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

Percentage Accurate: 75.3% → 87.6%

Time: 12.4s

Alternatives: 14

Speedup: 0.8×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 75.3% 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: 87.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{-300}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \mathbf{elif}\;t_1 \leq 0 \lor \neg \left(t_1 \leq 2 \cdot 10^{+299}\right):\\ \;\;\;\;\frac{z}{b} + \frac{\frac{t}{\frac{b}{x}}}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

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 -2e-300)
     (/ (+ x (* z (/ y t))) (+ (+ a 1.0) (* b (/ y t))))
     (if (or (<= t_1 0.0) (not (<= t_1 2e+299)))
       (+ (/ z b) (/ (/ t (/ b x)) y))
       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 <= -2e-300) {
		tmp = (x + (z * (y / t))) / ((a + 1.0) + (b * (y / t)));
	} else if ((t_1 <= 0.0) || !(t_1 <= 2e+299)) {
		tmp = (z / b) + ((t / (b / x)) / y);
	} 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 <= (-2d-300)) then
        tmp = (x + (z * (y / t))) / ((a + 1.0d0) + (b * (y / t)))
    else if ((t_1 <= 0.0d0) .or. (.not. (t_1 <= 2d+299))) then
        tmp = (z / b) + ((t / (b / x)) / y)
    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 <= -2e-300) {
		tmp = (x + (z * (y / t))) / ((a + 1.0) + (b * (y / t)));
	} else if ((t_1 <= 0.0) || !(t_1 <= 2e+299)) {
		tmp = (z / b) + ((t / (b / x)) / y);
	} 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 <= -2e-300:
		tmp = (x + (z * (y / t))) / ((a + 1.0) + (b * (y / t)))
	elif (t_1 <= 0.0) or not (t_1 <= 2e+299):
		tmp = (z / b) + ((t / (b / x)) / y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(Float64(a + 1.0) + Float64(Float64(y * b) / t)))
	tmp = 0.0
	if (t_1 <= -2e-300)
		tmp = Float64(Float64(x + Float64(z * Float64(y / t))) / Float64(Float64(a + 1.0) + Float64(b * Float64(y / t))));
	elseif ((t_1 <= 0.0) || !(t_1 <= 2e+299))
		tmp = Float64(Float64(z / b) + Float64(Float64(t / Float64(b / x)) / y));
	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 <= -2e-300)
		tmp = (x + (z * (y / t))) / ((a + 1.0) + (b * (y / t)));
	elseif ((t_1 <= 0.0) || ~((t_1 <= 2e+299)))
		tmp = (z / b) + ((t / (b / x)) / y);
	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[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e-300], N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t$95$1, 0.0], N[Not[LessEqual[t$95$1, 2e+299]], $MachinePrecision]], N[(N[(z / b), $MachinePrecision] + N[(N[(t / N[(b / x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < -2.00000000000000005e-300

   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. *-commutative 91.3%

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

      2. associate-/l* 94.3%

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

      3. associate-*l/ 93.0%

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

   3. Simplified 93.0%

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

      1. div-inv 93.1%

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

      2. clear-num 93.2%

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

   5. Applied egg-rr 93.2%

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

   if -2.00000000000000005e-300 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 0.0 or 2.0000000000000001e299 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))

   1. Initial program 30.7%

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

      1. *-commutative 30.7%

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

      2. associate-/l* 31.4%

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

      3. associate-*l/ 43.7%

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

   3. Simplified 43.7%

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

   4. Taylor expanded in y around -inf 58.7%

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

      1. +-commutative 58.7%

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

      2. associate-*r/ 58.7%

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

      3. distribute-lft-out-- 58.7%

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

      4. associate-*r* 58.7%

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

      5. metadata-eval 58.7%

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

      6. *-lft-identity 58.7%

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

   6. Simplified 64.7%

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

   7. Taylor expanded in b around inf 72.0%

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

      1. associate-/l* 76.4%

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

   9. Simplified 76.4%

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

   if 0.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 2.0000000000000001e299

   1. Initial program 98.6%

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

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -2 \cdot 10^{-300}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 0 \lor \neg \left(\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 2 \cdot 10^{+299}\right):\\ \;\;\;\;\frac{z}{b} + \frac{\frac{t}{\frac{b}{x}}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \end{array} \]

