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

Percentage Accurate: 75.0% → 90.3%

Time: 14.1s

Alternatives: 15

Speedup: 0.8×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 75.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 90.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot b}{t}\\ t_2 := \frac{x + \frac{y \cdot z}{t}}{t_1 + \left(a + 1\right)}\\ t_3 := \frac{x}{1 + \left(a + t_1\right)} + \frac{1}{\frac{t}{y} \cdot \frac{1 + \left(a + y \cdot \frac{b}{t}\right)}{z}}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+245}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq \infty:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* y b) t))
        (t_2 (/ (+ x (/ (* y z) t)) (+ t_1 (+ a 1.0))))
        (t_3
         (+
          (/ x (+ 1.0 (+ a t_1)))
          (/ 1.0 (* (/ t y) (/ (+ 1.0 (+ a (* y (/ b t)))) z))))))
   (if (<= t_2 (- INFINITY))
     t_3
     (if (<= t_2 5e+245) t_2 (if (<= t_2 INFINITY) t_3 (/ z b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y * b) / t;
	double t_2 = (x + ((y * z) / t)) / (t_1 + (a + 1.0));
	double t_3 = (x / (1.0 + (a + t_1))) + (1.0 / ((t / y) * ((1.0 + (a + (y * (b / t)))) / z)));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_3;
	} else if (t_2 <= 5e+245) {
		tmp = t_2;
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = t_3;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y * b) / t;
	double t_2 = (x + ((y * z) / t)) / (t_1 + (a + 1.0));
	double t_3 = (x / (1.0 + (a + t_1))) + (1.0 / ((t / y) * ((1.0 + (a + (y * (b / t)))) / z)));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_3;
	} else if (t_2 <= 5e+245) {
		tmp = t_2;
	} else if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = t_3;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (y * b) / t
	t_2 = (x + ((y * z) / t)) / (t_1 + (a + 1.0))
	t_3 = (x / (1.0 + (a + t_1))) + (1.0 / ((t / y) * ((1.0 + (a + (y * (b / t)))) / z)))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_3
	elif t_2 <= 5e+245:
		tmp = t_2
	elif t_2 <= math.inf:
		tmp = t_3
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y * b) / t)
	t_2 = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(t_1 + Float64(a + 1.0)))
	t_3 = Float64(Float64(x / Float64(1.0 + Float64(a + t_1))) + Float64(1.0 / Float64(Float64(t / y) * Float64(Float64(1.0 + Float64(a + Float64(y * Float64(b / t)))) / z))))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_3;
	elseif (t_2 <= 5e+245)
		tmp = t_2;
	elseif (t_2 <= Inf)
		tmp = t_3;
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (y * b) / t;
	t_2 = (x + ((y * z) / t)) / (t_1 + (a + 1.0));
	t_3 = (x / (1.0 + (a + t_1))) + (1.0 / ((t / y) * ((1.0 + (a + (y * (b / t)))) / z)));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_3;
	elseif (t_2 <= 5e+245)
		tmp = t_2;
	elseif (t_2 <= Inf)
		tmp = t_3;
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(t$95$1 + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x / N[(1.0 + N[(a + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(1.0 / N[(N[(t / y), $MachinePrecision] * N[(N[(1.0 + N[(a + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$3, If[LessEqual[t$95$2, 5e+245], t$95$2, If[LessEqual[t$95$2, Infinity], t$95$3, N[(z / b), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < -inf.0 or 5.00000000000000034e245 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < +inf.0

   1. Initial program 37.6%

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

      1. *-commutative 37.6%

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

      2. associate-*l/ 70.8%

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

      3. *-commutative 70.8%

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

      4. associate-*l/ 70.8%

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

   3. Simplified 70.8%

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

   4. Taylor expanded in x around 0 53.2%

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

      1. clear-num 53.1%

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

      2. inv-pow 53.1%

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

      3. times-frac 88.0%

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

      4. associate-/l* 82.5%

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

   6. Applied egg-rr 82.5%

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

      1. unpow-1 82.5%

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

      2. associate-/r/ 88.0%

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

      3. *-commutative 88.0%

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

   8. Simplified 88.0%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 5.00000000000000034e245

   1. Initial program 92.9%

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

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

   1. Initial program 0.0%

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

      1. *-commutative 0.0%

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

      2. associate-*l/ 0.6%

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

      3. *-commutative 0.6%

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

      4. associate-*l/ 12.6%

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

   3. Simplified 12.6%

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

   4. Taylor expanded in t around 0 93.7%

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

4. Final simplification 92.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -\infty:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)} + \frac{1}{\frac{t}{y} \cdot \frac{1 + \left(a + y \cdot \frac{b}{t}\right)}{z}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 5 \cdot 10^{+245}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq \infty:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)} + \frac{1}{\frac{t}{y} \cdot \frac{1 + \left(a + y \cdot \frac{b}{t}\right)}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 2: 87.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\frac{x + \frac{z}{\frac{t}{y}}}{a + \left(1 + \frac{y}{\frac{t}{b}}\right)}\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+286}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq \infty:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{1 + \left(a + y \cdot \frac{b}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (* y z) t)) (+ (/ (* y b) t) (+ a 1.0)))))
   (if (<= t_1 (- INFINITY))
     (/ (+ x (/ z (/ t y))) (+ a (+ 1.0 (/ y (/ t b)))))
     (if (<= t_1 2e+286)
       t_1
       (if (<= t_1 INFINITY)
         (* (/ y t) (/ z (+ 1.0 (+ a (* y (/ b t))))))
         (/ z b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + ((y * z) / t)) / (((y * b) / t) + (a + 1.0));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = (x + (z / (t / y))) / (a + (1.0 + (y / (t / b))));
	} else if (t_1 <= 2e+286) {
		tmp = t_1;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = (y / t) * (z / (1.0 + (a + (y * (b / t)))));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + ((y * z) / t)) / (((y * b) / t) + (a + 1.0));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = (x + (z / (t / y))) / (a + (1.0 + (y / (t / b))));
	} else if (t_1 <= 2e+286) {
		tmp = t_1;
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = (y / t) * (z / (1.0 + (a + (y * (b / t)))));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + ((y * z) / t)) / (((y * b) / t) + (a + 1.0))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = (x + (z / (t / y))) / (a + (1.0 + (y / (t / b))))
	elif t_1 <= 2e+286:
		tmp = t_1
	elif t_1 <= math.inf:
		tmp = (y / t) * (z / (1.0 + (a + (y * (b / t)))))
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(Float64(Float64(y * b) / t) + Float64(a + 1.0)))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(x + Float64(z / Float64(t / y))) / Float64(a + Float64(1.0 + Float64(y / Float64(t / b)))));
	elseif (t_1 <= 2e+286)
		tmp = t_1;
	elseif (t_1 <= Inf)
		tmp = Float64(Float64(y / t) * Float64(z / Float64(1.0 + Float64(a + Float64(y * Float64(b / t))))));
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + ((y * z) / t)) / (((y * b) / t) + (a + 1.0));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = (x + (z / (t / y))) / (a + (1.0 + (y / (t / b))));
	elseif (t_1 <= 2e+286)
		tmp = t_1;
	elseif (t_1 <= Inf)
		tmp = (y / t) * (z / (1.0 + (a + (y * (b / t)))));
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(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, (-Infinity)], N[(N[(x + N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + N[(1.0 + N[(y / N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+286], t$95$1, If[LessEqual[t$95$1, Infinity], N[(N[(y / t), $MachinePrecision] * N[(z / N[(1.0 + N[(a + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < -inf.0

