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

Percentage Accurate: 74.6% → 88.5%

Time: 17.4s

Alternatives: 24

Speedup: 0.6×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 74.6% 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: 88.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ t_2 := b \cdot \frac{y}{t}\\ t_3 := \left(a + y \cdot \frac{b}{t}\right) + 1\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-57}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{t\_3} + \frac{x}{t\_3}\\ \mathbf{elif}\;t\_1 \leq 10^{-293}:\\ \;\;\;\;x \cdot \left(\frac{-1}{\left(-1 - a\right) - t\_2} + \frac{y \cdot \frac{z}{t}}{x \cdot \left(\left(a + 1\right) + t\_2\right)}\right)\\ \mathbf{elif}\;t\_1 \leq 10^{+304}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{\frac{x \cdot t}{b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (* y z) t)) (+ (/ (* y b) t) (+ a 1.0))))
        (t_2 (* b (/ y t)))
        (t_3 (+ (+ a (* y (/ b t))) 1.0)))
   (if (<= t_1 -5e-57)
     (+ (* (/ y t) (/ z t_3)) (/ x t_3))
     (if (<= t_1 1e-293)
       (*
        x
        (+
         (/ -1.0 (- (- -1.0 a) t_2))
         (/ (* y (/ z t)) (* x (+ (+ a 1.0) t_2)))))
       (if (<= t_1 1e+304) t_1 (+ (/ z b) (/ (/ (* x t) b) y)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + ((y * z) / t)) / (((y * b) / t) + (a + 1.0));
	double t_2 = b * (y / t);
	double t_3 = (a + (y * (b / t))) + 1.0;
	double tmp;
	if (t_1 <= -5e-57) {
		tmp = ((y / t) * (z / t_3)) + (x / t_3);
	} else if (t_1 <= 1e-293) {
		tmp = x * ((-1.0 / ((-1.0 - a) - t_2)) + ((y * (z / t)) / (x * ((a + 1.0) + t_2))));
	} else if (t_1 <= 1e+304) {
		tmp = t_1;
	} else {
		tmp = (z / b) + (((x * t) / b) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (x + ((y * z) / t)) / (((y * b) / t) + (a + 1.0d0))
    t_2 = b * (y / t)
    t_3 = (a + (y * (b / t))) + 1.0d0
    if (t_1 <= (-5d-57)) then
        tmp = ((y / t) * (z / t_3)) + (x / t_3)
    else if (t_1 <= 1d-293) then
        tmp = x * (((-1.0d0) / (((-1.0d0) - a) - t_2)) + ((y * (z / t)) / (x * ((a + 1.0d0) + t_2))))
    else if (t_1 <= 1d+304) then
        tmp = t_1
    else
        tmp = (z / b) + (((x * t) / b) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + ((y * z) / t)) / (((y * b) / t) + (a + 1.0));
	double t_2 = b * (y / t);
	double t_3 = (a + (y * (b / t))) + 1.0;
	double tmp;
	if (t_1 <= -5e-57) {
		tmp = ((y / t) * (z / t_3)) + (x / t_3);
	} else if (t_1 <= 1e-293) {
		tmp = x * ((-1.0 / ((-1.0 - a) - t_2)) + ((y * (z / t)) / (x * ((a + 1.0) + t_2))));
	} else if (t_1 <= 1e+304) {
		tmp = t_1;
	} else {
		tmp = (z / b) + (((x * t) / b) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + ((y * z) / t)) / (((y * b) / t) + (a + 1.0))
	t_2 = b * (y / t)
	t_3 = (a + (y * (b / t))) + 1.0
	tmp = 0
	if t_1 <= -5e-57:
		tmp = ((y / t) * (z / t_3)) + (x / t_3)
	elif t_1 <= 1e-293:
		tmp = x * ((-1.0 / ((-1.0 - a) - t_2)) + ((y * (z / t)) / (x * ((a + 1.0) + t_2))))
	elif t_1 <= 1e+304:
		tmp = t_1
	else:
		tmp = (z / b) + (((x * t) / b) / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(Float64(Float64(y * b) / t) + Float64(a + 1.0)))
	t_2 = Float64(b * Float64(y / t))
	t_3 = Float64(Float64(a + Float64(y * Float64(b / t))) + 1.0)
	tmp = 0.0
	if (t_1 <= -5e-57)
		tmp = Float64(Float64(Float64(y / t) * Float64(z / t_3)) + Float64(x / t_3));
	elseif (t_1 <= 1e-293)
		tmp = Float64(x * Float64(Float64(-1.0 / Float64(Float64(-1.0 - a) - t_2)) + Float64(Float64(y * Float64(z / t)) / Float64(x * Float64(Float64(a + 1.0) + t_2)))));
	elseif (t_1 <= 1e+304)
		tmp = t_1;
	else
		tmp = Float64(Float64(z / b) + Float64(Float64(Float64(x * t) / b) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + ((y * z) / t)) / (((y * b) / t) + (a + 1.0));
	t_2 = b * (y / t);
	t_3 = (a + (y * (b / t))) + 1.0;
	tmp = 0.0;
	if (t_1 <= -5e-57)
		tmp = ((y / t) * (z / t_3)) + (x / t_3);
	elseif (t_1 <= 1e-293)
		tmp = x * ((-1.0 / ((-1.0 - a) - t_2)) + ((y * (z / t)) / (x * ((a + 1.0) + t_2))));
	elseif (t_1 <= 1e+304)
		tmp = t_1;
	else
		tmp = (z / b) + (((x * t) / b) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(a + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]}, If[LessEqual[t$95$1, -5e-57], N[(N[(N[(y / t), $MachinePrecision] * N[(z / t$95$3), $MachinePrecision]), $MachinePrecision] + N[(x / t$95$3), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e-293], N[(x * N[(N[(-1.0 / N[(N[(-1.0 - a), $MachinePrecision] - t$95$2), $MachinePrecision]), $MachinePrecision] + N[(N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision] / N[(x * N[(N[(a + 1.0), $MachinePrecision] + t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+304], t$95$1, N[(N[(z / b), $MachinePrecision] + N[(N[(N[(x * t), $MachinePrecision] / b), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -5.0000000000000002e-57

   1. Initial program 91.8%

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

      1. associate-/l* 90.5%

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

      2. associate-/l* 90.5%

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

   3. Simplified 90.5%

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

   5. Taylor expanded in x around 0 94.4%

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

      1. +-commutative 94.4%

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

      2. times-frac 95.8%

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

      3. associate-*l/ 95.8%

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

      4. *-commutative 95.8%

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

      5. associate-*l/ 95.8%

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

      6. *-commutative 95.8%

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

   7. Simplified 95.8%

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

   if -5.0000000000000002e-57 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 1.0000000000000001e-293

   1. Initial program 78.4%

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

      1. *-commutative 78.4%

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

      2. associate-/l* 84.1%

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

   4. Applied egg-rr 84.1%

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

   5. Taylor expanded in x around inf 76.9%

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

      1. associate-+r+ 76.9%

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

      2. associate-*r/ 81.2%

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

      3. associate-/r* 82.6%

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

      4. associate-/l* 84.1%

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

      5. *-commutative 84.1%

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

      6. associate-+r+ 84.1%

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

      7. associate-*r/ 85.5%

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

   7. Simplified 85.5%

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

   if 1.0000000000000001e-293 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 9.9999999999999994e303

   1. Initial program 99.6%

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

   if 9.9999999999999994e303 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t)))

   1. Initial program 10.6%

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

      1. associate-/l* 16.4%

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

      2. associate-/l* 22.0%

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

   3. Simplified 22.0%

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

   5. Taylor expanded in y around -inf 59.5%

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

      1. +-commutative 59.5%

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

      2. mul-1-neg 59.5%

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

      3. unsub-neg 59.5%

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

      4. distribute-lft-out-- 59.5%

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

      5. mul-1-neg 59.5%

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

      6. associate-/l* 53.4%

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

      7. associate-/l* 56.4%

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

      8. distribute-lft-out-- 56.4%

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

   7. Simplified 56.4%

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

   8. Taylor expanded in x around inf 86.4%

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

4. Final simplification 93.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -5 \cdot 10^{-57}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{\left(a + y \cdot \frac{b}{t}\right) + 1} + \frac{x}{\left(a + y \cdot \frac{b}{t}\right) + 1}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 10^{-293}:\\ \;\;\;\;x \cdot \left(\frac{-1}{\left(-1 - a\right) - b \cdot \frac{y}{t}} + \frac{y \cdot \frac{z}{t}}{x \cdot \left(\left(a + 1\right) + b \cdot \frac{y}{t}\right)}\right)\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 10^{+304}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{\frac{x \cdot t}{b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 88.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot z}{t}\\ t_2 := \frac{t\_1}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ t_3 := \left(a + y \cdot \frac{b}{t}\right) + 1\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+94}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{t\_3} + \frac{x}{t\_3}\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{-287}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + \frac{1}{\frac{t}{y \cdot b}}}\\ \mathbf{elif}\;t\_2 \leq 10^{+304}:\\ \;\;\;\;\frac{t\_1}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{\frac{x \cdot t}{b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (/ (* y z) t)))
        (t_2 (/ t_1 (+ (/ (* y b) t) (+ a 1.0))))
        (t_3 (+ (+ a (* y (/ b t))) 1.0)))
   (if (<= t_2 -5e+94)
     (+ (* (/ y t) (/ z t_3)) (/ x t_3))
     (if (<= t_2 -5e-287)
       (/ (+ x (* y (/ z t))) (+ (+ a 1.0) (/ 1.0 (/ t (* y b)))))
       (if (<= t_2 1e+304)
         (/ t_1 (+ (+ a 1.0) (* b (/ y t))))
         (+ (/ z b) (/ (/ (* x t) b) y)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + ((y * z) / t);
	double t_2 = t_1 / (((y * b) / t) + (a + 1.0));
	double t_3 = (a + (y * (b / t))) + 1.0;
	double tmp;
	if (t_2 <= -5e+94) {
		tmp = ((y / t) * (z / t_3)) + (x / t_3);
	} else if (t_2 <= -5e-287) {
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (1.0 / (t / (y * b))));
	} else if (t_2 <= 1e+304) {
		tmp = t_1 / ((a + 1.0) + (b * (y / t)));
	} else {
		tmp = (z / b) + (((x * t) / b) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x + ((y * z) / t)
    t_2 = t_1 / (((y * b) / t) + (a + 1.0d0))
    t_3 = (a + (y * (b / t))) + 1.0d0
    if (t_2 <= (-5d+94)) then
        tmp = ((y / t) * (z / t_3)) + (x / t_3)
    else if (t_2 <= (-5d-287)) then
        tmp = (x + (y * (z / t))) / ((a + 1.0d0) + (1.0d0 / (t / (y * b))))
    else if (t_2 <= 1d+304) then
        tmp = t_1 / ((a + 1.0d0) + (b * (y / t)))
    else
        tmp = (z / b) + (((x * t) / b) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + ((y * z) / t);
	double t_2 = t_1 / (((y * b) / t) + (a + 1.0));
	double t_3 = (a + (y * (b / t))) + 1.0;
	double tmp;
	if (t_2 <= -5e+94) {
		tmp = ((y / t) * (z / t_3)) + (x / t_3);
	} else if (t_2 <= -5e-287) {
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (1.0 / (t / (y * b))));
	} else if (t_2 <= 1e+304) {
		tmp = t_1 / ((a + 1.0) + (b * (y / t)));
	} else {
		tmp = (z / b) + (((x * t) / b) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + ((y * z) / t)
	t_2 = t_1 / (((y * b) / t) + (a + 1.0))
	t_3 = (a + (y * (b / t))) + 1.0
	tmp = 0
	if t_2 <= -5e+94:
		tmp = ((y / t) * (z / t_3)) + (x / t_3)
	elif t_2 <= -5e-287:
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (1.0 / (t / (y * b))))
	elif t_2 <= 1e+304:
		tmp = t_1 / ((a + 1.0) + (b * (y / t)))
	else:
		tmp = (z / b) + (((x * t) / b) / y)
	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 / Float64(Float64(Float64(y * b) / t) + Float64(a + 1.0)))
	t_3 = Float64(Float64(a + Float64(y * Float64(b / t))) + 1.0)
	tmp = 0.0
	if (t_2 <= -5e+94)
		tmp = Float64(Float64(Float64(y / t) * Float64(z / t_3)) + Float64(x / t_3));
	elseif (t_2 <= -5e-287)
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(Float64(a + 1.0) + Float64(1.0 / Float64(t / Float64(y * b)))));
	elseif (t_2 <= 1e+304)
		tmp = Float64(t_1 / Float64(Float64(a + 1.0) + Float64(b * Float64(y / t))));
	else
		tmp = Float64(Float64(z / b) + Float64(Float64(Float64(x * t) / b) / y));
	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 / (((y * b) / t) + (a + 1.0));
	t_3 = (a + (y * (b / t))) + 1.0;
	tmp = 0.0;
	if (t_2 <= -5e+94)
		tmp = ((y / t) * (z / t_3)) + (x / t_3);
	elseif (t_2 <= -5e-287)
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (1.0 / (t / (y * b))));
	elseif (t_2 <= 1e+304)
		tmp = t_1 / ((a + 1.0) + (b * (y / t)));
	else
		tmp = (z / b) + (((x * t) / b) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 / N[(N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(a + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+94], N[(N[(N[(y / t), $MachinePrecision] * N[(z / t$95$3), $MachinePrecision]), $MachinePrecision] + N[(x / t$95$3), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, -5e-287], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(1.0 / N[(t / N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+304], N[(t$95$1 / N[(N[(a + 1.0), $MachinePrecision] + N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z / b), $MachinePrecision] + N[(N[(N[(x * t), $MachinePrecision] / b), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -5.0000000000000001e94