Alternative 2: 55.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{b} + \frac{x \cdot \frac{t}{b}}{y}\\ t_2 := x + \frac{y \cdot z}{t}\\ t_3 := \frac{t_2}{a}\\ \mathbf{if}\;a \leq -5.8 \cdot 10^{+30}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -2.6 \cdot 10^{-23}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -6.8 \cdot 10^{-301}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{-230}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{-100}:\\ \;\;\;\;\frac{x}{1 + b \cdot \frac{y}{t}}\\ \mathbf{elif}\;a \leq 0.48:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{+35}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (/ z b) (/ (* x (/ t b)) y)))
        (t_2 (+ x (/ (* y z) t)))
        (t_3 (/ t_2 a)))
   (if (<= a -5.8e+30)
     t_3
     (if (<= a -2.6e-23)
       t_1
       (if (<= a -6.8e-301)
         (+ x (/ y (/ t z)))
         (if (<= a 1.85e-230)
           t_1
           (if (<= a 1.05e-100)
             (/ x (+ 1.0 (* b (/ y t))))
             (if (<= a 0.48) t_2 (if (<= a 1.5e+35) t_1 t_3)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z / b) + ((x * (t / b)) / y);
	double t_2 = x + ((y * z) / t);
	double t_3 = t_2 / a;
	double tmp;
	if (a <= -5.8e+30) {
		tmp = t_3;
	} else if (a <= -2.6e-23) {
		tmp = t_1;
	} else if (a <= -6.8e-301) {
		tmp = x + (y / (t / z));
	} else if (a <= 1.85e-230) {
		tmp = t_1;
	} else if (a <= 1.05e-100) {
		tmp = x / (1.0 + (b * (y / t)));
	} else if (a <= 0.48) {
		tmp = t_2;
	} else if (a <= 1.5e+35) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (z / b) + ((x * (t / b)) / y)
    t_2 = x + ((y * z) / t)
    t_3 = t_2 / a
    if (a <= (-5.8d+30)) then
        tmp = t_3
    else if (a <= (-2.6d-23)) then
        tmp = t_1
    else if (a <= (-6.8d-301)) then
        tmp = x + (y / (t / z))
    else if (a <= 1.85d-230) then
        tmp = t_1
    else if (a <= 1.05d-100) then
        tmp = x / (1.0d0 + (b * (y / t)))
    else if (a <= 0.48d0) then
        tmp = t_2
    else if (a <= 1.5d+35) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z / b) + ((x * (t / b)) / y);
	double t_2 = x + ((y * z) / t);
	double t_3 = t_2 / a;
	double tmp;
	if (a <= -5.8e+30) {
		tmp = t_3;
	} else if (a <= -2.6e-23) {
		tmp = t_1;
	} else if (a <= -6.8e-301) {
		tmp = x + (y / (t / z));
	} else if (a <= 1.85e-230) {
		tmp = t_1;
	} else if (a <= 1.05e-100) {
		tmp = x / (1.0 + (b * (y / t)));
	} else if (a <= 0.48) {
		tmp = t_2;
	} else if (a <= 1.5e+35) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z / b) + ((x * (t / b)) / y)
	t_2 = x + ((y * z) / t)
	t_3 = t_2 / a
	tmp = 0
	if a <= -5.8e+30:
		tmp = t_3
	elif a <= -2.6e-23:
		tmp = t_1
	elif a <= -6.8e-301:
		tmp = x + (y / (t / z))
	elif a <= 1.85e-230:
		tmp = t_1
	elif a <= 1.05e-100:
		tmp = x / (1.0 + (b * (y / t)))
	elif a <= 0.48:
		tmp = t_2
	elif a <= 1.5e+35:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z / b) + Float64(Float64(x * Float64(t / b)) / y))
	t_2 = Float64(x + Float64(Float64(y * z) / t))
	t_3 = Float64(t_2 / a)
	tmp = 0.0
	if (a <= -5.8e+30)
		tmp = t_3;
	elseif (a <= -2.6e-23)
		tmp = t_1;
	elseif (a <= -6.8e-301)
		tmp = Float64(x + Float64(y / Float64(t / z)));
	elseif (a <= 1.85e-230)
		tmp = t_1;
	elseif (a <= 1.05e-100)
		tmp = Float64(x / Float64(1.0 + Float64(b * Float64(y / t))));
	elseif (a <= 0.48)
		tmp = t_2;
	elseif (a <= 1.5e+35)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z / b) + ((x * (t / b)) / y);
	t_2 = x + ((y * z) / t);
	t_3 = t_2 / a;
	tmp = 0.0;
	if (a <= -5.8e+30)
		tmp = t_3;
	elseif (a <= -2.6e-23)
		tmp = t_1;
	elseif (a <= -6.8e-301)
		tmp = x + (y / (t / z));
	elseif (a <= 1.85e-230)
		tmp = t_1;
	elseif (a <= 1.05e-100)
		tmp = x / (1.0 + (b * (y / t)));
	elseif (a <= 0.48)
		tmp = t_2;
	elseif (a <= 1.5e+35)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z / b), $MachinePrecision] + N[(N[(x * N[(t / b), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 / a), $MachinePrecision]}, If[LessEqual[a, -5.8e+30], t$95$3, If[LessEqual[a, -2.6e-23], t$95$1, If[LessEqual[a, -6.8e-301], N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.85e-230], t$95$1, If[LessEqual[a, 1.05e-100], N[(x / N[(1.0 + N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 0.48], t$95$2, If[LessEqual[a, 1.5e+35], t$95$1, t$95$3]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -5.7999999999999996e30 or 1.49999999999999995e35 < a

   1. Initial program 72.9%

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

      1. *-commutative 72.9%

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

      2. associate-/l* 72.5%

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

      3. associate-*l/ 77.5%

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

   3. Simplified 77.5%

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

   4. Taylor expanded in a around inf 65.3%

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

   if -5.7999999999999996e30 < a < -2.6e-23 or -6.8000000000000004e-301 < a < 1.84999999999999991e-230 or 0.47999999999999998 < a < 1.49999999999999995e35

   1. Initial program 63.6%

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

      1. *-commutative 63.6%

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

      2. associate-/l* 65.6%

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

      3. associate-*l/ 68.2%

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

   3. Simplified 68.2%

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

   4. Taylor expanded in y around -inf 67.9%

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

      1. +-commutative 67.9%

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

      2. associate-*r/ 67.9%

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

      3. distribute-lft-out-- 67.9%

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

      4. associate-*r* 67.9%

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

      5. metadata-eval 67.9%

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

      6. *-lft-identity 67.9%

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

   6. Simplified 70.4%

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

   7. Taylor expanded in b around inf 71.0%

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

      1. associate-*l/ 73.4%

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

      2. *-commutative 73.4%

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

   9. Simplified 73.4%

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

   if -2.6e-23 < a < -6.8000000000000004e-301

   1. Initial program 70.4%

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

      1. *-commutative 70.4%

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

      2. associate-/l* 68.5%

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

      3. associate-*l/ 71.7%

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

   3. Simplified 71.7%

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

   4. Taylor expanded in b around 0 56.8%

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

      1. *-un-lft-identity 56.8%

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

      2. associate-/l* 58.6%

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

   6. Applied egg-rr 58.6%

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

   7. Taylor expanded in a around 0 56.8%

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

      1. *-un-lft-identity 56.8%

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

      2. associate-/l* 58.6%

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

   9. Applied egg-rr 58.6%

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

   if 1.84999999999999991e-230 < a < 1.05000000000000005e-100

   1. Initial program 83.8%

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

      1. *-commutative 83.8%

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

      2. associate-/l* 87.9%

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

      3. associate-*l/ 91.8%

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

   3. Simplified 91.8%

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

   4. Taylor expanded in x around inf 72.3%

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

   5. Taylor expanded in a around 0 68.3%

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

      1. associate-*l/ 72.3%

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

   7. Simplified 72.3%

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

   if 1.05000000000000005e-100 < a < 0.47999999999999998

   1. Initial program 86.9%

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

      1. *-commutative 86.9%

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

      2. associate-/l* 87.0%

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

      3. associate-*l/ 87.0%

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

   3. Simplified 87.0%

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

   4. Taylor expanded in b around 0 75.4%

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

      1. *-un-lft-identity 75.4%

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

      2. associate-/l* 67.8%

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

   6. Applied egg-rr 67.8%

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

   7. Taylor expanded in a around 0 66.0%

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

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.8 \cdot 10^{+30}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a}\\ \mathbf{elif}\;a \leq -2.6 \cdot 10^{-23}:\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot \frac{t}{b}}{y}\\ \mathbf{elif}\;a \leq -6.8 \cdot 10^{-301}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{-230}:\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot \frac{t}{b}}{y}\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{-100}:\\ \;\;\;\;\frac{x}{1 + b \cdot \frac{y}{t}}\\ \mathbf{elif}\;a \leq 0.48:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{+35}:\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot \frac{t}{b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a}\\ \end{array} \]

