	elseif (a <= 1.2e-276)
		tmp = t_1;
	elseif (a <= 4.3e-213)
		tmp = Float64(z / b);
	elseif (a <= 0.017)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + ((y * z) / t);
	t_2 = t_1 / a;
	tmp = 0.0;
	if (a <= -0.0135)
		tmp = t_2;
	elseif (a <= 1.2e-276)
		tmp = t_1;
	elseif (a <= 4.3e-213)
		tmp = z / b;
	elseif (a <= 0.017)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 / a), $MachinePrecision]}, If[LessEqual[a, -0.0135], t$95$2, If[LessEqual[a, 1.2e-276], t$95$1, If[LessEqual[a, 4.3e-213], N[(z / b), $MachinePrecision], If[LessEqual[a, 0.017], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -0.0134999999999999998 or 0.017000000000000001 < a

   1. Initial program 74.0%

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

      1. associate-/l* 72.5%

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

      2. associate-/l* 72.5%

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

   3. Simplified 72.5%

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

   5. Taylor expanded in a around inf 63.3%

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

   if -0.0134999999999999998 < a < 1.19999999999999991e-276 or 4.3000000000000003e-213 < a < 0.017000000000000001

   1. Initial program 79.3%

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

      1. associate-/l* 79.1%

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

      2. associate-/l* 78.2%

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

   3. Simplified 78.2%

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

   5. Taylor expanded in b around 0 55.8%

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

   6. Taylor expanded in a around 0 55.2%

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

   if 1.19999999999999991e-276 < a < 4.3000000000000003e-213

   1. Initial program 69.7%

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

      1. associate-/l* 69.3%

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

      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. Taylor expanded in y around inf 63.3%

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

4. Final simplification 59.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -0.0135:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a}\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-276}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{elif}\;a \leq 4.3 \cdot 10^{-213}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 0.017:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 81.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.6 \cdot 10^{-141} \lor \neg \left(t \leq 2.05 \cdot 10^{-89}\right):\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot t}{y \cdot b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -8.6e-141) (not (<= t 2.05e-89)))
   (/ (+ x (* y (/ z t))) (+ (+ a 1.0) (* y (/ b t))))
   (+ (/ z b) (/ (* x t) (* y b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -8.6e-141) || !(t <= 2.05e-89)) {
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)));
	} else {
		tmp = (z / b) + ((x * t) / (y * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-8.6d-141)) .or. (.not. (t <= 2.05d-89))) then
        tmp = (x + (y * (z / t))) / ((a + 1.0d0) + (y * (b / t)))
    else
        tmp = (z / b) + ((x * t) / (y * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -8.6e-141) || !(t <= 2.05e-89)) {
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)));
	} else {
		tmp = (z / b) + ((x * t) / (y * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -8.6e-141) or not (t <= 2.05e-89):
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)))
	else:
		tmp = (z / b) + ((x * t) / (y * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -8.6e-141) || !(t <= 2.05e-89))
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(Float64(a + 1.0) + Float64(y * Float64(b / t))));
	else
		tmp = Float64(Float64(z / b) + Float64(Float64(x * t) / Float64(y * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -8.6e-141) || ~((t <= 2.05e-89)))
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)));
	else
		tmp = (z / b) + ((x * t) / (y * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -8.6e-141], N[Not[LessEqual[t, 2.05e-89]], $MachinePrecision]], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z / b), $MachinePrecision] + N[(N[(x * t), $MachinePrecision] / N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -8.59999999999999948e-141 or 2.0499999999999999e-89 < t