   1. Initial program 36.3%

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

      1. *-commutative 36.3%

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

      2. associate-/l* 74.9%

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

      3. associate-*l/ 60.5%

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

      4. *-commutative 60.5%

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

      5. cancel-sign-sub 60.5%

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

      6. *-commutative 60.5%

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

      7. associate-*l/ 74.9%

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

      8. associate-+r- 74.9%

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

      9. associate-*l/ 60.5%

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

      10. *-commutative 60.5%

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

      11. cancel-sign-sub 60.5%

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

      12. *-commutative 60.5%

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

      13. associate-/r/ 74.9%

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

   3. Simplified 74.9%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 2.00000000000000007e286

   1. Initial program 92.9%

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

   if 2.00000000000000007e286 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < +inf.0

   1. Initial program 22.4%

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

      1. *-commutative 22.4%

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

      2. associate-*l/ 65.7%

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

      3. *-commutative 65.7%

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

      4. associate-*l/ 65.7%

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

   3. Simplified 65.7%

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

      1. frac-2neg 65.7%

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

      2. div-inv 66.0%

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

      3. +-commutative 66.0%

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

      4. associate-/r/ 65.8%

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

      5. div-inv 65.8%

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

      6. fma-def 65.8%

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

      7. clear-num 66.0%

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

      8. +-commutative 66.0%

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

      9. *-commutative 66.0%

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

      10. fma-def 66.0%

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

   5. Applied egg-rr 66.0%

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

      1. fma-udef 66.0%

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

      2. associate-*r/ 22.4%

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

      3. associate-*l/ 66.0%

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

      4. *-commutative 66.0%

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

      5. fma-udef 66.0%

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

      6. +-commutative 66.0%

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

      7. fma-def 66.0%

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

      8. associate-+r+ 66.0%

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

      9. fma-udef 66.0%

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

      10. +-commutative 66.0%

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

   7. Simplified 66.0%

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

   8. Taylor expanded in z around inf 29.9%

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

      1. times-frac 91.2%

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

      2. *-commutative 91.2%

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

      3. associate-*r/ 91.2%

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

   10. Simplified 91.2%

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

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

   1. Initial program 0.0%

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

      1. *-commutative 0.0%

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

      2. associate-*l/ 0.6%

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

      3. *-commutative 0.6%

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

      4. associate-*l/ 12.6%

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

   3. Simplified 12.6%

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

   4. Taylor expanded in t around 0 93.7%

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

4. Final simplification 91.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -\infty:\\ \;\;\;\;\frac{x + \frac{z}{\frac{t}{y}}}{a + \left(1 + \frac{y}{\frac{t}{b}}\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 2 \cdot 10^{+286}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq \infty:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{1 + \left(a + y \cdot \frac{b}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 3: 78.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{z}{\frac{t}{y}}}{a + \left(1 + \frac{y}{\frac{t}{b}}\right)}\\ \mathbf{if}\;t \leq -1.05 \cdot 10^{-125}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 8 \cdot 10^{-253}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq 5.1 \cdot 10^{-144}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-114}:\\ \;\;\;\;\frac{y \cdot z + x \cdot t}{y \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{y \cdot \frac{b}{t} + \left(a + 1\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ z (/ t y))) (+ a (+ 1.0 (/ y (/ t b)))))))
   (if (<= t -1.05e-125)
     t_1
     (if (<= t 8e-253)
       (/ z b)
       (if (<= t 5.1e-144)
         t_1
         (if (<= t 8.5e-114)
           (/ (+ (* y z) (* x t)) (* y b))
           (/ (+ x (* y (/ z t))) (+ (* y (/ b t)) (+ a 1.0)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + (z / (t / y))) / (a + (1.0 + (y / (t / b))));
	double tmp;
	if (t <= -1.05e-125) {
		tmp = t_1;
	} else if (t <= 8e-253) {
		tmp = z / b;
	} else if (t <= 5.1e-144) {
		tmp = t_1;
	} else if (t <= 8.5e-114) {
		tmp = ((y * z) + (x * t)) / (y * b);
	} else {
		tmp = (x + (y * (z / t))) / ((y * (b / 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) :: t_1
    real(8) :: tmp
    t_1 = (x + (z / (t / y))) / (a + (1.0d0 + (y / (t / b))))
    if (t <= (-1.05d-125)) then
        tmp = t_1
    else if (t <= 8d-253) then
        tmp = z / b
    else if (t <= 5.1d-144) then
        tmp = t_1
    else if (t <= 8.5d-114) then
        tmp = ((y * z) + (x * t)) / (y * b)
    else
        tmp = (x + (y * (z / t))) / ((y * (b / 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 t_1 = (x + (z / (t / y))) / (a + (1.0 + (y / (t / b))));
	double tmp;
	if (t <= -1.05e-125) {
		tmp = t_1;
	} else if (t <= 8e-253) {
		tmp = z / b;
	} else if (t <= 5.1e-144) {
		tmp = t_1;
	} else if (t <= 8.5e-114) {
		tmp = ((y * z) + (x * t)) / (y * b);
	} else {
		tmp = (x + (y * (z / t))) / ((y * (b / t)) + (a + 1.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + (z / (t / y))) / (a + (1.0 + (y / (t / b))))
	tmp = 0
	if t <= -1.05e-125:
		tmp = t_1
	elif t <= 8e-253:
		tmp = z / b
	elif t <= 5.1e-144:
		tmp = t_1
	elif t <= 8.5e-114:
		tmp = ((y * z) + (x * t)) / (y * b)
	else:
		tmp = (x + (y * (z / t))) / ((y * (b / t)) + (a + 1.0))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(z / Float64(t / y))) / Float64(a + Float64(1.0 + Float64(y / Float64(t / b)))))
	tmp = 0.0
	if (t <= -1.05e-125)
		tmp = t_1;
	elseif (t <= 8e-253)
		tmp = Float64(z / b);
	elseif (t <= 5.1e-144)
		tmp = t_1;
	elseif (t <= 8.5e-114)
		tmp = Float64(Float64(Float64(y * z) + Float64(x * t)) / Float64(y * b));
	else
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(Float64(y * Float64(b / t)) + Float64(a + 1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + (z / (t / y))) / (a + (1.0 + (y / (t / b))));
	tmp = 0.0;
	if (t <= -1.05e-125)
		tmp = t_1;
	elseif (t <= 8e-253)
		tmp = z / b;
	elseif (t <= 5.1e-144)
		tmp = t_1;
	elseif (t <= 8.5e-114)
		tmp = ((y * z) + (x * t)) / (y * b);
	else
		tmp = (x + (y * (z / t))) / ((y * (b / t)) + (a + 1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + N[(1.0 + N[(y / N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.05e-125], t$95$1, If[LessEqual[t, 8e-253], N[(z / b), $MachinePrecision], If[LessEqual[t, 5.1e-144], t$95$1, If[LessEqual[t, 8.5e-114], N[(N[(N[(y * z), $MachinePrecision] + N[(x * t), $MachinePrecision]), $MachinePrecision] / N[(y * b), $MachinePrecision]), $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]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.05e-125 or 8.0000000000000005e-253 < t < 5.1e-144