Alternative 3: 80.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{-199} \lor \neg \left(t \leq 6 \cdot 10^{-104}\right):\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{\frac{t}{\frac{b}{x}}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -1e-199) (not (<= t 6e-104)))
   (/ (+ x (* z (/ y t))) (+ (+ a 1.0) (* b (/ y t))))
   (+ (/ z b) (/ (/ t (/ b x)) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1e-199) || !(t <= 6e-104)) {
		tmp = (x + (z * (y / t))) / ((a + 1.0) + (b * (y / t)));
	} else {
		tmp = (z / b) + ((t / (b / x)) / 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 ((t <= (-1d-199)) .or. (.not. (t <= 6d-104))) then
        tmp = (x + (z * (y / t))) / ((a + 1.0d0) + (b * (y / t)))
    else
        tmp = (z / b) + ((t / (b / x)) / 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 ((t <= -1e-199) || !(t <= 6e-104)) {
		tmp = (x + (z * (y / t))) / ((a + 1.0) + (b * (y / t)));
	} else {
		tmp = (z / b) + ((t / (b / x)) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -1e-199) or not (t <= 6e-104):
		tmp = (x + (z * (y / t))) / ((a + 1.0) + (b * (y / t)))
	else:
		tmp = (z / b) + ((t / (b / x)) / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -1e-199) || !(t <= 6e-104))
		tmp = Float64(Float64(x + Float64(z * Float64(y / t))) / Float64(Float64(a + 1.0) + Float64(b * Float64(y / t))));
	else
		tmp = Float64(Float64(z / b) + Float64(Float64(t / Float64(b / x)) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -1e-199) || ~((t <= 6e-104)))
		tmp = (x + (z * (y / t))) / ((a + 1.0) + (b * (y / t)));
	else
		tmp = (z / b) + ((t / (b / x)) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -1e-199], N[Not[LessEqual[t, 6e-104]], $MachinePrecision]], N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z / b), $MachinePrecision] + N[(N[(t / N[(b / x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -9.99999999999999982e-200 or 6.0000000000000005e-104 < t

   1. Initial program 81.0%

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

      1. *-commutative 81.0%

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

      2. associate-/l* 81.9%

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

      3. associate-*l/ 87.4%

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

   3. Simplified 87.4%

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

      1. div-inv 87.4%

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

      2. clear-num 87.4%

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

   5. Applied egg-rr 87.4%

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

   if -9.99999999999999982e-200 < t < 6.0000000000000005e-104

   1. Initial program 48.4%

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

      1. *-commutative 48.4%

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

      2. associate-/l* 45.8%

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

      3. associate-*l/ 44.0%

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

   3. Simplified 44.0%

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

   4. Taylor expanded in y around -inf 64.3%

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

      1. +-commutative 64.3%

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

      2. associate-*r/ 64.3%

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

      3. distribute-lft-out-- 64.3%

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

      4. associate-*r* 64.3%

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

      5. metadata-eval 64.3%

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

      6. *-lft-identity 64.3%

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

   6. Simplified 61.0%

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

   7. Taylor expanded in b around inf 77.8%

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

      1. associate-/l* 73.1%

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

   9. Simplified 73.1%

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

4. Final simplification 84.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{-199} \lor \neg \left(t \leq 6 \cdot 10^{-104}\right):\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{\frac{t}{\frac{b}{x}}}{y}\\ \end{array} \]

Alternative 4: 56.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot z}{t}\\ t_2 := \frac{t_1}{a}\\ \mathbf{if}\;a \leq -8.5 \cdot 10^{+26}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -9.2 \cdot 10^{-23}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq -1.32 \cdot 10^{-82}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{-107}:\\ \;\;\;\;\frac{x}{1 + b \cdot \frac{y}{t}}\\ \mathbf{elif}\;a \leq 1:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (/ (* y z) t))) (t_2 (/ t_1 a)))
   (if (<= a -8.5e+26)
     t_2
     (if (<= a -9.2e-23)
       (/ z b)
       (if (<= a -1.32e-82)
         (+ x (/ y (/ t z)))
         (if (<= a 3.4e-107)
           (/ x (+ 1.0 (* b (/ y t))))
           (if (<= a 1.0) 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 <= -8.5e+26) {
		tmp = t_2;
	} else if (a <= -9.2e-23) {
		tmp = z / b;
	} else if (a <= -1.32e-82) {
		tmp = x + (y / (t / z));
	} else if (a <= 3.4e-107) {
		tmp = x / (1.0 + (b * (y / t)));
	} else if (a <= 1.0) {
		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 <= (-8.5d+26)) then
        tmp = t_2
    else if (a <= (-9.2d-23)) then
        tmp = z / b
    else if (a <= (-1.32d-82)) then
        tmp = x + (y / (t / z))
    else if (a <= 3.4d-107) then
        tmp = x / (1.0d0 + (b * (y / t)))
    else if (a <= 1.0d0) 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 <= -8.5e+26) {
		tmp = t_2;
	} else if (a <= -9.2e-23) {
		tmp = z / b;
	} else if (a <= -1.32e-82) {
		tmp = x + (y / (t / z));
	} else if (a <= 3.4e-107) {
		tmp = x / (1.0 + (b * (y / t)));
	} else if (a <= 1.0) {
		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 <= -8.5e+26:
		tmp = t_2
	elif a <= -9.2e-23:
		tmp = z / b
	elif a <= -1.32e-82:
		tmp = x + (y / (t / z))
	elif a <= 3.4e-107:
		tmp = x / (1.0 + (b * (y / t)))
	elif a <= 1.0:
		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 <= -8.5e+26)
		tmp = t_2;
	elseif (a <= -9.2e-23)
		tmp = Float64(z / b);
	elseif (a <= -1.32e-82)
		tmp = Float64(x + Float64(y / Float64(t / z)));
	elseif (a <= 3.4e-107)
		tmp = Float64(x / Float64(1.0 + Float64(b * Float64(y / t))));
	elseif (a <= 1.0)
		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 <= -8.5e+26)
		tmp = t_2;
	elseif (a <= -9.2e-23)
		tmp = z / b;
	elseif (a <= -1.32e-82)
		tmp = x + (y / (t / z));
	elseif (a <= 3.4e-107)
		tmp = x / (1.0 + (b * (y / t)));
	elseif (a <= 1.0)
		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, -8.5e+26], t$95$2, If[LessEqual[a, -9.2e-23], N[(z / b), $MachinePrecision], If[LessEqual[a, -1.32e-82], N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.4e-107], N[(x / N[(1.0 + N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.0], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -8.5e26 or 1 < a