   1. Initial program 84.7%

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

      1. associate-/l* 82.4%

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

      2. associate-/l* 82.3%

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

   3. Simplified 82.3%

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

   5. Taylor expanded in x around 0 89.5%

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

      1. +-commutative 89.5%

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

      2. times-frac 94.8%

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

      3. associate-*l/ 94.9%

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

      4. *-commutative 94.9%

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

      5. associate-*l/ 94.8%

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

      6. *-commutative 94.8%

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

   7. Simplified 94.8%

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

   if -5.0000000000000001e94 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -5.00000000000000025e-287

   1. Initial program 98.3%

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

      1. associate-/l* 99.7%

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

      2. associate-/l* 96.9%

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

   3. Simplified 96.9%

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

      1. associate-*r/ 99.7%

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

      2. clear-num 99.7%

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

   6. Applied egg-rr 99.7%

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

   if -5.00000000000000025e-287 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 9.9999999999999994e303

   1. Initial program 88.5%

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

      1. *-commutative 88.5%

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

      2. associate-/l* 89.3%

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

   4. Applied egg-rr 89.3%

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

   if 9.9999999999999994e303 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t)))

   1. Initial program 10.6%

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

      1. associate-/l* 16.4%

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

      2. associate-/l* 22.0%

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

   3. Simplified 22.0%

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

   5. Taylor expanded in y around -inf 59.5%

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

      1. +-commutative 59.5%

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

      2. mul-1-neg 59.5%

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

      3. unsub-neg 59.5%

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

      4. distribute-lft-out-- 59.5%

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

      5. mul-1-neg 59.5%

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

      6. associate-/l* 53.4%

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

      7. associate-/l* 56.4%

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

      8. distribute-lft-out-- 56.4%

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

   7. Simplified 56.4%

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

   8. Taylor expanded in x around inf 86.4%

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

4. Final simplification 92.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -5 \cdot 10^{+94}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{\left(a + y \cdot \frac{b}{t}\right) + 1} + \frac{x}{\left(a + y \cdot \frac{b}{t}\right) + 1}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -5 \cdot 10^{-287}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + \frac{1}{\frac{t}{y \cdot b}}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 10^{+304}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{\frac{x \cdot t}{b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 88.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot z}{t}\\ t_2 := \frac{t\_1}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ t_3 := \left(a + y \cdot \frac{b}{t}\right) + 1\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+94}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{t\_3} + \frac{x}{t\_3}\\ \mathbf{elif}\;t\_2 \leq 10^{+304}:\\ \;\;\;\;\frac{-1}{\frac{-1}{t\_1} - \left(\frac{a}{t\_1} + \frac{y \cdot b}{t \cdot t\_1}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{\frac{x \cdot t}{b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (/ (* y z) t)))
        (t_2 (/ t_1 (+ (/ (* y b) t) (+ a 1.0))))
        (t_3 (+ (+ a (* y (/ b t))) 1.0)))
   (if (<= t_2 -5e+94)
     (+ (* (/ y t) (/ z t_3)) (/ x t_3))
     (if (<= t_2 1e+304)
       (/ -1.0 (- (/ -1.0 t_1) (+ (/ a t_1) (/ (* y b) (* t t_1)))))
       (+ (/ z b) (/ (/ (* x t) b) y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + ((y * z) / t);
	double t_2 = t_1 / (((y * b) / t) + (a + 1.0));
	double t_3 = (a + (y * (b / t))) + 1.0;
	double tmp;
	if (t_2 <= -5e+94) {
		tmp = ((y / t) * (z / t_3)) + (x / t_3);
	} else if (t_2 <= 1e+304) {
		tmp = -1.0 / ((-1.0 / t_1) - ((a / t_1) + ((y * b) / (t * t_1))));
	} else {
		tmp = (z / b) + (((x * t) / b) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x + ((y * z) / t)
    t_2 = t_1 / (((y * b) / t) + (a + 1.0d0))
    t_3 = (a + (y * (b / t))) + 1.0d0
    if (t_2 <= (-5d+94)) then
        tmp = ((y / t) * (z / t_3)) + (x / t_3)
    else if (t_2 <= 1d+304) then
        tmp = (-1.0d0) / (((-1.0d0) / t_1) - ((a / t_1) + ((y * b) / (t * t_1))))
    else
        tmp = (z / b) + (((x * t) / b) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + ((y * z) / t);
	double t_2 = t_1 / (((y * b) / t) + (a + 1.0));
	double t_3 = (a + (y * (b / t))) + 1.0;
	double tmp;
	if (t_2 <= -5e+94) {
		tmp = ((y / t) * (z / t_3)) + (x / t_3);
	} else if (t_2 <= 1e+304) {
		tmp = -1.0 / ((-1.0 / t_1) - ((a / t_1) + ((y * b) / (t * t_1))));
	} else {
		tmp = (z / b) + (((x * t) / b) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + ((y * z) / t)
	t_2 = t_1 / (((y * b) / t) + (a + 1.0))
	t_3 = (a + (y * (b / t))) + 1.0
	tmp = 0
	if t_2 <= -5e+94:
		tmp = ((y / t) * (z / t_3)) + (x / t_3)
	elif t_2 <= 1e+304:
		tmp = -1.0 / ((-1.0 / t_1) - ((a / t_1) + ((y * b) / (t * t_1))))
	else:
		tmp = (z / b) + (((x * t) / b) / y)
	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 / Float64(Float64(Float64(y * b) / t) + Float64(a + 1.0)))
	t_3 = Float64(Float64(a + Float64(y * Float64(b / t))) + 1.0)
	tmp = 0.0
	if (t_2 <= -5e+94)
		tmp = Float64(Float64(Float64(y / t) * Float64(z / t_3)) + Float64(x / t_3));
	elseif (t_2 <= 1e+304)
		tmp = Float64(-1.0 / Float64(Float64(-1.0 / t_1) - Float64(Float64(a / t_1) + Float64(Float64(y * b) / Float64(t * t_1)))));
	else
		tmp = Float64(Float64(z / b) + Float64(Float64(Float64(x * t) / b) / y));
	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 / (((y * b) / t) + (a + 1.0));
	t_3 = (a + (y * (b / t))) + 1.0;
	tmp = 0.0;
	if (t_2 <= -5e+94)
		tmp = ((y / t) * (z / t_3)) + (x / t_3);
	elseif (t_2 <= 1e+304)
		tmp = -1.0 / ((-1.0 / t_1) - ((a / t_1) + ((y * b) / (t * t_1))));
	else
		tmp = (z / b) + (((x * t) / b) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 / N[(N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(a + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+94], N[(N[(N[(y / t), $MachinePrecision] * N[(z / t$95$3), $MachinePrecision]), $MachinePrecision] + N[(x / t$95$3), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+304], N[(-1.0 / N[(N[(-1.0 / t$95$1), $MachinePrecision] - N[(N[(a / t$95$1), $MachinePrecision] + N[(N[(y * b), $MachinePrecision] / N[(t * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z / b), $MachinePrecision] + N[(N[(N[(x * t), $MachinePrecision] / b), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -5.0000000000000001e94

   1. Initial program 84.7%

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

      1. associate-/l* 82.4%

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

      2. associate-/l* 82.3%

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

   3. Simplified 82.3%

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

   5. Taylor expanded in x around 0 89.5%

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

      1. +-commutative 89.5%

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

      2. times-frac 94.8%

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

      3. associate-*l/ 94.9%

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

      4. *-commutative 94.9%

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

      5. associate-*l/ 94.8%

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

      6. *-commutative 94.8%

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

   7. Simplified 94.8%

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

   if -5.0000000000000001e94 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 9.9999999999999994e303

   1. Initial program 92.0%

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

      1. *-commutative 92.0%

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

      2. associate-/l* 92.0%

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

   4. Applied egg-rr 92.0%

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

      1. associate-*r/ 88.8%

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

      2. *-commutative 88.8%

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

      3. associate-/r/ 88.7%

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

      4. clear-num 87.9%

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

      5. inv-pow 87.9%

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

      6. +-commutative 87.9%

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

      7. associate-/r/ 87.9%

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

      8. *-commutative 87.9%

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

      9. fma-define 87.9%

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

      10. +-commutative 87.9%

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

      11. fma-define 87.9%

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

   6. Applied egg-rr 87.9%

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

      1. unpow-1 87.9%

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

      2. +-commutative 87.9%

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

   8. Simplified 87.9%

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

   9. Taylor expanded in b around 0 93.1%

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

   if 9.9999999999999994e303 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t)))