   1. Initial program 84.9%

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

      1. *-commutative 84.9%

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

      2. associate-/l* 87.9%

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

      3. associate-*l/ 88.7%

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

      4. *-commutative 88.7%

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

      5. cancel-sign-sub 88.7%

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

      6. *-commutative 88.7%

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

      7. associate-*l/ 87.9%

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

      8. associate-+r- 87.9%

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

      9. associate-*l/ 88.7%

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

      10. *-commutative 88.7%

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

      11. cancel-sign-sub 88.7%

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

      12. *-commutative 88.7%

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

      13. associate-/r/ 87.9%

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

   3. Simplified 87.9%

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

   if -1.05e-125 < t < 8.0000000000000005e-253

   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. *-commutative 62.7%

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

      2. associate-*l/ 48.4%

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

      3. *-commutative 48.4%

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

      4. associate-*l/ 41.1%

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

   3. Simplified 41.1%

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

   4. Taylor expanded in t around 0 69.5%

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

   if 5.1e-144 < t < 8.5000000000000006e-114

   1. Initial program 51.9%

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

      1. *-commutative 51.9%

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

      2. associate-*l/ 51.9%

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

      3. *-commutative 51.9%

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

      4. associate-*l/ 19.6%

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

   3. Simplified 19.6%

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

   4. Taylor expanded in b around inf 68.6%

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

   5. Taylor expanded in t around 0 83.7%

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

   if 8.5000000000000006e-114 < t

   1. Initial program 79.2%

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

      1. *-commutative 79.2%

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

      2. associate-*l/ 85.8%

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

      3. *-commutative 85.8%

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

      4. associate-*l/ 92.2%

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

   3. Simplified 92.2%

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

4. Final simplification 85.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{-125}:\\ \;\;\;\;\frac{x + \frac{z}{\frac{t}{y}}}{a + \left(1 + \frac{y}{\frac{t}{b}}\right)}\\ \mathbf{elif}\;t \leq 8 \cdot 10^{-253}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq 5.1 \cdot 10^{-144}:\\ \;\;\;\;\frac{x + \frac{z}{\frac{t}{y}}}{a + \left(1 + \frac{y}{\frac{t}{b}}\right)}\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-114}:\\ \;\;\;\;\frac{y \cdot z + x \cdot t}{y \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{y \cdot \frac{b}{t} + \left(a + 1\right)}\\ \end{array} \]

Alternative 4: 55.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \frac{y}{t}\\ t_2 := \frac{t_1}{a}\\ \mathbf{if}\;a \leq -1:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -3.4 \cdot 10^{-133}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 6.4 \cdot 10^{-238}:\\ \;\;\;\;\frac{x}{1 + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{-117}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 6 \cdot 10^{-67}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 10^{+25}:\\ \;\;\;\;\frac{t}{b} \cdot \left(\frac{z}{t} + \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* z (/ y t)))) (t_2 (/ t_1 a)))
   (if (<= a -1.0)
     t_2
     (if (<= a -3.4e-133)
       t_1
       (if (<= a 6.4e-238)
         (/ x (+ 1.0 (* y (/ b t))))
         (if (<= a 5.5e-117)
           (/ z b)
           (if (<= a 6e-67)
             t_1
             (if (<= a 1e+25) (* (/ t b) (+ (/ z t) (/ x y))) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z * (y / t));
	double t_2 = t_1 / a;
	double tmp;
	if (a <= -1.0) {
		tmp = t_2;
	} else if (a <= -3.4e-133) {
		tmp = t_1;
	} else if (a <= 6.4e-238) {
		tmp = x / (1.0 + (y * (b / t)));
	} else if (a <= 5.5e-117) {
		tmp = z / b;
	} else if (a <= 6e-67) {
		tmp = t_1;
	} else if (a <= 1e+25) {
		tmp = (t / b) * ((z / t) + (x / y));
	} 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 + (z * (y / t))
    t_2 = t_1 / a
    if (a <= (-1.0d0)) then
        tmp = t_2
    else if (a <= (-3.4d-133)) then
        tmp = t_1
    else if (a <= 6.4d-238) then
        tmp = x / (1.0d0 + (y * (b / t)))
    else if (a <= 5.5d-117) then
        tmp = z / b
    else if (a <= 6d-67) then
        tmp = t_1
    else if (a <= 1d+25) then
        tmp = (t / b) * ((z / t) + (x / y))
    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 + (z * (y / t));
	double t_2 = t_1 / a;
	double tmp;
	if (a <= -1.0) {
		tmp = t_2;
	} else if (a <= -3.4e-133) {
		tmp = t_1;
	} else if (a <= 6.4e-238) {
		tmp = x / (1.0 + (y * (b / t)));
	} else if (a <= 5.5e-117) {
		tmp = z / b;
	} else if (a <= 6e-67) {
		tmp = t_1;
	} else if (a <= 1e+25) {
		tmp = (t / b) * ((z / t) + (x / y));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (z * (y / t))
	t_2 = t_1 / a
	tmp = 0
	if a <= -1.0:
		tmp = t_2
	elif a <= -3.4e-133:
		tmp = t_1
	elif a <= 6.4e-238:
		tmp = x / (1.0 + (y * (b / t)))
	elif a <= 5.5e-117:
		tmp = z / b
	elif a <= 6e-67:
		tmp = t_1
	elif a <= 1e+25:
		tmp = (t / b) * ((z / t) + (x / y))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(z * Float64(y / t)))
	t_2 = Float64(t_1 / a)
	tmp = 0.0
	if (a <= -1.0)
		tmp = t_2;
	elseif (a <= -3.4e-133)
		tmp = t_1;
	elseif (a <= 6.4e-238)
		tmp = Float64(x / Float64(1.0 + Float64(y * Float64(b / t))));
	elseif (a <= 5.5e-117)
		tmp = Float64(z / b);
	elseif (a <= 6e-67)
		tmp = t_1;
	elseif (a <= 1e+25)
		tmp = Float64(Float64(t / b) * Float64(Float64(z / t) + Float64(x / y)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (z * (y / t));
	t_2 = t_1 / a;
	tmp = 0.0;
	if (a <= -1.0)
		tmp = t_2;
	elseif (a <= -3.4e-133)
		tmp = t_1;
	elseif (a <= 6.4e-238)
		tmp = x / (1.0 + (y * (b / t)));
	elseif (a <= 5.5e-117)
		tmp = z / b;
	elseif (a <= 6e-67)
		tmp = t_1;
	elseif (a <= 1e+25)
		tmp = (t / b) * ((z / t) + (x / y));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 / a), $MachinePrecision]}, If[LessEqual[a, -1.0], t$95$2, If[LessEqual[a, -3.4e-133], t$95$1, If[LessEqual[a, 6.4e-238], N[(x / N[(1.0 + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.5e-117], N[(z / b), $MachinePrecision], If[LessEqual[a, 6e-67], t$95$1, If[LessEqual[a, 1e+25], N[(N[(t / b), $MachinePrecision] * N[(N[(z / t), $MachinePrecision] + N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1 or 1.00000000000000009e25 < a

   1. Initial program 79.8%

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

      1. *-commutative 79.8%

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

      2. associate-*l/ 79.1%

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

      3. *-commutative 79.1%

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

      4. associate-*l/ 77.0%

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

   3. Simplified 77.0%

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

   4. Taylor expanded in b around 0 68.2%

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

   5. Taylor expanded in a around inf 67.5%

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

      1. associate-*l/ 69.9%

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

      2. *-commutative 69.9%

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

   7. Simplified 69.9%

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

   if -1 < a < -3.40000000000000006e-133 or 5.50000000000000025e-117 < a < 6.00000000000000065e-67