   1. Initial program 72.1%

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

      1. *-commutative 72.1%

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

      2. associate-/l* 71.7%

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

      3. associate-*l/ 76.6%

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

   3. Simplified 76.6%

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

   4. Taylor expanded in a around inf 63.2%

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

   if -8.5e26 < a < -9.2000000000000004e-23

   1. Initial program 74.4%

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

      1. *-commutative 74.4%

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

      2. associate-/l* 80.4%

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

      3. associate-*l/ 73.9%

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

   3. Simplified 73.9%

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

   4. Taylor expanded in t around 0 61.5%

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

   if -9.2000000000000004e-23 < a < -1.32e-82

   1. Initial program 62.9%

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

      1. *-commutative 62.9%

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

      2. associate-/l* 62.6%

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

      3. associate-*l/ 68.7%

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

   3. Simplified 68.7%

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

   4. Taylor expanded in b around 0 63.7%

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

      1. *-un-lft-identity 63.7%

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

      2. associate-/l* 70.0%

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

   6. Applied egg-rr 70.0%

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

   7. Taylor expanded in a around 0 63.7%

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

      1. *-un-lft-identity 63.7%

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

      2. associate-/l* 70.0%

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

   9. Applied egg-rr 70.0%

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

   if -1.32e-82 < a < 3.39999999999999994e-107

   1. Initial program 73.3%

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

      1. *-commutative 73.3%

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

      2. associate-/l* 73.3%

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

      3. associate-*l/ 77.7%

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

   3. Simplified 77.7%

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

   4. Taylor expanded in x around inf 59.1%

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

   5. Taylor expanded in a around 0 55.6%

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

      1. associate-*l/ 59.1%

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

   7. Simplified 59.1%

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

   if 3.39999999999999994e-107 < a < 1

   1. Initial program 83.7%

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

      1. *-commutative 83.7%

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

      2. associate-/l* 83.7%

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

      3. associate-*l/ 83.7%

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

   3. Simplified 83.7%

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

   4. Taylor expanded in b around 0 72.5%

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

      1. *-un-lft-identity 72.5%

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

      2. associate-/l* 65.1%

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

   6. Applied egg-rr 65.1%

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

   7. Taylor expanded in a around 0 63.4%

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

4. Final simplification 62.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.5 \cdot 10^{+26}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a}\\ \mathbf{elif}\;a \leq -9.2 \cdot 10^{-23}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq -1.32 \cdot 10^{-82}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{-107}:\\ \;\;\;\;\frac{x}{1 + b \cdot \frac{y}{t}}\\ \mathbf{elif}\;a \leq 1:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a}\\ \end{array} \]

Alternative 5: 67.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{b} + \frac{\frac{t}{\frac{b}{x}}}{y}\\ \mathbf{if}\;b \leq -2.6 \cdot 10^{+154}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -1.32 \cdot 10^{+113}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \mathbf{elif}\;b \leq -3.7 \cdot 10^{+67}:\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot \frac{t}{b}}{y}\\ \mathbf{elif}\;b \leq 1.55 \cdot 10^{+47}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (/ z b) (/ (/ t (/ b x)) y))))
   (if (<= b -2.6e+154)
     t_1
     (if (<= b -1.32e+113)
       (/ x (+ (+ a 1.0) (* b (/ y t))))
       (if (<= b -3.7e+67)
         (+ (/ z b) (/ (* x (/ t b)) y))
         (if (<= b 1.55e+47) (/ (+ x (/ (* y z) t)) (+ a 1.0)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z / b) + ((t / (b / x)) / y);
	double tmp;
	if (b <= -2.6e+154) {
		tmp = t_1;
	} else if (b <= -1.32e+113) {
		tmp = x / ((a + 1.0) + (b * (y / t)));
	} else if (b <= -3.7e+67) {
		tmp = (z / b) + ((x * (t / b)) / y);
	} else if (b <= 1.55e+47) {
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z / b) + ((t / (b / x)) / y)
    if (b <= (-2.6d+154)) then
        tmp = t_1
    else if (b <= (-1.32d+113)) then
        tmp = x / ((a + 1.0d0) + (b * (y / t)))
    else if (b <= (-3.7d+67)) then
        tmp = (z / b) + ((x * (t / b)) / y)
    else if (b <= 1.55d+47) then
        tmp = (x + ((y * z) / t)) / (a + 1.0d0)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z / b) + ((t / (b / x)) / y);
	double tmp;
	if (b <= -2.6e+154) {
		tmp = t_1;
	} else if (b <= -1.32e+113) {
		tmp = x / ((a + 1.0) + (b * (y / t)));
	} else if (b <= -3.7e+67) {
		tmp = (z / b) + ((x * (t / b)) / y);
	} else if (b <= 1.55e+47) {
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z / b) + ((t / (b / x)) / y)
	tmp = 0
	if b <= -2.6e+154:
		tmp = t_1
	elif b <= -1.32e+113:
		tmp = x / ((a + 1.0) + (b * (y / t)))
	elif b <= -3.7e+67:
		tmp = (z / b) + ((x * (t / b)) / y)
	elif b <= 1.55e+47:
		tmp = (x + ((y * z) / t)) / (a + 1.0)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z / b) + Float64(Float64(t / Float64(b / x)) / y))
	tmp = 0.0
	if (b <= -2.6e+154)
		tmp = t_1;
	elseif (b <= -1.32e+113)
		tmp = Float64(x / Float64(Float64(a + 1.0) + Float64(b * Float64(y / t))));
	elseif (b <= -3.7e+67)
		tmp = Float64(Float64(z / b) + Float64(Float64(x * Float64(t / b)) / y));
	elseif (b <= 1.55e+47)
		tmp = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(a + 1.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z / b) + ((t / (b / x)) / y);
	tmp = 0.0;
	if (b <= -2.6e+154)
		tmp = t_1;
	elseif (b <= -1.32e+113)
		tmp = x / ((a + 1.0) + (b * (y / t)));
	elseif (b <= -3.7e+67)
		tmp = (z / b) + ((x * (t / b)) / y);
	elseif (b <= 1.55e+47)
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z / b), $MachinePrecision] + N[(N[(t / N[(b / x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.6e+154], t$95$1, If[LessEqual[b, -1.32e+113], N[(x / N[(N[(a + 1.0), $MachinePrecision] + N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -3.7e+67], N[(N[(z / b), $MachinePrecision] + N[(N[(x * N[(t / b), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.55e+47], N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -2.59999999999999989e154 or 1.55e47 < b