   1. Initial program 10.6%

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

      1. associate-/l* 16.4%

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

      2. associate-/l* 22.0%

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

   3. Simplified 22.0%

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

   5. Taylor expanded in y around -inf 59.5%

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

      1. +-commutative 59.5%

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

      2. mul-1-neg 59.5%

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

      3. unsub-neg 59.5%

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

      4. distribute-lft-out-- 59.5%

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

      5. mul-1-neg 59.5%

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

      6. associate-/l* 53.4%

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

      7. associate-/l* 56.4%

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

      8. distribute-lft-out-- 56.4%

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

   7. Simplified 56.4%

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

   8. Taylor expanded in x around inf 86.4%

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

4. Final simplification 92.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -5 \cdot 10^{+94}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{\left(a + y \cdot \frac{b}{t}\right) + 1} + \frac{x}{\left(a + y \cdot \frac{b}{t}\right) + 1}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 10^{+304}:\\ \;\;\;\;\frac{-1}{\frac{-1}{x + \frac{y \cdot z}{t}} - \left(\frac{a}{x + \frac{y \cdot z}{t}} + \frac{y \cdot b}{t \cdot \left(x + \frac{y \cdot z}{t}\right)}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{\frac{x \cdot t}{b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 54.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z + \frac{x \cdot t}{y}}{b}\\ t_2 := x + \frac{y \cdot z}{t}\\ \mathbf{if}\;a \leq -9 \cdot 10^{+44}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a}\\ \mathbf{elif}\;a \leq -6 \cdot 10^{-6}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.25 \cdot 10^{-93}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -3.5 \cdot 10^{-230}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -6.2 \cdot 10^{-261}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -9.2 \cdot 10^{-289}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{-260}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 1850000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_2}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ z (/ (* x t) y)) b)) (t_2 (+ x (/ (* y z) t))))
   (if (<= a -9e+44)
     (/ (+ x (* y (/ z t))) a)
     (if (<= a -6e-6)
       t_1
       (if (<= a -1.25e-93)
         t_2
         (if (<= a -3.5e-230)
           t_1
           (if (<= a -6.2e-261)
             t_2
             (if (<= a -9.2e-289)
               t_1
               (if (<= a 4.5e-260)
                 t_2
                 (if (<= a 1850000.0) t_1 (/ t_2 a)))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + ((x * t) / y)) / b;
	double t_2 = x + ((y * z) / t);
	double tmp;
	if (a <= -9e+44) {
		tmp = (x + (y * (z / t))) / a;
	} else if (a <= -6e-6) {
		tmp = t_1;
	} else if (a <= -1.25e-93) {
		tmp = t_2;
	} else if (a <= -3.5e-230) {
		tmp = t_1;
	} else if (a <= -6.2e-261) {
		tmp = t_2;
	} else if (a <= -9.2e-289) {
		tmp = t_1;
	} else if (a <= 4.5e-260) {
		tmp = t_2;
	} else if (a <= 1850000.0) {
		tmp = t_1;
	} else {
		tmp = t_2 / 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (z + ((x * t) / y)) / b
    t_2 = x + ((y * z) / t)
    if (a <= (-9d+44)) then
        tmp = (x + (y * (z / t))) / a
    else if (a <= (-6d-6)) then
        tmp = t_1
    else if (a <= (-1.25d-93)) then
        tmp = t_2
    else if (a <= (-3.5d-230)) then
        tmp = t_1
    else if (a <= (-6.2d-261)) then
        tmp = t_2
    else if (a <= (-9.2d-289)) then
        tmp = t_1
    else if (a <= 4.5d-260) then
        tmp = t_2
    else if (a <= 1850000.0d0) then
        tmp = t_1
    else
        tmp = t_2 / 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 t_1 = (z + ((x * t) / y)) / b;
	double t_2 = x + ((y * z) / t);
	double tmp;
	if (a <= -9e+44) {
		tmp = (x + (y * (z / t))) / a;
	} else if (a <= -6e-6) {
		tmp = t_1;
	} else if (a <= -1.25e-93) {
		tmp = t_2;
	} else if (a <= -3.5e-230) {
		tmp = t_1;
	} else if (a <= -6.2e-261) {
		tmp = t_2;
	} else if (a <= -9.2e-289) {
		tmp = t_1;
	} else if (a <= 4.5e-260) {
		tmp = t_2;
	} else if (a <= 1850000.0) {
		tmp = t_1;
	} else {
		tmp = t_2 / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + ((x * t) / y)) / b
	t_2 = x + ((y * z) / t)
	tmp = 0
	if a <= -9e+44:
		tmp = (x + (y * (z / t))) / a
	elif a <= -6e-6:
		tmp = t_1
	elif a <= -1.25e-93:
		tmp = t_2
	elif a <= -3.5e-230:
		tmp = t_1
	elif a <= -6.2e-261:
		tmp = t_2
	elif a <= -9.2e-289:
		tmp = t_1
	elif a <= 4.5e-260:
		tmp = t_2
	elif a <= 1850000.0:
		tmp = t_1
	else:
		tmp = t_2 / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + Float64(Float64(x * t) / y)) / b)
	t_2 = Float64(x + Float64(Float64(y * z) / t))
	tmp = 0.0
	if (a <= -9e+44)
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / a);
	elseif (a <= -6e-6)
		tmp = t_1;
	elseif (a <= -1.25e-93)
		tmp = t_2;
	elseif (a <= -3.5e-230)
		tmp = t_1;
	elseif (a <= -6.2e-261)
		tmp = t_2;
	elseif (a <= -9.2e-289)
		tmp = t_1;
	elseif (a <= 4.5e-260)
		tmp = t_2;
	elseif (a <= 1850000.0)
		tmp = t_1;
	else
		tmp = Float64(t_2 / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + ((x * t) / y)) / b;
	t_2 = x + ((y * z) / t);
	tmp = 0.0;
	if (a <= -9e+44)
		tmp = (x + (y * (z / t))) / a;
	elseif (a <= -6e-6)
		tmp = t_1;
	elseif (a <= -1.25e-93)
		tmp = t_2;
	elseif (a <= -3.5e-230)
		tmp = t_1;
	elseif (a <= -6.2e-261)
		tmp = t_2;
	elseif (a <= -9.2e-289)
		tmp = t_1;
	elseif (a <= 4.5e-260)
		tmp = t_2;
	elseif (a <= 1850000.0)
		tmp = t_1;
	else
		tmp = t_2 / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -9e+44], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[a, -6e-6], t$95$1, If[LessEqual[a, -1.25e-93], t$95$2, If[LessEqual[a, -3.5e-230], t$95$1, If[LessEqual[a, -6.2e-261], t$95$2, If[LessEqual[a, -9.2e-289], t$95$1, If[LessEqual[a, 4.5e-260], t$95$2, If[LessEqual[a, 1850000.0], t$95$1, N[(t$95$2 / a), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -9e44

   1. Initial program 78.4%

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

      1. associate-/l* 82.3%

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

      2. associate-/l* 80.4%

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

   3. Simplified 80.4%

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

   5. Taylor expanded in a around inf 69.0%

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

   if -9e44 < a < -6.0000000000000002e-6 or -1.24999999999999999e-93 < a < -3.49999999999999988e-230 or -6.1999999999999997e-261 < a < -9.2000000000000007e-289 or 4.4999999999999997e-260 < a < 1.85e6

   1. Initial program 68.0%

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

      1. associate-/l* 64.8%

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

      2. associate-/l* 66.8%

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

   3. Simplified 66.8%

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

   5. Taylor expanded in y around -inf 52.4%

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

      1. +-commutative 52.4%

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

      2. mul-1-neg 52.4%

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

      3. unsub-neg 52.4%

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

      4. distribute-lft-out-- 52.4%

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

      5. mul-1-neg 52.4%

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

      6. associate-/l* 48.0%

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

      7. associate-/l* 50.5%

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

      8. distribute-lft-out-- 50.6%

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

   7. Simplified 50.6%

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

   8. Taylor expanded in x around inf 65.4%

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

   9. Taylor expanded in b around 0 67.3%

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

       1. cancel-sign-sub-inv 67.3%

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

       2. metadata-eval 67.3%

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

       3. *-lft-identity 67.3%

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

   11. Simplified 67.3%

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

   if -6.0000000000000002e-6 < a < -1.24999999999999999e-93 or -3.49999999999999988e-230 < a < -6.1999999999999997e-261 or -9.2000000000000007e-289 < a < 4.4999999999999997e-260

   1. Initial program 91.6%

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

      1. associate-/l* 91.6%

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

      2. associate-/l* 93.6%

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

   3. Simplified 93.6%

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

   5. Taylor expanded in y around 0 78.4%

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

   6. Taylor expanded in a around 0 73.9%

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

   if 1.85e6 < a

   1. Initial program 89.7%

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

      1. associate-/l* 84.0%

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

      2. associate-/l* 82.6%

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

   3. Simplified 82.6%

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

   5. Taylor expanded in a around inf 84.5%

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

4. Final simplification 73.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9 \cdot 10^{+44}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a}\\ \mathbf{elif}\;a \leq -6 \cdot 10^{-6}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{elif}\;a \leq -1.25 \cdot 10^{-93}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{elif}\;a \leq -3.5 \cdot 10^{-230}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{elif}\;a \leq -6.2 \cdot 10^{-261}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{elif}\;a \leq -9.2 \cdot 10^{-289}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{-260}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{elif}\;a \leq 1850000:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 40.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{+133}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;a \leq -6 \cdot 10^{-6}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq -2.4 \cdot 10^{-73}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -3.1 \cdot 10^{-160}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq -1.16 \cdot 10^{-243}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.95 \cdot 10^{-288}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-259}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.28 \cdot 10^{-76}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -1.9e+133)
   (/ x a)
   (if (<= a -6e-6)
     (/ z b)
     (if (<= a -2.4e-73)
       x
       (if (<= a -3.1e-160)
         (/ z b)
         (if (<= a -1.16e-243)
           x
           (if (<= a -1.95e-288)
             (/ z b)
             (if (<= a 1.1e-259)
               x
               (if (<= a 1.28e-76) (/ z b) (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 <= -1.9e+133) {
		tmp = x / a;
	} else if (a <= -6e-6) {
		tmp = z / b;
	} else if (a <= -2.4e-73) {
		tmp = x;
	} else if (a <= -3.1e-160) {
		tmp = z / b;
	} else if (a <= -1.16e-243) {
		tmp = x;
	} else if (a <= -1.95e-288) {
		tmp = z / b;
	} else if (a <= 1.1e-259) {
		tmp = x;
	} else if (a <= 1.28e-76) {
		tmp = z / b;
	} 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 <= (-1.9d+133)) then
        tmp = x / a
    else if (a <= (-6d-6)) then
        tmp = z / b
    else if (a <= (-2.4d-73)) then
        tmp = x
    else if (a <= (-3.1d-160)) then
        tmp = z / b
    else if (a <= (-1.16d-243)) then
        tmp = x
    else if (a <= (-1.95d-288)) then
        tmp = z / b
    else if (a <= 1.1d-259) then
        tmp = x
    else if (a <= 1.28d-76) then
        tmp = z / b
    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 <= -1.9e+133) {
		tmp = x / a;
	} else if (a <= -6e-6) {
		tmp = z / b;
	} else if (a <= -2.4e-73) {
		tmp = x;
	} else if (a <= -3.1e-160) {
		tmp = z / b;
	} else if (a <= -1.16e-243) {
		tmp = x;
	} else if (a <= -1.95e-288) {
		tmp = z / b;
	} else if (a <= 1.1e-259) {
		tmp = x;
	} else if (a <= 1.28e-76) {
		tmp = z / b;
	} 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 <= -1.9e+133:
		tmp = x / a
	elif a <= -6e-6:
		tmp = z / b
	elif a <= -2.4e-73:
		tmp = x
	elif a <= -3.1e-160:
		tmp = z / b
	elif a <= -1.16e-243:
		tmp = x
	elif a <= -1.95e-288:
		tmp = z / b
	elif a <= 1.1e-259:
		tmp = x
	elif a <= 1.28e-76:
		tmp = z / b
	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 <= -1.9e+133)
		tmp = Float64(x / a);
	elseif (a <= -6e-6)
		tmp = Float64(z / b);
	elseif (a <= -2.4e-73)
		tmp = x;
	elseif (a <= -3.1e-160)
		tmp = Float64(z / b);
	elseif (a <= -1.16e-243)
		tmp = x;
	elseif (a <= -1.95e-288)
		tmp = Float64(z / b);
	elseif (a <= 1.1e-259)
		tmp = x;
	elseif (a <= 1.28e-76)
		tmp = Float64(z / b);
	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 <= -1.9e+133)
		tmp = x / a;
	elseif (a <= -6e-6)
		tmp = z / b;
	elseif (a <= -2.4e-73)
		tmp = x;
	elseif (a <= -3.1e-160)
		tmp = z / b;
	elseif (a <= -1.16e-243)
		tmp = x;
	elseif (a <= -1.95e-288)
		tmp = z / b;
	elseif (a <= 1.1e-259)
		tmp = x;
	elseif (a <= 1.28e-76)
		tmp = z / b;
	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, -1.9e+133], N[(x / a), $MachinePrecision], If[LessEqual[a, -6e-6], N[(z / b), $MachinePrecision], If[LessEqual[a, -2.4e-73], x, If[LessEqual[a, -3.1e-160], N[(z / b), $MachinePrecision], If[LessEqual[a, -1.16e-243], x, If[LessEqual[a, -1.95e-288], N[(z / b), $MachinePrecision], If[LessEqual[a, 1.1e-259], x, If[LessEqual[a, 1.28e-76], N[(z / b), $MachinePrecision], If[LessEqual[a, 1.0], x, N[(x / a), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.9000000000000001e133 or 1 < a

   1. Initial program 86.4%

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

      1. associate-/l* 83.6%

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

      2. associate-/l* 82.7%

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

   3. Simplified 82.7%

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

   5. Taylor expanded in y around 0 64.6%

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

   6. Taylor expanded in a around inf 64.1%

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

   if -1.9000000000000001e133 < a < -6.0000000000000002e-6 or -2.40000000000000006e-73 < a < -3.1e-160 or -1.15999999999999998e-243 < a < -1.9499999999999998e-288 or 1.10000000000000005e-259 < a < 1.28e-76

   1. Initial program 65.7%

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

      1. associate-/l* 65.5%

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

      2. associate-/l* 65.6%

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

   3. Simplified 65.6%

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

   5. Taylor expanded in y around inf 53.1%

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

   if -6.0000000000000002e-6 < a < -2.40000000000000006e-73 or -3.1e-160 < a < -1.15999999999999998e-243 or -1.9499999999999998e-288 < a < 1.10000000000000005e-259 or 1.28e-76 < a < 1