   1. Initial program 89.5%

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

      1. *-commutative 89.5%

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

      2. associate-*l/ 94.0%

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

      3. *-commutative 94.0%

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

      4. associate-*l/ 91.4%

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

   3. Simplified 91.4%

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

   4. Taylor expanded in b around 0 74.4%

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

   5. Taylor expanded in a around 0 72.3%

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

      1. associate-*l/ 80.0%

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

      2. *-commutative 80.0%

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

   7. Simplified 80.0%

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

   if -3.40000000000000006e-133 < a < 6.4000000000000005e-238

   1. Initial program 86.7%

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

      1. *-commutative 86.7%

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

      2. associate-*l/ 82.5%

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

      3. *-commutative 82.5%

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

      4. associate-*l/ 80.2%

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

   3. Simplified 80.2%

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

   4. Taylor expanded in x around inf 73.3%

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

   5. Taylor expanded in a around 0 73.3%

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

      1. associate-*l/ 71.0%

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

      2. *-commutative 71.0%

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

   7. Simplified 71.0%

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

   if 6.4000000000000005e-238 < a < 5.50000000000000025e-117

   1. Initial program 59.1%

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

      1. *-commutative 59.1%

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

      2. associate-*l/ 52.4%

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

      3. *-commutative 52.4%

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

      4. associate-*l/ 51.9%

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

   3. Simplified 51.9%

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

   4. Taylor expanded in t around 0 71.6%

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

   if 6.00000000000000065e-67 < a < 1.00000000000000009e25

   1. Initial program 48.9%

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

      1. *-commutative 48.9%

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

      2. associate-*l/ 53.6%

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

      3. *-commutative 53.6%

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

      4. associate-*l/ 67.4%

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

   3. Simplified 67.4%

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

   4. Taylor expanded in b around inf 35.0%

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

      1. times-frac 35.4%

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

      2. +-commutative 35.4%

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

      3. associate-*l/ 39.9%

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

      4. *-commutative 39.9%

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

      5. fma-udef 39.9%

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

   6. Simplified 39.9%

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

   7. Taylor expanded in z around 0 56.5%

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

4. Final simplification 70.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a}\\ \mathbf{elif}\;a \leq -3.4 \cdot 10^{-133}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{elif}\;a \leq 6.4 \cdot 10^{-238}:\\ \;\;\;\;\frac{x}{1 + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{-117}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 6 \cdot 10^{-67}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{elif}\;a \leq 10^{+25}:\\ \;\;\;\;\frac{t}{b} \cdot \left(\frac{z}{t} + \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a}\\ \end{array} \]

Alternative 5: 55.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \frac{y}{t}\\ t_2 := \frac{t_1}{a}\\ \mathbf{if}\;a \leq -1:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -2.4 \cdot 10^{-133}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 7 \cdot 10^{-236}:\\ \;\;\;\;\frac{x}{1 + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{-117}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{-67}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{+26}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* z (/ y t)))) (t_2 (/ t_1 a)))
   (if (<= a -1.0)
     t_2
     (if (<= a -2.4e-133)
       t_1
       (if (<= a 7e-236)
         (/ x (+ 1.0 (* y (/ b t))))
         (if (<= a 2.9e-117)
           (/ z b)
           (if (<= a 6.2e-67) t_1 (if (<= a 6.5e+26) (/ z b) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z * (y / t));
	double t_2 = t_1 / a;
	double tmp;
	if (a <= -1.0) {
		tmp = t_2;
	} else if (a <= -2.4e-133) {
		tmp = t_1;
	} else if (a <= 7e-236) {
		tmp = x / (1.0 + (y * (b / t)));
	} else if (a <= 2.9e-117) {
		tmp = z / b;
	} else if (a <= 6.2e-67) {
		tmp = t_1;
	} else if (a <= 6.5e+26) {
		tmp = z / b;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (z * (y / t))
    t_2 = t_1 / a
    if (a <= (-1.0d0)) then
        tmp = t_2
    else if (a <= (-2.4d-133)) then
        tmp = t_1
    else if (a <= 7d-236) then
        tmp = x / (1.0d0 + (y * (b / t)))
    else if (a <= 2.9d-117) then
        tmp = z / b
    else if (a <= 6.2d-67) then
        tmp = t_1
    else if (a <= 6.5d+26) then
        tmp = z / b
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z * (y / t));
	double t_2 = t_1 / a;
	double tmp;
	if (a <= -1.0) {
		tmp = t_2;
	} else if (a <= -2.4e-133) {
		tmp = t_1;
	} else if (a <= 7e-236) {
		tmp = x / (1.0 + (y * (b / t)));
	} else if (a <= 2.9e-117) {
		tmp = z / b;
	} else if (a <= 6.2e-67) {
		tmp = t_1;
	} else if (a <= 6.5e+26) {
		tmp = z / b;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (z * (y / t))
	t_2 = t_1 / a
	tmp = 0
	if a <= -1.0:
		tmp = t_2
	elif a <= -2.4e-133:
		tmp = t_1
	elif a <= 7e-236:
		tmp = x / (1.0 + (y * (b / t)))
	elif a <= 2.9e-117:
		tmp = z / b
	elif a <= 6.2e-67:
		tmp = t_1
	elif a <= 6.5e+26:
		tmp = z / b
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(z * Float64(y / t)))
	t_2 = Float64(t_1 / a)
	tmp = 0.0
	if (a <= -1.0)
		tmp = t_2;
	elseif (a <= -2.4e-133)
		tmp = t_1;
	elseif (a <= 7e-236)
		tmp = Float64(x / Float64(1.0 + Float64(y * Float64(b / t))));
	elseif (a <= 2.9e-117)
		tmp = Float64(z / b);
	elseif (a <= 6.2e-67)
		tmp = t_1;
	elseif (a <= 6.5e+26)
		tmp = Float64(z / b);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (z * (y / t));
	t_2 = t_1 / a;
	tmp = 0.0;
	if (a <= -1.0)
		tmp = t_2;
	elseif (a <= -2.4e-133)
		tmp = t_1;
	elseif (a <= 7e-236)
		tmp = x / (1.0 + (y * (b / t)));
	elseif (a <= 2.9e-117)
		tmp = z / b;
	elseif (a <= 6.2e-67)
		tmp = t_1;
	elseif (a <= 6.5e+26)
		tmp = z / b;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 / a), $MachinePrecision]}, If[LessEqual[a, -1.0], t$95$2, If[LessEqual[a, -2.4e-133], t$95$1, If[LessEqual[a, 7e-236], N[(x / N[(1.0 + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.9e-117], N[(z / b), $MachinePrecision], If[LessEqual[a, 6.2e-67], t$95$1, If[LessEqual[a, 6.5e+26], N[(z / b), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1 or 6.50000000000000022e26 < a

   1. Initial program 79.8%

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

      1. *-commutative 79.8%

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

      2. associate-*l/ 79.1%

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

      3. *-commutative 79.1%

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

      4. associate-*l/ 77.0%

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

   3. Simplified 77.0%

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

   4. Taylor expanded in b around 0 68.2%

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

   5. Taylor expanded in a around inf 67.5%

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

      1. associate-*l/ 69.9%

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

      2. *-commutative 69.9%

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

   7. Simplified 69.9%

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

   if -1 < a < -2.4e-133 or 2.9000000000000001e-117 < a < 6.2000000000000005e-67

   1. Initial program 89.5%

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

      1. *-commutative 89.5%

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

      2. associate-*l/ 94.0%

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

      3. *-commutative 94.0%

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

      4. associate-*l/ 91.4%

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

   3. Simplified 91.4%

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

   4. Taylor expanded in b around 0 74.4%

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

   5. Taylor expanded in a around 0 72.3%

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

      1. associate-*l/ 80.0%

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

      2. *-commutative 80.0%

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

   7. Simplified 80.0%

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

   if -2.4e-133 < a < 6.99999999999999988e-236

   1. Initial program 86.7%

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

      1. *-commutative 86.7%

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

      2. associate-*l/ 82.5%

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

      3. *-commutative 82.5%

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

      4. associate-*l/ 80.2%

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

   3. Simplified 80.2%

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

   4. Taylor expanded in x around inf 73.3%

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

   5. Taylor expanded in a around 0 73.3%

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

      1. associate-*l/ 71.0%

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

      2. *-commutative 71.0%

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

   7. Simplified 71.0%

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

   if 6.99999999999999988e-236 < a < 2.9000000000000001e-117 or 6.2000000000000005e-67 < a < 6.50000000000000022e26