   1. Initial program 56.6%

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

      1. *-commutative 56.6%

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

      2. associate-/l* 57.6%

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

      3. associate-*l/ 65.9%

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

   3. Simplified 65.9%

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

   4. Taylor expanded in y around -inf 55.3%

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

      1. +-commutative 55.3%

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

      2. associate-*r/ 55.3%

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

      3. distribute-lft-out-- 55.3%

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

      4. associate-*r* 55.3%

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

      5. metadata-eval 55.3%

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

      6. *-lft-identity 55.3%

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

   6. Simplified 63.2%

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

   7. Taylor expanded in b around inf 67.7%

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

      1. associate-/l* 73.0%

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

   9. Simplified 73.0%

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

   if -2.59999999999999989e154 < b < -1.31999999999999996e113

   1. Initial program 65.1%

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

      1. *-commutative 65.1%

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

      2. associate-/l* 65.3%

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

      3. associate-*l/ 85.8%

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

   3. Simplified 85.8%

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

   4. Taylor expanded in x around inf 65.5%

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

   if -1.31999999999999996e113 < b < -3.6999999999999997e67

   1. Initial program 47.1%

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

      1. *-commutative 47.1%

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

      2. associate-/l* 46.3%

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

      3. associate-*l/ 46.6%

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

   3. Simplified 46.6%

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

   4. Taylor expanded in y around -inf 62.4%

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

      1. +-commutative 62.4%

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

      2. associate-*r/ 62.4%

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

      3. distribute-lft-out-- 62.4%

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

      4. associate-*r* 62.4%

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

      5. metadata-eval 62.4%

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

      6. *-lft-identity 62.4%

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

   6. Simplified 62.4%

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

   7. Taylor expanded in b around inf 70.5%

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

      1. associate-*l/ 70.5%

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

      2. *-commutative 70.5%

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

   9. Simplified 70.5%

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

   if -3.6999999999999997e67 < b < 1.55e47

   1. Initial program 87.9%

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

      1. *-commutative 87.9%

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

      2. associate-/l* 87.5%

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

      3. associate-*l/ 86.7%

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

   3. Simplified 86.7%

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

   4. Taylor expanded in b around 0 78.6%

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

4. Final simplification 75.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.6 \cdot 10^{+154}:\\ \;\;\;\;\frac{z}{b} + \frac{\frac{t}{\frac{b}{x}}}{y}\\ \mathbf{elif}\;b \leq -1.32 \cdot 10^{+113}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \mathbf{elif}\;b \leq -3.7 \cdot 10^{+67}:\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot \frac{t}{b}}{y}\\ \mathbf{elif}\;b \leq 1.55 \cdot 10^{+47}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{\frac{t}{\frac{b}{x}}}{y}\\ \end{array} \]

Alternative 6: 66.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{b} + \frac{\frac{t}{\frac{b}{x}}}{y}\\ \mathbf{if}\;b \leq -1.6 \cdot 10^{+154}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -1.15 \cdot 10^{+106}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a + 1}\\ \mathbf{elif}\;b \leq -1.65 \cdot 10^{+70}:\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot \frac{t}{b}}{y}\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{+46}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (/ z b) (/ (/ t (/ b x)) y))))
   (if (<= b -1.6e+154)
     t_1
     (if (<= b -1.15e+106)
       (/ (+ x (/ y (/ t z))) (+ a 1.0))
       (if (<= b -1.65e+70)
         (+ (/ z b) (/ (* x (/ t b)) y))
         (if (<= b 6.5e+46) (/ (+ x (/ (* y z) t)) (+ a 1.0)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z / b) + ((t / (b / x)) / y);
	double tmp;
	if (b <= -1.6e+154) {
		tmp = t_1;
	} else if (b <= -1.15e+106) {
		tmp = (x + (y / (t / z))) / (a + 1.0);
	} else if (b <= -1.65e+70) {
		tmp = (z / b) + ((x * (t / b)) / y);
	} else if (b <= 6.5e+46) {
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z / b) + ((t / (b / x)) / y)
    if (b <= (-1.6d+154)) then
        tmp = t_1
    else if (b <= (-1.15d+106)) then
        tmp = (x + (y / (t / z))) / (a + 1.0d0)
    else if (b <= (-1.65d+70)) then
        tmp = (z / b) + ((x * (t / b)) / y)
    else if (b <= 6.5d+46) then
        tmp = (x + ((y * z) / t)) / (a + 1.0d0)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z / b) + ((t / (b / x)) / y);
	double tmp;
	if (b <= -1.6e+154) {
		tmp = t_1;
	} else if (b <= -1.15e+106) {
		tmp = (x + (y / (t / z))) / (a + 1.0);
	} else if (b <= -1.65e+70) {
		tmp = (z / b) + ((x * (t / b)) / y);
	} else if (b <= 6.5e+46) {
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z / b) + ((t / (b / x)) / y)
	tmp = 0
	if b <= -1.6e+154:
		tmp = t_1
	elif b <= -1.15e+106:
		tmp = (x + (y / (t / z))) / (a + 1.0)
	elif b <= -1.65e+70:
		tmp = (z / b) + ((x * (t / b)) / y)
	elif b <= 6.5e+46:
		tmp = (x + ((y * z) / t)) / (a + 1.0)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z / b) + Float64(Float64(t / Float64(b / x)) / y))
	tmp = 0.0
	if (b <= -1.6e+154)
		tmp = t_1;
	elseif (b <= -1.15e+106)
		tmp = Float64(Float64(x + Float64(y / Float64(t / z))) / Float64(a + 1.0));
	elseif (b <= -1.65e+70)
		tmp = Float64(Float64(z / b) + Float64(Float64(x * Float64(t / b)) / y));
	elseif (b <= 6.5e+46)
		tmp = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(a + 1.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z / b) + ((t / (b / x)) / y);
	tmp = 0.0;
	if (b <= -1.6e+154)
		tmp = t_1;
	elseif (b <= -1.15e+106)
		tmp = (x + (y / (t / z))) / (a + 1.0);
	elseif (b <= -1.65e+70)
		tmp = (z / b) + ((x * (t / b)) / y);
	elseif (b <= 6.5e+46)
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z / b), $MachinePrecision] + N[(N[(t / N[(b / x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.6e+154], t$95$1, If[LessEqual[b, -1.15e+106], N[(N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.65e+70], N[(N[(z / b), $MachinePrecision] + N[(N[(x * N[(t / b), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6.5e+46], N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.6e154 or 6.50000000000000008e46 < b