   1. Initial program 89.6%

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

      1. associate-/l* 86.9%

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

      2. associate-/l* 89.7%

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

   3. Simplified 89.7%

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

   5. Taylor expanded in y around 0 58.7%

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

   6. Taylor expanded in a around 0 57.0%

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

Alternative 6: 53.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot z}{t}\\ \mathbf{if}\;a \leq -1:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a}\\ \mathbf{elif}\;a \leq -6.2 \cdot 10^{-261}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -7.9 \cdot 10^{-289}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-260}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{-86}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 1:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_1}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (/ (* y z) t))))
   (if (<= a -1.0)
     (/ (+ x (* y (/ z t))) a)
     (if (<= a -6.2e-261)
       t_1
       (if (<= a -7.9e-289)
         (/ z b)
         (if (<= a 9.5e-260)
           t_1
           (if (<= a 2.5e-86) (/ z b) (if (<= a 1.0) t_1 (/ t_1 a)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + ((y * z) / t);
	double tmp;
	if (a <= -1.0) {
		tmp = (x + (y * (z / t))) / a;
	} else if (a <= -6.2e-261) {
		tmp = t_1;
	} else if (a <= -7.9e-289) {
		tmp = z / b;
	} else if (a <= 9.5e-260) {
		tmp = t_1;
	} else if (a <= 2.5e-86) {
		tmp = z / b;
	} else if (a <= 1.0) {
		tmp = t_1;
	} else {
		tmp = t_1 / 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) :: t_1
    real(8) :: tmp
    t_1 = x + ((y * z) / t)
    if (a <= (-1.0d0)) then
        tmp = (x + (y * (z / t))) / a
    else if (a <= (-6.2d-261)) then
        tmp = t_1
    else if (a <= (-7.9d-289)) then
        tmp = z / b
    else if (a <= 9.5d-260) then
        tmp = t_1
    else if (a <= 2.5d-86) then
        tmp = z / b
    else if (a <= 1.0d0) then
        tmp = t_1
    else
        tmp = t_1 / 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 t_1 = x + ((y * z) / t);
	double tmp;
	if (a <= -1.0) {
		tmp = (x + (y * (z / t))) / a;
	} else if (a <= -6.2e-261) {
		tmp = t_1;
	} else if (a <= -7.9e-289) {
		tmp = z / b;
	} else if (a <= 9.5e-260) {
		tmp = t_1;
	} else if (a <= 2.5e-86) {
		tmp = z / b;
	} else if (a <= 1.0) {
		tmp = t_1;
	} else {
		tmp = t_1 / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + ((y * z) / t)
	tmp = 0
	if a <= -1.0:
		tmp = (x + (y * (z / t))) / a
	elif a <= -6.2e-261:
		tmp = t_1
	elif a <= -7.9e-289:
		tmp = z / b
	elif a <= 9.5e-260:
		tmp = t_1
	elif a <= 2.5e-86:
		tmp = z / b
	elif a <= 1.0:
		tmp = t_1
	else:
		tmp = t_1 / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(Float64(y * z) / t))
	tmp = 0.0
	if (a <= -1.0)
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / a);
	elseif (a <= -6.2e-261)
		tmp = t_1;
	elseif (a <= -7.9e-289)
		tmp = Float64(z / b);
	elseif (a <= 9.5e-260)
		tmp = t_1;
	elseif (a <= 2.5e-86)
		tmp = Float64(z / b);
	elseif (a <= 1.0)
		tmp = t_1;
	else
		tmp = Float64(t_1 / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + ((y * z) / t);
	tmp = 0.0;
	if (a <= -1.0)
		tmp = (x + (y * (z / t))) / a;
	elseif (a <= -6.2e-261)
		tmp = t_1;
	elseif (a <= -7.9e-289)
		tmp = z / b;
	elseif (a <= 9.5e-260)
		tmp = t_1;
	elseif (a <= 2.5e-86)
		tmp = z / b;
	elseif (a <= 1.0)
		tmp = t_1;
	else
		tmp = t_1 / a;
	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]}, If[LessEqual[a, -1.0], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[a, -6.2e-261], t$95$1, If[LessEqual[a, -7.9e-289], N[(z / b), $MachinePrecision], If[LessEqual[a, 9.5e-260], t$95$1, If[LessEqual[a, 2.5e-86], N[(z / b), $MachinePrecision], If[LessEqual[a, 1.0], t$95$1, N[(t$95$1 / a), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1

   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. associate-/l* 81.0%

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

      2. associate-/l* 79.4%

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

   3. Simplified 79.4%

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

   5. Taylor expanded in a around inf 64.1%

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

   if -1 < a < -6.1999999999999997e-261 or -7.8999999999999999e-289 < a < 9.5000000000000001e-260 or 2.4999999999999999e-86 < a < 1

   1. Initial program 85.0%

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

      1. associate-/l* 84.0%

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

      2. associate-/l* 86.2%

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

   3. Simplified 86.2%

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

   5. Taylor expanded in y around 0 63.3%

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

   6. Taylor expanded in a around 0 61.8%

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

   if -6.1999999999999997e-261 < a < -7.8999999999999999e-289 or 9.5000000000000001e-260 < a < 2.4999999999999999e-86

   1. Initial program 55.7%

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

      1. associate-/l* 55.6%

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

      2. associate-/l* 57.8%

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

   3. Simplified 57.8%

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

   5. Taylor expanded in y around inf 63.1%

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

   if 1 < a

   1. Initial program 89.7%

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

      1. associate-/l* 84.0%

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

      2. associate-/l* 82.6%

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

   3. Simplified 82.6%

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

   5. Taylor expanded in a around inf 84.5%

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

Alternative 7: 53.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot z}{t}\\ t_2 := \frac{x + y \cdot \frac{z}{t}}{a}\\ \mathbf{if}\;a \leq -1:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -1.48 \cdot 10^{-260}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.9 \cdot 10^{-288}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{-260}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 8 \cdot 10^{-86}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 0.92:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (/ (* y z) t))) (t_2 (/ (+ x (* y (/ z t))) a)))
   (if (<= a -1.0)
     t_2
     (if (<= a -1.48e-260)
       t_1
       (if (<= a -1.9e-288)
         (/ z b)
         (if (<= a 5.5e-260)
           t_1
           (if (<= a 8e-86) (/ z b) (if (<= a 0.92) 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 = (x + (y * (z / t))) / a;
	double tmp;
	if (a <= -1.0) {
		tmp = t_2;
	} else if (a <= -1.48e-260) {
		tmp = t_1;
	} else if (a <= -1.9e-288) {
		tmp = z / b;
	} else if (a <= 5.5e-260) {
		tmp = t_1;
	} else if (a <= 8e-86) {
		tmp = z / b;
	} else if (a <= 0.92) {
		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 = (x + (y * (z / t))) / a
    if (a <= (-1.0d0)) then
        tmp = t_2
    else if (a <= (-1.48d-260)) then
        tmp = t_1
    else if (a <= (-1.9d-288)) then
        tmp = z / b
    else if (a <= 5.5d-260) then
        tmp = t_1
    else if (a <= 8d-86) then
        tmp = z / b
    else if (a <= 0.92d0) 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 = (x + (y * (z / t))) / a;
	double tmp;
	if (a <= -1.0) {
		tmp = t_2;
	} else if (a <= -1.48e-260) {
		tmp = t_1;
	} else if (a <= -1.9e-288) {
		tmp = z / b;
	} else if (a <= 5.5e-260) {
		tmp = t_1;
	} else if (a <= 8e-86) {
		tmp = z / b;
	} else if (a <= 0.92) {
		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 = (x + (y * (z / t))) / a
	tmp = 0
	if a <= -1.0:
		tmp = t_2
	elif a <= -1.48e-260:
		tmp = t_1
	elif a <= -1.9e-288:
		tmp = z / b
	elif a <= 5.5e-260:
		tmp = t_1
	elif a <= 8e-86:
		tmp = z / b
	elif a <= 0.92:
		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(Float64(x + Float64(y * Float64(z / t))) / a)
	tmp = 0.0
	if (a <= -1.0)
		tmp = t_2;
	elseif (a <= -1.48e-260)
		tmp = t_1;
	elseif (a <= -1.9e-288)
		tmp = Float64(z / b);
	elseif (a <= 5.5e-260)
		tmp = t_1;
	elseif (a <= 8e-86)
		tmp = Float64(z / b);
	elseif (a <= 0.92)
		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 = (x + (y * (z / t))) / a;
	tmp = 0.0;
	if (a <= -1.0)
		tmp = t_2;
	elseif (a <= -1.48e-260)
		tmp = t_1;
	elseif (a <= -1.9e-288)
		tmp = z / b;
	elseif (a <= 5.5e-260)
		tmp = t_1;
	elseif (a <= 8e-86)
		tmp = z / b;
	elseif (a <= 0.92)
		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[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[a, -1.0], t$95$2, If[LessEqual[a, -1.48e-260], t$95$1, If[LessEqual[a, -1.9e-288], N[(z / b), $MachinePrecision], If[LessEqual[a, 5.5e-260], t$95$1, If[LessEqual[a, 8e-86], N[(z / b), $MachinePrecision], If[LessEqual[a, 0.92], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1 or 0.92000000000000004 < a

   1. Initial program 85.7%

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

      1. associate-/l* 82.7%

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

      2. associate-/l* 81.1%

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

   3. Simplified 81.1%

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

   5. Taylor expanded in a around inf 72.1%

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

   if -1 < a < -1.4800000000000001e-260 or -1.8999999999999999e-288 < a < 5.50000000000000024e-260 or 8.00000000000000068e-86 < a < 0.92000000000000004

   1. Initial program 85.0%

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

      1. associate-/l* 84.0%

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

      2. associate-/l* 86.2%

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

   3. Simplified 86.2%

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

   5. Taylor expanded in y around 0 63.3%

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

   6. Taylor expanded in a around 0 61.8%

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

   if -1.4800000000000001e-260 < a < -1.8999999999999999e-288 or 5.50000000000000024e-260 < a < 8.00000000000000068e-86

   1. Initial program 55.7%

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

      1. associate-/l* 55.6%

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

      2. associate-/l* 57.8%

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

   3. Simplified 57.8%

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

   5. Taylor expanded in y around inf 63.1%

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

Alternative 8: 84.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{if}\;t\_1 \leq 10^{+304}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{\frac{x \cdot t}{b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (* y z) t)) (+ (/ (* y b) t) (+ a 1.0)))))
   (if (<= t_1 1e+304) t_1 (+ (/ z b) (/ (/ (* x t) b) y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + ((y * z) / t)) / (((y * b) / t) + (a + 1.0));
	double tmp;
	if (t_1 <= 1e+304) {
		tmp = t_1;
	} else {
		tmp = (z / b) + (((x * t) / b) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + ((y * z) / t)) / (((y * b) / t) + (a + 1.0d0))
    if (t_1 <= 1d+304) then
        tmp = t_1
    else
        tmp = (z / b) + (((x * t) / b) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + ((y * z) / t)) / (((y * b) / t) + (a + 1.0));
	double tmp;
	if (t_1 <= 1e+304) {
		tmp = t_1;
	} else {
		tmp = (z / b) + (((x * t) / b) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + ((y * z) / t)) / (((y * b) / t) + (a + 1.0))
	tmp = 0
	if t_1 <= 1e+304:
		tmp = t_1
	else:
		tmp = (z / b) + (((x * t) / b) / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(Float64(Float64(y * b) / t) + Float64(a + 1.0)))
	tmp = 0.0
	if (t_1 <= 1e+304)
		tmp = t_1;
	else
		tmp = Float64(Float64(z / b) + Float64(Float64(Float64(x * t) / b) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + ((y * z) / t)) / (((y * b) / t) + (a + 1.0));
	tmp = 0.0;
	if (t_1 <= 1e+304)
		tmp = t_1;
	else
		tmp = (z / b) + (((x * t) / b) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 1e+304], t$95$1, N[(N[(z / b), $MachinePrecision] + N[(N[(N[(x * t), $MachinePrecision] / b), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 9.9999999999999994e303

   1. Initial program 90.7%

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

   if 9.9999999999999994e303 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t)))