   1. Initial program 84.8%

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

      1. associate-/l* 88.0%

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

      2. associate-/l* 89.6%

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

   3. Simplified 89.6%

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

   if -8.59999999999999948e-141 < t < 2.0499999999999999e-89

   1. Initial program 56.4%

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

      1. associate-/l* 46.5%

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

      2. associate-/l* 40.4%

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

   3. Simplified 40.4%

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

   5. Taylor expanded in b around inf 49.7%

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

      1. times-frac 38.2%

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

      2. +-commutative 38.2%

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

      3. associate-*r/ 38.2%

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

      4. fma-undefine 38.2%

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

   7. Simplified 38.2%

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

   8. Taylor expanded in t around 0 74.4%

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

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.6 \cdot 10^{-141} \lor \neg \left(t \leq 2.05 \cdot 10^{-89}\right):\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot t}{y \cdot b}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 69.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + z \cdot \frac{y}{t}}{a + 1}\\ \mathbf{if}\;t \leq -1.56 \cdot 10^{+53}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-140}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{1 + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{-89}:\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot t}{y \cdot b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (* z (/ y t))) (+ a 1.0))))
   (if (<= t -1.56e+53)
     t_1
     (if (<= t -3.8e-140)
       (/ (+ x (/ (* y z) t)) (+ 1.0 (/ (* y b) t)))
       (if (<= t 8.8e-89) (+ (/ z b) (/ (* x t) (* y b))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + (z * (y / t))) / (a + 1.0);
	double tmp;
	if (t <= -1.56e+53) {
		tmp = t_1;
	} else if (t <= -3.8e-140) {
		tmp = (x + ((y * z) / t)) / (1.0 + ((y * b) / t));
	} else if (t <= 8.8e-89) {
		tmp = (z / b) + ((x * t) / (y * 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 = (x + (z * (y / t))) / (a + 1.0d0)
    if (t <= (-1.56d+53)) then
        tmp = t_1
    else if (t <= (-3.8d-140)) then
        tmp = (x + ((y * z) / t)) / (1.0d0 + ((y * b) / t))
    else if (t <= 8.8d-89) then
        tmp = (z / b) + ((x * t) / (y * 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 = (x + (z * (y / t))) / (a + 1.0);
	double tmp;
	if (t <= -1.56e+53) {
		tmp = t_1;
	} else if (t <= -3.8e-140) {
		tmp = (x + ((y * z) / t)) / (1.0 + ((y * b) / t));
	} else if (t <= 8.8e-89) {
		tmp = (z / b) + ((x * t) / (y * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + (z * (y / t))) / (a + 1.0)
	tmp = 0
	if t <= -1.56e+53:
		tmp = t_1
	elif t <= -3.8e-140:
		tmp = (x + ((y * z) / t)) / (1.0 + ((y * b) / t))
	elif t <= 8.8e-89:
		tmp = (z / b) + ((x * t) / (y * b))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(z * Float64(y / t))) / Float64(a + 1.0))
	tmp = 0.0
	if (t <= -1.56e+53)
		tmp = t_1;
	elseif (t <= -3.8e-140)
		tmp = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(1.0 + Float64(Float64(y * b) / t)));
	elseif (t <= 8.8e-89)
		tmp = Float64(Float64(z / b) + Float64(Float64(x * t) / Float64(y * b)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + (z * (y / t))) / (a + 1.0);
	tmp = 0.0;
	if (t <= -1.56e+53)
		tmp = t_1;
	elseif (t <= -3.8e-140)
		tmp = (x + ((y * z) / t)) / (1.0 + ((y * b) / t));
	elseif (t <= 8.8e-89)
		tmp = (z / b) + ((x * t) / (y * b));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.56e+53], t$95$1, If[LessEqual[t, -3.8e-140], N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(1.0 + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.8e-89], N[(N[(z / b), $MachinePrecision] + N[(N[(x * t), $MachinePrecision] / N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.56e53 or 8.80000000000000048e-89 < t