   1. Initial program 56.6%

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

      1. *-commutative 56.6%

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

      2. associate-/l* 57.6%

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

      3. associate-*l/ 65.9%

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

   3. Simplified 65.9%

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

   4. Taylor expanded in y around -inf 55.3%

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

      1. +-commutative 55.3%

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

      2. associate-*r/ 55.3%

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

      3. distribute-lft-out-- 55.3%

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

      4. associate-*r* 55.3%

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

      5. metadata-eval 55.3%

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

      6. *-lft-identity 55.3%

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

   6. Simplified 63.2%

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

   7. Taylor expanded in b around inf 67.7%

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

      1. associate-/l* 73.0%

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

   9. Simplified 73.0%

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

   if -1.6e154 < b < -1.1500000000000001e106

   1. Initial program 65.1%

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

      1. *-commutative 65.1%

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

      2. associate-/l* 65.3%

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

      3. associate-*l/ 85.8%

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

   3. Simplified 85.8%

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

   4. Taylor expanded in b around 0 61.0%

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

      1. *-un-lft-identity 61.0%

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

      2. associate-/l* 67.8%

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

   6. Applied egg-rr 67.8%

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

   if -1.1500000000000001e106 < b < -1.65000000000000008e70

   1. Initial program 47.1%

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

      1. *-commutative 47.1%

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

      2. associate-/l* 46.3%

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

      3. associate-*l/ 46.6%

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

   3. Simplified 46.6%

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

   4. Taylor expanded in y around -inf 62.4%

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

      1. +-commutative 62.4%

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

      2. associate-*r/ 62.4%

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

      3. distribute-lft-out-- 62.4%

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

      4. associate-*r* 62.4%

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

      5. metadata-eval 62.4%

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

      6. *-lft-identity 62.4%

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

   6. Simplified 62.4%

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

   7. Taylor expanded in b around inf 70.5%

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

      1. associate-*l/ 70.5%

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

      2. *-commutative 70.5%

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

   9. Simplified 70.5%

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

   if -1.65000000000000008e70 < b < 6.50000000000000008e46

   1. Initial program 87.9%

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

      1. *-commutative 87.9%

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

      2. associate-/l* 87.5%

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

      3. associate-*l/ 86.7%

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

   3. Simplified 86.7%

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

   4. Taylor expanded in b around 0 78.6%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.6 \cdot 10^{+154}:\\ \;\;\;\;\frac{z}{b} + \frac{\frac{t}{\frac{b}{x}}}{y}\\ \mathbf{elif}\;b \leq -1.15 \cdot 10^{+106}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a + 1}\\ \mathbf{elif}\;b \leq -1.65 \cdot 10^{+70}:\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot \frac{t}{b}}{y}\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{+46}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{\frac{t}{\frac{b}{x}}}{y}\\ \end{array} \]

Alternative 7: 54.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.1 \cdot 10^{+28} \lor \neg \left(b \leq 9.2 \cdot 10^{+46}\right):\\ \;\;\;\;\frac{z}{b} + \frac{\frac{t}{\frac{b}{x}}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -2.1e+28) (not (<= b 9.2e+46)))
   (+ (/ z b) (/ (/ t (/ b x)) y))
   (/ x (+ a 1.0))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -2.1e+28) || !(b <= 9.2e+46)) {
		tmp = (z / b) + ((t / (b / x)) / y);
	} else {
		tmp = x / (a + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-2.1d+28)) .or. (.not. (b <= 9.2d+46))) then
        tmp = (z / b) + ((t / (b / x)) / y)
    else
        tmp = x / (a + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -2.1e+28) || !(b <= 9.2e+46)) {
		tmp = (z / b) + ((t / (b / x)) / y);
	} else {
		tmp = x / (a + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -2.1e+28) or not (b <= 9.2e+46):
		tmp = (z / b) + ((t / (b / x)) / y)
	else:
		tmp = x / (a + 1.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -2.1e+28) || !(b <= 9.2e+46))
		tmp = Float64(Float64(z / b) + Float64(Float64(t / Float64(b / x)) / y));
	else
		tmp = Float64(x / Float64(a + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -2.1e+28) || ~((b <= 9.2e+46)))
		tmp = (z / b) + ((t / (b / x)) / y);
	else
		tmp = x / (a + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -2.1e+28], N[Not[LessEqual[b, 9.2e+46]], $MachinePrecision]], N[(N[(z / b), $MachinePrecision] + N[(N[(t / N[(b / x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -2.09999999999999989e28 or 9.2000000000000002e46 < b

   1. Initial program 57.1%

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

      1. *-commutative 57.1%

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

      2. associate-/l* 57.6%

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

      3. associate-*l/ 65.9%

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

   3. Simplified 65.9%

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

   4. Taylor expanded in y around -inf 52.8%

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

      1. +-commutative 52.8%

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

      2. associate-*r/ 52.8%

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

      3. distribute-lft-out-- 52.8%

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

      4. associate-*r* 52.8%

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

      5. metadata-eval 52.8%

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

      6. *-lft-identity 52.8%

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

   6. Simplified 58.6%

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

   7. Taylor expanded in b around inf 62.8%

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

      1. associate-/l* 66.6%

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

   9. Simplified 66.6%

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

   if -2.09999999999999989e28 < b < 9.2000000000000002e46

   1. Initial program 89.3%

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

      1. *-commutative 89.3%

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

      2. associate-/l* 89.1%

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

      3. associate-*l/ 88.2%

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

   3. Simplified 88.2%

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

   4. Taylor expanded in t around inf 52.6%

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

4. Final simplification 59.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.1 \cdot 10^{+28} \lor \neg \left(b \leq 9.2 \cdot 10^{+46}\right):\\ \;\;\;\;\frac{z}{b} + \frac{\frac{t}{\frac{b}{x}}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \]

Alternative 8: 62.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.62 \cdot 10^{-49} \lor \neg \left(t \leq 1.1 \cdot 10^{-102}\right):\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{\frac{t}{\frac{b}{x}}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -1.62e-49) (not (<= t 1.1e-102)))
   (/ x (+ 1.0 (+ a (/ (* y b) t))))
   (+ (/ z b) (/ (/ t (/ b x)) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.62e-49) || !(t <= 1.1e-102)) {
		tmp = x / (1.0 + (a + ((y * b) / t)));
	} else {
		tmp = (z / b) + ((t / (b / x)) / 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 ((t <= (-1.62d-49)) .or. (.not. (t <= 1.1d-102))) then
        tmp = x / (1.0d0 + (a + ((y * b) / t)))
    else
        tmp = (z / b) + ((t / (b / x)) / 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 ((t <= -1.62e-49) || !(t <= 1.1e-102)) {
		tmp = x / (1.0 + (a + ((y * b) / t)));
	} else {
		tmp = (z / b) + ((t / (b / x)) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -1.62e-49) or not (t <= 1.1e-102):
		tmp = x / (1.0 + (a + ((y * b) / t)))
	else:
		tmp = (z / b) + ((t / (b / x)) / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -1.62e-49) || !(t <= 1.1e-102))
		tmp = Float64(x / Float64(1.0 + Float64(a + Float64(Float64(y * b) / t))));
	else
		tmp = Float64(Float64(z / b) + Float64(Float64(t / Float64(b / x)) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -1.62e-49) || ~((t <= 1.1e-102)))
		tmp = x / (1.0 + (a + ((y * b) / t)));
	else
		tmp = (z / b) + ((t / (b / x)) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -1.62e-49], N[Not[LessEqual[t, 1.1e-102]], $MachinePrecision]], N[(x / N[(1.0 + N[(a + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z / b), $MachinePrecision] + N[(N[(t / N[(b / x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.62e-49 or 1.10000000000000006e-102 < t