   1. Initial program 54.3%

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

      1. *-commutative 54.3%

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

      2. associate-*l/ 52.9%

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

      3. *-commutative 52.9%

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

      4. associate-*l/ 59.2%

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

   3. Simplified 59.2%

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

   4. Taylor expanded in t around 0 63.5%

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

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a}\\ \mathbf{elif}\;a \leq -2.4 \cdot 10^{-133}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{elif}\;a \leq 7 \cdot 10^{-236}:\\ \;\;\;\;\frac{x}{1 + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{-117}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{-67}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{+26}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a}\\ \end{array} \]

Alternative 6: 78.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.62 \cdot 10^{-131} \lor \neg \left(t \leq 1.22 \cdot 10^{-254}\right):\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{y \cdot \frac{b}{t} + \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -1.62e-131) (not (<= t 1.22e-254)))
   (/ (+ x (* y (/ z t))) (+ (* y (/ b t)) (+ a 1.0)))
   (/ z b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.62e-131) || !(t <= 1.22e-254)) {
		tmp = (x + (y * (z / t))) / ((y * (b / 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 ((t <= (-1.62d-131)) .or. (.not. (t <= 1.22d-254))) then
        tmp = (x + (y * (z / t))) / ((y * (b / 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 ((t <= -1.62e-131) || !(t <= 1.22e-254)) {
		tmp = (x + (y * (z / t))) / ((y * (b / t)) + (a + 1.0));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -1.62e-131) or not (t <= 1.22e-254):
		tmp = (x + (y * (z / t))) / ((y * (b / t)) + (a + 1.0))
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -1.62e-131) || !(t <= 1.22e-254))
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(Float64(y * Float64(b / 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 ((t <= -1.62e-131) || ~((t <= 1.22e-254)))
		tmp = (x + (y * (z / t))) / ((y * (b / t)) + (a + 1.0));
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -1.62e-131], N[Not[LessEqual[t, 1.22e-254]], $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[(z / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.61999999999999988e-131 or 1.22e-254 < t

   1. Initial program 81.9%

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

      1. *-commutative 81.9%

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

      2. associate-*l/ 84.8%

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

      3. *-commutative 84.8%

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

      4. associate-*l/ 85.8%

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

   3. Simplified 85.8%

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

   if -1.61999999999999988e-131 < t < 1.22e-254

   1. Initial program 62.0%

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

      1. *-commutative 62.0%

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

      2. associate-*l/ 47.4%

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

      3. *-commutative 47.4%

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

      4. associate-*l/ 40.0%

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

   3. Simplified 40.0%

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

   4. Taylor expanded in t around 0 68.9%

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

4. Final simplification 82.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.62 \cdot 10^{-131} \lor \neg \left(t \leq 1.22 \cdot 10^{-254}\right):\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{y \cdot \frac{b}{t} + \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 7: 53.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{a + 1}\\ \mathbf{if}\;t \leq -1.15 \cdot 10^{-122}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.36 \cdot 10^{-121}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+158} \lor \neg \left(t \leq 1.75 \cdot 10^{+208}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (+ a 1.0))))
   (if (<= t -1.15e-122)
     t_1
     (if (<= t 1.36e-121)
       (/ z b)
       (if (or (<= t 1.4e+158) (not (<= t 1.75e+208)))
         t_1
         (* (/ y t) (/ z (+ a 1.0))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a + 1.0);
	double tmp;
	if (t <= -1.15e-122) {
		tmp = t_1;
	} else if (t <= 1.36e-121) {
		tmp = z / b;
	} else if ((t <= 1.4e+158) || !(t <= 1.75e+208)) {
		tmp = t_1;
	} else {
		tmp = (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) :: t_1
    real(8) :: tmp
    t_1 = x / (a + 1.0d0)
    if (t <= (-1.15d-122)) then
        tmp = t_1
    else if (t <= 1.36d-121) then
        tmp = z / b
    else if ((t <= 1.4d+158) .or. (.not. (t <= 1.75d+208))) then
        tmp = t_1
    else
        tmp = (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 t_1 = x / (a + 1.0);
	double tmp;
	if (t <= -1.15e-122) {
		tmp = t_1;
	} else if (t <= 1.36e-121) {
		tmp = z / b;
	} else if ((t <= 1.4e+158) || !(t <= 1.75e+208)) {
		tmp = t_1;
	} else {
		tmp = (y / t) * (z / (a + 1.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (a + 1.0)
	tmp = 0
	if t <= -1.15e-122:
		tmp = t_1
	elif t <= 1.36e-121:
		tmp = z / b
	elif (t <= 1.4e+158) or not (t <= 1.75e+208):
		tmp = t_1
	else:
		tmp = (y / t) * (z / (a + 1.0))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(a + 1.0))
	tmp = 0.0
	if (t <= -1.15e-122)
		tmp = t_1;
	elseif (t <= 1.36e-121)
		tmp = Float64(z / b);
	elseif ((t <= 1.4e+158) || !(t <= 1.75e+208))
		tmp = t_1;
	else
		tmp = Float64(Float64(y / t) * Float64(z / Float64(a + 1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (a + 1.0);
	tmp = 0.0;
	if (t <= -1.15e-122)
		tmp = t_1;
	elseif (t <= 1.36e-121)
		tmp = z / b;
	elseif ((t <= 1.4e+158) || ~((t <= 1.75e+208)))
		tmp = t_1;
	else
		tmp = (y / t) * (z / (a + 1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.15e-122], t$95$1, If[LessEqual[t, 1.36e-121], N[(z / b), $MachinePrecision], If[Or[LessEqual[t, 1.4e+158], N[Not[LessEqual[t, 1.75e+208]], $MachinePrecision]], t$95$1, N[(N[(y / t), $MachinePrecision] * N[(z / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.15000000000000003e-122 or 1.3599999999999999e-121 < t < 1.40000000000000001e158 or 1.75000000000000008e208 < t

   1. Initial program 83.5%

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

      1. *-commutative 83.5%

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

      2. associate-*l/ 85.9%

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

      3. *-commutative 85.9%

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

      4. associate-*l/ 87.1%

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

   3. Simplified 87.1%

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

   4. Taylor expanded in t around inf 62.3%

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

   if -1.15000000000000003e-122 < t < 1.3599999999999999e-121

   1. Initial program 66.9%

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

      1. *-commutative 66.9%

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

      2. associate-*l/ 54.0%

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

      3. *-commutative 54.0%

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

      4. associate-*l/ 47.5%

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

   3. Simplified 47.5%

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

   4. Taylor expanded in t around 0 63.8%

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

   if 1.40000000000000001e158 < t < 1.75000000000000008e208

   1. Initial program 71.7%

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

      1. *-commutative 71.7%

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

      2. associate-*l/ 94.1%

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

      3. *-commutative 94.1%

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

      4. associate-*l/ 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in b around 0 66.4%

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

   5. Taylor expanded in x around 0 22.9%

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

      1. times-frac 67.9%

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

   7. Simplified 67.9%

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

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{-122}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{elif}\;t \leq 1.36 \cdot 10^{-121}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+158} \lor \neg \left(t \leq 1.75 \cdot 10^{+208}\right):\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{a + 1}\\ \end{array} \]