   1. Initial program 10.6%

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

      1. associate-/l* 16.4%

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

      2. associate-/l* 22.0%

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

   3. Simplified 22.0%

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

   5. Taylor expanded in y around -inf 59.5%

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

      1. +-commutative 59.5%

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

      2. mul-1-neg 59.5%

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

      3. unsub-neg 59.5%

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

      4. distribute-lft-out-- 59.5%

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

      5. mul-1-neg 59.5%

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

      6. associate-/l* 53.4%

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

      7. associate-/l* 56.4%

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

      8. distribute-lft-out-- 56.4%

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

   7. Simplified 56.4%

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

   8. Taylor expanded in x around inf 86.4%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 10^{+304}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{\frac{x \cdot t}{b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 53.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.6 \cdot 10^{+130}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+86}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+157}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+189}:\\ \;\;\;\;\frac{t \cdot \frac{x}{y}}{b}\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+207}:\\ \;\;\;\;y \cdot \frac{\frac{z}{t}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -6.6e+130)
   (/ z b)
   (if (<= y 1.6e+86)
     (/ x (+ a 1.0))
     (if (<= y 2.7e+157)
       (/ z b)
       (if (<= y 1.8e+189)
         (/ (* t (/ x y)) b)
         (if (<= y 5e+207) (* y (/ (/ z t) (+ a 1.0))) (/ z b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -6.6e+130) {
		tmp = z / b;
	} else if (y <= 1.6e+86) {
		tmp = x / (a + 1.0);
	} else if (y <= 2.7e+157) {
		tmp = z / b;
	} else if (y <= 1.8e+189) {
		tmp = (t * (x / y)) / b;
	} else if (y <= 5e+207) {
		tmp = y * ((z / t) / (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 (y <= (-6.6d+130)) then
        tmp = z / b
    else if (y <= 1.6d+86) then
        tmp = x / (a + 1.0d0)
    else if (y <= 2.7d+157) then
        tmp = z / b
    else if (y <= 1.8d+189) then
        tmp = (t * (x / y)) / b
    else if (y <= 5d+207) then
        tmp = y * ((z / t) / (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 (y <= -6.6e+130) {
		tmp = z / b;
	} else if (y <= 1.6e+86) {
		tmp = x / (a + 1.0);
	} else if (y <= 2.7e+157) {
		tmp = z / b;
	} else if (y <= 1.8e+189) {
		tmp = (t * (x / y)) / b;
	} else if (y <= 5e+207) {
		tmp = y * ((z / t) / (a + 1.0));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -6.6e+130:
		tmp = z / b
	elif y <= 1.6e+86:
		tmp = x / (a + 1.0)
	elif y <= 2.7e+157:
		tmp = z / b
	elif y <= 1.8e+189:
		tmp = (t * (x / y)) / b
	elif y <= 5e+207:
		tmp = y * ((z / t) / (a + 1.0))
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -6.6e+130)
		tmp = Float64(z / b);
	elseif (y <= 1.6e+86)
		tmp = Float64(x / Float64(a + 1.0));
	elseif (y <= 2.7e+157)
		tmp = Float64(z / b);
	elseif (y <= 1.8e+189)
		tmp = Float64(Float64(t * Float64(x / y)) / b);
	elseif (y <= 5e+207)
		tmp = Float64(y * Float64(Float64(z / t) / Float64(a + 1.0)));
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -6.6e+130)
		tmp = z / b;
	elseif (y <= 1.6e+86)
		tmp = x / (a + 1.0);
	elseif (y <= 2.7e+157)
		tmp = z / b;
	elseif (y <= 1.8e+189)
		tmp = (t * (x / y)) / b;
	elseif (y <= 5e+207)
		tmp = y * ((z / t) / (a + 1.0));
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -6.6e+130], N[(z / b), $MachinePrecision], If[LessEqual[y, 1.6e+86], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.7e+157], N[(z / b), $MachinePrecision], If[LessEqual[y, 1.8e+189], N[(N[(t * N[(x / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[y, 5e+207], N[(y * N[(N[(z / t), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -6.6e130 or 1.6e86 < y < 2.7e157 or 4.9999999999999999e207 < y

   1. Initial program 39.0%

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

      1. associate-/l* 45.3%

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

      2. associate-/l* 51.6%

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

   3. Simplified 51.6%

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

   5. Taylor expanded in y around inf 70.8%

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

   if -6.6e130 < y < 1.6e86

   1. Initial program 95.1%

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

      1. associate-/l* 90.5%

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

      2. associate-/l* 87.9%

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

   3. Simplified 87.9%

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

   5. Taylor expanded in y around 0 59.6%

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

   if 2.7e157 < y < 1.80000000000000004e189

   1. Initial program 46.2%

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

      1. associate-/l* 46.2%

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

      2. associate-/l* 72.8%

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

   3. Simplified 72.8%

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

   5. Taylor expanded in y around -inf 57.7%

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

      1. +-commutative 57.7%

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

      2. mul-1-neg 57.7%

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

      3. unsub-neg 57.7%

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

      4. distribute-lft-out-- 57.7%

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

      5. mul-1-neg 57.7%

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

      6. associate-/l* 30.5%

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

      7. associate-/l* 31.1%

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

      8. distribute-lft-out-- 31.1%

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

   7. Simplified 31.1%

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

   8. Taylor expanded in x around inf 72.2%

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

   9. Taylor expanded in b around 0 71.6%

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

       1. cancel-sign-sub-inv 71.6%

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

       2. metadata-eval 71.6%

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

       3. *-lft-identity 71.6%

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

   11. Simplified 71.6%

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

   12. Taylor expanded in z around 0 57.9%

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

       1. associate-*r/ 58.8%

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

   14. Simplified 58.8%

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

   if 1.80000000000000004e189 < y < 4.9999999999999999e207

   1. Initial program 68.2%

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

      1. associate-/l* 68.2%

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

      2. associate-/l* 68.2%

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

   3. Simplified 68.2%

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

   5. Taylor expanded in y around 0 37.3%

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

   6. Taylor expanded in x around 0 70.3%

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

      1. associate-/l* 100.0%

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

      2. associate-/r* 99.5%

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

   8. Simplified 99.5%

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

4. Final simplification 62.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.6 \cdot 10^{+130}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+86}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+157}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+189}:\\ \;\;\;\;\frac{t \cdot \frac{x}{y}}{b}\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+207}:\\ \;\;\;\;y \cdot \frac{\frac{z}{t}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 54.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.6 \cdot 10^{+130}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+81}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+157}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+192}:\\ \;\;\;\;\frac{t \cdot \frac{x}{y}}{b}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+194}:\\ \;\;\;\;y \cdot \frac{z}{t \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -6.6e+130)
   (/ z b)
   (if (<= y 1.9e+81)
     (/ x (+ a 1.0))
     (if (<= y 2.7e+157)
       (/ z b)
       (if (<= y 1.4e+192)
         (/ (* t (/ x y)) b)
         (if (<= y 4e+194) (* y (/ z (* t a))) (/ z b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -6.6e+130) {
		tmp = z / b;
	} else if (y <= 1.9e+81) {
		tmp = x / (a + 1.0);
	} else if (y <= 2.7e+157) {
		tmp = z / b;
	} else if (y <= 1.4e+192) {
		tmp = (t * (x / y)) / b;
	} else if (y <= 4e+194) {
		tmp = y * (z / (t * 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 <= (-6.6d+130)) then
        tmp = z / b
    else if (y <= 1.9d+81) then
        tmp = x / (a + 1.0d0)
    else if (y <= 2.7d+157) then
        tmp = z / b
    else if (y <= 1.4d+192) then
        tmp = (t * (x / y)) / b
    else if (y <= 4d+194) then
        tmp = y * (z / (t * 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 <= -6.6e+130) {
		tmp = z / b;
	} else if (y <= 1.9e+81) {
		tmp = x / (a + 1.0);
	} else if (y <= 2.7e+157) {
		tmp = z / b;
	} else if (y <= 1.4e+192) {
		tmp = (t * (x / y)) / b;
	} else if (y <= 4e+194) {
		tmp = y * (z / (t * a));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -6.6e+130:
		tmp = z / b
	elif y <= 1.9e+81:
		tmp = x / (a + 1.0)
	elif y <= 2.7e+157:
		tmp = z / b
	elif y <= 1.4e+192:
		tmp = (t * (x / y)) / b
	elif y <= 4e+194:
		tmp = y * (z / (t * a))
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -6.6e+130)
		tmp = Float64(z / b);
	elseif (y <= 1.9e+81)
		tmp = Float64(x / Float64(a + 1.0));
	elseif (y <= 2.7e+157)
		tmp = Float64(z / b);
	elseif (y <= 1.4e+192)
		tmp = Float64(Float64(t * Float64(x / y)) / b);
	elseif (y <= 4e+194)
		tmp = Float64(y * Float64(z / Float64(t * 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 <= -6.6e+130)
		tmp = z / b;
	elseif (y <= 1.9e+81)
		tmp = x / (a + 1.0);
	elseif (y <= 2.7e+157)
		tmp = z / b;
	elseif (y <= 1.4e+192)
		tmp = (t * (x / y)) / b;
	elseif (y <= 4e+194)
		tmp = y * (z / (t * a));
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -6.6e+130], N[(z / b), $MachinePrecision], If[LessEqual[y, 1.9e+81], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.7e+157], N[(z / b), $MachinePrecision], If[LessEqual[y, 1.4e+192], N[(N[(t * N[(x / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[y, 4e+194], N[(y * N[(z / N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -6.6e130 or 1.9e81 < y < 2.7e157 or 3.99999999999999978e194 < y

   1. Initial program 40.0%

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

      1. associate-/l* 46.2%

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

      2. associate-/l* 52.4%

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

   3. Simplified 52.4%

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

   5. Taylor expanded in y around inf 69.6%

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

   if -6.6e130 < y < 1.9e81

   1. Initial program 95.1%

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

      1. associate-/l* 90.5%

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

      2. associate-/l* 87.9%

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

   3. Simplified 87.9%

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

   5. Taylor expanded in y around 0 59.6%

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

   if 2.7e157 < y < 1.39999999999999988e192

   1. Initial program 46.2%

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

      1. associate-/l* 46.2%

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

      2. associate-/l* 72.8%

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

   3. Simplified 72.8%

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

   5. Taylor expanded in y around -inf 57.7%

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

      1. +-commutative 57.7%

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

      2. mul-1-neg 57.7%

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

      3. unsub-neg 57.7%

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

      4. distribute-lft-out-- 57.7%

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

      5. mul-1-neg 57.7%

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

      6. associate-/l* 30.5%

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

      7. associate-/l* 31.1%

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

      8. distribute-lft-out-- 31.1%

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

   7. Simplified 31.1%

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

   8. Taylor expanded in x around inf 72.2%

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

   9. Taylor expanded in b around 0 71.6%

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

       1. cancel-sign-sub-inv 71.6%

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

       2. metadata-eval 71.6%

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

       3. *-lft-identity 71.6%

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

   11. Simplified 71.6%

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

   12. Taylor expanded in z around 0 57.9%

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

       1. associate-*r/ 58.8%

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

   14. Simplified 58.8%

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

   if 1.39999999999999988e192 < y < 3.99999999999999978e194

   1. Initial program 52.4%

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

      1. associate-/l* 52.4%

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

      2. associate-/l* 52.4%

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

   3. Simplified 52.4%

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

   5. Taylor expanded in a around inf 5.9%

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

   6. Taylor expanded in x around 0 55.5%

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

      1. associate-/l* 100.0%

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

      2. *-commutative 100.0%

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

   8. Simplified 100.0%

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

4. Final simplification 62.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.6 \cdot 10^{+130}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+81}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+157}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+192}:\\ \;\;\;\;\frac{t \cdot \frac{x}{y}}{b}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+194}:\\ \;\;\;\;y \cdot \frac{z}{t \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 54.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+130}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+79}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+157}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+191}:\\ \;\;\;\;\frac{t}{b} \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+194}:\\ \;\;\;\;y \cdot \frac{z}{t \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -7e+130)
   (/ z b)
   (if (<= y 7.2e+79)
     (/ x (+ a 1.0))
     (if (<= y 2.7e+157)
       (/ z b)
       (if (<= y 1.8e+191)
         (* (/ t b) (/ x y))
         (if (<= y 4e+194) (* y (/ z (* t a))) (/ z b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -7e+130) {
		tmp = z / b;
	} else if (y <= 7.2e+79) {
		tmp = x / (a + 1.0);
	} else if (y <= 2.7e+157) {
		tmp = z / b;
	} else if (y <= 1.8e+191) {
		tmp = (t / b) * (x / y);
	} else if (y <= 4e+194) {
		tmp = y * (z / (t * 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 <= (-7d+130)) then
        tmp = z / b
    else if (y <= 7.2d+79) then
        tmp = x / (a + 1.0d0)
    else if (y <= 2.7d+157) then
        tmp = z / b
    else if (y <= 1.8d+191) then
        tmp = (t / b) * (x / y)
    else if (y <= 4d+194) then
        tmp = y * (z / (t * 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 <= -7e+130) {
		tmp = z / b;
	} else if (y <= 7.2e+79) {
		tmp = x / (a + 1.0);
	} else if (y <= 2.7e+157) {
		tmp = z / b;
	} else if (y <= 1.8e+191) {
		tmp = (t / b) * (x / y);
	} else if (y <= 4e+194) {
		tmp = y * (z / (t * a));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -7e+130:
		tmp = z / b
	elif y <= 7.2e+79:
		tmp = x / (a + 1.0)
	elif y <= 2.7e+157:
		tmp = z / b
	elif y <= 1.8e+191:
		tmp = (t / b) * (x / y)
	elif y <= 4e+194:
		tmp = y * (z / (t * a))
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -7e+130)
		tmp = Float64(z / b);
	elseif (y <= 7.2e+79)
		tmp = Float64(x / Float64(a + 1.0));
	elseif (y <= 2.7e+157)
		tmp = Float64(z / b);
	elseif (y <= 1.8e+191)
		tmp = Float64(Float64(t / b) * Float64(x / y));
	elseif (y <= 4e+194)
		tmp = Float64(y * Float64(z / Float64(t * 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 <= -7e+130)
		tmp = z / b;
	elseif (y <= 7.2e+79)
		tmp = x / (a + 1.0);
	elseif (y <= 2.7e+157)
		tmp = z / b;
	elseif (y <= 1.8e+191)
		tmp = (t / b) * (x / y);
	elseif (y <= 4e+194)
		tmp = y * (z / (t * a));
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -7e+130], N[(z / b), $MachinePrecision], If[LessEqual[y, 7.2e+79], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.7e+157], N[(z / b), $MachinePrecision], If[LessEqual[y, 1.8e+191], N[(N[(t / b), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4e+194], N[(y * N[(z / N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -7.0000000000000002e130 or 7.1999999999999999e79 < y < 2.7e157 or 3.99999999999999978e194 < y