   1. Initial program 82.0%

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

      1. *-commutative 82.0%

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

      2. associate-/l* 84.3%

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

      3. associate-*l/ 90.6%

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

   3. Simplified 90.6%

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

   4. Taylor expanded in x around inf 61.1%

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

   if -1.62e-49 < t < 1.10000000000000006e-102

   1. Initial program 56.1%

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

      1. *-commutative 56.1%

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

      2. associate-/l* 52.0%

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

      3. associate-*l/ 50.7%

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

   3. Simplified 50.7%

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

   4. Taylor expanded in y around -inf 60.3%

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

      1. +-commutative 60.3%

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

      2. associate-*r/ 60.3%

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

      3. distribute-lft-out-- 60.3%

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

      4. associate-*r* 60.3%

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

      5. metadata-eval 60.3%

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

      6. *-lft-identity 60.3%

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

   6. Simplified 58.0%

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

   7. Taylor expanded in b around inf 71.2%

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

      1. associate-/l* 67.9%

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

   9. Simplified 67.9%

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

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.62 \cdot 10^{-49} \lor \neg \left(t \leq 1.1 \cdot 10^{-102}\right):\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{\frac{t}{\frac{b}{x}}}{y}\\ \end{array} \]

Alternative 9: 64.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{-47} \lor \neg \left(t \leq 1.1 \cdot 10^{-102}\right):\\ \;\;\;\;\frac{x}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{\frac{t}{\frac{b}{x}}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -1.4e-47) (not (<= t 1.1e-102)))
   (/ x (+ (+ a 1.0) (* b (/ y t))))
   (+ (/ z b) (/ (/ t (/ b x)) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.4e-47) || !(t <= 1.1e-102)) {
		tmp = x / ((a + 1.0) + (b * (y / t)));
	} else {
		tmp = (z / b) + ((t / (b / x)) / 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 ((t <= (-1.4d-47)) .or. (.not. (t <= 1.1d-102))) then
        tmp = x / ((a + 1.0d0) + (b * (y / t)))
    else
        tmp = (z / b) + ((t / (b / x)) / 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 ((t <= -1.4e-47) || !(t <= 1.1e-102)) {
		tmp = x / ((a + 1.0) + (b * (y / t)));
	} else {
		tmp = (z / b) + ((t / (b / x)) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -1.4e-47) or not (t <= 1.1e-102):
		tmp = x / ((a + 1.0) + (b * (y / t)))
	else:
		tmp = (z / b) + ((t / (b / x)) / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -1.4e-47) || !(t <= 1.1e-102))
		tmp = Float64(x / Float64(Float64(a + 1.0) + Float64(b * Float64(y / t))));
	else
		tmp = Float64(Float64(z / b) + Float64(Float64(t / Float64(b / x)) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -1.4e-47) || ~((t <= 1.1e-102)))
		tmp = x / ((a + 1.0) + (b * (y / t)));
	else
		tmp = (z / b) + ((t / (b / x)) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -1.4e-47], N[Not[LessEqual[t, 1.1e-102]], $MachinePrecision]], N[(x / N[(N[(a + 1.0), $MachinePrecision] + N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z / b), $MachinePrecision] + N[(N[(t / N[(b / x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.39999999999999996e-47 or 1.10000000000000006e-102 < t

   1. Initial program 82.0%

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

      1. *-commutative 82.0%

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

      2. associate-/l* 84.3%

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

      3. associate-*l/ 90.6%

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

   3. Simplified 90.6%

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

   4. Taylor expanded in x around inf 64.5%

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

   if -1.39999999999999996e-47 < t < 1.10000000000000006e-102

   1. Initial program 56.1%

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

      1. *-commutative 56.1%

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

      2. associate-/l* 52.0%

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

      3. associate-*l/ 50.7%

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

   3. Simplified 50.7%

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

   4. Taylor expanded in y around -inf 60.3%

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

      1. +-commutative 60.3%

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

      2. associate-*r/ 60.3%

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

      3. distribute-lft-out-- 60.3%

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

      4. associate-*r* 60.3%

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

      5. metadata-eval 60.3%

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

      6. *-lft-identity 60.3%

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

   6. Simplified 58.0%

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

   7. Taylor expanded in b around inf 71.2%

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

      1. associate-/l* 67.9%

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

   9. Simplified 67.9%

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

4. Final simplification 65.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{-47} \lor \neg \left(t \leq 1.1 \cdot 10^{-102}\right):\\ \;\;\;\;\frac{x}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{\frac{t}{\frac{b}{x}}}{y}\\ \end{array} \]

Alternative 10: 41.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.15 \cdot 10^{-41}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-185}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-155}:\\ \;\;\;\;x - x \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -2.15e-41)
   (/ z b)
   (if (<= y 1.6e-185) (/ x a) (if (<= y 5e-155) (- x (* x a)) (/ z b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.15e-41) {
		tmp = z / b;
	} else if (y <= 1.6e-185) {
		tmp = x / a;
	} else if (y <= 5e-155) {
		tmp = x - (x * a);
	} else {
		tmp = z / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-2.15d-41)) then
        tmp = z / b
    else if (y <= 1.6d-185) then
        tmp = x / a
    else if (y <= 5d-155) then
        tmp = x - (x * a)
    else
        tmp = z / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.15e-41) {
		tmp = z / b;
	} else if (y <= 1.6e-185) {
		tmp = x / a;
	} else if (y <= 5e-155) {
		tmp = x - (x * a);
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -2.15e-41:
		tmp = z / b
	elif y <= 1.6e-185:
		tmp = x / a
	elif y <= 5e-155:
		tmp = x - (x * a)
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -2.15e-41)
		tmp = Float64(z / b);
	elseif (y <= 1.6e-185)
		tmp = Float64(x / a);
	elseif (y <= 5e-155)
		tmp = Float64(x - Float64(x * a));
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -2.15e-41)
		tmp = z / b;
	elseif (y <= 1.6e-185)
		tmp = x / a;
	elseif (y <= 5e-155)
		tmp = x - (x * a);
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -2.15e-41], N[(z / b), $MachinePrecision], If[LessEqual[y, 1.6e-185], N[(x / a), $MachinePrecision], If[LessEqual[y, 5e-155], N[(x - N[(x * a), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.1499999999999999e-41 or 4.9999999999999999e-155 < y