Alternative 8: 65.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+34}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq -43000000000000:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+136}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b} \cdot \left(\frac{z}{t} + \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -4.5e+34)
   (/ z b)
   (if (<= y -43000000000000.0)
     (/ x (+ 1.0 (+ a (/ (* y b) t))))
     (if (<= y 5.2e+136)
       (/ (+ x (/ (* y z) t)) (+ a 1.0))
       (* (/ t b) (+ (/ z t) (/ x y)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -4.5e+34) {
		tmp = z / b;
	} else if (y <= -43000000000000.0) {
		tmp = x / (1.0 + (a + ((y * b) / t)));
	} else if (y <= 5.2e+136) {
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	} else {
		tmp = (t / b) * ((z / t) + (x / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-4.5d+34)) then
        tmp = z / b
    else if (y <= (-43000000000000.0d0)) then
        tmp = x / (1.0d0 + (a + ((y * b) / t)))
    else if (y <= 5.2d+136) then
        tmp = (x + ((y * z) / t)) / (a + 1.0d0)
    else
        tmp = (t / b) * ((z / t) + (x / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -4.5e+34) {
		tmp = z / b;
	} else if (y <= -43000000000000.0) {
		tmp = x / (1.0 + (a + ((y * b) / t)));
	} else if (y <= 5.2e+136) {
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	} else {
		tmp = (t / b) * ((z / t) + (x / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -4.5e+34:
		tmp = z / b
	elif y <= -43000000000000.0:
		tmp = x / (1.0 + (a + ((y * b) / t)))
	elif y <= 5.2e+136:
		tmp = (x + ((y * z) / t)) / (a + 1.0)
	else:
		tmp = (t / b) * ((z / t) + (x / y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -4.5e+34)
		tmp = Float64(z / b);
	elseif (y <= -43000000000000.0)
		tmp = Float64(x / Float64(1.0 + Float64(a + Float64(Float64(y * b) / t))));
	elseif (y <= 5.2e+136)
		tmp = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(a + 1.0));
	else
		tmp = Float64(Float64(t / b) * Float64(Float64(z / t) + Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -4.5e+34)
		tmp = z / b;
	elseif (y <= -43000000000000.0)
		tmp = x / (1.0 + (a + ((y * b) / t)));
	elseif (y <= 5.2e+136)
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	else
		tmp = (t / b) * ((z / t) + (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -4.5e+34], N[(z / b), $MachinePrecision], If[LessEqual[y, -43000000000000.0], N[(x / N[(1.0 + N[(a + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.2e+136], N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(t / b), $MachinePrecision] * N[(N[(z / t), $MachinePrecision] + N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.5e34

   1. Initial program 63.1%

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

      1. *-commutative 63.1%

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

      2. associate-*l/ 70.1%

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

      3. *-commutative 70.1%

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

      4. associate-*l/ 72.2%

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

   3. Simplified 72.2%

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

   4. Taylor expanded in t around 0 50.2%

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

   if -4.5e34 < y < -4.3e13

   1. Initial program 99.7%

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

      1. *-commutative 99.7%

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

      2. associate-*l/ 99.7%

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

      3. *-commutative 99.7%

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

      4. associate-*l/ 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in x around inf 99.7%

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

   if -4.3e13 < y < 5.2000000000000003e136

   1. Initial program 93.3%

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

      1. *-commutative 93.3%

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

      2. associate-*l/ 87.2%

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

      3. *-commutative 87.2%

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

      4. associate-*l/ 81.8%

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

   3. Simplified 81.8%

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

   4. Taylor expanded in b around 0 77.2%

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

   if 5.2000000000000003e136 < y

   1. Initial program 36.4%

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

      1. *-commutative 36.4%

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

      2. associate-*l/ 47.1%

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

      3. *-commutative 47.1%

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

      4. associate-*l/ 59.6%

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

   3. Simplified 59.6%

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

   4. Taylor expanded in b around inf 32.6%

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

      1. times-frac 47.6%

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

      2. +-commutative 47.6%

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

      3. associate-*l/ 42.2%

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

      4. *-commutative 42.2%

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

      5. fma-udef 42.2%

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

   6. Simplified 42.2%

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

   7. Taylor expanded in z around 0 67.4%

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

4. Final simplification 71.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+34}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq -43000000000000:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+136}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b} \cdot \left(\frac{z}{t} + \frac{x}{y}\right)\\ \end{array} \]

Alternative 9: 65.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{-131} \lor \neg \left(t \leq 5 \cdot 10^{-60}\right):\\ \;\;\;\;\left(x + \frac{y}{\frac{t}{z}}\right) \cdot \frac{1}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot z + x \cdot t}{y \cdot b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -1e-131) (not (<= t 5e-60)))
   (* (+ x (/ y (/ t z))) (/ 1.0 (+ a 1.0)))
   (/ (+ (* y z) (* x t)) (* y b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1e-131) || !(t <= 5e-60)) {
		tmp = (x + (y / (t / z))) * (1.0 / (a + 1.0));
	} else {
		tmp = ((y * 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 <= (-1d-131)) .or. (.not. (t <= 5d-60))) then
        tmp = (x + (y / (t / z))) * (1.0d0 / (a + 1.0d0))
    else
        tmp = ((y * 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 <= -1e-131) || !(t <= 5e-60)) {
		tmp = (x + (y / (t / z))) * (1.0 / (a + 1.0));
	} else {
		tmp = ((y * z) + (x * t)) / (y * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -1e-131) or not (t <= 5e-60):
		tmp = (x + (y / (t / z))) * (1.0 / (a + 1.0))
	else:
		tmp = ((y * z) + (x * t)) / (y * b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -1e-131) || !(t <= 5e-60))
		tmp = Float64(Float64(x + Float64(y / Float64(t / z))) * Float64(1.0 / Float64(a + 1.0)));
	else
		tmp = Float64(Float64(Float64(y * z) + Float64(x * t)) / Float64(y * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -1e-131) || ~((t <= 5e-60)))
		tmp = (x + (y / (t / z))) * (1.0 / (a + 1.0));
	else
		tmp = ((y * z) + (x * t)) / (y * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -1e-131], N[Not[LessEqual[t, 5e-60]], $MachinePrecision]], N[(N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(1.0 / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y * z), $MachinePrecision] + N[(x * t), $MachinePrecision]), $MachinePrecision] / N[(y * b), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -9.9999999999999999e-132 or 5.0000000000000001e-60 < t

   1. Initial program 82.4%

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

      1. *-commutative 82.4%

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

      2. associate-*l/ 86.8%

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

      3. *-commutative 86.8%

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

      4. associate-*l/ 89.0%

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

   3. Simplified 89.0%

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

   4. Taylor expanded in b around 0 71.5%

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

      1. div-inv 71.4%

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

      2. associate-/l* 75.7%

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

   6. Applied egg-rr 75.7%

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

   if -9.9999999999999999e-132 < t < 5.0000000000000001e-60

   1. Initial program 67.8%

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

      1. *-commutative 67.8%

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

      2. associate-*l/ 55.8%

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

      3. *-commutative 55.8%

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

      4. associate-*l/ 48.4%

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

   3. Simplified 48.4%

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

   4. Taylor expanded in b around inf 55.6%

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

   5. Taylor expanded in t around 0 65.4%

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

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{-131} \lor \neg \left(t \leq 5 \cdot 10^{-60}\right):\\ \;\;\;\;\left(x + \frac{y}{\frac{t}{z}}\right) \cdot \frac{1}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot z + x \cdot t}{y \cdot b}\\ \end{array} \]