   1. Initial program 40.0%

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

      1. associate-/l* 46.2%

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

      2. associate-/l* 52.4%

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

   3. Simplified 52.4%

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

   5. Taylor expanded in y around inf 69.6%

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

   if -7.0000000000000002e130 < y < 7.1999999999999999e79

   1. Initial program 95.1%

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

      1. associate-/l* 90.5%

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

      2. associate-/l* 87.9%

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

   3. Simplified 87.9%

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

   5. Taylor expanded in y around 0 59.6%

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

   if 2.7e157 < y < 1.8e191

   1. Initial program 46.2%

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

      1. associate-/l* 46.2%

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

      2. associate-/l* 72.8%

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

   3. Simplified 72.8%

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

   5. Taylor expanded in y around -inf 57.7%

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

      1. +-commutative 57.7%

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

      2. mul-1-neg 57.7%

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

      3. unsub-neg 57.7%

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

      4. distribute-lft-out-- 57.7%

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

      5. mul-1-neg 57.7%

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

      6. associate-/l* 30.5%

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

      7. associate-/l* 31.1%

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

      8. distribute-lft-out-- 31.1%

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

   7. Simplified 31.1%

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

   8. Taylor expanded in x around inf 72.2%

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

   9. Taylor expanded in z around 0 32.0%

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

       1. times-frac 57.4%

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

   11. Simplified 57.4%

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

   if 1.8e191 < y < 3.99999999999999978e194

   1. Initial program 52.4%

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

      1. associate-/l* 52.4%

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

      2. associate-/l* 52.4%

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

   3. Simplified 52.4%

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

   5. Taylor expanded in a around inf 5.9%

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

   6. Taylor expanded in x around 0 55.5%

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

      1. associate-/l* 100.0%

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

      2. *-commutative 100.0%

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

   8. Simplified 100.0%

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

4. Final simplification 62.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+130}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+79}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+157}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+191}:\\ \;\;\;\;\frac{t}{b} \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+194}:\\ \;\;\;\;y \cdot \frac{z}{t \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 80.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+157} \lor \neg \left(y \leq 2.7 \cdot 10^{+92}\right):\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -5.5e+157) (not (<= y 2.7e+92)))
   (/ (+ z (/ (* x t) y)) b)
   (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (* b (/ y t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -5.5e+157) || !(y <= 2.7e+92)) {
		tmp = (z + ((x * t) / y)) / b;
	} else {
		tmp = (x + ((y * z) / t)) / ((a + 1.0) + (b * (y / t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-5.5d+157)) .or. (.not. (y <= 2.7d+92))) then
        tmp = (z + ((x * t) / y)) / b
    else
        tmp = (x + ((y * z) / t)) / ((a + 1.0d0) + (b * (y / t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -5.5e+157) || !(y <= 2.7e+92)) {
		tmp = (z + ((x * t) / y)) / b;
	} else {
		tmp = (x + ((y * z) / t)) / ((a + 1.0) + (b * (y / t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -5.5e+157) or not (y <= 2.7e+92):
		tmp = (z + ((x * t) / y)) / b
	else:
		tmp = (x + ((y * z) / t)) / ((a + 1.0) + (b * (y / t)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -5.5e+157) || !(y <= 2.7e+92))
		tmp = Float64(Float64(z + Float64(Float64(x * t) / y)) / b);
	else
		tmp = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(Float64(a + 1.0) + Float64(b * Float64(y / t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -5.5e+157) || ~((y <= 2.7e+92)))
		tmp = (z + ((x * t) / y)) / b;
	else
		tmp = (x + ((y * z) / t)) / ((a + 1.0) + (b * (y / t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -5.5e+157], N[Not[LessEqual[y, 2.7e+92]], $MachinePrecision]], N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.5000000000000003e157 or 2.6999999999999999e92 < y

   1. Initial program 39.8%

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

      1. associate-/l* 45.4%

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

      2. associate-/l* 53.9%

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

   3. Simplified 53.9%

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

   5. Taylor expanded in y around -inf 52.2%

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

      1. +-commutative 52.2%

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

      2. mul-1-neg 52.2%

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

      3. unsub-neg 52.2%

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

      4. distribute-lft-out-- 52.2%

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

      5. mul-1-neg 52.2%

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

      6. associate-/l* 47.8%

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

      7. associate-/l* 48.1%

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

      8. distribute-lft-out-- 48.1%

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

   7. Simplified 48.1%

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

   8. Taylor expanded in x around inf 75.0%

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

   9. Taylor expanded in b around 0 76.4%

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

       1. cancel-sign-sub-inv 76.4%

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

       2. metadata-eval 76.4%

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

       3. *-lft-identity 76.4%

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

   11. Simplified 76.4%

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

   if -5.5000000000000003e157 < y < 2.6999999999999999e92

   1. Initial program 94.7%

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

      1. *-commutative 94.7%

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

      2. associate-/l* 94.7%

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

   4. Applied egg-rr 94.7%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+157} \lor \neg \left(y \leq 2.7 \cdot 10^{+92}\right):\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 82.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{-157} \lor \neg \left(t \leq 2.3 \cdot 10^{-139}\right):\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + \frac{y}{\frac{t}{b}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -1.2e-157) (not (<= t 2.3e-139)))
   (/ (+ x (* y (/ z t))) (+ (+ a 1.0) (/ y (/ t b))))
   (/ (+ z (/ (* x t) y)) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.2e-157) || !(t <= 2.3e-139)) {
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y / (t / b)));
	} else {
		tmp = (z + ((x * t) / y)) / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-1.2d-157)) .or. (.not. (t <= 2.3d-139))) then
        tmp = (x + (y * (z / t))) / ((a + 1.0d0) + (y / (t / b)))
    else
        tmp = (z + ((x * t) / y)) / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.2e-157) || !(t <= 2.3e-139)) {
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y / (t / b)));
	} else {
		tmp = (z + ((x * t) / y)) / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -1.2e-157) or not (t <= 2.3e-139):
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y / (t / b)))
	else:
		tmp = (z + ((x * t) / y)) / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -1.2e-157) || !(t <= 2.3e-139))
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(Float64(a + 1.0) + Float64(y / Float64(t / b))));
	else
		tmp = Float64(Float64(z + Float64(Float64(x * t) / y)) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -1.2e-157) || ~((t <= 2.3e-139)))
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y / (t / b)));
	else
		tmp = (z + ((x * t) / y)) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -1.2e-157], N[Not[LessEqual[t, 2.3e-139]], $MachinePrecision]], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(y / N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.2e-157 or 2.30000000000000012e-139 < t

   1. Initial program 88.3%

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

      1. associate-/l* 89.3%

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

      2. associate-/l* 90.7%

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

   3. Simplified 90.7%

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

      1. clear-num 90.7%

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

      2. un-div-inv 91.1%

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

   6. Applied egg-rr 91.1%

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

   if -1.2e-157 < t < 2.30000000000000012e-139

   1. Initial program 48.8%

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

      1. associate-/l* 35.9%

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

      2. associate-/l* 32.2%

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

   3. Simplified 32.2%

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

   5. Taylor expanded in y around -inf 57.4%

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

      1. +-commutative 57.4%

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

      2. mul-1-neg 57.4%

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

      3. unsub-neg 57.4%

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

      4. distribute-lft-out-- 57.4%

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

      5. mul-1-neg 57.4%

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

      6. associate-/l* 49.8%

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

      7. associate-/l* 48.1%

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

      8. distribute-lft-out-- 48.1%

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

   7. Simplified 48.1%

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

   8. Taylor expanded in x around inf 74.3%

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

   9. Taylor expanded in b around 0 74.4%

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

       1. cancel-sign-sub-inv 74.4%

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

       2. metadata-eval 74.4%

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

       3. *-lft-identity 74.4%

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

   11. Simplified 74.4%

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

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{-157} \lor \neg \left(t \leq 2.3 \cdot 10^{-139}\right):\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + \frac{y}{\frac{t}{b}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 82.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.4 \cdot 10^{-157} \lor \neg \left(t \leq 3.5 \cdot 10^{-139}\right):\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{y \cdot \frac{b}{t} + \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -5.4e-157) (not (<= t 3.5e-139)))
   (/ (+ x (* y (/ z t))) (+ (* y (/ b t)) (+ a 1.0)))
   (/ (+ z (/ (* x t) y)) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -5.4e-157) || !(t <= 3.5e-139)) {
		tmp = (x + (y * (z / t))) / ((y * (b / t)) + (a + 1.0));
	} else {
		tmp = (z + ((x * t) / y)) / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-5.4d-157)) .or. (.not. (t <= 3.5d-139))) then
        tmp = (x + (y * (z / t))) / ((y * (b / t)) + (a + 1.0d0))
    else
        tmp = (z + ((x * t) / y)) / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -5.4e-157) || !(t <= 3.5e-139)) {
		tmp = (x + (y * (z / t))) / ((y * (b / t)) + (a + 1.0));
	} else {
		tmp = (z + ((x * t) / y)) / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -5.4e-157) or not (t <= 3.5e-139):
		tmp = (x + (y * (z / t))) / ((y * (b / t)) + (a + 1.0))
	else:
		tmp = (z + ((x * t) / y)) / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -5.4e-157) || !(t <= 3.5e-139))
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(Float64(y * Float64(b / t)) + Float64(a + 1.0)));
	else
		tmp = Float64(Float64(z + Float64(Float64(x * t) / y)) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -5.4e-157) || ~((t <= 3.5e-139)))
		tmp = (x + (y * (z / t))) / ((y * (b / t)) + (a + 1.0));
	else
		tmp = (z + ((x * t) / y)) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -5.4e-157], N[Not[LessEqual[t, 3.5e-139]], $MachinePrecision]], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -5.4e-157 or 3.50000000000000001e-139 < t

   1. Initial program 88.3%

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

      1. associate-/l* 89.3%

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

      2. associate-/l* 90.7%

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

   3. Simplified 90.7%

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

   if -5.4e-157 < t < 3.50000000000000001e-139

   1. Initial program 48.8%

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

      1. associate-/l* 35.9%

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

      2. associate-/l* 32.2%

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

   3. Simplified 32.2%

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

   5. Taylor expanded in y around -inf 57.4%

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

      1. +-commutative 57.4%

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

      2. mul-1-neg 57.4%

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

      3. unsub-neg 57.4%

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

      4. distribute-lft-out-- 57.4%

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

      5. mul-1-neg 57.4%

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

      6. associate-/l* 49.8%

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

      7. associate-/l* 48.1%

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

      8. distribute-lft-out-- 48.1%

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

   7. Simplified 48.1%

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

   8. Taylor expanded in x around inf 74.3%

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

   9. Taylor expanded in b around 0 74.4%

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

       1. cancel-sign-sub-inv 74.4%

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

       2. metadata-eval 74.4%

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

       3. *-lft-identity 74.4%

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

   11. Simplified 74.4%

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

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.4 \cdot 10^{-157} \lor \neg \left(t \leq 3.5 \cdot 10^{-139}\right):\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{y \cdot \frac{b}{t} + \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 82.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{-145}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{y \cdot \frac{b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-139}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + \frac{y}{\frac{t}{b}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1e-145)
   (/ (+ x (/ y (/ t z))) (+ (* y (/ b t)) (+ a 1.0)))
   (if (<= t 4.2e-139)
     (/ (+ z (/ (* x t) y)) b)
     (/ (+ x (* y (/ z t))) (+ (+ a 1.0) (/ y (/ t b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1e-145) {
		tmp = (x + (y / (t / z))) / ((y * (b / t)) + (a + 1.0));
	} else if (t <= 4.2e-139) {
		tmp = (z + ((x * t) / y)) / b;
	} else {
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y / (t / b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-1d-145)) then
        tmp = (x + (y / (t / z))) / ((y * (b / t)) + (a + 1.0d0))
    else if (t <= 4.2d-139) then
        tmp = (z + ((x * t) / y)) / b
    else
        tmp = (x + (y * (z / t))) / ((a + 1.0d0) + (y / (t / b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1e-145) {
		tmp = (x + (y / (t / z))) / ((y * (b / t)) + (a + 1.0));
	} else if (t <= 4.2e-139) {
		tmp = (z + ((x * t) / y)) / b;
	} else {
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y / (t / b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1e-145:
		tmp = (x + (y / (t / z))) / ((y * (b / t)) + (a + 1.0))
	elif t <= 4.2e-139:
		tmp = (z + ((x * t) / y)) / b
	else:
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y / (t / b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1e-145)
		tmp = Float64(Float64(x + Float64(y / Float64(t / z))) / Float64(Float64(y * Float64(b / t)) + Float64(a + 1.0)));
	elseif (t <= 4.2e-139)
		tmp = Float64(Float64(z + Float64(Float64(x * t) / y)) / b);
	else
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(Float64(a + 1.0) + Float64(y / Float64(t / b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -1e-145)
		tmp = (x + (y / (t / z))) / ((y * (b / t)) + (a + 1.0));
	elseif (t <= 4.2e-139)
		tmp = (z + ((x * t) / y)) / b;
	else
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y / (t / b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1e-145], N[(N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.2e-139], N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(y / N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -9.99999999999999915e-146