   1. Initial program 86.6%

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

      1. associate-/l* 91.6%

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

      2. associate-/l* 96.0%

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

   3. Simplified 96.0%

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

   5. Taylor expanded in b around 0 79.5%

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

      1. *-commutative 86.6%

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

      2. associate-/l* 89.6%

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

   7. Applied egg-rr 81.1%

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

   if -1.56e53 < t < -3.79999999999999998e-140

   1. Initial program 80.1%

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

      1. associate-/l* 78.1%

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

      2. associate-/l* 72.2%

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

   3. Simplified 72.2%

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

   5. Taylor expanded in a around 0 63.9%

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

   if -3.79999999999999998e-140 < t < 8.80000000000000048e-89

   1. Initial program 56.4%

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

      1. associate-/l* 46.5%

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

      2. associate-/l* 40.4%

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

   3. Simplified 40.4%

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

   5. Taylor expanded in b around inf 49.7%

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

      1. times-frac 38.2%

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

      2. +-commutative 38.2%

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

      3. associate-*r/ 38.2%

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

      4. fma-undefine 38.2%

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

   7. Simplified 38.2%

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

   8. Taylor expanded in t around 0 74.4%

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

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.56 \cdot 10^{+53}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + 1}\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-140}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{1 + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{-89}:\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot t}{y \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 52.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.22 \cdot 10^{+97} \lor \neg \left(t \leq -1.6 \cdot 10^{-58} \lor \neg \left(t \leq -6.5 \cdot 10^{-140}\right) \land t \leq 3.8 \cdot 10^{-88}\right):\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -1.22e+97)
         (not
          (or (<= t -1.6e-58) (and (not (<= t -6.5e-140)) (<= t 3.8e-88)))))
   (/ x (+ a 1.0))
   (/ z b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.22e+97) || !((t <= -1.6e-58) || (!(t <= -6.5e-140) && (t <= 3.8e-88)))) {
		tmp = x / (a + 1.0);
	} else {
		tmp = z / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-1.22d+97)) .or. (.not. (t <= (-1.6d-58)) .or. (.not. (t <= (-6.5d-140))) .and. (t <= 3.8d-88))) then
        tmp = x / (a + 1.0d0)
    else
        tmp = z / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.22e+97) || !((t <= -1.6e-58) || (!(t <= -6.5e-140) && (t <= 3.8e-88)))) {
		tmp = x / (a + 1.0);
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -1.22e+97) or not ((t <= -1.6e-58) or (not (t <= -6.5e-140) and (t <= 3.8e-88))):
		tmp = x / (a + 1.0)
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -1.22e+97) || !((t <= -1.6e-58) || (!(t <= -6.5e-140) && (t <= 3.8e-88))))
		tmp = Float64(x / Float64(a + 1.0));
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -1.22e+97) || ~(((t <= -1.6e-58) || (~((t <= -6.5e-140)) && (t <= 3.8e-88)))))
		tmp = x / (a + 1.0);
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -1.22e+97], N[Not[Or[LessEqual[t, -1.6e-58], And[N[Not[LessEqual[t, -6.5e-140]], $MachinePrecision], LessEqual[t, 3.8e-88]]]], $MachinePrecision]], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.21999999999999997e97 or -1.6e-58 < t < -6.4999999999999995e-140 or 3.80000000000000011e-88 < t

   1. Initial program 86.9%

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

      1. associate-/l* 89.5%

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

      2. associate-/l* 90.9%

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

   3. Simplified 90.9%

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

   5. Taylor expanded in y around 0 58.9%

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

   if -1.21999999999999997e97 < t < -1.6e-58 or -6.4999999999999995e-140 < t < 3.80000000000000011e-88

   1. Initial program 63.2%

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

      1. associate-/l* 58.2%

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

      2. associate-/l* 54.9%

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

   3. Simplified 54.9%

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

   5. Taylor expanded in y around inf 53.2%

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

4. Final simplification 56.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.22 \cdot 10^{+97} \lor \neg \left(t \leq -1.6 \cdot 10^{-58} \lor \neg \left(t \leq -6.5 \cdot 10^{-140}\right) \land t \leq 3.8 \cdot 10^{-88}\right):\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 57.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{a + 1}\\ \mathbf{if}\;t \leq -1.22 \cdot 10^{+97}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-80}:\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot t}{y \cdot b}\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{+30}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (+ a 1.0))))
   (if (<= t -1.22e+97)
     t_1
     (if (<= t 1.25e-80)
       (+ (/ z b) (/ (* x t) (* y b)))
       (if (<= t 1.65e+30) (/ (+ x (/ (* y z) t)) a) t_1)))))