Alternative 10: 63.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{-132} \lor \neg \left(t \leq 1.3 \cdot 10^{-64}\right):\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot z + x \cdot t}{y \cdot b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -9e-132) (not (<= t 1.3e-64)))
   (/ (+ x (/ (* y z) t)) (+ a 1.0))
   (/ (+ (* y z) (* x t)) (* y b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -9e-132) || !(t <= 1.3e-64)) {
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	} else {
		tmp = ((y * 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 <= (-9d-132)) .or. (.not. (t <= 1.3d-64))) then
        tmp = (x + ((y * z) / t)) / (a + 1.0d0)
    else
        tmp = ((y * 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 <= -9e-132) || !(t <= 1.3e-64)) {
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	} else {
		tmp = ((y * z) + (x * t)) / (y * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -9e-132) or not (t <= 1.3e-64):
		tmp = (x + ((y * z) / t)) / (a + 1.0)
	else:
		tmp = ((y * z) + (x * t)) / (y * b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -9e-132) || !(t <= 1.3e-64))
		tmp = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(a + 1.0));
	else
		tmp = Float64(Float64(Float64(y * z) + Float64(x * t)) / Float64(y * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -9e-132) || ~((t <= 1.3e-64)))
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	else
		tmp = ((y * z) + (x * t)) / (y * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -9e-132], N[Not[LessEqual[t, 1.3e-64]], $MachinePrecision]], N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y * z), $MachinePrecision] + N[(x * t), $MachinePrecision]), $MachinePrecision] / N[(y * b), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -8.9999999999999999e-132 or 1.3e-64 < t

   1. Initial program 82.4%

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

      1. *-commutative 82.4%

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

      2. associate-*l/ 86.8%

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

      3. *-commutative 86.8%

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

      4. associate-*l/ 89.0%

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

   3. Simplified 89.0%

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

   4. Taylor expanded in b around 0 71.5%

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

   if -8.9999999999999999e-132 < t < 1.3e-64

   1. Initial program 67.8%

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

      1. *-commutative 67.8%

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

      2. associate-*l/ 55.8%

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

      3. *-commutative 55.8%

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

      4. associate-*l/ 48.4%

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

   3. Simplified 48.4%

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

   4. Taylor expanded in b around inf 55.6%

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

   5. Taylor expanded in t around 0 65.4%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{-132} \lor \neg \left(t \leq 1.3 \cdot 10^{-64}\right):\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot z + x \cdot t}{y \cdot b}\\ \end{array} \]

Alternative 11: 61.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{+33}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+142}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b} \cdot \left(\frac{z}{t} + \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -6.8e+33)
   (/ z b)
   (if (<= y 1.3e+142)
     (/ x (+ 1.0 (+ a (/ (* y b) t))))
     (* (/ t b) (+ (/ z t) (/ x y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -6.8e+33) {
		tmp = z / b;
	} else if (y <= 1.3e+142) {
		tmp = x / (1.0 + (a + ((y * b) / t)));
	} else {
		tmp = (t / b) * ((z / t) + (x / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-6.8d+33)) then
        tmp = z / b
    else if (y <= 1.3d+142) then
        tmp = x / (1.0d0 + (a + ((y * b) / t)))
    else
        tmp = (t / b) * ((z / t) + (x / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -6.8e+33) {
		tmp = z / b;
	} else if (y <= 1.3e+142) {
		tmp = x / (1.0 + (a + ((y * b) / t)));
	} else {
		tmp = (t / b) * ((z / t) + (x / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -6.8e+33:
		tmp = z / b
	elif y <= 1.3e+142:
		tmp = x / (1.0 + (a + ((y * b) / t)))
	else:
		tmp = (t / b) * ((z / t) + (x / y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -6.8e+33)
		tmp = Float64(z / b);
	elseif (y <= 1.3e+142)
		tmp = Float64(x / Float64(1.0 + Float64(a + Float64(Float64(y * b) / t))));
	else
		tmp = Float64(Float64(t / b) * Float64(Float64(z / t) + Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -6.8e+33)
		tmp = z / b;
	elseif (y <= 1.3e+142)
		tmp = x / (1.0 + (a + ((y * b) / t)));
	else
		tmp = (t / b) * ((z / t) + (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -6.8e+33], N[(z / b), $MachinePrecision], If[LessEqual[y, 1.3e+142], N[(x / N[(1.0 + N[(a + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t / b), $MachinePrecision] * N[(N[(z / t), $MachinePrecision] + N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.7999999999999999e33

   1. Initial program 63.1%

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

      1. *-commutative 63.1%

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

      2. associate-*l/ 70.1%

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

      3. *-commutative 70.1%

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

      4. associate-*l/ 72.2%

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

   3. Simplified 72.2%

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

   4. Taylor expanded in t around 0 50.2%

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

   if -6.7999999999999999e33 < y < 1.30000000000000011e142

   1. Initial program 93.5%

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

      1. *-commutative 93.5%

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

      2. associate-*l/ 87.6%

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

      3. *-commutative 87.6%

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

      4. associate-*l/ 82.3%

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

   3. Simplified 82.3%

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

   4. Taylor expanded in x around inf 71.6%

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

   if 1.30000000000000011e142 < y

   1. Initial program 36.4%

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

      1. *-commutative 36.4%

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

      2. associate-*l/ 47.1%

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

      3. *-commutative 47.1%

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

      4. associate-*l/ 59.6%

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

   3. Simplified 59.6%

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

   4. Taylor expanded in b around inf 32.6%

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

      1. times-frac 47.6%

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

      2. +-commutative 47.6%

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

      3. associate-*l/ 42.2%

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

      4. *-commutative 42.2%

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

      5. fma-udef 42.2%

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

   6. Simplified 42.2%

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

   7. Taylor expanded in z around 0 67.4%

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

4. Final simplification 67.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{+33}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+142}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b} \cdot \left(\frac{z}{t} + \frac{x}{y}\right)\\ \end{array} \]

Alternative 12: 42.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - x \cdot a\\ \mathbf{if}\;a \leq -1:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;a \leq -6.5 \cdot 10^{-31}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -8 \cdot 10^{-62}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 10^{-237}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 3.7 \cdot 10^{+27}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- x (* x a))))
   (if (<= a -1.0)
     (/ x a)
     (if (<= a -6.5e-31)
       t_1
       (if (<= a -8e-62)
         (/ z b)
         (if (<= a 1e-237) t_1 (if (<= a 3.7e+27) (/ z b) (/ x a))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - (x * a);
	double tmp;
	if (a <= -1.0) {
		tmp = x / a;
	} else if (a <= -6.5e-31) {
		tmp = t_1;
	} else if (a <= -8e-62) {
		tmp = z / b;
	} else if (a <= 1e-237) {
		tmp = t_1;
	} else if (a <= 3.7e+27) {
		tmp = z / b;
	} else {
		tmp = x / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (x * a)
    if (a <= (-1.0d0)) then
        tmp = x / a
    else if (a <= (-6.5d-31)) then
        tmp = t_1
    else if (a <= (-8d-62)) then
        tmp = z / b
    else if (a <= 1d-237) then
        tmp = t_1
    else if (a <= 3.7d+27) then
        tmp = z / b
    else
        tmp = x / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - (x * a);
	double tmp;
	if (a <= -1.0) {
		tmp = x / a;
	} else if (a <= -6.5e-31) {
		tmp = t_1;
	} else if (a <= -8e-62) {
		tmp = z / b;
	} else if (a <= 1e-237) {
		tmp = t_1;
	} else if (a <= 3.7e+27) {
		tmp = z / b;
	} else {
		tmp = x / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x - (x * a)
	tmp = 0
	if a <= -1.0:
		tmp = x / a
	elif a <= -6.5e-31:
		tmp = t_1
	elif a <= -8e-62:
		tmp = z / b
	elif a <= 1e-237:
		tmp = t_1
	elif a <= 3.7e+27:
		tmp = z / b
	else:
		tmp = x / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x - Float64(x * a))
	tmp = 0.0
	if (a <= -1.0)
		tmp = Float64(x / a);
	elseif (a <= -6.5e-31)
		tmp = t_1;
	elseif (a <= -8e-62)
		tmp = Float64(z / b);
	elseif (a <= 1e-237)
		tmp = t_1;
	elseif (a <= 3.7e+27)
		tmp = Float64(z / b);
	else
		tmp = Float64(x / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x - (x * a);
	tmp = 0.0;
	if (a <= -1.0)
		tmp = x / a;
	elseif (a <= -6.5e-31)
		tmp = t_1;
	elseif (a <= -8e-62)
		tmp = z / b;
	elseif (a <= 1e-237)
		tmp = t_1;
	elseif (a <= 3.7e+27)
		tmp = z / b;
	else
		tmp = x / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x - N[(x * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.0], N[(x / a), $MachinePrecision], If[LessEqual[a, -6.5e-31], t$95$1, If[LessEqual[a, -8e-62], N[(z / b), $MachinePrecision], If[LessEqual[a, 1e-237], t$95$1, If[LessEqual[a, 3.7e+27], N[(z / b), $MachinePrecision], N[(x / a), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1 or 3.70000000000000002e27 < a