   1. Initial program 89.2%

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

      1. associate-/l* 88.4%

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

      2. associate-/l* 90.3%

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

   3. Simplified 90.3%

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

      1. clear-num 90.2%

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

      2. un-div-inv 91.2%

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

   6. Applied egg-rr 91.2%

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

   if -9.99999999999999915e-146 < t < 4.20000000000000016e-139

   1. Initial program 52.3%

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

      1. associate-/l* 40.3%

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

      2. associate-/l* 35.3%

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

   3. Simplified 35.3%

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

   5. Taylor expanded in y around -inf 55.1%

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

      1. +-commutative 55.1%

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

      2. mul-1-neg 55.1%

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

      3. unsub-neg 55.1%

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

      4. distribute-lft-out-- 55.1%

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

      5. mul-1-neg 55.1%

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

      6. associate-/l* 48.1%

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

      7. associate-/l* 46.6%

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

      8. distribute-lft-out-- 46.6%

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

   7. Simplified 46.6%

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

   8. Taylor expanded in x around inf 74.4%

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

   9. Taylor expanded in b around 0 74.5%

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

       1. cancel-sign-sub-inv 74.5%

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

       2. metadata-eval 74.5%

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

       3. *-lft-identity 74.5%

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

   11. Simplified 74.5%

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

   if 4.20000000000000016e-139 < t

   1. Initial program 86.9%

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

      1. associate-/l* 89.9%

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

      2. associate-/l* 91.8%

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

   3. Simplified 91.8%

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

      1. clear-num 91.7%

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

      2. un-div-inv 91.8%

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

   6. Applied egg-rr 91.8%

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

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{-145}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{y \cdot \frac{b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-139}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + \frac{y}{\frac{t}{b}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 53.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{a + 1}\\ \mathbf{if}\;y \leq -2.4 \cdot 10^{+132}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq -1.06 \cdot 10^{-42}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{-109}:\\ \;\;\;\;\frac{y \cdot z}{t + y \cdot b}\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+77}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (+ a 1.0))))
   (if (<= y -2.4e+132)
     (/ z b)
     (if (<= y -1.06e-42)
       t_1
       (if (<= y -5.5e-109)
         (/ (* y z) (+ t (* y b)))
         (if (<= y 1.8e+77) t_1 (/ z b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a + 1.0);
	double tmp;
	if (y <= -2.4e+132) {
		tmp = z / b;
	} else if (y <= -1.06e-42) {
		tmp = t_1;
	} else if (y <= -5.5e-109) {
		tmp = (y * z) / (t + (y * b));
	} else if (y <= 1.8e+77) {
		tmp = t_1;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (a + 1.0d0)
    if (y <= (-2.4d+132)) then
        tmp = z / b
    else if (y <= (-1.06d-42)) then
        tmp = t_1
    else if (y <= (-5.5d-109)) then
        tmp = (y * z) / (t + (y * b))
    else if (y <= 1.8d+77) then
        tmp = t_1
    else
        tmp = z / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a + 1.0);
	double tmp;
	if (y <= -2.4e+132) {
		tmp = z / b;
	} else if (y <= -1.06e-42) {
		tmp = t_1;
	} else if (y <= -5.5e-109) {
		tmp = (y * z) / (t + (y * b));
	} else if (y <= 1.8e+77) {
		tmp = t_1;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (a + 1.0)
	tmp = 0
	if y <= -2.4e+132:
		tmp = z / b
	elif y <= -1.06e-42:
		tmp = t_1
	elif y <= -5.5e-109:
		tmp = (y * z) / (t + (y * b))
	elif y <= 1.8e+77:
		tmp = t_1
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(a + 1.0))
	tmp = 0.0
	if (y <= -2.4e+132)
		tmp = Float64(z / b);
	elseif (y <= -1.06e-42)
		tmp = t_1;
	elseif (y <= -5.5e-109)
		tmp = Float64(Float64(y * z) / Float64(t + Float64(y * b)));
	elseif (y <= 1.8e+77)
		tmp = t_1;
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (a + 1.0);
	tmp = 0.0;
	if (y <= -2.4e+132)
		tmp = z / b;
	elseif (y <= -1.06e-42)
		tmp = t_1;
	elseif (y <= -5.5e-109)
		tmp = (y * z) / (t + (y * b));
	elseif (y <= 1.8e+77)
		tmp = t_1;
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.4e+132], N[(z / b), $MachinePrecision], If[LessEqual[y, -1.06e-42], t$95$1, If[LessEqual[y, -5.5e-109], N[(N[(y * z), $MachinePrecision] / N[(t + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.8e+77], t$95$1, N[(z / b), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.4000000000000001e132 or 1.7999999999999999e77 < y

   1. Initial program 40.9%

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

      1. associate-/l* 46.3%

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

      2. associate-/l* 54.4%

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

   3. Simplified 54.4%

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

   5. Taylor expanded in y around inf 63.5%

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

   if -2.4000000000000001e132 < y < -1.0600000000000001e-42 or -5.5000000000000003e-109 < y < 1.7999999999999999e77

   1. Initial program 95.8%

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

      1. associate-/l* 91.8%

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

      2. associate-/l* 89.5%

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

   3. Simplified 89.5%

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

   5. Taylor expanded in y around 0 63.3%

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

   if -1.0600000000000001e-42 < y < -5.5000000000000003e-109

   1. Initial program 89.2%

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

      1. *-commutative 89.2%

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

      2. associate-/l* 89.3%

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

   4. Applied egg-rr 89.3%

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

   5. Taylor expanded in x around 0 66.3%

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

      1. associate-/r* 60.9%

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

      2. associate-/l* 50.5%

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

      3. associate-+r+ 50.5%

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

      4. associate-*r/ 50.5%

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

   7. Simplified 50.5%

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

   8. Taylor expanded in a around 0 55.7%

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

   9. Taylor expanded in t around 0 60.9%

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

       1. *-commutative 60.9%

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

   11. Simplified 60.9%

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

4. Final simplification 63.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+132}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq -1.06 \cdot 10^{-42}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{-109}:\\ \;\;\;\;\frac{y \cdot z}{t + y \cdot b}\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+77}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 67.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{+157} \lor \neg \left(y \leq 8.6 \cdot 10^{+91}\right):\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -4.1e+157) (not (<= y 8.6e+91)))
   (/ (+ z (/ (* x t) y)) b)
   (/ (+ x (/ (* y z) t)) (+ a 1.0))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -4.1e+157) || !(y <= 8.6e+91)) {
		tmp = (z + ((x * t) / y)) / b;
	} else {
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-4.1d+157)) .or. (.not. (y <= 8.6d+91))) then
        tmp = (z + ((x * t) / y)) / b
    else
        tmp = (x + ((y * z) / t)) / (a + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -4.1e+157) || !(y <= 8.6e+91)) {
		tmp = (z + ((x * t) / y)) / b;
	} else {
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -4.1e+157) or not (y <= 8.6e+91):
		tmp = (z + ((x * t) / y)) / b
	else:
		tmp = (x + ((y * z) / t)) / (a + 1.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -4.1e+157) || !(y <= 8.6e+91))
		tmp = Float64(Float64(z + Float64(Float64(x * t) / y)) / b);
	else
		tmp = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(a + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -4.1e+157) || ~((y <= 8.6e+91)))
		tmp = (z + ((x * t) / y)) / b;
	else
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -4.1e+157], N[Not[LessEqual[y, 8.6e+91]], $MachinePrecision]], N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.10000000000000016e157 or 8.6000000000000001e91 < y

   1. Initial program 39.8%

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

      1. associate-/l* 45.4%

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

      2. associate-/l* 53.9%

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

   3. Simplified 53.9%

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

   5. Taylor expanded in y around -inf 52.2%

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

      1. +-commutative 52.2%

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

      2. mul-1-neg 52.2%

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

      3. unsub-neg 52.2%

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

      4. distribute-lft-out-- 52.2%

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

      5. mul-1-neg 52.2%

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

      6. associate-/l* 47.8%

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

      7. associate-/l* 48.1%

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

      8. distribute-lft-out-- 48.1%

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

   7. Simplified 48.1%

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

   8. Taylor expanded in x around inf 75.0%

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

   9. Taylor expanded in b around 0 76.4%

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

       1. cancel-sign-sub-inv 76.4%

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

       2. metadata-eval 76.4%

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

       3. *-lft-identity 76.4%

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

   11. Simplified 76.4%

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

   if -4.10000000000000016e157 < y < 8.6000000000000001e91

   1. Initial program 94.7%

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

      1. associate-/l* 90.1%

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

      2. associate-/l* 87.6%

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

   3. Simplified 87.6%

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

   5. Taylor expanded in b around 0 77.2%

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

4. Final simplification 76.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{+157} \lor \neg \left(y \leq 8.6 \cdot 10^{+91}\right):\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 66.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+157} \lor \neg \left(y \leq 5.7 \cdot 10^{+88}\right):\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.6e+157) (not (<= y 5.7e+88)))
   (/ (+ z (/ (* x t) y)) b)
   (/ (+ x (/ y (/ t z))) (+ a 1.0))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.6e+157) || !(y <= 5.7e+88)) {
		tmp = (z + ((x * t) / y)) / b;
	} else {
		tmp = (x + (y / (t / z))) / (a + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-1.6d+157)) .or. (.not. (y <= 5.7d+88))) then
        tmp = (z + ((x * t) / y)) / b
    else
        tmp = (x + (y / (t / z))) / (a + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.6e+157) || !(y <= 5.7e+88)) {
		tmp = (z + ((x * t) / y)) / b;
	} else {
		tmp = (x + (y / (t / z))) / (a + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.6e+157) or not (y <= 5.7e+88):
		tmp = (z + ((x * t) / y)) / b
	else:
		tmp = (x + (y / (t / z))) / (a + 1.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.6e+157) || !(y <= 5.7e+88))
		tmp = Float64(Float64(z + Float64(Float64(x * t) / y)) / b);
	else
		tmp = Float64(Float64(x + Float64(y / Float64(t / z))) / Float64(a + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.6e+157) || ~((y <= 5.7e+88)))
		tmp = (z + ((x * t) / y)) / b;
	else
		tmp = (x + (y / (t / z))) / (a + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.6e+157], N[Not[LessEqual[y, 5.7e+88]], $MachinePrecision]], N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], N[(N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.6e157 or 5.70000000000000021e88 < y