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 (t <= -1.22e+97) {
		tmp = t_1;
	} else if (t <= 1.25e-80) {
		tmp = (z / b) + ((x * t) / (y * b));
	} else if (t <= 1.65e+30) {
		tmp = (x + ((y * z) / t)) / a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (a + 1.0d0)
    if (t <= (-1.22d+97)) then
        tmp = t_1
    else if (t <= 1.25d-80) then
        tmp = (z / b) + ((x * t) / (y * b))
    else if (t <= 1.65d+30) then
        tmp = (x + ((y * z) / t)) / a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a + 1.0);
	double tmp;
	if (t <= -1.22e+97) {
		tmp = t_1;
	} else if (t <= 1.25e-80) {
		tmp = (z / b) + ((x * t) / (y * b));
	} else if (t <= 1.65e+30) {
		tmp = (x + ((y * z) / t)) / a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (a + 1.0)
	tmp = 0
	if t <= -1.22e+97:
		tmp = t_1
	elif t <= 1.25e-80:
		tmp = (z / b) + ((x * t) / (y * b))
	elif t <= 1.65e+30:
		tmp = (x + ((y * z) / t)) / a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(a + 1.0))
	tmp = 0.0
	if (t <= -1.22e+97)
		tmp = t_1;
	elseif (t <= 1.25e-80)
		tmp = Float64(Float64(z / b) + Float64(Float64(x * t) / Float64(y * b)));
	elseif (t <= 1.65e+30)
		tmp = Float64(Float64(x + Float64(Float64(y * z) / t)) / a);
	else
		tmp = t_1;
	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 (t <= -1.22e+97)
		tmp = t_1;
	elseif (t <= 1.25e-80)
		tmp = (z / b) + ((x * t) / (y * b));
	elseif (t <= 1.65e+30)
		tmp = (x + ((y * z) / t)) / a;
	else
		tmp = t_1;
	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[t, -1.22e+97], t$95$1, If[LessEqual[t, 1.25e-80], N[(N[(z / b), $MachinePrecision] + N[(N[(x * t), $MachinePrecision] / N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.65e+30], N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.21999999999999997e97 or 1.65000000000000013e30 < t