   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. *-commutative 63.4%

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

      2. associate-/l* 63.6%

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

      3. associate-*l/ 69.1%

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

   3. Simplified 69.1%

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

   4. Taylor expanded in t around 0 45.6%

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

   if -2.1499999999999999e-41 < y < 1.5999999999999999e-185

   1. Initial program 93.5%

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

      1. *-commutative 93.5%

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

      2. associate-/l* 94.6%

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

      3. associate-*l/ 94.6%

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

   3. Simplified 94.6%

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

   4. Taylor expanded in t around inf 60.3%

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

   5. Taylor expanded in a around inf 36.4%

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

   if 1.5999999999999999e-185 < y < 4.9999999999999999e-155

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. associate-/l* 86.8%

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

      3. associate-*l/ 86.8%

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

   3. Simplified 86.8%

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

   4. Taylor expanded in t around inf 72.7%

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

   5. Taylor expanded in a around 0 72.9%

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

      1. +-commutative 72.9%

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

      2. mul-1-neg 72.9%

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

      3. unsub-neg 72.9%

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

      4. *-commutative 72.9%

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

   7. Simplified 72.9%

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

4. Final simplification 43.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.15 \cdot 10^{-41}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-185}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-155}:\\ \;\;\;\;x - x \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 11: 41.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{-38}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-188}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{-155}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -2.4e-38)
   (/ z b)
   (if (<= y 3.2e-188) (/ x a) (if (<= y 3.3e-155) x (/ z b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.4e-38) {
		tmp = z / b;
	} else if (y <= 3.2e-188) {
		tmp = x / a;
	} else if (y <= 3.3e-155) {
		tmp = x;
	} 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 (y <= (-2.4d-38)) then
        tmp = z / b
    else if (y <= 3.2d-188) then
        tmp = x / a
    else if (y <= 3.3d-155) then
        tmp = x
    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 (y <= -2.4e-38) {
		tmp = z / b;
	} else if (y <= 3.2e-188) {
		tmp = x / a;
	} else if (y <= 3.3e-155) {
		tmp = x;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -2.4e-38:
		tmp = z / b
	elif y <= 3.2e-188:
		tmp = x / a
	elif y <= 3.3e-155:
		tmp = x
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -2.4e-38)
		tmp = Float64(z / b);
	elseif (y <= 3.2e-188)
		tmp = Float64(x / a);
	elseif (y <= 3.3e-155)
		tmp = x;
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -2.4e-38)
		tmp = z / b;
	elseif (y <= 3.2e-188)
		tmp = x / a;
	elseif (y <= 3.3e-155)
		tmp = x;
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -2.4e-38], N[(z / b), $MachinePrecision], If[LessEqual[y, 3.2e-188], N[(x / a), $MachinePrecision], If[LessEqual[y, 3.3e-155], x, N[(z / b), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.40000000000000022e-38 or 3.29999999999999986e-155 < y

   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. *-commutative 63.4%

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

      2. associate-/l* 63.6%

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

      3. associate-*l/ 69.1%

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

   3. Simplified 69.1%

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

   4. Taylor expanded in t around 0 45.6%

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

   if -2.40000000000000022e-38 < y < 3.20000000000000022e-188

   1. Initial program 93.5%

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

      1. *-commutative 93.5%

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

      2. associate-/l* 94.6%

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

      3. associate-*l/ 94.6%

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

   3. Simplified 94.6%

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

   4. Taylor expanded in t around inf 60.3%

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

   5. Taylor expanded in a around inf 36.4%

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

   if 3.20000000000000022e-188 < y < 3.29999999999999986e-155

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. associate-/l* 86.8%

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

      3. associate-*l/ 86.8%

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

   3. Simplified 86.8%

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

   4. Taylor expanded in b around 0 100.0%

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

      1. *-un-lft-identity 100.0%

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

      2. associate-/l* 86.3%

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

   6. Applied egg-rr 86.3%

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

   7. Taylor expanded in a around 0 70.2%

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

   8. Taylor expanded in y around 0 71.4%

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

4. Final simplification 43.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{-38}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-188}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{-155}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 12: 55.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.9 \cdot 10^{-51} \lor \neg \left(t \leq 1.1 \cdot 10^{-102}\right):\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -4.9e-51) (not (<= t 1.1e-102))) (/ 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 <= -4.9e-51) || !(t <= 1.1e-102)) {
		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 <= (-4.9d-51)) .or. (.not. (t <= 1.1d-102))) 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 <= -4.9e-51) || !(t <= 1.1e-102)) {
		tmp = x / (a + 1.0);
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -4.9e-51) or not (t <= 1.1e-102):
		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 <= -4.9e-51) || !(t <= 1.1e-102))
		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 <= -4.9e-51) || ~((t <= 1.1e-102)))
		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, -4.9e-51], N[Not[LessEqual[t, 1.1e-102]], $MachinePrecision]], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.89999999999999974e-51 or 1.10000000000000006e-102 < t

   1. Initial program 82.0%

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

      1. *-commutative 82.0%

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

      2. associate-/l* 84.3%

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

      3. associate-*l/ 90.6%

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

   3. Simplified 90.6%

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

   4. Taylor expanded in t around inf 55.0%

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

   if -4.89999999999999974e-51 < t < 1.10000000000000006e-102

   1. Initial program 56.1%

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

      1. *-commutative 56.1%

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

      2. associate-/l* 52.0%

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

      3. associate-*l/ 50.7%

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

   3. Simplified 50.7%

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

   4. Taylor expanded in t around 0 61.9%

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

4. Final simplification 57.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.9 \cdot 10^{-51} \lor \neg \left(t \leq 1.1 \cdot 10^{-102}\right):\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 13: 41.5% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;a \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -1.0) (/ x a) (if (<= a 1.0) x (/ x a))))

C

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

Fortran

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

Java

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

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -1.0:
		tmp = x / a
	elif a <= 1.0:
		tmp = x
	else:
		tmp = x / a
	return tmp

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -1.0], N[(x / a), $MachinePrecision], If[LessEqual[a, 1.0], x, N[(x / a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -1 or 1 < a

   1. Initial program 72.3%

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

      1. *-commutative 72.3%

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

      2. associate-/l* 72.6%

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

      3. associate-*l/ 76.3%

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

   3. Simplified 76.3%

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

   4. Taylor expanded in t around inf 43.4%

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

   5. Taylor expanded in a around inf 43.4%

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

   if -1 < a < 1

   1. Initial program 74.1%

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

      1. *-commutative 74.1%

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

      2. associate-/l* 74.0%

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

      3. associate-*l/ 77.7%

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

   3. Simplified 77.7%

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

   4. Taylor expanded in b around 0 53.9%

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

      1. *-un-lft-identity 53.9%

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

      2. associate-/l* 52.5%

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

   6. Applied egg-rr 52.5%

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

   7. Taylor expanded in a around 0 52.1%

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

   8. Taylor expanded in y around 0 37.7%

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

4. Final simplification 40.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;a \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \]

Alternative 14: 19.9% 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 73.2%

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

   1. *-commutative 73.2%

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

   2. associate-/l* 73.3%

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

   3. associate-*l/ 77.0%

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

3. Simplified 77.0%

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

4. Taylor expanded in b around 0 57.4%

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

   1. *-un-lft-identity 57.4%

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

   2. associate-/l* 56.7%

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

6. Applied egg-rr 56.7%

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

7. Taylor expanded in a around 0 28.2%

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

8. Taylor expanded in y around 0 21.1%

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

9. Final simplification 21.1%

   \[\leadsto x \]

Developer target: 79.0% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023207 
(FPCore (x y z t a b)
  :name "Diagrams.Solve.Tridiagonal:solveCyclicTriDiagonal from diagrams-solve-0.1, B"
  :precision binary64

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

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