   1. Initial program 39.8%

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

      1. associate-/l* 45.4%

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

      2. associate-/l* 53.9%

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

   3. Simplified 53.9%

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

   5. Taylor expanded in y around -inf 52.2%

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

      1. +-commutative 52.2%

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

      2. mul-1-neg 52.2%

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

      3. unsub-neg 52.2%

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

      4. distribute-lft-out-- 52.2%

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

      5. mul-1-neg 52.2%

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

      6. associate-/l* 47.8%

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

      7. associate-/l* 48.1%

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

      8. distribute-lft-out-- 48.1%

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

   7. Simplified 48.1%

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

   8. Taylor expanded in x around inf 75.0%

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

   9. Taylor expanded in b around 0 76.4%

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

       1. cancel-sign-sub-inv 76.4%

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

       2. metadata-eval 76.4%

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

       3. *-lft-identity 76.4%

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

   11. Simplified 76.4%

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

   if -1.6e157 < y < 5.70000000000000021e88

   1. Initial program 94.7%

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

      1. associate-/l* 90.1%

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

      2. associate-/l* 87.6%

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

   3. Simplified 87.6%

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

   5. Taylor expanded in y around 0 75.1%

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

      1. clear-num 87.5%

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

      2. un-div-inv 88.1%

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

   7. Applied egg-rr 75.6%

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

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+157} \lor \neg \left(y \leq 5.7 \cdot 10^{+88}\right):\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 65.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.45 \cdot 10^{+157} \lor \neg \left(y \leq 2.3 \cdot 10^{+92}\right):\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -2.45e+157) (not (<= y 2.3e+92)))
   (/ (+ z (/ (* x t) y)) b)
   (/ (+ x (* y (/ z t))) (+ a 1.0))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.45e+157) || !(y <= 2.3e+92)) {
		tmp = (z + ((x * t) / y)) / b;
	} else {
		tmp = (x + (y * (z / t))) / (a + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-2.45d+157)) .or. (.not. (y <= 2.3d+92))) then
        tmp = (z + ((x * t) / y)) / b
    else
        tmp = (x + (y * (z / t))) / (a + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.45e+157) || !(y <= 2.3e+92)) {
		tmp = (z + ((x * t) / y)) / b;
	} else {
		tmp = (x + (y * (z / t))) / (a + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -2.45e+157) or not (y <= 2.3e+92):
		tmp = (z + ((x * t) / y)) / b
	else:
		tmp = (x + (y * (z / t))) / (a + 1.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -2.45e+157) || !(y <= 2.3e+92))
		tmp = Float64(Float64(z + Float64(Float64(x * t) / y)) / b);
	else
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(a + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -2.45e+157) || ~((y <= 2.3e+92)))
		tmp = (z + ((x * t) / y)) / b;
	else
		tmp = (x + (y * (z / t))) / (a + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -2.45e+157], N[Not[LessEqual[y, 2.3e+92]], $MachinePrecision]], N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.4500000000000001e157 or 2.29999999999999998e92 < y

   1. Initial program 39.8%

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

      1. associate-/l* 45.4%

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

      2. associate-/l* 53.9%

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

   3. Simplified 53.9%

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

   5. Taylor expanded in y around -inf 52.2%

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

      1. +-commutative 52.2%

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

      2. mul-1-neg 52.2%

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

      3. unsub-neg 52.2%

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

      4. distribute-lft-out-- 52.2%

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

      5. mul-1-neg 52.2%

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

      6. associate-/l* 47.8%

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

      7. associate-/l* 48.1%

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

      8. distribute-lft-out-- 48.1%

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

   7. Simplified 48.1%

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

   8. Taylor expanded in x around inf 75.0%

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

   9. Taylor expanded in b around 0 76.4%

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

       1. cancel-sign-sub-inv 76.4%

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

       2. metadata-eval 76.4%

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

       3. *-lft-identity 76.4%

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

   11. Simplified 76.4%

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

   if -2.4500000000000001e157 < y < 2.29999999999999998e92

   1. Initial program 94.7%

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

      1. associate-/l* 90.1%

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

      2. associate-/l* 87.6%

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

   3. Simplified 87.6%

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

   5. Taylor expanded in y around 0 75.1%

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

4. Final simplification 75.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.45 \cdot 10^{+157} \lor \neg \left(y \leq 2.3 \cdot 10^{+92}\right):\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 65.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{-59} \lor \neg \left(t \leq 8 \cdot 10^{-123}\right):\\ \;\;\;\;\frac{x}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -6.5e-59) (not (<= t 8e-123)))
   (/ x (+ (+ a 1.0) (* b (/ y t))))
   (/ (+ z (/ (* x t) y)) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -6.5e-59) || !(t <= 8e-123)) {
		tmp = x / ((a + 1.0) + (b * (y / t)));
	} else {
		tmp = (z + ((x * t) / y)) / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-6.5d-59)) .or. (.not. (t <= 8d-123))) then
        tmp = x / ((a + 1.0d0) + (b * (y / t)))
    else
        tmp = (z + ((x * t) / y)) / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -6.5e-59) || !(t <= 8e-123)) {
		tmp = x / ((a + 1.0) + (b * (y / t)));
	} else {
		tmp = (z + ((x * t) / y)) / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -6.5e-59) or not (t <= 8e-123):
		tmp = x / ((a + 1.0) + (b * (y / t)))
	else:
		tmp = (z + ((x * t) / y)) / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -6.5e-59) || !(t <= 8e-123))
		tmp = Float64(x / Float64(Float64(a + 1.0) + Float64(b * Float64(y / t))));
	else
		tmp = Float64(Float64(z + Float64(Float64(x * t) / y)) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -6.5e-59) || ~((t <= 8e-123)))
		tmp = x / ((a + 1.0) + (b * (y / t)));
	else
		tmp = (z + ((x * t) / y)) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -6.5e-59], N[Not[LessEqual[t, 8e-123]], $MachinePrecision]], N[(x / N[(N[(a + 1.0), $MachinePrecision] + N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -6.50000000000000017e-59 or 8.0000000000000005e-123 < t

   1. Initial program 88.1%

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

      1. *-commutative 88.1%

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

      2. associate-/l* 90.3%

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

   4. Applied egg-rr 90.3%

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

   5. Taylor expanded in x around inf 68.1%

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

      1. associate-+r+ 68.1%

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

      2. associate-*r/ 70.3%

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

   7. Simplified 70.3%

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

   if -6.50000000000000017e-59 < t < 8.0000000000000005e-123

   1. Initial program 62.7%

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

      1. associate-/l* 52.1%

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

      2. associate-/l* 47.4%

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

   3. Simplified 47.4%

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

   5. Taylor expanded in y around -inf 53.8%

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

      1. +-commutative 53.8%

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

      2. mul-1-neg 53.8%

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

      3. unsub-neg 53.8%

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

      4. distribute-lft-out-- 53.8%

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

      5. mul-1-neg 53.8%

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

      6. associate-/l* 48.8%

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

      7. associate-/l* 47.8%

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

      8. distribute-lft-out-- 47.8%

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

   7. Simplified 47.8%

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

   8. Taylor expanded in x around inf 68.4%

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

   9. Taylor expanded in b around 0 68.4%

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

       1. cancel-sign-sub-inv 68.4%

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

       2. metadata-eval 68.4%

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

       3. *-lft-identity 68.4%

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

   11. Simplified 68.4%

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

4. Final simplification 69.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{-59} \lor \neg \left(t \leq 8 \cdot 10^{-123}\right):\\ \;\;\;\;\frac{x}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 65.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.95 \cdot 10^{-61} \lor \neg \left(t \leq 3.7 \cdot 10^{-122}\right):\\ \;\;\;\;\frac{x}{\left(a + y \cdot \frac{b}{t}\right) + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -2.95e-61) (not (<= t 3.7e-122)))
   (/ x (+ (+ a (* y (/ b t))) 1.0))
   (/ (+ z (/ (* x t) y)) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -2.95e-61) || !(t <= 3.7e-122)) {
		tmp = x / ((a + (y * (b / t))) + 1.0);
	} else {
		tmp = (z + ((x * t) / y)) / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-2.95d-61)) .or. (.not. (t <= 3.7d-122))) then
        tmp = x / ((a + (y * (b / t))) + 1.0d0)
    else
        tmp = (z + ((x * t) / y)) / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -2.95e-61) || !(t <= 3.7e-122)) {
		tmp = x / ((a + (y * (b / t))) + 1.0);
	} else {
		tmp = (z + ((x * t) / y)) / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -2.95e-61) or not (t <= 3.7e-122):
		tmp = x / ((a + (y * (b / t))) + 1.0)
	else:
		tmp = (z + ((x * t) / y)) / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -2.95e-61) || !(t <= 3.7e-122))
		tmp = Float64(x / Float64(Float64(a + Float64(y * Float64(b / t))) + 1.0));
	else
		tmp = Float64(Float64(z + Float64(Float64(x * t) / y)) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -2.95e-61) || ~((t <= 3.7e-122)))
		tmp = x / ((a + (y * (b / t))) + 1.0);
	else
		tmp = (z + ((x * t) / y)) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -2.95e-61], N[Not[LessEqual[t, 3.7e-122]], $MachinePrecision]], N[(x / N[(N[(a + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.94999999999999986e-61 or 3.6999999999999997e-122 < t

   1. Initial program 88.1%

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

      1. associate-/l* 90.4%

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

      2. associate-/l* 93.1%

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

   3. Simplified 93.1%

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

   5. Taylor expanded in x around inf 68.1%

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

      1. associate-*l/ 69.7%

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

      2. *-commutative 69.7%

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

   7. Simplified 69.7%

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

   if -2.94999999999999986e-61 < t < 3.6999999999999997e-122

   1. Initial program 62.7%

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

      1. associate-/l* 52.1%

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

      2. associate-/l* 47.4%

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

   3. Simplified 47.4%

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

   5. Taylor expanded in y around -inf 53.8%

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

      1. +-commutative 53.8%

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

      2. mul-1-neg 53.8%

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

      3. unsub-neg 53.8%

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

      4. distribute-lft-out-- 53.8%

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

      5. mul-1-neg 53.8%

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

      6. associate-/l* 48.8%

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

      7. associate-/l* 47.8%

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

      8. distribute-lft-out-- 47.8%

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

   7. Simplified 47.8%

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

   8. Taylor expanded in x around inf 68.4%

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

   9. Taylor expanded in b around 0 68.4%

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

       1. cancel-sign-sub-inv 68.4%

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

       2. metadata-eval 68.4%

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

       3. *-lft-identity 68.4%

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

   11. Simplified 68.4%

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

4. Final simplification 69.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.95 \cdot 10^{-61} \lor \neg \left(t \leq 3.7 \cdot 10^{-122}\right):\\ \;\;\;\;\frac{x}{\left(a + y \cdot \frac{b}{t}\right) + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 55.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.6 \cdot 10^{+130} \lor \neg \left(y \leq 2.9 \cdot 10^{+83}\right):\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -6.6e+130) (not (<= y 2.9e+83))) (/ z b) (/ x (+ a 1.0))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -6.6e+130) || !(y <= 2.9e+83)) {
		tmp = z / b;
	} else {
		tmp = x / (a + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-6.6d+130)) .or. (.not. (y <= 2.9d+83))) then
        tmp = z / b
    else
        tmp = x / (a + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -6.6e+130) || !(y <= 2.9e+83)) {
		tmp = z / b;
	} else {
		tmp = x / (a + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -6.6e+130) or not (y <= 2.9e+83):
		tmp = z / b
	else:
		tmp = x / (a + 1.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -6.6e+130) || !(y <= 2.9e+83))
		tmp = Float64(z / b);
	else
		tmp = Float64(x / Float64(a + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -6.6e+130) || ~((y <= 2.9e+83)))
		tmp = z / b;
	else
		tmp = x / (a + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -6.6e+130], N[Not[LessEqual[y, 2.9e+83]], $MachinePrecision]], N[(z / b), $MachinePrecision], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.6e130 or 2.89999999999999999e83 < y

   1. Initial program 40.9%

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

      1. associate-/l* 46.3%

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

      2. associate-/l* 54.4%

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

   3. Simplified 54.4%

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

   5. Taylor expanded in y around inf 63.5%

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

   if -6.6e130 < y < 2.89999999999999999e83

   1. Initial program 95.1%

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

      1. associate-/l* 90.5%

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

      2. associate-/l* 87.9%

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

   3. Simplified 87.9%

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

   5. Taylor expanded in y around 0 59.6%

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

4. Final simplification 60.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.6 \cdot 10^{+130} \lor \neg \left(y \leq 2.9 \cdot 10^{+83}\right):\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 40.8% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if a < -1 or 1 < a

   1. Initial program 85.7%

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

      1. associate-/l* 82.7%

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

      2. associate-/l* 81.1%

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

   3. Simplified 81.1%

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

   5. Taylor expanded in y around 0 56.9%

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

   6. Taylor expanded in a around inf 56.5%

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

   if -1 < a < 1

   1. Initial program 74.7%

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

      1. associate-/l* 74.0%

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

      2. associate-/l* 76.2%

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

   3. Simplified 76.2%

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

   5. Taylor expanded in y around 0 35.9%

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

   6. Taylor expanded in a around 0 35.1%

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

4. Final simplification 45.5%

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

Alternative 24: 19.5% 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 80.1%

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

   1. associate-/l* 78.2%

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

   2. associate-/l* 78.6%

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

3. Simplified 78.6%

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

5. Taylor expanded in y around 0 46.2%

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

6. Taylor expanded in a around 0 20.0%

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

Developer target: 79.3% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024108 
(FPCore (x y z t a b)
  :name "Diagrams.Solve.Tridiagonal:solveCyclicTriDiagonal from diagrams-solve-0.1, B"
  :precision binary64

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

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