   1. Initial program 87.8%

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

      1. associate-/l* 93.7%

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

      2. associate-/l* 98.7%

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

   3. Simplified 98.7%

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

   5. Taylor expanded in y around 0 66.5%

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

   if -1.21999999999999997e97 < t < 1.25e-80

   1. Initial program 65.4%

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

      1. associate-/l* 60.4%

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

      2. associate-/l* 55.6%

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

   3. Simplified 55.6%

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

   5. Taylor expanded in b around inf 42.8%

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

      1. times-frac 39.3%

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

      2. +-commutative 39.3%

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

      3. associate-*r/ 40.0%

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

      4. fma-undefine 40.0%

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

   7. Simplified 40.0%

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

   8. Taylor expanded in t around 0 60.4%

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

   if 1.25e-80 < t < 1.65000000000000013e30

   1. Initial program 92.0%

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

      1. associate-/l* 87.9%

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

      2. associate-/l* 87.8%

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

   3. Simplified 87.8%

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

   5. Taylor expanded in a around inf 61.5%

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

4. Final simplification 62.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.22 \cdot 10^{+97}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-80}:\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot t}{y \cdot b}\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{+30}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 63.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -4.8 \cdot 10^{-83}:\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot t}{y \cdot b}\\ \mathbf{elif}\;b \leq 2850000000000:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot \frac{x}{b} + y \cdot \frac{z}{b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -4.8e-83)
   (+ (/ z b) (/ (* x t) (* y b)))
   (if (<= b 2850000000000.0)
     (/ (+ x (* z (/ y t))) (+ a 1.0))
     (/ (+ (* t (/ x b)) (* y (/ z b))) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -4.8e-83) {
		tmp = (z / b) + ((x * t) / (y * b));
	} else if (b <= 2850000000000.0) {
		tmp = (x + (z * (y / t))) / (a + 1.0);
	} else {
		tmp = ((t * (x / b)) + (y * (z / b))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-4.8d-83)) then
        tmp = (z / b) + ((x * t) / (y * b))
    else if (b <= 2850000000000.0d0) then
        tmp = (x + (z * (y / t))) / (a + 1.0d0)
    else
        tmp = ((t * (x / b)) + (y * (z / b))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -4.8e-83) {
		tmp = (z / b) + ((x * t) / (y * b));
	} else if (b <= 2850000000000.0) {
		tmp = (x + (z * (y / t))) / (a + 1.0);
	} else {
		tmp = ((t * (x / b)) + (y * (z / b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -4.8e-83:
		tmp = (z / b) + ((x * t) / (y * b))
	elif b <= 2850000000000.0:
		tmp = (x + (z * (y / t))) / (a + 1.0)
	else:
		tmp = ((t * (x / b)) + (y * (z / b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -4.8e-83)
		tmp = Float64(Float64(z / b) + Float64(Float64(x * t) / Float64(y * b)));
	elseif (b <= 2850000000000.0)
		tmp = Float64(Float64(x + Float64(z * Float64(y / t))) / Float64(a + 1.0));
	else
		tmp = Float64(Float64(Float64(t * Float64(x / b)) + Float64(y * Float64(z / b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -4.8e-83)
		tmp = (z / b) + ((x * t) / (y * b));
	elseif (b <= 2850000000000.0)
		tmp = (x + (z * (y / t))) / (a + 1.0);
	else
		tmp = ((t * (x / b)) + (y * (z / b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -4.8e-83], N[(N[(z / b), $MachinePrecision] + N[(N[(x * t), $MachinePrecision] / N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2850000000000.0], N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(t * N[(x / b), $MachinePrecision]), $MachinePrecision] + N[(y * N[(z / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -4.8000000000000002e-83