   1. Initial program 79.8%

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

      1. *-commutative 79.8%

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

      2. associate-*l/ 79.1%

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

      3. *-commutative 79.1%

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

      4. associate-*l/ 77.0%

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

   3. Simplified 77.0%

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

   4. Taylor expanded in x around inf 60.4%

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

   5. Taylor expanded in a around inf 54.7%

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

   if -1 < a < -6.49999999999999967e-31 or -8.0000000000000003e-62 < a < 9.9999999999999999e-238

   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. *-commutative 89.7%

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

      2. associate-*l/ 86.8%

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

      3. *-commutative 86.8%

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

      4. associate-*l/ 83.9%

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

   3. Simplified 83.9%

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

   4. Taylor expanded in t around inf 58.5%

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

   5. Taylor expanded in a around 0 58.1%

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

      1. mul-1-neg 58.1%

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

      2. unsub-neg 58.1%

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

      3. *-commutative 58.1%

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

   7. Simplified 58.1%

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

   if -6.49999999999999967e-31 < a < -8.0000000000000003e-62 or 9.9999999999999999e-238 < a < 3.70000000000000002e27

   1. Initial program 60.9%

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

      1. *-commutative 60.9%

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

      2. associate-*l/ 62.7%

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

      3. *-commutative 62.7%

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

      4. associate-*l/ 67.3%

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

   3. Simplified 67.3%

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

   4. Taylor expanded in t around 0 57.2%

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

4. Final simplification 56.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;a \leq -6.5 \cdot 10^{-31}:\\ \;\;\;\;x - x \cdot a\\ \mathbf{elif}\;a \leq -8 \cdot 10^{-62}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 10^{-237}:\\ \;\;\;\;x - x \cdot a\\ \mathbf{elif}\;a \leq 3.7 \cdot 10^{+27}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \]

Alternative 13: 54.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{-121} \lor \neg \left(t \leq 1.45 \cdot 10^{-121}\right):\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -7.5e-121) (not (<= t 1.45e-121))) (/ x (+ a 1.0)) (/ z b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -7.5e-121) || !(t <= 1.45e-121)) {
		tmp = x / (a + 1.0);
	} else {
		tmp = z / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-7.5d-121)) .or. (.not. (t <= 1.45d-121))) then
        tmp = x / (a + 1.0d0)
    else
        tmp = z / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -7.5e-121) || !(t <= 1.45e-121)) {
		tmp = x / (a + 1.0);
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -7.5e-121) or not (t <= 1.45e-121):
		tmp = x / (a + 1.0)
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -7.5e-121) || !(t <= 1.45e-121))
		tmp = Float64(x / Float64(a + 1.0));
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -7.5e-121) || ~((t <= 1.45e-121)))
		tmp = x / (a + 1.0);
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -7.5e-121], N[Not[LessEqual[t, 1.45e-121]], $MachinePrecision]], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -7.50000000000000027e-121 or 1.45e-121 < t

   1. Initial program 82.4%

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

      1. *-commutative 82.4%

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

      2. associate-*l/ 86.7%

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

      3. *-commutative 86.7%

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

      4. associate-*l/ 88.2%

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

   3. Simplified 88.2%

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

   4. Taylor expanded in t around inf 60.0%

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

   if -7.50000000000000027e-121 < t < 1.45e-121

   1. Initial program 66.9%

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

      1. *-commutative 66.9%

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

      2. associate-*l/ 54.0%

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

      3. *-commutative 54.0%

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

      4. associate-*l/ 47.5%

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

   3. Simplified 47.5%

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

   4. Taylor expanded in t around 0 63.8%

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

4. Final simplification 61.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{-121} \lor \neg \left(t \leq 1.45 \cdot 10^{-121}\right):\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 14: 43.3% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4800:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{+27}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -4800.0) (/ x a) (if (<= a 3.6e+27) (/ z b) (/ x a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -4800.0) {
		tmp = x / a;
	} else if (a <= 3.6e+27) {
		tmp = z / b;
	} else {
		tmp = x / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-4800.0d0)) then
        tmp = x / a
    else if (a <= 3.6d+27) then
        tmp = z / b
    else
        tmp = x / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -4800.0) {
		tmp = x / a;
	} else if (a <= 3.6e+27) {
		tmp = z / b;
	} else {
		tmp = x / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -4800.0:
		tmp = x / a
	elif a <= 3.6e+27:
		tmp = z / b
	else:
		tmp = x / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -4800.0)
		tmp = Float64(x / a);
	elseif (a <= 3.6e+27)
		tmp = Float64(z / b);
	else
		tmp = Float64(x / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -4800.0)
		tmp = x / a;
	elseif (a <= 3.6e+27)
		tmp = z / b;
	else
		tmp = x / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -4800.0], N[(x / a), $MachinePrecision], If[LessEqual[a, 3.6e+27], N[(z / b), $MachinePrecision], N[(x / a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -4800 or 3.59999999999999983e27 < a

   1. Initial program 79.8%

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

      1. *-commutative 79.8%

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

      2. associate-*l/ 79.1%

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

      3. *-commutative 79.1%

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

      4. associate-*l/ 77.0%

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

   3. Simplified 77.0%

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

   4. Taylor expanded in x around inf 60.4%

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

   5. Taylor expanded in a around inf 54.7%

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

   if -4800 < a < 3.59999999999999983e27

   1. Initial program 75.9%

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

      1. *-commutative 75.9%

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

      2. associate-*l/ 75.2%

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

      3. *-commutative 75.2%

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

      4. associate-*l/ 75.9%

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

   3. Simplified 75.9%

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

   4. Taylor expanded in t around 0 41.8%

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

4. Final simplification 48.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4800:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{+27}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \]

Alternative 15: 25.6% accurate, 5.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 77.9%

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

   1. *-commutative 77.9%

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

   2. associate-*l/ 77.2%

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

   3. *-commutative 77.2%

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

   4. associate-*l/ 76.5%

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

3. Simplified 76.5%

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

4. Taylor expanded in x around inf 56.5%

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

5. Taylor expanded in a around inf 30.3%

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

6. Final simplification 30.3%

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

Developer target: 78.9% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023271 
(FPCore (x y z t a b)
  :name "Diagrams.Solve.Tridiagonal:solveCyclicTriDiagonal from diagrams-solve-0.1, B"
  :precision binary64

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

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