   1. Initial program 63.4%

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

      1. associate-/l* 64.5%

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

      2. associate-/l* 65.7%

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

   3. Simplified 65.7%

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

   5. Taylor expanded in b around inf 38.0%

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

      1. times-frac 36.6%

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

      2. +-commutative 36.6%

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

      3. associate-*r/ 39.0%

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

      4. fma-undefine 39.0%

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

   7. Simplified 39.0%

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

   8. Taylor expanded in t around 0 60.3%

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

   if -4.8000000000000002e-83 < b < 2.85e12

   1. Initial program 89.8%

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

      1. associate-/l* 87.4%

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

      2. associate-/l* 87.4%

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

   3. Simplified 87.4%

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

   5. Taylor expanded in b around 0 79.9%

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

      1. *-commutative 89.8%

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

      2. associate-/l* 88.1%

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

   7. Applied egg-rr 81.1%

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

   if 2.85e12 < b

   1. Initial program 62.2%

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

      1. associate-/l* 62.2%

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

      2. associate-/l* 56.4%

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

   3. Simplified 56.4%

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

   5. Taylor expanded in b around inf 43.9%

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

      1. times-frac 38.7%

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

      2. +-commutative 38.7%

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

      3. associate-*r/ 38.7%

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

      4. fma-undefine 38.7%

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

   7. Simplified 38.7%

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

   8. Taylor expanded in x around inf 48.4%

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

      1. *-commutative 48.4%

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

   10. Simplified 48.4%

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

   11. Taylor expanded in y around 0 59.2%

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

       1. associate-/l* 61.3%

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

       2. associate-/l* 67.4%

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

   13. Simplified 67.4%

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

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.8 \cdot 10^{-83}:\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot t}{y \cdot b}\\ \mathbf{elif}\;b \leq 2850000000000:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot \frac{x}{b} + y \cdot \frac{z}{b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 40.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.22 \cdot 10^{+97}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-59}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+139}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.22e+97)
   (/ x a)
   (if (<= t 1.05e-59) (/ z b) (if (<= t 2.8e+139) (/ x a) x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.22e+97) {
		tmp = x / a;
	} else if (t <= 1.05e-59) {
		tmp = z / b;
	} else if (t <= 2.8e+139) {
		tmp = x / a;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-1.22d+97)) then
        tmp = x / a
    else if (t <= 1.05d-59) then
        tmp = z / b
    else if (t <= 2.8d+139) then
        tmp = x / a
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.22e+97) {
		tmp = x / a;
	} else if (t <= 1.05e-59) {
		tmp = z / b;
	} else if (t <= 2.8e+139) {
		tmp = x / a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1.22e+97:
		tmp = x / a
	elif t <= 1.05e-59:
		tmp = z / b
	elif t <= 2.8e+139:
		tmp = x / a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.22e+97)
		tmp = Float64(x / a);
	elseif (t <= 1.05e-59)
		tmp = Float64(z / b);
	elseif (t <= 2.8e+139)
		tmp = Float64(x / a);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -1.22e+97)
		tmp = x / a;
	elseif (t <= 1.05e-59)
		tmp = z / b;
	elseif (t <= 2.8e+139)
		tmp = x / a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.22e+97], N[(x / a), $MachinePrecision], If[LessEqual[t, 1.05e-59], N[(z / b), $MachinePrecision], If[LessEqual[t, 2.8e+139], N[(x / a), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.21999999999999997e97 or 1.04999999999999998e-59 < t < 2.7999999999999998e139

   1. Initial program 87.5%

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

      1. associate-/l* 92.4%

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

      2. associate-/l* 97.3%

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

   3. Simplified 97.3%

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

   5. Taylor expanded in y around 0 61.6%

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

   6. Taylor expanded in a around inf 41.2%

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

   if -1.21999999999999997e97 < t < 1.04999999999999998e-59

   1. Initial program 66.6%

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

      1. associate-/l* 61.3%

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

      2. associate-/l* 56.7%

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

   3. Simplified 56.7%

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

   5. Taylor expanded in y around inf 47.4%

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

   if 2.7999999999999998e139 < t

   1. Initial program 91.3%

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

      1. associate-/l* 96.7%

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

      2. associate-/l* 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in y around 0 66.0%

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

   6. Taylor expanded in a around 0 46.6%

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

4. Final simplification 45.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.22 \cdot 10^{+97}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-59}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+139}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 39.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6.8 \cdot 10^{-30} \lor \neg \left(a \leq 98\right):\\ \;\;\;\;\frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -6.8e-30) (not (<= a 98.0))) (/ x a) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -6.8e-30) || !(a <= 98.0)) {
		tmp = x / a;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((a <= (-6.8d-30)) .or. (.not. (a <= 98.0d0))) then
        tmp = x / a
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -6.8e-30) || !(a <= 98.0)) {
		tmp = x / a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -6.8e-30) or not (a <= 98.0):
		tmp = x / a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -6.8e-30) || !(a <= 98.0))
		tmp = Float64(x / a);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -6.8e-30) || ~((a <= 98.0)))
		tmp = x / a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -6.8e-30], N[Not[LessEqual[a, 98.0]], $MachinePrecision]], N[(x / a), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if a < -6.8000000000000006e-30 or 98 < a

   1. Initial program 74.8%

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

      1. associate-/l* 73.3%

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

      2. associate-/l* 73.3%

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

   3. Simplified 73.3%

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

   5. Taylor expanded in y around 0 47.3%

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

   6. Taylor expanded in a around inf 46.8%

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

   if -6.8000000000000006e-30 < a < 98

   1. Initial program 77.4%

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

      1. associate-/l* 77.2%

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

      2. associate-/l* 75.8%

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

   3. Simplified 75.8%

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

   5. Taylor expanded in y around 0 32.3%

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

   6. Taylor expanded in a around 0 32.3%

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

4. Final simplification 39.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.8 \cdot 10^{-30} \lor \neg \left(a \leq 98\right):\\ \;\;\;\;\frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 19.3% accurate, 17.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 76.2%

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

   1. associate-/l* 75.3%

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

   2. associate-/l* 74.6%

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

3. Simplified 74.6%

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

5. Taylor expanded in y around 0 39.5%

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

6. Taylor expanded in a around 0 18.9%

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

7. Final simplification 18.9%

   \[\leadsto x \]
8. Add Preprocessing

Developer target: 79.4% 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 2024067 
(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))))